CN116231646A - PMU optimal configuration method and system based on electric power system weakness and economy - Google Patents

PMU optimal configuration method and system based on electric power system weakness and economy Download PDF

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CN116231646A
CN116231646A CN202310514338.8A CN202310514338A CN116231646A CN 116231646 A CN116231646 A CN 116231646A CN 202310514338 A CN202310514338 A CN 202310514338A CN 116231646 A CN116231646 A CN 116231646A
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vulnerability
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pmu
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CN116231646B (en
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徐光辉
肖克
邓赟
刘备
李炳辉
张江易
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Hubei University of Technology
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    • H—ELECTRICITY
    • H02—GENERATION; CONVERSION OR DISTRIBUTION OF ELECTRIC POWER
    • H02J—CIRCUIT ARRANGEMENTS OR SYSTEMS FOR SUPPLYING OR DISTRIBUTING ELECTRIC POWER; SYSTEMS FOR STORING ELECTRIC ENERGY
    • H02J3/00—Circuit arrangements for ac mains or ac distribution networks
    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06F—ELECTRIC DIGITAL DATA PROCESSING
    • G06F30/00—Computer-aided design [CAD]
    • G06F30/20—Design optimisation, verification or simulation
    • G06F30/25—Design optimisation, verification or simulation using particle-based methods
    • H—ELECTRICITY
    • H02—GENERATION; CONVERSION OR DISTRIBUTION OF ELECTRIC POWER
    • H02J—CIRCUIT ARRANGEMENTS OR SYSTEMS FOR SUPPLYING OR DISTRIBUTING ELECTRIC POWER; SYSTEMS FOR STORING ELECTRIC ENERGY
    • H02J3/00—Circuit arrangements for ac mains or ac distribution networks
    • H02J3/24—Arrangements for preventing or reducing oscillations of power in networks
    • H02J3/242—Arrangements for preventing or reducing oscillations of power in networks using phasor measuring units [PMU]
    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06F—ELECTRIC DIGITAL DATA PROCESSING
    • G06F2113/00—Details relating to the application field
    • G06F2113/04—Power grid distribution networks
    • H—ELECTRICITY
    • H02—GENERATION; CONVERSION OR DISTRIBUTION OF ELECTRIC POWER
    • H02J—CIRCUIT ARRANGEMENTS OR SYSTEMS FOR SUPPLYING OR DISTRIBUTING ELECTRIC POWER; SYSTEMS FOR STORING ELECTRIC ENERGY
    • H02J2203/00—Indexing scheme relating to details of circuit arrangements for AC mains or AC distribution networks
    • H02J2203/20—Simulating, e g planning, reliability check, modelling or computer assisted design [CAD]

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Abstract

The invention provides a PMU optimal configuration method and a PMU optimal configuration system based on the vulnerability and the economy of a power system, fully considers the synergistic effect of the vulnerability and the economy, and can efficiently and accurately realize the PMU optimal configuration. The PMU optimal configuration method comprises the following steps: step 1, determining an index for measuring node vulnerability; step 2, determining the vulnerability of each configurable node in the power system based on the index; step 3, calculating the installation cost of each node in the power system; step 4, pre-configuration: based on the vulnerability of each node determined in the step 2, the high-vulnerability nodes with the vulnerability of 6-12% in the front in the power system are used as the nodes which are required to be configured; step 5, improving the position updating mode of the particle swarm optimization algorithmThe method comprises the steps of carrying out a first treatment on the surface of the Step 6, taking the nodes which are not configured as variables on the basis of the pre-configuration in the step 4; particle swarm optimization algorithm modified in step 5 based on objective functionFAnd carrying out optimizing calculation to obtain an optimal scheme of PMU configuration.

Description

PMU optimal configuration method and system based on electric power system weakness and economy
Technical Field
The invention belongs to the technical field of processing methods or systems suitable for prediction purposes, and particularly relates to a PMU optimal configuration method and system based on the weakness and economy of a power system.
Background
With the access of the distributed power supply, the structure and the operation mode of the power system are more and more complex, and the fault of some fragile nodes can cause cascading effect to cause the whole system to crash. Therefore, the rapid and accurate measurement of voltage and current is a guarantee of safe and stable operation of the power system. The monitoring and data acquisition, which are the traditional system state monitoring technology, cannot meet the operation control requirements of the system due to the problems of low measurement speed, low resolution and the like. The synchronous phasor measurement unit (Phase Measurement Unit, PMU) can measure signals such as node voltage, current phasor and the like in real time, 30 to 120 samples can be obtained per second, good effects are achieved in power distribution network state estimation and line fault detection, and necessary control measures are adopted for power system departments to timely master the system running state and abnormal conditions. All nodes are configured with PMUs, so that each node can be observed better, but the economic cost is not high, the configuration is complex, and the processing data volume is too large. Thus, the proper placement and number of PMUs is critical to the optimal configuration of the PMUs, taking into account the full observability of the system.
In the current study of the problem of optimal PMU configuration, students often treat each node in a system according to the same vulnerability, and the differences among the nodes are not considered. In addition, the installation costs of the respective nodes are not the same, so that the economical efficiency in the configuration is also sufficiently considered. Therefore, it is needed to propose a scheme for efficiently and accurately implementing the optimal configuration of the PMU by fully considering vulnerability and economy, reasonably utilizing limited computing and processing resources, and timely determining the optimal configuration of the PMU according to the change of the power system in the actual operation process, so as to implement safe and stable operation of the power system.
Disclosure of Invention
The invention is carried out to solve the problems, and aims to provide a PMU optimal configuration method and a PMU optimal configuration system based on the weakness and the economy of a power system, fully consider the synergistic effect of the weakness and the economy, and efficiently and accurately realize the PMU optimal configuration.
In order to achieve the above object, the present invention adopts the following scheme:
the invention provides a PMU optimal configuration method based on the weakness and economy of a power system, which comprises the following steps:
step 1, taking four indexes of the degree of a node in an electric power system to be configured, a first node connected with a radial bus, the number and the proximity of three electric devices connected with a load generator transformer as indexes for measuring node vulnerability;
step 2, determining the vulnerability of each configurable node in the power system based on the four indexes of step 1;
step 3, calculating the installation cost of each node in the power system as an installation cost index;
step 4, pre-configuration: based on the vulnerability of each node determined in the step 2, the high-vulnerability nodes with the vulnerability of 6-12% in the front in the power system are used as the nodes which are required to be configured;
step 5, improving the position updating mode of the particle swarm optimization algorithm based on the following functions;
Figure SMS_1
；
in the method, in the process of the invention,x gf is the firstgThe particles are at the firstfThe position in the dimension is such that,v gf is the firstgThe particles are at the firstfSpeed in dimension;
step 6, taking the nodes which are not configured as variables on the basis of the pre-configuration in the step 4; particle swarm optimization algorithm modified in step 5 based on objective functionFPerforming optimizing calculation to obtain an optimal scheme of PMU configuration;
target objectFunction ofFThe method comprises the following steps:
Figure SMS_2
；
in the method, in the process of the invention,
Figure SMS_3
is a nodeiVulnerability index of (2);I i for installing nodes in cost index matrixiIs a cost of installation index;mis the total number of nodes; when the nodeiIf PMU is installed, thenx i 1, otherwise 0;a、bis a constant coefficient, the values are positive numbersb＞aIs determined through experiments;
wherein, any step in the step 5 and the steps 1-4 has no sequential division.
Preferably, in the method for optimal PMU configuration based on vulnerability and economy of a power system provided by the present invention, in step 5, the inertia weight is:
Figure SMS_4
；
in the method, in the process of the invention,t c andTthe current iteration and the maximum iteration number are respectively.
Preferably, the method for PMU optimal configuration based on the weakness and economy of the power system, provided by the invention, sets the particle speed between [ -4,4] in step 5.
Preferably, in the method for optimally configuring the PMU based on the vulnerability and the economy of the power system, in step 4, the high vulnerability nodes of 10% of the power system are sequentially configured from large to small based on the vulnerability of each node determined in step 2.
Preferably, in step 3, the PMU optimal configuration method based on the vulnerability and economy of the power system configures the installation cost of each node of the PMU to form an installation cost index matrix based on the influence of communication facilities, the number of network buses and software cost on the installation cost of the PMU.
Preferably, the invention provides PMU optimization based on power system vulnerability and economyIn the configuration method, in step 3, for all nodes, the PMU basic installation cost is set to be 1p.u.; every time one AND node is addediThe installation costs of the connected devices increase by 0.1 p.u..
Preferably, in the method for optimal PMU configuration based on vulnerability and economy of the power system provided by the present invention, in step 6, a value is recommended:a=1，b=2。
preferably, in the method for optimally configuring the PMU based on the weakness and the economy of the power system, in the step 2, a corresponding node judgment matrix is constructed based on four indexes of the step 1AFor judgment matrixAThe weight of each index is comprehensively evaluated by adopting a subjective and objective weighting method-analytic hierarchy process and an entropy weighting method, and then vulnerability of each node is determined by utilizing TOPSIS.
Furthermore, the invention also provides a PMU optimal configuration system based on the weakness and economy of the power system, which comprises the following components:
the system comprises an index acquisition part, a control part and a control part, wherein the index acquisition part takes four indexes of the degree of a power system node, a first node connected with a radial bus, the number and the proximity of three electrical equipment connected with a load generator transformer in a power system to be configured as indexes for measuring node vulnerability;
a vulnerability calculating unit that determines the vulnerability of each configurable node in the power system based on four indices that measure the vulnerability of the node;
an installation cost matrix construction unit which calculates the installation cost of each node in the power system as an installation cost index;
a pre-configuration unit which uses the high-vulnerability nodes with the vulnerability of 6-12% in the front in the power system as the nodes which are required to be configured based on the vulnerability of each node;
an algorithm improving unit for improving the position updating mode of the particle swarm optimization algorithm based on the following functions;
Figure SMS_5
；
in the method, in the process of the invention,x gf is the firstgThe particles are at the firstfThe position in the dimension is such that,v gf is the firstgIndividual grainsSon at the firstfSpeed in dimension;
the PMU optimal configuration acquisition part takes nodes which are not configured as variables on the basis of pre-configuration; target function pair using improved particle swarm optimization algorithmFPerforming optimizing calculation to obtain an optimal scheme of PMU configuration; objective functionFThe method comprises the following steps:
Figure SMS_6
；
in the method, in the process of the invention,
Figure SMS_7
is a nodeiVulnerability index of (2);I i is a nodeiIs a cost of installation index;mis the total number of nodes; when the nodeiIf PMU is installed, thenx i 1, otherwise 0;a、bis a constant coefficient, the values are positive numbersb＞aIs determined through experiments;
the control part is communicated with the index acquisition part, the vulnerability calculation part, the installation cost matrix construction part, the pre-configuration part, the algorithm improvement part and the PMU optimal configuration acquisition part and controls the operation of the index acquisition part, the vulnerability calculation part, the installation cost matrix construction part, the pre-configuration part, the algorithm improvement part and the PMU optimal configuration acquisition part.
Preferably, the PMU optimal configuration system based on the weakness and economy of the power system provided by the invention further comprises: the input display part is communicated with the index acquisition part, the vulnerability calculation part, the installation cost matrix construction part, the pre-configuration part, the algorithm improvement part, the PMU optimal configuration acquisition part and the control part and is used for enabling a user to input an operation instruction and correspondingly display the operation instruction.
According to the PMU optimal configuration method and system based on the vulnerability and the economy of the power system, the vulnerability and the economy of each node in the power system are fully considered, the vulnerability of each node is determined, then the optimal configuration can be timely and accurately determined according to the change of the power system in the actual operation process (for example, when the change can cause the unobservable depth in the power system to be greater than 2) by taking the nodes which are not configured as variables and the nodes with the vulnerability of 6-12% as the nodes which are required to be configured, so as to obtain the optimal scheme of PMU configuration, the convergence speed is effectively improved, the algorithm is prevented from being trapped into local optimal in the high node system, the PMU optimal configuration acquisition efficiency is remarkably improved, the accuracy of the configuration result is improved, and the calculation and processing resources are reasonably and effectively utilized. The aforementioned advantages of the present invention are even more pronounced, particularly for large-scale nodal power systems.
Drawings
FIG. 1 is a flow chart of a method for optimal PMU configuration based on power system vulnerability and economy according to an embodiment of the present invention;
FIG. 2 is a diagram of an IEEE-57 node power system in accordance with an embodiment of the present invention;
FIG. 3 is a vulnerability index diagram of each node in an IEEE-57 node power system according to an embodiment of the present invention;
FIG. 4 is a diagram showing an iterative process of the invention and a PMU configuration for an IEEE-14 node power system by BPSO-1 according to an embodiment of the invention;
FIG. 5 is a schematic diagram illustrating an iterative process of configuring PMU for IEEE-57 node power system with BPSO-1 according to an embodiment of the present invention;
FIG. 6 is a schematic diagram illustrating an iterative process of configuring PMU for IEEE-118 node power system with BPSO-1 according to an embodiment of the present invention;
FIG. 7 is a schematic diagram illustrating an iterative process of configuring PMU for IEEE-14 node power system with BPSO-2 according to an embodiment of the present invention;
FIG. 8 is a schematic diagram illustrating an iterative process of configuring PMU for IEEE-57 node power system with BPSO-2 according to an embodiment of the present invention;
fig. 9 is a schematic diagram illustrating an iterative process of configuring PMU for an IEEE-118 node power system with BPSO-2 according to an embodiment of the present invention.
Detailed Description
The following describes in detail the specific embodiments of the method and system for optimal PMU configuration based on the vulnerability and economy of the power system according to the present invention with reference to the accompanying drawings.
Example 1
As shown in fig. 1 to 3, the PMU optimal configuration method based on the vulnerability and economy of the power system provided in this embodiment includes the following steps:
step 1, regarding a power system to be configured, taking four indexes of the degree of a power system node, a first node connected with a radial bus, the number and the proximity of three electrical equipment connected with a load generator transformer as indexes for measuring node vulnerability;
1-1, degree of node De:
the degree of the node represents the connection degree of the power system network itself and surrounding nodes, and is calculated according to the total number of branches connected by the node.
1-2, a first node Rb connecting a radial busbar:
Figure SMS_8
；
1-3, the number LDT of three electrical devices of a connection load, a generator and a transformer:
the transformer failure may cause the effects of fire, short circuit, etc. of the oil tank, considering the nodes directly connected to the transformer:
Figure SMS_9
；
the stability of the power system is damaged, which causes a large number of user power supply interruption and in severe cases, the whole system is broken down. The load and generator have a significant impact on system stability.
Figure SMS_10
；
Figure SMS_11
；
The vulnerability degree of the node is reflected by taking the number of three electrical equipment connected with a load generator transformer in the system as an index, wherein the number of the three electrical equipment is as follows:
LDT(i)=L(i)+D(i)+T(i),
1-4, proximity P:
the proximity reflects how well a node is centered in the power system, which describes how easily the node can reach other nodes through the network. The proximity of a node is the inverse of the sum of the shortest distances that the node reaches other nodes in the network.
Step 2, determining the vulnerability of each configurable node in the power system based on the four indexes of step 1;
in this embodiment, a subjective and objective weighting method-Analytic Hierarchy Process (AHP) and an Entropy Weighting Method (EWM) are combined to comprehensively evaluate the weights of the respective indexes, and then TOPSIS is used to determine vulnerability of each node.
The steps of 2-1 and AHP are as follows:
2-1-1, and constructing and judging a 4×4 matrix for the four evaluation indexes in the step 1AElements in a matrixa tq Represent the firsttImportance of each index and the firstqThe ratio of the importance of the individual indicators. In this embodiment, the determination matrix is constructed in the order of De, rb, LDT, P:
Figure SMS_12
；
in the formula, the first element (De, de) of the judgment matrix is 1, and the comparison between the same indexes is considered to have the same importance. Therefore, all diagonal elements of the decision matrix will be 1. For the second element (De, rb) is 1/7, indicating that Rb is 7 times more fragile than De.
2-1-2, by judgment matrixAAnd obtaining the characteristic vector between each layer. Consistency test: by solving forAMaximum characteristic value of (2)λ max To solve the consistency index CI and the consistency ratio CR, when CR<0.1, judging that the consistency of the matrix is acceptable; otherwise, the judgment matrix needs to be corrected.
2-1-3, after passing the consistency test, using judgmentThe matrix calculates the weight of each index. For the firstqThe weights obtained by the analytic hierarchy process are:
Figure SMS_13
；
the steps of 2-2 and EWM are as follows:
2-2-1, for one there ismThe power system of the individual nodes is such that,nindividual evaluation index [ ]n=4), the original data matrix forming the forward processing is:
Figure SMS_14
；
in the method, in the process of the invention,x mn is the firstmThe first nodenAnd (5) evaluating indexes.
2-2-2, normalizing the weightz tq ) And calculate the probability matrixP（p tq ）：
Figure SMS_15
；
Figure SMS_16
；
2-2-3, calculating the information entropy and entropy weight of each index. For the firstqThe calculation formulas of the information entropy and the entropy weight of the index are as follows:
Figure SMS_17
；
Figure SMS_18
；
comprehensively considering AHP and EWM evaluation methods to obtain the firstqThe comprehensive weight of each index is as follows:
Figure SMS_19
；
2-3, obtaining the vulnerability of each node of the power system based on the comprehensive weight and the TOPSIS method.
2-3-1, for one havingmThe power system of the individual nodes is such that,nthe index of each evaluation, the standardized matrix is:
Figure SMS_20
；
Figure SMS_21
；
maximum value matrix:
Figure SMS_22
；
minimum matrix:
Figure SMS_23
；
first, thei(i=1,2,..,m)Distance of each evaluation object (node) from the maximum value:
Figure SMS_24
；
first, theiDistance of each evaluation object from the minimum value:
Figure SMS_25
；
in the method, in the process of the invention,W j （j=1..4) is AHP and EWM combined weight;
first, theiThe unnormalized vulnerability scores of the individual evaluation subjects were:
Figure SMS_26
；
the vulnerability obtained after normalization is:
Figure SMS_27
；
and (4) sorting based on the vulnerability, wherein the nodes with high vulnerability are used as the priority configuration in the PMU optimal configuration problem in the subsequent step (4).
For example, there are 14 evaluation targets and 4 evaluation indexes for an IEEE-14 node. Then a matrix of 14×4 can be formed, after normalization, the maximum value and the minimum value of each column are found, the distances between each evaluation object and the maximum value and the minimum value are calculated, the vulnerability score is obtained based on the distances, and finally the vulnerability is obtained by normalization processing. The nodes 7 are arranged first in the following step 4, with the nodes 7 being the largest, ordered from big to small in vulnerability.
As shown in FIG. 2, for an IEEE-57 node system, the weights corresponding to the number and the proximity of the node degree, the first node connected with the radial bus and the three electrical devices connected with the load generator transformer are calculated by AHP respectivelyW 11 =0.1172，W 12 =0.8203，W 13 =0.0391，W 14 =0.0234; weights obtained by EWM are respectivelyW 21 =0.0089，W 22 =0.9102，W 23 =0.0777，W 24 =0.0032. The weights of the AHP and the EWM are integrated to obtain the integrated weight of each index as followsW 1 =0.0337，W 2 =0.8999，W 3 =0.0574，W 4 =0.0090. The vulnerability index of each node is determined using TOPSIS as shown in fig. 3. Nodes 32, 9, 1, 6 and 15 are sequentially prioritized in step 4 by ordering the node vulnerability indices.
And 3, calculating the installation cost of each node in the power system as an installation cost index.
In step 3, the PMU node installation costs are configured to form an installation cost index matrix based on the effects of the communication facilities, the number of network buses, and the software costs on the PMU installation costs. In this embodiment, for all nodes, the PMU base installation cost is set to 1p.u.; every time one AND node is addediThe installation costs of the connected devices increase by 0.1 p.u..
Step 4, pre-configuration: and (3) based on the vulnerability of each node determined in the step (2), pre-configuring the high-vulnerability nodes with the vulnerability of about 10% in the power system as the nodes which are required to be configured.
Step 5, setting the particle speed between [ -4,4], and improving the position updating mode of the particle swarm optimization algorithm based on the following functions, so as to further shorten the calculation time, improve the convergence speed and increase the logic diversity of the position updating;
Figure SMS_28
；
in the method, in the process of the invention,x gf is the firstgThe particles are at the firstfThe position in the dimension is such that,v gf is the firstgThe particles are at the firstfSpeed in dimension; the step 5 and any one of the above steps have no sequence.
And, the inertia weight is set as:
Figure SMS_29
；
in the method, in the process of the invention,t c andTthe current iteration and the maximum iteration number are respectively.
Binary particle swarm optimization algorithms have the problems of easy sinking into locally optimal solutions and too slow convergence. Therefore, the improved performance is improved by improving PSO, and the method is more suitable for solving the PMU optimal configuration problem.
Step 6, taking the nodes which are not configured as variables on the basis of the pre-configuration in the step 4; particle swarm optimization algorithm modified in step 5 based on objective functionFAnd carrying out optimizing calculation to obtain an optimal scheme of PMU configuration.
In this embodiment, the variable range is further reduced based on the constraint condition of the objective function:
Figure SMS_30
；
wherein, in boldXColumn vectors representing the number of nodes (the number of nodes being the decision variableA number); if at firstiThe PMU is configured by each nodex i 1, otherwise 0;
then based on the objective functionFAnd (3) optimizing calculation:
Figure SMS_31
；
in the method, in the process of the invention,
Figure SMS_32
is a nodeiVulnerability index of (2);I i is a nodeiIs a cost of installation index; when the nodeiIf PMU is installed, thenx i 1, otherwise 0;a=1，b=2。
to verify the effect of the present invention, the following examples are used for illustration:
as shown in fig. 4 to 6, the method of the present invention is distinguished from the prior art method 1 (BPSO-1, which is not preconfigured in step 4 and adopts an unmodified particle swarm optimization algorithm in step 5) to perform simulation test tests of different system nodes, the maximum iteration number of the two methods during the test is 200, the test runs for 30 times respectively, and the average value of the running results is taken as the final result. For IEEE-14 nodes, the method and the BPSO-1 method can obtain final configuration results, but as the number of nodes to be configured in a power system increases (IEEE-57 and 118 nodes), the BPSO method obviously falls into a local optimal solution (premature convergence), and compared with the method, the method has better optimization results.
Further, as shown in fig. 7 to 9, the simulation test of different system nodes is performed by comparing the method of the present invention with the prior art method 2 (BPSO-2, which is only different from the step 5 in that an unmodified particle swarm optimization algorithm is adopted), the maximum iteration number of the two methods is 200, the two methods are respectively tested and operated for 30 times, and the average value of the operation results is taken as the final result, and the results are shown in the following table 1. For IEEE-14 nodes, after node 7 is configured preferentially, the method and BPSO-2 method of the invention can obtain the final configuration result, but as the number of nodes to be configured in the power system increases, after IEEE-57 and 118 nodes configure 5 and 10 nodes preferentially,the BPSO-2 method still falls into a locally optimal solution, the PMU configuration quantity is more than that of the invention, andFthe value is higher; the method of the invention shows better optimizing result, the PMU configuration quantity is low, andFthe value is the lowest.
In the practical application process, the number of the nodes of the power system is very huge, thousands of advantages of the method are more obvious, the nodes of the power system are often required to be divided according to the areas in the prior art aiming at the situation, and the PMUs are configured according to the areas.
Table 1 comparison of experimental results
Figure SMS_33
Further, the processing efficiency of the method of the invention is compared:
TLBO is a meta heuristic proposed by yuv araju V et al, 2021, which does not require any algorithm specific parameters, requires less computational memory, and is easy to implement. Thus, the present invention demonstrates the superiority and effectiveness of the process of the present invention in terms of processing efficiency as compared to TLBO and BPSO.
Table 2 comparison results of execution times of three methods for different node power systems
Figure SMS_34
As can be seen from the data in Table 2 above, compared with TLBO and BPSO-2, the processing time required for obtaining the PMU optimal configuration by the method is far less than that of BPSO-2 and TLBO, and the method has more remarkable advantage in processing efficiency along with the increase of the number of nodes of the power system. For thousands of nodes of the power system in the practical application process, the method can integrally configure the PMU, and greatly improve the processing efficiency.
< example two >
The second embodiment provides a PMU optimal configuration system based on vulnerability and economy of a power system, which can automatically implement the method of the present invention, and the system includes an index acquisition unit, a vulnerability calculation unit, an installation cost matrix construction unit, a pre-configuration unit, an algorithm improvement unit, a PMU optimal configuration acquisition unit, an input display unit, and a control unit.
The index obtaining part executes the content described in the step 1, and takes four indexes of the degree of the power system node, the first node connected with the radial bus, the number and the proximity of three electrical devices connected with the load generator transformer in the power system to be configured as indexes for measuring the vulnerability of the node.
The vulnerability calculating section performs the content described in the above step 2, and determines the vulnerability of each configurable node in the power system based on four indicators measuring the vulnerability of the node.
The installation cost matrix construction section performs the content described in step 3 above, and calculates the installation cost of each node in the power system as an installation cost index.
The pre-configuration unit executes the description of step 4, and based on the vulnerability of each node, the high-vulnerability nodes with the vulnerability of 6-12% in the power system are used as the nodes which are required to be configured.
The algorithm improving unit performs the above description of step 5 to improve the position update method of the particle swarm optimization algorithm.
The PMU optimal configuration acquisition part executes the content described in the step 6, and takes nodes which are not configured as variables on the basis of pre-configuration; target function pair using improved particle swarm optimization algorithmFAnd carrying out optimizing calculation to obtain an optimal scheme of PMU configuration.
The input display part is used for enabling a user to input operation instructions and correspondingly displaying the input, output and processing procedures of each part according to the specific operation instructions.
The control part is communicated with the index acquisition part, the vulnerability calculation part, the installation cost matrix construction part, the pre-configuration part, the algorithm improvement part, the PMU optimal configuration acquisition part and the input display part, and controls the operation of the index acquisition part, the vulnerability calculation part, the installation cost matrix construction part, the pre-configuration part, the algorithm improvement part, the PMU optimal configuration acquisition part and the input display part.
The above embodiments are merely illustrative of the technical solutions of the present invention. The method and system for optimal PMU configuration based on the weakness and economy of the power system according to the present invention are not limited to the above embodiments, but the scope of the invention is defined by the claims. Any modifications, additions or equivalent substitutions made by those skilled in the art based on this embodiment are within the scope of the invention as claimed in the claims.

Claims (10)

1. The PMU optimal configuration method based on the weakness and economy of the power system is characterized by comprising the following steps of:
step 1, taking four indexes in a power system to be configured as indexes for measuring node vulnerability; the four indexes are respectively: the degree of the node is connected with the first node of the radial bus, and is connected with the number and the proximity of three kinds of electrical equipment, namely a load, a generator and a transformer;
step 2, determining the vulnerability of each configurable node in the power system based on the four indexes of step 1;
step 3, calculating the installation cost of each node in the power system as an installation cost index;
step 4, pre-configuration: based on the vulnerability of each node determined in the step 2, the high-vulnerability nodes with the vulnerability of 6-12% in the front in the power system are used as the nodes which are required to be configured;
step 5, improving the position updating mode of the particle swarm optimization algorithm based on the following functions;
Figure QLYQS_1
；
in the method, in the process of the invention,x gf is the firstgThe particles are at the firstfThe position in the dimension is such that,v gf is the firstgThe particles are at the firstfSpeed in dimension;
step 6, taking the nodes which are not configured as variables on the basis of the pre-configuration in the step 4; particle swarm optimization algorithm modified in step 5 based on objective functionFPerforming optimizing calculation to obtain an optimal scheme of PMU configuration;
objective functionFThe method comprises the following steps:
Figure QLYQS_2
；
in the method, in the process of the invention,
Figure QLYQS_3
is a nodeiVulnerability index of (2);I i is a nodeiIs a cost of installation index;mis the total number of nodes; when the nodeiIf PMU is installed, thenx i 1, otherwise 0;a、bis a constant coefficient, the values are positive numbersb＞aIs determined through experiments;
wherein, any step in the step 5 and the steps 1-4 has no sequential division.
2. The method for optimal configuration of a PMU based on vulnerability and economy of power system according to claim 1, wherein:
in step 5, the inertial weights are:
Figure QLYQS_4
；
in the method, in the process of the invention,t c andTthe current iteration and the maximum iteration number are respectively.
3. The method for optimal configuration of a PMU based on vulnerability and economy of power system according to claim 1, wherein:
wherein the particle velocity is set between [ -4,4] in step 5.
4. The method for optimal configuration of a PMU based on vulnerability and economy of power system according to claim 1, wherein:
in step 4, the high vulnerability nodes of the power system 10% are configured in order from the high vulnerability to the low vulnerability based on the nodes determined in step 2.
5. The method for optimal configuration of a PMU based on vulnerability and economy of power system according to claim 1, wherein:
in step 3, the installation cost index matrix is formed by configuring the installation cost of each node of the PMU based on the influences of the communication facilities, the number of network buses and the software cost on the installation cost of the PMU.
6. The method for optimal configuration of a PMU based on vulnerability and economy of power system according to claim 5, wherein:
in step 3, for all nodes, the PMU basic installation cost is set to be 1p.u.; every time one AND node is addediThe installation costs of the connected devices increase by 0.1 p.u..
7. The method for optimal configuration of a PMU based on vulnerability and economy of power system according to claim 1, wherein:
in step 6, a value is recommended:a=1，b=2。
8. the method for optimal configuration of a PMU based on vulnerability and economy of power system according to claim 1, wherein:
in step 2, a corresponding node judgment matrix is constructed based on the four indexes of step 1AFor judgment matrixAThe weight of each index is comprehensively evaluated by adopting a subjective and objective weighting method-analytic hierarchy process and an entropy weighting method, and then vulnerability of each node is determined by utilizing TOPSIS.
9. A PMU optimal configuration system based on power system vulnerability and economy, comprising:
the system comprises an index acquisition part, a control part and a control part, wherein the index acquisition part takes four indexes of the degree of a power system node, a first node connected with a radial bus, the number and the proximity of three electrical equipment connected with a load generator transformer in a power system to be configured as indexes for measuring node vulnerability;
a vulnerability calculating unit that determines the vulnerability of each configurable node in the power system based on four indices that measure the vulnerability of the node;
an installation cost matrix construction unit which calculates the installation cost of each node in the power system as an installation cost index;
a pre-configuration unit which uses the high-vulnerability nodes with the vulnerability of 6-12% in the front in the power system as the nodes which are required to be configured based on the vulnerability of each node;
an algorithm improving unit for improving the position updating mode of the particle swarm optimization algorithm based on the following functions;
Figure QLYQS_5
；
in the method, in the process of the invention,x gf is the firstgThe particles are at the firstfThe position in the dimension is such that,v gf is the firstgThe particles are at the firstfSpeed in dimension;
the PMU optimal configuration acquisition part takes nodes which are not configured as variables on the basis of pre-configuration; target function pair using improved particle swarm optimization algorithmFPerforming optimizing calculation to obtain an optimal scheme of PMU configuration; objective functionFThe method comprises the following steps:
Figure QLYQS_6
；
in the method, in the process of the invention,
Figure QLYQS_7
is a nodeiVulnerability index of (2);I i is a nodeiIs a cost of installation index;mis the total number of nodes; when the nodeiIf PMU is installed, thenx i 1, otherwise 0;a、bis a constant coefficient, the values are positive numbersb＞aIs determined through experiments;
the control part is communicated with the index acquisition part, the vulnerability calculation part, the installation cost matrix construction part, the pre-configuration part, the algorithm improvement part and the PMU optimal configuration acquisition part and controls the operation of the index acquisition part, the vulnerability calculation part, the installation cost matrix construction part, the pre-configuration part, the algorithm improvement part and the PMU optimal configuration acquisition part.
10. The power system vulnerability and economy based PMU optimal configuration system according to claim 9, further comprising:
the input display part is communicated with the index acquisition part, the vulnerability calculation part, the installation cost matrix construction part, the pre-configuration part, the algorithm improvement part, the PMU optimal configuration acquisition part and the control part and is used for enabling a user to input an operation instruction and correspondingly display the operation instruction.
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