JP5517646B2 - AC electric quantity measuring device and AC electric quantity measuring method - Google Patents

Description

  The present invention relates to an AC electricity quantity measuring device and an AC electricity quantity measuring method.

  In recent years, as the power flow in the power system has become more complex, the supply of highly reliable and high-quality power has been demanded. In particular, single-phase circuits and three-phase circuits that are essential for power system protection control devices are required. The need to improve the performance of AC electric quantity measuring devices in phase circuits and arbitrary multiphase circuits is increasing.

  The present inventor has already proposed that a countermeasure using a rotation vector on a complex plane is useful in order to improve control and protection performance of the power system (for example, Patent Document 1). This proposed method is based on the basic method of expressing AC voltage and AC current as a vector that rotates counterclockwise on a complex plane. Specifically, the voltage of the power system is measured at the timing of dividing one cycle of the reference wave equally by 4N (N is a positive integer), and the measured voltage is set to the real part coordinates, and the voltage measured 90 degrees ahead is measured. A voltage rotation vector having a tip with imaginary part coordinates is obtained, the chord length of the string connecting the tip of the voltage rotation vector and the tip of the previous voltage rotation vector is calculated, one timing and one period of the reference wave The voltage effective value is obtained from the voltage measured between before and the frequency of the power system is calculated from the phase angle of the voltage rotation vector calculated based on the added value of the chord length and the voltage effective value.

  On the other hand, there are some documents that disclose a method for measuring an alternating current electric quantity without using a rotation vector on the complex plane as described above (for example, Non-Patent Document 1, Patent Document 2 and the like). In this non-patent document 1, various AC electric quantity calculation formulas are presented. Patent Document 2 discloses a circuit configuration capable of realizing high-speed arithmetic processing and low cost of the apparatus in an apparatus that calculates reactive power from the AC current and AC voltage of the system under measurement.

JP 2004-361124 A Japanese Patent No. 3312006

“Development of Integral Method for Measuring RMS Active and Reactive Power in Single- and Multiphase Networks” pages 250-255, CEPSI 2002, Fukuoka.

  In the said nonpatent literature 1, system | strain rated frequency (50 Hz or 60 Hz) is used when measuring various alternating current electricity quantity. In Patent Document 2, it is necessary to perform a 90-degree phase shift operation on the instantaneous voltage waveform when calculating the reactive power amount. In this phase shift operation, a fixed sampling step size is used.

  Therefore, in the processes of Non-Patent Document 1 and Patent Document 2, an accurate value can be obtained only when the measurement target is operating at the system rated frequency. In other words, if the measurement target is operating outside the system rated frequency, a measurement error will occur, and the greater the degree of deviation from the system rated frequency, the greater the measurement error. It was.

  The present invention has been made in view of the above, and even when the measurement object is operating outside the system rated frequency, the AC electricity quantity measurement that enables highly accurate measurement of the AC electricity quantity is possible. It is an object of the present invention to provide an apparatus and an AC electric quantity measurement method.

  In order to solve the above-described problems and achieve the object, the AC electrical quantity measuring device according to the present invention is configured to sample at least four consecutive AC voltages to be measured at a sampling frequency that is twice or more the frequency of the AC voltage. A normalized voltage amplitude calculation unit that calculates a normalized voltage amplitude obtained by normalizing a voltage amplitude obtained by square integral calculation of the voltage instantaneous value data of a point with the amplitude value of the AC voltage, and is sampled at the sampling frequency, 4 voltages representing the tip-to-tip distance between two adjacent voltage instantaneous value data in at least 5 consecutive voltage instantaneous value data including the 4 voltage instantaneous value data used in calculating the normalized voltage amplitude Normalized voltage chord length calculation for calculating a normalized voltage chord length obtained by normalizing the voltage chord length obtained by the square integral calculation of the chord length instantaneous value data with the amplitude value of the AC voltage. A rotation phase angle calculation unit that calculates a rotation phase angle in one cycle time of sampling using the normalized voltage amplitude and the normalized voltage chord length, and using the normalized voltage amplitude and the rotation phase angle And an actual voltage amplitude calculator that calculates an actual voltage amplitude that is a true value of the AC voltage amplitude.

  The AC electricity quantity measuring apparatus according to the present invention has an effect that it is possible to measure the AC electricity quantity with high accuracy even when the measurement target is operating outside the system rated frequency.

FIG. 1 is a diagram illustrating voltage rotation vector groups on a complex plane. FIG. 2 is a diagram illustrating an example of a voltage rotation vector group and a current rotation vector group for explaining a method of calculating a normalized effective power effective value on a complex plane. FIG. 3 is a diagram illustrating an example of a voltage rotation vector group and a current rotation vector group for explaining a method of calculating a normalized reactive power effective value on a complex plane. FIG. 4 is a diagram showing a frequency-normalized voltage-current phase angle (N = 3, φ = 0) at a sampling frequency of 600 Hz. FIG. 5 is a diagram showing a normalized / actual voltage / current phase angle (N = 3, f = 50 Hz) at a sampling frequency of 600 Hz. FIG. 6 is a diagram illustrating a functional configuration of the AC electricity quantity measuring device according to the present embodiment. FIG. 7 is a flowchart showing the flow of processing in the AC electrical quantity measurement device. FIG. 8 is a model system diagram in this simulation. FIG. 9 is a diagram showing instantaneous values of the input voltage and input current in this simulation. FIG. 10 is a diagram showing the measurement result of the rotational phase angle in this simulation. FIG. 11 is a diagram showing the frequency measurement results in this simulation. FIG. 12 is a diagram showing the normalized voltage amplitude and the actual voltage amplitude in this simulation. FIG. 13 is a diagram showing the normalized current amplitude and the actual current amplitude in this simulation. FIG. 14 is a diagram showing the relationship between the normalized voltage-current phase angle and the actual voltage-current phase angle in this simulation. FIG. 15 is a diagram showing the normalized voltage-current phase angle and the actual voltage-current phase angle in this simulation. FIG. 16 is a diagram showing the normalized effective power effective value and the actual effective power effective value in this simulation. FIG. 17 is a diagram showing the normalized reactive power effective value and the actual reactive power effective value in this simulation.

  With reference to the accompanying drawings, an AC electric quantity measuring device according to an embodiment of the present invention will be described below. In addition, this invention is not limited by embodiment shown below.

<Embodiment>
In describing the AC electricity quantity measuring apparatus and the AC electricity quantity measuring method according to the present embodiment, first, the concept (algorithm) of the AC electricity quantity measuring method forming the gist of the present embodiment will be described, and then the present embodiment will be described. The configuration and operation of the AC electricity quantity measuring device according to the embodiment will be described.

  FIG. 1 is a diagram illustrating voltage rotation vector groups on a complex plane. In FIG. 1, on the complex plane, the current voltage rotation vector v (t) and the voltage rotation vector v (t−) at the time before the sampling 1 period T (time corresponding to the sampling frequency 1 step width) before the current time. T), voltage rotation vector v (t-2T) at the time point 2 sampling (2T) before the current time, voltage rotation vector v (t-3T) at the time point 3 sampling (3T) before the current time, and from the current time Also, the voltage rotation vector v (t−4T) at the time point before 4 sampling periods (4T) is shown. The four voltage rotation vectors form one voltage rotation vector group and rotate counterclockwise on the complex plane at the same rotation speed.

  Here, this voltage rotation vector group is reduced to one equivalent vector. The rotation axis of the reduced equivalent vector is at the center of symmetry between the voltage rotation vectors v (t−T) and v (t−2T), is referred to as a normalized voltage rotation axis, and is represented by the symbol Rv. The amplitude of this equivalent vector is referred to as a normalized voltage amplitude, and is calculated using the following equation.

Here, the sampling period (time of one sampling period) T in the above expression can be expressed by the following expression as an inverse number of the sampling frequency f _s .

In this specification, in order to facilitate the development of the calculation formula, instantaneous values {v _re (t), v _re (t−T),. (t), v (t−T),.

  With this expression, the real number instantaneous values of the four voltage rotation vectors belonging to the voltage rotation vector group can be expressed as the following equation.

In the above equation, V is an actual voltage amplitude, α is a rotation phase angle corresponding to one sampling period, and ω ₁ = 2πf ₁ is an angular frequency of the system. The actual voltage amplitude V is a true value of the AC voltage amplitude in the measurement target, and is a value that does not depend on the frequency of the AC voltage.

  Further, the rotational phase angle α is calculated as follows.

In the above equation, V _f2 is a normalized voltage chord length and is calculated using the following equation.

In the above equation (5), v ₂ (t), v ₂ (t−T), v ₂ (t−2T), and v ₂ (t−3T) are differential voltage instantaneous values, which are expressed by the following equations. Is done.

  The actual frequency is calculated as follows using the sampling period T and the rotational phase angle α obtained by the above equation (4).

  Further, if each expression of the above expression (3) is substituted into the right side of the above expression (1) and rearranged, the following expression is simplified.

  Further, if the above equation (8) is substituted into the equation (1), an analytical solution of the normalized voltage amplitude shown in the following equation can be obtained.

The normalized voltage amplitude is a voltage amplitude calculated using voltage rotation vector group data on the complex plane. In addition, the normalized voltage amplitude V _f has a property of being dependent on the frequency of the AC voltage, unlike the actual voltage amplitude V described above.

As shown in the above equation (9), it can be seen that the normalized voltage amplitude V _f is a result of multiplication of the actual voltage swing V and the sine function of the rotation phase angle α. Further, as a property thereof, the following relationship exists between the rotation speed, the rotation phase angle α, and the normalized voltage amplitude according to the value of the rotation phase angle α.

  When the rotational phase angle α is smaller than 90 degrees, the higher the rotational speed, the larger the rotational phase angle α and the normalized voltage amplitude.

When the rotation phase angle α is 90 degrees, the normalized voltage amplitude V _f and the actual voltage amplitude V are equal. For example, when the sampling frequency is 600 Hz and the input frequency to be measured is 150 Hz, the rotational phase angle α is 90 degrees, and the normalized voltage amplitude and the actual voltage amplitude are the same.

  On the other hand, when the rotational phase angle α is greater than 90 degrees, the faster the rotational speed, the larger the rotational phase angle α and the smaller the normalized voltage amplitude.

  When the rotational phase angle α is larger than 180 degrees, the frequency cannot be correctly measured, and the actual voltage amplitude V cannot be measured. The condition under which the frequency cannot be correctly measured is none other than satisfying the sampling theorem that the sampling frequency is required to be twice or more the measurement frequency.

  From the above equation (9), the actual voltage amplitude V is calculated using the following equation.

The normalized voltage amplitude V _f and the rotation phase angle α are calculated directly using the instantaneous time-series voltage values, respectively, and the actual voltage amplitude V is obtained. Further, the value obtained from the above equation is a true value that does not depend on the frequency of the AC voltage.

  Next, the concept of the sampling division number will be described. Table 1 is a list of sampling division numbers.

  In Table 1, the sampling division number N is shown in the leftmost column. Hereinafter, the sampling number of the voltage amplitude rotation vector group, the sampling number of the voltage chord length rotation vector group, and one sampling period that change according to the sampling division number N It represents the rotational phase angle of time. As can be seen from the change in the rotational phase angle shown in the rightmost column, the sampling division number N is a set value (settling value) for reducing the rotational phase angle (set to 1 / integer).

  FIG. 1 shows a voltage rotation vector group when the sampling division number N = 1.

  Moreover, if the voltage of Table 1 is replaced with a current, it can also be applied to the calculation of a current rotation vector. When the current and voltage are assumed to vibrate at the same frequency and the rotation phase angle obtained from the voltage calculation is used, the calculation of the current chord length rotation vector is not necessary.

Next, a normalized voltage amplitude calculation formula when the sampling division number takes an arbitrary value is proposed. The following expression is an expression representing the normalized voltage amplitude V _f corresponding to the voltage rotation vector group of the sampling division number N.

  Here, the real part instantaneous value of the voltage rotation vector v (t) of the sampling division number N is given by the following equation.

Similarly, the normalized voltage chord length V _f2 corresponding to the voltage rotation vector group of the sampling division number N is expressed as the following equation.

  Further, the differential voltage instantaneous value is expressed as the following equation by extending the above equation (6).

  By substituting the expression (12) into the right side of the normalized voltage amplitude calculation expression (11) and rearranging it, the following expression can be simplified.

  Further, if the above equation (15) is substituted into the equation (11), the calculation equation of the normalized voltage amplitude shown in the following equation is obtained.

  Here, paying attention to the equation (16), the following becomes clear as in the case of the sampling division number N = 1.

When N times the rotation phase angle α is 90 degrees, the normalized voltage amplitude V _f and the actual voltage amplitude V are equal. For example, in a measuring apparatus with a sampling frequency of 600 Hz and a sampling division number N = 3, when the input frequency to be measured is 50 Hz, N times the rotational phase angle α is 90 degrees (see Table 1), and the normalized voltage amplitude _Vf and actual voltage amplitude V take the same value.

  From the above equation (16), the actual voltage amplitude V is calculated using the following equation.

  If N times the rotational phase angle α is in the third quadrant (180 degrees to 270 degrees or a multiple thereof) or the fourth quadrant (270 degrees to 360 degrees or a multiple thereof), the value of sin (Nα) is negative. Therefore, an equation that takes the absolute value of sin (Nα) is used.

The relationship between the AC voltage effective value V _eff and the actual voltage amplitude V is as follows.

  The actual current amplitude I can also be measured by the same method as that for the actual voltage amplitude V. Specifically, the actual current amplitude I is as follows.

First, the normalized current amplitude I _f corresponding to the current rotation vector group sampling division number N is expressed by the following equation.

  Similarly to the equation (17), the actual current amplitude I is calculated using the following equation.

  Since it is assumed that the current is oscillating at the same frequency as the voltage, the actual current amplitude I may be calculated using a value N times the rotation phase angle α obtained by the voltage rotation vector group. Absent.

The relationship between the AC current effective value I _eff and the actual current amplitude I is as follows.

  Next, a method for calculating the active power and reactive power of the AC single-phase circuit will be described with reference to FIGS. First, FIG. 2 is a diagram illustrating an example of a voltage rotation vector group and a current rotation vector group for explaining a method of calculating a normalized effective power effective value on a complex plane. Normalized effective power effective value is the effective value of active power calculated using each data of voltage rotation vector group and current rotation vector group on the complex plane, and it depends on the frequency of AC voltage and AC current. There is a nature of being. The normalized effective power effective value is calculated using the following equation.

  Further, the real part instantaneous value of the voltage rotation vector is as shown in the above equation (3), and it will be described again here.

  On the other hand, the real part instantaneous value of the current rotation vector can be expressed as follows.

Here, if the real part instantaneous values of the voltage and current expressed by the above equations (3) and (23) are substituted into the above equation (22) and rearranged, the normalized effective power effective value P _f is It is simplified like the formula.

The above result is because the voltage rotation vector and the current rotation vector have symmetry on the complex plane, and this relationship is established as long as the voltage rotation vector and the current rotation vector are used. That is, when calculating the normalized effective power effective value P _f based on the voltage rotation vector and the current rotation vector, the following equation is established.

  FIG. 3 is a diagram illustrating an example of a voltage rotation vector group and a current rotation vector group for explaining a method of calculating a normalized reactive power effective value on the complex plane. Normalized reactive power effective value is the effective value of reactive power calculated using each data of voltage rotation vector group and current rotation vector group on the complex plane, and it depends on the frequency of AC voltage and AC current. There is a nature of being. The normalized reactive power effective value is calculated using the following equation.

Here, if the real part instantaneous values of the voltage and current shown in the above equations (3) and (23) are substituted into the above equation (26) and rearranged, the normalized reactive power effective value Q _f is It is simplified like the formula.

The above result is because the voltage rotation vector and the current rotation vector have symmetry on the complex plane, and this relationship is established as long as the voltage rotation vector and the current rotation vector are used. That is, when the normalized reactive power effective value Q _f is calculated based on the voltage rotation vector and the current rotation vector, the following equation is established.

From the above formulas (25) and (28), the phase angle between the alternating voltage and the alternating current calculated using the normalized active power effective value P _f and the normalized reactive power effective value Q _f (hereinafter referred to as “normalized”). Φ (referred to as “phase angle between voltage and current”) is calculated by the following equation.

  In the above equation (29), the following equation is established when the rotational phase angle α is 90 degrees.

In the first expression of the above expression (30), “P” and “Q” are the actual effective power effective value that is the true value of the effective power effective value in the measurement object and the true value of the reactive power effective value in the measurement object, respectively. The actual reactive power effective value is expressed by the second equation of the above equation (30). Φ _real is the phase angle between actual voltages and currents.

In addition, “P _f ” and “Q _f ” in the first equation of the above equation (30) are the normalized effective power effective value and the normalized reactive power effective value, respectively, and in the third equation of the above equation (30), expressed. Note that φ _f is a normalized voltage-current phase angle, and the normalized voltage-current phase angle φ _f and the actual voltage-current phase angle φ _real are different. In mathematical terms, they are elements of different topological spaces.

  Thus, when the rotational phase angle α is 90 degrees, the relationship between the normalized active power effective value and the normalized reactive power effective value is proportional to the relationship between the actual active power effective value and the actual reactive power effective value. More specifically, since the ratio between the cosine function and the sine function of the phase angle between the voltage and current in each phase space is the same, frequency correction is not necessary.

Also, the normalized effective power effective value P _f can be calculated similarly when the sampling division number takes an arbitrary value. The following equation is a formula for calculating the normalized effective power effective value P _f of the sampling division number N.

  The instantaneous voltage value and current instantaneous value of the sampling division number N are given by the following equations.

  Substituting the above equation (32) into equation (31), which is a calculation formula for the normalized effective power effective value, simplifies the following equation.

The above result is because the voltage rotation vector and the current rotation vector have symmetry on the complex plane, and this relationship is established as long as the voltage rotation vector and the current rotation vector are used. That is, when the normalized effective power effective value P _f of the sampling division number N is calculated based on the voltage rotation vector and the current rotation vector, the following equation is established.

Also, the normalized reactive power effective value Q _f can be calculated similarly when the sampling division number takes an arbitrary value. The following formula is a formula for calculating the normalized reactive power effective value Q _f of the sampling division number N.

  Substituting the above equation (32) into equation (35), which is a calculation formula for the normalized reactive power effective value, simplifies the following equation.

The above result is because the voltage rotation vector and the current rotation vector have symmetry on the complex plane, and this relationship is established as long as the voltage rotation vector and the current rotation vector are used. That is, when calculating the normalized reactive power effective value Q _f of the sampling division number N based on the voltage rotation vector and the current rotation vector, the following equation is established.

  From the above formulas (34) and (37), the relationship of the following formula is established between the normalized active power and the normalized reactive power of the sampling division number N.

  In the above equation (38), when N times the rotational phase angle α is 90 degrees, the relationship shown in the above equation (30) is established.

  Thus, when N times the rotation phase angle α is 90 degrees, the relationship between the normalized active power effective value and the normalized reactive power effective value is the relationship between the actual active power effective value and the actual reactive power effective value. Since the ratio of the cosine function and the sine function of the phase angle between the voltage and current in each phase space is equal, the frequency correction is not necessary.

  For example, in an electric power system with a rated frequency of 50 Hz, when the actually measured frequency is 50 Hz, if the sampling frequency is 600 Hz and the sampling division number N = 3, the rotational phase angle α is 30 degrees, and the rotational phase angle α is N Since the multiplication factor is 90 degrees, the ratio between the actual effective power effective value and the actual reactive power effective value is equal to the ratio between the normalized active power effective value and the normalized reactive power effective value, and frequency correction is not necessary. .

  Further, from the equation (38), the phase angle between the normalized voltage currents can be calculated using the following equation.

In the above formula (39), to change the phi to phi _f, the normalized voltage-current between the phase angle calculated by the equation is because it is dependent on the frequency.

  FIG. 4 is a diagram showing a frequency-normalized voltage-current phase angle (N = 3, φ = 0) at a sampling frequency of 600 Hz, and FIG. 5 is a normalized / real voltage-current phase angle (at a sampling frequency of 600 Hz). N = 3, f = 50 Hz).

As can be seen from FIG. 4, when the frequency f = 50 Hz, the normalized voltage-current phase angle φ _f matches the actual voltage-current phase angle φ. Further, as shown in FIG. 5, when the frequency f = 50 Hz, regardless of the value of the normalized voltage current between the phase angle phi _f, between the normalized voltage current between the phase angle phi _f and the actual voltage-current phase angle It can be seen that the values of φ match.

  Further, in a measuring apparatus with a sampling frequency of 600 Hz and a sampling division number N = 3, the correction calculation formula of the phase angle φ between the actual voltage and current when the system frequency is 50 Hz to 75 Hz is as follows.

In the above equation (40), φ _H90 is the upper limit value of the normalized voltage-current phase angle φ _f corresponding to the actual voltage-current phase angle φ of 90 degrees, and is expressed by the following equation.

  Further, in the measurement apparatus having the sampling frequency of 600 Hz and the sampling division number N = 3, the correction calculation formula of the phase angle φ between the actual voltage and current when the system frequency is 25 Hz to 50 Hz is as follows.

In the above equation (42), φ _L90 is the lower limit value of the normalized voltage-current phase angle φ _f corresponding to the actual voltage-current phase angle φ of 90 degrees, and is expressed by the following equation.

Finally, the correction direction is determined based on the values of the normalized active power and the normalized reactive power, and the actual voltage-current phase angle φ (here, φ _real ) is calculated using the following equation.

  In the above description, the correction calculation formula when the system frequency is 25 Hz to 75 Hz is shown, but the same correction calculation formula can be derived for other system frequencies.

  Further, the actual active power P and the actual reactive power Q are calculated using the following equations, respectively.

In the above equations (45) and (46), V is the actual voltage amplitude, I is the actual current amplitude, and φ _real is the phase angle between the actual current voltages.

  For comparison, a calculation formula (analysis solution) in the AC circuit theory of AC voltage, AC current, active power, reactive power, and apparent power in a single-phase circuit is shown below.

  First, the instantaneous voltage rotation vector is as follows.

  The instantaneous current rotation vector is as follows.

  The effective power effective value is as follows.

  The reactive power effective value is as follows.

  The apparent power effective value is as follows.

  As described above, the equations (45) and (46) derived in the present embodiment include equations (49) and (50) that are analytical solutions in a single-phase circuit, and the method according to the present embodiment. The correctness of this is proved.

  Next, the functional configuration and operation of the AC electricity quantity measuring apparatus according to the present embodiment will be described with reference to FIGS. 6 and 7. Here, FIG. 6 is a diagram showing a functional configuration of the AC electricity quantity measuring device 1 according to the present embodiment, and FIG. 7 is a flowchart showing a processing flow in the AC electricity quantity measuring device 1.

  As shown in FIG. 6, the AC electrical quantity measuring device 1 according to the present embodiment includes an AC voltage / current instantaneous value data input unit 2, a normalized voltage amplitude calculator 3, a normalized voltage chord length calculator 4, a rotation Phase angle calculation unit 5, frequency calculation unit 6, actual voltage amplitude calculation unit 7, normalized current amplitude calculation unit 8, actual current amplitude calculation unit 9, normalized active power effective value calculation unit 10, normalized reactive power effective value calculation Unit 11, normalized voltage / current phase angle calculation unit 12, actual voltage / current phase angle calculation unit 13, actual active power effective value calculation unit 14, actual reactive power effective value calculation unit 15, interface 16, and storage unit 17. It is prepared for. The interface 16 performs a process of outputting a calculation result or the like to a display device or an external device, and the storage unit 17 performs a process of storing measurement data, a calculation result, or the like.

  In the above configuration, the alternating voltage / current instantaneous value data input unit 2 performs a process of taking in the instantaneous voltage value and the instantaneous current value from the instrument transformer (PT) and the current transformer (CT) provided in the power system. This is performed (step S101). Note that the captured data of the instantaneous voltage value and the instantaneous current value are stored in the storage unit 17.

  The normalized voltage amplitude calculation unit 3 calculates the normalized voltage amplitude using a plurality of voltage instantaneous value data forming the voltage amplitude rotation vector group described above (step S102). The calculation processing of the normalized voltage amplitude can be explained as follows when it is described in a comprehensive manner including the above-described algorithm concept. That is, the normalized voltage amplitude calculation unit 3 satisfies, for example, the sampling theorem, for example, square integration of at least four consecutive instantaneous value data sampled at a sampling frequency twice or more the frequency of the AC voltage to be measured. A process of calculating the normalized voltage amplitude by normalizing the voltage amplitude obtained by the calculation with the amplitude value of the AC voltage is performed.

  Further, the normalized voltage string length calculation unit 4 calculates a normalized voltage string length using a plurality of voltage instantaneous value data forming the voltage amplitude rotation vector group described above (step S103). The normalized voltage chord length calculation unit 4 can also be described generally as follows. That is, the normalized voltage chord length calculation unit 4 is sampled at the sampling frequency and is adjacent to at least five consecutive instantaneous value data including the four instantaneous value data used in calculating the normalized voltage amplitude. Normalize the voltage chord length obtained by, for example, square integral calculation of the instantaneous value data (string length instantaneous value data) of the four points representing the distance between the tips of the two instantaneous values to be normalized with the amplitude value of the AC voltage. Processing to calculate the voltage chord length is performed.

  The rotational phase angle calculator 5 uses the normalized voltage amplitude calculated by the normalized voltage amplitude calculator 3 and the normalized voltage chord length calculated by the normalized voltage chord length calculator 4 to perform sampling 1 The rotational phase angle corresponding to the period is measured (step S104). The calculation formula of the rotational phase angle is as shown in the above equation (4).

  The frequency calculation unit 6 measures the frequency to be measured using the rotation phase angle and the sampling period calculated by the rotation phase angle calculation unit 5 (step S105). The calculation formula for frequency measurement is as shown in the above equation (7).

  The actual voltage amplitude calculation unit 7 calculates the actual voltage amplitude using the normalized voltage amplitude calculated by the normalized voltage amplitude calculation unit 3 and the rotation phase angle calculated by the rotation phase angle calculation unit 5. (Step S106). The calculation formula of the actual voltage amplitude is as shown in the above formulas (10) and (17).

  The normalized current amplitude calculation unit 8 calculates the normalized current amplitude using a plurality of current instantaneous value data forming the above-described current amplitude rotation vector group (step S107). In order to satisfy the sampling theorem, the normalized current amplitude calculation unit 8 performs, for example, a square integration operation of instantaneous value data of at least four consecutive points sampled at a sampling frequency twice or more the frequency of the alternating current to be measured. A process of calculating the normalized current amplitude by normalizing the obtained current amplitude with the amplitude value of the alternating current is performed.

  The actual current amplitude calculation unit 9 calculates the actual current amplitude using the normalized current amplitude calculated by the normalized current amplitude calculation unit 8 and the rotation phase angle calculated by the rotation phase angle calculation unit 5. (Step S108). The calculation formula of the actual current amplitude is as shown in the above equation (20).

  The normalized effective power effective value calculation unit 10 uses the plurality of voltage instantaneous value data forming the voltage amplitude rotation vector group and the plurality of current instantaneous value data forming the current amplitude rotation vector group, to normalize effective power effective value. Is calculated (step S109). More specifically, the normalized effective power effective value calculation unit 10 becomes the measurement target and the instantaneous value data of four consecutive points sampled at a sampling frequency twice or more the frequency of the AC voltage to be measured. The product (voltage / current product) of the instantaneous value data of three consecutive points sampled at a sampling frequency that is twice or more the frequency of the alternating current is calculated by, for example, square integration (the above (22) and (31) ) See formula).

  The normalized reactive power effective value calculation unit 11 uses the plurality of voltage instantaneous value data forming the voltage amplitude rotation vector group and the plurality of current instantaneous value data forming the current amplitude rotation vector group to normalize the reactive power effective value. Is calculated (step S110). More specifically, the normalized reactive power effective value calculation unit 11 is the measurement target and the instantaneous value data of three consecutive points sampled at a sampling frequency twice or more the frequency of the AC voltage to be measured. A product (voltage / current product) with three consecutive instantaneous value data sampled at a sampling frequency that is at least twice the frequency of the alternating current is calculated by, for example, square integration (the above (26) and (35) ) See formula).

  The normalized voltage-current phase angle calculation unit 12 includes a normalized active power effective value calculated by the normalized active power effective value calculation unit 10 and a normalized invalidity calculated by the normalized reactive power effective value calculation unit 11. The normalized voltage-current phase angle is calculated using the power effective value, the rotation phase angle calculated by the rotation phase angle calculation unit 5, and the sampling division number (step S111). The calculation formula for the normalized voltage-current phase angle is as shown in the above equation (39).

  The actual voltage-current phase angle calculation unit 13 calculates the normalized voltage-current phase angle calculated by the normalized voltage-current phase angle calculation unit 12, the frequency calculated by the frequency calculation unit 6, and the number of sampling divisions. By using this, the phase angle between the actual voltage and current is calculated (step S112). The calculation formula for the phase angle between the actual voltage and current is as shown in the above formulas (40) to (44).

  The actual effective power effective value calculation unit 14 includes the actual voltage amplitude calculated by the actual voltage amplitude calculation unit 7, the actual current amplitude calculated by the actual current amplitude calculation unit 9, and the phase angle calculation unit 13 between actual voltages and currents. The actual effective power effective value is calculated using the phase angle between the actual voltage and current calculated in step S113 (step S113). The calculation formula for the actual effective power effective value is as shown in the above equation (45).

  The actual reactive power effective value calculation unit 15 includes the actual voltage amplitude calculated by the actual voltage amplitude calculation unit 7, the actual current amplitude calculated by the actual current amplitude calculation unit 9, and the phase angle calculation unit 13 between actual voltages and currents. The actual reactive power effective value is calculated using the phase angle between the actual voltage and current calculated in step S114 (step S114). The calculation formula for the actual reactive power effective value is as shown in the above equation (46).

  In the last step S115, it is determined whether or not to end the above-described overall flow. If not (No in step S115), the processing from step S101 to S114 is repeated.

  Next, a simulation result performed on the AC electricity quantity measuring device of the present embodiment will be described. The parameters in this simulation are as shown in Table 2 below. As shown in Table 2, in this simulation, the AC voltage frequency is a non-integer.

  FIG. 8 is a model system diagram in this simulation. As shown in FIG. 8, in this simulation, an AC single phase circuit is shown as an example. Hereinafter, in the present embodiment, an AC single-phase circuit will be described as an example. However, the present invention is not limited to this, and can naturally be applied to a three-phase circuit and an arbitrary multiphase circuit. .

  FIG. 9 is a diagram showing the instantaneous values of the input voltage and input current in this simulation. A waveform v1 connected with a black triangle symbol represents an instantaneous voltage value, and a waveform i1 connected with a black square symbol represents an instantaneous current value. Represents.

  When the normalized voltage amplitude is calculated using the data of the voltage instantaneous value waveform v1 shown in FIG. 9, the following values are obtained. Note that the value of the normalized voltage amplitude obtained at this time is constant.

  Further, when the normalized voltage chord length is calculated using the data of the voltage instantaneous value waveform v1 shown in FIG. 9, the following values are obtained. Note that the value of the normalized voltage chord length obtained at this time is constant.

  Further, when the rotational phase angle corresponding to the input frequency of 62.07 Hz is calculated, the following values are obtained.

  Since the values of the normalized voltage amplitude and the normalized voltage chord length are constant, the calculated value of the rotational phase angle is also constant as shown in FIG. Further, since the calculated value of the rotational phase angle is constant, the calculated value of the frequency is also a constant value as shown in FIG. 11 and the following equation.

  As shown in the above equation (55), it can be seen that the input frequency parameter (62.07 Hz) in this simulation shown in Table 1 is correctly measured.

FIG. 12 is a diagram showing the normalized voltage amplitude and the actual voltage amplitude in this simulation, and also shows the same voltage instantaneous value waveform as that shown in FIG. 9 from the viewpoint of comparison. In FIG. 12, a waveform v1 connected with a black diamond symbol represents an instantaneous voltage value, a waveform V _f connected with a black square symbol represents a normalized voltage amplitude, and a waveform V connected with a black triangle symbol represents an actual voltage amplitude. Represents.

  When the actual voltage amplitude is calculated using the normalized voltage amplitude value obtained by the above equation (52) and the rotational phase angle value obtained by the above equation (54), the following values are obtained.

  The value of the above equation (56) matches the amplitude value of the input voltage shown in Table 1. As described above, although the normalized voltage amplitude value and the actual voltage amplitude value are different, the actual voltage amplitude is correctly measured by the frequency correction based on the rotation phase angle. In this case, if the input frequency is 50 Hz, the rotational phase angle α is 30 degrees, and the triple of the rotational phase angle α (N = 3) is 90 degrees. The amplitude is equal.

  Further, in this simulation, the AC voltage effective value is obtained as follows.

FIG. 13 is a diagram showing the normalized current amplitude and the actual current amplitude in this simulation, and also shows the same current instantaneous value waveform as that shown in FIG. 9 from the viewpoint of comparison. In FIG. 13, the waveform i1 connected with the black diamond symbol represents the instantaneous current value, the waveform _If connected with the black square symbol represents the normalized current amplitude, and the waveform I connected with the black triangle symbol represents the actual current amplitude. Represents.

When the normalized current amplitude _If is calculated using the data of the instantaneous current value waveform i1 shown in FIG. 13, I _f = 0.743172 (constant value) is obtained (the calculation formula is omitted). The value of this I _f, using the value of the rotational phase angle obtained in the above (54) wherein, when calculating the actual current amplitude is obtained the following values.

  The value of the above equation (58) matches the amplitude value of the input current shown in Table 1. As described above, although the value of the normalized current amplitude is different from the value of the actual current amplitude, the actual current amplitude is correctly measured by the frequency correction based on the rotation phase angle. In this case, when the input frequency is 50 Hz, the rotation phase angle α is 30 degrees, and the rotation phase angle α is three times (N = 3) is 90 degrees. The amplitude is equal.

  In this simulation, the AC current effective value is obtained as follows.

  In this simulation, when the normalized effective power effective value is calculated using the data of the instantaneous voltage value waveform v1 and the instantaneous current value waveform i1 shown in FIG. 9, the following values are obtained. The normalized effective power effective value obtained at this time is constant.

  Similarly, when the normalized reactive power effective value is calculated using the data of the voltage instantaneous value waveform v1 and the current instantaneous value waveform i1 shown in FIG. 9, the following values are obtained. Note that the normalized reactive power effective value obtained at this time is constant.

  Further, using the normalized effective power effective value obtained by the above equation (60), the normalized reactive power obtained by the above equation (61), and the rotational phase angle value obtained by the above equation (54). When the normalized voltage-current phase angle is calculated, the following values are obtained.

In this simulation, when the normalized voltage-current phase angle φ _H90 corresponding to the actual voltage-current phase angle φ of 90 degrees is calculated using the above equation (41), the following values are obtained.

Here, from the results of the above equations (62) and (63), the normalized voltage-current phase angle φ _f is smaller than φ _H90 which is the upper limit value of the normalized voltage-current phase angle φ _f , and the above (60 ) From the result of the equation, the normalized effective power effective value is also larger than zero. Therefore, when the phase angle φ _real between the actual voltages and currents is calculated using the above equation (40) that satisfies these conditions, the following values are obtained.

FIG. 14 is a diagram showing the relationship between the normalized voltage-current phase angle and the actual voltage-current phase angle in this simulation. In FIG. 14, the point K1 is φ _H90 which is the upper limit value of the normalized voltage-current phase angle φ _f , and the linear waveforms K2 and K3 represent the above equation (40). Further, referring to the point K4 on the linear waveform K2 corresponding to “−23.542 (Deg)” which is the calculation result of the above formula (62), φ = 20 (Deg), which is shown in Table 1. It matches the input data.

  FIG. 15 is a diagram showing the normalized voltage-current phase angle and the actual voltage-current phase angle in this simulation. In FIG. 15, a waveform dreal connecting black square symbols represents a phase angle between actual voltage currents, and a waveform dvi1 connecting black triangle symbols represents a phase angle between normalized voltage currents.

  In this way, even though the value of the normalized voltage-current phase angle is different from the value of the actual voltage-current phase angle, the actual voltage-current phase angle is correctly measured by the frequency correction based on the rotational phase angle. Yes. In this case, when the input frequency is 50 Hz, the rotation phase angle α is 30 degrees, and the rotation phase angle α is three times (N = 3) is 90 degrees, and the normalized voltage-current phase angle is And the phase angle between the actual voltage and current becomes equal.

  FIG. 16 is a diagram showing the normalized effective power effective value and the actual effective power effective value in this simulation. Now, when the actual active power is calculated by substituting the values of the input voltage current amplitude and the voltage-current phase angle into the equation (45), the following values are obtained.

  Although the presentation of the detailed calculation formula is omitted, based on the result ((65)) obtained using the steady AC circuit theory calculation formula ((45)) and the formula (60), the parameters shown in Table 2 are shown. These values agree with each other when compared with the effective power effective value calculated by using. Thus, although the normalized effective power effective value is different from the actual effective power effective value, the actual effective power effective value is correctly measured by the frequency correction based on the rotation phase angle. In this case, when the input frequency is 50 Hz, the rotation phase angle α is 30 degrees, and the rotation phase angle α is three times (N = 3) is 90 degrees, and the normalized effective power effective value and It becomes equal to the actual effective power effective value.

  FIG. 17 is a diagram showing the normalized reactive power effective value and the actual reactive power effective value in this simulation. Now, when the actual reactive power is calculated by substituting the values of the input voltage current amplitude and the voltage-current phase angle into the equation (46), the following values are obtained.

  Although the presentation of the detailed calculation formula is omitted, the parameters shown in Table 2 based on the result (Equation (66)) obtained using the steady AC circuit theory calculation equation (Equation (46)) and the equation (61) are shown. These values agree with each other when compared with the reactive power effective value calculated by using. Thus, although the normalized reactive power effective value is different from the actual reactive power effective value, the actual effective power effective value is correctly measured by the frequency correction based on the rotation phase angle. In this case, if the input frequency is 50 Hz, the rotational phase angle α is 30 degrees, and three times the rotational phase angle α (N = 3) is 90 degrees. The ratio of the reactive power effective value is equal to the ratio of the normalized active power effective value and the normalized reactive power effective value, and frequency correction is unnecessary.

  As described above, according to the AC electrical quantity measurement device of the present embodiment, the square integral of at least four consecutive instantaneous value data sampled at a sampling frequency that is twice or more the frequency of the AC voltage to be measured. The voltage amplitude obtained by the calculation is normalized with the amplitude value of the AC voltage and calculated as a normalized voltage amplitude, sampled at the sampling frequency, and includes instantaneous data of four points used in calculating the normalized voltage amplitude The voltage chord length obtained by the square integration calculation of the four chord length instantaneous value data representing the distance between the two adjacent instantaneous value data in the continuous instantaneous value data of at least five points is the amplitude value of the AC voltage. Normalized and calculated as the normalized voltage chord length, and using these normalized voltage amplitude and normalized voltage chord length, the rotation phase angle in one sampling period is calculated. Since the calculated rotation phase angle, normalized voltage amplitude, and normalized current amplitude are used to calculate the true values for AC voltage amplitude, AC current amplitude, active power, and reactive power, the measurement target is the system rated frequency. Even when the operation is out of the range, it is possible to measure the amount of alternating current electricity with high accuracy.

  In addition, according to the AC electrical quantity measuring apparatus of the present embodiment, the measured rotational phase angle, normalized voltage amplitude, normalized current amplitude, etc. are used without using the least square method that increases the calculation amount and the calculation load. AC voltage such as actual voltage amplitude and actual current amplitude can be calculated, and measured rotational phase angle, normalized voltage amplitude, normalized current amplitude, normalized active power effective value, normalized reactive power effective AC electric quantity such as actual effective power effective value and actual reactive power effective value can be calculated using the value, phase angle between normalized voltage and current, etc., enabling high-speed and highly accurate measurement of AC electric quantity. Become.

  As described above, the AC electricity quantity measuring device according to the present invention is useful as an invention that enables high-accuracy AC electricity quantity measurement even when the measurement target is operating outside the system rated frequency. It is.

DESCRIPTION OF SYMBOLS 1 AC electricity quantity measuring device 2 AC voltage / current instantaneous value data input part 3 Normalized voltage amplitude calculation part 4 Normalized voltage chord length calculation part 5 Rotation phase angle calculation part 6 Frequency calculation part 7 Actual voltage amplitude calculation part 8 Normalization Current amplitude calculation unit 9 Actual current amplitude calculation unit 10 Normalized effective power effective value calculation unit 11 Normalized reactive power effective value calculation unit 12 Normalized voltage current phase angle calculation unit 13 Real voltage current phase angle calculation unit 14 Actual effective Power effective value calculation unit 15 Actual reactive power effective value calculation unit 16 Interface 17 Storage unit

Claims (10)

The voltage amplitude obtained by the square integral calculation of at least four continuous voltage instantaneous value data obtained by sampling the AC voltage to be measured at a sampling frequency twice or more the frequency of the AC voltage is the amplitude value of the AC voltage. and the normalized voltage amplitude calculating unit for calculating a normalized voltage amplitude normalized by the AC voltage amplitude,
Between the adjacent two voltage instantaneous value data in at least five consecutive voltage instantaneous value data including the four voltage instantaneous value data sampled at the sampling frequency and used for calculating the normalized voltage amplitude. A normalized voltage chord length calculation unit for calculating a normalized voltage chord length obtained by normalizing a voltage chord length obtained by square integral calculation of four voltage chord length instantaneous value data representing a tip-to-tip distance with the AC voltage amplitude ;
A rotational phase angle calculator that calculates a rotational phase angle in one cycle time of sampling using the normalized voltage amplitude and the normalized voltage chord length;
An actual voltage amplitude calculation unit that calculates an actual voltage amplitude that is a true value of the AC voltage amplitude using the normalized voltage amplitude and the rotation phase angle;
An AC electric quantity measuring device comprising: Certain current amplitude determined by the square integral calculation of at least four points the current instantaneous value data successive sampled at least twice the sampling frequency of the frequency of the alternating current the alternating current to be measured in the amplitude of the alternating current A normalized current amplitude calculation unit that calculates a normalized current amplitude normalized by an alternating current amplitude ;
Between two adjacent current instantaneous value data in at least five continuous current instantaneous value data including four current instantaneous value data sampled at the sampling frequency and used for calculating the normalized current amplitude. A normalized current chord length calculation unit for calculating a normalized current chord length obtained by normalizing a current chord length obtained by square integral calculation of current chord length instantaneous value data of four points representing a distance between tips with the alternating current amplitude ;
A rotational phase angle calculation unit that calculates a rotational phase angle in one sampling period using the normalized current amplitude and the normalized current chord length;
An actual current amplitude calculating unit that calculates an actual current amplitude that is a true value of the alternating current amplitude using the normalized current amplitude and the rotation phase angle;
An AC electric quantity measuring device comprising: The voltage amplitude obtained by the square integral calculation of at least four continuous voltage instantaneous value data obtained by sampling the AC voltage to be measured at a sampling frequency twice or more the frequency of the AC voltage is the amplitude value of the AC voltage. and the normalized voltage amplitude calculating unit for calculating a normalized voltage amplitude normalized by the AC voltage amplitude,
Between the adjacent two voltage instantaneous value data in at least five consecutive voltage instantaneous value data including the four voltage instantaneous value data sampled at the sampling frequency and used for calculating the normalized voltage amplitude. A normalized voltage chord length calculation unit for calculating a normalized voltage chord length obtained by normalizing a voltage chord length obtained by square integral calculation of four voltage chord length instantaneous value data representing a tip-to-tip distance with the AC voltage amplitude ;
Certain current amplitude determined by the square integral calculation of at least four points the current instantaneous value data successive sampled at least twice the sampling frequency of the frequency of the alternating current the alternating current to be measured in the amplitude of the alternating current A normalized current amplitude calculation unit that calculates a normalized current amplitude normalized by an alternating current amplitude ;
A rotational phase angle calculator that calculates a rotational phase angle in one cycle time of sampling using the normalized voltage amplitude and the normalized voltage chord length;
An actual voltage amplitude calculation unit that calculates an actual voltage amplitude that is a true value of the AC voltage amplitude using the normalized voltage amplitude and the rotation phase angle;
An actual current amplitude calculating unit that calculates an actual current amplitude that is a true value of the alternating current amplitude using the normalized current amplitude and the rotation phase angle;
An AC electric quantity measuring device comprising: A frequency calculator that calculates the frequency of the AC voltage using the rotational phase angle;
Normalization obtained by normalizing the effective power effective value obtained by square-integral calculation of the product of the sampled voltage instantaneous value data of at least four consecutive points and the sampled current instantaneous value data of at least three points. A normalized active power effective value calculation unit for calculating an effective power effective value;
Normalization obtained by normalizing a reactive power effective value obtained by performing a square integration operation on a product of the sampled voltage instantaneous value data of at least three consecutive points and the sampled instantaneous current value data of at least three points. A normalized reactive power effective value calculation unit for calculating a reactive power effective value;
The normalized voltage-current phase angle between the normalized active power effective value and the normalized reactive power effective value using the normalized active power effective value, the normalized reactive power effective value, and the rotational phase angle A normalized voltage-current phase angle calculation unit for calculating
An actual voltage current that calculates a phase angle between actual voltage currents that is a true value of a phase angle between the AC voltage and the AC current, using the frequency calculated by the frequency calculation unit and the phase angle between the normalized voltage currents. An interphase angle calculation unit;
An actual active power effective value calculation unit that calculates an actual active power effective value that is a true value of the effective power effective value; and
The AC electric quantity measuring device according to claim 3, comprising: A frequency calculator that calculates the frequency of the AC voltage using the rotational phase angle;
Normalization obtained by normalizing the effective power effective value obtained by square-integral calculation of the product of the sampled voltage instantaneous value data of at least four consecutive points and the sampled current instantaneous value data of at least three points. A normalized active power effective value calculation unit for calculating an effective power effective value;
Normalization obtained by normalizing a reactive power effective value obtained by performing a square integration operation on a product of the sampled voltage instantaneous value data of at least three consecutive points and the sampled instantaneous current value data of at least three points. A normalized reactive power effective value calculation unit for calculating a reactive power effective value;
The normalized voltage-current phase angle between the normalized active power effective value and the normalized reactive power effective value using the normalized active power effective value, the normalized reactive power effective value, and the rotational phase angle A normalized voltage-current phase angle calculation unit for calculating
An actual voltage current that calculates a phase angle between actual voltage currents that is a true value of a phase angle between the AC voltage and the AC current, using the frequency calculated by the frequency calculation unit and the phase angle between the normalized voltage currents. An interphase angle calculation unit;
And the actual reactive power effective value calculating section for calculating an actual reactive power effective value is the true value of the reactive power effective value,
The AC electric quantity measuring device according to claim 3, comprising: A frequency calculator that calculates the frequency of the AC voltage using the rotational phase angle;
Normalization obtained by normalizing the effective power effective value obtained by square-integral calculation of the product of the sampled voltage instantaneous value data of at least four consecutive points and the sampled current instantaneous value data of at least three points. A normalized active power effective value calculation unit for calculating an effective power effective value;
Normalization obtained by normalizing a reactive power effective value obtained by performing a square integration operation on a product of the sampled voltage instantaneous value data of at least three consecutive points and the sampled instantaneous current value data of at least three points. A normalized reactive power effective value calculation unit for calculating a reactive power effective value;
The normalized voltage-current phase angle between the normalized active power effective value and the normalized reactive power effective value using the normalized active power effective value, the normalized reactive power effective value, and the rotational phase angle A normalized voltage-current phase angle calculation unit for calculating
An actual voltage current that calculates a phase angle between actual voltage currents that is a true value of a phase angle between the AC voltage and the AC current, using the frequency calculated by the frequency calculation unit and the phase angle between the normalized voltage currents. An interphase angle calculation unit;
An actual active power effective value calculation unit that calculates an actual active power effective value that is a true value of the effective power effective value; and
And the actual reactive power effective value calculating section for calculating an actual reactive power effective value is the true value of the reactive power effective value,
The AC electric quantity measuring device according to claim 3, comprising: The number of samplings in the data group including the four-point instantaneous value data to be processed by the normalized voltage amplitude calculation unit according to the sampling division number which is a set value for reducing the rotation phase angle in one sampling period And changing the number of samples in the data group including the instantaneous value data of 5 points to be processed by the normalized voltage chord length calculation unit,
Of the actual voltage amplitude, the actual current amplitude, the normalized active power effective value, the normalized reactive power effective value, and the normalized voltage / current phase angle, a calculated value that requires information on the rotational phase angle 7. The AC electrical quantity measurement device according to claim 4 , wherein the value is calculated by multiplying the value of the rotational phase angle by the sampling division number. 8. Obtaining the voltage amplitude of the AC voltage by square integration of at least four consecutive voltage instantaneous value data obtained by sampling the AC voltage to be measured at a sampling frequency that is twice or more the frequency of the AC voltage;
Normalizing the obtained voltage amplitude with an AC voltage amplitude that is an amplitude value of the AC voltage , and calculating as a normalized voltage amplitude;
Between the adjacent two voltage instantaneous value data in at least five consecutive voltage instantaneous value data including the four voltage instantaneous value data sampled at the sampling frequency and used for calculating the normalized voltage amplitude. Obtaining a voltage chord length by a square integral operation of four voltage chord length instantaneous value data representing the distance between the tips;
Calculating a normalized voltage string length obtained by normalizing the obtained voltage string length with the AC voltage amplitude ;
Calculating a rotational phase angle in one sampling period using the normalized voltage amplitude and the normalized voltage chord length;
Calculating an actual voltage amplitude that is a true value of the AC voltage amplitude using the normalized voltage amplitude and the rotation phase angle;
A method for measuring the amount of alternating current electricity, comprising: Obtaining a current amplitude of the alternating current by square integration calculation of at least four continuous current instantaneous value data obtained by sampling the alternating current to be measured at a sampling frequency that is twice or more the frequency of the alternating current;
Normalizing the obtained current amplitude with an alternating current amplitude which is an amplitude value of the alternating current and calculating as a normalized current amplitude;
Between two adjacent current instantaneous value data in at least five continuous current instantaneous value data including four current instantaneous value data sampled at the sampling frequency and used for calculating the normalized current amplitude. Obtaining a current chord length by a square integral operation of four points of current chord length instantaneous value data representing the distance between the tips;
Calculating a normalized current string length obtained by normalizing the obtained current string length by the alternating current amplitude ;
Calculating a rotation phase angle in one sampling period using the normalized current amplitude and the normalized current chord length;
Calculating an actual current amplitude that is a true value of the alternating current amplitude using the normalized current amplitude and the rotation phase angle;
A method for measuring the amount of alternating current electricity, comprising: Obtaining the voltage amplitude of the AC voltage by square integration of at least four consecutive voltage instantaneous value data obtained by sampling the AC voltage to be measured at a sampling frequency that is twice or more the frequency of the AC voltage;
Normalizing the obtained voltage amplitude with an AC voltage amplitude that is an amplitude value of the AC voltage , and calculating as a normalized voltage amplitude;
Between the adjacent two voltage instantaneous value data in at least five consecutive voltage instantaneous value data including the four voltage instantaneous value data sampled at the sampling frequency and used for calculating the normalized voltage amplitude. Obtaining a voltage chord length by a square integral operation of four voltage chord length instantaneous value data representing the distance between the tips;
Calculating a normalized voltage string length obtained by normalizing the obtained voltage string length with the AC voltage amplitude ;
Obtaining a current amplitude of the alternating current by square integration calculation of at least four continuous current instantaneous value data obtained by sampling the alternating current to be measured at a sampling frequency that is twice or more the frequency of the alternating current;
Normalizing the obtained current amplitude with an alternating current amplitude which is an amplitude value of the alternating current and calculating as a normalized current amplitude;
Calculating a rotational phase angle in one sampling period using the normalized voltage amplitude and the normalized voltage chord length;
Calculating an actual voltage amplitude that is a true value of the AC voltage amplitude using the normalized voltage amplitude and the rotation phase angle;
Calculating an actual current amplitude that is a true value of the alternating current amplitude using the normalized current amplitude and the rotation phase angle;
A method for measuring the amount of alternating current electricity, comprising:

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