Power distribution network distribution robust optimization planning method and system

Abstract

The invention discloses a robust optimization planning method and system for distribution of a power distribution network. The method comprises the steps of collecting first data, second data and third data of the power distribution network; based on the preprocessed data, considering source load uncertainty and demand response, and constructing a two-stage distribution robust optimization model; decomposing and converting the two-stage distribution robust optimization model through a first algorithm and a second algorithm; and solving the converted model, and determining the optimal access point and the optimal installation capacity of distributed photovoltaic and energy storage. According to the invention, consumption of the power grid on distributed photovoltaic power generation is promoted, and safe, reliable and economical operation of the power distribution network is realized.

Description

Technical Field

[0001] The present invention relates to the technical field of grid distributed photovoltaic planning, and particularly to a distribution robust optimization planning method and system for a distribution network. Background Art

[0002] To contribute to the realization of the "dual carbon" goal, distributed photovoltaics have been massively connected to the distribution network due to their characteristics such as cleanliness, renewability, and pollution-free. However, due to factors such as the volatility, uncertainty of distributed photovoltaic output, and the mismatch of load demand time series, large-scale grid connection is likely to cause problems such as voltage over-limit and power backflow, bringing major challenges to the safe and stable operation of the distribution network, making the traditional planning based on power balance and reserve difficult to continue, and flexibility becoming the core index to measure the adaptability of the power grid to the volatility of new energy. Therefore, it is very necessary to comprehensively consider the uncertainty of source and load and the joint site selection and capacity determination planning design of flexibility resources.

[0003] To alleviate the problems brought by high-penetration distributed photovoltaic power generation, the effective utilization of configured energy storage devices and flexible loads based on demand response has become the main solution for absorbing photovoltaic power generation. However, the installation of energy storage devices is limited by its high cost, while demand response has significant advantages in terms of economy. However, due to the limited user load responding to time-of-use electricity prices, combining demand response with energy storage can effectively absorb photovoltaic power and reduce the installation capacity and planning cost of the energy storage system. Based on this background, the joint planning of the distribution network and resources needs to comprehensively consider aspects such as economy, safety, system operation flexibility, and uncertainty of new energy output, and conduct joint planning and design of distributed photovoltaics, energy storage systems, and flexibility resources.

[0004] Distribution robust optimization constructs an uncertainty set to describe the fluctuations of random variables and solves the uncertainty decision problem based on the principle of "seeking the best from the worst". In recent years, some scholars have optimized the traditional deterministic optimization planning method and considered the uncertainty problems of distributed photovoltaic output and load. Many scholars have conducted distribution robust planning research on its combination with photovoltaic energy storage configuration. At present, there are many methods to optimize the configuration of distributed photovoltaic power sources and energy storage systems by improving the photovoltaic absorption capacity, but few literatures have applied the consideration of uncertainty and demand-side response to the distribution robust planning of distributed photovoltaics and energy storage systems. Summary of the Invention

[0005] The purpose of this part is to outline some aspects of the embodiments of the present invention and briefly introduce some preferred embodiments. Some simplifications or omissions may be made in this part, as well as in the abstract and title of the present application, to avoid obscuring the purpose of this part, the abstract, and the title, and such simplifications or omissions shall not be used to limit the scope of the present invention.

[0006] In view of the above existing problems, the present invention is proposed.

[0007] Therefore, the present invention provides a distributionally robust optimization planning method and system for a distribution network to solve the problem of large-scale distributed photovoltaic access to the distribution network planning.

[0008] To solve the above technical problems, the present invention provides the following technical solutions:

[0009] In a first aspect, the present invention provides a distributionally robust optimization planning method for a distribution network, including:

[0010] Collect the first data, second data, and third data of the distribution network;

[0011] Based on the preprocessed data, considering the uncertainty of power sources and loads and demand response, construct a two-stage distributionally robust optimization model;

[0012] Decompose and transform the two-stage distributionally robust optimization model through the first algorithm and the second algorithm;

[0013] Solve the transformed model to determine the optimal access points and optimal installation capacities of distributed photovoltaics and energy storage.

[0014] As a preferred solution of the distributionally robust optimization planning method for a distribution network according to the present invention, wherein:

[0015] The first data includes various load types and magnitudes, as well as the installation capacities of various load devices;

[0016] The second data includes light intensity, temperature, humidity, cloud cover, rainfall, rated power and actual power of photovoltaic power generation, maximum photovoltaic output, photovoltaic module parameters, unit power investment cost of distributed photovoltaics, operation cost, maintenance cost, and electricity selling price;

[0017] The third data includes topological structure, number of nodes, connection relationships, power sources, lines, and load data.

[0018] As a preferred solution of the distributionally robust optimization planning method for a distribution network according to the present invention, wherein:

[0019] The two-stage distributionally robust optimization model includes a first-stage planning layer constructed with the goal of minimizing the annual total cost and a second-stage operation layer constructed with the goal of optimizing the operation cost of the distribution network under the worst-case scenario;

[0020] The constraint conditions of the first-stage planning layer include the node installation quantity and capacity constraints of distributed photovoltaics and energy storage, the capacity constraints of distributed photovoltaics and energy storage, the upfront investment cost constraints of distributed photovoltaics and energy storage, topological constraints, and reconstruction constraints;

[0021] The constraint conditions of the second-stage operation layer include distribution network power flow constraints, system safe operation constraints, line power transmission capacity constraints, distributed photovoltaic system output constraints, energy storage system operation constraints, demand response constraints, and interruptible load constraints;

[0022] For the non-linear constraints in the constraint conditions, the penalty factor method is used for linearization.

[0023] As a preferred solution of the distributionally robust optimization planning method for the distribution network described in the present invention, wherein: the decomposition and transformation of the two-stage distributionally robust optimization model through the first algorithm and the second algorithm includes the following steps:

[0024] Using the column and constraint generation algorithm, the two-stage robust optimization model is decomposed into a master problem and a sub-problem;

[0025] Using the max-min sub-problem decomposition algorithm, the sub-problem is divided into an outer layer and an inner layer;

[0026] Through the strong duality theory, the maximization problem of the outer layer is transformed into a minimization problem to obtain a single-layer optimization problem.

[0027] As a preferred solution of the distributionally robust optimization planning method for the distribution network described in the present invention, wherein: the solution of the transformed model includes the following steps:

[0028] Using an intelligent heuristic algorithm to solve the master problem, and continuously introducing new variables and constraints related to the sub-problem during the solution process;

[0029] According to the result obtained by solving the master problem, a data-driven Wasserstein distance is used to construct a probability distribution fuzzy set of distributed photovoltaic output and load, and the Wasserstein ball radius is calculated;

[0030] Taking the probability distribution fuzzy set and the Wasserstein ball radius as input parameters, using the linear mathematical programming method to solve the sub-problem, and the solution result is the probability distribution of distributed photovoltaic and load and the distribution network operation cost under the worst-case scenario, and the solution result is returned to the master problem for the next iteration.

[0031] As a preferred solution of the distributionally robust optimization planning method for the distribution network described in the present invention, wherein:

[0032] The objective function of the first-stage planning layer is expressed as:

[0033] minC inv =C PV,in +C ESS,in +C GC,in

[0034]

[0035] Among them, C PV,in , C ESS,in , C GC,in are the annual investment cost of distributed photovoltaics, the annual investment cost of the energy storage system, and the investment cost of the grid network line respectively; G(·) and H(·) are the constraint conditions of the first-stage planning layer respectively;

[0036] The objective function of the second-stage operation layer is expressed as:

[0037] maxE(minC op (x inv , x op ))

[0038] C op = C PV,o + C ESS,o + C loss + C CL + C PV + C grid

[0039]

[0040] Among them, C PV,o , C ESS,o , C loss , C CL , C PV , C grid are the annual operation and maintenance cost of distributed photovoltaics, the annual operation and maintenance cost of the energy storage system, the annual network loss cost, the interruptible load response cost, the curtailment penalty cost, and the power purchase cost respectively; g(·) and h(·) are the constraint conditions of the second-stage operation layer respectively.

[0041] As a preferred solution of the distribution robust optimization planning method for the distribution network described in the present invention, wherein: the comprehensive objective function of the two-stage distribution robust optimization model is expressed as:

[0042] minF = {C inv + maxE(minC op )}

[0043] Among them, F is the comprehensive cost of the distribution network, C inv is the average annual investment cost of the distributed photovoltaic and energy storage system, C op is the average annual operation cost of the distribution network, and E(·) represents taking the mathematical expectation.

[0044] In a second aspect, the present invention provides a distribution robust optimization planning system for a distribution network, including:

[0045] An acquisition module, configured to acquire first data, second data, and third data of the distribution network;

[0046] A construction module, configured to construct a two-stage distributionally robust optimization model based on preprocessed data, considering the uncertainties of power generation and load and demand response;

[0047] A decomposition module, configured to decompose and transform the two-stage distributionally robust optimization model by a first algorithm and a second algorithm;

[0048] A solution module, configured to solve the transformed model to determine the optimal connection points and optimal installation capacities of distributed photovoltaic and energy storage.

[0049] In a third aspect, the present invention provides a computing device, including:

[0050] A memory, configured to store a program;

[0051] A processor, configured to execute the computer-executable instructions, and when the computer-executable instructions are executed by the processor, the steps of the distributionally robust optimization planning method for a distribution network are implemented.

[0052] In a fourth aspect, the present invention provides a computer-readable storage medium, including: when the program is executed by a processor, the steps of the distributionally robust optimization planning method for a distribution network are implemented.

[0053] Advantages of the present invention: The present invention uses a construction method of a probability distribution fuzzy set based on the Wasserstein distance to describe the uncertainties of distributed photovoltaic power output and random load, which can make full use of historical data and has good convergence. Considering the constraints such as the capacities of distributed photovoltaic and energy storage systems, the safe operation of the distribution network, the operation of the energy storage system, demand response and interruptible load, and the power flow of the distribution network, the column and constraint generation algorithm and the max-min subproblem decomposition algorithm are used to implement two-stage distributionally robust optimization solution, determine the connection points and connection capacities of distributed photovoltaic and energy storage systems, and reduce the solution time while taking into account site selection and capacity determination. Description of the Drawings

[0054] In order to more clearly illustrate the technical solutions of the embodiments of the present invention, the drawings required for description in the embodiments will be briefly introduced below. Obviously, the drawings in the following description are only some embodiments of the present invention, and those of ordinary skill in the art can also obtain other drawings based on these drawings without creative efforts. Among them:

[0055] Figure 1 It is a schematic diagram of the basic process of a distributionally robust optimization planning method for a distribution network provided by an embodiment of the present invention. Detailed Embodiments

[0056] To make the above objects, features, and advantages of the present invention more apparent and understandable, the following provides a detailed description of the specific embodiments of the present invention in conjunction with the accompanying drawings of the specification. Obviously, the described embodiments are only a part of the embodiments of the present invention, rather than all of them. Based on the embodiments of the present invention, all other embodiments obtained by those of ordinary skill in the art without creative efforts shall fall within the scope of protection of the present invention.

[0057] In the following description, many specific details are set forth to facilitate a full understanding of the present invention. However, the present invention may be implemented in other ways different from those described herein. Those skilled in the art can make similar extensions without departing from the connotation of the present invention. Therefore, the present invention is not limited by the specific embodiments disclosed below.

[0058] Secondly, the so-called "one embodiment" or "embodiment" herein refers to a specific feature, structure, or characteristic that may be included in at least one implementation manner of the present invention. The phrase "in one embodiment" appearing in different places in this specification does not necessarily refer to the same embodiment, nor is it an independent or alternative embodiment that excludes other embodiments.

[0059] The present invention is described in detail in conjunction with schematic diagrams. When detailing the embodiments of the present invention, for ease of explanation, the cross-sectional views showing the device structure will be enlarged locally in a non-general proportion, and the schematic diagrams are only examples and should not limit the scope of protection of the present invention here. In addition, in actual production, three-dimensional spatial dimensions including length, width, and depth should be included.

[0060] At the same time, in the description of the present invention, it should be noted that the orientation or positional relationships indicated by terms such as "upper, lower, inner, and outer" are based on the orientation or positional relationships shown in the drawings, and are only for facilitating the description of the present invention and simplifying the description, rather than indicating or implying that the device or element referred to must have a specific orientation, be constructed and operated in a specific orientation, and thus should not be construed as a limitation to the present invention. In addition, the terms "first, second, or third" are only used for descriptive purposes and cannot be construed as indicating or implying relative importance.

[0061] Unless otherwise clearly defined and limited in the present invention, the terms "mounted, connected, and coupled" should be understood in a broad sense. For example, it can be a fixed connection, a detachable connection, or an integral connection; it can also be a mechanical connection, an electrical connection, or a direct connection, or can be indirectly connected through an intermediate medium, or can be the communication inside two elements. For those of ordinary skill in the art, the specific meanings of the above terms in the present invention can be understood according to specific circumstances.

[0062] Embodiment 1

[0063] Refer to Figure 1, which is an embodiment of the present invention, provides a distribution robust optimization planning method for a distribution network, including:

[0064] S1: Collect the first data, second data, and third data of the distribution network;

[0065] S2: Based on the preprocessed data, considering the uncertainty of the source and load and demand response, construct a two-stage distribution robust optimization model;

[0066] S3: Decompose and transform the two-stage distribution robust optimization model through the first algorithm and the second algorithm;

[0067] S4: Solve the transformed model to determine the optimal access points and optimal installation capacities of distributed photovoltaics and energy storage.

[0068] It should be noted that for the problem of large-scale distributed photovoltaic access to the distribution network planning, the present invention proposes a distribution robust optimization planning method for distributed photovoltaic access to the distribution network considering the uncertainty of the source and load and demand response. First, considering the total economic benefits of the photovoltaic and energy storage system, a two-stage distribution robust optimization planning model for distributed photovoltaics and energy storage systems with the goal of minimizing cost is constructed. The first-stage planning layer aims to minimize the annual total cost, and the second-stage operation layer considers the uncertainty of distributed photovoltaics and loads, aiming to find the optimal operation strategy for the worst-case operation cost of the distribution network. Secondly, the Wasserstein distance is used to construct a probability distribution fuzzy set to describe the uncertainty of distributed photovoltaic output and load. Then, the column and constraint generation algorithm and the max-min algorithm are used to decompose the two-stage robust optimization into a min-max-min three-layer robust optimization problem, and the model is transformed using linearization means such as the strong duality theory and the big M method, and the intelligent optimization algorithm and the linear mathematical programming algorithm are combined to solve. Through the two-stage distribution robust optimization of the distributed photovoltaic and energy storage system, the optimal access points and optimal installation capacities of distributed photovoltaics and energy storage are determined, promoting the grid's consumption of distributed photovoltaic power generation and realizing the safe, reliable, and economic operation of the distribution network.

[0069] Embodiment 2

[0070] Refer to Figure 1 , which is an embodiment of the present invention, provides a distribution robust optimization planning method for a distribution network based on the previous embodiment, including:

[0071] In the embodiment of the present application, step S1 includes collecting historical load data, distributed photovoltaic power station data, and access distribution network parameters, and cleaning and preprocessing the data;

[0072] In the embodiment of the present application, the load data in step S1 includes various load types and sizes, as well as the installation capacities of various load devices, etc.;

[0073] In the embodiment of the present application, the distributed photovoltaic power station data in step S1 includes light intensity, temperature, humidity, cloud cover, rainfall, rated power and actual power of photovoltaic power generation, maximum photovoltaic output, photovoltaic module parameters, investment cost per unit power of distributed photovoltaic, operating cost, maintenance cost, and electricity selling price, etc.;

[0074] In the embodiment of the present application, the distribution network parameters in step S1 include topological structure, number of nodes, connection relationship, power source, line, and load data, etc.

[0075] In the embodiment of the present application, the preprocessing in step S1 mainly includes detection and correction of abnormal and missing data, as well as normalization processing.

[0076] In the embodiment of the present application, in step S2, considering the uncertainty of source and load and demand response, a two-stage distributionally robust optimization model is constructed;

[0077] In the embodiment of the present application, in step S2, considering the total economic benefit of the photovoltaic and energy storage system, a two-stage distributionally robust optimization planning model of distributed photovoltaic and energy storage systems with the goal of minimizing cost is constructed. The first-stage planning layer aims to minimize the annual total cost, and the second-stage operation layer considers the uncertainty of distributed photovoltaic and load, with the goal of finding the optimal operation strategy for the operation cost of the distribution network in the worst case.

[0078] In the embodiment of the present application, in step S2, considering the uncertainty of source and load and demand response, a two-stage distributionally robust planning model of distributed photovoltaic and energy storage is constructed, and the objective function is:

[0079] minF={C inv +maxE(minC op )}

[0080] Among them, F is the comprehensive cost of the distribution network, C inv is the average annual investment cost of the distributed photovoltaic and energy storage system, C op is the average annual operating cost of the distribution network, and E(·) represents taking the mathematical expectation.

[0081] In the embodiment of the present application, in the first-stage planning layer problem of step S2, the deployment of distributed photovoltaic power sources and energy storage is determined with the goal of minimizing the annual total cost, and the total investment cost and operating cost of the system need to be considered, including the investment cost of distributed photovoltaic power sources and energy storage, and the investment cost of overhead lines; the decision variables are the installation locations and configuration capacities of distributed photovoltaic and energy storage, and the construction of grid lines; its mathematical model expression is:

[0082] minC inv =C PV,in +C ESS,in +C GC,in

[0083]

[0084] Among them, C PV,in , C ESS,in , C GC,in are the annual investment cost of distributed PV, the annual investment cost of energy storage system, and the investment cost of grid network lines respectively; G(·) and H(·) are the constraint conditions of the first-stage planning layer respectively;

[0085] In the embodiment of the present application, the problem of the second-stage operation layer in step S2 is solved with the solution of the first stage as the known input. On the given planning scheme, in the predefined uncertainty set, an operation scheme with the optimal operation cost of the distribution network under the worst scenario is found. Among them, the fuzzy sets based on the Wasserstein distance are used to describe the probability distributions of distributed PV output and stochastic load under different typical daily scenarios respectively. The decision variables are the operation strategies such as distributed PV output, energy storage system output, interruption status and interruption amount of interruptible load, and line reconfiguration. The model is as follows:

[0086] maxE(minC op (x inv ,x op ))

[0087] C op =C PV,o +C ESS,o +C loss +C CL +C PV +C grid

[0088]

[0089] Among them, C PV,o , C ESS,o , C loss , C CL , C PV , C grid are the annual operation and maintenance cost of distributed PV, the annual operation and maintenance cost of energy storage system, the annual network loss cost, the interruptible load response cost, the curtailment penalty cost, and the power purchase cost respectively; g(·) and h(·) are the constraint conditions of the second-stage operation layer respectively.

[0090] In the embodiment of the present application, in step S2, after optimizing and determining the deployment of distributed photovoltaic and energy storage devices and the grid line layout in the first stage, it is transmitted to the second-stage optimization model; the inner-layer min optimization model of the second stage aims to minimize the annual operation cost of the distribution network, and determines the operation strategies of the distribution network power flow, distributed photovoltaic, and energy storage systems; the outer-layer max optimization model of the second stage aims to determine the probability distribution under the most adverse scenarios of distributed photovoltaic and energy storage systems when the operation cost of the distribution network is minimized. The operation strategies and probability distributions are fed back to the first stage as input parameters of the first stage. Through interactive iteration, a configuration plan of distributed photovoltaic and energy storage systems with the minimum total cost of the distribution network is determined.

[0091] In the embodiment of the present application, the constraint conditions of the first-stage optimization model in step S2 include the node installation quantity and capacity constraints of distributed photovoltaic and energy storage, the capacity constraints of distributed photovoltaic and energy storage, the upfront investment cost constraints of distributed photovoltaic and energy storage, topology constraints, and reconstruction constraints; the constraint conditions of the second-stage optimization model include distribution network power flow constraints, system safe operation constraints (node voltage limit constraints, line current constraints), line power transmission capacity constraints, distributed photovoltaic system output constraints, energy storage system operation constraints, demand response constraints, and interruptible load constraints; for the non-linear constraints in the constraint conditions, the penalty factor method is used to linearize them.

[0092] Specifically as follows:

[0093] Constraint conditions of the first-stage planning layer model:

[0094] 1) Distributed photovoltaic access capacity constraint

[0095]

[0096] In the formula, S min,PV is the minimum photovoltaic access capacity of the distribution network, S i,PV is the photovoltaic capacity accessed by node i, and S max,PV is the maximum photovoltaic access capacity of the distribution network specified by the project.

[0097] 2) Energy storage capacity constraint

[0098]

[0099] Among them, P ESS,min , P ESS,max are the upper and lower limits of the rated power of the energy storage system to be planned respectively; E ESS,min , E ESS,max are the upper and lower limits of the rated capacity of the energy storage system to be planned respectively; P ESS,i , E ESS,i are the rated capacity and rated power installed at node i of the energy storage system respectively.

[0100] 3) Node installation quantity constraints for distributed photovoltaic and energy storage

[0101]

[0102] Among them, N i,PV is the actual installed quantity of the distributed photovoltaic system on node i, N max,PV is the upper limit of the installed quantity of distributed photovoltaic on node i, N i,ESS is the actual installed quantity of the energy storage system on node i, N max,ESS is the upper limit of the installed quantity of the energy storage system on node i.

[0103] 4) Early investment cost constraints for distributed photovoltaic and energy storage

[0104] C inv ≤C inv,max

[0105] Among them, C inv 、C inv,max are the annual investment limits of the distribution network respectively.

[0106] 5) Topological constraint: When planning the distribution network grid, the radial constraint should be satisfied. Let the total number of branches be the difference between the total number of nodes and the number of root nodes, as follows:

[0107]

[0108] Among them, D l is the set of all lines in the distribution network, x ij is the starting state of the line, 0 means disconnected, 1 means closed, and n s represents the number of root nodes of the system.

[0109] 6) Reconfiguration constraint

[0110] To avoid loop or island situations, the distribution network should satisfy the following reconfiguration constraints:

[0111]

[0112] In the formula, NL k and L k represent the total number and set of branches in the kth loop respectively, n r represents the total number of loops, and l k represents the set of branches connected to the kth node.

[0113] Second-stage operation layer model constraint conditions:

[0114] 1) Distribution network DistFlow power flow constraint

[0115]

[0116] Among them, AL(j, :) is the set of the end nodes of the branches with j as the head node, and AL(:, j) is the set of the head nodes of the branches with j as the end node; P ij , P jk and Q ij , Q jk are the active and reactive powers on lines ij and jk respectively; X ij is the reactance of line ij, P j,load , Q j,load are the magnitudes of the active and reactive powers of the original load at node j respectively, and U i is the magnitude of the voltage at node i.

[0117] 2) System safe operation constraints

[0118]

[0119] I ij ≤ I ij,max

[0120] Among them, U i is the node voltage, are the lower and upper limit values of the node voltage at node i respectively, I ij is the current on line ij, and I ij,max is the maximum allowable current value that line ij can carry.

[0121] 3) Line power transmission capacity constraints

[0122] |S ij | ≤ S ij,max

[0123] Among them, S ij , S ij,max are the transmission power and upper limit value of line ij respectively.

[0124] 4) Distributed photovoltaic system output constraints

[0125]

[0126] Among them, P i,PV , are the active output and its upper and lower limit values of distributed photovoltaic power source i respectively; Q i,PV , are the reactive output and its upper and lower limit values of distributed photovoltaic power source i respectively.

[0127] 5) Energy storage system operation constraints

[0128] SOC min ≤ SOC ≤ SOC max

[0129] SOC start = SOC end

[0130]

[0131]

[0132] where SOC is the state of charge of the energy storage system, SOC min and SOC max are the minimum and maximum states of charge of the energy storage system, respectively are the charging power and discharging power of the energy storage system at node i at time t, respectively are the upper and lower limits of the charging and discharging power, respectively are 0-1 variables indicating whether the energy storage system is charging or discharging, respectively is the power at node i at time t in scenario s, t0 is the last operating time of a period, η C and η D are the charging efficiency and discharging efficiency of the energy storage system, respectively

[0133] 6) Demand response load constraint

[0134]

[0135] where P i,t and are the total loads of the distribution network before and after implementing time-of-use electricity prices at node i at time t, respectively, and N is the total number of system nodes

[0136] 7) Interruptible load response constraint

[0137]

[0138] where P i,CL,min and P i,CL,max are the upper and lower limits of the interruptible load capacity at node i, respectively, N CL is the maximum number of interruptions of the interruptible load within a period, and T i,CL,max is the maximum interruption time of the interruptible load at node i

[0139] In an alternative embodiment, the first algorithm in step S3 may be a column and constraint generation algorithm, or a Benders decomposition algorithm, or a PHA algorithm

[0140] In an alternative embodiment, the column-and-constraint generation algorithm includes solving the master problem to obtain dual variable information, indicating whether there are variables that have not been considered but can reduce the objective function value. If so, these variables are added as new columns to the core problem, and it is checked whether the existing solution violates any constraints that are not explicitly included in the core problem. If it is found that some constraints are violated, these constraints need to be explicitly added to the core problem. Incorporate the newly generated columns and / or newly added constraints into the core problem. When no new columns for improving the solution can be found anymore, or when all constraints are satisfied and no new constraints are added, the algorithm converges and the iteration stops.

[0141] In an alternative embodiment, the Benders decomposition algorithm includes solving the master problem to obtain a set of preliminary planning decisions. For each possible uncertainty scenario, use the sub-problem to evaluate the performance of this set of decisions under different scenarios and calculate the corresponding operating costs. If it is found in the sub-problem that the current planning decisions cannot handle some scenarios (i.e., resulting in excessive operating costs or violating some restrictions), then this information is fed back to the master problem in the form of a Benders cut. After adding the new cut, the master problem is re-solved to obtain updated planning decisions. Repeat the above process until no new cuts can be added. When the gap between the master problem and all sub-problems is small enough, the iteration ends.

[0142] In an alternative embodiment, the PHA algorithm includes specifying the long-term planning decision variables in the first stage (such as the installation locations and capacities of distributed photovoltaic and energy storage systems), and the short-term operation decision variables in the second stage (such as the scheduling strategies under different photovoltaic power outputs and load scenarios). According to the uncertainties (such as the changes in photovoltaic power generation and load demand), construct a scenario tree representing all possible scenarios, associate a set of Lagrange multipliers with each scenario. In each iteration, solve the optimization problem independently for each scenario, with the goal of minimizing the cost of that scenario plus the penalty term for violating the consistency condition weighted by the current Lagrange multipliers. Adjust the Lagrange multipliers according to the differences between the scenario solutions obtained in the previous step. Once the PHA converges, a common solution can be extracted from each scenario.

[0143] It should be noted that the column-and-constraint generation algorithm gradually approaches the optimal solution, only considering the currently most important variables and constraints in each iteration. This helps manage computational resources, can be dynamically adjusted according to the specific characteristics of the problem, and can flexibly adjust the strategy in each iteration step. Although there are multiple algorithms to choose from, the column-and-constraint generation algorithm performs excellently in solving such problems due to its high efficiency, dynamic adaptability, and flexibility.

[0144] In an alternative embodiment, the second algorithm in step S3 may be a max-min subproblem decomposition algorithm, or an RC algorithm, or a DRO algorithm;

[0145] In an alternative embodiment, the max-min subproblem decomposition algorithm includes defining a two-stage optimization model, constructing a min-max-min three-layer structure, based on the current planning decision, solving the optimization problem of the first stage to obtain a set of preliminary long-term decision variables. For each possible uncertainty scenario, use the optimization problem of the second stage to evaluate the performance of this set of decisions under different scenarios, and calculate the corresponding operating costs. In the most adverse scenario, optimize the short-term operating decision again, feedback the information of the most adverse scenario to the outer optimization problem, adjust the long-term planning decision, and continuously execute the above iterative process until the cost no longer changes after several consecutive iterations.

[0146] In an alternative embodiment, the RC algorithm includes establishing a robust optimization model based on the installation location and capacity of the distributed photovoltaic and energy storage systems, transforming the original uncertain optimization problem into a deterministic equivalent problem, and using standard mathematical programming techniques (such as linear programming, mixed-integer linear programming, etc.) to solve the transformed deterministic problem. The solution obtained from the deterministic problem is a robust solution that can cope with all scenarios in the uncertainty set;

[0147] In an alternative embodiment, the DRO algorithm includes defining the uncertainty sets of photovoltaic power output and load, introducing fuzzy sets, constructing an optimization model, and using duality theory to solve the worst-case consideration for all probability distributions within the fuzzy set to find a solution that can perform well in the worst case.

[0148] It should be noted that the concept and implementation of the max-min algorithm are relatively simple, easy to understand, and convenient for developers and researchers to apply to specific problems. Especially when the uncertainty set has a good structure, the max-min algorithm can effectively solve the problem and provide fast approximate solutions or exact solutions. Although there are multiple methods that can replace the max-min algorithm, in dealing with worst-case optimization problems, the max-min algorithm stands out for its simplicity, robustness, and computational efficiency.

[0149] In the embodiment of the present application, the decomposition and transformation of the two-stage distributionally robust optimization model in step S3 include the following steps:

[0150] Adopt the column-and-constraint generation algorithm to decompose the two-stage robust optimization model into an alternating iterative solution of the master problem and the subproblem, and determine the distribution network planning scheme for the access of distributed photovoltaic and energy storage with the minimum total cost. In each iteration process, according to the results of the subproblem, new variables and constraints are added to the master problem.

[0151] The max-min subproblem decomposition algorithm is adopted to divide the subproblems into an outer layer and an inner layer;

[0152] Through the strong duality theory, the maximization problem of the outer layer is transformed into a minimization problem, and a single-layer optimization problem is obtained.

[0153] In the embodiment of the present application, in step S3, for the proposed two-stage distributionally robust optimization model, the column and constraint generation (C&CG) algorithm is used for solving. The two-stage robust optimization model is decomposed into a master problem and a subproblem, and they are solved by alternating iteration to determine the distribution network planning scheme for the access of distributed photovoltaic and energy storage with the minimum total cost. In each iteration process, according to the results of the subproblem, new variables and constraints are added to the master problem.

[0154] In the embodiment of the present application, in step S4, the transformed model is solved, including the following steps:

[0155] An intelligent heuristic algorithm is used to solve the master problem. During the solving process, new variables and constraints related to the subproblem are continuously introduced to determine the configuration scheme of the distributed photovoltaic and energy storage systems;

[0156] According to the configuration scheme obtained by solving the master problem, a data-driven Wasserstein distance is used to construct the probability distribution fuzzy sets of the distributed photovoltaic output and the load, and the Wasserstein ball radius is calculated;

[0157] The probability distribution fuzzy sets and the Wasserstein ball radius are used as input parameters, and a linear mathematical programming method is used to solve the subproblem. The solution results are the probability distributions of the distributed photovoltaic and the load and the distribution network operation cost under the worst-case scenario, and the solution results are returned to the master problem for the next iteration.

[0158] In the embodiment of the present application, in step S4, a data-driven Wasserstein distance is used to construct the probability distribution fuzzy sets of the distributed photovoltaic output and the load, and the Wasserstein ball radius is calculated, specifically as follows:

[0159] 1) A data-driven method is adopted to perform probability distribution fitting on the historical distributed photovoltaic system output data and load data to generate an empirical distribution:

[0160]

[0161] Among them, is the sample value of ξ, N S is the sample size, is the Dirac measure of.

[0162] 2) Calculate the Wasserstein distance between the empirical distribution and the true distribution. The calculation formula is as follows:

[0163] d w (P, Q) = inf{∫||ξ p , ξ p ||∏(dξ p , dξ p )}

[0164] where d w (P, Q) represents the Wasserstein distance between distributions P and Q; ξ p , ξ q represent the uncertain variables of distributions P and Q respectively; ||ξ p , ξ q || represents any norm; ∏(dξ p , dξ q ) represents the joint probability distribution defined on P and Q; inf represents the infimum.

[0165] 3) Calculate the distance between the empirical distribution and the true distribution using the Wasserstein distance, and construct the fuzzy sets of the historical distributed photovoltaic system output and random load;

[0166]

[0167] where the fuzzy set F is a Wasserstein ball centered at the empirical distribution with a radius of ρ; the ball radius ρ can be regarded as a function related to the sample size N s and the confidence level β, and its expression is:

[0168]

[0169] where C is a constant.

[0170] In the embodiment of the present application, the decomposed main problem in step S4 still aims to minimize the planning cost, and the solution result is the lower bound of the optimal value. It belongs to a mixed-integer second-order cone programming problem and is solved using intelligent heuristic algorithms such as simulated annealing algorithm, genetic algorithm, ant colony algorithm, etc. During the solution process, variables and constraints related to the sub-problems are continuously introduced to reduce the number of iterations and improve the solution efficiency, thereby determining the configuration scheme of the distributed photovoltaic and energy storage systems;

[0171] In the embodiment of the present application, the sub-problems decomposed in step S4 belong to the max-min two-layer optimization problem. The outer max problem can be transformed into a min problem through the strong duality theory to obtain a single-layer optimization problem, which is solved by linear mathematical programming methods such as the simplex method and the interior point method. The solution results are the probability distributions of distributed photovoltaic and load under the worst-case scenario and the operating cost of the distribution network, and the solution results are returned to the main problem for the next iteration. Professional solvers such as CPLEX, Gurobi, and GAMS can be used to solve the optimization model.

[0172] Embodiment 3

[0173] The above is a schematic solution of a distributionally robust optimization planning method for a distribution network in this embodiment. It should be noted that the technical solution of the distributionally robust optimization planning system of the distribution network belongs to the same concept as the technical solution of the above distributionally robust optimization planning method for the distribution network. For the details not described in detail in the technical solution of the distributionally robust optimization planning system of the distribution network in this embodiment, reference can be made to the description of the technical solution of the above distributionally robust optimization planning method for the distribution network.

[0174] This embodiment also provides a system for a distributionally robust optimization planning method for a distribution network, including:

[0175] An acquisition module for acquiring the first data, the second data, and the third data of the distribution network;

[0176] A construction module for constructing a two-stage distributionally robust optimization model based on the preprocessed data, considering the uncertainty of the source and load and the demand response;

[0177] A decomposition module for decomposing and transforming the two-stage distributionally robust optimization model through the first algorithm and the second algorithm;

[0178] A solution module for solving the transformed model to determine the optimal access points and the optimal installation capacities of distributed photovoltaic and energy storage.

[0179] This embodiment also provides a computing device applicable to the situation of distributionally robust optimization planning of a distribution network, including: a memory and a processor; the memory is used to store computer-executable instructions, and the processor is used to execute the computer-executable instructions to implement the distributionally robust optimization planning method proposed in the above embodiment.

[0180] This embodiment also provides a storage medium, on which a computer program is stored, and when the program is executed by a processor, it implements the distributionally robust optimization planning method proposed in the above embodiment.

[0181] The storage medium proposed in this embodiment and the method for realizing distribution network distribution robust optimization planning proposed in the above embodiment belong to the same inventive concept. Technical details not described in detail in this embodiment can be referred to the above embodiment, and this embodiment has the same beneficial effects as the above embodiment.

[0182] From the above description of the embodiments, those skilled in the art can clearly understand that the present invention can be implemented by means of software and necessary general-purpose hardware, and of course, it can also be implemented by hardware.

[0183] Based on such an understanding, the technical solution of the present invention, in essence, or the part that contributes to the prior art can be embodied in the form of a software product. The computer software product can be stored in a computer-readable storage medium, such as a floppy disk, read-only memory (ROM), random access memory (RAM), flash memory (FLASH), hard disk, or optical disc of a computer, etc., including several instructions for causing a computer device (which can be a personal computer, a server, or a network device, etc.) to execute the methods of various embodiments of the present invention.

[0184] It should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention and are not restrictive. Although the present invention has been described in detail with reference to the preferred embodiments, those of ordinary skill in the art should understand that the technical solutions of the present invention can be modified or equivalently replaced without departing from the spirit and scope of the technical solutions of the present invention, and they should all be covered by the scope of the claims of the present invention.

Claims

1. A distribution robust optimization planning method for a distribution network, characterized in that Including: Collecting the first data, second data and third data of the distribution network; Based on the preprocessed data, considering the uncertainty of source and load and demand response, constructing a two-stage distributionally robust optimization model; Decomposing and transforming the two-stage distributionally robust optimization model through the first algorithm and the second algorithm; Solving the transformed model to determine the optimal connection points and optimal installation capacities of distributed photovoltaics and energy storage.

2. The distribution robust optimization planning method for a distribution network according to claim 1, characterized in that: The first data includes various load types and magnitudes, as well as the installation capacities of various load devices; The second data includes light intensity, temperature, humidity, cloud cover, rainfall, rated power and actual power of photovoltaic power generation, maximum photovoltaic output, photovoltaic module parameters, investment cost per unit power of distributed photovoltaics, operating cost, maintenance cost and electricity selling price; The third data includes topological structure, number of nodes, connection relationships, power sources, lines and load data.

3. The distribution robust optimal planning method for a distribution network according to claim 1 or 2, characterized in that: The two-stage distributionally robust optimization model includes a first-stage planning layer constructed with the goal of minimizing the annual total cost and a second-stage operation layer constructed with the goal of optimizing the operation cost of the distribution network under the worst-case scenario; The constraint conditions of the first-stage planning layer include the node installation quantity and capacity constraints of distributed photovoltaics and energy storage, the capacity constraints of distributed photovoltaics and energy storage, the upfront investment cost constraints of distributed photovoltaics and energy storage, topological constraints, and reconstruction constraints; The constraint conditions of the second-stage operation layer include distribution network power flow constraints, system safe operation constraints, line power transmission capacity constraints, distributed photovoltaic system output constraints, energy storage system operation constraints, demand response constraints, and interruptible load constraints; For the non-linear constraints in the constraint conditions, the penalty factor method is used for linearization processing.

4. The distribution robust optimal planning method for a distribution network according to claim 3, wherein: The decomposing and transforming the two-stage distributionally robust optimization model through the first algorithm and the second algorithm includes the following steps: Using the column and constraint generation algorithm to decompose the two-stage robust optimization model into a master problem and a sub-problem; Using the max-min sub-problem decomposition algorithm to divide the sub-problem into an outer layer and an inner layer; Through the strong duality theory, transforming the maximization problem of the outer layer into a minimization problem to obtain a single-layer optimization problem.

5. The distribution robust optimal planning method for a distribution network according to claim 4, characterized in that: The solving the transformed model includes the following steps: Using an intelligent heuristic algorithm to solve the master problem, continuously introducing new variables and constraints related to the sub-problem during the solving process to determine the configuration scheme of the distributed photovoltaic and energy storage systems; According to the configuration scheme obtained by solving the master problem, using the data-driven Wasserstein distance to construct the probability distribution fuzzy sets of distributed photovoltaic output and load, and calculating the Wasserstein ball radius; Taking the probability distribution fuzzy sets and the Wasserstein ball radius as input parameters, using the linear mathematical programming method to solve the sub-problem, and the solution result is the probability distributions of distributed photovoltaics and loads and the operation cost of the distribution network under the worst-case scenario, and returning the solution result to the master problem for the next iteration.

6. The distribution robust optimization planning method for a distribution network according to claim 5, wherein: The objective function of the first-stage planning layer is expressed as: minC inv = C PV,in + C ESS,in + C GC,in Among them, C PV,in , C ESS,in , C GC,in are the annual investment cost of distributed photovoltaics, the annual investment cost of the energy storage system, and the investment cost of the grid network line respectively; G(·) and H(·) are the constraint conditions of the first-stage planning layer respectively; The objective function of the second-stage operation layer is expressed as: maxE(minC op (x inv ,x op )) C op = C PV,o + C ESS,o + C loss + C CL + C PV + C grid Among them, C PV,o , C ESS,o , C loss , C CL , C PV , C grid are respectively the annual operation and maintenance cost of distributed photovoltaics, the annual operation and maintenance cost of the energy storage system, the annual network loss cost, the interruptible load response cost, the curtailment penalty cost, and the power purchase cost; g(·) and h(·) are respectively the constraint conditions of the second-stage operation layer.

7. The distribution robust optimization planning method for a distribution network according to claim 6, characterized in that: The comprehensive objective function of the two-stage distributionally robust optimization model is expressed as: minF = {C inv + maxE(minC op )} Among them, F is the comprehensive cost of the distribution network, and C inv is the average annual investment cost of the distributed photovoltaic and energy storage system, and C op is the average annual operating cost of the distribution network. E(·) represents the mathematical expectation.

8. A system for the distribution robust optimization planning method of the distribution network according to claim 1, characterized in that: A collection module, configured to collect the first data, the second data and the third data of the distribution network; A construction module, configured to construct a two-stage distribution robust optimization model based on the preprocessed data, considering the uncertainty of power sources and loads and demand response; A decomposition module, configured to decompose and transform the two-stage distribution robust optimization model through a first algorithm and a second algorithm; A solution module, configured to solve the transformed model to determine the optimal access points and the optimal installation capacities of distributed photovoltaic and energy storage.

9. A computing device, characterized in that, Including: A memory, configured to store programs; A processor, configured to load the program to execute the steps of the distribution network distribution robust optimization planning method according to any one of claims 1-7.

10. A computer-readable storage medium stores a program, characterized in that, When the program is executed by the processor, the steps of the distribution network distribution robust optimization planning method according to any one of claims 1-7 are implemented.

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