CN106291113A

CN106291113A - A kind of three phase line power frequency sequence impedance On-line Measuring Method

Info

Publication number: CN106291113A
Application number: CN201610595848.2A
Authority: CN
Inventors: 梁海峰; 曹大卫; 于立杰
Original assignee: North China Electric Power University
Current assignee: North China Electric Power University
Priority date: 2016-07-27
Filing date: 2016-07-27
Publication date: 2017-01-04

Abstract

A kind of three phase line power frequency sequence impedance On-line Measuring Method, first described method according to the impedance parameter equivalent-circuit model of asymmetrical three-phase circuit, draws the less qualitative equation group of circuit model.Then less qualitative for impedance computation equation group, by taking multiple measurements the associated voltage of circuit and the magnitude of current and processing, forms over-determined systems.Finally utilize the method for least square in complex field, over-determined systems is solved, be calculated asymmetrical three-phase transmission line of electricity each sequence impedance parameter.This method considers the asymmetric situation of transmission line of electricity, and the mutual impedance counted and exist between circuit, it is possible to for the on-line measurement of generally transmission line of electricity sequence impedance parameter, and provide the foundation data to the on-line analysis of power system and state estimation.Emulate by building three-phase imbalance circuit, demonstrate the effectiveness of institute's extracting method.

Description

A kind of three phase line power frequency sequence impedance On-line Measuring Method

Technical field

Present invention is generally directed to three phase line and be in the on-line measurement problem of power frequency sequence impedance under asymmetrical state, carry Go out a kind of measuring method, belong to observation and control technology field.

Background technology

The main thoroughfare that transmission line of electricity transmits as electric energy, the online of its power frequency sequence impedance parameter is accurately measured, for electricity The work such as energy normal transmission, Load flow calculation, stability analysis, relay protection setting have important practical significance.For tradition from Line measuring method complex operation, problem poor for applicability, research is convenient, the On-line Measuring Method of transmission line of electricity impedance accurately, is One needs the problem explored.

On-line measurement is alternatively referred to as live line measurement, refers in the condition that all circuits do not have a power failure or not exclusively have a power failure Under, utilize new equipment and technology to realize the measurement of transmission line parameter.On-line measurement power transmission line power frequency parameter has following excellent Point: (1) on-line measurement must the condition of having a power failure can not be retrained by circuit, it is to avoid make line outage in turn result in because of measuring Loss, improve economy and the reliability of power system.(2) by line parameter circuit value is carried out on-line measurement, can be to it State carries out on-line checking, it is possible to finds the hidden danger existed as early as possible and gets rid of in time.

Along with the development of power system, the ratio that the arrangement of the parallel erection of many loop lines accounts in systems is more and more higher, Electromagnetic coupled effect is increasing on the impact of line impedance parameter.The accurate measurement of transmission line of electricity impedance parameter, it is necessary to examine Consider the coupling between circuit.Owing to transmission line of electricity is likely to be at asymmetric running status, so its impedance parameter is online Also to consider during measurement that it affects.Therefore, this paper presents a kind of new three phase line power frequency sequence impedance parameter to survey online The method of amount.

Summary of the invention

Present invention aims to deficiency present in current power transmission line impedance Parameter Measuring method, propose A kind of power frequency sequence impedance On-line Measuring Method considering transmission line parameter unsymmetry accurately, for the safe and reliable fortune of system Row provides reference.

Problem of the present invention realizes according to following technical proposals:

A kind of three phase line power frequency sequence impedance On-line Measuring Method, described method initially sets up asymmetrical three-phase transmission of electricity The circuit model of circuit, draws the less qualitative equation that transmission line of electricity impedance parameter calculates；Then for the calculating side of impedance parameter Journey, forms over-determined systems；Finally utilize the method for least square in complex field, derive asymmetrical three-phase power transmission line power frequency each The computing formula of sequence impedance parameter.

Above-mentioned a kind of three phase line power frequency sequence impedance On-line Measuring Method, described method follows the steps below:

A) analyze the feature of asymmetrical three-phase circuit, set up the circuit model of asymmetrical three-phase transmission line of electricity, draw transmission of electricity The equation group that line impedance parameter calculates, equation group is less qualitative；

B) less qualitative, by the associated voltage of circuit is carried out with the magnitude of current for line impedance parameter group of equations Repetitive measurement, forms over-determined systems；

C) utilize the method for least square in complex field, over-determined systems is solved, derive asymmetrical three-phase transmission of electricity The computing formula of circuit power frequency each sequence impedance parameter.

Above-mentioned a kind of three phase line power frequency sequence impedance On-line Measuring Method, sets up the electricity of asymmetrical three-phase transmission line of electricity Road model, draws specifically comprising the following steps that of the less qualitative equation that parameter calculates

1. according to Circuit theory, analyze the feature of three-phase circuit, only consider the impedance parameter of circuit, between meter and circuit Mutual impedance, can obtain the impedance parameter equivalent circuit of asymmetric transmission line of electricity.See accompanying drawing 1.

2. according to the relation between equivalent circuit self-impedance, mutual impedance and voltage x current amount, the algebraically of equivalent circuit is drawn Shown in equation group such as formula (1), equation group is less qualitative.

\{\begin{matrix} {\overset{\cdot}{U}}_{a} = Z_{a} {\overset{\cdot}{I}}_{a} + Z_{a b} {\overset{\cdot}{I}}_{b} + Z_{a c} {\overset{\cdot}{I}}_{c} \\ {\overset{\cdot}{U}}_{b} = Z_{a b} {\overset{\cdot}{I}}_{a} + Z_{b} {\overset{\cdot}{I}}_{b} + Z_{b c} {\overset{\cdot}{I}}_{c} \\ {\overset{\cdot}{U}}_{c} = Z_{a c} {\overset{\cdot}{I}}_{a} + Z_{b c} {\overset{\cdot}{I}}_{b} + Z_{c} {\overset{\cdot}{I}}_{c} \end{matrix} - - - (1)

In formula, Z_a, Z_b, Z_cIt is respectively each phase self-impedance；Z_ab, Z_bc, Z_acIt is respectively every biphase mutual impedance；Respectively For transmission line of electricity A, the electric current of B, C three-phase； It is transmission line of electricity A respectively, the voltage of B, C three-phase front and back end.

Above-mentioned a kind of three phase line power frequency sequence impedance On-line Measuring Method, chooses suitable voltage current measurement object and enters Row repetitive measurement, and to specifically comprising the following steps that measured signal processes

Select the magnitude of current of each phase transmission line of electricity front and back end voltage with each phase is taken multiple measurements, and to measured electricity Current voltage signal sample data carries out Fourier decomposition, removes the impact of harmonic wave, extracts the information of power frequency component, forms overdetermination side Journey group.Each measurement data of voltage and current signal wants strict guarantee to come from synchronization.

Above-mentioned a kind of three phase line power frequency sequence impedance On-line Measuring Method, deficient for route parameter calculation equation is determined Property, form specifically comprising the following steps that of overdetermined equation

According to the less qualitative equation group of formula (1), utilize the voltage and electric current power frequency component obtained after Fourier decomposition Information, the following over-determined systems solving line impedance parameter of foundation:

\{\begin{matrix} {\overset{\cdot}{U}}_{a}^{(1)} = Z_{a} {\overset{\cdot}{I}}_{a}^{(1)} + Z_{a b} {\overset{\cdot}{I}}_{b}^{(1)} + Z_{a c} {\overset{\cdot}{I}}_{c}^{(1)} \\ {\overset{\cdot}{U}}_{b}^{(1)} = Z_{a b} {\overset{\cdot}{I}}_{a}^{(1)} + Z_{b} {\overset{\cdot}{I}}_{b}^{(1)} + Z_{b c} {\overset{\cdot}{I}}_{c}^{(1)} \\ {\overset{\cdot}{U}}_{c}^{(1)} = Z_{a c} {\overset{\cdot}{I}}_{a}^{(1)} + Z_{b c} {\overset{\cdot}{I}}_{b}^{(1)} + Z_{c} {\overset{\cdot}{I}}_{c}^{(1)} \\ . \\ . \\ . \\ {\overset{\cdot}{U}}_{m}^{(1)} = Z_{a} {\overset{\cdot}{I}}_{a}^{(m)} + Z_{a b} {\overset{\cdot}{I}}_{b}^{(m)} + Z_{a c} {\overset{\cdot}{I}}_{c}^{(m)} \\ {\overset{\cdot}{U}}_{b}^{(m)} = Z_{a b} {\overset{\cdot}{I}}_{a}^{(m)} + Z_{b} {\overset{\cdot}{I}}_{b}^{(m)} + Z_{b c} {\overset{\cdot}{I}}_{c}^{(m)} \\ {\overset{\cdot}{U}}_{c}^{(m)} = Z_{a c} {\overset{\cdot}{I}}_{a}^{(m)} + Z_{b c} {\overset{\cdot}{I}}_{b}^{(m)} + Z_{c} {\overset{\cdot}{I}}_{c}^{(m)} \end{matrix} - - - (2)

In formula,For measuring, to the m time, the A phase voltage power frequency component obtained for the first time,It is first The A phase current power frequency component that secondary to the m time is measured, B, C phase is in like manner.

Write as matrix form:

\overset{\cdot}{U} = \overset{\cdot}{I} Z - - - (3)

In formula,Z=[Z_aZ_bZ_cZ_abZ_bcZ_ac]^T；

I = [\begin{matrix} I_{a}^{(1)} & 0 & 0 & I_{b}^{(1)} & 0 & I_{c}^{(1)} \\ 0 & I_{b}^{(1)} & 0 & I_{a}^{(1)} & I_{c}^{(1)} & 0 \\ 0 & 0 & I_{c}^{(1)} & 0 & I_{c}^{(1)} & I_{a}^{(1)} \\ . & . & . & . & . & . \\ . & . & . & . & . & . \\ . & . & . & . & . & . \\ I_{a}^{(m)} & 0 & 0 & I_{b}^{(m)} & 0 & I_{c}^{(m)} \\ 0 & I_{b}^{(m)} & 0 & I_{a}^{(m)} & I_{c}^{(m)} & 0 \\ 0 & 0 & I_{c}^{(m)} & 0 & I_{c}^{(m)} & I_{a}^{(m)} \end{matrix}]

The impedance parameter matrix obtaining transmission line of electricity is:

Z = {({\overset{\cdot}{I}}^{T} \overset{\cdot}{I})}^{- 1} ({\overset{\cdot}{I}}^{T} \overset{\cdot}{U}) - - - (4)

Accompanying drawing explanation

Accompanying drawing 1 is transmission line of electricity impedance parameter equivalent circuit.

Detailed description of the invention

The present invention proposes a kind of impedance On-line Measuring Method considering transmission line parameter unsymmetry, for the peace of system Full reliability service provides reference.In order to realize the accurate measurement to line impedance parameter, establish consider circuit mutual impedance etc. Effect circuit.The enforcement of the method for the invention mainly has three partial contents.One is the circuit setting up asymmetrical three-phase transmission line of electricity Model, obtains the less qualitative equation group that transmission line of electricity impedance parameter calculates；Two is less qualitative for equation group, chooses relevant Voltage and the magnitude of current, form the over-determined systems of impedance computation；Finally utilize the method for least square in complex field, derive three-phase The computing formula of asymmetric power transmission line power frequency each sequence impedance parameter.

The present invention carried line impedance measuring method unlike conventional method, conventional method just in circuit from Under line states, its impedance is measured, and this method is applicable to the on-line operation state of circuit；Additionally, this method considers line There is unsymmetry and mutual impedance between road, and finally give each sequence impedance of circuit.

The present invention sets up transmission line of electricity equivalent circuit, obtains the tool of the less qualitative equation group that transmission line of electricity impedance parameter calculates Body embodiment is as follows:

According to Circuit theory, analyze the feature of three-phase circuit, only consider the impedance parameter of circuit, mutual between meter and circuit Impedance, can obtain the impedance parameter equivalent circuit of asymmetric transmission line of electricity.See accompanying drawing 1.

According to the relation between equivalent circuit self-impedance, mutual impedance and voltage x current amount, obtain the algebraically side of equivalent circuit Journey group is as follows:

\{\begin{matrix} {\overset{\cdot}{U}}_{a} = Z_{a} {\overset{\cdot}{I}}_{a} + Z_{a b} {\overset{\cdot}{I}}_{b} + Z_{a c} {\overset{\cdot}{I}}_{c} \\ {\overset{\cdot}{U}}_{b} = Z_{a b} {\overset{\cdot}{I}}_{a} + Z_{b} {\overset{\cdot}{I}}_{b} + Z_{b c} {\overset{\cdot}{I}}_{c} \\ {\overset{\cdot}{U}}_{c} = Z_{a c} {\overset{\cdot}{I}}_{a} + Z_{b c} {\overset{\cdot}{I}}_{b} + Z_{c} {\overset{\cdot}{I}}_{c} \end{matrix} - - - (5)

In the algebraic equation of above-mentioned asymmetrical three-phase transmission line of electricity equivalent model, Z_a, Z_b, Z_c, Z_ab, Z_bc, Z_acIt is to wait to ask not The amount of knowing, but only three equations, it is clear that equation group is less qualitative.

The present invention is directed to the less qualitative of route parameter calculation equation group, the detailed description of the invention forming overdetermined equation is as follows:

Phase front and back end each to transmission line of electricity voltage is selected to take multiple measurements, in order to remove harmonic wave pair with the magnitude of current of each phase The interference of power frequency sequence impedance on-line measurement, carries out Fourier decomposition to measured voltage and current signal, and extracts power frequency component Amplitude and phase information form over-determined systems.In addition, it is ensured that often group voltage and the magnitude of current are both from synchronization Measured value.For ensureing the accuracy of line impedance parameter measurement, the most many to the voltage of circuit and the measurement of electric current In 5 groups of data.

The over-determined systems that foundation solves line impedance is as follows:

\{\begin{matrix} {\overset{\cdot}{U}}_{a}^{(1)} = Z_{a} {\overset{\cdot}{I}}_{a}^{(1)} + Z_{a b} {\overset{\cdot}{I}}_{b}^{(1)} + Z_{a c} {\overset{\cdot}{I}}_{c}^{(1)} \\ {\overset{\cdot}{U}}_{b}^{(1)} = Z_{a b} {\overset{\cdot}{I}}_{a}^{(1)} + Z_{b} {\overset{\cdot}{I}}_{b}^{(1)} + Z_{b c} {\overset{\cdot}{I}}_{c}^{(1)} \\ {\overset{\cdot}{U}}_{c}^{(1)} = Z_{a c} {\overset{\cdot}{I}}_{a}^{(1)} + Z_{b c} {\overset{\cdot}{I}}_{b}^{(1)} + Z_{c} {\overset{\cdot}{I}}_{c}^{(1)} \\ . \\ . \\ . \\ {\overset{\cdot}{U}}_{m}^{(1)} = Z_{a} {\overset{\cdot}{I}}_{a}^{(m)} + Z_{a b} {\overset{\cdot}{I}}_{b}^{(m)} + Z_{a c} {\overset{\cdot}{I}}_{c}^{(m)} \\ {\overset{\cdot}{U}}_{b}^{(m)} = Z_{a b} {\overset{\cdot}{I}}_{a}^{(m)} + Z_{b} {\overset{\cdot}{I}}_{b}^{(m)} + Z_{b c} {\overset{\cdot}{I}}_{c}^{(m)} \\ {\overset{\cdot}{U}}_{c}^{(m)} = Z_{a c} {\overset{\cdot}{I}}_{a}^{(m)} + Z_{b c} {\overset{\cdot}{I}}_{b}^{(m)} + Z_{c} {\overset{\cdot}{I}}_{c}^{(m)} \end{matrix} - - - (6)

Write as matrix form:

\overset{\cdot}{U} = \overset{\cdot}{I} Z - - - (7)

In formula,Z=[Z_aZ_bZ_cZ_abZ_bcZ_ac]^T；

I = [\begin{matrix} I_{a}^{(1)} & 0 & 0 & I_{b}^{(1)} & 0 & I_{c}^{(1)} \\ 0 & I_{b}^{(1)} & 0 & I_{a}^{(1)} & I_{c}^{(1)} & 0 \\ 0 & 0 & I_{c}^{(1)} & 0 & I_{c}^{(1)} & I_{a}^{(1)} \\ . & . & . & . & . & . \\ . & . & . & . & . & . \\ . & . & . & . & . & . \\ I_{a}^{(m)} & 0 & 0 & I_{b}^{(m)} & 0 & I_{c}^{(m)} \\ 0 & I_{b}^{(m)} & 0 & I_{a}^{(m)} & I_{c}^{(m)} & 0 \\ 0 & 0 & I_{c}^{(m)} & 0 & I_{c}^{(m)} & I_{a}^{(m)} \end{matrix}]

The present invention calculates overdetermined equation to impedance parameter and solves, and the detailed description of the invention obtaining each sequence impedance is as follows:

The impedance parameter matrix of transmission line of electricity is:

Z = {({\overset{\cdot}{I}}^{T} \overset{\cdot}{I})}^{- 1} ({\overset{\cdot}{I}}^{T} \overset{\cdot}{U}) - - - (8)

After obtaining the overdetermined equation that transmission line of electricity calculates, utilize the method for least square in complex field, can be to three-phase The impedance parameter of asymmetric transmission line of electricity calculates, and then can solve each sequence impedance of circuit.By impedance matrix:

Z_{a b c} = [\begin{matrix} Z_{a} & Z_{a b} & Z_{a c} \\ Z_{a b} & Z_{b} & Z_{b c} \\ Z_{a c} & Z_{b c} & Z_{c} \end{matrix}] - - - (9)

With transition matrix:

A = [\begin{matrix} 1 & 1 & 1 \\ 1 & a^{2} & a \\ 1 & a & a^{2} \end{matrix}] - - - (10)

Can obtain each sequence impedance of circuit:

Z_{012} = A^{- 1} Z_{a b c} A = [\begin{matrix} Z_{0} & Z_{01} & Z_{02} \\ Z_{01} & Z_{1} & Z_{12} \\ Z_{02} & Z_{12} & Z_{2} \end{matrix}] - - - (11)

Instance analysis

It addition, in order to verify effectiveness of the invention and accuracy, carry out following experiment:

According to said method, building the phantom of the three asymmetric transmission lines of electricity of phase of impedance, three phase line is a length of 20 kilometers, line voltage distribution is 220kV, and load is 100MW.Relevant voltage is taken multiple measurements with electric current, uses above-mentioned side Method, the zero sequence impedance of computing electric power line and positive sequence impedance.Result is as shown in table 1.

Table 1 the simulation results

Simulation result shows, zero sequence impedance modulus value and impedance angle angle value error are respectively 0.2501% and 0.1533%, just Sequence impedance magnitude and impedance angle angle value error are respectively 0.1974% and 0.1011%.Its error is much smaller than the error of Practical Project Requirement, shows that the method has effectiveness and accuracy.

Claims

1. a three phase line power frequency sequence impedance On-line Measuring Method, is characterized in that, sets up the resistance of asymmetric transmission line of electricity Anti-parameter equivalent circuit, draws Algebraic Equation set；Then less qualitative according to Algebraic Equation set, chooses suitable voltage current measurement Object takes multiple measurements, and processes measured signal, forms overdetermined equation；Finally utilize the young waiter in a wineshop or an inn in complex field Multiplication, solves the overdetermined equation of impedance computation, obtains power transmission line power frequency each sequence impedance parameter.

Impedance parameter equivalent circuit according to asymmetric transmission line of electricity the most according to claim 1, draws Algebraic Equation set, It is characterized in that: transmission line of electricity is utilized ∏ type circuit equivalent, and only considers impedance parameter, the mutual impedance between meter and circuit, Equivalent circuit to asymmetric transmission line of electricity impedance parameter.According to the relation between impedance and line voltage distribution electric current, obtain equivalence The less qualitative Algebraic Equation set of circuit is as follows:

\{\begin{matrix} {\overset{\cdot}{U}}_{a} = Z_{a} {\overset{\cdot}{I}}_{a} + Z_{a b} {\overset{\cdot}{I}}_{b} + Z_{a c} {\overset{\cdot}{I}}_{c} \\ {\overset{\cdot}{U}}_{b} = Z_{a b} {\overset{\cdot}{I}}_{a} + Z_{b} {\overset{\cdot}{I}}_{b} + Z_{b c} {\overset{\cdot}{I}}_{c} \\ {\overset{\cdot}{U}}_{c} = Z_{a c} {\overset{\cdot}{I}}_{a} + Z_{b c} {\overset{\cdot}{I}}_{b} + Z_{c} {\overset{\cdot}{I}}_{c} \end{matrix} - - - (1)

In formula, Z_a, Z_b, Z_cIt is respectively each phase self-impedance；Z_ab, Z_bc, Z_acIt is respectively every biphase mutual impedance；It is respectively power transmission line Road A, the electric current of B, C three-phase； It is transmission line of electricity A respectively, the voltage of B, C three-phase front and back end.

Suitable voltage current measurement object of choosing the most according to claim 1 takes multiple measurements, and to measured signal Process, it is characterized in that: select the magnitude of current of each phase transmission line of electricity front and back end voltage with each phase is taken multiple measurements, and right Measured voltage and current signal sampled data carries out Fourier decomposition, removes the impact of harmonic wave, extracts the information of power frequency component Calculating data as overdetermined equation.Each measurement data of voltage and current signal wants strict guarantee to come from synchronization.

4. solve the over-determined systems of line impedance according to the foundation described in claim 1 and claim 3, it is characterized in that: profit By the voltage after Fourier decomposition and electric current power frequency component information, set up following over-determined systems:

\{\begin{matrix} {\overset{\cdot}{U}}_{a}^{(1)} = Z_{a} {\overset{\cdot}{I}}_{a}^{(1)} + Z_{a b} {\overset{\cdot}{I}}_{b}^{(1)} + Z_{a c} {\overset{\cdot}{I}}_{c}^{(1)} \\ {\overset{\cdot}{U}}_{b}^{(1)} = Z_{a b} {\overset{\cdot}{I}}_{a}^{(1)} + Z_{b} {\overset{\cdot}{I}}_{b}^{(1)} + Z_{b c} {\overset{\cdot}{I}}_{c}^{(1)} \\ {\overset{\cdot}{U}}_{c}^{(1)} = Z_{a c} {\overset{\cdot}{I}}_{a}^{(1)} + Z_{b c} {\overset{\cdot}{I}}_{b}^{(1)} + Z_{c} {\overset{\cdot}{I}}_{c}^{(1)} \\ \begin{matrix} . \\ . \\ . \end{matrix} \\ {\overset{\cdot}{U}}_{a}^{(m)} = Z_{a} {\overset{\cdot}{I}}_{a}^{(m)} + Z_{a b} {\overset{\cdot}{I}}_{b}^{(m)} + Z_{a c} {\overset{\cdot}{I}}_{c}^{(m)} \\ {\overset{\cdot}{U}}_{b}^{(m)} = Z_{a b} {\overset{\cdot}{I}}_{a}^{(m)} + Z_{b} {\overset{\cdot}{I}}_{b}^{(m)} + Z_{b c} {\overset{\cdot}{I}}_{c}^{(m)} \\ {\overset{\cdot}{U}}_{c}^{(m)} = Z_{a c} {\overset{\cdot}{I}}_{a}^{(m)} + Z_{b c} {\overset{\cdot}{I}}_{b}^{(m)} + Z_{c} {\overset{\cdot}{I}}_{c}^{(m)} \end{matrix} - - - (2)

In formula,For measuring, to the m time, the A phase power frequency component voltage obtained for the first time；For arriving for the first time Measure the A phase power frequency component electric current obtained the m time；B, C phase is in like manner.

Then the method for least square in complex field is utilized can overdetermined equation to be solved, and then can be in the hope of each sequence of circuit Impedance.