CN110414816B - Least square-based power system state estimation method - Google Patents

Least square-based power system state estimation method Download PDF

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CN110414816B
CN110414816B CN201910653752.0A CN201910653752A CN110414816B CN 110414816 B CN110414816 B CN 110414816B CN 201910653752 A CN201910653752 A CN 201910653752A CN 110414816 B CN110414816 B CN 110414816B
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黄伟鹏
廖兴旺
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Abstract

The invention discloses a least square-based power system state estimation method, which relates to a power system and comprises the following steps: first, determining the identification parameter matrix as eta(n)＝(‑[YLL]‑1YLG‑[YLL]‑1) (ii) a Then, collecting a power supply voltage phasor on a generator node, a load voltage and a current phasor on a load node; then, solving the identification parameter matrix eta(n)Is estimated value of
Figure DDA0003242990090000011
From the matrix to be identified
Figure DDA0003242990090000012
Splitting the load admittance matrix YLGThe inter-charge admittance matrix YLLSolving said load admittance matrix YLGThe rate of change of the items within; finally, a load admittance matrix Y is extractedLGAnd determining the first transmission line matched with the fault item as a fault line when the internal change rate is greater than the fault item of the preset value. According to the invention, the previous data are removed, so that the calculation processing amount is reduced, the data far away from the current moment are removed, the system estimation precision is effectively improved, and the fault route of the power system can be effectively identified.

Description

Least square-based power system state estimation method
Technical Field
The invention relates to the field of power systems, in particular to a least square-based power system state estimation method.
Background
The electric power system is an electric energy production and consumption system which consists of links such as a power plant, a power transmission and transformation line, a power supply and distribution station, power utilization and the like. The function of the device is to convert the primary energy of the nature into electric energy through a power generation device, and then supply the electric energy to each user through power transmission, power transformation and power distribution. In order to realize the function, the power system is also provided with corresponding information and control systems at each link and different levels, and the production process of the electric energy is measured, regulated, controlled, protected, communicated and scheduled so as to ensure that users obtain safe and high-quality electric energy.
The main structures of the power system include a power source (power plants such as hydropower stations, thermal power plants, and nuclear power plants), a substation (a step-up substation, a load center substation, and the like), a power transmission and distribution line, and a load center. The power supply points are also mutually connected to realize the exchange and regulation of electric energy among different regions, thereby improving the safety and the economical efficiency of power supply. The network formed by the transmission line and the substation is usually called a power network. The information and control system of the power system consists of various detection devices, communication devices, safety protection devices, automatic control devices and automatic monitoring and dispatching systems. The structure of the power system should ensure reasonable coordination of power generation and consumption on the basis of advanced technical equipment and high economic benefit.
A typical power system model includes a plurality of generator nodes, a plurality of load nodes, and a power network.
Because the power system is a complex time-varying system, the data processing amount is larger and larger along with the operation of the system, and the required computer processing capacity for processing data is greatly increased, so that the data processing speed is reduced or the data processing cost is increased. In addition, in the prior art, a forgetting factor is used for weighting to perform recursive least square method, on one hand, old data cannot be completely eliminated, and on the other hand, in some prior arts, the total weighted value of the old data and new data is greater than 1, so that the solved value is shifted.
Disclosure of Invention
In view of some of the above-mentioned drawbacks of the prior art, the present invention provides a method for estimating a state of an electric power system based on least squares, which aims to optimize the solution of parameter estimation of an electric power system network, only retain the most recent data, perform parameter identification, and increase the solution speed of system parameter estimation.
In order to achieve the above object, the present invention provides a least square-based power system state estimation method, including:
step S1, determining the identification parameter matrix as eta(n)＝(-[YLL]-1YLG -[YLL]-1) (ii) a Said Y isLLIs an inter-load admittance matrix Y between load nodes of the power systemLLSaid Y isLGFor load transmitting admittance matrix Y between load node and generator node of power systemLG(ii) a The model of the power system satisfies:
Figure GDA0003242990080000021
Figure GDA0003242990080000022
being a full admittance matrix of the power system, E, IGGenerator node voltage phasor and generator node current phasor respectively, and V, I load node voltage phasor and load node current phasor respectively;
step S2, collecting power supply voltage phasor E on each generator node on the power system networknLoad voltage V on the load nodenAnd the current phasor I at the load noden(ii) a The supply voltage phasor En＝[E(1,n),E(2,n),...,E(i,n)]TA load voltage V on said load noden＝[V(1,n),V(2,n),...,V(j,n)]TCurrent phasor I at the load noden＝[I(1,n),I(2,n),...,I(j,n)]T(ii) a The i is the node number of the generator node, the j is the node number of the load node, and the n is the serial number of the sampling data;
step S3, responding n > p, solving eta after increasing nth sampling data(n-1,add n)Is estimated value of
Figure GDA0003242990080000031
The above-mentioned
Figure GDA0003242990080000032
Satisfies the following conditions:
Figure GDA0003242990080000033
wherein the content of the first and second substances,
Figure GDA0003242990080000034
V n＝[Vn-p+1 Vn-p+2 ... Vn]，
Figure GDA0003242990080000035
the above-mentioned
Figure GDA0003242990080000036
I is an identity matrix; p is a preset positive integer; the p is greater than the number of parameters to be estimated and
Figure GDA0003242990080000037
a full rank;
step S4, in response to n > p and the
Figure GDA0003242990080000038
Solving the identification parameter matrix eta after removing the n-p times of sampling data(n)Is estimated value of
Figure GDA0003242990080000039
The above-mentioned
Figure GDA00032429900800000310
Satisfies the following conditions:
Figure GDA00032429900800000311
wherein the content of the first and second substances,
Figure GDA00032429900800000312
step S5, responding to the matrix to be identified
Figure GDA00032429900800000313
The data in the matrix to be identified fluctuates
Figure GDA00032429900800000314
After stabilization, from the matrix to be identified
Figure GDA00032429900800000315
Splitting the load admittance matrix YLGThe inter-charge admittance matrix YLLSolving said load admittance matrix YLGThe rate of change of the items within;
step S6, extracting the load admittance matrix YLGAnd acquiring a first load node and a second generator node corresponding to the fault item when the internal change rate of the fault item is greater than a preset value, and determining a first transmission line between the first load node and the second generator node as a fault line.
In one embodiment, in the step S2, the power voltage phasor EnLoad voltage V on the load nodenAnd the current phasor I at the load nodenIs synchronous sampling.
In one embodiment, in the step S2, the power voltage phasor EnLoad voltage V on the load nodenAnd the current phasor I at the load nodenThe sampling period of (2) is 10ms-1000 ms.
In one embodiment, in the step S5, the charging admittance matrix YLGThe change rate of each item in the data storage is the ratio of a first stable state before the data fluctuates to a second stable state after the data fluctuates.
In a specific embodiment, the step S6 further includes:
obtaining the load admittance matrix YLGThe load node number and the generator node number of the fault item, a first load node is determined according to the load node number, and a second generator node is determined according to the generator node number.
The invention has the beneficial effects that: in the invention, the upper limit of data is kept as p items by limiting the number of data items of the power system, namely, in the actual operation, the first addition of the second addition can be adoptedn times sampling data Hn、VnThen deleting the first data of the current sequence and maintaining the length of the data sequence. On one hand, the invention eliminates the previous data, so that the calculation processing amount is reduced, and meanwhile, as the power system is a gradual change system, the data accuracy is lower when the power system is farther from the current time node, the farther data from the current time is eliminated, and the system precision is effectively improved. In addition, the two-step solution is carried out through the formula, the higher the obtained parameter estimation precision is, and the parameter estimation accuracy is enhanced. The invention can effectively identify the fault route of the power system on line, improve the efficiency of fault identification and reduce the fault maintenance cost of the power system.
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FIG. 1 is a schematic flow chart of a least squares based power system state estimation method according to an embodiment of the present invention;
FIG. 2 is a model of a multi-source, multi-load power system in accordance with an embodiment of the present invention.
Detailed Description
The invention is further illustrated by the following examples in conjunction with the accompanying drawings:
the power system is a complex time-varying system, such as a multi-source and multi-load power system shown in fig. 2, the total number of generators is i, the total number of loads is j, a node admittance matrix is introduced, and a power network model based on the whole network can be obtained based on kirchhoff voltage and current laws:
Figure GDA0003242990080000051
the following can be obtained:
V＝-[YLL]-1YLGE-[YLL]-1I (1)
obtaining power supply voltage phasor E on each generator node through continuous sampling of synchronous Phasor Measurement Unit (PMU) on network node of power systemnLoad voltage V on the load nodenAnd the current phasor I at the load noden(ii) a The supply voltage phasor En＝[E(1,n),E(2,n),...,E(i,n)]TA load voltage V on said load noden＝[V(1,n),V(2,n),...,V(j,n)]TCurrent phasor I at the load noden＝[I(1,n),I(2,n),...,I(j,n)]T(ii) a The i is the node number of the generator node, the j is the node number of the load node, and the n is the serial number of the sampling data;
and (3) simultaneously obtaining the comprehensive power grid model by the n times of sampling data:
Figure GDA0003242990080000061
namely:
Figure GDA0003242990080000062
note the book
Figure GDA0003242990080000063
According to the least square method, forV n＝η(n) H nIn a term of (A), (B), (C)H n)(H n)TWhen the device is not in a strange state,
Figure GDA0003242990080000064
obtaining a minimum value:
Figure GDA0003242990080000065
for the power system model, the model is the same asH n、V nIncreasing the nth sample data
Figure GDA0003242990080000066
[Vn]Then, the following are respectively changed:
Figure GDA0003242990080000067
V n-1_add_n＝[Vn-p Vn-p+1 ... Vn-1 Vn] (7)
order to
Figure GDA0003242990080000068
The following can be obtained:
H n-1_add_n＝[H n-1 Hn] (8)
V n-1_add_n＝[V n-1 Vn] (9)；
then η(n-1,add n)Is estimated value of
Figure GDA0003242990080000071
Satisfies the following conditions:
Figure GDA0003242990080000072
according to a matrix inversion formula, the method is simplified to obtain:
Figure GDA0003242990080000073
in the same way, the above steps are carried outH n-1_add_n、V n-1_add_nDelete leader, getH n、V n(ii) a Wherein the content of the first and second substances,
Figure GDA0003242990080000074
V n-1_add_n＝[Vn-p Vn-p ... Vn-1 Vn] (13)
Figure GDA0003242990080000075
V n+1＝[Vn-p+1 Vn-p+2 ... Vn] (15)
namely:
H n-1_add_n＝[Hn-p H n] (16)
V n-1_add_n＝[Vn-p V n] (17)
then η(n-1,add n)Is estimated value of
Figure GDA0003242990080000076
Satisfies the following conditions:
Figure GDA0003242990080000081
according to a matrix inversion formula, the method is simplified to obtain:
Figure GDA0003242990080000082
in the invention, the upper limit of the data is kept to be p items by limiting the number of data items of the power system, namely, in the actual operation, the nth sampling data H can be increased firstlyn、VnThen deleting the first data of the current sequence and maintaining the length of the data sequence.
On one hand, the previous data are removed, so that the calculation processing amount is reduced, and meanwhile, as the power system is a gradual change system, the data accuracy is lower when the power system is farther from the current time node, the data farther from the current time are removed, and the system precision is effectively improved. In addition, the two-step solution is carried out through the formula, the higher the obtained parameter estimation precision is, and the parameter estimation accuracy is enhanced.
Specifically, as shown in fig. 1, in a first example of the present invention, there is provided a least-squares-based power system state estimation method, the method including:
step S1, determining the identification parameter matrix as eta(n)＝(-[YLL]-1YLG -[YLL]-1) (ii) a Said Y isLLIs an inter-load admittance matrix Y between load nodes of the power systemLLSaid Y isLGFor load transmitting admittance matrix Y between load node and generator node of power systemLG(ii) a The model of the power system satisfies:
Figure GDA0003242990080000083
Figure GDA0003242990080000091
being a full admittance matrix of the power system, E, IGGenerator node voltage phasor and generator node current phasor respectively, and V, I load node voltage phasor and load node current phasor respectively;
step S2, collecting power supply voltage phasor E on each generator node on the power system networknLoad voltage V on the load nodenAnd the current phasor I at the load noden(ii) a The supply voltage phasor En＝[E(1,n),E(2,n),...,E(i,n)]TA load voltage V on said load noden＝[V(1,n),V(2,n),...,V(j,n)]TCurrent phasor I at the load noden＝[I(1,n),I(2,n),...,I(j,n)]T(ii) a The i is the node number of the generator node, the j is the node number of the load node, and the n is the serial number of the sampling data;
step S3, responding n > p, solving eta after increasing nth sampling data(n-1,add n)Is estimated value of
Figure GDA0003242990080000092
The above-mentioned
Figure GDA0003242990080000093
Satisfies the following conditions:
Figure GDA0003242990080000094
wherein the content of the first and second substances,
Figure GDA0003242990080000095
V n＝[Vn-p+1 Vn-p+2 ... Vn]，
Figure GDA0003242990080000096
the above-mentioned
Figure GDA0003242990080000097
I is an identity matrix; p is a preset positive integer;
step S4, in response to n > p and the
Figure GDA0003242990080000098
Solving the identification parameter matrix eta after removing the n-p times of sampling data(n)Is estimated value of
Figure GDA0003242990080000099
The above-mentioned
Figure GDA00032429900800000910
Satisfies the following conditions:
Figure GDA0003242990080000101
wherein the content of the first and second substances,
Figure GDA0003242990080000102
step S5, responding to the matrix to be identified
Figure GDA0003242990080000103
The data in the matrix to be identified fluctuates
Figure GDA0003242990080000104
After stabilization, from the matrix to be identified
Figure GDA0003242990080000105
Splitting the load admittance matrix YLGThe inter-charge admittance matrix YLLSolving said load admittance matrix YLGThe rate of change of the items within;
step S6, extracting the load admittance matrix YLGAnd acquiring a first load node and a second generator node corresponding to the fault item when the internal change rate of the fault item is greater than a preset value, and determining a first transmission line between the first load node and the second generator node as a fault line.
In this embodiment, in the step S2, the power supply voltage phasor EnLoad voltage V on the load nodenAnd the current phasor I at the load nodenIs synchronous sampling.
In this embodiment, in the step S2, the power supply voltage phasor EnLoad voltage V on the load nodenAnd the current phasor I at the load nodenThe sampling period of (2) is 10ms-1000 ms.
In this embodiment, in the step S5, the load admittance matrix YLGThe change rate of each item in the data storage is the ratio of a first stable state before the data fluctuates to a second stable state after the data fluctuates.
In this embodiment, the step S6 further includes:
obtaining the load admittance matrix YLGThe load node number and the generator node number of the fault item, a first load node is determined according to the load node number, and a second generator node is determined according to the generator node number.
The foregoing detailed description of the preferred embodiments of the invention has been presented. It should be understood that numerous modifications and variations could be devised by those skilled in the art in light of the present teachings without departing from the inventive concepts. Therefore, the technical solutions available to those skilled in the art through logic analysis, reasoning and limited experiments based on the prior art according to the concept of the present invention should be within the scope of protection defined by the claims.

Claims (5)

1. A least squares based power system state estimation method, the method comprising:
step S1, determining the identification parameter matrix as eta(n)＝(-[YLL]-1YLG -[YLL]-1) (ii) a Said Y isLLIs an inter-load admittance matrix Y between load nodes of the power systemLLSaid Y isLGFor load transmitting admittance matrix Y between load node and generator node of power systemLG(ii) a The model of the power system satisfies:
Figure FDA0003242990070000011
Figure FDA0003242990070000012
being a full admittance matrix of the power system, E, IGGenerator node voltage phasor and generator node current phasor respectively, and V, I load node voltage phasor and load node current phasor respectively;
step S2, collecting power supply voltage phasor E on each generator node on the power system networknLoad voltage V on the load nodenAnd the current phasor I at the load noden(ii) a The supply voltage phasor En＝[E(1,n),E(2,n),...,E(i,n)]TA load voltage V on said load noden＝[V(1,n),V(2,n),...,V(j,n)]TCurrent phasor I at the load noden＝[I(1,n),I(2,n),...,I(j,n)]T(ii) a The i is the node number of the generator node, the j is the node number of the load node, and the n is the serial number of the sampling data;
step S3, responding n > p, solving eta after increasing nth sampling data(n-1,add n)Is estimated value of
Figure FDA0003242990070000013
The above-mentioned
Figure FDA0003242990070000014
Satisfies the following conditions:
Figure FDA0003242990070000015
wherein the content of the first and second substances,
Figure FDA0003242990070000021
V n＝[Vn-p+1 Vn-p+2 ... Vn]，
Figure FDA0003242990070000022
the above-mentioned
Figure FDA0003242990070000023
I is an identity matrix; p is a preset positive integer;
step S4, in response to n > p and the
Figure FDA0003242990070000024
Solving the identification parameter matrix eta after removing the n-p times of sampling data(n)Is estimated value of
Figure FDA0003242990070000025
The above-mentioned
Figure FDA0003242990070000026
Satisfies the following conditions:
Figure FDA0003242990070000027
wherein the content of the first and second substances,
Figure FDA0003242990070000028
step S5, responding to the matrix to be identified
Figure FDA0003242990070000029
The data in the matrix to be identified fluctuates
Figure FDA00032429900700000210
After stabilization, from the matrix to be identified
Figure FDA00032429900700000211
Splitting the load admittance matrix YLGThe inter-charge admittance matrix YLLSolving said load admittance matrix YLGThe rate of change of the items within;
step S6, extracting the load admittance matrix YLGAnd acquiring a first load node and a second generator node corresponding to the fault item when the internal change rate of the fault item is greater than a preset value, and determining a first transmission line between the first load node and the second generator node as a fault line.
2. The least squares-based power system state estimation method of claim 1, wherein in the step S2, the supply voltage phasor EnLoad voltage V on the load nodenAnd the current phasor I at the load nodenIs synchronous sampling.
3. The least squares-based power system state estimation method of claim 1, wherein in the step S2, the supply voltage phasor EnLoad voltage V on the load nodenAnd the current phasor I at the load nodenThe sampling period of (2) is 10ms-1000 ms.
4. A substrate as claimed in claim 1In the least square power system state estimation method, in the step S5, the load admittance matrix YLGThe change rate of each item in the data storage is the ratio of a first stable state before the data fluctuates to a second stable state after the data fluctuates.
5. The least squares-based power system state estimation method of claim 1, wherein the step S6 further comprises:
obtaining the load admittance matrix YLGThe load node number and the generator node number of the fault item, a first load node is determined according to the load node number, and a second generator node is determined according to the generator node number.
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