A distribution network optimization method considering the uncertainty of photovoltaic and line switch states

Abstract

The present invention relates to distribution network optimization technology, and specifically to a distribution network optimization method considering the uncertainty of photovoltaic and line switch states. First, the uncertainty of photovoltaic output is considered, and a photovoltaic output model for multiple periods is established; then the uncertainty of line switch states in the distribution network is analyzed, and based on Shannon's information theory, a line switch state uncertainty model under multiple scenarios is established; after the distribution network is reconfigured, the Latin hypercube sampling method is used to determine the line switch state when the uncertainty budget is different; finally, considering the uncertainty of photovoltaic output and line switch state in the worst case, a control model is proposed to improve the stability of the distribution network with the minimum maintenance cost. The method qualitatively abstracts the characteristics of photovoltaic output uncertainty and line switch state, and provides practical technical support for the distribution network through scheduling strategies. The impact caused by the uncertainty of photovoltaic output and line switch state is reduced.

Description

Technical Field

[0001] The present invention belongs to the technical field of power distribution network optimization, and in particular relates to a power distribution network optimization method taking into account the uncertainty of photovoltaic and line switch states. Background Art

[0002] With the advancement of smart grid construction, the application of various information and intelligent technologies in smart grids has gradually deepened, and smart grids have gradually developed into information-physical coupling systems. As an important part of smart grids, the distribution network provides key basic support for ensuring power supply quality, optimizing user services, and improving the level of social electrification. Its intelligent research has also made great progress. However, due to the increasing access to distributed energy and intelligent sensors and communication equipment, the distribution network faces huge challenges. In particular, the photovoltaic access distribution network with random power generation power, the stronger the randomness of photovoltaic power generation power, the more frequent the power exchange, and the distribution network relies more on line switches for network flow control. Once the state of the line switch cannot be determined, there will be problems such as reduced power supply reliability and deterioration of power quality. The unidirectional radial power supply mode will also change, which will cause a series of power safety accidents in serious cases.

[0003] The research on distribution network mainly focuses on control mode, distributed power planning, demand management on the power supply side and the user side, and the safety position of distribution network. The impact of random photovoltaic output and random line switch status on distribution network is not considered specifically. At present, the impact of random photovoltaic output is mainly analyzed from the safety risk assessment outside the distribution network, and the impact of uncertain line switch status is analyzed from the system reliability assessment inside the distribution network. Existing research methods have achieved good research results. Mathematical optimization and algorithm prediction are used to reduce the impact of photovoltaic output uncertainty. The specific form of line switch status uncertainty in the distribution network is characterized by modeling switch information disturbances and faults in the information network. The impact caused by different scenarios and different factors is analyzed on the basis of distribution network reconstruction. However, this kind of research idea cannot accurately analyze the characteristics of the distribution network when the random photovoltaic output and the uncertainty of line switch status act together, and cannot provide a reference for dispatchers. Summary of the invention

[0004] In view of the problems existing in the background technology, the present invention provides a distribution network optimization method taking into account the uncertainty of photovoltaic and line switch states.

[0005] In order to solve the above technical problems, the present invention adopts the following technical solution: a distribution network optimization method considering the uncertainty of photovoltaic and line switch states, comprising the following steps:

[0006] Step 1: Establish a photovoltaic output uncertainty model. Based on the actual photovoltaic output curve, determine the best fitting curve through mathematical fitting, and characterize the randomness of photovoltaic output through photovoltaic output errors that obey different distributions;

[0007] Step 2: Establish a line switch state uncertainty model, and establish a mathematical relationship of line switch state uncertainty in different scenarios through the correspondence between the actual cyber-physical system and the node system;

[0008] Step 3: Establish a multi-objective two-level planning model; consider the uncertainty of photovoltaic power and determine the set of photovoltaic power by fitting; consider the uncertainty of line switch status in various situations and use entropy to screen the scenarios; take the maximum output cost and the maximum line failure cost as the worst case and minimize the maintenance cost by simulating the commands from the dispatch center;

[0009] Step 4: Solve the model in combination with the LHS method; expand the model to a minimize-maximize-maximize three-level programming model for solution, and use the LHS method to determine the state of the line when the uncertainty budget is different.

[0010] In the above distribution network optimization method considering the uncertainty of photovoltaic and line switch states, the implementation of step 1 includes:

[0011] Step 1.1: According to the principle of photovoltaic power generation, the relationship between photovoltaic output and light intensity is obtained:

[0012]

[0013] Represents photovoltaic output, P i pv represents the rated photovoltaic output, L represents the light intensity, L i Represents the rated light intensity, L max Represents the maximum light intensity;

[0014] Step 1.2: Obtain the relationship between photovoltaic output and time by mathematical fitting:

[0015] P pv =at 2 +bt+c (2)

[0016] P pv Represents the fitted photovoltaic output. When the light intensity is determined, it is calculated by formula (1) With P pv The same, a, b, c represent fitting coefficients respectively, and t represents time. The fitting coefficients are determined by formula (2) to establish the relationship between light intensity and time;

[0017] Step 1.3: Establish the photovoltaic output error misoperation model:

[0018]

[0019]

[0020]

[0021] Represents the maximum value of the photovoltaic error output fluctuation at time t+1, P t pv,f represents the photovoltaic fitting output obtained at time t+1 and time t according to formula (2), Represents the photovoltaic error output at time t+1, represents the actual photovoltaic output error at time t+1, f y represents the distribution function. When y=1, it represents Gaussian distribution; when y=2, it represents Laplace distribution; when y=3, it represents Cauchy distribution;

[0022] The relationship between photovoltaic output error and photovoltaic fitting output is established, and photovoltaic error outputs with different distributions are used to express the randomness of photovoltaic output;

[0023]

[0024] Represents the photovoltaic output at time t proposed by the present invention.

[0025] In the above distribution network optimization method considering the uncertainty of photovoltaic and line switch states, the implementation of step 2 includes:

[0026] Step 2.1, establish a simplified model of the actual cyber-physical system node system;

[0027] The distribution network is regarded as a node system, including nodes, generators and line switches. The status information of the line switches is controlled by information channels and physical channels, and the transmission lines are controlled through the operation of the line switches.

[0028] The distribution network is regarded as a cyber-physical system (CPS), which includes a physical system and a network system. The physical system includes circuit breakers, disconnectors, interconnection switches, transmission lines, loads, generators and energy storage devices to realize the collection and transmission of power data. The network system includes application platforms, control platforms, software and communication systems. The communication system includes optical fiber, microwave, Ethernet, routing and carrier.

[0029] The node system and the cyber-physical system CPS establish connections through information channels and physical channels: the interconnected switches and transmission lines in the cyber-physical system CPS constitute the main body of the physical channels in the node system, and the software and communication system in the cyber-physical system CPS constitute the main body of the information channels in the node system; the loads in the cyber-physical system CPS are simplified to nodes in the node system; the loads collect voltage and current information from power users; the software is used to transmit digital information; the generators in the cyber-physical system CPS are simplified to photovoltaic generators and system generators; the optical fiber and microwave, Ethernet and line communications in the cyber-physical system CPS simplify the network channels and physical channels in the node system, the hardware devices are used to collect and transmit data, and the communication devices are used to receive and execute commands; the circuit breakers, disconnectors, and interconnected switches in the cyber-physical system CPS are incorporated into the line switches in the node system, and the application platform and control platform in the cyber-physical system CPS are simplified to the dispatching center in the node system;

[0030] Step 2.2, establish a physical equipment failure model;

[0031]

[0032] p phy represents the probability of physical device failure, w e1 Represents the weight of abnormal operation of the transmission line, p eb represents the probability of abnormal operation of the circuit breaker, p ec represents the probability of abnormal operation of the interconnected switch, p es represents the probability of abnormal operation of the disconnector, w e2 Represents the weight of abnormal operation of physical components, p ea represents the probability that a physical component performs an abnormal operation, p er Represents the probability of a physical component failing to perform an operation;

[0033] Step 2.3, establish a communication transmission failure model;

[0034] p link =pl1*pl2*…*pl n (8)

[0035] p link represents the probability of communication transmission failure, p link =0 indicates that a communication transmission failure has occurred, p link =1 indicates that communication transmission failure has not occurred; p li Indicates the status of the information component, p li =0 means the information link is not connected, p li =1 indicates that the information link is connected; n indicates the number of information links;

[0036] Step 2.4, establish a scheduling control failure model;

[0037] p control =p bite p delay (9)

[0038] p control represents the probability of scheduling control failure, p bite Indicates that there is a misalignment in the information link, p delay represents the probability of delayed execution in the information link; under state information failure, p bite 、p delay 1 in all information chains;

[0039] The probability of uncertainty in the state of the line switch (p r )for:

[0040] p r =w p1 p phy +w p2 p link +w p3 p control (10)

[0041] w p1 、w p2 、w p3 Yes phy 、p link 、p control The standardized weights of different combinations of w p1 、w p2 、w p3 、p phy 、p link 、p control , p r Different, forming a variety of scenarios r distributed.

[0042] In the above distribution network optimization method considering the uncertainty of photovoltaic and line switch states, the implementation of step 3 includes:

[0043] Step 3.1, establish the objective function:

[0044] f=minC cons {maxC aloss} (11)

[0045]

[0046] C aloss =C pvp +C pfom (13)

[0047]

[0048]

[0049] C cons Represents all operation and maintenance costs, C aloss Represents all loss costs, represents the operation and maintenance cost of a single line at time t, η ij,t represents the operation and maintenance status of a single line at time t, η ij,t =1 means maintenance is required, η ij,t =0 means no maintenance is required, C pvp Represents the total photovoltaic output cost, C pfom represents the cost of all line failures, c pv,t represents the unit photovoltaic output cost at time t, represents photovoltaic output, c omij,t represents the unit line failure cost at time t, represents the actual line status at time t, Indicates that the actual line status is closed. represents the actual line status is disconnected, i represents the node index, ij represents the branch index, t represents the time index, Ω l represents the branch set, Ω dg represents a collection of generators;

[0050] Step 3.2: The linearized DistFlow equation is used to describe the complex power flow of the branch, and the node power flow constraint is:

[0051]

[0052]

[0053]

[0054]

[0055] represents the active power from node i to node j at time t in scenario s, represents the active power demand of node j at time t in scenario s, represents the active load shedding of node j at time t in scenario s, represents the active power of the generator injected into node j at time t in scenario s, represents the active power of the photovoltaic generator injected into node j at time t in scenario s, represents the reactive power from node i to node j at time t in scenario s, represents the reactive power demand of node j at time t in scenario s, represents the reactive load shedding of node j at time t in scenario s, represents the reactive power of the generator injected into node j at time t in scenario s, r ij,t represents the resistance of branch ij at time t, x ij,t represents the reactance of branch ij at time t, represents the voltage amplitude of node i at time t, M1 represents the coefficient of the large M number method, i and j represent node indexes, ij represents branch index, t represents time index, and s represents scene index;

[0056] Step 3.3: The uncertainty constraint of photovoltaic output is:

[0057]

[0058]

[0059]

[0060] represents the active power of the photovoltaic generator injected into node j at time t in scenario s, represents the fitted PV generator active power injected into node j at time t in scenario s, represents the active error power of the photovoltaic generator injected by node j at time t in scenario s, represents the fitted photovoltaic generator active power 1 injected into node j at time t in scenario s, represents the active error power 1 of the photovoltaic generator injected by node j at time t in scenario s, where j represents the node index, t represents the time index, and s represents the scenario index;

[0061] Equations (20) to (22) represent the relationship between photovoltaic output and time. Equation (21) assumes that the output of the jth photovoltaic generator at time t is Through fitting, it is obtained that Equation (22) assumes that the photovoltaic output error of the jth photovoltaic generator is Obtained through the distribution function;

[0062] Step 3.4: The uncertainty constraint of the line switch state is:

[0063]

[0064]

[0065] represents the state of branch ij at time t in scenario s, Indicates that the line is closed due to the uncertain state of the line switch. Indicates that the line is disconnected due to the uncertain status of the line switch. represents the probability of uncertainty of line switching on branch ij at time t in scenario s, represents the probability of uncertainty in line switching on branch ij at time t in scenario s1, W represents the uncertainty budget, ij represents the branch index, t represents the time index, and s represents the scenario index;

[0066] Formula (23) and Formula (24) represent the relationship between the uncertainty budget set by the dispatch center and the probability of uncertainty in the state of the line switch; Formula (23) is based on Shannon's information theory, and W is the uncertainty budget determined by the dispatch center; Formula (24) provides a set of state uncertainties, representing the probability of uncertainty in the state of the line switch under multiple scenarios;

[0067] Step 3.5, line state constraint;

[0068]

[0069]

[0070]

[0071]

[0072]

[0073]

[0074]

[0075]

[0076] It represents the situation s that branch ij receives the command from the dispatch center at time t. The branch ij receives the instruction from the dispatch center to close. The branch ij receives the instruction from the dispatch center to disconnect. Represents the state of branch ij at time t in scenario s due to the uncertainty of the line switch state. The branch ij is closed due to the uncertainty of the line switch state. The branch ij is disconnected due to the uncertain state of the line switch. represents the actual line status of branch ij at time t in scenario s, The actual state of branch ij is closed. The actual state of branch ij is disconnected. represents the maintenance status of branch ij at time t in scenario s, Indicates that branch ij needs maintenance. This means that branch ij does not need maintenance. Represents the auxiliary variable at time t in scene s, ij represents the branch index, t represents the time index, and s represents the scene index;

[0077] Step,3.6 Voltage and power constraints;

[0078]

[0079]

[0080]

[0081]

[0082]

[0083]

[0084]

[0085] Represents the actual state of branch ij at time t in scenario s, The actual state of branch ij is closed. The actual state of branch ij is disconnected. Represents the maximum active power of branch ij, P ij,t represents the active power of branch ij at time t, Represents the maximum reactive power of branch ij, Q ij,t represents the reactive power of branch ij at time t, Represents the minimum active power of the generator, represents the active power injected by the generator at node j at time t in scenario s, Represents the maximum active power of the generator, Represents the minimum reactive power of the generator, represents the reactive power injected by the generator at node j at time t in scenario s, Represents the maximum reactive power of the generator, represents the minimum voltage amplitude of node j, represents the voltage amplitude of node j at time t in scenario s, represents the maximum voltage amplitude at node j, represents the active load shedding of node j at time t, represents the maximum active load shedding of node j at time t, represents the reactive load shedding of node j at time t, represents the maximum reactive load shedding of node j at time t, i represents the node index, ij represents the branch index, t represents the time index, and s represents the scene index;

[0086] Step 3.7, island constraint;

[0087]

[0088]

[0089]

[0090] Represents the line status including the virtual branch at time t in scenario s, represents the closure of branch ij, Indicates that branch ij is disconnected, n b Represents the number of nodes in the node system, represents the power flow including the virtual branch at time t in scenario s, Indicates that there is a load demand between this branch and the generator, photovoltaic, and fault line endpoints. Indicates that there is no load demand between the branch and the generator, photovoltaic, and fault line endpoints. M2 represents the coefficient of the large M number method. Ω l_vir represents the set of virtual branches, Ω l represents the branch set, ij represents the branch index, t represents the time index, and s represents the scene index;

[0091] Constraints (40)-(42) ensure the radial topology of the distribution network when the line switch state is uncertain; constraint (40) ensures that the number of branches and the number of nodes are consistent with the connectivity of the distribution network, constraint (41) assumes that the line including the fictitious branch has 1 unit load demand; constraint (42) limits the fictitious power flow of branch ij.

[0092] In the above distribution network optimization method considering the uncertainty of photovoltaic and line switch states, the implementation of step 4 includes: As the first layer of variable solution, the maximum photovoltaic output cost is obtained, and the variable of line failure cost is As the second layer variable solution, the maximum line failure cost is obtained, and the variable of line maintenance cost is As the variable solution of the third layer, the minimum line maintenance cost is obtained;

[0093] Step 4.1, set the lower limit and upper limit of time, solve the variables of the first layer, obtain the maximum photovoltaic output cost, update the lower limit and upper limit of time, and obtain the lower limit and upper limit of photovoltaic power;

[0094] Step 4.2 sets the uncertainty budget and the number of line switch states, solves for the variables in the second layer, obtains the maximum line fault cost using the LHS method, and updates the lower and upper limits of the PV power with the optimal values;

[0095] Step 4.3 solves the variables in the third layer based on the optimized PV power and line switch status to obtain the minimum line operation and maintenance cost.

[0096] Compared with the prior art, the present invention comprehensively considers the uncertainty of photovoltaic and line switch states, improves the ability of the distribution network to cope with the uncertainty of photovoltaic output and the uncertainty of line switch states, improves the reliability of the distribution network with the minimum line operation and maintenance cost, and reduces the cost of distribution network maintenance; in addition, the present invention expands the application prospects through the correlation analysis between the node system and the distribution network, and solves the proposed three-stage planning model through hypercube sampling. The sampling is more in line with the actual situation, the solution idea is clearer, and the calculation results are more reliable. The present invention qualitatively abstracts the characteristics of photovoltaic output uncertainty and line switch state, and provides practical technical support for the distribution network through scheduling strategies. BRIEF DESCRIPTION OF THE DRAWINGS

[0097] Figure 1 Schematic diagram of a minimization-maximization multi-objective bi-level programming model according to an embodiment of the present invention;

[0098] Figure 2 is a photovoltaic output curve diagram fitted according to actual photovoltaic output in an embodiment of the present invention;

[0099] Figure 3 is a schematic diagram of randomness of photovoltaic output according to an embodiment of the present invention;

[0100] Figure 4 It is a schematic diagram of the information physical system and node system of an embodiment of the present invention. DETAILED DESCRIPTION

[0101] The technical solutions in the embodiments of the present invention will be described clearly and completely below in combination with the embodiments of the present invention. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of the present invention.

[0102] It should be noted that, in the absence of conflict, the embodiments of the present invention and the features in the embodiments may be combined with each other.

[0103] The present invention will be further described below in conjunction with specific embodiments, but the present invention is not limited thereto.

[0104] This embodiment provides an uncertainty model of line switch state, and analyzes the uncertainty of line switch state in actual distribution network and node system. Based on Shannon information theory, the LHS method is used to maximize the line failure cost after the distribution network is reconfigured. Considering the situation where the uncertainty of photovoltaic output and line switch state work together, a control model is provided to improve the stability of the distribution network with minimum maintenance cost. Through the proposed minimization-maximization multi-objective bi-level programming model, the security of the distribution network is improved, and the goal is to reduce the impact caused by the uncertainty of photovoltaic output and line switch state. First, the uncertainty of photovoltaic output is considered, and a multi-period photovoltaic output model is established; then the uncertainty of line switch state in the distribution network is analyzed, and according to Shannon's information theory, a line switch state uncertainty model under multiple scenarios is established; after the distribution network is reconfigured, the Latin hypercube sampling method is used to determine the line switch state when the uncertainty budget is different; finally, considering the uncertainty of photovoltaic output and line switch state in the worst case, a control model is proposed to improve the stability of the distribution network with minimum maintenance cost. This method qualitatively abstracts the characteristics of photovoltaic output uncertainty and line switch state, and provides practical technical support for the distribution network through scheduling strategies.

[0105] This embodiment is implemented by the following technical solution, a distribution network optimization method considering the uncertainty of photovoltaic and line switch states, characterized in that it includes the following steps:

[0106] 1) Establish a photovoltaic output uncertainty model. Based on the actual photovoltaic output curve, determine the best fitting curve through mathematical fitting. Characterize the randomness of photovoltaic output through photovoltaic output errors that obey different distributions, and establish the relationship between light intensity and time.

[0107] 2) Establish a line switch state uncertainty model, and establish a mathematical relationship between the uncertainty of line switch states in different scenarios through the correspondence between the actual cyber-physical system and the node system. That is, establish a simplified model of the actual cyber-physical system and the node system, including establishing a physical equipment failure model; establishing a communication transmission failure model; and establishing a scheduling control failure model.

[0108] 3) Establish a multi-objective two-level programming model. The goal of this invention is to minimize the maintenance cost in the worst case. First, the uncertainty of photovoltaic power is considered, and the set of photovoltaic power is determined by fitting; then, the uncertainty of line switch status in various situations is considered, and the scenarios are screened by entropy; finally, we take the maximum output cost and the maximum line failure cost as the worst case, and minimize the maintenance cost by simulating commands from the dispatch center. Including proposing photovoltaic output uncertainty constraints; proposing line switch status uncertainty constraints; proposing line status constraints; proposing island constraints.

[0109] 4) Solve the model by combining the LHS method. The present invention expands the model into a minimization-maximization-maximization three-level programming model for solving, and uses the LHS method to determine the state of the line when the uncertainty budget is different. The specific operation method is as follows:

[0110] Set the lower and upper limits of time, solve the first layer, obtain the maximum photovoltaic output cost, update the lower and upper limits of time, and obtain the lower and upper limits of photovoltaic power.

[0111] The uncertainty budget and the number of line switch states are set, the second layer is solved, the maximum line fault cost is obtained using the LHS method, and the lower and upper bounds of the PV power are updated with the optimal values.

[0112] Based on the optimized PV power and line switch status, the third layer is solved to obtain the minimum line operation and maintenance cost.

[0113] In specific implementation, a distribution network optimization method considering the uncertainty of photovoltaic and line switch states is proposed, such as Figure 1 As shown, the following steps are included:

[0114] S1, establish a photovoltaic output uncertainty model, based on the actual photovoltaic output curve, determine the best fitting curve through mathematical fitting, and characterize the randomness of photovoltaic output through photovoltaic output errors that obey different distributions. The specific method of establishing the photovoltaic output uncertainty model is as follows:

[0115] S1.1 According to the principle of photovoltaic power generation, the relationship between photovoltaic output and light intensity is obtained:

[0116]

[0117] Represents photovoltaic output, P i pv represents the rated photovoltaic output, L represents the light intensity, L i Represents the rated light intensity, L max Represents the maximum light intensity.

[0118] S1.2 The relationship between photovoltaic output and time is obtained by mathematical fitting:

[0119] P pv =at 2 +bt+c (2)

[0120] P pv Represents the fitted photovoltaic output. When the light intensity is determined, it is calculated by formula (1) With P pv The same, a, b, c represent the fitting coefficients, and t represents time.

[0121] like Figure 2 As shown, this embodiment determines the fitting coefficient through formula (2) to indirectly establish the relationship between light intensity and time.

[0122] S1.3 Establish photovoltaic output error misoperation model:

[0123]

[0124]

[0125]

[0126] Represents the maximum value of the photovoltaic error output fluctuation at time t+1, P t pv,f represents the photovoltaic fitting output obtained at time t+1 and time t according to formula (2), Represents the photovoltaic error output at time t+1, represents the actual photovoltaic output error at time t+1, f y Represents the distribution function. When y=1, it represents Gaussian distribution. When y=2, it represents Laplace distribution. When y=3, it represents Cauchy distribution.

[0127] like Figure 3 As shown, this embodiment establishes the relationship between the photovoltaic output error and the photovoltaic fitting output, and uses photovoltaic error outputs with different distributions to represent the randomness of the photovoltaic output.

[0128]

[0129] Represents the photovoltaic output at time t proposed in this embodiment.

[0130] S2, establish the uncertainty model of the line switch state, and establish the mathematical relationship of the uncertainty of the line switch state in different scenarios through the correspondence between the actual information physical system and the node system. The specific method of establishing the line switch uncertainty model is as follows:

[0131] S2.1 Establish a simplified model of the actual cyber-physical system node system.

[0132] like Figure 4 As shown in Figure 1, the distribution network can be abstracted as a node system consisting of nodes, generators and line switches. The line switch mainly plays a connecting role, and its status information is mainly controlled by information channels and physical channels. Through the operation of the line switch, the transmission line can be controlled.

[0133] The actual distribution network can be regarded as a cyber-physical system (CPS), which is formed by the combination of physical systems and network systems. The physical system includes circuit breakers, disconnectors, interconnection switches, transmission lines, loads, generators and energy storage devices to realize the collection and transmission of power data. The information system includes application platforms, control platforms, software, and communication systems (optical fiber, microwave, routing, carrier, etc.).

[0134] The relationship between the node system and CPS is established through information channels and physical channels: the switches and transmission lines in the CPS constitute the main body of the physical channels in the node system, and the software and communication systems in the CPS constitute the main body of the information channels in the node system. The load in the CPS can be simplified to the node in the node system; the sensors in the load collect voltage and current information from the power users; the software in the load is used to transmit digital information. The generator in the CPS can be simplified to a photovoltaic generator and a system generator; the optical fiber and microwave, Ethernet and line communication in the CPS can simplify the main part of the network channel and physical channel in the node system, their hardware devices are used to collect and transmit data, and their communication devices are used to receive and execute commands. The circuit breakers, disconnectors, and interconnection switches in the CPS can be incorporated into the line switches in the node system, and the application platform and control platform in the CPS can be simplified to the dispatch center in the node system.

[0135] S2.2 Establish a physical equipment failure model. The actual distribution network contains a large number of physical devices. Once these devices fail, the commands from the dispatch center will not be executed; and the dispatch center cannot obtain the status information of the equipment.

[0136]

[0137] p phy represents the probability of physical device failure, w e1 Represents the weight of abnormal operation of the transmission line, p eb represents the probability of abnormal operation of the circuit breaker, p ec represents the probability of abnormal operation of the interconnected switch, p es represents the probability of abnormal operation of the disconnector, w e2 Represents the weight of abnormal operation of physical components, p ea represents the probability that a physical component performs an abnormal operation, p er Represents the probability of a physical component failing to perform an operation.

[0138] S2.3 Establish a communication transmission failure model. In actual distribution networks, various communication technologies and protocols are inseparable from information links, and their connectivity is directly related to the reliability of information transmission. Once the connectivity of the information link is destroyed, the dispatch center cannot obtain the status information of the physical device, the physical device cannot receive the instructions issued by the dispatch center, or the status information of the physical device cannot be transmitted.

[0139] p link =pl1*pl2*…*pl n (8)

[0140] p link represents the probability of communication transmission failure, p link =0 indicates that a communication transmission failure has occurred, p link =1 indicates that communication transmission failure has not occurred; p li Indicates the status of the information component, p li =0 means the information link is not connected, p li =1 indicates that the information link is connected; n indicates the number of information links.

[0141] S2.4 Establish a dispatch control failure model. In the information link, the command of the schedule center may be delayed during the transmission process, resulting in inconsistency in command execution. This is a form of uncertainty in the state of the line switch.

[0142] p control =p bite p delay (9)

[0143] p control represents the probability of scheduling control failure, p bite Indicates that there is a misalignment in the information link, p delay represents the probability of delayed execution in the information link. In this embodiment, the software failure is considered to be a state information failure. In this case, p bite 、p delay It is 1 in all message chains.

[0144] Then the probability of uncertainty of the line switch state (p r )for:

[0145] p r =w p1 p phy +w p2 p link +w p3 p control (10)

[0146] w p1 、w p2 、w p3Yes phy ,pli n k, p control The standardized weights of different combinations of w p1 、w p2 、w p3 、p phy ,pli n k, p control , p r Different, forming a variety of scenarios r distributed.

[0147] S3, establish a multi-objective two-level programming model. The goal of this embodiment is to minimize the maintenance cost in the worst case. First, consider the uncertainty of photovoltaic power and determine the set of photovoltaic power by fitting; then, consider the uncertainty of line switch status in multiple situations and use entropy to screen the scenarios; finally, we take the maximum output cost and the maximum line failure cost as the worst case, and minimize the maintenance cost by simulating the commands from the dispatch center.

[0148] S3.1 Objective function.

[0149] f=minC cons {maxC aloss} (11)

[0150]

[0151] C aloss =C pvp +C pfom (13)

[0152]

[0153]

[0154] C cons Represents all operation and maintenance costs, C aloss Represents all loss costs, represents the operation and maintenance cost of a single line at time t, η ij,t represents the operation and maintenance status of a single line at time t, η ij,t =1 means maintenance is required, η ij,t =0 means no maintenance is required, C pvp Represents the total photovoltaic output cost, C pfom represents the cost of all line failures, c pv,t represents the unit photovoltaic output cost at time t, represents photovoltaic output, c omij,t represents the unit line failure cost at time t, represents the actual line status at time t, Indicates that the actual line status is closed. represents the actual line status is disconnected, i represents the node index, ij represents the branch index, t represents the time index, Ω l represents the branch set, Ω dg Represents a collection of generators.

[0155] In particular, this embodiment proposes that the objective function is to minimize the line maintenance cost under the worst case scenario.

[0156] S3.2 Node flow constraints.

[0157]

[0158]

[0159]

[0160]

[0161] represents the active power from node i to node j at time t in scenario s, represents the active power demand of node j at time t in scenario s, represents the active load shedding of node j at time t in scenario s, represents the active power of the generator injected into node j at time t in scenario s, represents the active power of the photovoltaic generator injected into node j at time t in scenario s, represents the reactive power from node i to node j at time t in scenario s, represents the reactive power demand of node j at time t in scenario s, represents the reactive load shedding of node j at time t in scenario s, represents the reactive power of the generator injected into node j at time t in scenario s, r ij,t represents the resistance of branch ij at time t, x ij,t represents the reactance of branch ij at time t, represents the voltage amplitude of node i at time t, M1 represents the coefficient of the big M number method, i and j represent node indexes, ij represents branch index, t represents time index, and s represents scene index.

[0162] In particular, this embodiment proposes to use a linearized DistFlow equation to describe the complex power flow of the branch.

[0163] S3.3 Uncertain constraints on photovoltaic output.

[0164]

[0165]

[0166]

[0167] represents the active power of the photovoltaic generator injected into node j at time t in scenario s, represents the fitted PV generator active power injected into node j at time t in scenario s, represents the active error power of the photovoltaic generator injected by node j at time t in scenario s, e.g. represents the fitted photovoltaic generator active power 1 injected into node j at time t in scenario s, represents the active error power 1 of the photovoltaic generator injected by node j at time t in scenario s, where j represents the node index, t represents the time index, and s represents the scenario index.

[0168] Formulas (20)-(22) represent the relationship between PV output and time. Equation (21) assumes that the output of the jth PV generator at time t is It can be obtained by fitting, Equation (22) assumes that the photovoltaic output error of the jth photovoltaic generator is It can be obtained through the distribution function.

[0169] S3.4 Line switch state uncertainty constraint.

[0170]

[0171]

[0172] represents the state of branch ij at time t in scenario s, Indicates that the line is closed due to the uncertain state of the line switch. Indicates that the line is disconnected due to the uncertain status of the line switch. represents the probability of uncertainty of line switching on branch ij at time t in scenario s, for example represents the probability of uncertainty of line switch on branch ij at time t in scenario s1, W represents the uncertainty budget, ij represents the branch index, t represents the time index, and s represents the scenario index.

[0173] Constraints (23) and (24) represent the relationship between the uncertainty budget set by the dispatch center and the probability of line switch state uncertainty. Constraint (23) is based on Shannon's information theory, where W is the uncertainty budget that can be determined by the dispatch center. Constraint (24) provides a set of state uncertainties, representing the probability of line switch state uncertainty under multiple scenarios.

[0174] In particular, this embodiment proposes that a line state with a higher uncertainty probability occupies less uncertainty budget when a fault occurs.

[0175] S3.5 Line state constraints.

[0176]

[0177]

[0178]

[0179]

[0180]

[0181]

[0182]

[0183]

[0184] It represents the situation s that branch ij receives the command from the dispatch center at time t. The branch ij receives the instruction from the dispatch center to close. The branch ij receives the instruction from the dispatch center to disconnect. Represents the state of branch ij at time t in scenario s due to the uncertainty of the line switch state. The branch ij is closed due to the uncertainty of the line switch state. The branch ij is disconnected due to the uncertain state of the line switch. represents the actual line status of branch ij at time t in scenario s, The actual state of branch ij is closed. The actual state of branch ij is disconnected. represents the maintenance status of branch ij at time t in scenario s, Indicates that branch ij needs maintenance. This means that branch ij does not need maintenance. Represents the auxiliary variable at time t in scene s, ij represents the branch index, t represents the time index, and s represents the scene index.

[0185] In particular, this embodiment proposes to establish the relationship between line maintenance cost, line failure cost, and photovoltaic output cost through constraints (25)-(32).

[0186] S3.6 Voltage and power constraints.

[0187]

[0188]

[0189]

[0190]

[0191]

[0192]

[0193]

[0194] Represents the actual state of branch ij at time t in scenario s, The actual state of branch ij is closed. The actual state of branch ij is disconnected. Represents the maximum active power of branch ij, P ij,t represents the active power of branch ij at time t, Represents the maximum reactive power of branch ij, Q ij,t represents the reactive power of branch ij at time t, Represents the minimum active power of the generator, represents the active power injected by the generator at node j at time t in scenario s, Represents the maximum active power of the generator, Represents the minimum reactive power of the generator, represents the reactive power injected by the generator at node j at time t in scenario s, Represents the maximum reactive power of the generator, represents the minimum voltage amplitude of node j, represents the voltage amplitude of node j at time t in scenario s, represents the maximum voltage amplitude at node j, represents the active load shedding of node j at time t, represents the maximum active load shedding of node j at time t, represents the reactive load shedding of node j at time t, represents the maximum reactive load shedding of node j at time t, i represents the node index, ij represents the branch index, t represents the time index, and s represents the scene index.

[0195] S3.7 Island constraints.

[0196]

[0197]

[0198]

[0199] Represents the line status including the virtual branch at time t in scenario s, represents the closure of branch ij, Indicates that branch ij is disconnected, n b Represents the number of nodes in the node system, represents the power flow including the virtual branch at time t in scenario s, Indicates that there is a load demand between this branch and the generator, photovoltaic, and fault line endpoints. Indicates that there is no load demand between the branch and the generator, photovoltaic, and fault line endpoints. M2 represents the coefficient of the large M number method. Ω l_vir represents the set of virtual branches, Ω l represents the branch set, ij represents the branch index, t represents the time index, and s represents the scene index.

[0200] Constraints (40)-(42) ensure the radial topology of the distribution network when the line switch status is uncertain. Constraint (40) ensures that the number of branches and the number of nodes are consistent with the connectivity of the distribution network. Constraint (41) assumes that the line including the fictitious branch has a unit load demand. Constraint (42) limits the fictitious power flow of branch ij.

[0201] In particular, this embodiment considers that the virtual branch is determined by the generator, photovoltaic generator, and disconnected branch. When we only consider the uncertainty of photovoltaic power, as the photovoltaic power decreases, the node load demand decreases and the load shedding increases, the load demand on the branch may be completely eliminated, and the reconfiguration of the distribution network is also considered. When we consider the case where photovoltaic output and line switches are regarded as uncertain, constraints (40)-(42) can ensure that the radial topology remains unchanged during the reconfiguration of the distribution network, which is closer to the actual situation.

[0202] S4, combined with the LHS method to solve the model. The variable representing the cost of photovoltaic output, A variable representing the cost of line failure, The variable representing the line maintenance cost, this embodiment expands the model into a minimization-maximization-maximization three-level programming model for solving. As the first layer of variable solution, the maximum photovoltaic output cost is obtained. As the second layer variable solution, the maximum line failure cost is obtained. As the third-level variable solution, the minimum line maintenance cost is obtained. This embodiment uses the LHS method to determine the state of the line when the uncertainty budget is different. The LHS method improves the sampling strategy and achieves a higher sampling accuracy with a smaller sampling scale. Its sampling results are closer to the actual situation.

[0203] S4.1 sets the lower and upper limits of time, solves the first layer, obtains the maximum photovoltaic output cost, updates the lower and upper limits of time, and obtains the lower and upper limits of photovoltaic power.

[0204] S4.2 sets the uncertainty budget and the number of line switch states, solves the second layer, obtains the maximum line fault cost using the LHS method, and updates the lower and upper bounds of the PV power with the optimal values.

[0205] S4.3 solves the third layer based on the optimized PV power and line switch status to obtain the minimum line operation and maintenance cost.

[0206] The above are only preferred embodiments of the present invention, and are not intended to limit the implementation methods and protection scope of the present invention. Those skilled in the art should be aware that all solutions obtained by equivalent substitutions and obvious changes made using the contents of the specification of the present invention should be included in the protection scope of the present invention.

Claims

1. A distribution network optimization method considering the uncertainty of photovoltaic and line switch states, characterized by: The following steps are involved: Step 1: Establish a photovoltaic output uncertainty model. Based on the actual photovoltaic output curve, determine the best fitting curve through mathematical fitting, and characterize the randomness of photovoltaic output through photovoltaic output errors that obey different distributions; Step 2: Establish a line switch state uncertainty model, and establish a mathematical relationship of line switch state uncertainty in different scenarios through the correspondence between the actual cyber-physical system and the node system; Step 3: Establish a multi-objective two-level planning model; consider the uncertainty of photovoltaic power and determine the set of photovoltaic power by fitting; consider the uncertainty of line switch status in various situations and use entropy to screen the scenarios; take the maximum output cost and the maximum line failure cost as the worst case and minimize the maintenance cost by simulating the commands from the dispatch center; The implementation of step 3 includes: Establish the objective function: （11） （12） （13） （14） （15） Represents all operation and maintenance costs, Represents all loss costs, represent The operation and maintenance cost of a single line at any given moment. represent The operation and maintenance status of a single line at all times. =1 means maintenance is required. =0 means no maintenance is required. Represents the total photovoltaic output cost, represents the failure cost of all lines, represent The photovoltaic output cost per unit time, Represents photovoltaic output, represent Unit line failure cost at time, represent Actual line status at all times, =1 means the actual line status is closed, =0 means the actual line status is disconnected, Represents the node index, Represents the branch index, represents the time index, represents a branch set, represents a collection of generators; Step 4: Solve the model by combining the LHS method; expand the model into a minimization-maximization-maximization three-level programming model for solution, and use the LHS method to determine the status of the line when the uncertainty budget is different; The implementation of step 4 includes: As the first layer of variable solution, the maximum photovoltaic output cost is obtained, and the variable of line failure cost is As the second layer variable solution, the maximum line failure cost is obtained, and the variable of line maintenance cost is As the variable solution of the third layer, the minimum line maintenance cost is obtained; Step 4.1, set the lower limit and upper limit of time, solve the variables of the first layer, obtain the maximum photovoltaic output cost, update the lower limit and upper limit of time, and obtain the lower limit and upper limit of photovoltaic power; Step 4.2 Set the uncertainty budget and the number of line switch states, solve the variables of the second layer, use the LHS method to obtain the maximum line fault cost, and update the lower and upper limits of the PV power with the optimal values; Step 4.3 Based on the optimized PV power and line switch status, solve the variables in the third layer to obtain the minimum line operation and maintenance cost.

2. The method for optimizing the distribution network considering the uncertainty of photovoltaic and line switch states according to claim 1, characterized in that: The implementation of step 1 includes: Step 1.1: According to the principle of photovoltaic power generation, the relationship between photovoltaic output and light intensity is obtained: Represents photovoltaic output, Represents the rated photovoltaic output, represents the light intensity, Represents the rated light intensity, Represents the maximum light intensity; Step 1.2: Obtain the relationship between photovoltaic output and time through mathematical fitting: Represents the fitted photovoltaic output. When the light intensity is determined, it is calculated by formula (1) and same, , , represent the fitting coefficients, represents time; the fitting coefficient is determined by formula (2) to establish the relationship between light intensity and time; Step 1.3: Establish the photovoltaic output error misoperation model: represent The maximum value of the photovoltaic error output fluctuation at any moment, , represent time, The photovoltaic fitting output obtained according to formula (2) at each moment is: represent Photovoltaic error output at all times, represent The actual photovoltaic output at each moment, represents the distribution function, when =1, represents Gaussian distribution, when =2, represents Laplace distribution, when =3, represents Cauchy distribution; The relationship between photovoltaic output error and photovoltaic fitting output is established, and photovoltaic error outputs with different distributions are used to express the randomness of photovoltaic output; The present invention proposes Photovoltaic output at all times.

3. The method for optimizing the distribution network considering the uncertainty of photovoltaic and line switch states according to claim 1, characterized in that: The implementation of step 2 includes: Step 2.1, establish a simplified model of the actual cyber-physical system node system; The distribution network is regarded as a node system, including nodes, generators and line switches. The status information of the line switches is controlled by information channels and physical channels, and the transmission lines are controlled through the operation of the line switches. The distribution network is regarded as a cyber-physical system (CPS), which includes a physical system and a network system. The physical system includes circuit breakers, disconnectors, interconnection switches, transmission lines, loads, generators and energy storage devices to realize the collection and transmission of power data. The network system includes application platforms, control platforms, software and communication systems. The communication system includes optical fiber, microwave, Ethernet, routing and carrier. The node system and the cyber-physical system CPS establish connections through information channels and physical channels: the interconnected switches and transmission lines in the cyber-physical system CPS constitute the main body of the physical channels in the node system, and the software and communication system in the cyber-physical system CPS constitute the main body of the information channels in the node system; the loads in the cyber-physical system CPS are simplified to nodes in the node system; the loads collect voltage and current information from power users; the software is used to transmit digital information; the generators in the cyber-physical system CPS are simplified to photovoltaic generators and system generators; the optical fiber and microwave, Ethernet and line communications in the cyber-physical system CPS simplify the network channels and physical channels in the node system, the hardware devices are used to collect and transmit data, and the communication devices are used to receive and execute commands; the circuit breakers, disconnectors, and interconnected switches in the cyber-physical system CPS are incorporated into the line switches in the node system, and the application platform and control platform in the cyber-physical system CPS are simplified to the dispatching center in the node system; Step 2.2, establish a physical equipment failure model; represents the probability of physical device failure, Represents the weight of abnormal operation of the transmission line, Represents the probability of abnormal operation of the circuit breaker, Represents the probability of abnormal operation of the interconnection switch, Represents the probability of abnormal operation of the disconnector, Represents the weight of abnormal operation of physical components, Represents the probability of a physical component performing an abnormal operation, Represents the probability of a physical component failing to perform an operation; Step 2.3: Establish a communication transmission failure model; represents the probability of communication transmission failure, =0 indicates that a communication transmission failure has occurred. =1 indicates that communication transmission failure did not occur; Indicates the status of the information component, = 0 means the information link is not connected, = 1 indicates that the information link is connected; Indicates the number of information links; Step 2.4: Establish a scheduling control failure model; represents the probability of scheduling control failure, Indicates that there is a misalignment in the information link. represents the probability of delayed execution in the information link; in the case of state information failure, , 1 in all information chains; The probability of uncertainty in the state of the line switch ( )for: , , yes , , The standardized weights of different combinations , , , , , , Different, forming a variety of scenarios distributed.

4. The method for optimizing the distribution network considering the uncertainty of photovoltaic and line switch states according to claim 1, characterized in that: The implementation of step 3 also includes: Step 3.1: The linearized DistFlow equation is used to describe the complex power flow of the branch, and the node power flow constraint is: represent Scenario Time Node To Node The active power, represent Scenario Time Node The active demand, represent Scenario Time Node Active load shedding, represent Scenario Time Node The injected generator active power, represent Scenario Time Node The injected active power of the photovoltaic generator, represent Scenario Time Node To Node The reactive power, represent Scenario Time Node The reactive power demand, represent Scenario Time Node Reactive load shedding, represent Scenario Time Node Injected generator reactive power, represent Time Branch The resistance, represent Time Branch The reactance, represent Time Node The voltage amplitude, represents the coefficients of the large M number method, , Represents the node index, represents the branch index, Represents the time index, Represents the scene index; Step 3.2: The uncertainty constraint of photovoltaic output is: represent Scenario Time Node The injected active power of the photovoltaic generator, represent Scenario Time Node The injected active power of the fitted photovoltaic generator, represent Scenario Time Node The injected photovoltaic generator active error power, represent Scenario Time Node The injected active power of the fitted photovoltaic generator is 1, represent Scenario Time Node The injected photovoltaic generator active error power 1, Represents the node index, represents the time index, Represents the scene index; Equations (20) to (22) represent the relationship between photovoltaic output and time. Equation (21) assumes The moment Output of photovoltaic generators Through fitting, we get that formula (22) assumes that Photovoltaic output error of a photovoltaic generator Obtained through the distribution function; Step 3.3: The uncertainty constraint of the line switch state is: represent Scenario Time Branch status, =0 means the line is closed due to the uncertainty of the line switch state. =1 means the line is disconnected due to uncertain line switch status. represent Scenario Time Branch The probability of upper line switching uncertainty, represent Scenario Time Branch The probability of upper line switching uncertainty, Represents an uncertain budget, represents the branch index, Represents the time index, Represents the scene index; Equations (23) and (24) represent the relationship between the uncertainty budget set by the dispatch center and the uncertainty probability of the line switch state; Equation (23) is based on Shannon's information theory, is the uncertainty budget determined by the dispatch center; Equation (24) provides a set of state uncertainties, representing the probability of line switch state uncertainty under multiple scenarios; Step 3.4, line state constraint; represent Scenario Time branch Receive instructions from the dispatch center. =1 represents branch The command received from the dispatch center is to close. =0 represents branch The command received from the dispatch center is to disconnect. represent Scenario Time branch Due to the uncertain state of the circuit breaker, =0 represents branch Closing due to uncertain circuit breaker status, =1 represents branch Disconnection due to uncertain circuit breaker status, represent Scenario Time branch The actual line status, =1 represents branch The actual state is closed. =0 represents branch The actual state is disconnected. represent Scenario Time branch The maintenance status of =1 represents branch Needs repair, =0 represents branch No maintenance required, represent Scenario Auxiliary variables at time, Represents the branch index, represents the time index, Represents the scene index; Step,3.5, voltage and power constraints; represent Scenario Time Branch The actual state, =1 represents branch The actual state is closed. =0 represents branch The actual state is disconnected. Representative branch Maximum active power, represent Time Branch The active power, Representative branch Maximum reactive power, represent Time Branch The reactive power, Represents the minimum active power of the generator, represent Scenario Moment generator at node The injected active power, Represents the maximum active power of the generator, Represents the minimum reactive power of the generator, represent Scenario Moment generator at node The injected reactive power, Represents the maximum reactive power of the generator, Representative Node The minimum voltage amplitude, represent Scenario Time Node The voltage amplitude, Representative Node The maximum voltage amplitude, represent Time Node Active load shedding, represent Time Node Maximum active load shedding, represent Time Node Reactive load shedding, represent Time Node Maximum reactive load shedding, Represents the node index, represents the branch index, Represents the time index, Represents the scene index; Step 3.6, island constraint; represent Scenario The line status of the virtual branch is always included. =1 represents branch closure, =0 represents branch disconnect, Represents the number of nodes in the node system, represent Scenario The flow of virtual branches is always included. =1 means that there is a load demand between the branch and the generator, photovoltaic, and fault line endpoints. =0 means that there is no load demand between this branch and the generator, photovoltaic, or fault line endpoint. represents the coefficients of the large M number method, represents a set of virtual branches, represents a branch set, represents the branch index, Represents the time index, Represents the scene index; Constraints (40)-(42) ensure the radial topology of the distribution network when the line switch status is uncertain; Constraint (40) ensures that the number of branches and the number of nodes are consistent with the connectivity of the distribution network, and Constraint (41) assumes that the line including the fictitious branch has a unit load demand; Constraint (42) limits the branch The fictitious power flow.

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