WO2024013415A1 - Use of currents, method and device for analysing a 4wd transformer - Google Patents
Use of currents, method and device for analysing a 4wd transformer Download PDFInfo
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- G—PHYSICS
- G01—MEASURING; TESTING
- G01R—MEASURING ELECTRIC VARIABLES; MEASURING MAGNETIC VARIABLES
- G01R21/00—Arrangements for measuring electric power or power factor
- G01R21/001—Measuring real or reactive component; Measuring apparent energy
- G01R21/005—Measuring apparent power
Definitions
- the present invention refers generally to the field of transformers, and more specifically to the analysis of delta-delta distribution transformers with neutral conductor, also called 4WD transformers.
- Triangle transformers - triangle with neutral conductor also called “high-leg”, “wild-leg” or “Four Wire Delta” (4WD) are transformers widely used in the distribution networks of the United States of America to power installations. single-phase, preferably residential and lighting, at 120 V, and three-phase industrial installations, at 240 V.
- the correct measurement of the apparent power of the transformers of the electrical networks is a necessity for the operators of said networks, as well as for the manufacturers of instruments for measuring electrical power, among others.
- the value of the apparent power determines the combined effects of all the energies present in the transformers and, therefore, this magnitude is used for the correct design of these machines, while providing information about their operation.
- the apparent power of the transformers of electrical networks can be measured in the primary or secondary.
- the measurement of the apparent power in the primary of distribution transformers entails certain risks for the operator, as they have to work with high voltages, and the use of more complex measuring instruments, given that the primary voltages cannot be measured directly. , being necessary the use of voltage measurement transformers. Due to these drawbacks, it is preferred to measure the apparent power in the secondary.
- the apparent power of the secondary is always slightly lower than the apparent power measured in the primary, due to the effect of the currents. emptiness and losses.
- a formula for the apparent power of 4WD transformers used by the main manufacturers of electrical power measuring instruments is as follows:
- the inventors of the present invention have investigated the errors in the calculation of the apparent power of 4WD transformers from the secondary, derived from the use of the equations of the prior art, and have developed a new concept of currents, called "effective currents", whose application allows for an analysis closer to the reality of this type of transformers.
- effective currents have been initially developed from the need to avoid errors in the calculation of the apparent power from the secondary, thanks to their particular nature, effective currents can also be applied to calculate other magnitudes of 4WD transformers such as , for example, the impact of delta loads on the transformer, the impact of star loads on the transformer, the currents in the primary coils, and/or the actual currents in the secondary coils.
- the errors in the calculation of the apparent power of 4WD transformers from the secondary are not due to the absence of proportionality between the apparent powers and the losses in the copper. These errors are due to the fact that the magnetomotive forces of each phase of the secondary, calculated with the real currents in the coils of said winding , are not equal to the magnetomotive forces of each phase of the primary. This This fact is of great importance in the analysis of this type of transformers.
- the proportionality between apparent powers and energy losses of this type of transformers continues to be valid, but new currents must be used that equalize the magnetic effects of the primary and secondary. These new currents are the effective currents that the inventors have conceived.
- the present invention discloses a use of currents for the analysis of a 4WD transformer, which are those currents that circulate through the secondary coils of a DD transformer equivalent to the 4WD transformer under analysis, the effective currents being called I due to the particularity that the application of the effective currents in the secondary coils of the 4WD transformer, replacing the real currents that circulate through said coils, gives rise to the same magnetic effects than the currents that circulate through the primary coils of the 4WD transformer
- a 4WD transformer is understood as a triangle-triangle transformer with three coils in the secondary and a neutral conductor connected to the center of one of said coils, called a neutral-linked coil to differentiate it from the rest of the secondary coils, called neutral-free coils.
- a DD transformer means a delta-delta transformer without a neutral conductor. Equivalent is understood as that theoretical DD transformer that gives rise to the circulation of the same currents in the primary coils. and on the secondary lines (than the 4WD transformer.
- the present invention also provides a procedure for the analysis of a 4WD transformer based on the use of the effective currents of the first aspect of the invention.
- the procedure comprises obtaining, by means of a measuring device, the value of at least one magnitude selected from the group that includes symmetrical components of the effective currents.
- the value of the effective currents is obtained by one of the following options: b1) using the expressions [25] where a is a verser of value a - They are the symmetric components of the effective currents; b2) through the expressions [14] in which
- N p is the number of turns of the primary of the 4WD transformer
- N s are the number of turns of the secondary of the 4WD transformer, s are the currents in the primary coils of the 4WD transformer; b3) through an emulation system with a DD transformer as the equivalent to the 4WD transformer under analysis, so that in the DD transformer of the emulation system the same currents are reproduced in the primary coils and in the secondary lines that 4WD transformer object analysis, and the currents that circulate through the secondary coils of said DD transformer are measured, which are the effective currents c) the value of the apparent power (S) of the 4WD transformer is obtained using one of the following options: c1) using equation [18] c2) by equation [19] c3) by equation [20] in which are the effective values of the secondary line voltages of the 4WD transformer are the effective values of the effective currents are the effective values of the symmetric components of the effective currents are the effective values of the symmetrical components of the secondary line currents with the particularity that equation [19] is derived from equation [18] by application of Fortescue
- T bn is the real current that circulates through the first half of the coil linked to the neutral, in the secondary of the 4WD transformer;
- Tan is the real current that circulates through a second half of the coil linked to the neutral, in the secondary of the 4WD transformer;
- T ca are the real currents that circulate through the respective neutral-free coils, in the secondary of the 4WD transformer;
- T n is the real current that circulates through the neutral conductor of the secondary of the 4WD transformer, they are the effective currents; g) the value of the currents in the primary coils of the transformer It is obtained through the following expressions: in which
- N p is the number of turns of the primary of the 4WD transformer
- N s are the number of turns of the secondary of the 4WD transformer, they are the effective currents.
- the present invention also provides a device for the analysis of a 4WD transformer based on the use of the effective currents of the first aspect of the invention.
- the device includes:
- - a measurement program, responsible for obtaining the value of one or several electrical magnitudes from the 4WD transformer.
- the present invention allows the apparent power of 4WD transformers to be correctly measured, as well as to measure, separately, the impacts produced by star loads and the impacts produced by delta loads on the 4WD transformer under analysis. avoiding measurement errors that are committed in the prior art, for example, the technologies used by manufacturers of apparent power measuring instruments.
- the present invention also allows other quantities to be measured based on the effective currents, such as, for example, the real currents in the secondary coils, the currents in the primary coils, etc.
- the present invention allows these magnitudes to be measured by recording the values of the necessary voltages and currents at the secondary terminals, avoiding the placement of internal sensors in the transformer windings.
- the present invention allows measuring the apparent power, the impacts of delta and star loads, and the currents in the primary coils, without the need to measure any magnitude in the neutral conductor.
- Figure 1 schematically represents the constitution of a 4WD transformer to whose analysis the present invention refers.
- Figure 2 schematically represents a 4WD transformer feeding delta and star loads, with the voltages and currents in the different parts of the service.
- Figure 3 shows the circulation of currents through the coils of the secondary winding of the 4WD transformer in figure 2 when there is no current circulation through the neutral conductor.
- Figure 4 shows the circulation of currents through the coils of the secondary winding of the 4WD transformer in Figure 2 when there is current circulation through the neutral conductor.
- Figure 5 includes two drawings (figure 5a and figure 5b) that, together, help to interpret the concept of effective currents of the present invention.
- Figure 5a shows a 4WD transformer under analysis, as well as the currents that circulate through it.
- Figure 5b shows a D-D transformer equivalent to the 4WD transformer under analysis, as well as the currents that circulate through it.
- Figure 6 shows the circulation of effective currents in the secondary winding of a 4WD transformer under analysis.
- Figures 7 and 8 show two current systems into which the real secondary currents of a 4WD transformer can be decomposed, as well as the circulation of the currents of said systems through the different coils of the secondary winding.
- the current system shown in Figure 7 is formed by the currents that circulate through individual coils of the secondary of the transformer, without current circulation through the neutral conductor.
- the current system shown in figure 8 is formed by the neutral current that circulates through the middle of the coil of the first phase of the secondary of the transformer.
- Figure 9 represents currents whose circulation through the secondary coils produce the same magnetic effects as the current system shown in Figure 7.
- Figure 10 is a diagram that shows the operational sequence of a procedure for the analysis of 4WD transformers, according to a preferred embodiment of the present invention, applicable to instruments for measuring the apparent power and other magnitudes of 4WD transformers.
- Figure 11 is a diagram that represents a measurement device for the analysis of 4WD transformers with sensor vapors installed in the electrical network, according to a preferred embodiment of the present invention.
- Figure 12 is a diagram that represents the programming modules for measuring the apparent power of 4WD transformers, and the impacts of star and delta loads, according to a preferred embodiment of the present invention.
- Figure 13 is a diagram that represents the programming modules for measuring the real secondary currents of 4WD transformers, according to a preferred embodiment of the present invention.
- Figure 14 presents a possible configuration of the information displayed in a display means of the measuring device, according to a preferred embodiment of the present invention.
- Figure 1 shows how a 4WD transformer is constituted, the analysis of which the present invention refers to.
- a 4WD transformer is a delta-delta transformer with three coils in the secondary and a neutral conductor connected in the center of one of said coils.
- the coil linked to the neutral is called the secondary coil in which the neutral is connected; and neutral-free coil, to a secondary coil without connection to neutral.
- 4WD transformers operate by supplying delta loads connected to terminals a, b and c of the secondary, and star loads. which are connected between terminals a and b of the secondary and the neutral conductor, as seen in figure 2. Terminal c of the secondary is never used to power star loads.
- N p and N s are the number of turns of the primary and secondary, respectively, are the currents in the primary coils, and are the currents in the secondary coils.
- the load losses calculated from the primary are substantially equal to those calculated from the secondary, expression in which the coefficients R cc and r cc are proportional to the short-circuit resistances of the transformer obtained from the primary or from the secondary, respectively.
- the coefficients are equal to three times the short circuit resistances obtained from the primary or from the secondary, respectively.
- load losses calculated from primary currents are different from load losses using actual secondary currents. More specifically, the copper losses calculated from the primary, have a different value than those calculated from the secondary,
- the currents circulating through the secondary coils do not satisfy Fortescue's theorem, since the positive and negative sequence components of this current system are not related to the positive (direct) and negative (reverse) sequence components of the secondary line currents i.e.
- the present invention discloses currents for the analysis of 4WD transformers called "effective currents.”
- the currents Effective are those currents that circulate through the secondary coils of a DD transformer equivalent to the 4WD transformer under analysis.
- a DD transformer is a delta-delta transformer without a neutral conductor.
- “DD transformer equivalent to the 4WD transformer under analysis” must be understood as that DD transformer (as shown in Figure 5b) that gives rise to the circulation of the same currents in the primary coils. And on the secondary lines that the 4WD transformer object analysis (as shown in Figure 5a).
- Effective currents allow the operation of 4WD transformers to be analyzed based on the theory of delta-delta transformers, simply by applying a one-to-one transformation [T] between the set of effective secondary currents of the equivalent DD transformer and the set of the real secondary currents of the 4WD transformer. More specifically, according to a preferred embodiment, the Effective currents are related to actual transformer secondary currents
- T bn is the real current that circulates through the first half of the coil linked to the neutral, in the secondary of the 4WD transformer; are the real currents that circulate through the respective neutral-free coils, in the secondary of the 4WD transformer;
- T n is the current that circulates through the neutral conductor of the secondary of the 4WD transformer; and the one-to-one transformation matrix [T] is:
- the first current system shown in figure 7, is formed by three currents that circulate respectively through each of the secondary coils of the transformer, without current circulation through the neutral.
- the zero sequence (homopolar) component of this current system is:
- the second system of currents is due to the circulation of the neutral current for only half an of the coil of the first phase of the secondary of the 4WD transformer, as shown in figure 8.
- the magnetomotive force it produces is; that is, the effects magnetic forces caused by T n are the same as those that would produce a current of value circulating throughout the coil ab.
- the magnetic effects of the neutral current T n are equivalent to those derived from the circulation of the following currents through each of the secondary coils:
- the effective currents of the secondary part of the 4WD transformer can be expressed as the sum of the corresponding currents of the first and second current systems, as shown below:
- the positive and negative sequence components of the effective currents are related to the positive and negative sequence components of the secondary line currents according to the following equations: Therefore, they satisfy Fortescue's theorem and, more importantly, verify the Principle of Conservation of Energy with the active and reactive powers measured in the windings and secondary lines. Likewise, Fortescue's theorem is also satisfied by the zero sequence (homopolar) components of the effective currents,
- This component of the effective currents must necessarily be zero, because the secondary of the transformer is symmetrical, that is, its electromotive forces are balanced and the impedances of each phase are equal.
- the present invention provides a procedure for the analysis of a 4WD transformer based on the concept of effective currents.
- the effective currents explained above it is possible to apply them to obtain one or several magnitudes of the 4WD transformer for the analysis of said transformer, such as, for example, the positive and negative sequence components of the effective currents, the effective currents, the apparent power of the transformer, the impact of star loads on the transformer, the impact of delta loads on the transformer, the currents in the primary coils, the real currents in the secondary coils, according to the particularities included in the following sections a)-g).
- a) below are several particularities regarding obtaining the positive and negative sequence components of the effective currents also referred to herein as symmetric components of effective currents.
- the positive and negative sequence components of the effective currents are obtained by the following expressions: in which are the positive and negative sequence components of the currents secondary line currents, also referred to herein as symmetrical components of secondary line currents.
- aJbJc are the secondary line currents.
- - current samples are acquired by means of an acquisition means, preferably sensors arranged in the secondary lines of the transformer;
- the effective currents are obtained through the following expressions [25] where a is a value version are the positive and negative sequence components of the currents effective. Preferably they are obtained as explained above. in section a).
- the effective currents are obtained through the following expressions [14] in which
- Np is the number of turns of the primary of the 4WD transformer
- N s are the number of turns of the secondary of the 4WD transformer, they are the currents in the primary coils of the 4WD transformer.
- the value of the effective currents can be obtained in another way at the indicated above.
- the value of the effective currents is obtained through an emulation system with a D-transformer.
- the apparent power (S) of this type of transformers can be expressed using the proportionality between apparent powers and copper losses, as follows: in which are the effective values of the secondary line voltages of the 4WD transformer are the effective values of the effective currents (
- the apparent power (S) of 4WD transformers can also be expressed in terms of the symmetric components of the effective currents, as follows: in which are the effective values of the secondary line voltages of the 4WD transformer ( s on l° s effective values of the positive and negative sequence components of the effective currents Starting from the expression [19], and taking into account the relationships between the positive and negative sequence components of the effective currents and the positive and negative sequence components of secondary line currents indicated by the expressions [15], another possible expression of the apparent power (S) of 4WD transformers is the following: in which are the effective values of the secondary line voltages of the 4WD transformer are the effective values of the positive and negative sequence components ( a) of the secondary line currents
- the apparent power (S) of the 4WD transformer under analysis can be obtained using any of the equations [18], [19] and [20]. The following should be noted:
- Equation [19] explicitly integrates the symmetric components of the effective currents; and is derived from equation [18], so it implicitly integrates the concept of effective currents.
- Equation [20] does not explicitly integrate effective currents into the expression. However, this expression is the result of several developments from the concept of “effective currents”. Specifically, equation [20] is derived from equation [19] which, in turn, is derived from equation [18], so the concept of effective currents is implicitly integrated into equation [20],
- the apparent power (S) of the 4WD transformer is obtained by means of equation [18],
- the apparent power (S) of the 4WD transformer is obtained by equation [19]:
- the apparent power (S) of the 4WD transformer is obtained by equation [20]:
- I a+ and I a _ are obtained by the expressions [21]:
- l a , l b and I c are obtained as explained above in section a).
- V ab , V bc and V ca are obtained as explained in the previous section c1).
- the line voltages and currents of the secondary of the 4WD transformer are acquired.
- Voltage and current samples are acquired using an acquisition means, preferably sensors arranged on the secondary lines of the 4WD transformer; and digital processing of the acquired samples is carried out to obtain the effective values and corresponding initial phases.
- any of the equations [19], [20], or [21] are especially useful in industrial practice, since they allow the apparent power of 4WD transformers to be determined from the measurement of line voltages and currents.
- the impact of delta loads (S A ) on the 4WD transformer can be expressed by analogy to equation [20], simply by substituting in said equation [20] the effective values of the positive and negative sequence components of line currents of the secondary by the effective values of the sequence components positive and negative of the line currents absorbed by the delta loads (also called in this document symmetric components of the line currents absorbed by the delta loads), giving rise to equation [22], Based on the above According to a preferred embodiment, the calculation of the impact of delta loads ( SA ) on the 4WD transformer is carried out using equation [22]: in which are the effective values of the transformer secondary line voltages are the effective values of the positive and negative sequence components of line currents absorbed by delta loads
- the secondary line voltages of the 4WD transformer and the line currents absorbed by the delta loads are obtained from as follows: voltage and current samples are acquired by means of an acquisition means, preferably sensors arranged on the secondary lines of the transformer and on the lines of the delta loads; Digital processing of the acquired samples is carried out to obtain the effective values and corresponding initial phases.
- voltage and current samples are acquired by means of an acquisition means, preferably sensors arranged on the secondary lines of the transformer and on the lines of the delta loads; Digital processing of the acquired samples is carried out to obtain the effective values and corresponding initial phases.
- the exclusive impact of the star loads ( Sr ) on the 4WD transformer is obtained by the following equation: in which
- S is obtained according to any of options c1), c2) or c3), as explained above in section c).
- S ⁇ is obtained as explained above in section d).
- the real currents in the secondary coils of the transformer are obtained by the following expressions: in which
- T bn is the real current that circulates through the first half of the coil linked to the neutral, in the secondary of the 4WD transformer;
- Tan is the real current that circulates through a second half of the coil linked to the neutral, in the secondary of the 4WD transformer; They are the real currents that circulate through the respective neutral-free coils, in the secondary of the 4WD transformer;
- T n is the current that circulates through the neutral conductor of the secondary of the 4WD transformer; are the effective currents.
- T are obtained as explained above in reference to any of options b1), b2) or b3); and T n is obtained by acquiring a current sample using an acquisition means, preferably a sensor arranged in the neutral of the secondary of the transformer, and performing digital processing of the acquired sample to obtain the effective value and corresponding initial phase.
- an acquisition means preferably a sensor arranged in the neutral of the secondary of the transformer
- the currents in the primary coils of the transformer 4WD UABJBCJCA are obtained by the following expressions: in which p is the number of turns of the primary of the 4WD transformer, are the number of turns of the secondary of the 4WD transformer, They are the effective currents.
- T are obtained as explained above in reference to any one of options b1) or b3).
- the 4WD transformer used in this comparative example has a nominal power of 300 kVA, transformation ratio 12470 / 240V, relative short circuit voltage 4.5%, no-load current 2.3%, nominal load losses 3600 W and no-load losses 800 W.
- the 4WD transformer supplies impedance star loads and balanced loads in an impedance triangle ⁇ l, as seen in figure 2. The loads They can work together or separately.
- Electrical signals are acquired from the 4WD transformer under analysis, and said signals are stored, preferably according to the following particularities: if it is desired to obtain the apparent power due to all the loads (S), the electrical signals that are acquired in the present action ( in 1 of Figure 10) are, at least, voltage samples and line current samples of the secondary of the transformer; If it is desired to obtain the exclusive impacts of delta loads (S A ) on the 4WD transformer, at least samples of secondary line voltages and samples of line currents absorbed by the delta loads are acquired. If it is desired to obtain the exclusive impacts of star loads (S r ) on the transformer, at least samples of voltages from the secondary of the transformer, samples of line currents from the secondary of the transformer, are acquired. transformer and samples of line currents absorbed by the loads in triangle if you want to obtain the real currents in the secondary coils of the transformer
- the matrices of effective values and corresponding initial phases are obtained (in 2 of Figure 10).
- the harmonic components are obtained, preferably, by Fourier Signs.
- the acquisition of electrical signals (1 in Figure 10), the analysis of signals (2 in Figure 10) and the obtaining of the symmetry of the line currents (3 in Figure 10) are actions common to obtaining any of the mentioned magnitudes (that is, to obtaining the apparent power due to all the loads, the exclusive impact of delta loads, the exclusive impact of star loads, and the currents real in the secondary coils).
- the rest of the actions are carried out as follows.
- the effective currents in the secondary coils are obtained (in 6 according to Figure 10) by means of the expressions [25]
- the calculation of the impact of delta loads on the 4WD transformer involves carrying out actions 1, 2, 3, 4, 7 and 8.
- Actions 4 and 7 can be carried out in one or another order without distinction, so the calculation of the impact of star loads on the 4WD transformer can follow any of the operational sequences 1-2-3-4-7-8 or 1-2-3- 7-4-8.
- the present invention also provides a device (A) for the analysis of a 4WD transformer based on the concept of effective currents described above.
- the device (A) allows carrying out the procedure described above; Specifically, by means of the device (A) of the present invention, one or more magnitudes of the 4WD transformer under analysis can be obtained, such as, for example, symmetrical components of the effective currents, effective currents, apparent power, impact of star loads on the transformer, impact of delta loads on the transformer, currents in the primary coils, real currents in the secondary coils, etc.
- the device (A) of the present invention is a measurement device that comprises: a physical system for measuring and acquiring electrical signals (D); a processing system (E); and a measurement program (P), responsible for obtaining the value of one or several electrical magnitudes of the 4WD transformer (T) under analysis.
- the device (A) of the present invention can also comprise a display means (V), preferably a screen, where the value of the electrical magnitude or magnitudes obtained is displayed, which allows the behavior of the 4WD transformer to be analyzed.
- the physical system for measuring and acquiring electrical signals comprises: current measurement sensors (B); some tension measurement sensors (C); some signal conditioners; and a data acquisition card.
- the signal conditioners are responsible for adapting instantaneous values of the currents and voltages obtained by the current measurement sensors (B) and the voltage measurement sensors (C), so that the voltages at the outputs of the signal conditioners are applicable to the analog inputs of the data acquisition card.
- the data acquisition card converts the analog voltage and current signals into a series of discrete samples, which are used as inputs to the measurement program (P).
- the physical system for measuring and acquiring electrical signals (D) is arranged in the secondary lines of the transformer as shown in Figure 11, so that it can acquire voltage signals. and the secondary line currents of the 4WD transformer, both the total currents (J and the currents due to delta loads and neutral current (/ n ).
- the measuring device (A) acquires all the indicated signals through the physical system of measurement and acquisition of electrical signals (D) and stores them, to later use only the necessary ones depending on the magnitude or magnitudes that you wish to obtain.
- the measuring device (A) acquires exclusively the signals that are needed depending on the magnitude or magnitudes that are desired to be obtained.
- the processing system (E) is connected to a motherboard, to which the data acquisition card is also connected, which allows the discrete samples of the voltage and intensity signals to be exchanged with the measurement program ( P).
- the measurement program (P) comprises the following modules: a digital signal processing module (P1); a signal analysis module (P2); a symmetric line current module (P3); and one or more modules selected from the group comprising: effective current symmetry module (P4); effective currents module (P5); apparent power module (P6); load impact modulus (P7); secondary real currents module (P8).
- this group can also comprise other modules to obtain other magnitudes of the 4WD transformer under analysis; for example, a primary current module.
- the measurement program (P) may also comprise a visualization module (P9).
- the digital signal processing module (P1) is responsible for receiving voltage and current samples, and storing them in a vector for each of them.
- the signal analysis module (P2) is responsible for obtaining, from the samples received in the digital signal processing module (P1), the effective values and the initial phases of said samples.
- the line current symmetry module (P3) is responsible for obtaining the direct and reverse sequence components of the line currents of the secondary of the 4WD transformer, both the components corresponding to the total currents and those corresponding to the line currents. of triangle charges in effective value and in angle, from the information obtained in the signal analysis module (P2).
- this module (P3) is responsible for obtaining _ according to the expressions [21] and according to the expressions [23],
- the effective current symmetry module (P4) is responsible for obtaining the effective values and the angle of the positive and negative sequence components of the effective currents of the secondary of the transformer from the components of positive and negative sequences of the 4WD transformer line currents obtained in the line current symmetry module (P3).
- this module (P4) is responsible for obtaining according to the expressions [15]
- the effective currents module (P5) is responsible for obtaining the effective values and angle of the effective currents of the secondary of the 4WD transformer ⁇ a from its symmetric components obtained in the symmetric module of effective currents (P4).
- this module (P5) is responsible for obtaining according to the expressions [25],
- the apparent power module (P6) is responsible for obtaining the apparent power value (S) of the 4WD transformer, preferably from the effective values of the secondary line voltages (V ab , V bc , V ca ). obtained in the signal analysis module (P2), and the current information obtained in any of the following modules: line current symmetry module (P3), effective current symmetry module (P4), currents module effective (P5).
- the apparent power module (P6) is responsible for obtaining the apparent power (S) according to expression [20], from the voltage matrices V ab , V bc , V ac obtained in module P2 and currents obtained in the line current symmetry module (P3); according to expression [19], from the voltage matrices V ab , V bc , V ca obtained in the P2 module and currents obtained in the symmetric module of effective currents (P4); either according to expression [18], from the voltage matrices V ab , V bc , V ca obtained in the P2 module and currents obtained in the effective currents module (P5).
- the load impact module (P7) is responsible for obtaining the value of the apparent power of the 4WD transformer due to the operation of the star loads (S r ), and the value of the apparent power of the 4WD transformer due to the operation of the triangle charges (S A ).
- this module (P7) is responsible for obtaining S & according to the expressions [22] and [23]; and S Y according to the expression [24],
- the secondary real currents module (P8) is responsible for obtaining the effective values and angles of the real currents of the secondary coils of the 4WD transformer, from the values of the effective currents obtained in the effective current module (P5), and the neutral current obtained in the signal analysis module (P2).
- this module (P8) is responsible for obtaining ⁇ ca according to the expressions [26],
- the primary current module is responsible for obtaining the effective values and angles of the currents of the primary coils of the 4WD transformer, preferably, from the values of the effective currents obtained in the module of effective currents (P5), the number of turns of the primary (N p ) and the number of turns of the secondary (N s ).
- the primary current module is responsible for obtaining according to the expressions [14],
- the display module (P9) is responsible for displaying on the display means (V) the information of one or several magnitudes of the 4WD transformer obtained by the device (A), preferably one or several electrical magnitudes selected from the group that comprises: components of positive and negative sequence of the effective currents, effective currents, apparent power of the transformer, impact of star loads on the transformer, impact of delta loads on the transformer, currents in the primary coils of the transformer and real currents in the coils of the secondary of the transformer.
- the display module (P9) displays on the display means (V) numerical information of the apparent power of the 4WD transformer, the impacts of delta and star loads, as well as currents. real in the secondary coils of the 4WD transformer (“Secondary Currents” in figure 14).
- the measurement program (P) comprises the modules P1-P9 mentioned above. More specifically, Figure 12 shows the modules of the measurement program (P) configured to intervene in the measurement and visualization of the apparent power and the impacts of the loads, both star and delta (specifically the modules P1-P7 and P9); and Figure 13 shows the modules of the measurement program (P) configured to intervene in the measurement and visualization of the real currents of the secondary coils (specifically, the modules P1-P5, P8-P9).
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Abstract
The present invention discloses the use of effective currents for analysing a 4WD transformer, where the use of said currents in the secondary coils of the 4WD transformer, replacing the actual currents of said coils, results in the same magnetic effects as the currents in the primary coils. The invention also discloses a method based on the use of the effective currents, said method comprising obtaining at least one magnitude of the group comprising: symmetrical components of the effective currents, effective currents, apparent power, impact of delta loads, impact of star loads, currents in the primary coils and actual currents in the secondary coils. The invention also discloses a device (A) for analysing a 4WD transformer (T), said device comprising a physical system for measuring and acquiring electrical signals (D); a processing system (E); and a measuring program (P).
Description
DESCRIPCIÓN DESCRIPTION
Uso de corrientes, procedimiento y dispositivo para el análisis de un transformador 4WD Use of currents, procedure and device for the analysis of a 4WD transformer
SECTOR DE LA TÉCNICA TECHNIQUE SECTOR
La presente invención se refiere de manera general al campo de los transformadores, y más concretamente al análisis de transformadores de distribución triángulo - triángulo con conductor neutro, también denominados transformadores 4WD. The present invention refers generally to the field of transformers, and more specifically to the analysis of delta-delta distribution transformers with neutral conductor, also called 4WD transformers.
ANTECEDENTES DE LA INVENCIÓN BACKGROUND OF THE INVENTION
Los transformadores triángulo - triángulo con conductor neutro, también llamados “high- leg”, “wild-leg” o “Four Wire Delta” (4WD), son transformadores bastante utilizados en las redes de distribución de los Estados Unidos de América para alimentar instalaciones monofásicas, preferentemente residenciales y de alumbrado, a 120 V, e instalaciones industriales trifásicas, a 240 V. Triangle transformers - triangle with neutral conductor, also called “high-leg”, “wild-leg” or “Four Wire Delta” (4WD), are transformers widely used in the distribution networks of the United States of America to power installations. single-phase, preferably residential and lighting, at 120 V, and three-phase industrial installations, at 240 V.
Tal y como es conocido en la técnica, básicamente son transformadores con los devanados primario y secundario conectados en triángulo, con la particularidad de que una de las bobinas del secundario incorpora un terminal en su centro que divide la bobina en dos mitades y permite la conexión de un conductor neutro. As is known in the art, they are basically transformers with the primary and secondary windings connected in a triangle, with the particularity that one of the secondary coils incorporates a terminal in its center that divides the coil into two halves and allows the connection of a neutral conductor.
Para poder analizar transformadores es necesario determinar una o varias magnitudes asociadas como, por ejemplo, potencia aparente del transformador, impactos que producen las cargas en triángulo y/o en estrella sobre el transformador, corrientes en las bobinas del primario del transformador, corrientes en las bobinas del secundario del transformador, etc. En particular, la medida correcta de la potencia aparente de los transformadores de las redes eléctricas es una necesidad para los operadores de dichas redes, así como para los fabricantes de instrumentos de medida de la potencia eléctrica, entre otros. El valor de la potencia aparente determina los efectos combinados de todas las energías presentes en los transformadores y, por tanto, esta magnitud es utilizada para el correcto diseño de estas máquinas, a la vez que proporciona información acerca de su funcionamiento. In order to analyze transformers, it is necessary to determine one or several associated magnitudes such as, for example, apparent power of the transformer, impacts produced by delta and/or star loads on the transformer, currents in the primary coils of the transformer, currents in the transformer secondary coils, etc. In particular, the correct measurement of the apparent power of the transformers of the electrical networks is a necessity for the operators of said networks, as well as for the manufacturers of instruments for measuring electrical power, among others. The value of the apparent power determines the combined effects of all the energies present in the transformers and, therefore, this magnitude is used for the correct design of these machines, while providing information about their operation.
La potencia aparente de los transformadores de las redes eléctricas puede ser medida en el primario o en el secundario. La medida de la potencia aparente en el primario de los transformadores de distribución entraña ciertos riesgos para el operario, al tener que trabajar con tensiones elevadas, y el uso de instrumentos de medida más complejos, dado que las tensiones del primario no pueden ser medidas directamente, siendo necesario el empleo de transformadores de medida de tensión. Por estos inconvenientes, se prefiere hacer las medidas de la potencia aparente en el secundario. La potencia aparente del secundario siempre es ligeramente inferior a la potencia aparente medida en el primario, por efecto de las corrientes de
vacío y las pérdidas. The apparent power of the transformers of electrical networks can be measured in the primary or secondary. The measurement of the apparent power in the primary of distribution transformers entails certain risks for the operator, as they have to work with high voltages, and the use of more complex measuring instruments, given that the primary voltages cannot be measured directly. , being necessary the use of voltage measurement transformers. Due to these drawbacks, it is preferred to measure the apparent power in the secondary. The apparent power of the secondary is always slightly lower than the apparent power measured in the primary, due to the effect of the currents. emptiness and losses.
Una fórmula de la potencia aparente de los transformadores 4WD utilizada por los principales fabricantes de instrumentos de medida de la potencia eléctrica es la siguiente:
A formula for the apparent power of 4WD transformers used by the main manufacturers of electrical power measuring instruments is as follows:
Esta expresión ha sido desarrollada bajo la consideración de que existe una proporcionalidad entre el valor de la potencia aparente, obtenida en base a los valores eficaces de las tensiones compuestas
y de las corrientes circulantes por las bobinas del
devanado secundario del transformador, y las pérdidas en el cobre del transformador, calculadas en base a dichas corrientes. This expression has been developed under the consideration that there is a proportionality between the value of the apparent power, obtained based on the effective values of the composite voltages and the currents circulating through the coils of the secondary winding of the transformer, and the losses in the copper of the transformer, calculated based on said currents.
La proporcionalidad entre las potencias aparentes y las pérdidas debidas a la carga ha sido utilizada por ingenieros como L.S. Czarnecki y A.E. Emanuel. L.S. Czarnecki utilizó la proporcionalidad entre potencias aparentes y pérdidas energéticas para establecer la expresión de la potencia aparente en sistemas trifásicos, en su artículo “Orthogonal Decomposition of the Currents in a 3-Phase Nonlinear Asymmetrical Circuit with a Nonsinusoidal Voltage Source”, publicado en la revista IEEE Transactions on Instrumentation and Measurement, Vol. 37, No 1 , March 1988, pp. 30-34. A.E. Emanuel utilizó la proporcionalidad antes mencionada para la formulación de su potencia aparente en sistemas eléctricos, que está actualmente incluida en la IEEE Standard 1459-2010. Ninguno de estos autores ha desarrollado expresiones de la potencia aparente para transformadores 4WD. The proportionality between apparent powers and losses due to load has been used by engineers such as L.S. Czarnecki and A.E. Emanuel. L.S. Czarnecki used the proportionality between apparent powers and energy losses to establish the expression of apparent power in three-phase systems, in his article “Orthogonal Decomposition of the Currents in a 3-Phase Nonlinear Asymmetrical Circuit with a Nonsinusoidal Voltage Source”, published in the journal IEEE Transactions on Instrumentation and Measurement, Vol. 37, No 1, March 1988, pp. 30-34. A.E. Emanuel used the aforementioned proportionality for the formulation of his apparent power in electrical systems, which is currently included in the IEEE Standard 1459-2010. None of these authors have developed apparent power expressions for 4WD transformers.
En el año 2015, aplicando también la proporcionalidad entre potencia aparente y pérdidas energéticas, los propios inventores de la presente invención desarrollaron la siguiente expresión de la potencia aparente de los transformadores 4WD:
In 2015, also applying the proportionality between apparent power and energy losses, the inventors of the present invention themselves developed the following expression for the apparent power of 4WD transformers:
Esta expresión fue publicada en un artículo de la revista Energies 2015 - 8, titulado “Four-Wire Delta Service Sinusoidal Operation and Compensation Simulator”, pp. 11276-11294, doi:10.3390/en81011276. Los valores de la potencia aparente obtenidos con la fórmula [2] son idénticos a los determinados con la fórmula [1], con la ventaja de que la medida de las corrientes se realiza en las línea Y en e> neutro del secundario. Con la expresión [2] se evita
la dificultad de utilizar sensores internos para medir las corrientes en las bobinas del secundario del transformador. This expression was published in an article in the magazine Energies 2015 - 8, titled “Four-Wire Delta Service Sinusoidal Operation and Compensation Simulator”, pp. 11276-11294, doi:10.3390/en81011276. The values of the apparent power obtained with formula [2] are identical to those determined with formula [1], with the advantage that the current measurement is carried out in the lines Y in e > neutral of the secondary. With the expression [2] we avoid the difficulty of using internal sensors to measure currents in the secondary coils of the transformer.
No obstante, las potencias aparentes obtenidas con las expresiones [1] y [2] dan valores mayores que las potencias aparentes calculadas con las tensiones y corrientes del primario, justamente lo contrario de lo que sucede en la práctica industrial, como ya se ha apuntado anteriormente. Este resultado es indicativo de que las expresiones [1] y [2] no calculan correctamente el valor de la potencia aparente de los transformadores 4WD.
Los errores en la medida de la potencia aparente derivados del empleo de las ecuaciones [1] Y [2] ya se intuían cuando se publicó el artículo “Four-Wire Delta Service Sinusoidal Operation and Compensation Simulator”. Por esa razón, en dicho artículo se expresaron separadamente las potencias aparentes del primario y del secundario. No obstante, en aquel entonces, no se dio solución a este problema. However, the apparent powers obtained with expressions [1] and [2] give higher values than the apparent powers calculated with the primary voltages and currents, exactly the opposite of what happens in industrial practice, as has already been pointed out. previously. This result is indicative that expressions [1] and [2] do not correctly calculate the value of the apparent power of the 4WD transformers. The errors in the measurement of the apparent power derived from the use of equations [1] and [2] were already apparent when the article “Four-Wire Delta Service Sinusoidal Operation and Compensation Simulator” was published. For this reason, in said article the apparent powers of the primary and secondary were expressed separately. However, at that time, there was no solution to this problem.
Por tanto, sigue existiendo en la técnica la necesidad de proporcionar una solución a los inconvenientes mencionados anteriormente, con el fin de mejorar el análisis de transformadores 4WD. Therefore, there remains a need in the art to provide a solution to the drawbacks mentioned above, in order to improve the analysis of 4WD transformers.
SUMARIO DE LA INVENCIÓN SUMMARY OF THE INVENTION
Los inventores de la presente invención han investigado los errores en el cálculo de la potencia aparente de transformadores 4WD desde el secundario, derivados del empleo de las ecuaciones de la técnica anterior, y han desarrollado un nuevo concepto de corrientes, denominadas “corrientes efectivas”, cuya aplicación permite realizar un análisis más cercano a la realidad de este tipo de transformadores. The inventors of the present invention have investigated the errors in the calculation of the apparent power of 4WD transformers from the secondary, derived from the use of the equations of the prior art, and have developed a new concept of currents, called "effective currents", whose application allows for an analysis closer to the reality of this type of transformers.
Aunque las corrientes efectivas se han desarrollado inicialmente a partir de la necesidad de evitar errores en el cálculo de la potencia aparente desde el secundario, gracias a su naturaleza particular, las corrientes efectivas también pueden aplicarse para el cálculo de otras magnitudes de los transformadores 4WD como, por ejemplo, el impacto de cargas en triángulo sobre el transformador, el impacto de cargas en estrella sobre el transformador, las corrientes en las bobinas del primario, y/o las corrientes reales en las bobinas del secundario. Although effective currents have been initially developed from the need to avoid errors in the calculation of the apparent power from the secondary, thanks to their particular nature, effective currents can also be applied to calculate other magnitudes of 4WD transformers such as , for example, the impact of delta loads on the transformer, the impact of star loads on the transformer, the currents in the primary coils, and/or the actual currents in the secondary coils.
Para poder desarrollar el concepto de “corrientes efectivas” los inventores han estudiado el comportamiento de los transformadores 4WD, que es muy singular. Cuando no existe circulación de corriente por el conductor neutro se comportan como transformadores triángulo - triángulo convencionales, sin conductor neutro (también denominados transformadores D-D). En el caso más habitual en que existe circulación de corriente por el conductor neutro, las corrientes que circulan por las bobinas del secundario no dan lugar a los mismos efectos magnéticos que las corrientes de las bobinas del primario. Es decir, la fuerza magnetomotriz del primario, en cada columna del circuito magnético, no es igual a la fuerza magnetomotriz del secundario, calculada con las corrientes reales del secundario. In order to develop the concept of “effective currents”, the inventors have studied the behavior of 4WD transformers, which is very unique. When there is no current circulation through the neutral conductor, they behave like conventional delta-delta transformers, without a neutral conductor (also called D-D transformers). In the most common case in which there is current circulation through the neutral conductor, the currents that circulate through the secondary coils do not give rise to the same magnetic effects as the currents in the primary coils. That is, the primary magnetomotive force, in each column of the magnetic circuit, is not equal to the secondary magnetomotive force, calculated with the real secondary currents.
En base al comportamiento estudiado, los inventores han determinado lo siguiente: Los errores en el cálculo de la potencia aparente de transformadores 4WD desde el secundario no se deben a la ausencia de proporcionalidad entre las potencias aparentes y las pérdidas en el cobre. Estos errores son debidos a que las fuerzas magnetomotrices de cada fase del secundario, calculadas con las corrientes reales en las bobinas de dicho devanado no son iguales a las fuerzas magnetomotrices de cada fase del primario. Este
hecho tiene gran importancia en el análisis de este tipo de transformadores. La proporcionalidad
entre potencias aparentes y pérdidas energéticas de este tipo de transformadores continúa siendo válida, pero deben ser utilizadas unas nuevas corrientes que igualen los efectos magnéticos del primario y del secundario. Estas nuevas corrientes son las corrientes efectivas que han concebido los inventores. Based on the behavior studied, the inventors have determined the following: The errors in the calculation of the apparent power of 4WD transformers from the secondary are not due to the absence of proportionality between the apparent powers and the losses in the copper. These errors are due to the fact that the magnetomotive forces of each phase of the secondary, calculated with the real currents in the coils of said winding , are not equal to the magnetomotive forces of each phase of the primary. This This fact is of great importance in the analysis of this type of transformers. The proportionality between apparent powers and energy losses of this type of transformers continues to be valid, but new currents must be used that equalize the magnetic effects of the primary and secondary. These new currents are the effective currents that the inventors have conceived.
Según lo expuesto, para solucionar los inconvenientes mencionados de la técnica anterior, según un primer aspecto, la presente invención da a conocer un uso de corrientes para el análisis de un transformador 4WD, que son aquellas corrientes que circulan por las bobinas del secundario de un transformador D-D equivalente al transformador 4WD objeto de análisis, denominándose corrientes efectiva con Ia particularidad de que la aplicación
de las corrientes efectivas en las bobinas del secundario del transformador 4WD, en sustitución de las corrientes reales que circulan por dichas bobinas da lugar a los mismos
efectos magnéticos que las corrientes que circulan por las bobinas del primario del transformador 4WD
According to the above, to solve the aforementioned drawbacks of the prior art, according to a first aspect, the present invention discloses a use of currents for the analysis of a 4WD transformer, which are those currents that circulate through the secondary coils of a DD transformer equivalent to the 4WD transformer under analysis, the effective currents being called I due to the particularity that the application of the effective currents in the secondary coils of the 4WD transformer, replacing the real currents that circulate through said coils, gives rise to the same magnetic effects than the currents that circulate through the primary coils of the 4WD transformer
Por transformador 4WD se entiende un transformador triángulo - triángulo con tres bobinas en el secundario y un conductor neutro conectado en el centro de una de dichas bobinas, denominada bobina ligada al neutro para diferenciarla del resto de bobinas del secundario, denominadas bobinas libres de neutro. Por transformador D-D se entiende un transformador triángulo - triángulo sin conductor neutro. Por equivalente se entiende aquel transformador D-D teórico que da lugar a la circulación de las mismas corrientes en las bobinas del primario
y en las líneas del secundario ( que el transformador 4WD.
A 4WD transformer is understood as a triangle-triangle transformer with three coils in the secondary and a neutral conductor connected to the center of one of said coils, called a neutral-linked coil to differentiate it from the rest of the secondary coils, called neutral-free coils. A DD transformer means a delta-delta transformer without a neutral conductor. Equivalent is understood as that theoretical DD transformer that gives rise to the circulation of the same currents in the primary coils. and on the secondary lines (than the 4WD transformer.
Según un segundo aspecto, la presente invención también proporciona un procedimiento para el análisis de un transformador 4WD en base al uso de las corrientes efectivas del primer aspecto de la invención. El procedimiento comprende obtener, mediante un dispositivo de medida, el valor de al menos una magnitud seleccionada del grupo que comprende componentes simétricas de las corrientes efectivas
corrientes efectivas
potencia aparente (S), impacto de cargas en triángulo (SΔ) sobre el transformador, impacto de cargas en estrella (Sr) sobre el transformador, corrientes en las bobinas del primario
y corrientes reales en las bobinas del secundario según las particularidades de
los siguientes apartados: a) el valor de las componentes simétricas de las corrientes efectivas se obtiene
mediante las siguientes expresiones:
en las que son las componentes simétricas de las corrientes de línea del secundario.
b) el valor de las corrientes efectivas se obtiene mediante una de las siguientes
opciones: b1) mediante las expresiones [25]
en las que a es un versor de valor a
-
son las componentes simétricas de las corrientes efectivas; b2) mediante las expresiones [14]
en las que According to a second aspect, the present invention also provides a procedure for the analysis of a 4WD transformer based on the use of the effective currents of the first aspect of the invention. The procedure comprises obtaining, by means of a measuring device, the value of at least one magnitude selected from the group that includes symmetrical components of the effective currents. effective currents apparent power (S), impact of delta loads (S Δ ) on the transformer, impact of star loads (S r ) on the transformer, currents in the primary coils and real currents in the secondary coils according to the particularities of the following sections: a) the value of the symmetric components of the effective currents is obtained through the following expressions: in which are the symmetric components of the secondary line currents. b) the value of the effective currents is obtained by one of the following options: b1) using the expressions [25] where a is a verser of value a - They are the symmetric components of the effective currents; b2) through the expressions [14] in which
Np es el número de espiras del primario del transformador 4WD, N p is the number of turns of the primary of the 4WD transformer,
Ns son el número de espiras del secundario del transformador 4WD, son las corrientes en las bobinas del primario del transformador 4WD;
b3) mediante un sistema de emulación con un transformador D-D como el equivalente al transformador 4WD objeto de análisis, de manera que en el transformador D-D del sistema de emulación se reproducen las mismas corrientes en las bobinas del primario y en las líneas del secundario que transformador 4WD objeto de
análisis, y se miden las corrientes que circulan por las bobinas del secundario de dicho transformador D-D, que son las corrientes efectivas
c) el valor de la potencia aparente (S) del transformador 4WD se obtiene mediante una de las siguientes opciones: c1) mediante la ecuación [18]
c2) mediante la ecuación [19]
c3) mediante la ecuación [20]
en las que son los valores eficaces de las tensiones de línea del secundario del
transformador 4WD
son l°s valores eficaces de las corrientes efectivas
son l°s valores eficaces de las componentes simétricas de
las corrientes efectivas
son l°s valores eficaces de las componentes simétricas de las corrientes de línea del secundario
con la particularidad de que la ecuación [19] deriva de la ecuación [18] por aplicación del teorema de Fortescue; y la ecuación [20] deriva de la ecuación [19] por aplicación de las relaciones existentes entre las componentes y las componentes
según las siguientes expresiones: N s are the number of turns of the secondary of the 4WD transformer, s are the currents in the primary coils of the 4WD transformer; b3) through an emulation system with a DD transformer as the equivalent to the 4WD transformer under analysis, so that in the DD transformer of the emulation system the same currents are reproduced in the primary coils and in the secondary lines that 4WD transformer object analysis, and the currents that circulate through the secondary coils of said DD transformer are measured, which are the effective currents c) the value of the apparent power (S) of the 4WD transformer is obtained using one of the following options: c1) using equation [18] c2) by equation [19] c3) by equation [20] in which are the effective values of the secondary line voltages of the 4WD transformer are the effective values of the effective currents are the effective values of the symmetric components of the effective currents are the effective values of the symmetrical components of the secondary line currents with the particularity that equation [19] is derived from equation [18] by application of Fortescue's theorem; and equation [20] is derived from equation [19] by application of the existing relationships between the components and the components according to the following expressions:
[15];
d) el valor del impacto de cargas en triángulo (SA) sobre el transformador 4WD se obtiene mediante la siguiente ecuación:
en la que
son l°s valores eficaces de las tensiones de línea del secundario del transformador[fifteen]; d) the value of the impact of delta loads (S A ) on the 4WD transformer is obtained by the following equation: in which are the effective values of the line voltages of the secondary of the transformer
4WD (
son los valores eficaces de las componentes simétricas de las comentes
de línea absorbidas por las cargas en triángulo ;
con la particularidad de que la ecuación [22] se obtiene por analogía a la ecuación [20]; e) el valor del impacto de cargas en estrella (Sr) sobre el transformador 4WD se obtiene mediante la siguiente ecuación:
en la que 4WD ( are the effective values of the symmetric components of the currents of line absorbed by the triangle loads; with the particularity that equation [22] is obtained by analogy to equation [20]; e) the value of the impact of star loads (S r ) on the 4WD transformer is obtained by the following equation: in which
S es la potencia aparente del transformador 4WD, S is the apparent power of the 4WD transformer,
SΔ es el Impacto de cargas en triángulo, obtenido mediante la ecuación [22] conforme al apartado d); f) el valor de las corrientes reales en las bobinas del secundario del transformador 4WD se obtiene mediante las siguientes expresiones:
en las que S Δ is the Impact of triangle loads, obtained using equation [22] according to section d); f) the value of the real currents in the secondary coils of the 4WD transformer is obtained using the following expressions: in which
Tbn es la corriente real que circula por una primera mitad de la bobina ligada al neutro, en el secundario del transformador 4WD; T bn is the real current that circulates through the first half of the coil linked to the neutral, in the secondary of the 4WD transformer;
Tan es la corriente real que circula por una segunda mitad de la bobina ligada al neutro, en el secundario del transformador 4WD; Tan is the real current that circulates through a second half of the coil linked to the neutral, in the secondary of the 4WD transformer;
I be , Tca son las corrientes reales que circulan por las respectivas bobinas libres de neutro, en el secundario del transformador 4WD; I be, T ca are the real currents that circulate through the respective neutral-free coils, in the secondary of the 4WD transformer;
Tn es la corriente real que circula por el conductor neutro del secundario del transformador 4WD, son las corrientes efectivas;
g) el valor de las corrientes en las bobinas del primario del transformador
SE obtiene mediante las siguientes expresiones:
en las que T n is the real current that circulates through the neutral conductor of the secondary of the 4WD transformer, they are the effective currents; g) the value of the currents in the primary coils of the transformer It is obtained through the following expressions: in which
Np es el número de espiras del primario del transformador 4WD, N p is the number of turns of the primary of the 4WD transformer,
Ns son el número de espiras del secundario del transformador 4WD, son las corrientes efectivas.
N s are the number of turns of the secondary of the 4WD transformer, they are the effective currents.
Según un tercer aspecto, la presente invención también proporciona un dispositivo para el análisis de un transformador 4WD en base al uso de las corrientes efectivas del primer aspecto de la invención. El dispositivo comprende: According to a third aspect, the present invention also provides a device for the analysis of a 4WD transformer based on the use of the effective currents of the first aspect of the invention. The device includes:
- un sistema físico de medida y adquisición de señales eléctricas; - a physical system for measuring and acquiring electrical signals;
- un sistema procesador; - a processing system;
- un programa de medida, encargado obtener el valor de una o vahas magnitudes eléctricas del transformador 4WD. - a measurement program, responsible for obtaining the value of one or several electrical magnitudes from the 4WD transformer.
Gracias a las comentes efectivas, la presente invención permite medir correctamente la potencia aparente de transformadores 4WD, así como medir, separadamente, los impactos que producen las cargas en estrella y los impactos que producen las cargas en triángulo sobre el transformador 4WD objeto de análisis, evitando los errores de medida que se cometen en la técnica anterior, por ejemplo, las tecnologías utilizadas por los fabricantes de instrumentos de medida de la potencia aparente. Thanks to the effective currents, the present invention allows the apparent power of 4WD transformers to be correctly measured, as well as to measure, separately, the impacts produced by star loads and the impacts produced by delta loads on the 4WD transformer under analysis. avoiding measurement errors that are committed in the prior art, for example, the technologies used by manufacturers of apparent power measuring instruments.
Asimismo, la presente invención también permite medir otras magnitudes en base a las corrientes efectivas como, por ejemplo, las corrientes reales en las bobinas del secundario, las corrientes en las bobinas del primario, etc. Likewise, the present invention also allows other quantities to be measured based on the effective currents, such as, for example, the real currents in the secondary coils, the currents in the primary coils, etc.
La presente invención permite medir dichas magnitudes registrando los valores de las tensiones y corrientes necesarias en los terminales del secundario, evitándose la colocación de sensores internos en los devanados del transformador. The present invention allows these magnitudes to be measured by recording the values of the necessary voltages and currents at the secondary terminals, avoiding the placement of internal sensors in the transformer windings.
Además, la presente invención permite medir la potencia aparente, los impactos de cargas en triángulo y en estrella, y las corrientes en las bobinas del primario, sin necesidad medir ninguna magnitud en el conductor neutro. Furthermore, the present invention allows measuring the apparent power, the impacts of delta and star loads, and the currents in the primary coils, without the need to measure any magnitude in the neutral conductor.
A lo largo de la descripción y las reivindicaciones la palabra "comprende" y sus variantes no pretenden excluir otras características técnicas, componentes o pasos. Además, la palabra "comprende" incluye el caso "consiste en". Para los expertos en la materia, otros objetos, ventajas y características de la invención se desprenderán en parte de la descripción y en parte de la práctica de la invención. Los siguientes ejemplos se proporcionan a modo de ilustración, y no se pretende que sean limitativos de la presente invención. Además, la presente invención cubre todas las posibles combinaciones de realizaciones aquí indicadas.
BREVE DESCRIPCIÓN DE LOS DIBUJOS Throughout the description and claims the word "comprises" and its variants are not intended to exclude other technical characteristics, components or steps. Furthermore, the word "comprises" includes the case "consists of." For those skilled in the art, other objects, advantages and features of the invention will emerge partly from the description and partly from the practice of the invention. The following examples are provided by way of illustration, and are not intended to be limiting of the present invention. Furthermore, the present invention covers all possible combinations of embodiments indicated herein. BRIEF DESCRIPTION OF THE DRAWINGS
La presente invención se entenderá mejor con referencia a las siguientes figuras, en donde con carácter ilustrativo y no limitativo, se ha representado lo siguiente: The present invention will be better understood with reference to the following figures, where, for illustrative and non-limiting purposes, the following has been represented:
La figura 1 representa esquemáticamente la constitución de un transformador 4WD a cuyo análisis se refiere la presente invención. Figure 1 schematically represents the constitution of a 4WD transformer to whose analysis the present invention refers.
La figura 2 representa esquemáticamente un transformador 4WD alimentando a cargas en triángulo y en estrella, con las tensiones y corrientes en las diferentes partes del servicio. Figure 2 schematically represents a 4WD transformer feeding delta and star loads, with the voltages and currents in the different parts of the service.
La figura 3 muestra la circulación de las corrientes por las bobinas del devanado secundario del transformador 4WD de la figura 2 cuando no hay circulación de corriente por el conductor neutro. Figure 3 shows the circulation of currents through the coils of the secondary winding of the 4WD transformer in figure 2 when there is no current circulation through the neutral conductor.
La figura 4 muestra la circulación de las corrientes por las bobinas del devanado secundario del transformador 4WD de la figura 2 cuando hay circulación de corriente por el conductor neutro. Figure 4 shows the circulation of currents through the coils of the secondary winding of the 4WD transformer in Figure 2 when there is current circulation through the neutral conductor.
La figura 5 incluye dos dibujos (figura 5a y figura 5b) que, conjuntamente, ayudan a interpretar el concepto de corrientes efectivas de la presente invención. La figura 5a muestra un transformador 4WD objeto de análisis, así como las corrientes que circulan por él. La figura 5b muestra un transformador D-D equivalente al transformador 4WD objeto de análisis, así como las corrientes que circulan por él. Figure 5 includes two drawings (figure 5a and figure 5b) that, together, help to interpret the concept of effective currents of the present invention. Figure 5a shows a 4WD transformer under analysis, as well as the currents that circulate through it. Figure 5b shows a D-D transformer equivalent to the 4WD transformer under analysis, as well as the currents that circulate through it.
La figura 6 muestra la circulación de las corrientes efectivas en el devanado secundario de un transformador 4WD objeto de análisis. Figure 6 shows the circulation of effective currents in the secondary winding of a 4WD transformer under analysis.
Las figuras 7 y 8 muestran dos sistemas de corrientes en que se pueden descomponer las corrientes reales del secundario de un transformador 4WD, así como la circulación de las corrientes de dichos sistemas por las diferentes bobinas del devanado secundario. El sistema de corrientes mostrado en la figura 7 está formado por las corrientes que circulan por sendas bobinas del secundario del transformador, sin circulación de corriente por el conductor neutro. El sistema de corrientes mostrado en la figura 8 está formado por la corriente del neutro que circula por la mitad de la bobina de la primera fase del secundario del transformador. Figures 7 and 8 show two current systems into which the real secondary currents of a 4WD transformer can be decomposed, as well as the circulation of the currents of said systems through the different coils of the secondary winding. The current system shown in Figure 7 is formed by the currents that circulate through individual coils of the secondary of the transformer, without current circulation through the neutral conductor. The current system shown in figure 8 is formed by the neutral current that circulates through the middle of the coil of the first phase of the secondary of the transformer.
La figura 9 representa unas corrientes cuya circulación por las bobinas del secundario producen los mismos efectos magnéticos que el sistema de corrientes mostrado en la figura 7. Figure 9 represents currents whose circulation through the secondary coils produce the same magnetic effects as the current system shown in Figure 7.
La figura 10 es un diagrama que muestra la secuencia operational de un procedimiento para el análisis de transformadores 4WD, según una realización preferida de la presente invención, aplicable a instrumentos de medida de la potencia aparente y de otras magnitudes de los transformadores 4WD. Figure 10 is a diagram that shows the operational sequence of a procedure for the analysis of 4WD transformers, according to a preferred embodiment of the present invention, applicable to instruments for measuring the apparent power and other magnitudes of 4WD transformers.
La figura 11 es un diagrama que representa un dispositivo de medida para el análisis de transformadores 4WD con vahos sensores instalados en la red eléctrica, según una realización preferida de la presente invención.
La figura 12 es un diagrama que representa los módulos de programación para la medida de la potencia aparente de transformadores 4WD, y los impactos de las cargas en estrella y en triángulo, según una realización preferida de la presente invención. Figure 11 is a diagram that represents a measurement device for the analysis of 4WD transformers with sensor vapors installed in the electrical network, according to a preferred embodiment of the present invention. Figure 12 is a diagram that represents the programming modules for measuring the apparent power of 4WD transformers, and the impacts of star and delta loads, according to a preferred embodiment of the present invention.
La figura 13 es un diagrama que representa los módulos de programación para la medida de las corrientes reales del secundario de transformadores 4WD, según una realización preferida de la presente invención. Figure 13 is a diagram that represents the programming modules for measuring the real secondary currents of 4WD transformers, according to a preferred embodiment of the present invention.
La figura 14 presenta una posible configuración de la información mostrada en un medio de visualization del dispositivo de medida, según una realización preferida de la presente invención. Figure 14 presents a possible configuration of the information displayed in a display means of the measuring device, according to a preferred embodiment of the present invention.
MODOS DE REALIZACIÓN DE LA INVENCIÓN MODES OF EMBODIMENT OF THE INVENTION
En la figura 1 se muestra cómo está constituido un transformador 4WD a cuyo análisis se refiere la presente invención. Tal y como es conocido en la técnica, un transformador 4WD es un transformador triángulo - triángulo con tres bobinas en el secundario y un conductor neutro conectado en el centro de una de dichas bobinas. A modo identificativo, en el presente documento se denomina bobina ligada al neutro a la bobina del secundario en la que se conecta el neutro; y bobina libre de neutro, a una bobina del secundario sin conexión a neutro. Figure 1 shows how a 4WD transformer is constituted, the analysis of which the present invention refers to. As is known in the art, a 4WD transformer is a delta-delta transformer with three coils in the secondary and a neutral conductor connected in the center of one of said coils. By way of identification, in this document the coil linked to the neutral is called the secondary coil in which the neutral is connected; and neutral-free coil, to a secondary coil without connection to neutral.
Generalmente, los transformadores 4WD funcionan alimentando cargas en triángulo \ conectadas a los terminales a, b y c del secundario, y cargas en estrella
que están conectadas entre los terminales a y b del secundario y el conductor neutro, tal como se observa en la figura 2. El terminal c del secundario nunca se utiliza para alimentar cargas en estrella. Generally, 4WD transformers operate by supplying delta loads connected to terminals a, b and c of the secondary, and star loads. which are connected between terminals a and b of the secondary and the neutral conductor, as seen in figure 2. Terminal c of the secondary is never used to power star loads.
Los transformadores 4WD tienen dos tipos de funcionamiento, dependiendo de que el valor de la corriente del neutro (/n) sea cero o distinto de cero, según se explica a continuación: I) Si no hay circulación de corriente por el conductor neutro (Tn = 0), ya sea porque no haya cargas conectadas a ese terminal, o bien, porque las cargas conectadas entre los terminales a-n tengan las mismas impedancias que las cargas conectadas entre los terminales
Zb\ los transformadores 4WD funcionan como transformadores triángulo - triángulo convencionales sin conductor neutro (también denominados transformadores D-D), tal como se observa en la figura 3. En estas condiciones, se producen las siguientes circunstancias:4WD transformers have two types of operation, depending on whether the value of the neutral current (/ n ) is zero or non-zero, as explained below: I) If there is no current circulation through the neutral conductor (T n = 0), either because there are no loads connected to that terminal, or because the loads connected between the terminals still have the same impedances as the loads connected between the terminals Z b \ 4WD transformers function as conventional delta-delta transformers without a neutral conductor (also called DD transformers), as seen in figure 3. Under these conditions, the following circumstances occur:
- La suma vectorial de las fuerzas magnetomotrices del primario y del secundario en cada columna del circuito magnético de estos transformadores es aproximadamente igual a cero. Más específicamente, las fuerzas magnetomotrices de cada fase de los devanados primario y secundario verifican las siguientes ecuaciones magnéticas:
en donde Np y Ns son el número de espiras del primario y del secundario, respectivamente, son las corrientes en las bobinas del primario, y son las corrientes
en las bobinas del secundarlo. - The vector sum of the primary and secondary magnetomotive forces in each column of the magnetic circuit of these transformers is approximately equal to zero. More specifically, the magnetomotive forces of each phase of the primary and secondary windings verify the following magnetic equations: where N p and N s are the number of turns of the primary and secondary, respectively, are the currents in the primary coils, and are the currents in the secondary coils.
Las pérdidas debidas a la carga calculadas desde el primario son sensiblemente ¡guales a las calculadas desde el secundario,
expresión en la que los coeficientes Rcc y rcc son proporcionales a las resistencias de cortocircuito del transformador obtenidas desde el primario o desde el secundario, respectivamente. De acuerdo con el teorema de Rosen-Kennelly, los coeficientes
son ¡guales a tres veces las resistencias de cortocircuito obtenidas desde el primario o desde el secundario, respectivamente. The load losses calculated from the primary are substantially equal to those calculated from the secondary, expression in which the coefficients R cc and r cc are proportional to the short-circuit resistances of the transformer obtained from the primary or from the secondary, respectively. According to the Rosen-Kennelly theorem, the coefficients They are equal to three times the short circuit resistances obtained from the primary or from the secondary, respectively.
II) Sin embargo, si hay circulación de corriente por el conductor neutro (Tn + 0), dicha circulación perturba el funcionamiento del transformador 4WD. Tal y como se observa en la figura 4, cada mitad de la fase partida del secundario es recorrida por una corriente de diferente valo
, tal que:
[5]. II) However, if there is current circulation through the neutral conductor (T n + 0), said circulation disturbs the operation of the 4WD transformer. As seen in Figure 4, each half of the split phase of the secondary is traveled by a current of different value. , such that: [5].
En estas condiciones, se producen las siguientes circunstancias: Under these conditions, the following circumstances occur:
- La suma vectorial de las fuerzas magnetomotrices del primario y del secundario en cada columna del núcleo del transformador difiere sensiblemente de cero, dado que las corrientes en las bobinas del secundario no contrarrestan los efectos magnéticos de las corrientes de las bobinas del primario. Más específicamente, las corrientes circulantes por las bobinas del secundario no están directamente relacionadas con las
corrientes de las bobinas del primario
puesto que no satisfacen las ecuaciones del circuito magnético, expresadas por [3], - The vector sum of the magnetomotive forces of the primary and secondary in each column of the transformer core differs significantly from zero, since the currents in the secondary coils do not counteract the magnetic effects of the currents in the primary coils. More specifically, the currents circulating through the secondary coils are not directly related to the primary coil currents since they do not satisfy the equations of the magnetic circuit, expressed by [3],
- Asimismo, las pérdidas debidas a la carga calculadas a partir de las corrientes del primario son diferentes de las pérdidas debidas a la carga utilizando las corrientes reales del secundario. Más específicamente, las pérdidas en el cobre calculadas desde el primario,
tienen un valor diferente que las calculadas desde el secundario,
- Also, load losses calculated from primary currents are different from load losses using actual secondary currents. More specifically, the copper losses calculated from the primary, have a different value than those calculated from the secondary,
Estas últimas pérdidas son, en general, mayores que las calculadas con las corrientes del primario. These latter losses are, in general, greater than those calculated with the primary currents.
- Además, las corrientes circulantes por las bobinas del secundario no
satisfacen el teorema de Fortescue, ya que las componentes de secuencias positiva y negativa de este sistema de corrientes ) no están relacionadas con las
componentes de secuencias positiva (directa) y negativa (inversa) de las corrientes de línea del secundari es decir,
- Furthermore, the currents circulating through the secondary coils do not satisfy Fortescue's theorem, since the positive and negative sequence components of this current system are not related to the positive (direct) and negative (reverse) sequence components of the secondary line currents i.e.
[8].
Este último resultado conduciría a la Incongruencia de que la potencia activa y la potencia reactiva medidas en bornes del secundario del transformador tendrían valores diferentes, dependiendo de que las medidas se realizaran internamente, en las bobinas, o externamente, en las líneas del secundario del transformador. [8]. This last result would lead to the inconsistency that the active power and reactive power measured at the secondary terminals of the transformer would have different values, depending on whether the measurements were made internally, in the coils, or externally, in the secondary lines of the transformer. .
De todo lo anterior, se deduce que, aunque son corrientes reales medidas en
las bobinas del secundario, no sirven para explicar correctamente el funcionamiento de los transformadores 4WD cuando hay circulación de corriente por el conductor neutro, ni tampoco pueden ser utilizadas esas corrientes para medir correctamente determinadas magnitudes del transformador 4WD como, por ejemplo, la potencia aparente. From all of the above, it follows that, although they are real currents measured in The secondary coils do not serve to correctly explain the operation of the 4WD transformers when there is current circulation through the neutral conductor, nor can these currents be used to correctly measure certain magnitudes of the 4WD transformer, such as, for example, the apparent power.
Para solucionar este problema, según un primer aspecto, la presente invención da a conocer unas corrientes para el análisis de transformadores 4WD denominadas “corrientes efectivas” Tal y como se establece en la presente invención, las corrientes
efectivas son aquellas corrientes que circulan por las bobinas del secundario de un transformador D-D equivalente al transformador 4WD objeto de análisis. To solve this problem, according to a first aspect, the present invention discloses currents for the analysis of 4WD transformers called "effective currents." As established in the present invention, the currents Effective are those currents that circulate through the secondary coils of a DD transformer equivalent to the 4WD transformer under analysis.
Según es conocido en la técnica, un transformador D-D es un transformador triángulo - triángulo sin conductor neutro. En el presente documento, por “transformador D-D equivalente al transformador 4WD objeto de análisis” ha de entenderse aquel transformador D-D (tal y como se muestra en la figura 5b) que da lugar a la circulación de las mismas corrientes en las bobinas del primario
Y en las líneas del secundario que el transformador 4WD objeto
de análisis (tal y como se muestra en la figura 5a). As is known in the art, a DD transformer is a delta-delta transformer without a neutral conductor. In this document, “DD transformer equivalent to the 4WD transformer under analysis” must be understood as that DD transformer (as shown in Figure 5b) that gives rise to the circulation of the same currents in the primary coils. And on the secondary lines that the 4WD transformer object analysis (as shown in Figure 5a).
El funcionamiento de un transformador 4WD puede ser explicado, en general, tanto con circulación como sin circulación de corriente por el conductor neutro, considerando que por las bobinas del secundario circulan las mencionadas corrientes efectivas tal como
se representa en la figura 6. Las corrientes que circulan por las bobinas del primario del transformador producen los mismos efectos magnéticos que las corrientes que
circulan por las bobinas del secundario del transformador 4WD, considerando que éstas últimas corrientes son las corrientes efectivas
The operation of a 4WD transformer can be explained, in general, both with and without circulation of current through the neutral conductor, considering that the aforementioned effective currents circulate through the secondary coils, as is represented in figure 6. The currents that circulate through the primary coils of the transformer produce the same magnetic effects as the currents that circulate through the secondary coils of the 4WD transformer, considering that these latter currents are the effective currents
En definitiva, la aplicación de las corrientes efectivas en las bobinas del secundario del transformador 4WD, en sustitución de las corrientes reales que circulan por dichas bobinas
da lugar a los mismos efectos magnéticos que las corrientes que circulan por las bobinas del primario del transformador
In short, the application of the effective currents in the secondary coils of the 4WD transformer, replacing the real currents that circulate through said coils gives rise to the same magnetic effects as the currents that circulate through the primary coils of the transformer
El concepto de corrientes efectivas permite analizar el funcionamiento de los transformadores 4WD en base a la teoría de los transformadores triángulo - triángulo, sin más que aplicar una transformación biunívoca [T] entre el conjunto de las corrientes efectivas del secundario del transformador D-D equivalente y el conjunto de las corrientes reales del secundario del transformador 4WD. Más específicamente, según una realización preferida, las
corrientes efectivas están relacionadas con corrientes reales del secundario del transformadorThe concept of effective currents allows the operation of 4WD transformers to be analyzed based on the theory of delta-delta transformers, simply by applying a one-to-one transformation [T] between the set of effective secondary currents of the equivalent DD transformer and the set of the real secondary currents of the 4WD transformer. More specifically, according to a preferred embodiment, the Effective currents are related to actual transformer secondary currents
4WD objeto de análisis por aplicación de una matriz de transformación biunívoca [T], según la siguiente expresión:
en la que 4WD object of analysis by application of a one-to-one transformation matrix [T], according to the following expression: in which
Tbn es la corriente real que circula por una primera mitad de la bobina ligada al neutro, en el secundario del transformador 4WD;
son las corrientes reales que circulan por las respectivas bobinas libres de neutro, en el secundario del transformador 4WD; T bn is the real current that circulates through the first half of the coil linked to the neutral, in the secondary of the 4WD transformer; are the real currents that circulate through the respective neutral-free coils, in the secondary of the 4WD transformer;
Tn es la corriente que circula por el conductor neutro del secundario del transformador 4WD; y la matriz de transformación biunívoca [T] es:
T n is the current that circulates through the neutral conductor of the secondary of the 4WD transformer; and the one-to-one transformation matrix [T] is:
A continuación, se incluye una explicación detallada que justifica la relación entre las corrientes efectivas y las corrientes reales del secundario del transformador 4WD objeto de análisis, según las expresiones [27] y [28], Las corrientes efectivas se pueden obtener a partir de las corrientes reales
considerando que estas últimas están formadas por la superposición de dos sistemas de corrientes: Below is a detailed explanation that justifies the relationship between the effective currents and the real secondary currents of the 4WD transformer under analysis, according to expressions [27] and [28]. The effective currents can be obtained from the real currents considering that the latter are formed by the superposition of two current systems:
I) El primer sistema de corrientes, mostrado en la figura 7, está formado por tres corrientes que circulan respectivamente por cada una de las bobinas del secundario del
transformador, sin circulación de corriente por el neutro. I) The first current system, shown in figure 7, is formed by three currents that circulate respectively through each of the secondary coils of the transformer, without current circulation through the neutral.
Los valores de estas corrientes son:
[9].The values of these currents are: [9].
La componente de secuencia cero (homopolar) de este sistema de corrientes es:
The zero sequence (homopolar) component of this current system is:
II) El segundo sistema de corrientes es debido a la circulación de la corriente del neutro
por sólo por la mitad a-n de la bobina de la primera fase del secundario del transformador 4WD, como muestra la figura 8. II) The second system of currents is due to the circulation of the neutral current for only half an of the coil of the first phase of the secondary of the 4WD transformer, as shown in figure 8.
En este caso, como la corriente del neutro sólo circula por la mitad de las espiras de la bobina a-b del secundario \ la fuerza magnetomotriz que produce es ; es decir, los efectos
magnéticos que origina Tn son los mismos que produciría una corriente de valor circulando por toda la bobina a-b.
En definitiva, los efectos magnéticos de la corriente del neutro Tn son equivalentes a los derivados de la circulación de las siguientes corrientes por cada una de las bobinas del secundario:
In this case, since the neutral current only circulates through half of the turns of the secondary coil ab, the magnetomotive force it produces is; that is, the effects magnetic forces caused by T n are the same as those that would produce a current of value circulating throughout the coil ab. In short, the magnetic effects of the neutral current T n are equivalent to those derived from the circulation of the following currents through each of the secondary coils:
Estas corrientes están representadas en la figura 9 y su componente de secuencia ceroThese currents are represented in figure 9 and their zero sequence component
(homopolar) es:
(homopolar) is:
Por tanto, las comentes efectivas del secundarlo del transformador 4WD, representadas en la figura 6, pueden expresarse como la suma de las corrientes correspondientes del primer y del segundo sistema de corrientes, tal y como se muestra a continuación:
Therefore, the effective currents of the secondary part of the 4WD transformer, represented in Figure 6, can be expressed as the sum of the corresponding currents of the first and second current systems, as shown below:
Estas ecuaciones [13] son ecuaciones de transformación que, expresadas en forma matricial, conforman la expresión [27], en la que [T] es la matriz de transformación biunívoca de la expresión [28], These equations [13] are transformation equations that, expressed in matrix form, make up the expression [27], in which [T] is the one-to-one transformation matrix of the expression [28],
A continuación, se incluyen varios argumentos que justifican la idoneidad de las corrientes efectivas para explicar el funcionamiento de los transformadores 4WD: Below are several arguments that justify the suitability of effective currents to explain the operation of 4WD transformers:
- Las corrientes efectivas satisfacen las ecuaciones magnéticas del transformador 4WD, puesto que las fuerzas magnetomotrices del secundario, calculadas con ellas, son aproximadamente ¡guales a las fuerzas magnetomotrices del primario:
tal como sucedía en el transformador cuando no había circulación de corriente por el conductor neutro. - The effective currents satisfy the magnetic equations of the 4WD transformer, since the secondary magnetomotive forces, calculated with them, are approximately equal to the primary magnetomotive forces: just as it happened in the transformer when there was no current circulation through the neutral conductor.
Las componentes de secuencias positiva y negativa de las corrientes efectivas
están relacionadas con las componentes de secuencias positiva y negativa de las corrientes de línea del secundario según las siguientes ecuaciones:
por lo que satisfacen el teorema de Fortescue y, más importante, verifican el Principio de Conservación de la Energía con las potencias activas y reactivas medidas en los devanados y en las líneas del secundario.
Asimismo, el teorema de Fortescue también es satisfecho por las componentes de secuencia cero (homopolar) de las corrientes efectivas,
The positive and negative sequence components of the effective currents are related to the positive and negative sequence components of the secondary line currents according to the following equations: Therefore, they satisfy Fortescue's theorem and, more importantly, verify the Principle of Conservation of Energy with the active and reactive powers measured in the windings and secondary lines. Likewise, Fortescue's theorem is also satisfied by the zero sequence (homopolar) components of the effective currents,
Esta componente de las corrientes efectivas debe ser necesariamente cero, porque el secundario del transformador es simétrico, es decir, sus fuerzas electromotrices son equilibradas y las impedancias de cada fase son ¡guales. This component of the effective currents must necessarily be zero, because the secondary of the transformer is symmetrical, that is, its electromotive forces are balanced and the impedances of each phase are equal.
Además, las pérdidas en el cobre calculadas con las corrientes efectivas,
son sensiblemente ¡guales a las obtenidas con las corrientes del primario, utilizando la ecuación [6], como es habitual en todos los transformadores triángulo - triángulo. Furthermore, the losses in the copper calculated with the effective currents, They are sensibly equal to those obtained with the primary currents, using equation [6], as is usual in all delta-delta transformers.
Vista la idoneidad de las corrientes efectivas del secundario Para
explicar el funcionamiento de los transformadores 4WD, según un segundo aspecto, la presente invención proporciona un procedimiento para el análisis de un transformador 4WD en base al concepto de las corrientes efectivas. Considering the suitability of the effective secondary currents for explain the operation of 4WD transformers, according to a second aspect, the present invention provides a procedure for the analysis of a 4WD transformer based on the concept of effective currents.
Gracias a la naturaleza particular de las corrientes efectivas explicadas anteriormente, es posible su aplicación en la obtención de una o vahas magnitudes del transformador 4WD para el análisis de dicho transformador como, por ejemplo, las componentes de secuencia positiva y negativa de las corrientes efectivas, las corrientes efectivas, la potencia aparente del transformador, el impacto de cargas en estrella sobre el transformador, el impacto de cargas en triángulo sobre el transformador, las corrientes en las bobinas del primario, las corrientes reales en las bobinas del secundario, según las particularidades incluidas en los siguientes apartados a)-g). a) A continuación, se incluyen varias particularidades con respecto a la obtención de las componentes de secuencia positiva y negativa de las corrientes efectivas
también denominadas en el presente documento componentes simétricas de las corrientes efectivas. Thanks to the particular nature of the effective currents explained above, it is possible to apply them to obtain one or several magnitudes of the 4WD transformer for the analysis of said transformer, such as, for example, the positive and negative sequence components of the effective currents, the effective currents, the apparent power of the transformer, the impact of star loads on the transformer, the impact of delta loads on the transformer, the currents in the primary coils, the real currents in the secondary coils, according to the particularities included in the following sections a)-g). a) Below are several particularities regarding obtaining the positive and negative sequence components of the effective currents also referred to herein as symmetric components of effective currents.
Según una realización preferida, las componentes de secuencia positiva y negativa de las corrientes efectivas se obtienen mediante las siguientes expresiones:
en las que son las componentes de secuencias positiva y negativa de las corrientes
de línea del secundario, también denominadas en el presente documento componentes simétricas de las corrientes de línea del secundario. According to a preferred embodiment, the positive and negative sequence components of the effective currents are obtained by the following expressions: in which are the positive and negative sequence components of the currents secondary line currents, also referred to herein as symmetrical components of secondary line currents.
Preferiblemente,
se obtienen mediante las siguientes expresiones:
en las que a es un versor de valor a =1z120°,
aJbJc son las corrientes de línea del secundario. Preferably, are obtained by the following expressions: in which a is a converter of value a =1z120°, aJbJc are the secondary line currents.
Preferiblemente, se obtienen de la siguiente manera:
Preferably, they are obtained in the following way:
- se adquieren muestras de corriente mediante un medio de adquisición, preferiblemente sensores dispuestos en las líneas del secundario del transformador; - current samples are acquired by means of an acquisition means, preferably sensors arranged in the secondary lines of the transformer;
- se realiza un procesado digital de las muestras adquiridas para obtener los valores eficaces y fases iniciales correspondientes. b) A continuación, se incluyen varias particularidades con respecto a la obtención de las corrientes efectivas
Atendiendo al concepto de corrientes efectivas, los valores de estas corrientes se pueden obtener de diferentes maneras: b1) Según una realización preferida, las corrientes efectivas se obtienen
mediante las siguientes expresiones [25]
en las que a es un versor de valor
son las componentes de secuencias positiva y negativa de las corrientes
efectivas. Preferiblement se obtienen como se ha explicado anteriormente
en el apartado a). b2) Según otra realización preferida, las corrientes efectivas se obtienen
mediante las siguientes expresiones [14]
en las que - Digital processing of the acquired samples is carried out to obtain the effective values and corresponding initial phases. b) Below are several particularities regarding obtaining the effective currents Taking into account the concept of effective currents, the values of these currents can be obtained in different ways: b1) According to a preferred embodiment, the effective currents are obtained through the following expressions [25] where a is a value version are the positive and negative sequence components of the currents effective. Preferably they are obtained as explained above. in section a). b2) According to another preferred embodiment, the effective currents are obtained through the following expressions [14] in which
Np es el número de espiras del primario del transformador 4WD, Np is the number of turns of the primary of the 4WD transformer,
Ns son el número de espiras del secundario del transformador 4WD, son las corrientes en las bobinas del primario del transformador 4WD.
N s are the number of turns of the secondary of the 4WD transformer, they are the currents in the primary coils of the 4WD transformer.
Preferiblemente, se obtienen de la siguiente manera:
Preferably, they are obtained in the following way:
- se adquieren muestras de corriente en las bobinas del primario del transformador 4WD mediante un medio de adquisición, preferiblemente sensores; - current samples are acquired in the primary coils of the 4WD transformer using an acquisition means, preferably sensors;
- se realiza un procesado digital de las muestras adquiridas para obtener los valores eficaces y fases iniciales correspondientes. b3) El valor de las corrientes efectivas puede obtenerse de otra manera a las
indicadas anteriormente. Por ejemplo, según una realización particular, el valor de las corrientes efectivas se obtiene mediante un sistema de emulación con un transformador D-- Digital processing of the acquired samples is carried out to obtain the effective values and corresponding initial phases. b3) The value of the effective currents can be obtained in another way at the indicated above. For example, according to a particular embodiment, the value of the effective currents is obtained through an emulation system with a D-transformer.
D como el equivalente al transformador 4WD objeto de análisis, de la siguiente manera: En el transformador D-D del sistema de emulación se reproducen las mismas corrientes en las bobinas del primario
y en las líneas del secundario que e>
transformador 4WD objeto de análisis, y se miden las corrientes que circulan por las bobinas del secundario de dicho transformador D-D, que son las corrientes efectivas
D as the equivalent of the 4WD transformer under analysis, as follows: In the DD transformer of the emulation system, the same currents are reproduced in the primary coils and in the secondary lines that e > 4WD transformer under analysis, and the currents that circulate through the secondary coils of said DD transformer are measured, which are the effective currents
Preferiblemente, se obtienen de la siguiente manera:
Preferably, they are obtained in the following way:
- se adquieren muestras de corriente en las bobinas del primario y en las líneas del secundario del transformador 4WD mediante un medio de adquisición, preferiblemente sensores; se realiza un procesado digital de las muestras adquiridas para obtener los valores eficaces y fases iniciales correspondientes. c) A continuación, se incluyen vahas particularidades con respecto a la obtención del valor de la potencia aparente (S) del transformador 4WD. - current samples are acquired in the primary coils and in the secondary lines of the 4WD transformer using an acquisition means, preferably sensors; Digital processing of the acquired samples is carried out to obtain the effective values and corresponding initial phases. c) Below are several particularities regarding obtaining the value of the apparent power (S) of the 4WD transformer.
La potencia aparente (S) de este tipo de transformadores puede expresarse utilizando la proporcionalidad entre potencias aparentes y pérdidas en el cobre, de la siguiente manera:
en la que
son los valores eficaces de las tensiones de línea del secundario del transformador 4WD
son los valores eficaces de las corrientes efectivas (
The apparent power (S) of this type of transformers can be expressed using the proportionality between apparent powers and copper losses, as follows: in which are the effective values of the secondary line voltages of the 4WD transformer are the effective values of the effective currents (
Partiendo de la expresión [18], si se aplica el teorema de Fortescue a las corrientes efectivas, la potencia aparente (S) de transformadores 4WD también puede expresarse en función de las componentes simétricas de las corrientes efectivas, de la siguiente manera:
en la que son los valores eficaces de las tensiones de línea del secundario del
transformador 4WD (
son l°s valores eficaces de las componentes de secuencias positiva y negativa
de las corrientes efectivas
Partiendo de la expresión [19], y teniendo en cuenta las relaciones entre las componentes de secuencias positiva y negativa de las corrientes efectivas Y las
componentes de secuencias positiva y negativa de las corrientes de línea del secundario
ndicadas por las expresiones [15], otra posible expresión de la potencia aparente (S) de transformadores 4WD es la siguiente:
en la que son los valores eficaces de las tensiones de línea del secundario del
transformador 4WD
son l°s valores eficaces de las componentes de secuencias positiva y negativa (
a ) de las corrientes de línea del secundario
Starting from the expression [18], if the Fortescue theorem is applied to the effective currents, the apparent power (S) of 4WD transformers can also be expressed in terms of the symmetric components of the effective currents, as follows: in which are the effective values of the secondary line voltages of the 4WD transformer ( s on l° s effective values of the positive and negative sequence components of the effective currents Starting from the expression [19], and taking into account the relationships between the positive and negative sequence components of the effective currents and the positive and negative sequence components of secondary line currents indicated by the expressions [15], another possible expression of the apparent power (S) of 4WD transformers is the following: in which are the effective values of the secondary line voltages of the 4WD transformer are the effective values of the positive and negative sequence components ( a) of the secondary line currents
En definitiva, atendiendo al concepto de corrientes efectivas, la potencia aparente (S) del transformador 4WD objeto de análisis puede obtenerse mediante cualquiera de las ecuaciones [18], [19] y [20], Cabe señalar lo siguiente: In short, taking into account the concept of effective currents, the apparent power (S) of the 4WD transformer under analysis can be obtained using any of the equations [18], [19] and [20]. The following should be noted:
- La ecuación [18] integra explícitamente las corrientes efectivas
- Equation [18] explicitly integrates the effective currents
- La ecuación [19] integra explícitamente las componentes simétricas de las corrientes efectivas; y deriva de la ecuación [18], por lo que integra implícitamente el concepto de las corrientes efectivas. - Equation [19] explicitly integrates the symmetric components of the effective currents; and is derived from equation [18], so it implicitly integrates the concept of effective currents.
La ecuación [20] no integra explícitamente las corrientes efectivas en la expresión. No obstante, esta expresión es el resultado de varios desarrollos a partir del concepto de las “corrientes efectivas”. Concretamente, la ecuación [20] deriva de la ecuación [19] que, a su vez, deriva de la ecuación [18], por lo que el concepto de las corrientes efectivas queda integrado implícitamente en la ecuación [20], Equation [20] does not explicitly integrate effective currents into the expression. However, this expression is the result of several developments from the concept of “effective currents”. Specifically, equation [20] is derived from equation [19] which, in turn, is derived from equation [18], so the concept of effective currents is implicitly integrated into equation [20],
En base a lo expuesto, a continuación se exponen varias realizaciones para la obtención de la potencia aparente del transformador 4WD: c1) Según una realización preferida, la potencia aparente (S) del transformador 4WD se obtiene mediante la ecuación [18],
Based on the above, several embodiments are presented below to obtain the apparent power of the 4WD transformer: c1) According to a preferred embodiment, the apparent power (S) of the 4WD transformer is obtained by means of equation [18],
Preferiblemente se obtienen como se ha explicado anteriormente en el
apartado b) (según una cualquiera de las opciones b1), b2) o b3)). Preferably they are obtained as explained above in the section b) (according to any of options b1), b2) or b3)).
Preferiblement se obtiene adquiriendo muestras de tensión mediante un medio
de adquisición, preferiblemente sensores dispuestos en las líneas del secundario del transformador 4WD; y realizando un procesado digital de las muestras adquiridas para obtener los valores eficaces y fases iniciales correspondientes. c2) Según otra realización preferida, la potencia aparente (S) del transformador 4WD se obtiene mediante la ecuación [19]:
Preferably it is obtained by acquiring tension samples through a means acquisition, preferably sensors arranged on the secondary lines of the 4WD transformer; and carrying out digital processing of the acquired samples to obtain the effective values and corresponding initial phases. c2) According to another preferred embodiment, the apparent power (S) of the 4WD transformer is obtained by equation [19]:
Preferiblemente
se obtienen como ha explicado anteriormente en el apartado a). Preferiblemente se obtienen como se ha explicado en el apartado anterior
c1). c3) Según otra realización preferida, la potencia aparente (S) del transformador 4WD se obtiene mediante la ecuación [20]:
Preferably are obtained as explained previously in section a). Preferably they are obtained as explained in the previous section. c1). c3) According to another preferred embodiment, the apparent power (S) of the 4WD transformer is obtained by equation [20]:
Preferiblemente, Ia+ y Ia_ se obtienen mediante las expresiones [21]:
Preferably, I a+ and I a _ are obtained by the expressions [21]:
Preferiblemente, la, lb y Ic se obtienen como se ha explicado anteriormente en el apartado a). Preferiblemente Vab, Vbc y Vca se obtienen como se ha explicado en el apartado anterior c1). Preferably, l a , l b and I c are obtained as explained above in section a). Preferably V ab , V bc and V ca are obtained as explained in the previous section c1).
En base a lo expuesto, las tensiones y comentes que Intervienen en la opción c1) con
según b1), en la opción c2) y en la opción c3) provienen de señales en las líneas del secundario del transformador 4WD
En este caso, para obtener la potencia aparente (S) del transformador 4WD, preferiblemente, se adquieren las tensiones y corrientes de línea del secundario del transformador 4WD
previamente, de la siguiente manera: Se adquieren muestras de tensión y corriente mediante un medio de adquisición, preferiblemente sensores dispuestos en las líneas del secundario del transformador 4WD; y se realiza un procesado digital de las muestras adquiridas para obtener los valores eficaces y fases iniciales correspondientes. En este caso, cualquiera de las ecuaciones [19], [20], o [21] son especialmente útiles en la práctica industrial, pues permiten determinar la potencia aparente de los transformadores 4WD a partir de la medición de las tensiones y corrientes de línea del secundario del transformador 4WD
únicamente, sin necesidad de conocer el valor de la corriente del neutro y, sobre todo, evitando la colocación de sensores internos para la medida de las corrientes en los devanados del
secundario. d) A continuación, se incluyen vahas particularidades con respecto a la obtención del impacto de cargas en triángulo (SA) sobre el transformador 4WD. Based on the above, the tensions and currents involved in option c1) with according to b1), in option c2) and in option c3) they come from signals on the secondary lines of the 4WD transformer In this case, to obtain the apparent power (S) of the 4WD transformer, preferably, the line voltages and currents of the secondary of the 4WD transformer are acquired. previously, as follows: Voltage and current samples are acquired using an acquisition means, preferably sensors arranged on the secondary lines of the 4WD transformer; and digital processing of the acquired samples is carried out to obtain the effective values and corresponding initial phases. In this case, any of the equations [19], [20], or [21] are especially useful in industrial practice, since they allow the apparent power of 4WD transformers to be determined from the measurement of line voltages and currents. 4WD transformer secondary only, without needing to know the value of the neutral current and, above all, avoiding the placement of internal sensors to measure currents in the windings of the neutral. secondary. d) Below are several particularities regarding obtaining the impact of delta loads (S A ) on the 4WD transformer.
Dado que las cargas en triángulo no dan lugar a la circulación de corrientes por el conductor neutro, el impacto de esas cargas sobre el transformador 4WD puede obtenerse en base a razonamientos análogos a los que han dado lugar a la ecuación [20], De este modo, el impacto de las cargas en triángulo (SA) sobre el transformador 4WD puede expresarse por analogía a la ecuación [20], sin más que sustituir en dicha ecuación [20] los valores eficaces de las componentes de secuencias positiva y negativa de las corrientes de línea
del secundario por los valores eficaces de las componentes de secuencias
positiva y negativa de las corrientes de línea absorbidas por las cargas en triángulo (también denominadas en el presente documento componentes simétricas de las corrientes de línea absorbidas por las cargas en triángulo), dando lugar a la ecuación [22], En base a lo expuesto, según una realización preferida, el cálculo del impacto de cargas en triángulo (SA) sobre el transformador 4WD se realiza mediante la ecuación [22]:
en la que
son los valores eficaces de las tensiones de línea del secundario del transformador
son los valores eficaces de las componentes de secuencias positiva y negativa
de las corrientes de línea absorbidas por las cargas en triángulo
Since the delta loads do not give rise to the circulation of currents through the neutral conductor, the impact of these loads on the 4WD transformer can be obtained based on reasoning analogous to those that have given rise to equation [20]. Thus, the impact of delta loads (S A ) on the 4WD transformer can be expressed by analogy to equation [20], simply by substituting in said equation [20] the effective values of the positive and negative sequence components of line currents of the secondary by the effective values of the sequence components positive and negative of the line currents absorbed by the delta loads (also called in this document symmetric components of the line currents absorbed by the delta loads), giving rise to equation [22], Based on the above According to a preferred embodiment, the calculation of the impact of delta loads ( SA ) on the 4WD transformer is carried out using equation [22]: in which are the effective values of the transformer secondary line voltages are the effective values of the positive and negative sequence components of line currents absorbed by delta loads
Preferiblemente se obtienen mediante las siguientes expresiones:
en las que son las corrientes de línea absorbidas por las cargas en triángulo,
a es un versor de valor
Preferably they are obtained using the following expressions: in which are the line currents absorbed by the delta loads, a is a value versifier
Cabe señalar que, al igual que sucede entre las expresiones [20] y [22], también existe analogía entre las expresiones [21] y [23], Concretamente, las componentes de secuencias positiva y negativa de las corrientes de línea absorbidas por las cargas en
triángulo se expresan por analogía a la expresión [21], sin más que sustituir en dicha expresión [21] las corrientes de línea del secundario
por las corrientes de línea absorbidas por las cargas en triángulo dando lugar a la expresión [23],
Preferiblemente, las tensiones de línea del secundario del transformador 4WD y las corrientes de línea absorbidas por las cargas en triángulo se obtienen de
la siguiente manera: se adquieren muestras de tensión y corriente mediante un medio de adquisición, preferiblemente sensores dispuestos en las líneas del secundario del transformador y en las líneas de las cargas en triángulo; se realiza un procesado digital de las muestras adquiridas para obtener los valores eficaces y fases iniciales correspondientes. e) A continuación, se incluyen vahas particularidades con respecto a la obtención del impacto de cargas en estrella (Sr) sobre el transformador 4WD. It should be noted that, as occurs between expressions [20] and [22], there is also an analogy between expressions [21] and [23], Specifically, the positive and negative sequence components of the line currents absorbed by the loads on triangle are expressed by analogy to expression [21], simply substituting in said expression [21] the line currents of the secondary by the line currents absorbed by the delta loads giving rise to the expression [23], Preferably, the secondary line voltages of the 4WD transformer and the line currents absorbed by the delta loads are obtained from as follows: voltage and current samples are acquired by means of an acquisition means, preferably sensors arranged on the secondary lines of the transformer and on the lines of the delta loads; Digital processing of the acquired samples is carried out to obtain the effective values and corresponding initial phases. e) Below are several particularities regarding obtaining the impact of star loads (S r ) on the 4WD transformer.
Según una realización preferida, el impacto exclusivo de las cargas en estrella (Sr) sobre el transformador 4WD se obtiene mediante la siguiente ecuación:
en la que According to a preferred embodiment, the exclusive impact of the star loads ( Sr ) on the 4WD transformer is obtained by the following equation: in which
S es la potencia aparente del transformador 4WD, S is the apparent power of the 4WD transformer,
S& es el impacto de cargas en triángulo. S & is the impact of triangle loads.
Preferiblemente, S se obtiene conforme a cualquiera de las opciones c1), c2) o c3), tal y como se ha explicado anteriormente en el apartado c). Preferiblemente, SΔ se obtiene como se ha explicado anteriormente en el apartado d). f) A continuación, se incluyen varias particularidades con respecto a la obtención de las corrientes reales en las bobinas del secundario del transformador 4WD
Preferably, S is obtained according to any of options c1), c2) or c3), as explained above in section c). Preferably, S Δ is obtained as explained above in section d). f) Below are several particularities regarding obtaining the real currents in the secondary coils of the 4WD transformer
Según una realización preferida, las corrientes reales en las bobinas del secundario del transformador se obtienen mediante las siguientes expresiones:
en las que According to a preferred embodiment, the real currents in the secondary coils of the transformer are obtained by the following expressions: in which
Tbn es la corriente real que circula por una primera mitad de la bobina ligada al neutro, en el secundario del transformador 4WD; T bn is the real current that circulates through the first half of the coil linked to the neutral, in the secondary of the 4WD transformer;
Tan es la corriente real que circula por una segunda mitad de la bobina ligada al neutro, en el secundario del transformador 4WD;
son las corrientes reales que circulan por las respectivas bobinas libres de neutro, en el secundario del transformador 4WD; Tan is the real current that circulates through a second half of the coil linked to the neutral, in the secondary of the 4WD transformer; They are the real currents that circulate through the respective neutral-free coils, in the secondary of the 4WD transformer;
Tn es la corriente que circula por el conductor neutro del secundario del transformador 4WD;
son las corrientes efectivas. T n is the current that circulates through the neutral conductor of the secondary of the 4WD transformer; are the effective currents.
Preferiblemente, T se obtienen como se ha explicado anteriormente en
referencia a cualquiera de las opciones b1), b2) o b3); y Tn se obtiene adquiriendo una
muestra de corriente mediante un medio de adquisición, preferiblemente un sensor dispuesto en el neutro del secundario del transformador, y realizando un procesado digital de la muestra adquirida para obtener el valor eficaz y fase inicial correspondiente. g) A continuación, se incluyen varias particularidades con respecto a la obtención de las corrientes en las bobinas del primario del transformador
Preferably, T are obtained as explained above in reference to any of options b1), b2) or b3); and T n is obtained by acquiring a current sample using an acquisition means, preferably a sensor arranged in the neutral of the secondary of the transformer, and performing digital processing of the acquired sample to obtain the effective value and corresponding initial phase. g) Below are several particularities with respect to obtaining the currents in the primary coils of the transformer
Según una realización preferida, las corrientes en las bobinas del primario del transformador 4WD UABJBCJCA) se obtienen mediante las siguientes expresiones:
en las que p es el número de espiras del primario del transformador 4WD, son el número de espiras del secundario del transformador 4WD,
son las corrientes efectivas. According to a preferred embodiment, the currents in the primary coils of the transformer 4WD UABJBCJCA) are obtained by the following expressions: in which p is the number of turns of the primary of the 4WD transformer, are the number of turns of the secondary of the 4WD transformer, They are the effective currents.
Preferiblemente, T se obtienen como se ha explicado anteriormente en
referencia a una cualquiera de las opciones b1) o b3). Preferably, T are obtained as explained above in reference to any one of options b1) or b3).
A título sólo de ejemplificar las ventajas de la presente invención frente a otras tecnologías, a continuación se incluye una tabla comparativa que muestra de manera resumida los valores de las potencias aparentes medidas desde el primario y el secundario, así como los valores de las potencias activas y reactivas del secundario, utilizando la tecnología de la presente invención (con cualquiera de las ecuaciones [18], [19] o [20]), y utilizando las tecnologías correspondientes a las ecuaciones [1] y [2], El transformador 4WD utilizado en este ejemplo comparativo tiene una potencia nominal de 300 kVA, relación de transformación 12470 / 240V, tensión relativa de cortocircuito 4,5%, corriente de vacío 2,3%, pérdidas en carga nominales 3600 W y pérdidas en vacío 800 W. El transformador 4WD alimenta a cargas en estrella de impedancias
y cargas equilibradas en triángulo de impedancias íl, tal como se observa en la figura 2. Las cargas
pueden funcionar conjuntamente o por separado.
Just to exemplify the advantages of the present invention over other technologies, a comparative table is included below that briefly shows the values of the apparent powers measured from the primary and secondary, as well as the values of the active powers. and reactive of the secondary, using the technology of the present invention (with any of the equations [18], [19] or [20]), and using the technologies corresponding to equations [1] and [2], The 4WD transformer used in this comparative example has a nominal power of 300 kVA, transformation ratio 12470 / 240V, relative short circuit voltage 4.5%, no-load current 2.3%, nominal load losses 3600 W and no-load losses 800 W. The 4WD transformer supplies impedance star loads and balanced loads in an impedance triangle íl, as seen in figure 2. The loads They can work together or separately.
A la vista de la tabla, se deduce lo siguiente: Looking at the table, the following is deduced:
El modelo de funcionamiento de los transformadores 4WD basado en tecnologías cuyas potencias aparentes se calculan según [1] y [2] funciona correctamente cuando sólo hay cargas en triángulo. En estas condiciones, las potencias aparentes, activas y reactivas según el modelo de la presente invención y el de las tecnologías [1] y [2] tienen los mismos valores (ver quinta columna “Sólo cargas en triángulo" de la tabla). The operating model of 4WD transformers based on technologies whose apparent powers are calculated according to [1] and [2] works correctly when there are only delta loads. Under these conditions, the apparent, active and reactive powers according to the model of the present invention and that of technologies [1] and [2] have the same values (see fifth column “Only triangle loads” of the table).
Sin embargo, cuando hay circulación de corriente por el neutro, las potencias aparentes calculadas en el secundario, según los modelos de funcionamiento basados en [1] y [2], son mayores que en el primario; y las potencias activas y reactivas en el secundario son diferentes que las potencias activas y reactivas en las líneas (ver columna 3 “Todas las cargas, conjuntamente" y columna 4 “Sólo cargas en estrella” de la tabla). Estos resultados son incorrectos y tanto más erróneos cuando sólo hay cargas en estrella. En la práctica, la potencia aparente del primario debe ser ligeramente mayor, por efecto de las corrientes de vacío, que la potencia aparente determinada en el secundario; mientras que las potencias activas y reactivas en el secundario deben ser ¡guales a las potencias activas y reactivas en las líneas, para que se cumpla el Principio de Conservación de la Energía. El modelo de
funcionamiento de los transformadores 4WD descrito en la presente invención satisface estas últimas condiciones para todo tipo de cargas, tal y como se observa en la tabla. However, when there is current circulation through the neutral, the apparent powers calculated in the secondary, according to the operating models based on [1] and [2], are greater than in the primary; and the active and reactive powers in the secondary are different than the active and reactive powers in the lines (see column 3 "All loads together" and column 4 "Only star loads" of the table). These results are incorrect and all the more erroneous when there are only star loads. In practice, the apparent power of the primary must be slightly greater, due to the effect of the vacuum currents, than the apparent power determined in the secondary; while the active and reactive powers in the secondary power must be equal to the active and reactive powers in the lines, so that the Principle of Conservation of Energy is fulfilled. The operation of the 4WD transformers described in the present invention satisfies these latter conditions for all types of loads, as seen in the table.
A continuación, con apoyo de la figura 10, se explica la secuencia operacional de un ejemplo aplicativo según una realización preferida de la presente invención. Esta realización se centra en la medida de una o vahas de las siguientes magnitudes del transformador 4WD objeto de análisis: potencia aparente debida a todas las cargas (denominada en la figura: potencia aparente del transformador), impacto exclusivo de cargas en triángulo, impacto exclusivo de cargas en estrella, corrientes reales en las bobinas del secundario. El procedimiento mostrado en la figura 10 comprende las siguientes acciones: Next, with the support of Figure 10, the operational sequence of an application example according to a preferred embodiment of the present invention is explained. This embodiment focuses on the measurement of one or several of the following magnitudes of the 4WD transformer under analysis: apparent power due to all loads (denoted in the figure: apparent power of the transformer), exclusive impact of delta loads, exclusive impact of star loads, real currents in the secondary coils. The procedure shown in Figure 10 includes the following actions:
I) Adquisición de señales eléctricas (1 en la figura 10): I) Acquisition of electrical signals (1 in figure 10):
Se adquieren señales eléctricas del transformador 4WD objeto de análisis, y se almacenan dichas señales, preferiblemente según las siguientes particularidades: si se desea obtener la potencia aparente debida a todas las cargas (S), las señales eléctricas que se adquieren en la presente acción (en 1 de la figura 10) son, al menos, muestras de tensiones y muestras de corrientes de línea del secundario del
transformador; si se desea obtener los impactos exclusivos de cargas en triangulo (SA) sobre el transformador 4WD, se adquieren, al menos, muestras de tensiones de línea del secundario y muestras de corrientes de línea absorbidas por las cargas en triángulo
si se desea obtener los impactos exclusivos de cargas en estrella (Sr) sobre el transformador, se adquieren, al menos, muestras de tensiones del secundario del transformador muestras de corrientes de línea del secundario del
transformador y muestras de corrientes de línea absorbidas por las cargas en
triángulo
si se desea obtener las corrientes reales en las bobinas del secundario del transformadorElectrical signals are acquired from the 4WD transformer under analysis, and said signals are stored, preferably according to the following particularities: if it is desired to obtain the apparent power due to all the loads (S), the electrical signals that are acquired in the present action ( in 1 of Figure 10) are, at least, voltage samples and line current samples of the secondary of the transformer; If it is desired to obtain the exclusive impacts of delta loads (S A ) on the 4WD transformer, at least samples of secondary line voltages and samples of line currents absorbed by the delta loads are acquired. If it is desired to obtain the exclusive impacts of star loads (S r ) on the transformer, at least samples of voltages from the secondary of the transformer, samples of line currents from the secondary of the transformer, are acquired. transformer and samples of line currents absorbed by the loads in triangle if you want to obtain the real currents in the secondary coils of the transformer
4WD se adquieren, al menos, muestras de corrientes de línea del
secundario del transformador \ y de la corriente que circula por el conductor neutro
del secundario (/n) del transformador. 4WD, at least samples of line currents are acquired from the secondary of the transformer \ and the current that circulates through the neutral conductor of the secondary (/ n ) of the transformer.
Cabe señalar que se puede proceder de dos maneras: adquirir y almacenar todas las señales eléctricas indicadas en este apartado para
posteriormente utilizar únicamente las necesarias dependiendo de la magnitud o magnitudes que se deseen obtener; o según una opción alternativa, adquirir exclusivamente las señales que se necesiten.
II) Análisis de señales (2 en la figura 10): It should be noted that you can proceed in two ways: acquire and store all the electrical signals indicated in this section to subsequently use only the necessary ones depending on the magnitude or magnitudes you wish to obtain; or according to an alternative option, acquire only the signals that are needed. II) Signal analysis (2 in figure 10):
Tras adquirir las señales eléctricas (en 1 de la figura 10), se obtienen (en 2 de la figura 10) las matrices de valores eficaces y fases iniciales correspondientes. Opcionalmente, en el caso de que una señal eléctrica adquirida tenga armónicos, se obtienen las componentes armónicas, preferiblemente, por Señes de Fourier. After acquiring the electrical signals (in 1 of Figure 10), the matrices of effective values and corresponding initial phases are obtained (in 2 of Figure 10). Optionally, in the event that an acquired electrical signal has harmonics, the harmonic components are obtained, preferably, by Fourier Signs.
III) Simétricas de las corrientes de línea (3 en la figura 10): III) Symmetric line currents (3 in figure 10):
A partir de las matrices obtenidas en la acción anterior (2 en la figura 10), se obtienen (en 3 de la figura 10) los valores eficaces y las fases iniciales de las componentes de secuencias positiva (directa) y negativa (inversa) de las corrientes de línea del secundario del transformador 4WD y/o de las corrientes de línea absorbidas por las cargas en
triángulo según las expresiones [21], y [23], respectivamente, dependiendo de
la magnitud o magnitudes que se desean obtener. From the matrices obtained in the previous action (2 in figure 10), the effective values and the initial phases of the positive (direct) and negative (inverse) sequence components of the secondary line currents of the 4WD transformer and/or the line currents absorbed by the loads in triangle according to the expressions [21], and [23], respectively, depending on the magnitude or magnitudes that you want to obtain.
Concretamente, si se desea obtener la potencia aparente (S) y/o las corrientes reales en las bobinas del secundario del trasformador 4WD, en la presente acción (3 en
la figura 10) se obtienen, al menos, los valores eficaces y las fases iniciales de las componentes de secuencias positiva (directa) y negativa (inversa) de las corrientes de línea del secundario
según la expresión [21]
si se desea obtener el impacto de cargas en triángulo (SA) sobre el transformador 4WD, en la presente acción (3 en la figura 10) se obtienen, al menos, los valores eficaces y las fases iniciales de las componentes de secuencias positiva (directa) y negativa (inversa) de las corrientes de línea absorbidas por las cargas en triángulo según la expresión
[23]
si se desea obtener el impacto de cargas en estrella (Sr) sobre el transformador 4WD, en la presente la presente acción (3 en la figura 10) se obtienen los valores eficaces y las fases iniciales de las componentes de secuencias positiva (directa) y negativa (inversa) de las corrientes de línea del secundario según la expresión [21], así como los valores
eficaces y las fases iniciales de las componentes de secuencias positiva (directa) y negativa (inversa) de las corrientes de línea absorbidas por las cargas en triángulo según
la expresión [23], Specifically, if you want to obtain the apparent power (S) and/or the real currents in the secondary coils of the 4WD transformer, in the present action (3 in Figure 10), at least the effective values and initial phases of the positive (direct) and negative (reverse) sequence components of the secondary line currents are obtained. according to the expression [21] If it is desired to obtain the impact of delta loads (S A ) on the 4WD transformer, in the present action (3 in Figure 10) at least the effective values and the initial phases of the positive sequence components are obtained ( direct) and negative (inverse) of the line currents absorbed by the delta loads according to the expression [23] If it is desired to obtain the impact of star loads (S r ) on the 4WD transformer, in the present action (3 in Figure 10) the effective values and the initial phases of the positive (direct) sequence components are obtained. and negative (inverse) of the secondary line currents according to expression [21], as well as the values effective and the initial phases of the positive (forward) and negative (reverse) sequence components of the line currents absorbed by the delta loads according to the expression [23],
Cabe señalar que se puede proceder de dos maneras: obtener los valores eficaces y las fases iniciales tanto de las componente como de las componentes para
posteriormente utilizar únicamente lo que se necesite dependiendo de la magnitud o magnitudes que se deseen obtener; o según una opción alternativa, obtener exclusivamente
los valores eficaces y las fases Iniciales de las componentes que se necesiten. It should be noted that you can proceed in two ways: obtain the effective values and the initial phases of both the components and the components to subsequently use only what is needed depending on the magnitude or magnitudes you wish to obtain; or according to an alternative option, obtain exclusively the effective values and the initial phases of the components that are needed.
Opcionalmente, en el caso de que una señal eléctrica adquirida tenga armónicos, se procede con las acciones de este apartado III (3 en la figura 10) para cada una de las frecuencias de las componentes armónicas, obtenidas en el análisis de señales del apartado II (2 en la figura 10). Optionally, in the event that an acquired electrical signal has harmonics, the actions of this section III (3 in figure 10) are carried out for each of the frequencies of the harmonic components, obtained in the signal analysis of section II. (2 in figure 10).
Según la realización preferida mostrada en la figura 10, la adquisición de señales eléctricas (1 en la figura 10), el análisis de señales (2 en la figura 10) y la obtención de las simétricas de las corrientes de línea (3 en la figura 10) son acciones comunes a la obtención de cualquiera de las magnitudes mencionadas (es decir, a la obtención de la potencia aparente debida a todas las cargas, el impacto exclusivo de cargas en triángulo, el impacto exclusivo de cargas en estrella, y las corrientes reales en las bobinas del secundario). El resto de las acciones (acciones 4-10 en la figura 10) se llevan a cabo según se expone a continuación. According to the preferred embodiment shown in Figure 10, the acquisition of electrical signals (1 in Figure 10), the analysis of signals (2 in Figure 10) and the obtaining of the symmetry of the line currents (3 in Figure 10) are actions common to obtaining any of the mentioned magnitudes (that is, to obtaining the apparent power due to all the loads, the exclusive impact of delta loads, the exclusive impact of star loads, and the currents real in the secondary coils). The rest of the actions (actions 4-10 in Figure 10) are carried out as follows.
IV) Cálculo de la potencia aparente del transformador (4 en la figura 10). La potencia aparente (S) del transformador 4WD objeto de análisis puede obtenerse de las siguientes maneras: IV. a) Cálculo de la potencia aparente (S) según la expresión [20]: IV) Calculation of the apparent power of the transformer (4 in figure 10). The apparent power (S) of the 4WD transformer under analysis can be obtained in the following ways: IV. a) Calculation of the apparent power (S) according to expression [20]:
A partir de los valores eficaces de las tensiones de línea del secundario (obtenidos en 2 según la figura 10) y de las componentes de secuencias positiva y negativa de las corrientes de línea del secundario (determinadas en 3 según la figura 10, mediante las expresiones [21]), se obtiene la potencia aparente del transformador 4WD (en 4 según la figura 10) mediante la expresión [20],
From the effective values of the secondary line voltages (obtained at 2 according to Figure 10) and the positive and negative sequence components of the secondary line currents (determined at 3 according to Figure 10, using the expressions [21]), the apparent power of the 4WD transformer (in 4 according to figure 10) is obtained by expression [20],
De este modo, tal y como se muestra en la figura 10, el cálculo de la potencia aparente del transformador 4WD según la expresión [20] sigue la secuencia operational 1-2-3- 4. In this way, as shown in Figure 10, the calculation of the apparent power of the 4WD transformer according to expression [20] follows the operational sequence 1-2-3-4.
IV. b) Cálculo de la potencia aparente (S) según la expresión [19]: IV. b) Calculation of the apparent power (S) according to the expression [19]:
A partir de las componentes de secuencias positiva y negativa de las corrientes de línea del secundario, determinadas (en 3 según la figura 10) mediante las expresiones [21], se obtienen (en 5 según la figura 10) las componentes de secuencias positiva y negativa de las corrientes efectivas de las bobinas del secundario, mediante las expresiones [15] 30° [15].
From the positive and negative sequence components of the secondary line currents, determined (at 3 according to Figure 10) by the expressions [21], the positive and negative sequence components are obtained (at 5 according to Figure 10). negative of the effective currents of the secondary coils, using the expressions [15] 30° [15].
A partir de los valores eficaces de las tensiones de línea del secundario (obtenidos en 2 según la figura 10) y de las componentes de secuencias positiva y negativa de las
comentes efectivas del secundario (obtenidos en 5 según la figura 10), se obtiene la potencia aparente del transformador 4WD (en 4 según la figura 10) mediante la expresión [19],
From the effective values of the secondary line voltages (obtained in 2 according to Figure 10) and the positive and negative sequence components of the effective currents of the secondary (obtained at 5 according to figure 10), the apparent power of the 4WD transformer is obtained (at 4 according to figure 10) by means of expression [19],
De este modo, tal y como se muestra en la figura 10, el cálculo de la potencia aparente del transformador 4WD según la expresión [19] sigue la secuencia operacional 1-2-3- 5-4. Thus, as shown in Figure 10, the calculation of the apparent power of the 4WD transformer according to expression [19] follows the operational sequence 1-2-3-5-4.
IV. c) Cálculo de la potencia aparente (S) según la expresión [18]: IV. c) Calculation of the apparent power (S) according to expression [18]:
A partir de las componentes de secuencias positiva y negativa de las corrientes de línea del secundario, determinadas (en 3 según la figura 10) mediante las expresiones [21], se obtienen (en 5 según la figura 10) las componentes de secuencias positiva y negativa de las corrientes efectivas de las bobinas del secundario, mediante las expresiones [15] From the positive and negative sequence components of the secondary line currents, determined (at 3 according to Figure 10) by the expressions [21], the positive and negative sequence components are obtained (at 5 according to Figure 10). negative of the effective currents of the secondary coils, using the expressions [15]
[15].
[fifteen].
A partir de las componentes de secuencias positiva y negativa de las corrientes efectivas del secundario, se obtienen (en 6 según la figura 10) las corrientes efectivas en las bobinas del secundario mediante las expresiones [25]
From the positive and negative sequence components of the effective secondary currents, the effective currents in the secondary coils are obtained (in 6 according to Figure 10) by means of the expressions [25]
A partir de los valores eficaces de las tensiones de línea (obtenidos en 2 según la figura 10) y de las corrientes efectivas del secundario (obtenidas en 6 según la figura 10), se obtiene la potencia aparente del transformador (en 4 según la figura 10) mediante la expresión [18]
From the effective values of the line voltages (obtained in 2 according to figure 10) and the effective currents of the secondary (obtained in 6 according to figure 10), the apparent power of the transformer is obtained (in 4 according to figure 10) through the expression [18]
De este modo, tal y como se muestra en la figura 10, el cálculo de la potencia aparente del transformador 4WD según la expresión [18] sigue la secuencia operacional 1-2-3- 5-6-4. In this way, as shown in Figure 10, the calculation of the apparent power of the 4WD transformer according to expression [18] follows the operational sequence 1-2-3- 5-6-4.
V) Cálculo del impacto de cargas en triángulo (7 en la figura 10): V) Calculation of the impact of triangle loads (7 in figure 10):
A partir de los valores eficaces de las tensiones de línea (obtenidos en 2 según la figura 10) y de las componentes de secuencias positiva y negativa de las corrientes de línea absorbidas por las cargas en triángulo (determinadas en 3 según la figura 10, mediante las expresiones [23]), se obtiene (en 7 según la figura 10) el impacto de las cargas en triángulo sobre el transformador 4WD (SA), mediante la expresión [22]
From the effective values of the line voltages (obtained at 2 according to Figure 10) and the positive and negative sequence components of the line currents absorbed by the delta loads (determined at 3 according to Figure 10, by the expressions [23]), the impact of the delta loads on the 4WD transformer (S A ) is obtained (in 7 according to figure 10) by means of the expression [22]
De este modo, tal y como se muestra en la figura 10, el cálculo del impacto de cargas en triángulo sobre el transformador 4WD sigue la secuencia operational 1 -2-3-7. In this way, as shown in figure 10, the calculation of the impact of delta loads on the 4WD transformer follows the operational sequence 1 -2-3-7.
VI) Cálculo del impacto de cargas en estrella (8 en la figura 10): VI) Calculation of the impact of star loads (8 in figure 10):
A partir del valor de la potencia aparente (S) del transformador (obtenido en 4 según la figura 10, mediante una cualquiera de las expresiones [20], [18] o [19]), y del impacto de las cargas en triángulo (determinado en 7 según la figura 10, mediante la expresión [22]), se obtiene (en 8 según la figura 10) el impacto de las cargas en estrella (Sr), mediante la expresión [24]
From the value of the apparent power (S) of the transformer (obtained in 4 according to figure 10, using any of the expressions [20], [18] or [19]), and the impact of the delta loads ( determined at 7 according to figure 10, by expression [22]), the impact of the star loads (S r ) is obtained (at 8 according to figure 10), by expression [24]
De este modo, tal y como se muestra en la figura 10, el cálculo del impacto de cargas en triángulo sobre el transformador 4WD conlleva la realización de las acciones 1 , 2, 3, 4, 7 y 8. Las acciones 4 y 7 pueden llevarse a cabo en uno u otro orden indistintamente, por lo que el cálculo del impacto de cargas en estrella sobre el transformador 4WD puede seguir cualquiera de las secuencias operationales 1-2-3-4-7-8 o 1-2-3-7-4-8. In this way, as shown in figure 10, the calculation of the impact of delta loads on the 4WD transformer involves carrying out actions 1, 2, 3, 4, 7 and 8. Actions 4 and 7 can be carried out in one or another order without distinction, so the calculation of the impact of star loads on the 4WD transformer can follow any of the operational sequences 1-2-3-4-7-8 or 1-2-3- 7-4-8.
Vil) Cálculo de las corrientes reales del secundario (9 en la figura 10): Vil) Calculation of the real secondary currents (9 in figure 10):
A partir de los valores de las corrientes efectivas en el secundario del transformador (obtenidos en 6 según la figura 10) y del valor de la corriente del neutro del secundario (obtenido en 2 según la figura 10), se obtienen (en 9 según la figura 10) las corrientes reales en las bobinas del secundario mediante las expresiones [26]
From the values of the effective currents in the secondary of the transformer (obtained in 6 according to figure 10) and the value of the neutral current of the secondary (obtained in 2 according to figure 10), they are obtained (in 9 according to figure 10) Figure 10) the real currents in the secondary coils using the expressions [26]
De este modo, tal y como se muestra en la figura 10, de las corrientes reales del secundario del transformador 4WD sigue la secuencia operational 1-2-3-5-6-9. In this way, as shown in Figure 10, the actual secondary currents of the 4WD transformer follow the operational sequence 1-2-3-5-6-9.
VIII) Cabe señalar que, aunque no se muestra en la figura 10, también es posible obtener el valor de otras magnitudes como, por ejemplo, las corrientes reales en las bobinas del primario del transformador 4WD \ según se ha explicado anteriormente.
Concretamente, a partir de los valores de las corrientes efectivas en el secundario (obtenidos en 6 según la figura 10), del número de espiras del primario (jVp) y del secundario (Ns), se pueden obtener las corrientes en las bobinas del primario (IAB, IBC, ICA) mediante las expresiones [14]
VIII) It should be noted that, although not shown in figure 10, it is also possible to obtain the value of other quantities such as, for example, the real currents in the primary coils of the 4WD transformer \ as explained above. Specifically, from the values of the effective currents in the secondary (obtained in 6 according to figure 10), the number of turns of the primary (jV p ) and the secondary (N s ), the currents in the coils can be obtained of the primary (I AB , I BC , I CA ) using the expressions [14]
IX) Visualization (10 en la figura 10):
Los valores de la magnitud o magnitudes obtenidos según el procedimiento (potencia aparente del transformador, impacto causado por las cargas en triángulo, impacto causado por las cargas en estrella, corrientes reales en las bobinas del secundario, etc.) se muestran en un medio de visualization. IX) Visualization (10 in figure 10): The values of the magnitude or magnitudes obtained according to the procedure (apparent power of the transformer, impact caused by delta loads, impact caused by star loads, real currents in the secondary coils, etc.) are displayed in a medium of visualization.
Según un tercer aspecto, la presente invención también proporciona un dispositivo (A) para el análisis de un transformador 4WD en base al concepto de corrientes efectivas descrito anteriormente. Asimismo, el dispositivo (A) permite llevar a cabo el procedimiento descrito anteriormente; concretamente, mediante el dispositivo (A) de la presente invención se puede obtener una o vahas magnitudes del transformador 4WD objeto de análisis, como, por ejemplo, componentes simétricas de las corrientes efectivas, corrientes efectivas, potencia aparente, impacto de cargas en estrella sobre el transformador, impacto de cargas en triángulo sobre el transformador, corrientes en las bobinas del primario, corrientes reales en las bobinas del secundario, etc. According to a third aspect, the present invention also provides a device (A) for the analysis of a 4WD transformer based on the concept of effective currents described above. Likewise, the device (A) allows carrying out the procedure described above; Specifically, by means of the device (A) of the present invention, one or more magnitudes of the 4WD transformer under analysis can be obtained, such as, for example, symmetrical components of the effective currents, effective currents, apparent power, impact of star loads on the transformer, impact of delta loads on the transformer, currents in the primary coils, real currents in the secondary coils, etc.
Tal y como se muestra en la figura 11 , el dispositivo (A) de la presente invención es un dispositivo de medida que comprende: un sistema físico de medida y adquisición de señales eléctricas (D); un sistema procesador (E); y un programa de medida (P), encargado de obtener el valor de una o vahas magnitudes eléctricas del transformador 4WD (T) objeto de análisis. Opcionalmente, el dispositivo (A) de la presente invención también puede comprender un medio de visualization (V), preferiblemente una pantalla, en donde se visualiza el valor de la magnitud o magnitudes eléctricas obtenidas, que permiten analizar el comportamiento del transformador 4WD. As shown in Figure 11, the device (A) of the present invention is a measurement device that comprises: a physical system for measuring and acquiring electrical signals (D); a processing system (E); and a measurement program (P), responsible for obtaining the value of one or several electrical magnitudes of the 4WD transformer (T) under analysis. Optionally, the device (A) of the present invention can also comprise a display means (V), preferably a screen, where the value of the electrical magnitude or magnitudes obtained is displayed, which allows the behavior of the 4WD transformer to be analyzed.
Según una realización preferida, el sistema físico de medida y adquisición de señales eléctricas (D) comprende: unos sensores de medida de corrientes (B); unos sensores de medida de tensiones (C); unos acondicionadores de señal; y una tarjeta de adquisición de datos. Los acondicionadores de señal se encargan de adaptar valores instantáneos de las corrientes y tensiones obtenidos mediante los sensores de medida de corrientes (B) y los sensores de medida de tensiones (C), de manera que las tensiones en las salidas de los acondicionadores de señal sean aplicables a las entradas analógicas de la tarjeta de adquisición de datos. La tarjeta de adquisición de datos convierte las señales analógicas de tensión y corriente en una serie de muestras discretas, que se utilizan como entradas del programa de medida (P). According to a preferred embodiment, the physical system for measuring and acquiring electrical signals (D) comprises: current measurement sensors (B); some tension measurement sensors (C); some signal conditioners; and a data acquisition card. The signal conditioners are responsible for adapting instantaneous values of the currents and voltages obtained by the current measurement sensors (B) and the voltage measurement sensors (C), so that the voltages at the outputs of the signal conditioners are applicable to the analog inputs of the data acquisition card. The data acquisition card converts the analog voltage and current signals into a series of discrete samples, which are used as inputs to the measurement program (P).
Preferiblemente, el sistema físico de medida y adquisición de señales eléctricas (D) se dispone en las líneas del secundario del transformador tal y como se muestra en la figura 11 , de manera que puede adquirir señales de las tensiones
y las corrientes de línea del secundario del transformador 4WD, tanto las corrientes totales (J como las corrientes
debidas a las cargas en triángulo y la corriente del neutro (/n). Según una opción, el
dispositivo (A) de medida adquiere todas las señales indicadas
por medio del sistema físico de medida y adquisición de
señales eléctricas (D) y las almacena, para posteriormente utilizar únicamente las necesarias dependiendo de la magnitud o magnitudes que se deseen obtener. Según una opción alternativa, el dispositivo (A) de medida adquiere exclusivamente las señales que se necesiten dependiendo de la magnitud o magnitudes que se deseen obtener. Preferably, the physical system for measuring and acquiring electrical signals (D) is arranged in the secondary lines of the transformer as shown in Figure 11, so that it can acquire voltage signals. and the secondary line currents of the 4WD transformer, both the total currents (J and the currents due to delta loads and neutral current (/ n ). According to one option, the measuring device (A) acquires all the indicated signals through the physical system of measurement and acquisition of electrical signals (D) and stores them, to later use only the necessary ones depending on the magnitude or magnitudes that you wish to obtain. According to an alternative option, the measuring device (A) acquires exclusively the signals that are needed depending on the magnitude or magnitudes that are desired to be obtained.
Según una realización preferida, el sistema procesador (E) se conecta a una placa base, a la que también se conecta la tarjeta de adquisición de datos, que permite intercambiar las muestras discretas de las señales de tensión e intensidad con el programa de medida (P). According to a preferred embodiment, the processing system (E) is connected to a motherboard, to which the data acquisition card is also connected, which allows the discrete samples of the voltage and intensity signals to be exchanged with the measurement program ( P).
Según una realización preferida, el programa de medida (P) comprende los siguientes módulos: un módulo de procesado digital de señales (P1); un módulo de análisis de señales (P2); un módulo de simétricas de corrientes de línea (P3); y uno o varios módulos seleccionados del grupo que comprende: módulo de simétricas de corrientes efectivas (P4); módulo de corrientes efectivas (P5); módulo de potencia aparente (P6); módulo de impacto de las cargas (P7); módulo de corrientes reales del secundario (P8). Opcionalmente este grupo también puede comprender otros módulos para obtener otras magnitudes del transformador 4WD objeto de análisis; por ejemplo, un módulo de corrientes del primario. Opcionalmente, el programa de medida (P) también puede comprender un módulo de visualization (P9). According to a preferred embodiment, the measurement program (P) comprises the following modules: a digital signal processing module (P1); a signal analysis module (P2); a symmetric line current module (P3); and one or more modules selected from the group comprising: effective current symmetry module (P4); effective currents module (P5); apparent power module (P6); load impact modulus (P7); secondary real currents module (P8). Optionally, this group can also comprise other modules to obtain other magnitudes of the 4WD transformer under analysis; for example, a primary current module. Optionally, the measurement program (P) may also comprise a visualization module (P9).
El módulo de procesado digital de señales (P1) se encarga de recibir muestras de tensión y corriente, y almacenarlas en un vector para cada una de ellas. The digital signal processing module (P1) is responsible for receiving voltage and current samples, and storing them in a vector for each of them.
El módulo de análisis de señales (P2) se encarga de obtener, a partir de las muestras recibidas en el módulo de procesado digital de señales (P1), los valores eficaces y las fases iniciales de dichas muestras. The signal analysis module (P2) is responsible for obtaining, from the samples received in the digital signal processing module (P1), the effective values and the initial phases of said samples.
El módulo de simétricas de corrientes de línea (P3) se encarga de obtener las componentes de secuencia directa e inversa de las corrientes de línea del secundario del transformador 4WD, tanto las componentes correspondientes a las corrientes totales ) como las correspondientes a las corrientes de línea de las cargas en triángulo
en valor eficaz y en ángulo, a partir de la información obtenida en el módulo de análisis de señales (P2). Preferiblemente, en coherencia con lo explicado anteriormente sobre el procedimiento, este módulo (P3) se encarga de obtener _ según las expresiones [21] y
según las expresiones [23],
The line current symmetry module (P3) is responsible for obtaining the direct and reverse sequence components of the line currents of the secondary of the 4WD transformer, both the components corresponding to the total currents and those corresponding to the line currents. of triangle charges in effective value and in angle, from the information obtained in the signal analysis module (P2). Preferably, in consistency with what was previously explained about the procedure, this module (P3) is responsible for obtaining _ according to the expressions [21] and according to the expressions [23],
El módulo de simétricas de corrientes efectivas (P4) se encarga de obtener los valores eficaces y el ángulo de las componentes de secuencias positiva y negativa de las corrientes efectivas del secundario del transformado a partir de las componentes de
secuencias positiva y negativa de las corrientes de línea del transformador 4WD obtenidas en el módulo de simétricas de corrientes de línea (P3). Preferiblemente, en coherencia con lo explicado anteriormente sobre el procedimiento, este módulo (P4) se encarga de obtener según las expresiones [15],
El módulo de corrientes efectivas (P5) se encarga de obtener los valores eficaces y el ángulo de las corrientes efectivas del secundario del transformador 4WD \ a
partir de sus componentes simétricas obtenidas en el módulo de simétricas de
corrientes efectivas (P4). Preferiblemente, en coherencia con lo explicado anteriormente sobre el procedimiento, este módulo (P5) se encarga de obtene según las expresiones
[25], The effective current symmetry module (P4) is responsible for obtaining the effective values and the angle of the positive and negative sequence components of the effective currents of the secondary of the transformer from the components of positive and negative sequences of the 4WD transformer line currents obtained in the line current symmetry module (P3). Preferably, in consistency with what was previously explained about the procedure, this module (P4) is responsible for obtaining according to the expressions [15], The effective currents module (P5) is responsible for obtaining the effective values and angle of the effective currents of the secondary of the 4WD transformer \ a from its symmetric components obtained in the symmetric module of effective currents (P4). Preferably, in consistency with what was previously explained about the procedure, this module (P5) is responsible for obtaining according to the expressions [25],
El módulo de potencia aparente (P6) se encarga de obtener el valor de la potencia aparente (S) del transformador 4WD, preferiblemente, a partir de los valores eficaces de las tensiones de línea del secundario (Vab, Vbc, Vca) obtenidos en el módulo de análisis de señales (P2), y de la información sobre corrientes obtenida en cualquiera de los siguientes módulos: módulo de simétricas de corrientes de línea (P3), módulo de simétricas de corrientes efectivas (P4), módulo de corrientes efectivas (P5). The apparent power module (P6) is responsible for obtaining the apparent power value (S) of the 4WD transformer, preferably from the effective values of the secondary line voltages (V ab , V bc , V ca ). obtained in the signal analysis module (P2), and the current information obtained in any of the following modules: line current symmetry module (P3), effective current symmetry module (P4), currents module effective (P5).
Preferiblemente, en coherencia con lo explicado anteriormente sobre el procedimiento, el módulo de potencia aparente (P6) se encarga de obtener la potencia aparente (S) según la expresión [20], a partir de las matrices de tensiones Vab, Vbc, Vca obtenidas en el módulo P2 y corrientes
obtenidas en el módulo de simétricas de corrientes de línea (P3); según la expresión [19], a partir de las matrices de tensiones Vab, Vbc,Vca obtenidas en el módulo P2 y corrientes obtenidas en el módulo de simétricas de corrientes efectivas (P4); o
según la expresión [18], a partir de las matrices de tensiones Vab, Vbc,Vca obtenidas en el módulo P2 y corrientes obtenidas en el módulo de corrientes efectivas (P5).
Preferably, in consistency with what was previously explained about the procedure, the apparent power module (P6) is responsible for obtaining the apparent power (S) according to expression [20], from the voltage matrices V ab , V bc , V ac obtained in module P2 and currents obtained in the line current symmetry module (P3); according to expression [19], from the voltage matrices V ab , V bc , V ca obtained in the P2 module and currents obtained in the symmetric module of effective currents (P4); either according to expression [18], from the voltage matrices V ab , V bc , V ca obtained in the P2 module and currents obtained in the effective currents module (P5).
El módulo de impacto de las cargas (P7) se encarga de obtener el valor de la potencia aparente del transformador 4WD debido al funcionamiento de las cargas en estrella (Sr), y el valor de la potencia aparente del transformador 4WD debido al funcionamiento de las cargas en triángulo (SA). Preferiblemente, en coherencia con lo explicado anteriormente sobre el procedimiento, este módulo (P7) se encarga de obtener S& según las expresiones [22] y [23]; y SY según la expresión [24], The load impact module (P7) is responsible for obtaining the value of the apparent power of the 4WD transformer due to the operation of the star loads (S r ), and the value of the apparent power of the 4WD transformer due to the operation of the triangle charges (S A ). Preferably, in consistency with what was previously explained about the procedure, this module (P7) is responsible for obtaining S & according to the expressions [22] and [23]; and S Y according to the expression [24],
El módulo de corrientes reales del secundario (P8) se encarga de obtener los valores eficaces y los ángulos de las corrientes reales de las bobinas del secundari del
transformador 4WD, a partir de los valores de las corrientes efectivas
obtenidas en el módulo de corrientes efectivas (P5), y de la corriente del neutro obtenida en
el módulo de análisis de señales (P2). Preferiblemente, en coherencia con lo explicado anteriormente sobre el procedimiento, este módulo (P8) se encarga de obtener
íca según las expresiones [26], The secondary real currents module (P8) is responsible for obtaining the effective values and angles of the real currents of the secondary coils of the 4WD transformer, from the values of the effective currents obtained in the effective current module (P5), and the neutral current obtained in the signal analysis module (P2). Preferably, in coherence with what was previously explained about the procedure, this module (P8) is responsible for obtaining íca according to the expressions [26],
El módulo de corrientes del primario se encarga de obtener los valores eficaces y los ángulos de las corrientes de las bobinas del primario del transformador 4WD,
preferiblemente, a partir de los valores de las corrientes efectivas obtenidas
en el módulo de corrientes efectivas (P5), del número de espiras del primario (Np) y del número de espiras del secundario (Ns). Preferiblemente, en coherencia con lo explicado anteriormente sobre el procedimiento, el módulo de corrientes del primario se encarga de obtener según las expresiones [14],
The primary current module is responsible for obtaining the effective values and angles of the currents of the primary coils of the 4WD transformer, preferably, from the values of the effective currents obtained in the module of effective currents (P5), the number of turns of the primary (N p ) and the number of turns of the secondary (N s ). Preferably, in consistency with what was previously explained about the procedure, the primary current module is responsible for obtaining according to the expressions [14],
El módulo de visualization (P9) se encarga de mostrar en el medio de visualization (V) la información de una o vahas magnitudes del transformador 4WD obtenidas por el dispositivo (A), preferiblemente una o vahas magnitudes eléctricas seleccionadas del grupo que comprende: componentes de secuencia positiva y negativa de las corrientes efectivas, corrientes efectivas, potencia aparente del transformador, impacto de cargas en estrella sobre el transformador, impacto de cargas en triángulo sobre el transformador, corrientes en las bobinas del primario del transformador y corrientes reales en las bobinas del secundario del transformador. The display module (P9) is responsible for displaying on the display means (V) the information of one or several magnitudes of the 4WD transformer obtained by the device (A), preferably one or several electrical magnitudes selected from the group that comprises: components of positive and negative sequence of the effective currents, effective currents, apparent power of the transformer, impact of star loads on the transformer, impact of delta loads on the transformer, currents in the primary coils of the transformer and real currents in the coils of the secondary of the transformer.
Según la realización preferida de la figura 14, el módulo de visualization (P9) muestra en el medio de visualization (V) información numérica de la potencia aparente del transformador 4WD, los impactos de las cargas en triángulo y en estrella, así como las corrientes reales en las bobinas del secundario del transformador 4WD (“Corrientes Secundario” en la figura 14). According to the preferred embodiment of Figure 14, the display module (P9) displays on the display means (V) numerical information of the apparent power of the 4WD transformer, the impacts of delta and star loads, as well as currents. real in the secondary coils of the 4WD transformer (“Secondary Currents” in figure 14).
Según una realización preferida mostrada en las figuras 12 y 13, el programa de medida (P) comprende los módulos P1-P9 mencionados anteriormente. Más específicamente, la figura 12 muestra los módulos del programa de medida (P) configurados para intervenir en la medida y visualization de la potencia aparente y de los impactos de las cargas, tanto en estrella como en triángulo (concretamente los módulos P1-P7 y P9); y la figura 13 muestra los módulos del programa de medida (P) configurados para intervenir en la medida y visualization de las corrientes reales de las bobinas del secundario (concretamente, los módulos P1-P5, P8-P9). According to a preferred embodiment shown in Figures 12 and 13, the measurement program (P) comprises the modules P1-P9 mentioned above. More specifically, Figure 12 shows the modules of the measurement program (P) configured to intervene in the measurement and visualization of the apparent power and the impacts of the loads, both star and delta (specifically the modules P1-P7 and P9); and Figure 13 shows the modules of the measurement program (P) configured to intervene in the measurement and visualization of the real currents of the secondary coils (specifically, the modules P1-P5, P8-P9).
Aunque se ha descrito la presente invención con referencia a opciones y realizaciones particulares de la misma, los expertos en la técnica podrán realizar modificaciones y variaciones a las enseñanzas anteriores sin por ello apartarse del alcance y el espíritu de la presente invención.
Although the present invention has been described with reference to particular options and embodiments thereof, those skilled in the art may make modifications and variations to the foregoing teachings without departing from the scope and spirit of the present invention.
Claims
REIVINDICACIONES
1- Uso de corrientes para el análisis de un transformador 4WD, caracterizado por que dichas corrientes son aquellas que circulan por las bobinas del secundario de un transformador D-D equivalente al transformador 4WD objeto de análisis, denominándose corrientes efectivas
entendiendo por transformador 4WD un transformador triángulo - triángulo con tres bobinas en el secundario y un conductor neutro conectado en el centro de una de dichas bobinas, denominada bobina ligada al neutro para diferenciarla del resto de bobinas del secundario, denominadas bobinas libres de neutro; entendiendo por transformador D-D un transformador triángulo - triángulo sin conductor neutro; entendiendo por equivalente aquel transformador D-D teórico que da lugar a la circulación de las mismas corrientes en las bobinas del primari Y en las líneas del secundario
que el transformador 4WD; con la particularidad de que la aplicación de las corrientes efectivas en las bobinas del secundario del transformador 4WD, en sustitución de las corrientes reales que circulan por dichas bobina da lugar a los mismos efectos magnéticos que las corrientes
que circulan por las bobinas del primario del transformador 4WD
1- Use of currents for the analysis of a 4WD transformer, characterized in that said currents are those that circulate through the secondary coils of a DD transformer equivalent to the 4WD transformer under analysis, called effective currents A 4WD transformer is understood to be a triangle-triangle transformer with three coils in the secondary and a neutral conductor connected to the center of one of said coils, called a neutral-linked coil to differentiate it from the rest of the secondary coils, called neutral-free coils; DD transformer being understood as a triangle - triangle transformer without a neutral conductor; equivalent being understood as that theoretical DD transformer that gives rise to the circulation of the same currents in the coils of the primary AND in the lines of the secondary than the 4WD transformer; with the particularity that the application of the effective currents in the secondary coils of the 4WD transformer, replacing the real currents that circulate through said coil, gives rise to the same magnetic effects as the currents. that circulate through the primary coils of the 4WD transformer
2- Uso de corrientes efectivas según la reivindicación 1 , con la particularidad de que las corrientes efectivas están relacionadas con corrientes reales del secundario del transformador2- Use of effective currents according to claim 1, with the particularity that the effective currents are related to real currents of the secondary of the transformer
4WD por aplicación de una matriz de transformación biunívoca [T] según la siguiente expresión:
en la que es la corriente real que circula por una primera mitad de la bobina ligada al neutro, en el
secundario del transformador 4WD; son las corrientes reales que circulan por las respectivas bobinas libres de neutro, en
el secundario del transformador 4WD; 4WD by application of a one-to-one transformation matrix [T] according to the following expression: in which is the real current that circulates through a first half of the coil linked to the neutral, in the 4WD transformer secondary; are the real currents that circulate through the respective neutral-free coils, in the secondary of the 4WD transformer;
Tn es la corriente que circula por el conductor neutro del secundario del transformador 4WD;T n is the current that circulates through the neutral conductor of the secondary of the 4WD transformer;
Y la matriz de transformación biunívoca [T] es:
And the one-to-one transformation matrix [T] is:
3- Procedimiento para el análisis de un transformador 4WD en base al uso de corrientes efectivas descrito en cualquiera de las reivindicaciones 1 o 2, caracterizado por que comprende obtener, mediante un dispositivo de medida, el valor de al menos una magnitud del transformador 4WD seleccionada del grupo que comprende componentes simétricas de las corrientes efectivas corrientes efectivas potencia aparente (S), impacto de
cargas en triángulo (SA) sobre el transformador, impacto de cargas en estrella (Sr) sobre el transformador, corrientes en las bobinas del primario Y corrientes reales en las
bobinas del secundario según las particularidades de los siguientes
apartados: a) el valor de las componentes simétricas de las corrientes efectiva e obtiene
mediante las siguientes expresiones: 3- Procedure for the analysis of a 4WD transformer based on the use of effective currents described in any of claims 1 or 2, characterized in that it comprises obtaining, by means of a measuring device, the value of at least one magnitude of the selected 4WD transformer. of the group comprising symmetrical components of the effective currents effective currents apparent power (S), impact of delta loads (S A ) on the transformer, impact of star loads (S r ) on the transformer, currents in the primary coils and real currents in the secondary coils according to the particularities of the following sections: a) the value of the symmetric components of the effective currents e is obtained through the following expressions:
[15],
en las que son las componentes simétricas de las corrientes de línea del
secundario, que se obtienen mediante las siguientes expresiones:
en las que son las corrientes de línea del secundario, que se obtienen adquiriendo muestras
de corriente mediante sensores dispuestos en las líneas del secundario del transformador 4WD, y realizando un procesado digital de las muestras adquiridas para obtener los valores eficaces y fases iniciales correspondientes, y a es un versor de valor a =1z120°; b) el valor de las corrientes efectivas se obtiene mediante una de las
siguientes opciones: b1) mediante las expresiones [25]
en las que a es un versor de valor a
son las componentes simétricas de las corrientes efectivas;
b2) mediante las expresiones [14]
en las que [fifteen], in which are the symmetric components of the line currents of the secondary, which are obtained through the following expressions: in which are the secondary line currents , which are obtained by acquiring samples of current through sensors arranged in the secondary lines of the 4WD transformer, and performing digital processing of the acquired samples to obtain the effective values and corresponding initial phases, it is now a value converter at =1z120°; b) the value of the effective currents is obtained by one of the following options: b1) using the expressions [25] where a is a verser of value a are the symmetrical components of the effective currents; b2) through the expressions [14] in which
Np es el número de espiras del primario del transformador 4WD, N p is the number of turns of the primary of the 4WD transformer,
Ns son el número de espiras del secundario del transformador 4WD, son las corrientes en las bobinas del primario del transformador 4WD,
que se obtienen adquiriendo muestras de corriente en las bobinas del primario del transformador 4WD mediante sensores, y realizando un procesado digital de las muestras adquiridas ppaarraa obtener los valores eficaces y fases iniciales correspondientes; b3) mediante un sistema de emulación con un transformador D-D como el equivalente al transformador 4WD objeto de análisis, de manera que en el transformador D-D del sistema de emulación se reproducen las mismas corrientes en las bobinas del primario y en las líneas del secundario que el transformador 4WD objeto
de análisis, y se miden las corrientes que circulan por las bobinas del secundario de dicho transformador D-D, que son las corrientes efectivas con la
particularidad de que se obtienen adquiriendo muestras de
corriente en las bobinas del primario y en las líneas del secundario del transformador 4WD mediante sensores, y realizando un procesado digital de las muestras adquiridas para obtener los valores eficaces y fases iniciales correspondientes; c) el valor de la potencia aparente (S) del transformador 4WD se obtiene mediante una de las siguientes opciones: c1) mediante la ecuación [18]
c2) mediante la ecuación [19]
c3) mediante la ecuación [20]
en las que son los valores eficaces de las tensiones de línea del secundario del
transformador 4WD Que se obtienen adquiriendo muestras de tensión
mediante sensores dispuestos en las líneas del secundario del transformador 4WD, y realizando un procesado digital de las muestras adquiridas para obtener los valores eficaces y fases iniciales correspondientes, son l°s valores eficaces de las corrientes efectivas
I J son l°s valores eficaces de las componentes simétricas de las
corrientes efectivas
son los valores eficaces de las componentes simétricas de las corrientes
de línea del secundario, obteniéndose Ta+ y Ta_ mediante las siguientes expresiones:
en las que son las corrientes de línea del secundario, que se obtienen adquiriendo muestras
de corriente mediante sensores dispuestos en las líneas del secundario del transformador 4WD, y realizando un procesado digital de las muestras adquiridas para obtener los valores eficaces y fases iniciales correspondientes, y a es un versor de valor
con la particularidad de que la ecuación [19] deriva de la ecuación [18] por aplicación del teorema de Fortescue; y la ecuación [20] deriva de la ecuación [19] por aplicación de las relaciones existentes entre las componentes y las componentes
según las siguientes expresiones: N s are the number of turns of the secondary of the 4WD transformer, they are the currents in the primary coils of the 4WD transformer, which are obtained by acquiring current samples in the primary coils of the 4WD transformer using sensors, and performing digital processing of the acquired samples to obtain the corresponding effective values and initial phases; b3) through an emulation system with a DD transformer as the equivalent to the 4WD transformer under analysis, so that in the DD transformer of the emulation system the same currents are reproduced in the primary coils and in the secondary lines that the transformer 4WD object of analysis, and the currents that circulate through the secondary coils of said DD transformer are measured, which are the effective currents with the particularity that are obtained by acquiring samples of current in the primary coils and in the secondary lines of the 4WD transformer using sensors, and performing digital processing of the acquired samples to obtain the corresponding effective values and initial phases; c) the value of the apparent power (S) of the 4WD transformer is obtained using one of the following options: c1) using equation [18] c2) by equation [19] c3) by equation [20] in which are the effective values of the secondary line voltages of the 4WD transformer which are obtained by acquiring voltage samples Using sensors arranged in the secondary lines of the 4WD transformer, and performing digital processing of the acquired samples to obtain the effective values and corresponding initial phases, these are the effective values of the effective currents. IJ are the effective values of the symmetric components of the effective currents are the effective values of the symmetric components of the currents secondary line, obtaining T a+ and T a _ using the following expressions: in which are the secondary line currents, which are obtained by acquiring samples of current through sensors arranged in the secondary lines of the 4WD transformer, and carrying out digital processing of the acquired samples to obtain the effective values and corresponding initial phases, it is now a value converter with the particularity that equation [19] is derived from equation [18] by application of Fortescue's theorem; and equation [20] is derived from equation [19] by application of the existing relationships between the components and the components according to the following expressions:
[15];
d) el valor del impacto de cargas en triángulo (SA) sobre el transformador 4WD se obtiene mediante la siguiente ecuación:
en la que son los valores eficaces de las tensiones de línea del secundario del
transformador 4WD que se obtienen adquiriendo muestras de tensión
mediante sensores dispuestos en las líneas del secundario del transformador 4WD, y realizando un procesado digital de las muestras adquiridas para obtener los valores eficaces y fases iniciales correspondientes, son l°s valores e de las
ficaces de las componentes simétricas
corrientes de línea absorbidas por las cargas en triángulo, obteniéndose
mediante las siguientes expresiones:
en las que son las corrientes de línea absorbidas por las cargas en triángulo, que se
obtienen adquiriendo muestras de corriente mediante sensores dispuestos en las líneas de las cargas en triángulo, y realizando un procesado digital de las muestras adquiridas para obtener los valores eficaces y fases iniciales correspondientes, y a es un versor de valor a
con la particularidad de que la ecuación [22] se obtiene por analogía a la ecuación [20];
e) el valor del Impacto de cargas en estrella (Sr) sobre el transformador 4WD se obtiene mediante la siguiente ecuación:
en la que [fifteen]; d) the value of the impact of delta loads (S A ) on the 4WD transformer is obtained by the following equation: in which are the effective values of the secondary line voltages of the 4WD transformer that are obtained by acquiring voltage samples through sensors arranged in the secondary lines of the 4WD transformer, and performing digital processing of the acquired samples to obtain the effective values and corresponding initial phases, are the e values of the effectiveness of symmetrical components line currents absorbed by the delta loads, obtaining through the following expressions: in which are the line currents absorbed by the delta loads, which are obtained by acquiring current samples through sensors arranged on the lines of the delta loads, and carrying out digital processing of the acquired samples to obtain the effective values and corresponding initial phases, it is already a value converter. with the particularity that equation [22] is obtained by analogy to equation [20]; e) the value of the Impact of star loads (S r ) on the 4WD transformer is obtained by the following equation: in which
S es la potencia aparente del transformador 4WD, S is the apparent power of the 4WD transformer,
SΔ es el impacto de cargas en triángulo, obtenido mediante la ecuación [22] conforme al apartado d); f) el valor de las corrientes reales en las bobinas del secundario del transformador 4WD se obtiene mediante las siguientes expresiones:
en las que
es la corriente real que circula por una primera mitad de la bobina ligada al neutro, en el secundario del transformador 4WD; es la corriente real que circula por una segunda mitad de la bobina ligada al neutro, en
el secundario del transformador 4WD; son las corrientes reales que circulan por las respectivas bobinas libres de neutro,
en el secundario del transformador 4WD; S Δ is the impact of triangle loads, obtained by equation [22] according to section d); f) the value of the real currents in the secondary coils of the 4WD transformer is obtained using the following expressions: in which is the real current that circulates through the first half of the coil linked to the neutral, in the secondary of the 4WD transformer; is the real current that circulates through a second half of the coil linked to the neutral, in the secondary of the 4WD transformer; are the real currents that circulate through the respective neutral-free coils, on the secondary of the 4WD transformer;
Tn es la corriente real que circula por el conductor neutro del secundario del transformador 4WD, que se obtiene adquiriendo una muestra de corriente mediante un medio de adquisición, preferiblemente un sensor dispuesto en el neutro del secundario del transformador 4WD; y realizando un procesado digital de la muestra adquirida para obtener el valor eficaz y fase inicial correspondiente, son las corrientes efectivas;
g) el valor de las corrientes en las bobinas del primario del transformador 4WD
se obtiene mediante las siguientes expresiones:
en las que T n is the actual current that circulates through the neutral conductor of the secondary of the 4WD transformer, which is obtained by acquiring a current sample by means of an acquisition means, preferably a sensor arranged in the neutral of the secondary of the 4WD transformer; and performing digital processing of the acquired sample to obtain the effective value and corresponding initial phase, are the effective currents; g) the value of the currents in the primary coils of the 4WD transformer is obtained through the following expressions: in which
Np es el número de espiras del primario del transformador 4WD, N p is the number of turns of the primary of the 4WD transformer,
Ns son el número de espiras del secundario del transformador 4WD, son las corrientes efectivas.
N s are the number of turns of the secondary of the 4WD transformer, they are the effective currents.
4- Dispositivo (A) para el análisis de un transformador 4WD (T) en base al uso de corrientes efectivas descrito en cualquiera de las reivindicaciones 1 o 2, caracterizado por que comprende: 4- Device (A) for the analysis of a 4WD transformer (T) based on the use of effective currents described in any of claims 1 or 2, characterized in that it comprises:
- un sistema físico de medida y adquisición de señales eléctricas (D);
un sistema procesador (E); un programa de medida (P), encargado de obtener el valor de una o varias magnitudes eléctricas del transformador 4WD (T). - a physical system for measuring and acquiring electrical signals (D); a processing system (E); a measurement program (P), responsible for obtaining the value of one or several electrical quantities of the 4WD transformer (T).
5- Dispositivo (A) según la reivindicación 4, en el que el sistema físico de medida y adquisición de señales eléctricas (D) comprende: 5- Device (A) according to claim 4, wherein the physical system for measuring and acquiring electrical signals (D) comprises:
- unos sensores de medida de corrientes (B); - current measurement sensors (B);
- unos sensores de medida de tensiones (C); - tension measurement sensors (C);
- unos acondicionadores de señal; - some signal conditioners;
- una tarjeta de adquisición de datos; con la particularidad de que los acondicionadores de señal se encargan de adaptar valores instantáneos de las corrientes y tensiones obtenidos mediante los sensores de medida de corrientes (B) y los sensores de medida de tensiones (C), de manera que las tensiones en las salidas de los acondicionadores de señal puedan ser aplicables a las entradas analógicas de la tarjeta de adquisición de datos, la cual convierte las señales analógicas de tensión y corriente en una señe de muestras discretas, que se utilizan como entradas del programa de medida (P). - a data acquisition card; with the particularity that the signal conditioners are responsible for adapting instantaneous values of the currents and voltages obtained by the current measurement sensors (B) and the voltage measurement sensors (C), so that the voltages at the outputs of the signal conditioners can be applicable to the analog inputs of the data acquisition card, which converts the analog voltage and current signals into a signal of discrete samples, which are used as inputs to the measurement program (P).
6- Dispositivo (A) según cualquiera de las reivindicaciones 4 o 5, en el que el programa de medida (P) comprende: 6- Device (A) according to any of claims 4 or 5, wherein the measurement program (P) comprises:
- un módulo de procesado digital de señales (P1), encargado de recibir muestras de tensión y corriente, y almacenarlas en un vector para cada una de ellas. - a digital signal processing module (P1), responsible for receiving voltage and current samples, and storing them in a vector for each of them.
- un módulo de análisis de señales (P2), encargado de obtener, a partir de las muestras recibidas en el módulo de procesado digital de señales (P1), los valores eficaces y las fases iniciales de dichas muestras; - a signal analysis module (P2), responsible for obtaining, from the samples received in the digital signal processing module (P1), the effective values and the initial phases of said samples;
- un módulo de simétricas de corrientes de línea (P3), encargado de obtener las componentes simétricas de las corrientes de línea del secundario del transformador 4WD, tanto las correspondientes a las corrientes totales
como las correspondientes a las corrientes de línea de las cargas en triángulo en valor eficaz y en ángulo, a
partir de la información obtenida en el módulo de análisis de señales (P2). - a symmetrical line current module (P3), responsible for obtaining the symmetrical components of the line currents of the secondary of the 4WD transformer, both those corresponding to the total currents as those corresponding to the line currents of the delta loads in effective value and in angle, to from the information obtained in the signal analysis module (P2).
- uno o varios de los siguientes módulos: - one or more of the following modules:
• un módulo de simétricas de corrientes efectivas (P4), encargado de obtener los valores eficaces y el ángulo de las componentes simétricas de las corrientes efectivas del secundario del transformador a partir de las componentes
simétricas de las corrientes de línea del transformador 4WD obtenidas en el módulo de simétricas de corrientes de línea (P3);
• un módulo de corrientes efectivas (P5), encargado de obtener los valores eficaces y el ángulo de las corrientes efectivas del secundario del transformador
a partir de sus componentes simétricas , obtenidas en el módulo
de simétricas de corrientes efectivas (P4); • a symmetrical effective current module (P4), responsible for obtaining the effective values and angle of the symmetrical components of the effective currents of the secondary of the transformer from the components symmetrical of the 4WD transformer line currents obtained in the line current symmetrical module (P3); • an effective current module (P5), responsible for obtaining the effective values and angle of the effective currents of the secondary of the transformer from its symmetric components, obtained in the module of symmetrical effective currents (P4);
• un módulo de potencia aparente (P6), encargado de obtener el valor de la potencia aparente (S) del transformador 4WD, a partir de los valores eficaces de las tensiones de línea del secundario obtenidos en el módulo de análisis de señales (P2), y
de la información sobre corrientes obtenida en cualquiera de los siguientes módulos: módulo de simétricas de corrientes de línea (P3), módulo de simétricas de corrientes efectivas (P4), módulo de corrientes efectivas (P5); • an apparent power module (P6), responsible for obtaining the value of the apparent power (S) of the 4WD transformer, from the effective values of the secondary line voltages obtained in the signal analysis module (P2) , and of the information on currents obtained in any of the following modules: line current symmetry module (P3), effective current symmetry module (P4), effective currents module (P5);
• un módulo de impacto de las cargas (P7), encargado de obtener el valor de la potencia aparente del transformador 4WD debido al funcionamiento de las cargas en estrella (Sr), y el valor de la potencia aparente del transformador 4WD debido al funcionamiento de las cargas en triángulo (SA); • a load impact module (P7), responsible for obtaining the value of the apparent power of the 4WD transformer due to the operation of the star loads (S r ), and the value of the apparent power of the 4WD transformer due to the operation of the triangle charges (S A );
• un módulo de corrientes reales del secundario (P8), encargado de obtener los valores eficaces y los ángulos de las corrientes reales de las bobinas del secundario
del transformador 4WD, a partir de los valores de las corrientes efectivas obtenidas en el módulo de corrientes efectivas (P5), y de la
corriente del neutro (/n) obtenida en el módulo de análisis de señales (P2); • a secondary real currents module (P8), responsible for obtaining the effective values and angles of the real currents of the secondary coils of the 4WD transformer, from the values of the effective currents obtained in the effective currents module (P5), and from the neutral current (/ n ) obtained in the signal analysis module (P2);
• un módulo de corrientes del primario, encargado de obtener los valores eficaces y los ángulos de las corrientes de las bobinas del primario
del transformador 4WD, a partir de los valores de las corrientes efectivas obtenidas en
el módulo de corrientes efectivas (P5), del número de espiras del primario (Np) y del número de espiras del secundario (Ns). • a primary current module, responsible for obtaining the effective values and angles of the currents of the primary coils of the 4WD transformer, from the values of the effective currents obtained in the module of effective currents (P5), the number of turns of the primary (N p ) and the number of turns of the secondary (N s ).
7- Dispositivo (A) según cualquiera de las reivindicaciones 4 a 6, que comprende un medio de visualization (V); y el programa de medida (P) comprende un módulo de visualization (P9), encargado de mostrar en el medio de visualization (V) la información de una o varias magnitudes eléctricas del transformador 4WD (T) obtenidas por el dispositivo (A). 7- Device (A) according to any of claims 4 to 6, comprising a visualization means (V); and the measurement program (P) comprises a visualization module (P9), responsible for displaying on the visualization means (V) the information of one or several electrical magnitudes of the 4WD transformer (T) obtained by the device (A).
8- Dispositivo (A) según la reivindicación 7, en el que el medio de visualization (V) muestra una o vahas magnitudes eléctricas seleccionadas del grupo que comprende: potencia aparente del transformador 4WD, impacto de cargas en estrella sobre el transformador 4WD, impacto de cargas en triángulo sobre el transformador 4WD, y corrientes reales en las bobinas del secundario del transformador 4WD.
8- Device (A) according to claim 7, wherein the display means (V) shows one or several electrical magnitudes selected from the group that comprises: apparent power of the 4WD transformer, impact of star loads on the 4WD transformer, impact of delta loads on the 4WD transformer, and actual currents in the secondary coils of the 4WD transformer.
Applications Claiming Priority (2)
| Application Number | Priority Date | Filing Date | Title |
|---|---|---|---|
| ES202230635A ES2921405B2 (en) | 2022-07-11 | 2022-07-11 | Use of currents, procedure and device for the analysis of a 4WD transformer |
| ESP202230635 | 2022-07-11 |
Publications (1)
| Publication Number | Publication Date |
|---|---|
| WO2024013415A1 true WO2024013415A1 (en) | 2024-01-18 |
Family
ID=82940071
Family Applications (1)
| Application Number | Title | Priority Date | Filing Date |
|---|---|---|---|
| PCT/ES2023/070408 WO2024013415A1 (en) | 2022-07-11 | 2023-06-23 | Use of currents, method and device for analysing a 4wd transformer |
Country Status (2)
| Country | Link |
|---|---|
| ES (1) | ES2921405B2 (en) |
| WO (1) | WO2024013415A1 (en) |
Citations (2)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| US6141626A (en) * | 1997-05-09 | 2000-10-31 | Abb Power T&D Company Inc. | Two-element energy meter having systems for automatic service type detection |
| US20180224486A1 (en) * | 2017-02-01 | 2018-08-09 | Landis+Gyr Llc | VA Metering in Delta-Wired Electrical Service |
-
2022
- 2022-07-11 ES ES202230635A patent/ES2921405B2/en active Active
-
2023
- 2023-06-23 WO PCT/ES2023/070408 patent/WO2024013415A1/en unknown
Patent Citations (2)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| US6141626A (en) * | 1997-05-09 | 2000-10-31 | Abb Power T&D Company Inc. | Two-element energy meter having systems for automatic service type detection |
| US20180224486A1 (en) * | 2017-02-01 | 2018-08-09 | Landis+Gyr Llc | VA Metering in Delta-Wired Electrical Service |
Non-Patent Citations (3)
| Title |
|---|
| DUGAN R.C.: "Experiences with the center-tapped wye-delta transformer test case", POWER ENGINEERING SOCIETY GENERAL MEETING, 2004. IEEE, IEEE, PISCATAWAY, NJ, USA, 6 June 2004 (2004-06-06) - 10 June 2004 (2004-06-10), Piscataway, NJ, USA , pages 867 - 871, XP010756470, ISBN: 978-0-7803-8465-1, DOI: 10.1109/PES.2004.1372943 * |
| LEÓN-MARTÍNEZ VICENTE, MONTAÑANA-ROMEU JOAQUÍN, RADDA PETER, CAZORLA-NAVARRO ANTONIO: "Four-Wire Delta Service Sinusoidal Operation and Compensation Simulator", ENERGIES, M D P I AG, CH, vol. 8, no. 10, CH , pages 11276 - 11294, XP093130069, ISSN: 1996-1073, DOI: 10.3390/en81011276 * |
| PENIDO, D. R. R. ET AL.: "Three-Phase Power Flow Based on Four-Conductor Current Injection Method for Unbalanced Distribution Networks", IEEE TRANSACTIONS ON POWER SYSTEMS, vol. 23, no. 2, 1 May 2008 (2008-05-01), USA, pages 494 - 503, XP011207990, ISSN: 0885-8950, [retrieved on 20220802] * |
Also Published As
| Publication number | Publication date |
|---|---|
| ES2921405A1 (en) | 2022-08-25 |
| ES2921405B2 (en) | 2023-03-01 |
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