CN110568260B - Power transmission line harmonic parameter estimation method for power grid harmonic analysis - Google Patents

Power transmission line harmonic parameter estimation method for power grid harmonic analysis Download PDF

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CN110568260B
CN110568260B CN201910847943.0A CN201910847943A CN110568260B CN 110568260 B CN110568260 B CN 110568260B CN 201910847943 A CN201910847943 A CN 201910847943A CN 110568260 B CN110568260 B CN 110568260B
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transmission line
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徐群伟
吴俊�
黄弘扬
楼伯良
吕文韬
马智泉
李培
陈�峰
许双婷
王杨
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Electric Power Research Institute of State Grid Zhejiang Electric Power Co Ltd
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    • G01—MEASURING; TESTING
    • G01R—MEASURING ELECTRIC VARIABLES; MEASURING MAGNETIC VARIABLES
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Abstract

The invention discloses a power transmission line harmonic parameter estimation method for power grid harmonic analysis, which comprises the following steps: monitoring the power transmission line to obtain a harmonic voltage effective value, harmonic active power and harmonic reactive power at two ends; establishing a relation among a harmonic parameter of the power transmission line, the harmonic voltage effective value at two ends, the harmonic active power and the harmonic reactive power based on a power transmission line distribution parameter model; randomly selecting a plurality of point data for each data segment, and obtaining an equation set by utilizing multipoint estimation; and solving the equation set through a nonlinear optimization algorithm to obtain the harmonic parameters of the power transmission line. The harmonic parameters obtained by the method are utilized to carry out more accurate harmonic modeling, and the method has important significance for power grid harmonic load flow calculation, state estimation, harmonic source positioning and the like.

Description

Power transmission line harmonic parameter estimation method for power grid harmonic analysis
Technical Field
The invention relates to the field of power systems, in particular to a power transmission line harmonic parameter estimation method for power grid harmonic analysis.
Background
With more and more nonlinear loads accessed to a power grid, the problem of harmonic pollution of the power grid becomes more and more serious, so that harmonic analysis on the system, including harmonic load flow calculation, harmonic state estimation, harmonic source positioning and the like, is significant, and harmonic modeling on each element of the system and harmonic parameter estimation are the premise of harmonic analysis. In recent years, fundamental wave parameter identification technology of a power transmission line is mature, but related research on harmonic parameter estimation is less.
The traditional harmonic parameter estimation of the power transmission line is based on the premise assumption that the impedance and the admittance value of the line in unit length are not changed, the harmonic resistance is consistent with the fundamental wave, the harmonic reactance is h times of the fundamental wave reactance, and the parallel conductance of the line is ignored. However, due to the conductor skin effect and the frequency response of the earth loop impedance, the unit impedance of the transmission line actually changes with the frequency, and in the simulation example, the resistance and reactance value per unit length of the transmission line change with the frequency as shown in fig. 2. Therefore, when the harmonic frequency increases, the precondition assumption of the conventional method is not satisfied, and the estimation error of the harmonic parameter becomes larger.
On the other hand, the harmonic parameters of the power transmission line can be accurately calculated by using a Carson formula and a Bessel function, but the calculation process is complex, and the accurate structural parameters of the power transmission line, including the sectional area and height of a conductor, the direct current resistance and the like, need to be known.
Disclosure of Invention
In order to solve the problem that the existing power transmission line harmonic parameter estimation method neglects the frequency response of unit impedance, so that parameter estimation is inaccurate, the power transmission line harmonic parameter estimation method for power grid harmonic analysis is provided, and the power transmission line harmonic parameter can be estimated accurately.
A power transmission line harmonic parameter estimation method for power grid harmonic analysis comprises the following steps:
s100: monitoring the power transmission line to obtain a harmonic voltage effective value, harmonic active power and harmonic reactive power at two ends;
s200: establishing a relation among a harmonic parameter of the power transmission line, the harmonic voltage effective value at two ends, the harmonic active power and the harmonic reactive power based on a power transmission line distribution parameter model;
s300: according to the relational expression, randomly selecting a plurality of point data for each data segment, and obtaining an equation set by utilizing multipoint estimation;
s400: and solving the equation set through a nonlinear optimization algorithm to obtain the harmonic parameters of the power transmission line.
Preferably, the step S100: the PQ monitoring device monitors the transmission end and the receiving end of the power transmission line to obtain: harmonic voltage effective value V of transmission end of power transmission line1Harmonic voltage effective value V of sum receiving end2Harmonic active power P of sending end1Harmonic active power P of receiving end2Harmonic reactive power Q of sending terminal1Harmonic reactive power Q of receiving end2。
Preferably, the distribution parameters of the power transmission lines in step S200 can be calculated from the centralized parameters,
Figure GDA0003206533990000021
Figure GDA0003206533990000022
wherein the content of the first and second substances,
Figure GDA0003206533990000023
R0、X0、G0、B0as the lumped parameter, R0And X0To concentrate series resistance and reactance, G0And B0The method is characterized in that parallel conductance and susceptance are concentrated, wherein R and X are equivalent series resistance and reactance, and G and B are equivalent parallel conductance and susceptance;
the current through the series impedance is calculated from the transmit and receive data,
Figure GDA0003206533990000031
the harmonic active power loss of the transmission line caused by the series resistance R and the reactance X is,
(IL)2R＝((P1-|V1|2G/2)+(P2-|V2|2G/2))
the harmonic reactive power loss of the transmission line caused by the parallel conductance G and the susceptance B is,
(IL)2X＝((Q1+|V1|2G/2)+(Q2+|V2|2G/2))。
preferably, the step S300:
randomly selecting a plurality of point data for each data segment, obtaining an equation set by utilizing multipoint estimation,
Figure GDA0003206533990000032
wherein
Figure GDA0003206533990000033
Figure GDA0003206533990000034
Figure GDA0003206533990000035
Figure GDA0003206533990000036
Figure GDA0003206533990000037
Epsilon is the estimation error of the equation, i-1, 2,3, … n represents the ith data point, and n is the total data point.
Preferably, in the step S400,
the Levenberg-Marquardt method is adopted for solving, the objective function is,
Figure GDA0003206533990000041
wherein Z is [ R ]0；X0；G0；B0]The i is 1,2, 10, and the centralized parameters of the power transmission line are obtained through iterative solution;
and calculating the distribution parameters of the power transmission line according to the centralized parameters.
According to another aspect of the present invention, there is provided an electronic device comprising at least one processor, and a memory communicatively coupled to the at least one processor; the memory stores instructions executable by the at least one processor to enable the at least one processor to perform the method of any one of the above.
Compared with the prior art, the invention has the beneficial effects that:
1. the frequency response of unit resistance and reactance of the power transmission line is calculated, and harmonic parameters of the power transmission line can be accurately estimated;
2. the parallel conductance of the power transmission line is calculated, and when the power transmission line has corona loss, compared with the traditional method, the parameter estimation error is smaller;
3. the harmonic parameter estimation process only needs the effective value of harmonic voltage and the harmonic active and reactive power values at two ends of the line, data can be obtained from the electric energy quality monitoring device, the calculation is simple and convenient, and the engineering practicability is realized.
The harmonic parameters obtained by the method are utilized to carry out more accurate harmonic modeling, and the method has important significance for power grid harmonic load flow calculation, state estimation, harmonic source positioning and the like.
Description of the drawings:
FIG. 1 is a schematic flow chart of the present invention.
Fig. 2 is a schematic diagram of the frequency response of the impedance per unit length of the transmission line.
Fig. 3 is a schematic diagram of a transmission line lumped parameter model.
Fig. 4 is a schematic diagram of a distribution parameter model of the power transmission line.
Fig. 5 is a schematic of 3 rd harmonic voltage, real and reactive power values in example 1.
Fig. 6 is a schematic diagram of calculation errors of example 1.
Fig. 7 is a schematic structural diagram of an electronic device according to an embodiment of the invention.
Detailed Description
The present invention will be described in further detail with reference to test examples and specific embodiments. It should be understood that the scope of the above-described subject matter is not limited to the following examples, and any techniques implemented based on the disclosure of the present invention are within the scope of the present invention.
As shown in fig. 1, a method for estimating harmonic parameters of a power transmission line for power grid harmonic analysis includes:
s100: monitoring the power transmission line to obtain harmonic voltage, harmonic active power and harmonic reactive power at two ends;
the step S100: the PQ monitoring device monitors the transmission end and the receiving end of the power transmission line to obtain: harmonic voltage effective value V of transmission end of power transmission line1Harmonic voltage effective value V of sum receiving end2Harmonic active power P of sending end1Harmonic active power P of receiving end2Harmonic reactive power Q of sending terminal1Harmonic reactive power Q of receiving end2。
S200: establishing a relation among a harmonic parameter of the power transmission line and the harmonic voltage, the harmonic active power and the harmonic reactive power at two ends based on a power transmission line distribution parameter model;
the lumped parameter model of the transmission line is shown in FIG. 3, where R0And X0To concentrate series resistance and reactance, G0And B0To concentrate parallel conductance and susceptance. With the increase of the harmonic frequency and the increase of the harmonic wavelength, the ratio of the length of the transmission line to the wavelength of the electromagnetic wave is reduced, and the harmonic voltage and the current along the transmission line have volatility, so that the harmonic analysis of the transmission line needs to adopt a distributed parameter model, and the model is shown in fig. 4. Wherein, R and X are equivalent series resistance and reactance, G and B are equivalent parallel conductance and susceptance,V1and V2Amplitude of the voltage at the sending and receiving ends, P, respectively1And P2Harmonic active power, Q, of the transmitting and receiving ends, respectively1And Q2Respectively a sending end and a receiving end
And end harmonic active power. The distribution parameters of the transmission line can be calculated from the centralized parameters,
Figure GDA0003206533990000061
Figure GDA0003206533990000062
wherein the content of the first and second substances,
Figure GDA0003206533990000063
R0、X0、G0、B0as the lumped parameter, R0And X0To concentrate series resistance and reactance, G0And B0In order to concentrate parallel conductance and susceptance, R and X are equivalent series resistance and reactance, and G and B are equivalent parallel conductance and susceptance.
The current through the series impedance is calculated from the transmit and receive data,
Figure GDA0003206533990000064
the harmonic active power loss of the transmission line caused by the series resistance R and the reactance X is,
(IL)2R＝((P1-|V1|2G/2)+(P2-|V2|2G/2))
the harmonic reactive power loss of the transmission line caused by the parallel conductance G and the susceptance B is,
Figure GDA0003206533990000071
at this time, the unknown R, X, G, B is greater than the number of equations and cannot be directly solved. To solve this problem, the present invention proposes a multi-point method, i.e., step S300.
S300: randomly selecting a plurality of point data for each data segment, and obtaining an equation set by utilizing multipoint estimation; randomly selecting a plurality of point data for each data segment (such as 10min), obtaining an equation set by utilizing multipoint estimation,
Figure GDA0003206533990000072
wherein
Figure GDA0003206533990000073
Figure GDA0003206533990000074
Figure GDA0003206533990000075
Figure GDA0003206533990000076
Figure GDA0003206533990000077
Epsilon is the estimation error of the equation, i is 1,2,3, … n represents the ith data point, n is the total data point, and the equation set contains 4 unknowns R in total0、X0、G0、B0。
Therefore, when n is greater than or equal to 2, the number of equations is greater than or equal to the number of unknowns, and a nonlinear optimization algorithm is used for solving, namely step S400.
S400: and solving the equation set through a nonlinear optimization algorithm to obtain the harmonic parameters of the power transmission line.
The Levenberg-Marquardt method is adopted for solving, the objective function is,
Figure GDA0003206533990000078
wherein Z is [ R ]0；X0；G0；B0]The i is 1,2, 10, and the centralized parameters of the power transmission line are obtained through iterative solution;
and calculating the distribution parameters of the power transmission line according to the centralized parameters.
According to the method, the frequency response of unit resistance and reactance of the power transmission line is calculated, and harmonic parameters of the power transmission line can be accurately estimated; the parallel conductance of the power transmission line is calculated, and when the power transmission line has corona loss, compared with the traditional method, the parameter estimation error is smaller; the harmonic parameter estimation process only needs the effective value of harmonic voltage and the harmonic active and reactive power values at two ends of the line, data can be obtained from the electric energy quality monitoring device, the calculation is simple and convenient, and the engineering practicability is realized.
Example 1
And (3) carrying out simulation verification on the 500kV power transmission line with the length of 300km by using PSCAD, setting parameters as shown in table 1, and setting the effective value of each equivalent harmonic voltage source at the transmitting end to be 1% of the effective value of the fundamental voltage. And extracting accurate values of transmission line harmonic parameters from a parameter file output by PSCAD, wherein the simulation time length is 24h, and 17280 simulation data are obtained at sampling intervals of 5 s.
TABLE 1 simulation model parameter set-up
Figure GDA0003206533990000081
First, harmonic voltage, active power and reactive power values at two ends of the power transmission line are obtained, and in the simulation case, the 3-order harmonic voltage, active power and reactive power values are shown in fig. 5.
Secondly, randomly sampling and grouping data, wherein the sampling data of 10 minutes is 120 points, the random sampling 10 points are used as a group, and 144 groups of data are totally sampled in one day;
thirdly, iteratively solving the formula (7) by utilizing an LM method for each group of data, and taking the average value of each group of calculation results as a harmonic concentrated parameter value of the power transmission line;
fourthly, solving by using the formula (1) to obtain the distribution parameter values of the power transmission line, wherein the calculation result is shown in table 2 (wherein the method 1 is a traditional method, and the method 2 is the method provided by the invention);
table 2 example 1 calculation results
Figure GDA0003206533990000091
Calculating the relative error, the result is shown in fig. 6, and it can be concluded that: with the increase of frequency, the traditional method has larger estimation errors of equivalent resistance and conductance, even reaching about 40%. The method for estimating the harmonic parameters of the power transmission line provided by the invention has higher estimation accuracy.
Example 2
The traditional harmonic parameter estimation of the transmission line ignores equivalent parallel conductance, and when the transmission line has corona loss, a distributed parameter model (the mutual influence among four parameters) is considered, G is ignored0The accuracy of the estimation of other parameters may be degraded. Therefore, on the basis of the formula 1, the corona loss of the transmission line is considered to be 5kW/km (G)00.0015), the calculation error is as shown in table 3,
table 3 example 2 calculation error
Figure GDA0003206533990000101
As can be seen from table 3, the errors of the equivalent parallel resistance and the conductance of the power transmission line estimated by the conventional method are large, and the calculation errors of the equivalent conductance are high at all harmonic frequencies, but the calculation errors of the parameters of the method provided by the present invention are within 5%. It can be concluded that: under the condition that the power transmission line has corona loss, the traditional method ignores the parallel conductance to cause the increase of conductance estimation error, and the estimation accuracy of the power transmission line harmonic parameter estimation method provided by the invention is still higher.
FIG. 7 illustrates an electronic device (e.g., a computer server with program execution functionality) including at least one processor, a power source, and a memory and input-output interface communicatively coupled to the at least one processor, according to an exemplary embodiment of the invention; the memory stores instructions executable by the at least one processor to enable the at least one processor to perform the method disclosed in any one of the preceding embodiments; the input and output interface can comprise a display, a keyboard, a mouse and a USB interface and is used for inputting and outputting data; the power supply is used for supplying electric energy to the electronic equipment.
Those skilled in the art will understand that: all or part of the steps for realizing the method embodiments can be completed by hardware related to program instructions, the program can be stored in a computer readable storage medium, and the program executes the steps comprising the method embodiments when executed; and the aforementioned storage medium includes: various media that can store program codes, such as a removable memory device, a Read Only Memory (ROM), a magnetic disk, or an optical disk.
When the integrated unit of the present invention is implemented in the form of a software functional unit and sold or used as a separate product, it may also be stored in a computer-readable storage medium. Based on such understanding, the technical solutions of the embodiments of the present invention may be essentially implemented or a part contributing to the prior art may be embodied in the form of a software product, which is stored in a storage medium and includes several instructions for causing a computer device (which may be a personal computer, a server, or a network device) to execute all or part of the methods described in the embodiments of the present invention. And the aforementioned storage medium includes: a removable storage device, a ROM, a magnetic or optical disk, or other various media that can store program code.
The foregoing is merely a detailed description of specific embodiments of the invention and is not intended to limit the invention. Various alterations, modifications and improvements will occur to those skilled in the art without departing from the spirit and scope of the invention.

Claims (4)

1. A power transmission line harmonic parameter estimation method for power grid harmonic analysis is characterized by comprising the following steps:
s100: monitoring the power transmission line to obtain a harmonic voltage effective value, harmonic active power and harmonic reactive power at two ends;
s200: establishing a relation among a harmonic parameter of the power transmission line, the harmonic voltage effective value at two ends, the harmonic active power and the harmonic reactive power based on a power transmission line distribution parameter model;
s300: according to the relational expression, randomly selecting a plurality of point data for each data segment, and obtaining an equation set by utilizing multipoint estimation;
s400: solving the equation set through a nonlinear optimization algorithm to obtain harmonic parameters of the power transmission line;
wherein the distribution parameters of the power transmission lines in the step S200 can be calculated from lumped parameters,
Figure FDA0003206533980000011
Figure FDA0003206533980000012
wherein
Figure FDA0003206533980000013
R0、X0、G0、B0As the lumped parameter, R0And X0To concentrate series resistance and reactance, G0And B0For concentrating parallel conductance and susceptance, itWherein, R and X are equivalent series resistance and reactance, G and B are equivalent parallel conductance and susceptance;
the current through the series impedance is calculated from the transmit and receive data,
Figure FDA0003206533980000014
the harmonic active power loss of the transmission line caused by the series resistance R and the reactance X is,
(IL)2R＝((P1-|V1|2G/2)+(P2-|V2|2G/2))
the harmonic reactive power loss of the transmission line caused by the parallel conductance G and the susceptance B is,
(IL)2X＝((Q1+|V1|2G/2)+(Q2+|V2|2G/2))
the PQ monitoring device monitors the transmission end and the receiving end of the power transmission line to obtain: harmonic voltage effective value V of transmission end of power transmission line1Harmonic voltage effective value V of sum receiving end2Harmonic active power P of sending end1Harmonic active power P of receiving end2Harmonic reactive power Q of sending terminal1Harmonic reactive power Q of receiving end2。
2. The method for estimating harmonic parameters of power transmission lines for harmonic analysis of power grids of claim 1, wherein the step S300:
randomly selecting a plurality of point data for each data segment, obtaining an equation set by utilizing multipoint estimation,
Figure FDA0003206533980000021
wherein
Figure FDA0003206533980000022
Figure FDA0003206533980000023
Figure FDA0003206533980000024
Figure FDA0003206533980000025
Figure FDA0003206533980000026
Epsilon is the estimation error of the equation, i-1, 2,3, … n represents the ith data point, and n is the total data point.
3. The method for estimating harmonic parameters of power transmission lines for harmonic analysis of power grids of claim 2, wherein the step S400,
the Levenberg-Marquardt method is adopted for solving, the objective function is,
Figure FDA0003206533980000027
wherein Z is [ R ]0；X0；G0；B0]The i is 1,2, 10, and the centralized parameters of the power transmission line are obtained through iterative solution;
and calculating the distribution parameters of the power transmission line according to the centralized parameters.
4. An electronic device comprising at least one processor, and a memory communicatively coupled to the at least one processor; the memory stores instructions executable by the at least one processor to enable the at least one processor to perform the method of any one of claims 1-3.
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