Power distribution network FTU optimal configuration method considering reliability and state estimation

Abstract

The invention discloses a power distribution network FTU optimal configuration method considering reliability and state estimation, and the method comprises the steps: obtaining the information of a power distribution network, dividing sections according to the positions of FTUs, and constructing a power distribution network topological graph based on a directed graph; analyzing the fault power failure loss and the fault probability of the section, and calculating a system EDNS value; an FTU configuration quantity Nf is given, a mathematical model is constructed based on a directed graph method with the aim of minimizing the system EDNS, and an FTU configuration scheme with the highest reliability is obtained through solving; and performing state estimation analysis on the FTU configuration scheme, if the precision requirement is not met, increasing the FTU configuration number Nf, and selecting the minimum FTU number meeting the state estimation precision requirement as the final configuration scheme. According to the method, the FTU configuration scheme with the highest reliability can be obtained, the minimization of the number of FTUs under the condition that the system precision requirement is met can be realized by matching state estimation analysis on the basis, and the FTU configuration cost is reduced to the greatest extent under the condition that the reliability of the power distribution network and the system state estimation precision are considered.

Description

Technical Field

[0001] The present invention belongs to the field of distribution network measurement configuration, and in particular relates to a distribution network FTU optimization configuration method considering reliability and state estimation. Background Art

[0002] Driven by global environmental issues, new energy generation technology has developed rapidly. The continuous access of distributed energy and electric vehicles has made the current distribution more complicated when the distribution network fails, bringing new challenges to the safe and stable operation of the distribution network. Fast and accurate fault location is a key prerequisite for eliminating distribution network faults, restoring power supply and ensuring power supply reliability. At present, fault location usually relies on feeder terminal units (FTUs). Increasing the investment in FTUs can help reduce power outage losses and improve power supply reliability. In addition, FTUs can provide accurate measurement data. Increasing the configuration of FTUs can significantly improve the accuracy of state estimation and provide accurate basic data for distribution network situation awareness, operation optimization and risk analysis.

[0003] However, due to the limitation of configuration cost, it is not realistic to configure FTU in distribution network on a large scale. Therefore, it is necessary to study the optimal measurement configuration scheme, namely the measurement optimization configuration problem. At present, the goals of most optimization problems usually include ensuring the reliability of the whole network, improving the accuracy of state estimation and reducing the configuration cost, but the existing scheme can only take one of them into consideration, and it is impossible to take all three into consideration at the same time. The optimization configuration needs to be improved. Summary of the invention

[0004] Purpose of the invention: In order to overcome the deficiencies in the prior art, a distribution network FTU optimization configuration method considering reliability and state estimation is provided, which minimizes the configuration cost of the FTU while taking into account the reliability of the distribution network and the accuracy of system state estimation.

[0005] Technical solution: To achieve the above-mentioned purpose, the present invention provides a distribution network FTU optimization configuration method considering reliability and state estimation, comprising the following steps:

[0006] S1: Obtain distribution network information, divide the sections according to the FTU locations, and construct a distribution network topology map based on a directed graph;

[0007] S2: Analyze the power outage loss and failure probability of the section;

[0008] S3: Given FTU configuration quantity N f , with the goal of minimizing the expected demand not supplied (EDNS) of the system, a mathematical model is constructed based on the directed graph method according to the power outage loss and failure probability, and the FTU configuration scheme with the highest reliability is solved;

[0009] S4: Perform state estimation analysis on the FTU configuration scheme. If it does not meet the accuracy requirements given by the system, increase the number of FTU configurations N. f , the minimum number of FTUs that meets the state estimation accuracy requirements is selected as the final configuration solution.

[0010] Furthermore, the method for constructing the distribution network topology map based on the directed graph in step S1 is:

[0011] When the distribution network is in open-loop operation, the topology is radial and connected. It can be regarded as a tree with the busbar as the node and the power supply line as the branch. FTU is configured on the sectionalizer of the distribution network feeder and is configured on the side with a smaller node number. It is stipulated that the line configured with FTU is disconnected in the topology. In this way, N is configured in the feeder. f FTU, the distribution network can be divided into N f +1 section.

[0012] In order to maintain the connectivity of the topology, a virtual source point G is constructed in the graph, and the virtual source point is connected to one of the nodes in each section. The line connecting the virtual source point and the node is called a virtual branch, and the node connected to the virtual source point is called a section source point. It is stipulated that the topology still has a radial structure after the introduction, so it must be ensured that there is only one virtual branch between each section and the virtual source point. The virtual source point G transmits virtual flow to each section through the virtual branch. Similar to the power system flow, the virtual flow can be transmitted on the line and has a certain flow direction. It is stipulated that the virtual flow is injected from the node with the smallest number in the section, so that the virtual flow on the power supply line can flow from the node with a small number to the node with a large number. Each node consumes a part of the virtual flow, which is called virtual load. The size of the virtual flow transmitted by the virtual source point G to a section is equal to the sum of the virtual loads in the section. The default power export line is equipped with relay protection and SCADA measurement, so in the subsequent optimization model, FTU is not configured on the power export line.

[0013] Furthermore, the current transmitted on the virtual branch in step S1 is a virtual flow. The virtual flow is transmitted on the line and has a certain flow direction. It is stipulated that the virtual flow is injected from the node with the smallest number in the segment, so that the virtual flow on the power supply line can flow from the node with a small number to the node with a large number; each node consumes a part of the virtual flow, which is called virtual load. The size of the virtual flow transmitted by the virtual source point G to a certain segment is equal to the sum of the virtual loads in the segment. The default power export line is equipped with relay protection and SCADA measurement, so in the subsequent optimization model, FTU is not configured on the power export line.

[0014] Furthermore, the step S2 is specifically as follows:

[0015] After analysis, it is found that the power outage loss of the section is the sum of the loads in the faulty section: when a line fault occurs in the distribution network, the faulty section can be located through distribution automation technology, and then the FTU will control the line section switch to open and close, isolate the faulty section, and then carry out fault repair work on the faulty section, during which all loads in the faulty section will lose power. For other non-faulty sections, if the fault occurs downstream of the distribution network, the section will not be affected by the fault; if the fault occurs upstream of the section, all loads in the section will also lose power, but the actual distribution network is a closed-loop structure, open-loop operation, with a tie line between feeders, and the tie line switch has been configured with FTU for control of opening and closing. Under normal operation of the distribution network, the tie line is in a disconnected state. When a fault occurs and the faulty section has been isolated, the tie line can be closed to realize power transfer, so that the power outage time of the load in the non-faulty section is only the time for locating the faulty section, isolating and restoring the non-faulty section. Compared with the fault repair time, this time is short, and the load power outage loss in this short time can be ignored. Therefore, it can be considered that the power outage loss after a fault occurs is the sum of the loads in the fault section, and the present invention mainly considers the active load.

[0016] The probability of line failure is random. Failure may occur at any position of each line. Assuming that the probability of failure per unit length of the line is the same, the size is f. The probability of line failure is proportional to its length. The length of the line with node i as the end node (i is the side with a larger node number) is l. i , then the line failure probability L of the line with node i as the end node i for:

[0017] L i =f·l i (1)

[0018] Accordingly, the failure rate of a section is the sum of the failure rates of all lines in the section.

[0019] Furthermore, the specific process of constructing the mathematical model based on the directed graph method in step S3 is:

[0020] By configuring a certain number of FTUs, the distribution network can be divided into different sections. The power outage losses and section failure probability of each section can be calculated. EDNS is used to evaluate the system power supply reliability. The smaller the EDNS, the higher the reliability. Therefore, the goal of FTU optimization configuration is to minimize the system EDNS value. According to the directed graph method, the objective function can be written as

[0021]

[0022] Where n is the number of nodes; i is the node number, node 1 is the power node and does not participate in the optimization; d i and r iare all non-negative continuous variables, where d i represents the power outage loss caused by the fault in the section where node i is located; r i represents the failure probability of the segment where node i is located;

[0023] Each line can choose to configure FTU, using 0-1 variable m ij Indicates whether FTU is configured on line ij. A value of 1 indicates that FTU is configured on the line. The number of configured FTUs should be equal to the given number N. f ,Right now

[0024] ∑m ij =N f (3)

[0025] For the radial structure distribution network, configure N f FTU, the distribution network is divided into N f +1 segment, there is only one virtual branch between each segment and the virtual source point, so the number of virtual branches should be equal to the number of segments, that is,

[0026]

[0027] Among them, b i is a 0-1 variable, and taking 1 means that node i is connected to the virtual source point through a virtual branch;

[0028] It is stipulated that two virtual flows are transmitted from the source point to each section to calculate the total active load and failure rate in the section. These two virtual flows are independent of each other and can be considered separately. The active virtual flow and failure rate virtual flow of the virtual flow transmitted on line ij are defined as F ij and R ij , are non-negative continuous variables; similar to the power flow calculation of the power system, for any node of the system, the power balance constraint of the virtual flow needs to be satisfied, that is,

[0029]

[0030] Where i = 2, 3, ..., n, k is the node number connected to node i and smaller than i, S i is the set of node numbers connected to i and greater than i; P i is the active load of node i, L i is the failure probability of the line with node i as the end node; the positive and negative signs in the formula constrain the virtual flow direction from the node with a smaller number in the section to the node with a larger number;

[0031] There is an upper limit constraint on the virtual flow transmitted on line ij, F ij and R ij The maximum active load will not exceed the total active load P of the system. Mand the sum of all line failure probabilities L M In addition, when FTU is configured on line ij, line ij is disconnected from the network topology and does not transmit virtual flows. The inequality constraints considering the above problems are:

[0032]

[0033] The virtual flows on the line are all transmitted from the virtual source point through the virtual branch, so d i and r i There is also an upper limit constraint, and it only has a value when node i is the source point of the segment, otherwise it is 0. Considering the above problems, the inequality constraint is

[0034]

[0035] Formulas (2) to (7) constitute the FTU optimization configuration model with the highest reliability represented by the minimum system EDNS value. This model is a quadratic mixed integer programming model.

[0036] Furthermore, in step S3, the constructed mathematical model is solved by Gurobi solver.

[0037] Furthermore, the method for performing state estimation analysis on the FTU configuration scheme in step S4 is: for a distribution network with n nodes, when the topology structure and branch parameters are known, a state estimation calculation is performed based on all measurement data, and the measurement equation for state estimation is:

[0038] z=h(x)+e(8)

[0039] Wherein: z is an m-dimensional measurement vector, x is a (2n-1)-dimensional state vector, and the present invention selects node voltage amplitude and phase angle (except for balanced nodes) as state quantities; h(x) is an m×(2n-1)-dimensional measurement function matrix, which reflects the nonlinear relationship between the measurement and the state quantity; e is an m-dimensional measurement error vector, which is assumed to obey the normal distribution;

[0040] State estimation improves the real state of the system through redundant measurement data. Therefore, the state estimation calculation needs to satisfy the dimension of the measurement vector is greater than the dimension of the state vector, that is,

[0041] dim(z)>dim(x)(9)

[0042] Where: dim(z) is the dimension of the measurement vector, dim(x) is the dimension of the state vector;

[0043] In actual systems, it is impossible to configure FTU on each line. Only based on FTU measurement data, it cannot guarantee that equation (9) is valid. Therefore, pseudo measurement needs to be introduced to improve measurement redundancy. Pseudo measurement is generally achieved through load forecasting. Compared with FTU measurement, the accuracy is lower. The injected power of each node can be obtained. The corresponding measurement equation is:

[0044]

[0045] Where i represents the node number, i = 1, 2, ..., n; and are the active and reactive measurements injected into node i, ΔP i and ΔQ i is the corresponding measurement error; U i and θ i are state variables, representing the voltage amplitude and phase angle of node i respectively. Let θ ij =θ i -θ j represents the phase angle difference between node i and node j, G ij and B ij are the real and imaginary parts of the elements in the i-th row and j-th column of the system admittance matrix respectively;

[0046] Compared with pseudo measurement, FTU measurement has higher data accuracy and can measure the branch power, branch current amplitude and voltage amplitude of the node connected to FTU. The measurement equation corresponding to FTU measurement is:

[0047]

[0048] In the formula, and are the measured values ​​of active power and reactive power flowing into the branch ij from the node i side, ΔP ij and ΔQ ij is the corresponding measurement error; g ij and b ij are the conductance and susceptance on branch ij respectively; and ΔI ij are the measured value of the current amplitude flowing into the branch ij from the node i side and the corresponding measurement error respectively; and ΔU i are the voltage amplitude measurement value and the corresponding measurement error of node i respectively;

[0049] The state estimation is solved by weighted least squares (WLS), the goal of which is to minimize the weighted sum of squares of measurement errors in all measurement equations, that is,

[0050] minJ(x)=[zh(x)]T W[zh(x)](12)

[0051] Where J(x) represents the weighted sum of squares of measurement errors, W is the m×m-dimensional measurement weight matrix, which is a diagonal matrix, specifically:

[0052] W=diag[w1,w2,w3,...,w m ](13)

[0053] Among them, w i (i=1,2,…,m) represents the weight of the i-th measurement, which is usually expressed as the inverse of the measurement variance;

[0054] Since the measurement function h(x) in equation (12) is nonlinear, it is difficult to directly find the minimum value of J(x). We can use the Newton iteration method to iteratively correct the solution according to equation (14):

[0055]

[0056] In the formula, x (k) is the state vector of the kth iteration, Δx (k) is the state vector of the kth iteration, H(x) is the Jacobian matrix of the measurement function h(x);

[0057] When Δx (k) When the iteration reaches the value of formula (15), the iteration is considered to have converged and the iteration is stopped; where ε is the given iteration allowable error, which is taken as 10 in the present invention. -4 ;

[0058] max|Δx (k) |≤ε (15)

[0059] The state vector x obtained after the iteration is completed is the state estimation value, which contains the voltage amplitude estimation value U of all nodes. i and the phase angle estimate θ i (Except the balance node), the deviation between the estimated value and the true value is calculated according to formula (16) to evaluate the accuracy of state estimation

[0060]

[0061] In the formula, and are the voltage amplitude true value and phase angle true value respectively, and Represent the absolute errors of voltage amplitude and phase angle estimation respectively. If and satisfy

[0062]

[0063] Then the FTU configuration meets the system state estimation accuracy requirement, otherwise it is necessary to increase the number of FTU configurations to improve the state estimation accuracy; U and σ θ are the maximum estimation errors of voltage amplitude and phase angle allowed by the system respectively.

[0064] Beneficial effect: Compared with the prior art, the present invention introduces the minimized system power shortage expected value EDNS into the distribution network FTU optimization configuration, establishes and solves a mathematical model with the goal of minimizing the system EDNS, and can obtain the most reliable FTU configuration scheme. On this basis, combined with the state estimation analysis, it can achieve the minimization of the number of FTUs while meeting the system accuracy requirements. While taking into account the reliability of the distribution network and the accuracy of the system state estimation, the configuration cost of the FTU is minimized. BRIEF DESCRIPTION OF THE DRAWINGS

[0065] Figure 1 A directed topological diagram of the distribution network of the FTU provided in this embodiment;

[0066] Figure 2 Corrected system topology diagram for IEEE-33 nodes;

[0067] Figure 3 is the relationship between the maximum voltage amplitude and phase angle estimation error and the number of FTU configurations;

[0068] Figure 4 Configure the optimal result graph for FTU. DETAILED DESCRIPTION

[0069] The present invention is further explained below in conjunction with the accompanying drawings and specific embodiments. It should be understood that these embodiments are only used to illustrate the present invention and are not used to limit the scope of the present invention. After reading the present invention, various equivalent forms of modifications to the present invention by those skilled in the art all fall within the scope defined by the claims attached to this application.

[0070] The present invention provides a distribution network FTU optimization configuration method considering reliability and state estimation, comprising the following steps:

[0071] S1: Obtain distribution network information, divide the sections according to the FTU locations, and construct a distribution network topology map based on a directed graph:

[0072] The construction method of the distribution network topology diagram based on the directed graph is:

[0073] When the distribution network is in open-loop operation, the topology is radial and connected. It can be regarded as a tree with the busbar as the node and the power supply line as the branch. FTU is configured on the sectionalizer of the distribution network feeder and is configured on the side with a smaller node number. It is stipulated that the line configured with FTU is disconnected in the topology. In this way, N is configured in the feeder. f FTU, the distribution network can be divided into N f +1 section.

[0074] In order to maintain the connectivity of the topology, a virtual source point G is constructed in the graph, and the virtual source point is connected to one of the nodes in each section. The line connecting the virtual source point and the node is called a virtual branch, and the node connected to the virtual source point is called a section source point. It is stipulated that the topology still has a radial structure after the introduction, so it must be ensured that there is only one virtual branch between each section and the virtual source point. The virtual source point G transmits virtual flow to each section through the virtual branch. Similar to the power system flow, the virtual flow can be transmitted on the line and has a certain flow direction. It is stipulated that the virtual flow is injected from the node with the smallest number in the section, so that the virtual flow on the power supply line can flow from the node with a small number to the node with a large number. Each node consumes a part of the virtual flow, which is called virtual load. The size of the virtual flow transmitted by the virtual source point G to a section is equal to the sum of the virtual loads in the section. The default power export line is equipped with relay protection and SCADA measurement, so in the subsequent optimization model, FTU is not configured on the power export line.

[0075] The current transmitted on the virtual branch is a virtual flow. The virtual flow is transmitted on the line with a certain flow direction. It is stipulated that the virtual flow is injected from the node with the smallest number in the section, so that the virtual flow on the power supply line flows from the node with a small number to the node with a large number; each node consumes a part of the virtual flow, which is called virtual load. The size of the virtual flow transmitted by the virtual source point G to a certain section is equal to the sum of the virtual loads in the section. The default power export line is equipped with relay protection and SCADA measurement, so in the subsequent optimization model, FTU is not configured on the power export line.

[0076] S2: Analyze the power outage loss and failure probability of the section:

[0077] After analysis, it is found that the power outage loss of the section is the sum of the loads in the faulty section: when a line fault occurs in the distribution network, the faulty section can be located through distribution automation technology, and then the FTU will control the line section switch to open and close, isolate the faulty section, and then carry out fault repair work on the faulty section, during which all loads in the faulty section will lose power. For other non-faulty sections, if the fault occurs downstream of the distribution network, the section will not be affected by the fault; if the fault occurs upstream of the section, all loads in the section will also lose power, but the actual distribution network is a closed-loop structure, open-loop operation, with a tie line between feeders, and the tie line switch has been configured with FTU for control of opening and closing. Under normal operation of the distribution network, the tie line is in a disconnected state. When a fault occurs and the faulty section has been isolated, the tie line can be closed to realize power transfer, so that the power outage time of the load in the non-faulty section is only the time for locating the faulty section, isolating and restoring the non-faulty section. Compared with the fault repair time, this time is short, and the load power outage loss in this short time can be ignored. Therefore, it can be considered that the power outage loss after a fault occurs is the sum of the loads in the fault section, and the present invention mainly considers the active load.

[0078] The probability of line failure is random. Failure may occur at any position of each line. Assuming that the probability of failure per unit length of the line is the same, the size is f. The probability of line failure is proportional to its length. The length of the line with node i as the end node (i is the side with a larger node number) is l. i , then the line failure probability L of the line with node i as the end node i for:

[0079] L i =f·l i (1)

[0080] Accordingly, the failure rate of a section is the sum of the failure rates of all lines in the section.

[0081] S3: Given FTU configuration quantity N f , with the goal of minimizing the system EDNS, according to the power outage loss and failure probability, a mathematical model is constructed based on the directed graph method to solve the FTU configuration scheme with the highest reliability:

[0082] The specific process of constructing a mathematical model based on the directed graph method is as follows:

[0083] By configuring a certain number of FTUs, the distribution network can be divided into different sections. The power outage losses and section failure probability of each section can be calculated. EDNS is used to evaluate the system power supply reliability. The smaller the EDNS, the higher the reliability. Therefore, the goal of FTU optimization configuration is to minimize the system EDNS value. According to the directed graph method, the objective function can be written as

[0084]

[0085] Where n is the number of nodes; i is the node number, node 1 is the power node and does not participate in the optimization; d i and r i are all non-negative continuous variables, where d i represents the power outage loss caused by the fault in the section where node i is located; r i represents the failure probability of the segment where node i is located;

[0086] Each line can choose to configure FTU, using 0-1 variable m ij Indicates whether FTU is configured on line ij. A value of 1 indicates that FTU is configured on the line. The number of configured FTUs should be equal to the given number N. f ,Right now

[0087] ∑m ij =N f (3)

[0088] For the radial structure distribution network, configure N f FTU, the distribution network is divided into N f +1 segment, there is only one virtual branch between each segment and the virtual source point, so the number of virtual branches should be equal to the number of segments, that is,

[0089]

[0090] Among them, b i is a 0-1 variable, and taking 1 means that node i is connected to the virtual source point through a virtual branch;

[0091] It is stipulated that two virtual flows are transmitted from the source point to each section to calculate the total active load and failure rate in the section. These two virtual flows are independent of each other and can be considered separately. The active virtual flow and failure rate virtual flow of the virtual flow transmitted on line ij are defined as F ij and R ij , are non-negative continuous variables; similar to the power flow calculation of the power system, for any node of the system, the power balance constraint of the virtual flow needs to be satisfied, that is,

[0092]

[0093] Where i = 2, 3, ..., n, k is the node number connected to node i and smaller than i, S i is the set of node numbers connected to i and greater than i; P i is the active load of node i, L i is the failure probability of the line with node i as the end node; the positive and negative signs in the formula constrain the virtual flow direction from the node with a smaller number in the section to the node with a larger number;

[0094] There is an upper limit constraint on the virtual flow transmitted on line ij, F ij and R ij The maximum active load will not exceed the total active load P of the system. M and the sum of all line failure probabilities L M In addition, when FTU is configured on line ij, line ij is disconnected from the network topology and does not transmit virtual flows. The inequality constraints considering the above problems are:

[0095]

[0096] The virtual flows on the line are all transmitted from the virtual source point through the virtual branch, so d i and r i There is also an upper limit constraint, and it only has a value when node i is the source point of the segment, otherwise it is 0. Considering the above problems, the inequality constraint is

[0097]

[0098] Formulas (2) to (7) constitute the FTU optimization configuration model with the highest reliability represented by the minimum system EDNS value, which is a quadratic mixed integer programming model. The constructed mathematical model is solved by Gurobi solver.

[0099] S4: Perform state estimation analysis on the FTU configuration scheme. If it does not meet the accuracy requirements given by the system, increase the number of FTU configurations N. f , select the minimum number of FTUs that meets the state estimation accuracy requirements as the final configuration solution:

[0100] The method for state estimation analysis of the FTU configuration scheme is as follows: for a distribution network with n nodes, when the topology structure and branch parameters are known, the state estimation calculation is performed based on all the measured data. The measurement equation for state estimation is:

[0101] z=h(x)+e(8)

[0102] Wherein: z is an m-dimensional measurement vector, x is a (2n-1)-dimensional state vector, and the present invention selects node voltage amplitude and phase angle (except for balanced nodes) as state quantities; h(x) is an m×(2n-1)-dimensional measurement function matrix, which reflects the nonlinear relationship between the measurement and the state quantity; e is an m-dimensional measurement error vector, which is assumed to obey the normal distribution;

[0103] State estimation improves the real state of the system through redundant measurement data. Therefore, the state estimation calculation needs to satisfy the dimension of the measurement vector is greater than the dimension of the state vector, that is,

[0104] dim(z)>dim(x)(9)

[0105] Where: dim(z) is the dimension of the measurement vector, dim(x) is the dimension of the state vector;

[0106] In actual systems, it is impossible to configure FTU on each line. Only based on FTU measurement data, it cannot guarantee that equation (9) is valid. Therefore, pseudo measurement needs to be introduced to improve measurement redundancy. Pseudo measurement is generally achieved through load forecasting. Compared with FTU measurement, the accuracy is lower. The injected power of each node can be obtained. The corresponding measurement equation is:

[0107]

[0108] Where i represents the node number, i = 1, 2, ..., n; and are the active and reactive measurements injected into node i, ×P i and ×Q i is the corresponding measurement error; U i and θ i are state variables, representing the voltage amplitude and phase angle of node i respectively. Let θ ij =θ i -θ j represents the phase angle difference between node i and node j, G ij and B ij are the real and imaginary parts of the elements in the i-th row and j-th column of the system admittance matrix respectively;

[0109] Compared with pseudo measurement, FTU measurement has higher data accuracy and can measure the branch power, branch current amplitude and voltage amplitude of the node connected to FTU. The measurement equation corresponding to FTU measurement is:

[0110]

[0111] In the formula, and are the measured values ​​of active power and reactive power flowing into the branch ij from the node i side, ΔP ij and ΔQ ij is the corresponding measurement error; g ij and b ij are the conductance and susceptance on branch ij respectively; and ΔI ij are the measured value of the current amplitude flowing into the branch ij from the node i side and the corresponding measurement error respectively; and ΔU i are the voltage amplitude measurement value and the corresponding measurement error of node i respectively;

[0112] The state estimation is solved by weighted least squares (WLS), the goal of which is to minimize the weighted sum of squares of measurement errors in all measurement equations, that is,

[0113] minJ(x)=[zh(x)] T W[zh(x)](12)

[0114] Where J(x) represents the weighted sum of squares of measurement errors, W is the m×m-dimensional measurement weight matrix, which is a diagonal matrix, specifically:

[0115] W=diag[w1,w2,w3,...,w m ](13)

[0116] Among them, w i (i=1,2,…,m) represents the weight of the i-th measurement, which is usually expressed as the inverse of the measurement variance;

[0117] Since the measurement function h(x) in equation (12) is nonlinear, it is difficult to directly find the minimum value of J(x). We can use the Newton iteration method to iteratively correct the solution according to equation (14):

[0118]

[0119] In the formula, x (k) is the state vector of the kth iteration, Δx (k) is the state vector of the kth iteration, H(x) is the Jacobian matrix of the measurement function h(x);

[0120] When Δx (k) When the iteration reaches the value of formula (15), the iteration is considered to have converged and the iteration is stopped; where ε is the given iteration allowable error, which is taken as 10 in the present invention. -4 ;

[0121] max|Δx (k) |≤ε (15)

[0122] The state vector x obtained after the iteration is completed is the state estimation value, which contains the voltage amplitude estimation value U of all nodes. i and the phase angle estimate θ i (Except the balance node), the deviation between the estimated value and the true value is calculated according to formula (16) to evaluate the accuracy of state estimation

[0123]

[0124] In the formula, and are the voltage amplitude true value and phase angle true value respectively, and Represent the absolute errors of voltage amplitude and phase angle estimation respectively. If and satisfy

[0125]

[0126] Then the FTU configuration meets the system state estimation accuracy requirement, otherwise it is necessary to increase the number of FTU configurations to improve the state estimation accuracy; U and σ θ are the maximum estimation errors of voltage amplitude and phase angle allowed by the system respectively.

[0127] In order to verify the effectiveness and effect of the method of the present invention, the above scheme is applied as an example in this embodiment, as follows:

[0128] Reference Figure 1 Node 1 is the power node. It can be seen that after configuring one FTU on line 3-4, the distribution network is divided into two sections. Similarly, when N f FTU, the distribution network can be divided into N f +1 segment. The virtual source point G is connected to nodes 2 and 4 through virtual branches. The direction of the virtual flow is shown by the arrows in the figure, which is from the node with a smaller number to the node with a larger number.

[0129] Reference Figure 2 , this embodiment is simulated and tested in the IEEE-33 node correction system. For the convenience of analysis, it is assumed in the example that the line failure probability is proportional to the line length, the length of each line in the system is equal, and the corresponding failure probability of each line is 0.01. SCADA measurement is configured on the default line 1-2 and is not included in the total number of FTU configurations. Table 1 shows the active load per unit value of all nodes in the system, and the power reference value is 1MVA, which is used to calculate the power outage loss caused by the fault.

[0130] Table 1 IEEE-33 node load information

[0131]

[0132] Set the number of FTUs to be configured N f Initially it is 1, and then the optimization model is solved one by one, and the relationship between the objective function value EDNS and the number of FTU configurations is shown in Table 2. It can be seen that with the increase in the number of configured FTUs, the number of divided sections increases, the total load in the section and the total length of the line decrease, thereby reducing the fault outage loss in each section, so the system EDNS value is constantly decreasing.

[0133] Table 2 Relationship between EDNS and FTU configuration quantity

[0134]

[0135] Take σ U =0.01pu,σ θ =0.5°, perform state estimation simulation on the FTU configuration scheme under each number, select the minimum number of FTUs that meet the state estimation accuracy requirements, and confirm that the optimal FTU configuration result under this number is the final configuration scheme. The true value of the simulation system is obtained by power flow calculation, and the measurement data is generated by superimposing the normal distribution random error on the true value of the power flow. The measurement is divided into FTU measurement and pseudo-measurement, among which the maximum error of the voltage amplitude measurement measured by FTU is 1%, the maximum error of the branch current amplitude measurement is 2%, and the maximum error of the power measurement is 3%; the pseudo-measurement is the load power value of each node obtained according to the load forecast. Since the load forecast has large uncertainty, the maximum error of the pseudo-measurement is set to 40%. Since the measurement error is random, the state estimation result is also random, so the simulation is repeated 1000 times, and then the average value of the node voltage amplitude and phase angle estimation value in all simulations is taken as the final state estimation result. The relationship between the maximum voltage amplitude and phase angle estimation error and the number of FTU configurations is obtained as follows Figure 3 As shown in the figure, it can be seen that when the number of configured FTUs is at least 7, the maximum voltage amplitude and phase angle estimation errors are 9.35e-3pu and 0.42° respectively, which meet the given accuracy requirements. Therefore, it is confirmed that the final number of FTUs configured is 7. The specific configuration results are as follows: Figure 4 As shown in the figure, the product of the power outage loss due to section fault and the fault probability has been marked near each section, and their sum is equal to the EDNS value of the system, which is 0.13855.

Claims

1. A distribution network FTU optimization configuration method considering reliability and state estimation, characterized in that: The steps include: S1: Obtain distribution network information, divide the sections according to the FTU locations, and construct a distribution network topology map based on a directed graph; S2: Analyze the power outage loss and failure probability of the section; S3: Given FTU configuration quantity N f , with the goal of minimizing EDNS, a mathematical model is constructed based on the directed graph method according to the power outage loss and failure probability, and the FTU configuration scheme with the highest reliability is solved; S4: Perform state estimation analysis on the FTU configuration scheme. If it does not meet the accuracy requirements given by the system, increase the number of FTU configurations N. f , the minimum number of FTUs that meets the state estimation accuracy requirements is selected as the final configuration solution.

2. A distribution network FTU optimization configuration method considering reliability and state estimation according to claim 1, characterized in that: The method for constructing the distribution network topology map based on the directed graph in step S1 is: Configure N in the feeder f FTU, the distribution network is divided into N f +1 segment; A virtual source point G is constructed in the graph, and the virtual source point is connected to one of the nodes in each segment. The line connecting the virtual source point and the node is called a virtual branch, and the node connected to the virtual source point is called a segment source point, ensuring that there is only one virtual branch between each segment and the virtual source point.

3. A distribution network FTU optimization configuration method considering reliability and state estimation according to claim 2, characterized in that: The current transmitted on the virtual branch in step S1 is a virtual flow. The virtual flow is transmitted on the line with a certain flow direction. It is stipulated that the virtual flow is injected from the node with the smallest number in the segment to ensure that the virtual flow on the power supply line flows from the node with a small number to the node with a large number. Each node consumes a part of the virtual flow, which is called virtual load. The size of the virtual flow transmitted by the virtual source point G to a certain segment is equal to the sum of the virtual loads in the segment.

4. A distribution network FTU optimization configuration method considering reliability and state estimation according to claim 1, characterized in that: The step S2 is specifically as follows: After analysis, it is found that the power outage loss of a section is the sum of the loads in the fault section; After analysis, the failure probability of the line is: L i =f·l i (1) Among them, L i is the failure probability of the line with node i as the end node, l i is the length of the line with node i as the end node, and f is the probability of failure per unit length of the line; accordingly, the failure rate of a section is the sum of the failure rates of all lines in the section.

5. A distribution network FTU optimization configuration method considering reliability and state estimation according to claim 4, characterized in that: The specific process of constructing the mathematical model based on the directed graph method in step S3 is: Taking minimizing EDNS as the goal, the objective function of FTU optimization configuration is obtained as follows: Where n is the number of nodes; i is the node number, node 1 is the power node and does not participate in the optimization; d i and r i are all non-negative continuous variables, where d i represents the power outage loss caused by the fault in the section where node i is located; r i represents the failure probability of the segment where node i is located; Use 0-1 variable m ij Indicates whether FTU is configured on line ij. A value of 1 indicates that FTU is configured on the line. The number of configured FTUs should be equal to the given number N. f ,Right now ∑m ij =N f (3) For the radial structure distribution network, configure N f FTU, the distribution network is divided into N f +1 segment, there is only one virtual branch between each segment and the virtual source point, so the number of virtual branches should be equal to the number of segments, that is, Among them, b i is a 0-1 variable, and taking 1 means that node i is connected to the virtual source point through a virtual branch; Define the active virtual flow and failure rate virtual flow of the virtual flow transmitted on line ij as F ij and R ij , are non-negative continuous variables; for any node in the system, the power balance constraint of the virtual flow needs to be satisfied, that is, Where i = 2, 3, ..., n, k is the node number connected to node i and smaller than i, S i is the set of node numbers connected to i and greater than i; P i is the active load of node i, L i is the failure probability of the line with node i as the end node; the positive and negative signs in the formula constrain the virtual flow direction from the node with a smaller number in the section to the node with a larger number; There is an upper limit constraint on the virtual flow transmitted on line ij, F ij and R ij The maximum active load will not exceed the total active load P of the system. M and the sum of all line failure probabilities L M In addition, when FTU is configured on line ij, line ij is disconnected from the network topology and does not transmit virtual flows. The inequality constraints considering the above problems are: The virtual flows on the line are all transmitted from the virtual source point through the virtual branch, so d i and r i There is also an upper limit constraint, and it only has a value when node i is the source point of the segment, otherwise it is 0. Considering the above problems, the inequality constraint is Formulas (2) to (7) constitute the FTU optimization configuration model with the highest reliability represented by the minimum system EDNS value. This model is a quadratic mixed integer programming model.

6. A distribution network FTU optimization configuration method considering reliability and state estimation according to claim 5, characterized in that: In step S3, the constructed mathematical model is solved by Gurobi solver.

7. A distribution network FTU optimization configuration method considering reliability and state estimation according to claim 5, characterized in that: The method for performing state estimation analysis on the FTU configuration scheme in step S4 is: for a distribution network with n nodes, when the topology structure and branch parameters are known, a state estimation calculation is performed based on all measurement data, and the measurement equation for state estimation is: z=h(x)+e(8) Where: z is the m-dimensional measurement vector, x is the (2n-1)-dimensional state vector, and the node voltage amplitude and phase angle are selected as state quantities; h(x) is the m×(2n-1)-dimensional measurement function matrix, which reflects the nonlinear relationship between the measurement and the state quantity; e is the m-dimensional measurement error vector, which is assumed to obey the normal distribution; State estimation improves the real state of the system through redundant measurement data. Therefore, the state estimation calculation needs to satisfy the dimension of the measurement vector is greater than the dimension of the state vector, that is, dim(z)>dim(x)(9) Where: dim(z) is the dimension of the measurement vector, dim(x) is the dimension of the state vector; Pseudo-measurement is introduced to improve measurement redundancy. The corresponding measurement equation is: Where i represents the node number, i = 1, 2, ..., n; and are the active and reactive measurements injected into node i, ΔP i and ΔQ i is the corresponding measurement error; U i and θ i are state variables, representing the voltage amplitude and phase angle of node i respectively. Let θ ij =θ i -θ j represents the phase angle difference between node i and node j, G ij and B ij are the real and imaginary parts of the elements in the i-th row and j-th column of the system admittance matrix respectively; The measurement equation corresponding to FTU measurement is: In the formula, and are the measured values ​​of active power and reactive power flowing into the branch ij from the node i side, ΔP ij and ΔQ ij is the corresponding measurement error; g ij and b ij are the conductance and susceptance on branch ij respectively; and ΔI ij are the measured value of the current amplitude flowing into the branch ij from the node i side and the corresponding measurement error respectively; and ΔU i are the voltage amplitude measurement value and the corresponding measurement error of node i respectively; The goal of state estimation is to minimize the weighted sum of squares of measurement errors in all measurement equations, that is, minJ(x)=[zh(x)] T W[zh(x)](12) Where J(x) represents the weighted sum of squares of the measurement error, W is the m×m-dimensional measurement weight matrix, which is a diagonal matrix, specifically W=diag[w1,w2,w3,...,w m ](13) Among them, w i (i=1,2,…,m) represents the weight of the i-th measurement; Since the measurement function h(x) in equation (12) is nonlinear, the Newton iteration method is used to iterate and correct the solution according to equation (14): In the formula, x (k) is the state vector of the kth iteration, Δx (k) is the state vector of the kth iteration, H(x) is the Jacobian matrix of the measurement function h(x); When Δx (k) When the iteration reaches the value of equation (15), the iteration is considered to have converged and the iteration is stopped; where ε is the given iteration allowable error; max|Δx (k) |≤ε (15) The state vector x obtained after the iteration is completed is the state estimation value, which contains the voltage amplitude estimation value U of all nodes. i and the phase angle estimate θ i , the deviation between the estimated value and the true value is calculated to evaluate the accuracy of state estimation.

8. A distribution network FTU optimization configuration method considering reliability and state estimation according to claim 7, characterized in that: In step S4, the deviation between the estimated value and the true value is calculated according to formula (16) to evaluate the state estimation accuracy. In the formula, and are the voltage amplitude true value and phase angle true value respectively, and Represent the absolute error of voltage amplitude and phase angle estimation respectively. If and satisfy Then the FTU configuration meets the system state estimation accuracy requirement, otherwise the number of FTU configurations needs to be increased; σ U and σ θ are the maximum estimation errors of voltage amplitude and phase angle allowed by the system respectively.

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