RU2826221C1 - Method of determining complex value of technical losses of full power in power three-phase two-winding transformers used in urban and industrial power supply systems - Google Patents

Abstract

FIELD: power supply systems.

SUBSTANCE: invention relates to power supply systems, in particular to a method of determining a complex value of technical losses of full power in power three-phase two-winding transformers. Based on the transformer nameplate data, the rated current in the high voltage (HV) winding is calculated, active, total and inductive resistance of windings of power three-phase double-winding transformer, active and inductive resistance of HV winding and reduced active and inductive resistance of dissipation of winding of low voltage (LV), rated current of idle run (IR) are calculated. Using the value of rated current of IR, the total active, total and inductive resistance of the magnetization branch and the scattering branch of the HV winding of the transformer are calculated. Further, knowing the values of active and inductive resistances of the dispersion branch of the HV winding, the active and inductive resistances of the magnetization branch are found. Using the measuring instruments installed in the input cell, the LV supply bus of the transformer substation (TS), to which the final consumer of electrical energy (load) is connected, for each of three phases and for each harmonic component, starting from 1st to 40th, values of active power consumed by the load connected to the transformer, current strength in the LV winding of the transformer and the load and voltage at the terminals of the LV winding of the power three-phase two-winding transformer and the load, active, total and reactive (inductive) resistances from 1st to 40th harmonic components of the load are calculated for each phase connected to the terminals of the low-voltage transformer winding. Given the transformation ratio, the reduced active, reactive and complex impedances are found for each harmonic component of the load of each phase connected to the terminals of the low-voltage transformer. Knowing the previously calculated parameters of the T-shaped equivalent circuit of the transformer phases, for each harmonic component of each phase conditionally constant coefficients are calculated A _{1 ν}, A _{2 ν}, A _{3 ν}, B _{1 ν}, B _{2 ν}, B _{3 ν}, C _{1 ν}, C _{2 ν}, C _{3 ν}, D _{1 ν}, D _{2 ν}, D _{3 ν}. Using their values, as well as the values of the reduced active, total and reactive resistances for each harmonic component of the load of each phase, complex values of total power losses in transformer phases are calculated for each νharmonic component. By summing them, the complex value of total losses of full power in each phase of the transformer is found taking into account additional losses from higher harmonic components. By adding complex values of total losses of full power, calculated for each phase, complex value of technical losses of full power in power three-phase two-winding transformer is calculated taking into account additional losses from higher harmonic components.

EFFECT: higher accuracy.

1 cl, 9 dwg

Description

The invention relates to power supply systems, namely to urban and industrial power supply systems, in particular to a method for determining the complex value of technical losses of total power in three-phase two-winding power transformers used for transporting electrical energy to the end consumer.

The invention makes it possible to determine the complex value of technical losses of total power in three-phase two-winding power transformers used for transporting electrical energy to the end consumer, in order to assess the efficiency of their operation.

The invention can be used for reliable and prompt detection of three-phase two-winding power transformers with an increased level of complex value of technical losses of total power, which allows promptly taking technical and organizational measures to eliminate the causes of losses. The invention can be used in the construction of automated information and measuring systems for technical metering of electricity as their additional function.

Electricity consumption is associated with the use of a wide range of different household and industrial electrical appliances that use direct current voltage for their operation, obtained by rectifying alternating current voltage and smoothing it using a capacitive filter [Chernysheva D.V. Influence of non-sinusoidality of voltage and current on elements of the power supply system // Bulletin of the South-West State University. Engineering and Technology. 2012. No. 2-1. Pp. 100-105]. For the power supply system, the specified equipment represents a non-linear electrical load and consumes non-sinusoidal current. This creates distortions in the power supply network and voltage distortion, which affects other equipment receiving electricity from a common source [Prischepa D.N., Zagrutdinov Yu.A. Negative impact of non-linear load on the power supply system // Proceedings of the A.F. Mozhaisky Military Space Academy. [2014. No. 644. P. 199-203]. In recent years, there has been a significant deterioration in the quality of electrical energy in the networks of industrial and non-industrial consumers [Boyarskaya N.P., Temerbaev S.A., Dovgun V.P., Kabak A.L., Kolmakov V.O. Analysis of the spectral composition of currents and voltages of LED and gas-discharge light sources // Bulletin of the Krasnoyarsk State Agrarian University. 2013. No. 8. P. 180-184]. Deterioration in the quality of electricity in distribution networks is typical for most developed countries, since there are fewer and fewer electrical receivers with linear volt-ampere characteristics [Leshchinskaya T.B., Taranov M.M. Study of emission currents of household electrical receivers // Bulletin of the Federal State Educational Institution of Higher Professional Education "Moscow State Agroengineering University named after V.P. Goryachkina". 2009. No. 2. P. 54-61.].

Power supply cannot be implemented without the use of transformers, with the help of which electric power is economically transmitted over a distance and rationally distributed between consumers. Transformers, being an integral part of the power system, are present at all voltage levels and play the role of a matching element between the network and the consumer. Higher harmonic components of current create additional losses in the transformer windings and additional losses due to eddy currents in the magnetic circuit. All this leads to a decrease in the efficiency of electric power transmission processes and a reduction in the estimated service life of electrical equipment and electrical networks due to accelerated thermal and electrical aging of the insulation [Guzhov S., Polischuk A., Turkin A. Street lighting networks with semiconductor control devices and light sources: control and calculation of modes // Semiconductor lighting technology. 2009. No. 1. P. 42-46].

A method is known for determining technological losses of electrical energy in the equipment of traction substations included in the traction power supply system [Patent RU 2573098, IPC B60M 3/00, G01R 21/133, published. 20.01.2016], consisting of measurements at a DC traction substation of voltage and current at a voltage level of 3.3 kV, characterized in that measurements at the input of the traction substation converters and, in addition to them, amplification devices are carried out synchronously with measurements on the high-voltage side of the AC converter transformer, the measurement results are transmitted to the data processing server via a corporate data transmission network from traction substations, on the basis of which technological losses of electric power for traction in the equipment of the traction substation for the analyzed period of time are determined as the difference between the consumption of electric power determined according to the data of the automated commercial metering system and the consumption of electric power according to the data of the measuring systems installed at the inputs of the converter units of DC traction substations, as well as the amplification devices of the traction power supply system.

The main disadvantage of the described method is the fact that only the energy consumption indicators are recorded and analyzed, based on the difference of which the process losses are determined by measurement intervals, which does not allow the use of the specified method for an arbitrary point in time at different load values.

The specified method also contains a drawback associated with a high error in determining technical losses, since when assessing losses in the power supply system based on the difference in electricity consumption, it is not possible to isolate technical losses, due to the presence of commercial and instrumental losses, as well as electricity consumption for the substation's own needs.

A method is known for determining the complex value of total technical losses of total power in urban and industrial power supply systems [Patent RU 2815674, IPC G01R 21/133, SPC G01R 21/133, published. 19.03.2024], adopted as a prototype, consisting in the fact that the nominal current in the high-voltage winding is calculated, then the active, total and inductive resistances of the windings are calculated, after which the active and inductive leakage resistances of the high-voltage winding and the reduced active and inductive leakage resistances of the low-voltage winding are calculated, then the values of the complex total leakage resistance of the high-voltage winding and the reduced complex total leakage resistance of the low-voltage winding are determined, after which the nominal no-load current of the three-phase two-winding power transformer is calculated and, using its value, the total active, total and inductive resistances of the magnetization branch and the leakage branch of the high-voltage winding are calculated, after which, knowing the values of the active and inductive resistances of the leakage branch of the high-voltage winding, the active and inductive resistances of the magnetization branch are found and the complex total resistance of the magnetization branch is determined, based on the linear parameters of the power transmission line, included in the power supply system, find the active and inductive resistances, as well as the complex full impedance of the power transmission line, after which calculate the total complex full impedance of the power transmission line and the leakage of the high-voltage winding, based on the data synchronously measured using measuring instruments or specified arbitrarily, determine the voltage of the supply network at the connection point of the power transmission line of the power supply system, the active power consumed by the load connected to the three-phase two-winding power transformer, the current in the lower voltage winding and the load and the voltage at the terminals of the lower voltage winding, after which calculate the active, full and inductive resistances of the load connected to the terminals of the lower voltage winding, after which calculate the value of the transformation ratio of the three-phase two-winding power transformer, and, using this value, find the value of the reduced active and inductive resistances of the load, as well as the complex full impedance of the load connected to the terminals of the lower voltage winding, then calculate the reduced complex full leakage impedance of the lower voltage winding and the load and perform calculation of the complex value of total technical losses of total power in one phase of the power supply system.

The disadvantage of the described method is the fact that when using it, it is not possible to isolate from the complex value of the total technical losses of total power in the power supply system the amount of losses separately in the three-phase two-winding power transformer.

The specified method also contains a drawback associated with the error in determining the technical losses of total power, since when assessing losses, additional losses associated with the presence of higher harmonic components in the power supply system, caused by the presence of a non-linear electrical load consuming a non-sinusoidal current, are not taken into account.

The objective of the invention is to consider as a whole the combination of a three-phase two-winding power transformer and a load, connected by a common operating mode, using in calculations known passport data of power transformers and the values of active power, current and voltage measured at the terminals of the low-voltage winding of a three-phase two-winding power transformer for each harmonic component.

The technical result consists in increasing the accuracy of determining the complex value of technical losses of total power in three-phase two-winding power transformers used in urban and industrial power supply systems.

The technical result is achieved due to the fact that in accordance with the method for determining the complex value of technical losses of total power in three-phase two-winding power transformers used in urban and industrial power supply systems based on the passport data of the three-phase two-winding power transformer included in the power supply system, the nominal current in the high-voltage (HV) winding is calculated, then the active, total and inductive resistances of the windings of the three-phase two-winding power transformer are calculated, after which the active and inductive leakage resistances of the HV winding and the reduced active and inductive leakage resistances of the low-voltage (LV) winding of the three-phase two-winding power transformer are calculated. After that, the nominal no-load current (NLC) of the three-phase two-winding power transformer is calculated and, using its value, the total active, total and inductive resistances of the magnetization branch and the leakage branch of the high-voltage winding of the three-phase two-winding power transformer are calculated. Next, knowing the values of the active and inductive resistances of the leakage branch of the high-voltage winding, the active and inductive resistances of the magnetization branch are found. Using the values of active power consumed by the load connected to the three-phase two-winding power transformer, the current in the LV winding of the three-phase two-winding power transformer and the load, and the voltage at the terminals of the LV winding of the three-phase two-winding power transformer and the load, measured by measuring instruments installed in the input cell, the LV supply bus of the transformer substation (TS), to which the end consumer of electric energy (load) is connected, for each of the three phases and for each harmonic component starting from the 1st to the 40th, the voltage at the terminals of the LV winding of the three-phase two-winding power transformer, the active, total, and reactive (inductive) resistances of the fundamental harmonic component of the load for one phase connected to the terminals of the LV winding of the three-phase two-winding power transformer are calculated. Then the active, reactive, and total resistances are calculated for the remaining harmonic components of the load of this phase from the 2nd to the 40th. Knowing the transformation ratio of a three-phase two-winding power transformer, we find the reduced active, reactive and complex total impedance for each harmonic component of the load of one phase connected to the terminals of the LV winding of a three-phase two-winding power transformer. Knowing the previously calculated parameters of the T-shaped equivalent circuit of one phase of a three-phase two-winding power transformer, the following values (α _ν , β _ν , γ _ν , δ _ν , θ _ν , ε _ν , τ _ν and μ _ν ) are calculated for each harmonic component, which are then used to calculate the conditionally constant coefficients ( A _{1 ν} , A _{2 ν , A 3} ν _, B _{1 ν} , B _{2 ν} , B _{3 ν} , C 1 ν , C 2 _ν , C _{3 ν} , D _{1 ν} , D _{2 ν} , D _{3 ν} ) for each harmonic component. Using the calculated conditionally constant coefficients for each harmonic component, as well as the values of the reduced active, total and reactive resistances for each harmonic component of the load of one phase, the complex values of the total power losses in one phase of the three-phase two-winding power transformer are calculated for each harmonic component, and then, summing them up, the complex value of the total total power losses in one phase of the three-phase two-winding power transformer is found, taking into account additional losses from higher harmonic components. For the remaining two phases, using as initial data the values of active power consumed by the load connected to the two-winding power transformer, the current in the LV winding of the three-phase two-winding power transformer and the load, and the voltage at the terminals of the LV winding of the three-phase two-winding power transformer and the load, measured with the measuring devices installed in the input cell, the LV TP supply bus, for each harmonic component starting from the 1st to the 40th, similar calculation actions are carried out to those described earlier for one phase, in order to obtain complex values of the total losses of apparent power in each of these phases, taking into account additional losses from higher harmonic components. Having added the complex values of the total losses of apparent power calculated for each phase of the three-phase two-winding power transformer taking into account additional losses from higher harmonic components, the complex value of technical losses of apparent power in the three-phase two-winding power transformer is calculated taking into account additional losses from higher harmonic components.

Fig. 1 shows the equivalent circuit of one phase of the power supply system, which is a combination of a three-phase two-winding power transformer and a non-sinusoidal load.

Fig. 2 shows Table 1, which contains the passport data of a three-phase two-winding power transformer.

Fig. 3 shows Table 2, which provides the calculated parameters of the equivalent circuit for the phase of a three-phase two-winding power transformer.

Fig. 4 shows Table 3, which contains data measured for phase L1 for harmonic components of the load from 1st to 40th using an electric power quality analyzer installed in the input cell of the LV power supply busbar of the transformer substation.

Fig. 5 shows Table 4, which provides the calculated values of the reduced active and reactive resistance for phase L1 for harmonic components of the load from the 1st to the 40th, connected to the terminals of the LV winding of a three-phase two-winding power transformer.

Fig. 6 shows Table 5, which provides the calculated values of the conditionally constant coefficients for each harmonic component from the 1st to the 40th, calculated for the phase of a three-phase two-winding power transformer.

Fig. 7 shows Table 6, which provides complex values of total power losses in one phase of a three-phase two-winding power transformer for each harmonic component from the 1st to the 40th.

Fig. 8 shows Table 7, which contains data measured for phase L2 for harmonic components of the load from 1st to 40th using an electric power quality analyzer installed in the input cell of the LV supply busbar of the transformer substation.

Fig. 9 shows Table 8, which contains data measured for phase L3 for harmonic components of the load from 1st to 40th using an electric power quality analyzer installed in the input cell of the LV power supply busbar of the transformer substation.

Let's consider an example of implementing the method.

Based on the passport data of a three-phase two-winding power transformer: no-load losses (Δ Р _XX, kW), short-circuit (SC) losses (Δ Р _KS , kW), rated power ( S _н , kVA), short-circuit voltage ( u _KS , %), no-load current ( I _XX , %), rated voltage of the high-voltage winding ( U _HV , kV), rated voltage of the low-voltage winding ( U _LV , kV), which is part of the power supply system, the rated current in the high-voltage winding is calculated:

, A. (1)

Next, the active resistance of the windings of a three-phase two-winding power transformer is calculated:

, Ohm, (2)

total resistance of windings of a three-phase two-winding power transformer:

, Ohm, (3)

and the inductive resistance of the windings of a three-phase two-winding power transformer:

, Ohm. (4)

To implement the method, a T-shaped equivalent circuit of a three-phase two-winding power transformer is used (Fig. 1), which is assumed to be symmetrical, assuming that the complex value of the total resistance of the high-voltage winding is equal to the reduced complex value of the total resistance of the low-voltage winding. This assumption is close to reality and does not introduce significant errors into the calculations [Bruskin D.E., Zorokhovich A.E., Khvostov V.S. Electrical Machines: In 2 parts. Part 1: Textbook for electrical engineering specialty universities. - 2nd ed. revised and enlarged - Moscow: Higher. school, 1987, p. 78].

Next, the active leakage resistance of the high-voltage winding and the reduced active leakage resistance of the low-voltage winding of a three-phase two-winding power transformer are calculated:

, Ohm, (5)

inductive leakage reactance of the high voltage winding and reduced inductive leakage reactance of the low voltage winding of a three-phase two-winding power transformer:

, Ohm. (6)

After this, the nominal current of the idle three-phase two-winding power transformer is calculated:

, A. (7)

Next, using the obtained value of the nominal current XX, the total active resistance of the magnetization branch and the leakage branch of the high-voltage winding of a three-phase two-winding power transformer is calculated:

, Ohm, (8)

the total impedance of the magnetization branch and the leakage branch of the high-voltage winding of a three-phase two-winding power transformer:

, Ohm, (9)

and the total inductive resistance of the magnetization branch and the leakage branch of the high-voltage winding of a three-phase two-winding power transformer:

, Ohm. (10)

Knowing the values of the active and inductive resistances of the leakage branch of the high-voltage winding, we find the active resistance of the magnetization branch of a three-phase two-winding power transformer:

, Ohm, (11)

and the inductive resistance of the magnetization branch of a three-phase two-winding power transformer:

, Ohm. (12)

Based on the data (active power consumed by the load connected to the power technical phase two-winding transformer ( P _{n ν} , W), current in the LV winding of the three-phase two-winding power transformer and the load ( I _{n ν} , A); voltage at the terminals of the LV winding of the three-phase two-winding power transformer and the load ( U _{n ν} , V), where ν is the ordinal number of the harmonic component) measured for each of the three phases and for each harmonic component starting from the 1st to the 40th using measuring devices (electrical energy quality analyzers, electrical network parameter meters) installed in the input cell, the LV supply bus of the transformer substation (TS) to which the end consumer of electrical energy (load) is connected, the active resistance of the fundamental (ν = 1) harmonic component of the load is calculated for one phase connected to the terminals of the LV winding of the power three-phase two-winding transformer:

, Ohm, (13)

the total resistance of the fundamental harmonic component of the load of one phase connected to the terminals of the LV winding of a three-phase two-winding power transformer:

, Ohm, (14)

and the reactive (inductive) resistance of the fundamental harmonic component of the load of one phase, connected to the terminals of the LV winding of a three-phase two-winding power transformer:

, Ohm. (15)

Calculations of active, total and reactive resistances, similar to those performed earlier for the fundamental harmonic component of the load of one phase, are carried out for the remaining harmonic components of the load of this phase from the 2nd to the 40th, obtaining the values r _{н 2…40} , Z _{н 2…40} and x _{н 2…40} .

Knowing the transformation ratio of a power two-phase two-winding transformer equal to

o.e., (16)

find the reduced active resistance for each harmonic component of the load of one phase connected to the terminals of the LV winding of a three-phase two-winding power transformer:

, Ohm, (17)

and the reduced reactance for each harmonic component of the load of one phase connected to the terminals of the LV winding of a three-phase two-winding power transformer:

, Ohm, (18)

and also the reduced complex impedance for each harmonic component of the load of one phase connected to the terminals of the LV winding of a three-phase two-winding power transformer:

. (19)

Knowing the previously calculated parameters of the T-shaped equivalent circuit of one phase of a three-phase two-winding power transformer (Fig. 1), the following values are calculated for each harmonic component:

; ; ;

; ; ;

; .

Using the calculated values (α _ν , β _ν , γ _ν , δ _ν , θ _ν , ε _ν , τ _ν and μ _ν ) for each harmonic component, in order to calculate the losses in a three-phase two-winding power transformer taking into account additional losses from higher harmonic components, conditionally constant coefficients are calculated for each harmonic component:

;

; ; ;

;

; ;

;

;

; ; .

Using the calculated conditionally constant coefficients for each harmonic component, as well as the values of the reduced active, total and reactive resistances for each harmonic component of the load of one phase, the complex values of the total power losses in one phase of a three-phase two-winding power transformer are calculated for each harmonic component:

. (20)

By summing up the complex values of the total power losses in a three-phase two-winding power transformer, calculated for each harmonic component, we find the complex value of the total total power losses in one phase of a three-phase two-winding power transformer, taking into account additional losses from higher harmonic components

. (21)

For the remaining two phases ( L 2 and L 3), using as initial data the measured active power consumed by the load connected to the two-winding power transformer, the current in the LV winding of the three-phase two-winding power transformer and the load, and the voltage at the terminals of the LV winding of the three-phase two-winding power transformer and the load, for each harmonic component starting from the 1st to the 40th, calculation actions similar to those described earlier for phase L 1 are carried out in order to obtain the values And .

By adding up the complex values of the total losses of total power calculated for each phase of a three-phase two-winding power transformer taking into account additional losses from higher harmonic components, the complex value of technical losses of total power in a three-phase two-winding power transformer is calculated taking into account additional losses from higher harmonic components:

.

The parameters ( P _{n ν} , I _{n ν} , U _{n ν} ), measured using measuring instruments for each phase, can be set arbitrarily, which will allow calculating the total power losses in a three-phase two-winding power transformer, taking into account additional losses from higher harmonic components, for an arbitrary moment in time at different load values.

Let us consider an example of the implementation of the method for determining the complex value of technical losses of total power in three-phase two-winding power transformers used in urban and industrial power supply systems, using the example of a power supply system for which the following are adopted:

- three-phase two-winding power transformer of the TMZ brand with a rated power of 1000 kVA, with rated winding voltages of HV - 10 kV and LV - 0.4 kV;

- non-sinusoidal load.

The single-line electrical circuit diagram of the power supply system under consideration is shown in (Fig. 1), and the nominal parameters of the three-phase two-winding power transformer used to transport electrical energy to the end consumer, operated in the power supply system under consideration, are given in Table 1.

Using the nominal parameters of the three-phase two-winding power transformer given in Table 1 in accordance with expression (1), the value of the nominal current in the HV winding is calculated. Using formulas (2-4), the active, total and inductive resistances of the windings of the three-phase two-winding power transformer are calculated. Using formulas (5) and (6), the active and inductive leakage resistances of the HV winding and the reduced active and inductive leakage resistances of the LV winding of the three-phase two-winding power transformer are calculated. Using expression (7), the nominal no-load current of the three-phase two-winding power transformer is calculated. Using formulas (8-10), the total active, total and inductive resistances of the magnetization branch and the leakage branch of the HV winding of the three-phase two-winding power transformer are calculated. Using formulas (11) and (12), knowing the values of the active and inductive resistances of the leakage branch of the high-voltage winding, we calculate the active and inductive resistances of the magnetization branch of a three-phase two-winding power transformer.

The calculated parameters of the equivalent circuit for one phase of a three-phase two-winding power transformer, shown in Fig. 1, are given in Table 2.

The measured data obtained using the power quality analyzer installed in the input cell of the LV power supply busbar of the transformer substation for phase L 1 for harmonic components of the load from 1st to 40th are given in Table 3.

Using the measured data given in Table 3, in accordance with expressions (13-15), the active, full and reactive resistances of the fundamental harmonic component of the load of one phase connected to the terminals of the LV winding of a three-phase two-winding power transformer are calculated. Similarly, using expressions (13-15) and the measurement results for the remaining harmonic components given in Table 3, the active, full and reactive resistances of the harmonic components of the load from the 2nd to the 40th of one phase connected to the terminals of the LV winding of a three-phase two-winding power transformer are calculated.

Using the values of the nominal voltages of the HV and LV windings given in Table 1, the value of the transformation ratio of the power three-phase two-winding transformer is calculated using formula (16), which will be 25. Using the value of the transformation ratio and expressions (17) - (19), the reduced active, reactive and total resistance are calculated for each harmonic component of the load of one phase connected to the terminals of the LV winding of the power three-phase two-winding transformer.

The calculated values of the reduced active and reactive resistance for phase L 1 for harmonic components of the load from the 1st to the 40th, connected to the terminals of the LV winding of a three-phase two-winding power transformer are given in Table 4.

Knowing the previously calculated parameters of the equivalent circuit of one phase of a three-phase two-winding power transformer, presented in Table 2, the values (α _ν , β _ν , γ _ν , δ _ν , θ _ν , ε _ν , τ _ν and μ _ν ) are calculated for each harmonic component, and, using these values, the conditionally constant coefficients are calculated for each harmonic component ( A _{1 ν} , A _{2 ν} , A _{3 ν} , B _{1 ν} , B 2 ν , B _{3 ν} , C _{1 ν} , C _{2 ν} , C _{3 ν} , D _{1 ν} , D _{2 ν} , D _{3 ν} ). The calculated values of the conditionally constant coefficients for each harmonic component from the 1st to the 40th, calculated for the phase of a three-phase two-winding power transformer, are given in Table 5.

Using the calculated conditionally constant coefficients for each harmonic component given in Table 5, as well as the values of the reduced active, total and reactive resistances for each harmonic component of the load of one phase given in Table 4, in accordance with formula (20), the complex values of the total power losses in one phase of the three-phase two-winding power transformer are calculated for each harmonic component. The complex values of the total power losses in one phase of the three-phase two-winding power transformer for each harmonic component from the 1st to the 40th are given in Table 6.

By summing up the complex values of the total power losses in a three-phase two-winding power transformer, calculated for each harmonic component from the 1st to the 40th, given in Table 6, in accordance with formula (21), we find the complex value of the total total power losses in one phase of a three-phase two-winding power transformer, taking into account additional losses from higher harmonic components, which will be:

V·A.

For the remaining two phases ( L 2 and L 3), using as initial data the measured active power consumed by the load connected to the two-winding power transformer, the current in the LV winding of the three-phase two-winding power transformer and the load, and the voltage at the terminals of the LV winding of the three-phase two-winding power transformer and the load, for each harmonic component starting from the 1st to the 40th, given in Table 7 and Table 8, calculation actions similar to those described earlier for phase L 1 are carried out. Based on the results of the calculations performed

V·A.

V·A.

By adding up the complex values of the total losses of total power calculated for each phase of a three-phase two-winding power transformer taking into account additional losses from higher harmonic components, the complex value of technical losses of total power in a three-phase two-winding power transformer is calculated taking into account additional losses from higher harmonic components:

V·A.

The given description of the implementation confirms the achievement of the technical result - the possibility of using the specified method, in particular, for an arbitrary moment in time at different load values and to isolate technical losses in a three-phase two-winding power transformer, as well as to increase the accuracy of determining the complex value of technical losses of total power in three-phase two-winding power transformers operated in urban and industrial power supply systems, due to the consideration of additional losses associated with the presence of higher harmonic components in the power supply system, caused by the presence of a non-linear electrical load consuming a non-sinusoidal current.

Claims (1)

A method for determining the complex value of technical losses of apparent power in three-phase two-winding power transformers used in urban and industrial power supply systems, consisting in the fact that, based on the passport data of a three-phase two-winding power transformer included in the power supply system, the rated current in the high-voltage winding is calculated, then the active, total and inductive resistances of the windings are calculated, after which the active and inductive leakage resistances of the high-voltage winding and the reduced active and inductive leakage resistances of the low-voltage winding are calculated, after which the rated no-load current is calculated and, using its value, the total active, total and inductive resistances of the magnetization branch and the leakage branch of the high-voltage winding are calculated, then, knowing the values of the active and inductive resistances of the leakage branch of the high-voltage winding, the active and inductive resistances of the magnetization branch are found, after which, using the values measured by measuring instruments installed in the input cell, the low-voltage busbar supply of the transformer substation to which the end consumer of electric energy is connected - the load, for each of the three phases and for each harmonic component, starting from the 1st to the 40th, the values of the active power consumed by the load connected to the three-phase two-winding power transformer, the current in the low-voltage winding and the load and the voltage at the terminals of the low-voltage winding and the load, calculate the active, complete and reactive inductive resistance of the fundamental harmonic component of the load for one phase connected to the terminals of the low-voltage winding, then calculate the active, reactive and complete resistances for the remaining harmonic components of the load of this phase from the 2nd to the 40th, knowing the transformation ratio of the three-phase two-winding power transformer, find the reduced active, reactive and complex complete resistance for each harmonic component of the load of one phase connected to the terminals of the low-voltage winding, and, knowing the previously calculated parameters of the T-shaped equivalent circuits of one phase of a three-phase two-winding power transformer, for each harmonic component the following values are calculated: α _ν , β _ν , γ _ν , δ _ν , θ _ν , ε _ν , τ _ν and μ _ν , which are then used to calculate the conditionally constant coefficients A _{1 ν} , A _{2 ν} , A _{3 ν} , B 1 ν , B _{2 ν} , B _{3 ν} , C _{1 ν} , C _{2 ν} , C _{3 ν} , D _{1 ν} , D _{2 ν} , D _{3 ν} for each harmonic component, using their values, as well as the values of the reduced active, total and reactive resistances for each harmonic component of the load of one phase, the complex values of the apparent power losses are calculated in one phase of a three-phase two-winding power transformer for each harmonic component, and then, summing them up, find the complex value of the total losses of apparent power in one phase taking into account additional losses from higher harmonic components, then for the remaining two phases, using the values of active power consumed by the load connected to the two-winding power transformer, measured with the measuring instruments installed in the input cell, the low-voltage supply bus of the transformer substation, the current in the low-voltage winding and the load, and the voltage at the terminals of the low-voltage winding and the load, for each harmonic component starting from the 1st to the 40th, carry out calculations similar to those described earlier for one phase to obtain the complex values of the total losses of apparent power in each of these phases taking into account additional losses from higher harmonic components, after which, adding up the complex values of the total losses of apparent power, calculated for each phase taking into account additional losses from higher harmonic components, calculate the complex value of the technical losses of apparent power in the power three-phase two-winding transformer taking into account additional losses from higher harmonic components.

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