RU2752765C1 - Method for estimating contribution of nonlinear consumers to voltage distortion at point of common connection - Google Patents

Abstract

FIELD: power distribution.

SUBSTANCE: invention relates to the field of electric power engineering, in particular to methods for determining the influence of nonlinear electric power consumers on the non-sinusoidal voltage at the point of common connection (PCC). The amplitudes and phases of the currents of the higher harmonics of consumers connected to the general connection node, and the amplitudes and phases of the currents of the higher harmonics of the power supply system are measured. Based on the measured data for each harmonic separately for all consumers, the consumer's contribution to the distortion of voltage and current at the point of common connection is calculated as the ratio of the projection of the current vector of the consumer's higher harmonic on the current vector of the higher harmonic of the power supply system to the current of the higher harmonic of the power supply system according to the corresponding formula.

EFFECT: assessment of the contribution of each electricity consumer to voltage distortions in the PCC as a percentage ratio.

1 cl, 2 dwg

Description

The invention relates to the field of electric power industry, in particular to methods for determining the influence of nonlinear electricity consumers on non-sinusoidal voltage at the point of common connection (TOC). This invention can be used to regulate commercial relations between the electricity supplier and consumers in the issue of assessing the contribution of each of the consumers to the deterioration of the voltage quality in the TOP in percentage terms.

A known method for determining the consumer, distorting the quality indicators of electrical energy in the node of the power supply organization, and its contribution to the distortion (RF patent No. 2244313, publ. 10.01.2005). This method involves calculating the resistances of non-distorting loads and calculating the distortion currents of the distorting loads of each consumer. After that, the obtained values of the currents are correlated with the total values.

The disadvantage of this method is the fact that the authors take the algebraic sum of consumer currents as the total value of the distortion currents, arguing that such an assumption will not affect the value of the share contributions. However, it is obvious that the vector sum of the currents will differ significantly from the algebraic one, since the mutual arrangement of the current vectors of each of the branches can be any.

There is a known method for determining the share of the load and the power system in changing the voltage quality (RF patent No. 2307364, publ. 09/27/2007), which includes the measurement and determination of the integral components of the abnormal voltages of the branches with EMF and the abnormal components of the currents of the load branches, on the basis of which the shares are calculated each power facility.

The disadvantage of this method is a significant amount of initial data concerning both the power supply system (instantaneous EMF values of the system) and consumers (inductance L). For a correct assessment of the shares of each power facility, it is necessary to constantly determine the above values.

A known method of identifying the actual contribution of the subjects of electrical networks to the distortion of the quality of electrical energy at the point of common connection in the electrical network (RF patent No. 2364875, publ. 20.08.2009). According to this method, the contribution of each subject of the power system is determined on the basis of the effective value of the voltage of the backward wave, while the voltage of each harmonic in the FOC is decomposed into the components of the forward and backward waves using the T-transformation.

The disadvantages are the need to determine in real time the wave impedance of the network at each harmonic, since its value is constantly changing and depends on the operating mode of each of the subjects of the power system.

There is a known method for identifying the source of higher harmonics (RF patent No. 2573706, publ. 27.01.2016), in which the source of higher harmonics is determined by the dependence of the current of the higher harmonics of the power supply system on the active resistance of the filter compensating device installed in parallel to one of the loads.

The disadvantage of this method is that this method only allows you to determine whether the source of distortion is a consumer or a power supply system, but does not allow assessing the contribution of each of them to total distortions in percentage terms.

There is a known method for assessing the influence of a consumer on voltage distortion at the point of common connection (RF patent No. 2627195, publ. 03.08.2017), which includes determining the parameters of autonomous voltage for each consumer separately, calculating the coefficient of its influence on voltage distortions and comparing the calculated parameters with acceptable ...

The disadvantage of this method is the need to calculate the parameters of the equivalent circuit, such as the conductivity of each consumer, which introduces an additional error in the final result. The authors note that the relative error in determining the parameters of the equivalent circuit when using the proposed method does not exceed 7%, which is a significant value. In addition, as a result, not the consumer's contribution to general distortions is determined, but only its influence is compared with the permissible value and a conclusion is made about the admissibility or inadmissibility of such a mode of operation of the consumer.

The known method is a method for determining the actual contribution of sources of distortion to the values of indicators of the quality of electricity at the point of common connection (RF patent No. 2236016, publ. 09/10/2004) adopted as a prototype. The actual contribution of each subject-source of distortion is considered to be directly proportional to the projection of the current of the subject-source of distortion on the total current of all subjects-sources of distortion.

The disadvantage of this method is that all subjects are divided into sources and consumers of distortion, while in real power systems, most consumers are a set of various linear and non-linear loads. Such loads, according to this method, result exclusively in the subject-source or subject-consumer. In this case, the contribution of the subjects-consumers of distortion is overlooked, while they also contain sources of higher harmonics. In addition, the belonging of the subject to the sources or consumers of distortions is determined by the phase angles of the shift between the distortion voltage and the corresponding higher harmonic current. In other words, according to the sign of the distortion power at each of the harmonics. However, the distortion voltage at the node of the electrical network is the result of the joint operation of all distortion sources connected to the TOP. If there is a significant phase difference between the distortion currents of consumers, one or more distorting consumers will have positive distortion powers and will be perceived as non-distorting.

The technical result is an accurate assessment of the contribution of each consumer of electricity to voltage and current distortions in the TOP as a percentage.

The technical result is achieved by measuring the amplitudes and phases of the currents of the higher harmonics of the power supply system, based on the measured data for each harmonic separately for all consumers, the consumer's contribution to the voltage and current distortion at the point of common connection is calculated as the ratio of the projection of the current vector of the consumer's higher harmonic to the current vector of the higher harmonic of the power supply system to the current of the higher harmonic of the power supply system according to the formula

- вклад n-ого потребителя в искажение напряжения и тока в точке общего присоединения на гармонике h,where,

- the contribution of the n- th consumer to the voltage and current distortion at the point of common connection at the harmonic h ,

- амплитуда вектора тока гармоники h n-ого потребителя,

- the amplitude of the current vector of the harmonic of the hn th consumer,

- косинус угла между фазой вектора тока высшей гармоники n-ого потребителя и вектора тока высшей гармоники системы электроснабжения,

- cosine of the angle between the phase of the current vector of the higher harmonic of the n- th consumer and the current vector of the higher harmonic of the power supply system,

- амплитуда вектора тока гармоники h системы электроснабжения, затем производят сравнение рассчитанных вкладов потребителей в искажение напряжения и тока в точке общего присоединения на гармонике h и производят компенсацию токов высших гармоник потребителей с наибольшими вкладами.

- the amplitude of the harmonic current vector h of the power supply system, then the calculated contributions of consumers to the distortion of voltage and current at the point of common connection at the harmonic h are compared and the currents of higher harmonics of consumers with the greatest contributions are compensated.

The method is illustrated by the following figures:

fig. 1 - equivalent circuit of two consumers connected to one power supply system;

fig. 2 - dependence of the consumer's contribution to voltage distortions in the TOP on the percentage of generated current in relation to the total generated current in the system, and on the percentage of consumer power in relation to the total power of consumers in the system;

1 - complex resistance of SES;

2 - SES current meter;

3 - first consumer current meter;

4 - current meter for the second consumer;

5 - complex resistance of the first line;

6 - complex resistance of the second line;

7 - non-linear load of the first consumer;

8 - linear load of the first consumer;

9 - non-linear load of the second consumer;

10 - linear load of the second consumer.

The method is carried out as follows. In the energy system considered at each harmonic h, a current meter SES 2 is installed separately, which determines the amplitudes and phases of the currents of the higher harmonics of the SES flowing through the complex resistance of the SES 1, a current meter of the first consumer 3 is installed, which determines the amplitudes and phases of the higher harmonic currents flowing through the complex resistance of the first line 5, a current meter of the second consumer 4 is installed, which determines the amplitudes and phases of the higher harmonic currents flowing through the complex resistance of the second line 6.nonlinear load first consumer 7.

If the quality of electrical energy at the point of common connection deviates from the norms established by the standards, the following actions are performed.

For each harmonic h, the angles between the vectors of consumer currents and SES currents are calculated according to formulas (1) and (2):

where

- фаза вектора тока гармоники h, определенная измерителем тока первого потребителя 3;

- the phase of the harmonic current vector h , determined by the current meter of the first consumer 3;

- фаза вектора тока гармоники h, определенная измерителем тока второго потребителя 4;

- the phase of the harmonic current vector h , determined by the current meter of the second consumer 4;

- фаза вектора тока гармоники h, определенная измерителем тока СЭС 2;

- the phase of the harmonic current vector h , determined by the SES 2 current meter;

- угол между фазами

и

;

- angle between phases

and

;

- угол между фазами

и

.

- angle between phases

and

...

Then, for each harmonic h, the projections of the consumers' current vectors onto the SES current vector are calculated using formulas (3) and (4):

where

- амплитуда вектора тока гармоники h, определенная измерителем тока первого потребителя 3;

- the amplitude of the harmonic current vector h , determined by the current meter of the first consumer 3;

- амплитуда вектора тока гармоники h, определенная измерителем тока второго потребителя 4;

- the amplitude of the harmonic current vector h , determined by the current meter of the second consumer 4;

- амплитуда вектора тока гармоники h, определенная измерителем тока СЭС 2;

- the amplitude of the harmonic current vector h , determined by the SES 2 current meter;

- проекция амплитуды вектора

на амплитуду вектора

;

is the projection of the amplitude of the vector

on the amplitude of the vector

;

- проекция амплитуды вектора

на амплитуду вектора

;

is the projection of the amplitude of the vector

on the amplitude of the vector

;

Next, the contribution of each consumer to the current and voltage distortions in the TOP is calculated according to the expression (5):

where:

- вклад n-ого потребителя в искажение напряжения и тока в ТОП на гармонике h;

- the contribution of the n- th consumer to the voltage and current distortion in the CCD at the h harmonic;

- амплитуда вектора тока гармоники h n-ого потребителя;

- amplitude of the current vector of the harmonic of the hn -th consumer;

- угол между фазами вектора тока гармоники h n-ого потребителя

и

.

- the angle between the phases of the harmonic current vectorhnth consumer

and

...

The validity of using this approach is confirmed by the following. From the diagram in FIG. 1 it can be seen that the non-sinusoidal voltage of the network Ů _{0 is} proportional to the vector sum of the currents of the first and second consumers, provided that the resistance of the network Z _{0 is} constant according to the formula (6):

where

- напряжение гармоники h в ТОП;

- voltage of harmonic h in TOP;

- величина комплексного сопротивления СЭС 1.

- the value of the complex resistance of SES 1.

,

,

использовались следующие коэффициенты (7-11), характеризующие структуру рассматриваемой системы электроснабжения: During the analytical determination of currents

,

,

the following coefficients were used (7-11), characterizing the structure of the considered power supply system:

where

- коэффициент, показывающий во сколько раз комплексное сопротивление линейной нагрузки первого потребителя 8 больше комплексного сопротивления СЭС на гармонике h;

- coefficient showing how many times the complex resistance of the linear load of the first consumer 8 is greater than the complex resistance of the SES at the harmonich;

- коэффициент, показывающий во сколько раз комплексное сопротивление линейной нагрузки второго потребителя 10 больше комплексного сопротивления СЭС на гармонике h;

- coefficient showing how many times the complex resistance of the linear load of the second consumer 10 is greater than the complex resistance of the SES at the harmonic h ;

- коэффициент, показывающий во сколько раз комплексное сопротивление первой линии 5 больше комплексного сопротивления СЭС на гармонике h;

- coefficient showing how many times the complex resistance of the first line 5 is greater than the complex resistance of the SES at the harmonic h ;

- коэффициент, показывающий во сколько раз комплексное сопротивление второй линии 6 больше комплексного сопротивления СЭС на гармонике h;

- coefficient showing how many times the complex resistance of the second line 6 is greater than the complex resistance of the SES at the harmonic h ;

Then the expressions for the current flowing in the line of the power supply system (12) and the currents of the first (13) and second (14) consumer take the following form:

where

- ток, генерируемый нелинейной нагрузкой первого потребителя 7;

- the current generated by the non-linear load of the first consumer 7;

- ток, генерируемый нелинейной нагрузкой второго потребителя 9.

- the current generated by the non-linear load of the second consumer 9.

и

видно, что генерируемый ток высших гармоник потребителей распределяется как в систему, так и на другого потребителя. Однако, они несут информацию о структуре всей системы электроснабжения в целом, а значит считать их за погрешность способа ошибочно, так как в данном случае рассматривается взаимное влияние всех объектов друг на друга, а не каждый объект в отдельности. By components

and

it can be seen that the generated higher harmonic current of consumers is distributed both to the system and to another consumer. However, they carry information about the structure of the entire power supply system as a whole, which means that it is erroneous to consider them as an error of the method, since in this case the mutual influence of all objects on each other is considered, and not each object separately.

As a result, a comparison is made of the calculated contributions of consumers to the voltage and current distortion at the point of common connection at the harmonic h in percentage ratio, then the currents of higher harmonics of consumers with the greatest contributions are compensated primarily by any of the developed methods of compensation of the higher harmonic current, for example, using passive or active filters higher harmonics.

The method is illustrated by the following examples. The calculation of the non-sinusoidal mode for the power supply system shown in Fig. 1. The parameters of the circuit are presented in Table 1.

Table 1 Initial data for calculating the equivalent circuit Resistance of the power supply system

0.435 Ohm Line resistance from the first consumer to the TOP

= 0.380 Ohm Line inductance from first consumer to TOP

= 0.430 mH Line resistance from the second consumer to the TOP

= 0.380 Ohm Line inductance from the second consumer to the TOP

= 0.430 mH Total active power of two consumers

= 4 MW Total reactive power of two consumers

= 3 Mvar Total third harmonic current generated by two consumers

= 72.27 A

In the course of the calculations, the shares of the generated current of each consumer changed, provided that the value of the total generated current of the higher harmonics of the two consumers was preserved, and the ratio of the consumers' power with constant power consumption at the first harmonic in the entire system as a whole changed.

Let us carry out the calculation for a particular case in which the share of the power of the first consumer is 40%, and the third harmonic current generated by the first consumer is 60% of the third harmonic current generated in total by the first and second consumers.

,

,

, а в случае аналитического подхода - рассчитать их по формулам (12)-(14). According to the proposed method, in practice, it is necessary to measure currents

,

,

, and in the case of an analytical approach, calculate them using formulas (12) - (14).

Before that, the inductive part of the complex resistance of SES 1 is calculated (equal to the total complex resistance in this particular case:

where

h - harmonic number.

For the third harmonic:

Then the phase of the complex resistance of SES 1 at the third harmonic:

The inductive part of the complex resistance of the first line 5:

where

ƒ - main frequency of the network.

For the third harmonic:

Total complex impedance of the first line 5:

For the third harmonic:

Phase of the complex impedance of the first line of the 5th third harmonic:

Similarly for the complex resistance of the second line 6:

where

- индуктивная часть комплексного сопротивления второй линии 6;

- the inductive part of the complex resistance of the second line 6;

- полное комплексное сопротивление второй линии 6;

- total complex impedance of the second line 6;

- фаза комплексного сопротивления второй линии 6.

- the phase of the complex resistance of the second line 6.

Next, the parameters of the linear load of the first consumer 8 are calculated. The active and reactive powers are determined as follows:

where

- доля мощности первого потребителя по отношению к суммарной мощности всех потребителей системы.

- the share of the power of the first consumer in relation to the total power of all consumers of the system.

Since electricity consumers are traditionally replaced by a parallel connection of active and reactive resistance, we calculate the following values:

where

- базовое напряжение, к которому приведены значения всех элементов системы,

- base voltage, to which the values of all elements of the system are reduced,

- активное сопротивление линейной нагрузки первого потребителя 8;

- active resistance of the linear load of the first consumer 8;

- реактивное сопротивление линейной нагрузки первого потребителя 8.

- the reactance of the linear load of the first consumer 8.

However, for further calculations, it is necessary to equivalent the parallel connection to the serial

where

- эквивалентное активное сопротивление линейной нагрузки первого потребителя 8;

- equivalent active resistance of the linear load of the first consumer 8;

- эквивалентное реактивное сопротивление линейной нагрузки первого потребителя 8.

- equivalent reactance of the linear load of the first consumer 8.

For the third harmonic:

Then

where

- эквивалентное полное сопротивление линейной нагрузки первого потребителя 8.

- equivalent impedance of the linear load of the first consumer 8.

- фаза линейной нагрузки первого потребителя 8.

- phase of the linear load of the first consumer 8.

The parameters of the linear load of the second consumer 10 are calculated in a similar way.

Where

- активное сопротивление линейной нагрузки второго потребителя 10;

- active resistance of the linear load of the second consumer 10;

- реактивное сопротивление линейной нагрузки второго потребителя 10;

- the reactance of the linear load of the second consumer 10;

- эквивалентное активное сопротивление линейной нагрузки второго потребителя 10;

- equivalent active resistance of the linear load of the second consumer 10;

- эквивалентное реактивное сопротивление линейной нагрузки второго потребителя 10;

- the equivalent reactance of the linear load of the second consumer 10;

- эквивалентное полное сопротивление линейной нагрузки второго потребителя 10;

- equivalent impedance of the linear load of the second consumer 10;

- фаза линейной нагрузки второго потребителя 10.

- phase of the linear load of the second consumer 10.

,

,

,

,

Next, the parameters are calculated, which are necessary to determine the coefficients

,

,

,

,

where

Then, taking into account the peculiarities of actions on complex quantities, the following values are calculated using formulas (10) - (14):

;

;

;

;

;

;

;

;

.

...

Next, the third harmonic current of the nonlinear load of the first consumer is calculated 7.

where

- доля тока высших гармоник первого потребителя по отношению к суммарному току, генерируемому двумя потребителями;

- the fraction of the current of the highest harmonics of the first consumer in relation to the total current generated by the two consumers;

- ток третьей гармоники, генерируемый первым потребителем.

- the third harmonic current generated by the first consumer.

Similarly, the third harmonic current of the nonlinear load of the second consumer 9:

Taking into account all the obtained values, as well as setting the zero phase of the currents generated by consumers, the calculation is performed using formulas (15) - (17):

,

и тока СЭС

по формулам (1) и (2):Next, the angles between the vectors of the consumer currents are calculated

,

and SES current

according to formulas (1) and (2):

,

на амплитуду вектора

по формулам (3) и (4):Then the projections of the amplitudes of the vectors

,

on the amplitude of the vector

according to formulas (3) and (4):

As a result, the contribution of the first and second consumers to the distortions of current and voltage in the TOP is calculated according to expressions (5) and (6):

The calculation for other shares of the power of the first consumer in relation to the total power of all consumers of the system and other fractions of the current of higher harmonics of the first consumer in relation to the total current generated by two consumers was carried out in a similar way.

The calculation results for the third harmonic are presented in Fig. 2, which shows the values of the contribution of the first consumer to the distortion of the current and, as a consequence, the voltage in the TOP at various generated currents and powers of the consumers.

It can be seen that the obtained values practically do not depend on the ratio of the consumers' capacities, while with high accuracy they correspond to the fractions of the generated current at the first enterprise, which indicates insignificant values of the higher harmonic currents flowing between enterprises and not entering the power supply system, as well as the possibility of using the proposed method for any ratio of consumer capacities.

Thus, the developed method for assessing the contribution of nonlinear consumers to voltage distortion in the TOP allows us to determine the share of participation of each of the consumers connected to the TOP in percentage, taking into account not only the higher harmonic current generated by the consumer's nonlinear load, but also the structural features of the entire power supply system as a whole. ...

Claims (6)

A method for assessing the contribution of nonlinear consumers to voltage distortion at a common connection point, including measuring the amplitude and phase of the higher harmonic currents of consumers connected to the common connection node, characterized in that the amplitudes and phases of the higher harmonic currents of the power supply system are measured based on the measured data for each harmonic separately for all consumers, the consumer's contribution to the voltage and current distortion at the point of common connection is calculated as the ratio of the projection of the current vector of the consumer's higher harmonic to the current vector of the higher harmonic of the power supply system to the current of the higher harmonic of the power supply system according to the formula

where

- the contribution of the n- th consumer to the voltage and current distortion at the point of common connection at the harmonic h ,

- the amplitude of the current vector of the harmonic of the hn th consumer,

- cosine of the angle between the phase of the current vector of the higher harmonic of the n- th consumer and the current vector of the higher harmonic of the power supply system,

- the amplitude of the harmonic current vector h of the power supply system, then the calculated contributions of consumers to the distortion of voltage and current at the point of common connection at the harmonic h are compared and the currents of higher harmonics of consumers with the greatest contributions are compensated.

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