CN114357373A - Optimized configuration method of micro synchronous phasor measurement unit considering state estimation error - Google Patents

Optimized configuration method of micro synchronous phasor measurement unit considering state estimation error Download PDF

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CN114357373A
CN114357373A CN202111642882.8A CN202111642882A CN114357373A CN 114357373 A CN114357373 A CN 114357373A CN 202111642882 A CN202111642882 A CN 202111642882A CN 114357373 A CN114357373 A CN 114357373A
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陈腾鹏
刘方岩
任和
李璐
李钷
张景瑞
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Abstract

A method for optimizing and configuring a micro synchrophasor measurement unit (PSCU) by considering state estimation errors comprises the following steps: 1) forming a node admittance matrix and a node-branch model according to the node connection mode and branch impedance of the power distribution network; 2) installing mu PMUs at all nodes of the formed admittance matrix and node branch models to read measurement values and obtain measurement models; 3) carrying out t distribution fitting on the measurement noise according to the measurement value historical data; 4) constructing a maximum likelihood estimator based on the measurement model, and obtaining a state estimation error calculated based on the maximum likelihood estimator according to the influence function IF; 5) and incorporating the sum of the state estimation errors and the maximum value of the state estimation variance into the constraint condition of the mu PMU optimization configuration. The invention considers the precision of the subsequent link (state estimation result) in the optimized configuration, is beneficial to the design and the upgrade of the measurement system and has good application prospect.

Description

Optimized configuration method of micro synchronous phasor measurement unit considering state estimation error
Technical Field
The invention relates to the technical field of sensor layout, in particular to an optimal configuration method of a micro synchronous phasor measurement unit considering state estimation errors.
Background
The intelligent power distribution network has a control center for realizing coordinated optimization management, the response speed of the power grid is high, the distributed renewable energy sources can be accessed in an friendly manner, the consumption level of the renewable resources is improved, and the reliability of power supply and the quality of electric energy are improved. However, the basis of the coordinated optimization control and the quick decision of the intelligent power distribution network lies in an advanced measurement device. The use of Micro-Synchronous Phasor Measurement Units (PMU) in power distribution networks has also received increasing attention in the industry. PMU measurements are highly accurate but cannot be installed at all nodes because of their relatively high cost. In order to implement large-scale deployment of the mu PMU in the intelligent power distribution network, optimal configuration of the mu PMU layout is an important means for saving cost and ensuring considerable overall situation of the system. In addition, the state estimation is used as a basic function of a Distribution Management System (DMS), and as a core block of a "situation awareness tool", and mainly processes a PMU raw measurement value, which is a key technology for acquiring an accurate state quantity of the whole network. The layout result of the PMU plays a decisive role in the result of the state estimation. The existing mu PMU configuration method only ensures whether the whole network is observable, but neglects the link of state estimation and breaks the relationship between mu PMU configuration and state estimation. Therefore, the effect of state estimation errors should be considered during the PMU optimization configuration phase.
Disclosure of Invention
The main objective of the present invention is to overcome the above-mentioned drawbacks in the prior art, and to obtain a new state estimation error (expressed by variance) calculation formula in consideration of the measurement error of the PMU even following non-gaussian distribution, thereby providing a PMU optimal configuration method in consideration of the state estimation error.
The invention adopts the following technical scheme:
the optimized configuration method of the micro synchronous phasor measurement unit considering the state estimation error comprises the following steps: 1) forming a node admittance matrix and a node branch model according to the node connection mode and the branch impedance of the power distribution network; 2) installing mu PMUs at all nodes of the formed admittance matrix and node branch models to read measurement values and obtain measurement models; 3) carrying out t distribution fitting on the measurement noise according to the measurement value historical data; it is characterized by also comprising: 4) constructing a maximum likelihood estimator based on the measurement model, and obtaining a state estimation error calculated based on the maximum likelihood estimator according to the influence function IF; 5) and incorporating the sum of the state estimation errors and the maximum value of the state estimation variance into the constraint condition of the mu PMU optimization configuration.
Assuming that there are b nodes in the distribution network, V ═ 1.. and b ] is the set of all nodes, the configuration vector of μ PMU is
p＝[p1，p2，...，pb]T
Wherein
Figure BDA0003443432620000021
Assuming that all nodes are equipped with mu PMUs, the measurement matrix is formed as
Figure BDA0003443432620000022
Wherein
Figure BDA0003443432620000023
J is 1.. and b is a measurement matrix formed when a PMU is installed at node j.
The measurement model is z (k) ═ hx (k) — (k), z (k) is a measurement value, k represents a sampling time, x (k) is a state quantity of the power distribution network at the k-th time, H is a measurement matrix, and ^ k is measurement noise.
In step 3), the probability density function of t distribution is:
Figure BDA0003443432620000024
wherein ^ niRepresents the ith measurement noise, i is 1iIs the proportionality coefficient viIs the form factor.
In step 4), a maximum likelihood estimator is constructed based on the measurement model, and the maximum likelihood estimator is realized by minimizing the following objective equation:
Figure BDA0003443432620000025
taking the derivative of J to obtain:
Figure BDA0003443432620000026
wherein,
Figure BDA0003443432620000027
represents a state estimate, WiIs the ith element of the weight diagonal matrix W.
In step 4), the state estimation error is expressed as:
Figure BDA0003443432620000031
wherein F ([ integral ] F) is a joint density function, an
Figure BDA0003443432620000032
Figure BDA0003443432620000033
Figure BDA0003443432620000034
Figure BDA0003443432620000035
Further, the basic form of the variance is estimated with respect to the state according to a weighted least squares method
Figure BDA0003443432620000036
Constructing a diagonal matrix
Figure BDA0003443432620000037
The following conditions are met:
Figure BDA0003443432620000038
in step 5), the constraint conditions are as follows:
Figure BDA0003443432620000039
wherein
Figure BDA00034434326200000310
Representation matrix
Figure BDA00034434326200000311
Up to full rank, trace represents the sum of the variances of the estimates of the various states, δtAnd deltamIs a set tolerance value.
It can be known from the above description of the present invention that the prior art is based on the assumption of gaussian noise, but the actual PMU noise often follows non-gaussian noise distribution, so the existing techniques are not accurate enough, and the present invention considers the measurement error of PMU and even follows non-gaussian distribution, and obtains a new state estimation error calculation formula expressed by variance, which is more suitable for practical situations. In addition, the invention directly considers the precision of the subsequent link (state estimation result) in the optimization configuration, is beneficial to the design and the upgrade of the measurement system and has good application prospect.
Drawings
Fig. 1 is a test chart of an IEEE 14 node according to an embodiment of the present invention.
Fig. 2 is a test result of the present invention in an IEEE 14 node system, in which the maximum value of state quantity estimation variance (MSEEV) and the unit of state estimation variance (SEE): 10-5。
The invention is described in further detail below with reference to the figures and specific examples.
Detailed Description
The invention is further described below by means of specific embodiments.
The optimized configuration method of the micro synchronous phasor measurement unit considering the state estimation error comprises the following steps:
1) according to the node connection mode and branch impedance of the power distribution network, a node admittance matrix and a node-branch model, that is, a power distribution network topological structure, are formed, as shown in fig. 1, assuming that there are b distribution network nodes, and V ═ 1.. and b ] is a set of all nodes, a configuration vector of a μ PMU is
p＝[p1，p2，...，pb]T
Wherein
Figure BDA0003443432620000041
2) And installing mu PMUs at all nodes of the formed admittance matrix and node branch models to read measurement values and obtain measurement models.
In this step, assuming that all nodes are installed with mu PMUs, the measurement matrix formed is
Figure BDA0003443432620000042
Wherein
Figure BDA0003443432620000043
J is 1.. and b is a measurement matrix formed when a PMU is installed at node j.
The following relation between the state x (k) of the distribution network at the kth time and the measurement value is assumed, that is, the measurement model is: z (k) ═ hx (k) ++ (k), z (k) is a measurement value, k denotes the sampling time, x (k) is the state quantity of the distribution network at the k-th time, H is the measurement matrix, and ^ k is the measurement noise. The metrology model will be used for the calculation of the state estimate variance.
3) And performing t distribution fitting on the measurement noise according to the measurement value historical data.
In the invention, based on the t distribution and the Gaussian distribution, the t distribution and the Gaussian distribution are respectively fitted to the historical data of the measured value, and the result of fitting the measured data of the t distribution is better by comparison, so that the adopted measuring noise model is a t distribution model. The probability density function of the t-distribution is then:
Figure BDA0003443432620000051
wherein ^ niRepresents the ith measurement noise, i is 1iIs the proportionality coefficient viIs the form factor. When the shape factor viWhen the distribution approaches infinity, the t distribution becomes Gaussian distribution; therefore, t distribution has great flexibility, and Gaussian noise or non-Gaussian noise can be conveniently simulated. the probability density function of the t-distribution will be used for the calculation of the state estimate variance.
4) And constructing a maximum likelihood estimator based on the measurement model, and obtaining a state estimation error calculated based on the maximum likelihood estimator according to the influence function IF.
In this step, the maximum likelihood estimator is robust and can be implemented by minimizing the following objective equation
Figure BDA0003443432620000052
Taking the derivative of J to obtain:
Figure BDA0003443432620000053
wherein,
Figure BDA0003443432620000054
represents a state estimate, WiIs the ith element of the weight diagonal matrix W. From the influence function IF, the state estimation error (expressed in variance) calculated based on the maximum likelihood estimator can be obtained as:
Figure BDA0003443432620000061
wherein F ([ integral ] F) is a joint density function, an
Figure BDA0003443432620000062
Figure BDA0003443432620000063
Figure BDA0003443432620000064
Figure BDA0003443432620000065
Basic form of state estimation variance based on weighted least squares
Figure BDA0003443432620000066
Constructing a diagonal matrix
Figure BDA0003443432620000067
The following conditions are met:
Figure BDA0003443432620000068
5) and incorporating the sum of the state estimation errors and the maximum value of the state estimation variance into the constraint condition of the mu PMU optimization configuration.
In the step, the state estimation errors are considered, the sum of the state estimation errors is considered at the same time, the maximum value of the state estimation variance is considered at the same time, and the maximum value is used as a constraint condition and merged into the mu PMU optimization configuration problem. Namely, the constraint conditions are:
Figure BDA0003443432620000069
wherein
Figure BDA00034434326200000610
Representation matrix
Figure BDA00034434326200000611
Up to full rank, trace represents the sum of the variances of the estimates of the various states, δtAnd deltamIs a set tolerance value.
Where the element of p is 0 or 1, where 1 indicates that mu PMU should be installed at the corresponding node location, deltatAnd deltamThe method is used for setting the allowable value of the state estimation variance, represents the limit on the state estimation precision, and has the advantages that the precision of a subsequent link (a state estimation result) is directly considered in the optimization configuration, the design and the upgrade of a measurement system are facilitated, and the application prospect is good. FIG. 2 illustrates a mu PMU of the present applicationThe optimal configuration method can fully consider the constraint of state estimation variance to obtain the optimal mu PMU configuration scheme, and the final MSEEV and SEE results are in the added constraint range.
The above description is only an embodiment of the present invention, but the design concept of the present invention is not limited thereto, and any insubstantial modifications made by using the design concept should fall within the scope of infringing the present invention.

Claims (8)

1. The optimized configuration method of the micro synchronous phasor measurement unit considering the state estimation error comprises the following steps: 1) forming a node admittance matrix and a node-branch model according to the node connection mode and branch impedance of the power distribution network; 2) installing mu PMUs at all nodes of the formed admittance matrix and node branch models to read measurement values and obtain measurement models; 3) carrying out t distribution fitting on the measurement noise according to the measurement value historical data; it is characterized by also comprising: 4) constructing a maximum likelihood estimator based on the measurement model, and obtaining a state estimation error calculated based on the maximum likelihood estimator according to the influence function IF; 5) and incorporating the sum of the state estimation errors and the maximum value of the state estimation variance into the constraint condition of the mu PMU optimization configuration.
2. The method of claim 1, wherein the optimal configuration of the micro synchrophasor measurement unit considering the state estimation error comprises: assuming that there are b nodes in the distribution network, V ═ 1.. and b ] is the set of all nodes, the configuration vector of μ PMU is
p＝[p1，p2，...，pb]T
Wherein
Figure FDA0003443432610000011
3. The method of claim 2, wherein the optimal configuration of the micro synchrophasor measurement unit considering the state estimation error comprises: assuming that all nodes are installed with mu PMUs, the measurement matrix is formed
Figure FDA0003443432610000012
Wherein
Figure FDA0003443432610000013
J is 1.. and b is a measurement matrix formed when a PMU is installed at node j.
4. The method of claim 1, wherein the optimal configuration of the micro synchrophasor measurement unit considering the state estimation error comprises: the measurement model is z (k) ═ hx (k) ++ (k), z (k) is a measurement value, k represents a sampling time, x (k) is a state quantity of the power distribution network at the k-th time, H is a measurement matrix, and ^ k is measurement noise.
5. The method of claim 1, wherein the optimal configuration of the micro synchrophasor measurement unit considering the state estimation error comprises: in step 3), the probability density function of t distribution is:
Figure FDA0003443432610000014
wherein ^ niRepresents the ith measurement noise, i is 1iIs the proportionality coefficient viIs the form factor.
6. The method of claim 5, wherein the optimal configuration of the SSPMTUs considering the state estimation error comprises: in step 4), a maximum likelihood estimator is constructed based on the measurement model, and the maximum likelihood estimator is realized by minimizing the following objective equation:
Figure FDA0003443432610000021
taking the derivative of J to obtain:
Figure FDA0003443432610000022
wherein,
Figure FDA0003443432610000023
represents a state estimate, WiIs the ith element of the weight diagonal matrix W.
7. The method of claim 6, wherein the optimal configuration of the micro synchrophasor measurement unit considering the state estimation error comprises: in step 4), the state estimation error is expressed as:
Figure FDA0003443432610000024
wherein F ([ integral ] F) is a joint density function, an
Figure FDA0003443432610000025
Figure FDA0003443432610000026
Figure FDA0003443432610000027
Figure FDA0003443432610000028
Further, the basic form of the variance is estimated with respect to the state according to a weighted least squares method
Figure FDA0003443432610000029
Constructing a diagonal matrix
Figure FDA00034434326100000210
The following conditions are met:
Figure FDA00034434326100000211
8. the method of claim 7, wherein the optimal configuration of the micro synchrophasor measurement unit considering the state estimation error comprises: in step 5), the constraint conditions are as follows:
Figure FDA0003443432610000031
wherein
Figure FDA0003443432610000032
Representation matrix
Figure FDA0003443432610000033
Up to full rank, trace represents the sum of the variances of the estimates of the various states, δtAnd deltamIs a set tolerance value.
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