RU2763121C1 - Method for analyzing the quality of electrical energy in a three-phase electrical network - Google Patents

Abstract

FIELD: measuring equipment.

SUBSTANCE: invention relates to measuring equipment, namely to the assessment of indicators of the quality of electrical energy (EEQ) in a three-phase electrical network and can be used to determine the influence of indicators of EEQ on the functioning of end consumers and the subsequent assessment of the need for control actions to restore their normal power supply. The set of electrical quantities is measured, while the set contains one electrical quantity for each phase, a space vector is formed based on an instant three-dimensional transformation of the set of measured electrical quantities, the set is determined containing at least one parameter characterizing the quality of electrical energy in a three-phase electrical network. The output signal characterizing the results of the analysis of the quality of electrical energy is formed on the basis of selective control of the generalized indicator of the quality of electrical energy, which is obtained by comparing individual indicators of the quality of electrical energy with their normalized values ​​for the current operating mode of the electrical network, as well as the weighted summation of the comparison results. Weighted summation coefficients are obtained by expert assessments or simulation modeling of damages to consumers when each of the power quality indicators deviates from the standardized value. For sampling, a sequential analysis procedure is used, the setting values ​​for which are determined based on the results of simulation of the electrical network, taking into account the operating modes of consumers' electrical consumers.

EFFECT: ensuring a comprehensive accounting of the influence of deviations of various EEQ indicators on the functioning of consumers' power consumers.

1 cl, 2 dwg, 1 tbl

Description

The proposed invention relates to measuring technology, namely the assessment of indicators of the quality of electrical energy (EQI) in a three-phase electrical network. It can be used to determine the influence of the EEC indicators in a three-phase system on the functioning of electrical consumers of end industrial and non-industrial consumers and then assess the need to implement control actions in order to restore their normal power supply.

A known method for determining the quality indicators of electrical energy of a three-phase network [USSR author's certificate No. 1109655, IPC G01R 19/00, publ. 08/23/1984, Bul. No. 31] by comparing the input and reference voltages, determine the initial phase of the positive sequence of voltages of the three-phase network, form a three-phase reference voltage system of positive sequence, the initial phase of which is equal to the initial phase of the positive sequence of voltages of the three-phase network, and the amplitude is equal to the nominal value of the voltage amplitude of the three-phase network, and then, from the difference between the input and reference voltages, symmetric voltage components are isolated, by the magnitude of which the EEC in a three-phase network is judged.

The disadvantage of the known method for determining the EEC indicators in a three-phase network is the impossibility of a comprehensive accounting of the influence of deviations in the EEC indicators on the functioning of electrical receivers of various consumers.

A known method for analyzing the quality of electrical energy in a three-phase industrial power supply system [RF Patent No. 2741269, IPC G01R 19/00, publ. 01/22/2021 Bul. No. 3], containing the stages at which: measure the set of electrical quantities, while the set contains one electrical quantity for each phase; a spatial vector is formed on the basis of an instant three-dimensional transformation of a set of measured electrical quantities. According to the proposal, the current set of complex instantaneous values of the space vector is normalized in a given sliding window and then fed to the recognition unit, to the other inputs of which similar sets of complex instantaneous values of the space vector, which are characteristic and corresponding to violations of the quality indicators of electrical energy in the analyzed system, are fed to the other inputs. power supply of an industrial consumer, according to the results of comparison in the recognition unit of the current set of complex instantaneous values of the space vector with the sets of complex instantaneous values of the space vector obtained from the results of simulation, the corresponding simulation conditions are determined, as well as the degree and source of distortions of currents and voltages in a three-phase system industrial power supply, while generating a signal characterizing violations of the quality of electric ctric energy at the output of the recognition unit.

Although in the method of analyzing the quality of electrical energy in a three-phase industrial power supply system, a generalized indicator of the CEE is introduced in the form of a set of complex instantaneous values of the space vector, it does not fully provide a deep analysis of the effect and combination of deviations of individual CEE indicators on the functioning of power consumers of different consumers.

The closest technical solution to the proposed invention is a method for analyzing the quality of electrical energy in a three-phase electrical network [RF Patent No. 2613584, IPC G01R 19/25, publ. 11/27/2015, Bul. No. 33], containing the steps at which: measure the set of electrical quantities, while the set contains one electrical quantity for each phase, form a space vector based on the instant three-dimensional transformation of the set of measured electrical quantities, determine the set containing at least one parameter characterizing the quality of electrical energy in a three-phase electrical network, depending on the time-dependent space vector calculated in the sliding window.

The parameters of the prototype method characterizing the quality of electrical energy in a three-phase electrical network, for example, may include:

- parameter ( k _D ), characterizing the imbalance of voltage or current in a three-phase network;

- parameter ( k _C ) characterizing the voltage or current drop;

- parameter ( k _S ), characterizing overvoltage or a jump in current strength; - parameter ( k _F ), characterizing voltage flickering;

- parameter ( k _H ) characterizing voltage or current harmonic pollution.

In the prototype method and the device that implements it, the analysis of the CEE using the above parameters is performed using the indication means. In this case, the indication can differ in several levels of detail. In addition, it can include alarms when violations are detected.

It is important to note that a complex indicator that takes into account the cumulative effect of individual KEE indicators on consumers' electrical installations in the prototype method is not introduced. Also, the prototype method does not include the procedure for making a decision on the admissibility of deviations in the aggregate accounting of EEE indicators (their different combinations) and the impact on electrical consumers of different consumers.

The disadvantage of the prototype method is the impossibility of a comprehensive accounting of the influence of deviations in the EEC indicators on the functioning of electrical receivers of various consumers.

Introduced in our country by regulatory documents, the KEE indicator system (GOST 32144-2013) determines only the composition and permissible ranges of deviations of individual indicators. In practice, there is a complex (integrated) impact on consumers' electrical installations. Distortions of currents and voltages as a result of cumulative deviations of the CEE indicators, which are at the limits of permissible values, can lead to significant damage for various groups of consumers. When organizing the procedure for analyzing the CEE indicators, it is advisable to implement the following tasks:

- the formation of a generalized parameter KEE, with the help of which it is possible to assess the complex effects of a set of deviations of the KEE indicators on the functioning of a particular consumer;

- determination of the ranges of permissible deviations of the generalized parameter EEE that do not lead to damage to consumers due to these deviations. It is advisable to form such permissible ranges using simulation data for specific circuit-mode conditions of the consumer's functioning, including in the main repair schemes of external power supply;

- development of a procedure for monitoring the CEE indicators based on a generalized parameter for subsequent decision-making on the implementation of organizational and technical measures in order to introduce the CEE indicators into acceptable ranges.

With regard to the EEC indicators, it should be noted that their deviations at the point of connection (GOST 32144-2013) are divided into long-term changes and random events, which, due to the short duration of the latter, usually do not have any effect on the electrical installations of consumers, and according to the results of such deviations organizational and technical measures should not be taken to restore the CEE indicators. On the other hand, power supply systems with distributed generation sources, including facilities based on renewable energy sources, are characterized by rapidly changing modes, accompanied by significant deviations in the CEE indicators. At the same time, for the assessment of currents and voltages in power supply systems, short time intervals (sliding data window) are allocated, constituting, for example, [Ilyushin P. V., Kulikov A. L. Automation of control of normal and emergency modes of power districts with distributed generation / P.V. Ilyushin, A.L. Kulikov. - Nizhny Novgorod: NRU RANEPA. 2019. - 364 s], one period of power frequency. The required frequency resolution to determine, for example, distorting harmonics [eg Ribeiro Paulo F., Duque Carlos A., da Silveira Paulo M., Serqueira Augusto S. Signal processing in smart grids of power systems. - M .: TEKHNOSPHERA. 2020. - 480 s.] At such short time intervals cannot be achieved. As a result, the results of calculating some CEE indicators will be inaccurate and inadequate to the real situation with distortions of currents and voltages.

Establishing compliance with the requirements of standards (GOSTs, technical specifications for technological installations of consumers, etc.) is ensured by monitoring the monitoring of the EEE indicators. Depending on the features of the power supply system, as well as the financial capabilities of consumers and enterprises of electrical networks, both continuous and selective control of the CEE indicators can be organized. With continuous monitoring, the evaluation of the EEE is carried out at each moment in time at all points of connection of consumers and with the calculation of all EEC indicators. Based on economic feasibility, this form of control is often unacceptable. Alternatively, it is possible to organize sampling control, when the EEC indicators are assessed, for example, at separate sampling intervals, at predetermined control points, with the calculation of only those EEC indicators that are critical for a particular consumer, taking into account its technological features.

It is advisable to organize selective control of the EEE indicators using special selective procedures of mathematical statistics [for example, Belyaev Yu.K. Probabilistic sampling methods. - M .: Nauka, 1975. - 408 p.]. With such control, for example, by observing on a limited (short) time interval, a conclusion is formed on the compliance with the requirements for the CEE indicators for the time period until the next sampling control.

It is advisable to organize the control of CEE indicators on a quantitative basis [for example, Cowden D. Statistical methods of quality control. Per. from English - M .: Fizmatgiz, 1961. - 623 p.]. With such control at the points of connection of electrical installations of consumers, according to the totality of the calculated CEE indicators, it is possible to establish the validity of alternative hypotheses about their compliance or non-compliance with the requirements of regulatory documents (first of all, GOST 32144-2013).

The objective of the invention is to develop a method for analyzing the quality of electrical energy in a three-phase system, providing a comprehensive account of the influence of deviations of various EEC indicators on the functioning of consumers' power consumers.

The task is achieved by the method of analyzing the quality of electrical energy in a three-phase electrical network, containing the stages at which: measure the set of electrical quantities, while the set contains one electrical quantity for each phase, form a space vector based on the instant three-dimensional transformation of the set of measured electrical quantities, determine the set containing at least one parameter characterizing the quality of electrical energy in a three-phase electrical network. According to the proposal, the output signal characterizing the results of the analysis of the quality of electrical energy in a three-phase electrical network is formed on the basis of selective control of the generalized indicator of the quality of electrical energy, which is obtained by comparing individual indicators of the quality of electrical energy with their normalized values for the current operating mode of the electrical network, as well as the weighted summation of the results of comparisons, the coefficients for weighted summation are obtained by expert assessments or simulation modeling of damage to consumers with deviations of each of the power quality indicators from the normalized value; in sampling control, a sequential analysis procedure is used, the setting values for which are determined based on the results of simulation of the electric network, taking into account the modes work of consumers' electrical consumers.

FIG. 1 shows a block diagram of a device that implements a method for analyzing the quality of electrical energy in a three-phase electrical network.

FIG. 2 illustrates the process of sequential decision-making regarding the deviations of the generalized indicator of the CEE.

A device that implements a method for analyzing the quality of electrical energy in a three-phase electrical network (Fig. 1) includes a series-connected data collection module 1; three-dimensional transformation module 2; module 3 for determining the parameters characterizing the CEE; comparison unit 4; multiplication block 5; group adder 6; block of sequential analysis 7; and also block 8 memory. The outputs of block 3 from the first to the Nth through the corresponding circuits 4 ₁ ... 4 _N comparison of block 4 and multipliers 5 ₁ ... 5 _{N of} block 5 are connected respectively to the inputs from the first to N -th group adder 6. Second inputs of circuits 4 ₁ ... 4 _N comparisons of block 4 are combined and connected to the first group of outputs of the memory block 8. Similarly, the second inputs of the multipliers 5 ₁ ... 5 _{N of} block 5 are combined and connected to the second group of outputs of the memory block 8. The output of the group adder 6 through the block of sequential analysis 7 is connected to the output devices. The third group of outputs of the memory unit 8 is connected to the second input of the sequential analysis unit 7. The first and second inputs of the memory unit 8 receive information about the current operating mode of the electrical network, the results of simulation, as well as the numerical values of expert estimates. The input of the data collection module 1 is connected to the input of a device that implements a method for analyzing the quality of electrical energy in a three-phase electrical network.

The device (Fig. 1), which implements a method for analyzing the quality of electrical energy in a three-phase electrical network, operates as follows.

The development of a method for analyzing the quality of electrical energy in a three-phase electrical network is associated with the properties of the load of industrial and non-industrial consumers, the amount of damage to consumers caused by deviations in the EEC indicators, as well as the economic feasibility of conducting selective control when analyzing the EEC indicators.

Each individual point of connection to the electrical network will have its own set of sinusoidal distortions of currents and voltages, depending on the technological characteristics of the load and the modes of operation of the electrical network, determined, inter alia, by means of simulation.

To ensure the effective functioning of the method for analyzing the quality of electrical energy in a three-phase electrical network, preliminary simulation modeling is implemented, the goals of which are:

- determination of the modes of operation of the electrical network, taking into account the characteristics of the connected consumers, as well as the possibilities of carrying out repair and maintenance work;

- identification of modes and points of connection of consumers' electrical receivers, in which significant deviations of the EEC indicators are possible, requiring the implementation of selective control of the EEC indicators and measures to restore the normal functioning of the electrical network;

- determination of the permissible ranges of deviation of the generalized indicator of the CEE, as well as the indicators of the CEE for carrying out the appropriate sampling procedure in the modeled modes and analyzed points of connection.

When implementing the method for analyzing the quality of electrical energy and performing preliminary simulation modeling, a database of permissible deviations of the generalized parameter EEC is formed in the analyzed points of connection and modes of operation of the electric network, as well as the required EEC indicators for the sampling procedure. The results of the simulation are entered into the memory of the memory block 8 (Fig. 1). In addition, the memory block 8 receives information about possible damages inherent to consumers at a particular point of connection to the electrical network, formed either by the results of simulation modeling, or by expert assessments, taking into account the deviations of each individual indicator of the CEE.

Module 1 of a device that implements a method for analyzing the quality of electrical energy in a three-phase electrical network (Fig. 1) is configured to connect to each phase of a three-phase electrical network and periodically measure phase values of currents and voltages at the analyzed connection points. In module 1, analog-to-digital conversion is performed and instantaneous values of phase currents and voltages are supplied to its output.

Module 1 (Fig. 1) is connected to three-dimensional transformation module 2. At each moment in time, module 2 takes instantaneous values of phase currents and / or voltages x _a ( n ), x _b ( n ), x _c ( n ) (where n is the current discrete time), measured at the analyzed point of connection of a three-phase electrical network. In module 2, the Clarke transform is carried out, which is a kind of transformation of symmetric components,

(1)

(one)

The first two components obtained as a result of transformation (1) are combined to obtain a complex number that depends on discrete time and is called a space vector:

x ( n ) = x _α ( n ) + jx _β ( n ). (2)

The space vector contains all the necessary information about the original three-phase system for the analysis of the CEE [RF Patent No. 2613584, IPC G01R 19/25, publ. 03/17/2017, Bul. No. 8].

The instantaneous values of the complex vector from the module 2 of the device are fed to the module 3 for determining the parameters characterizing the EEC. In module 3, the CEE parameters are calculated based on the instantaneous values of the complex space vector. The composition of the calculated parameters of the CEE is determined in advance, taking into account the characteristics of the consumers of the electrical network, as well as their damage when the parameters of the CEE deviate from the standardized values. The number of calculated parameters may, for example, include parameters from the group determined by GOST 32144-2013, or calculated, for example, in accordance with [RF Patent No. 2613584, IPC G01R 19/25, publ. 03/17/2017, Bul. No. 8]:

- parameter ( k _D ), characterizing the imbalance of voltage or current in a three-phase network;

- parameter ( k _C ) characterizing the voltage or current drop;

- parameter ( k _S ), characterizing overvoltage or a jump in current strength; - parameter ( k _F ), characterizing voltage flickering;

- parameter ( k _H ) characterizing voltage or current harmonic pollution.

The use of simulation modeling creates the prerequisites for a more thorough analysis of the CEE indicators using sampling control. At the same time, it is advisable to switch from a set of individual indicators of the CEE to a generalized (complex) indicator with the use of control simultaneously for several signs.

Since the control can be implemented by several parameters, the analysis of the EEC can be performed on the basis of two approaches: both by the magnitude of deviations of the EEC parameters, and by the number of their exceeding the standardized values for the period of time allocated for sampling. In both cases, the analysis assumes that the SEE parameters are independent. From the point of view of planning subsequent organizational and technical measures, it is advisable to assess and form a generalized indicator of the CEE by the magnitude of deviations of individual CEE parameters to determine the corresponding source of CEE violations, and by the total number of detected discrete deviations at a given time interval - to check compliance with the requirements of regulatory documents [GOST 32144 -2013].

Let's look at the second approach first. It is assumed that KEE is characterized by N independent indicators. Then the result of the EEE control at an arbitrary time of the sampling inspection is determined by the N -dimensional column vector x = ( x ₁ , x ₂ , ..., x _j , ..., x _N ) ^T , in which each component x _j is binary and has the value 1 in the conditions of unacceptable deviation of the EEC for the j- th parameter, and 0 - in the conditions of admissible deviations. The task is to assess the CEE based on the results of sampling.

Let the sampling control be carried out on an interval including m readings of the voltage (current) signal. We denote by y _j (0 ≤ y _j ≤ m , j = 1, 2,…, N ) the number of deviations in the j- th parameter of the SEE and set a random N -dimensional vector y = ( y ₁ ,…, y _j ,…, y _N ). Let the component y _{j be} distributed according to the binomial law with the parameters n and q _j , where q _j is the probability of a deviation of the parameter y _j from the permissible value. Under the condition of independence of the EEC parameters, the distribution law of the vector y takes the form

C _n ^yj ⋅q _j ^yj ⋅(1 – q _j ) ^{n – yj} . (1) P _n ( y ) =

C _n ^yj ⋅ q _j ^yj ⋅ (1 - q _j ) ^{n - yj} . (one)

An estimate of the probabilities q _j for a specific electrical network can be obtained from the results of simulation modeling or taking into account the results of monitoring the power supply system over a long time interval.

Let us introduce a generalized indicator of the EEE in the form

c _j ⋅y _j , (2) ξ =

c _j ⋅ y _j , (2)

where c = ( c ₁ ,…, c _j ,…, c _N ) ^T is a column vector of weight coefficients that determines the ratio of damages in case of violations of the CEE for individual parameters.

The grouping of the monitored EEE parameters can be implemented when choosing the weight coefficients c _j ( j = 1, 2, ..., N ), based on the degree of damage associated with the deviation of the EEC indicator for an individual parameter or group, with the assignment of its own weight c _j . The grouping of monitored parameters can also be performed using the method of expert assessments.

Since in expression (2) each component of the vector y distributed according to the binomial law with independent ofn probability, then the random variable ξ, as a linear combination of asymptotically normal quantitiesy _j (j = 1, 2, ...,N), also has an asymptotically normal distribution with mathematical expectationm _ξ and varianceσ _ξ ²

c _j ⋅q _j ; σ _ξ ² = n⋅

c _j ⋅q _j ⋅(1 - q _j ). (3) m _ξ = n ⋅

c _j ⋅ q _j ; σ _ξ ² = n ⋅

c _j ⋅ q _j ⋅ (1 - q _j ). (3)

The degree of approximation of the distribution ξ to the normal law largely depends on the vector c and the numerical values of the probabilities q _j .

In the case of the first approach, at each arbitrary moment of time, underN - dimensional vector y = (y _one, ...,y _j , ...,y _N ) is understood as the vector of numerical values of the deviations of the EEC parameters from the normalized values. The formation of the generalized indicator KEE is carried out in a similar way, in accordance with expression (2), taking into account the damagec _j for consumers and the magnitude of deviationsy _j ... Moreover, the random variable ξ also has a normal distribution with the mathematical expectationm _ξ and varianceσ _ξ ²...

In the further presentation, we assume that ξ is a random value of the generalized SEE parameter with a time-varying average value of m _ξ and a known variance σ _ξ ² , determined by the current mode of the electrical network and the accuracy characteristics of the measurements of currents and voltages (by the corresponding methods of digital signal processing (DSP) ).

In the course of sampling at a specific point connection of consumers with respect to the selected generalized index EER £ solve the following statistical problem: to test the hypothesis that _£ m is less than or equal to the specified value ustavochnomu m _{ξ mouth.}

Let there be a set of sequential instantaneous sample values of the KEE indicator ξ on the analyzed sampling time interval. It is assumed that the ratio between the analyzed time interval of the sample control of the SEE relative to the sampling interval with the DSP of currents and voltages is very large. The fixation of deviations of the set of KEE indicators [for example, GOST 32144-2013] from the normalized values is carried out according to the estimate of the mathematical expectation m _{ξ of the} random variable ξ . At each moment in time, the values of the random variable ξ in the general case may differ from each other, but the variance of the deviations σ _ξ ² is a known value (determined by the accuracy of the parameter estimation), and the mathematical expectation (average value) m _ξ on the analyzed time interval is unknown.

To illustrate the logic of decision-making regarding the generalized indicator of the CEE, let us agree that it is preferable to have a smaller value of m _ξ (for example, a smaller value of the deviation from the normalized value). In this case, the setting value m _{ξ mouth} is set such that when m _ξ < m _{ξ mouth,} deviations of the generalized indicator of the EEC are considered acceptable, and when m _ξ > m _{ξ mouth} , a decision is made about the discrepancy between the generalized indicator of the EEC and the normalized values. When m _ξ = m _{ξ mouth,} a boundary situation takes place, for which it does not matter which of the decisions on the compliance of the KEE indicator with the established requirements will be made. If m _ξ increases (decreases) in the course of sampling tests, then the degree of confidence in the EEC for the analyzed mode of the electrical network decreases (increases) accordingly.

]m _{ξ 0}; m _{ξ 1}[, является областью безразличия.To carry out selective sequential tests, the following values are established: m _{ξ 0} and m _{ξ 1} ( m _{ξ 0} < m _{ξ set} and m _{ξ 1} > m _{ξ set} ) that the decision regarding the compliance of the generalized indicator of the CEE with the established standards is considered in certain risks (damages). If m _ξ ≤ m _{ξ 0} , then the erroneous decision about the non-compliance of the CEE is characterized by the so-called "supplier risk", and the decision on the compliance of the CEE, if m _ξ > m _{ξ 1 is} characteristic of the "consumer risk" [for example, GOST R 50779.50- 95, GOST R 50779.11-2000]. Thus, the region index corresponding generalized EEF normalized values determined by the set values m _ξ, for which m _ξ ≤ m _{ξ 0,} and the domain disparity - set of values m _ξ, for which m _ξ ≥ m _{ξ 1.} The region for which m _ξ

] m _{ξ 0} ; m _{ξ 1} [, is an area of indifference.

The risks inherent in the choice of m _{ξ 0} and m _{ξ 1} correspond to the values of α and β and are characterized by the probabilities of wrong decisions. The use of a consistent criterion of the ratio of probabilities in the implementation of the decision-making procedure leads to the following relationships.

Let ξ ₁ , ξ ₂ ,… a sequence of instantaneous values of the observed quantity ξ , characterizing the generalized indicator of the EEC. The probability density of the sample ξ ₁ , ξ ₂ , ..., ξ _m , if m _ξ = m _{ξ 0} corresponds to the expression

(ξ _i - m _{ξ 0})²/(2σ ²)}, (4) р ₀ ( m ) = (2π σ ² ) ^{- m / 2} ⋅ exp {-

( ξ _i - m _{ξ 0} ) ² / (2 σ ² )}, (4)

and, if m _ξ = m _{ξ 1} , then the expression

(ξ _i - m _{ξ 1})²/(2σ ²)}. (5) р ₁ ( m ) = (2 πσ ² ) ^{- m / 2} ⋅ exp {-

( ξ _i - m _{ξ 1} ) ² / (2 σ ² )}. (5)

In the course of sequential analysis, at each step, the likelihood ratio is calculated, which is determined by the equality

η ( m ) = p ₁ ( m ) / p ₀ ( m ). (6)

Step-by-step calculations are carried out as long as the conditions are met

(ξ _i - m _{ξ 1})²/(2σ ²)} / exp{-

(ξ _i - m _{ξ 0})²/(2σ ²)} < A. (7) В < η ( m ) = exp {-

( ξ _i - m _{ξ 1} ) ² / (2 σ ² )} / exp {-

( ξ _i - m _{ξ 0} ) ² / (2 σ ² )} < A . (7)

The sequential procedure ends with a decision: on deviations of the generalized indicator of the EEE, if

(ξ _i - m _{ξ 1})²/(2σ²)} / exp{-

(ξ _i - m _{ξ 0})²/(2σ²)} ≥ A; (8) η ( m ) = exp {-

( ξ _i - m _{ξ 1} ) ² / (2σ ² )} / exp {-

( ξ _i - m _{ξ 0} ) ² / (2σ ² )} ≥ A ; (eight)

on the belonging of the generalized KEE indicator to the permissible range of deviations, if

(ξ _i - m _{ξ 1})²/(2σ²)} / exp{-

(ξ _i – m _{ξ 0})²/(2σ²)} ≤ B. (9) η ( m ) = exp {-

(ξ _i - m _{ξ 1} ) ² / (2σ ² )} / exp {-

(ξ _i - m _{ξ 0} ) ² / (2σ ² )} ≤ B. (9)

The setpoint values A and B are determined by the expressions

A = (1 -β) / α; B = β / (1 - α). (10)

Taking the logarithm and transforming expressions (7) - (9), we obtain

ξ _i + m⋅ (m ² _{ξ 0} – m ² _{ξ 1})/(2σ²) < ln[(1 - β)/α], (11) ln [β / (1 - α)] <[( m _{ξ 1} - m _{ξ 0} ) / σ ² ] ⋅

ξ _i + m⋅ ( m ² _{ξ 0} - m ² _{ξ 1} ) / (2σ ² ) < ln [(1 - β) / α], (11)

ξ _i + m⋅(m ² _{ξ 0} - m ² _{ξ 1})/(2σ²) ≤ ln[β/(1 - α)], (12)[( m _{ξ 1} - m _{ξ 0} ) / σ ² ] ⋅

ξ _i + m ⋅ ( m ² _{ξ 0} - m ² _{ξ 1} ) / (2σ ² ) ≤ ln [ β / (1 - α)], (12)

ξ _i + m⋅(m ² _{ξ 0} - m ² _{ξ 1})/(2σ ²) ≥ ln[(1 - β)/α]. (13)[( m _{ξ 1} - m _{ξ 0} ) / σ ² ] ⋅

ξ _i + m ⋅ ( m ² _{ξ 0} - m ² _{ξ 1} ) / (2 σ ² ) ≥ ln [(1 - β) / α]. (thirteen)

Adding to both sides of the inequalities the term - m ⋅ ( m ² _{ξ 0} - m ² _{ξ 1} ) / (2 σ ² ) and dividing by ( m _{ξ 1} - m _{ξ 0} ) / σ ² , we arrive at the relations

ξ _i < [( σ ² / ( m _{ξ 1} - m _{ξ 0} )] ⋅ ln [ β / (1 - α )] + m ⋅ ( m _{ξ 0} + m _{ξ 1} ) / 2 <

ξ _i <

<[( σ ² / ( m _{ξ 1} - m _{ξ 0} )] ⋅ ln [(1 - β ) / α ] + m ⋅ ( m _{ξ 0} + m _{ξ 1} ) / 2, (14)

ξ _i < [(σ ²/(m _{ξ 1} - m _{ξ 0})]⋅ln[β/(1 - α)] + m⋅(m _{ξ 0} + m _{ξ 1})/2, (15)

ξ _i <[( σ ² / ( m _{ξ 1} - m _{ξ 0} )] ⋅ ln [ β / (1 - α )] + m ⋅ ( m _{ξ 0} + m _{ξ 1} ) / 2, (15)

ξ _i < [(σ ²/(m _{ξ 1} - m _{ξ 0})]⋅ln[(1 - β)/α] + m⋅(m _{ξ 0} + m _{ξ 1})/2. (16)

ξ _i <[( σ ² / ( m _{ξ 1} - m _{ξ 0} )] ⋅ ln [(1 - β ) / α ] + m ⋅ ( m _{ξ 0} + m _{ξ 1} ) / 2. (16)

The last three inequalities make it possible to implement the control of the generalized indicator of the CEE using the "acceptance" numbers.

For each step m of the sequential analysis procedure, an “acceptance” number is calculated

a ( m ) = [( σ ² / ( m _{ξ 1} - m _{ξ 0} )] ⋅ ln [ β / (1 - α )] + m ⋅ ( m _{ξ 0} + m _{ξ 1} ) / 2 (17)

and the "rejection" number

b ( m ) = [( σ ² / ( m _{ξ 1} - m _{ξ 0} )] ⋅ ln [(1 - β ) / α ] + m ⋅ ( m _{ξ 0} + m _{ξ 1} ) / 2. (18)

The numbers (dependencies a ( m ), b ( m )) are calculated in advance and used as set values. The sequential analysis procedure is performed as long as the inequalities are met

ξ _i < b(m). (19) a ( m ) <

ξ _i < b ( m ). (nineteen)

ξ _i выходит за пределы интервала ]а(m), b(m)[ принимается решение относительно допустимости или недопустимости отклонений обобщенного показателя КЭЭ.When the amount

ξ _i goes beyond the interval] a ( m ), b ( m ) [a decision is made regarding the admissibility or inadmissibility of deviations of the generalized indicator of the CEE.

Example: Let, taking into account the weight coefficients of the individual components of the generalized indicator of the CEE, the mathematical expectations m _{ξ 0} and m _{ξ 1 of the} generalized indicator of the CEE ξ take the values m _{ξ 0} = 130, m _{ξ 1} = 155. The value of the variance ξ under the normal distribution law is σ ² = 225. Let's set α = 0.01, and β = 0.03. Then the acceptance and rejection numbers are determined by the expressions

a ( m ) = [225 / (155-130)] ⋅ ln [0.03 / (1-0.01)] + m ⋅ (130 + 155) / 2 = 142.5⋅ m - 87.5;

b ( m ) = [225 / (155-130)] ⋅ ln [(1-0.03) / 0.01] + m ⋅ (130 + 155) / 2 = 142.5⋅ m + 114.37.

ξ _i , а(m) и b(m).Let there be sequential sample time readings of the variable ξ, the values of which are reflected in Table 1. Additionally, Table 1 includes variable values varying from step to step of the sequential procedure

ξ _i , a ( m ) and b ( m ).

Table 1. The values of the variables used in the procedure for sequential decision-making regarding the deviations of the generalized indicator of the EEE.

m one 2 3 4 5 6 7 eight 9 ξ 149 151 154 155 148 160 156 154 150

ξ _i

ξ _i 149 300 454 609 757 917 1073 1227 1377 a ( m ) 55 197.5 340 482.5 625 767.5 910 1052.5 1195 b ( m ) 256.9 399.4 541.9 684.4 826.9 969.4 1111.9 1254.4 1396.9

10 eleven 12 thirteen 14 15 sixteen 17 eighteen nineteen 140 142 135 154 150 160 162 158 156 160 1517 1659 1794 1948 2098 2258 2420 2578 2734 2894 1337.5 1480 1622.5 1765 1907.5 2050 2192.5 2335 2477.5 2620 1539.4 1681.9 1824.4 1966.9 2109.4 2251.9 2394.4 2536.9 2679.4 2821.9

ξ _i ), характеризующие процесс принятия решения. Коэффициент s, определяющий угловой наклон уставочных границ, соответствует выражениюFIG. 2 illustrates the process of sequential decision-making in the analysis of the generalized indicator of the EEE. Points ( m ,

ξ _i ) characterizing the decision-making process. The coefficient s , which determines the angular slope of the setting limits, corresponds to the expression

s = ( m _{ξ 0} + m _{ξ 1} ) / 2. (twenty)

Setting limits are shifted relative to each other by

[( σ ² / ( m _{ξ 1} - m _{ξ 0} )] ⋅ { ln [(1 - β ) / α ] - ln [ β / (1 - α )]}. (21)

The area between the set limits is the area of uncertainty corresponding to the continuation of the test. Analysis of FIG. 2 shows that the sequential analysis process ends at step m = 15 with a decision on the discrepancy between the generalized KEE indicator and the established standard values.

With regard to the device (Fig. 1), a set of processing operations (calculations) is implemented as follows.

At each sample time, the calculated values of the EEC indicators are received at the first inputs of the comparison circuits 4 ₁ ... 4 _N. For example, for [RF Patent No. 2613584, IPC G01R 19/25, publ. 03/17/2017, Bul. No. 8] the parameters are calculated: k _D , k _C , k _S , k _H. The second inputs of the comparison circuits 4 ₁ ... 4 _N from the first group of outputs of the memory unit 8 receive the normalized values of the SEE indicators, characteristic of the current operating mode of the electrical network. According to the results of the comparison performed in block 4, a vector y = ( y ₁ , ..., y _j , ..., y _N ) is formed, the components of which in block 5 are multiplied by the corresponding coefficients included in the column vector c = ( c ₁ , …, C _j ,…, c _N ) ^Т - weight coefficients that determine the ratio of damages in case of violations of the CEE for individual parameters. To perform computational operations in block 5, the corresponding multipliers 5 ₁ ... 5 _{N are used} . The group adder 6 is designed to obtain a generalized indicator of the CEE according to expression (2), and from its output, sample values ξ _i are fed to the input of block 7 to implement the sequential analysis procedure. The other input of block 7 receives arrays of values a ( m ) and b ( m ), the components of which correspond to the set values for each step of the sequential analysis procedure.

FIG. 2 illustrates the decision-making process in sequential analysis using the generalized CEE parameter, the sequential analysis process ends with the adoption of the hypothesis of unacceptable deviations of the generalized CEE indicator.

The memory unit 8 of the device (Fig. 1), which implements the method for analyzing the quality of electrical energy in a three-phase electrical network, receives information about the current mode, expressed, for example, in the form of a mode number. Such information can come, for example, from the SCADA system or from the dispatch and technological control systems of the electrical network (operational information complex - OIC). The mode number determines the normalized values of the EEC indicators, the weight coefficients c ₁ , ..., c _j , ..., c _N and the current set of set values a ( m ), b ( m ), issued from the outputs of the memory block 8 to the comparison block 4, block 5 multiplication and block 7 in the analysis of controlled points of connection of the electrical network. Along with information about the current mode, before the implementation of the method for analyzing the quality of electrical energy in a three-phase electrical network, simulation data, expert assessments and other information necessary for the operation of the device are fed to the input of the memory unit 7 (Fig. 1).

The results of the analysis of the SEE indicators are expressed in the values of the discrete signal from the output of the unit 7 of sequential analysis. The appearance of a single signal from the output of block 7 indicates a deviation of the CEE indicators from the standardized values, which can lead to damage to the consumer, and the need to implement organizational and technical measures in order to introduce the CEE indicators into the permissible ranges.

Thus, the aim of the invention is achieved, which is to develop a method for analyzing the quality of electrical energy in a three-phase system, providing a comprehensive account of the influence of deviations of various EEC indicators on the functioning of electrical consumers of end industrial and non-industrial consumers.

Claims (1)

A method for analyzing the quality of electrical energy in a three-phase electrical network, comprising the stages at which: a set of electrical quantities is measured, while the set contains one electrical quantity for each phase, a spatial vector is formed based on an instant three-dimensional transformation of a set of measured electrical quantities, the set is determined containing, at least one parameter characterizing the quality of electrical energy in a three-phase electrical network, characterized in that the output signal characterizing the results of analyzing the quality of electrical energy in a three-phase electrical network is generated on the basis of selective control of the generalized indicator of the quality of electrical energy, which is obtained by comparison individual indicators of the quality of electrical energy with their normalized values for the current operating mode of the electrical network, as well as the weighted summation of the results of comparisons, the coefficients for weighted m summation is obtained by expert assessments or simulation modeling of damages to consumers with deviations of each of the power quality indicators from the standardized value; in sampling control, a sequential analysis procedure is used, the setting values for which are determined based on the results of simulation modeling of the electric network, taking into account the operating modes of consumers' power consumers.

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