A method and apparatus for power distribution network planning based on mixed integer programming

Abstract

The application discloses a power distribution network planning method and device based on mixed integer programming, comprising: acquiring the topological structure, equipment information and load characteristics of a power distribution network; taking an investment mode as an input parameter, and constructing a mixed model according to the topological structure, equipment information and load characteristics; acquiring a preset problem matrix, and obtaining an optimal investment objective function based on the mixed model and in combination with the preset problem matrix; constructing an uncertainty function according to the uncertainty of power distribution network planning; adjusting variables in the optimal investment objective function according to the uncertainty function, and obtaining a mixed integer optimization model; and solving the mixed integer optimization model through a greedy algorithm to obtain an optimal investment mode and corresponding optimal profit. The model can accurately describe the operation and development of the power distribution network, more accurately evaluate risks and adjust investment strategies, improve the reliability and robustness of investment decisions, and improve the solving efficiency.

Description

Technical Field

[0001] This invention relates to the field of power system distribution network asset planning technology, and in particular to a distribution network planning method and apparatus based on mixed integer programming. Background Technology

[0002] With the growth of electricity demand and the adjustment of energy structure, traditional power distribution networks face many challenges, including the upgrading of aging facilities, the management of load fluctuations, the integration of renewable energy, and the continuous improvement of network reliability and efficiency.

[0003] Traditional power distribution network investment decisions are often based on rules of thumb or static methods based on simulation optimization, mainly focusing on static optimization, dynamic programming, and probabilistic analysis. Static optimization methods are typically based on fixed load conditions and equipment states, failing to adequately consider dynamic changes in the network. While dynamic programming methods consider the time factor, they often face high computational complexity and difficulty in solving. Probabilistic analysis methods, although able to account for uncertainties, lack overall optimization for multi-period investment decisions. Therefore, existing technologies cannot comprehensively consider the dynamic characteristics of power distribution networks, multi-period investment decisions, and uncertainties to formulate a comprehensive optimal investment strategy. Summary of the Invention

[0004] The technical problem to be solved by the present invention is to provide a distribution network planning method and apparatus based on mixed integer programming, so as to realize the comprehensive consideration of various factors of the distribution network and formulate a comprehensive optimal investment strategy.

[0005] To solve the above-mentioned technical problems, the technical solution adopted by the present invention is as follows:

[0006] A power distribution network planning method based on mixed-integer programming includes:

[0007] Obtain the topology, equipment information, and load characteristics of the power distribution network;

[0008] The investment method is used as an input parameter, and a hybrid model is constructed based on the topology, equipment information, and load characteristics.

[0009] Obtain a preset problem matrix, and combine the preset problem matrix with the hybrid model to obtain the optimal investment objective function;

[0010] Construct an uncertainty function based on the uncertainty of power distribution network planning;

[0011] By adjusting the variables in the optimal investment objective function based on the uncertainty function, a mixed-integer optimization model is obtained.

[0012] The optimal investment approach and corresponding best profit are obtained by solving the mixed integer optimization model using a greedy algorithm.

[0013] To solve the above-mentioned technical problems, another technical solution adopted by the present invention is as follows:

[0014] A power distribution network planning device based on mixed integer programming includes a memory, a processor, and a computer program stored in the memory and executable on the processor. When the processor executes the computer program, it implements the various steps of the power distribution network planning method based on mixed integer programming as described above.

[0015] The beneficial effects of this invention are as follows: By establishing a mixed-integer optimization model that includes variables such as network state, equipment state, and cost function, the model takes into account network topology constraints, equipment operating limitations, and the impact of investment decisions, ensuring that the model can accurately describe the operation and development of the power distribution network; at the same time, by introducing practical factors such as load demand and market changes, and by describing the uncertainty of these practical factors based on an uncertainty function, the model can more accurately assess risks and adjust investment strategies, thereby improving the reliability and robustness of investment decisions; finally, by using a greedy algorithm for solving the problem, the solution efficiency is improved. Attached Figure Description

[0016] Figure 1 This is a flowchart illustrating the steps of a power distribution network planning method based on hybrid integer programming in an embodiment of the present invention.

[0017] Figure 2 This is a schematic diagram of a power distribution network planning device based on hybrid integer programming in an embodiment of the present invention. Detailed Implementation

[0018] To explain in detail the technical content, objectives, and effects of the present invention, the following description is provided in conjunction with the embodiments and accompanying drawings.

[0019] In the operation and management of power distribution networks, investment decision-making is a crucial step in achieving sustainable development and optimal operation. However, traditional investment decision-making methods often fail to fully consider multi-period, dynamic, and uncertain factors, leading to potentially unscientific and unreliable decision results. This invention aims to solve the technical problems existing in power distribution network investment decision-making, specifically as follows:

[0020] Multi-period investment decision-making problems: Traditional static optimization methods cannot effectively handle long-term investment decision-making problems, while dynamic programming methods face the challenge of high computational complexity. Therefore, how to formulate the optimal investment strategy over multiple periods to ensure the sustainability and maximization of benefits in the long-term development of the network is a key issue worthy of research.

[0021] Dynamic Issues: The dynamic nature of the power distribution network's operating environment necessitates that investment decisions consider factors such as load changes and equipment lifespan evolution. Traditional methods often struggle to fully account for the network's actual operating conditions. Therefore, effectively mitigating the challenges posed by network dynamism to investment decisions and ensuring the flexibility and effectiveness of investment solutions is a crucial issue.

[0022] Uncertainty Issues: Various uncertainties exist in the operation of power distribution networks, such as fluctuations in future load demand and changes in market prices. These factors bring risks and challenges to investment decisions. Therefore, how to consider these uncertainties and make corresponding adjustments during the investment planning process to improve the risk control capability and feasibility of investments has become a challenging issue that needs to be addressed.

[0023] To solve the above-mentioned technical problems, the technical solution adopted by the present invention is as follows:

[0024] Please refer to Figure 1 A distribution network planning method based on mixed-integer programming includes:

[0025] Obtain the topology, equipment information, and load characteristics of the power distribution network;

[0026] The investment method is used as an input parameter, and a hybrid model is constructed based on the topology, equipment information, and load characteristics.

[0027] Obtain a preset problem matrix, and combine the preset problem matrix with the hybrid model to obtain the optimal investment objective function;

[0028] Construct an uncertainty function based on the uncertainty of power distribution network planning;

[0029] By adjusting the variables in the optimal investment objective function based on the uncertainty function, a mixed-integer optimization model is obtained.

[0030] The optimal investment approach and corresponding best profit are obtained by solving the mixed integer optimization model using a greedy algorithm.

[0031] As described above, the beneficial effects of this invention are as follows: By establishing a mixed-integer optimization model that includes variables such as network state, equipment state, and cost function, the model takes into account network topology constraints, equipment operating limitations, and the impact of investment decisions, ensuring that the model can accurately describe the operation and development of the power distribution network; at the same time, by introducing practical factors such as load demand and market changes, and by describing the uncertainty of these practical factors based on an uncertainty function, risks can be assessed more accurately and investment strategies adjusted, improving the reliability and robustness of investment decisions; finally, a greedy algorithm is used for solving the problem, improving the solution efficiency.

[0032] Furthermore, the step of using the investment method as an input parameter and constructing a hybrid model based on the topology, equipment information, and load characteristics includes:

[0033]

[0034] Where Y = {0, 1, ..., N} is the set of time periods, and i ∈ Y represents the index of the time period; determine continuous input. Indicated in each region The funds invested in maintenance It is a finite set of distribution network areas; The input is in binary format, indicating whether a network upgrade is necessary. This represents the investment in the region from the initial time period to the i∈Y year. Funding for localized improvements; binary state Indicates whether the line upgrade was completed before time period i∈Y; ∨ is a logical OR; This represents a set of investment issues.

[0035] As described above, by taking the funds used for maintenance and network upgrade decisions in each region as inputs, and combining them with the investment problem set to describe the changes in regional funds and lines, the model can accurately describe the operation and development of the power distribution network.

[0036] Furthermore, it also includes identifying the set of investment issues:

[0037]

[0038]

[0039] Among them, l ij ΔL represents the minute-by-minute loss value for user j in region i within time period i, with the subscript 0 indicating the initial loss; lj The quality growth of region j is represented by f; f is an affine function. Represents the coefficients of the function; Funds for phased investment are The specific values ​​of j are as follows: the subscript j represents the region, and the superscripts 1, 2, 3, and 4 represent the number of segments in the piecewise function. Indicates the cost of investment l; U max It is the maximum amount that can be invested each year (i).

[0040] As described above, by using the minute loss values ​​of users in corresponding regions at different time periods, and by linking the improvement in quality with the funds invested in each region through affine functions, it is possible to more accurately predict the relationship between the invested funds and the improvement in power grid quality.

[0041] Furthermore, the step of obtaining a preset problem matrix and combining the preset problem matrix with the hybrid model to obtain the optimal investment objective function includes:

[0042]

[0043] Where c, f, A, b, W, h, and T represent different preset problem matrices; u is the decision variable, including all z is an auxiliary variable.

[0044] As can be seen from the above description, by describing the actual problems such as future load demand and market changes during the operation of the power grid based on a variety of different preset problem matrices, the model can achieve sustainable development and maximum benefits of the network.

[0045] Furthermore, by adjusting the variables in the optimal investment objective function according to the uncertainty function, a mixed-integer optimization model is obtained;

[0046]

[0047] Where, f(E) i ), T(E i ), W(E i ), h(E i ) represents the functional form related to the uncertainty Ei; Q represents the probability quantity of the uncertain variable; z i Let be the auxiliary variable for the i-th uncertain scenario.

[0048] As described above, using stochastic programming to address uncertainty in investment decisions and introducing probability distribution functions to analyze real-world issues such as future loads and market prices in an uncertain manner can more accurately assess risks and adjust investment strategies, thereby improving the reliability and robustness of investment decisions.

[0049] Furthermore, an uncertainty function is constructed based on the uncertainties in power distribution network planning:

[0050] Obtain random variables that are related to the uncertainty of the relationship between investment methods and user minute costs;

[0051] Sample each of the random variables to obtain the number of possible values ​​for each random variable;

[0052] The probability number of the uncertain variable is obtained by multiplying the number of possible values ​​corresponding to each random variable.

[0053] As described above, by sampling each random variable to obtain the number of its corresponding possible values, and then based on the number of possible values ​​of each random variable, the probability of uncertain variables is obtained, thereby covering all possible uncertain scenarios.

[0054] Furthermore, the step of solving the mixed-integer optimization model using a greedy algorithm to obtain the optimal investment method and the corresponding best profit includes:

[0055] An optimality index is obtained based on the ratio between profit and investment cost, and additional investment is generated based on the optimality index.

[0056] In each iteration of the greedy algorithm, the additional investment is added to the current solution, and the cost of the additional investment is subtracted from the remaining budget.

[0057] The mixed-integer optimization model is solved based on investment constraints until the solution no longer optimizes.

[0058] As described above, by adding additional investment to the current solution in each iteration of the greedy algorithm, it is possible to effectively determine whether the current solution is the optimal solution.

[0059] Furthermore, the investment constraints include:

[0060]

[0061] in, For regional indexes.

[0062] As described above, by solving for each region j where the investment is yet to be determined, under the condition of satisfying the investment constraints, the optimal solution can be obtained.

[0063] Furthermore, the optimality index obtained based on the ratio between profit and investment cost includes:

[0064]

[0065] Among them, I j (k) represents the optimality index; Let r represent the profit of the optimal investment that can be completed in region j during the k-th iteration; r is the discount rate.

[0066] As described above, the optimality index evaluates the profit of the best investment that can be completed in region j, as well as the remaining budget after k-1 iterations, so that in each iteration, the current solution and budget can be updated by selecting the investment project with the maximum optimality index.

[0067] Another embodiment of the present invention provides a power distribution network planning device based on mixed integer programming, including a memory, a processor, and a computer program stored in the memory and executable on the processor. When the processor executes the computer program, it implements the various steps of the power distribution network planning method based on mixed integer programming as described above.

[0068] The distribution network planning method and apparatus based on mixed integer programming provided by this invention can be applied to power grid investment planning scenarios. The following detailed embodiments illustrate this method:

[0069] Example 1

[0070] Please refer to Figure 1 A distribution network planning method based on mixed-integer programming includes:

[0071] S1. Obtain the topology, equipment information, and load characteristics of the power distribution network;

[0072] S2. Using investment method as input parameter, and constructing a hybrid model based on topology, equipment information, and load characteristics; using data such as the topology, equipment information, and load characteristics of the distribution network, establish a mixed integer optimization model that includes variables such as network status, equipment status, and cost function; the model takes into account the network topology constraints, equipment operating limitations, and the impact of investment decisions to ensure that the model can accurately describe the operation and development of the distribution network.

[0073] Specifically, an optimal control problem is first established to determine the optimal allocation of maintenance and upgrade investments for the power distribution network on a multi-cycle time basis. The distribution network is treated as a large-scale discrete-time dynamic system with a sampling time of one year (decision is made on an annual basis). Its state is defined as the quality of energy supply in each region, and its input is the amount of investment in that region in a given year. The optimal investment decision depends on the prediction of the network quality evolution over a certain number of N years. According to the rolling time domain principle, the prediction is repeated once a year, moving forward one year on the horizon of a multi-year period.

[0074] In each time interval i∈Y, Y={0,1,…,N}, the continuous input is determined. This input is in each region The funds invested in maintenance; and binary input This input determines whether a network upgrade is necessary (1 for a network upgrade, 0 for no upgrade). Therefore, the equations determining the system dynamics are:

[0075]

[0076] in, It is a finite set of distribution network areas; This represents the investment in the region from the initial time period to the i∈Y year. Funding for partial improvements; ∨ is logical OR.

[0077] Furthermore, This represents a set of investment problems, where the l-th investment is defined by the investment cost and the quality increase in each affected region. (Binary state) This indicates whether the line upgrade was completed before time period i∈Y (1 indicates completed, 0 indicates not completed). The cost of investment l is used for... The quality growth of region j is represented by ΔL. lj Indicate; l ij This represents the minute-by-minute loss value for user j in region i during time period i, with the subscript 0 indicating the initial loss, described in the following form:

[0078]

[0079]

[0080] The affine function f links the improvement in quality to the funds invested in each region. These represent function coefficients (coefficients are constants and have no specific physical meaning; the specific values ​​of the parameters can be determined by fitting the function parameters based on historical data); Funds for phased investment are The specific values ​​of j are as follows: the subscript j represents the region, and the superscripts 1, 2, 3, and 4 represent the number of segments in the piecewise function.

[0081] The dynamics of each region j are coupled only through binary upgrade decisions, with the other coupling arising from the constraint on the capital that can be invested in each time period i, namely:

[0082]

[0083] U max It is the maximum amount that can be invested each year (i).

[0084] S3. Obtain the preset problem matrix and, based on the hybrid model, combine the preset problem matrix to obtain the optimal investment objective function. That is, based on the hybrid integer optimization model established in step S2, use optimal control theory to determine the best investment strategy over multiple periods; by considering factors such as future load demand and market changes, formulate investment plans for consecutive periods to achieve sustainable network development and maximum benefits; the optimal control problem providing the required investment allocation can be redefined as the following optimization problem, with the specific expression as follows:

[0085]

[0086] Where c, f, A, b, W, h, and T represent different preset problem matrices (depending on the actual problem parameters and the system model); the model parameters in this embodiment are the system's own parameters, which can be determined based on the system's own parameters and manually set parameters; for example, the constraint Au≤b in equation (5) corresponds to equation (4); u is the decision variable, including all A is a coefficient, corresponding to the value in equation (4). b is a coefficient, corresponding to U in equation (4). max The other parameters are similar. z is an auxiliary variable, a virtual decision variable that can be considered to have the same function as u, but u has a specific physical meaning, while z is a virtual auxiliary variable set up only to introduce the previously constructed piecewise function f. It has no actual physical meaning itself, but by introducing function f, it is incorporated into the optimization problem, realizing the role of evaluating dynamics and cost functions. For example, in this embodiment, the affine function f links the improvement in quality to the funds invested in each region. Therefore, in addition to considering the original decision variable u, the optimization problem also considers the meaning represented by f. That is, the optimization variables u and z are subdivided into two categories: "actual" decision variables. It constitutes the investment strategy within the forecast range; and an auxiliary variable z, which is introduced to evaluate the dynamics and cost functions.

[0087] S4. Construct an uncertainty function based on the uncertainty of power distribution network planning. In actual power distribution network planning, numerous issues in production planning and scheduling, site selection, transportation, finance, and engineering design require decisions to be made under conditions of uncertainty. In the problem addressed in this embodiment, uncertainty affects the function between supply quality and funds invested in improvement projects. Therefore, this embodiment innovatively adopts stochastic programming to handle the uncertainty problem in investment decisions, introducing a probability distribution function to describe uncertainty factors, so as to more accurately assess risks and adjust investment strategies, thereby improving the reliability and robustness of investment decisions.

[0088] Since the quality improvement resulting from an investment project is difficult to predict, the user-minute cost in each region is subject to uncertainty, meaning the model (1)-(2) constructed in step S2 is uncertain. Therefore, all variables (and constraints) defined to evaluate profit are subject to uncertainty, depending on the quality level of each region and period. Stochastic programming optimizes the average cost function while considering causality, which means that the available funds must be invested before the true effect of the investment project is known, i.e., before the values ​​of the random variables and the actual evolution of the user-minute cost in each region are known.

[0089] Constructing an uncertainty function involves the following steps: obtaining random variables, which are associated with the uncertainty of the relationship between investment methods and user minute costs; sampling each random variable to obtain the number of possible values ​​for each random variable; and obtaining the probability of the uncertain variable by multiplying the number of possible values ​​for each random variable. For example, variable E = {ξ} i ,ξ l Collect all random variables associated with the uncertainty of the relationship between improvement / upgrade investment and user minute costs; for each independent continuous distribution ξ i,l Sampling is performed, ξ j,l The general formula for representing random variables is ξ, but the specific form depends on the actual random variable. If there is only one type of index value, it is represented as: ξ i or ξ l If there are two index values, it is represented as ξ. i,l The number q of possible values ​​for each uncertain variable determines the complexity of the stochastic optimal control problem; the number q is determined according to the specific physical meaning of the random variable. For example, for equipment upgrades, the variable includes two cases: upgrade and no upgrade, so the number of possible values ​​for this variable is q = 2. Since each variable is independent, the uncertain variable E can be expressed with probabilities p1, ..., p... Q The values ​​are E1, ..., E Q , where Q = q D+I The probability quantity Q of the uncertain variable is a combination of different quantities of the variable, and therefore is the product of the possible values ​​q of each variable; D is the total number of regions, and I is the number of time periods. The set of regions and the set of time periods have been defined above.

[0090] S5. Adjust the variables in the optimal investment objective function according to the uncertainty function to obtain the mixed integer optimization model. Specifically: for each fixed uncertainty E i This is called a scenario; all problem parameters f(E) i ), T(E i ), W(E i ), h(E i All are fixed. Problem parameters refer to matrices f, T, W, and h in formula (5), which represent system parameters. However, due to the presence of uncertainty, they are expressed as functions related to the uncertainty Ei. By listing all possible Q scenarios, a large-scale mixed integer linear programming (MILP) problem is proposed. For each scenario, a set of auxiliary variables z is assigned. i However, this problem actually only optimizes one set of decision variables u, and the equivalent MILP problem is described as follows:

[0091]

[0092] Q represents the probability quantity of the uncertain variable; z i Let be the auxiliary variable for the i-th uncertain scenario. After reducing the number of scenarios in each smaller subproblem related to a single region, the stochastic equivalence problem of the optimization problem (5) can be solved using the MILP model (6), thus obtaining a feasible suboptimal investment policy that takes into account the uncertainty of each investment project.

[0093] S6. Solve the mixed-integer optimization model using a greedy algorithm to obtain the optimal investment method and corresponding best profit. Given the computational challenges of complex problems, a heuristic solution is introduced to improve solution efficiency. By optimizing algorithm design and heuristic search strategies, a fast and feasible solution is provided for large-scale problems, optimizing the solution process for multi-period dynamic investment decisions. The heuristic algorithm used in this embodiment is a greedy algorithm. This algorithm starts with a simple solution, iteratively changes the relevant variables, and each time selects the variable that achieves the maximum immediate improvement in the objective function. Furthermore, once the value of a variable is fixed, it will not be changed again.

[0094] In each iteration k of the greedy algorithm, an additional investment U is added to the current solution, and the cost of U is subtracted from the remaining budget. Simultaneously, the additional investment U is selected based on an optimality index, which is the ratio between the corresponding profit and the investment cost U. Investments with an optimality index are selected from local improvement projects in each region and different network upgrades. For each region j where the investment is not yet determined, the obtained profit and the corresponding optimal investment are obtained by solving (5) / (6) under the following additional constraints:

[0095]

[0096] in, For regional indexes.

[0097] This problem evaluates the profit of the optimal investment that can be completed in region j. And the remaining budget after k-1 iterations; then, the optimality index I of the investment options in region j. j (k) is given by the following formula:

[0098]

[0099] Among them, I j (k) represents the optimality index; Let r represent the profit of the optimal investment that can be completed in region j during the k-th iteration; r is the discount rate.

[0100] This optimization problem is easy to solve because most decision variables (i.e., the system inputs) are fixed; since the dynamics of each region are independent, the problem can be solved by considering only the variables and constraints of that region; in each iteration, the investment project with the maximum optimality index is selected, and the current solution and budget are updated as follows:

[0101]

[0102] If there is I j (k)=I * (k), then we have:

[0103]

[0104] Run the iterative algorithm until the solution no longer optimizes, i.e., J profit (k) = (k-1); feasible suboptimal solution is derived from Provided.

[0105] Example 2

[0106] Please refer to Figure 2 A power distribution network planning device based on mixed integer programming includes a memory, a processor, and a computer program stored in the memory and executable on the processor. When the processor executes the computer program, it implements the various steps in the power distribution network planning method based on mixed integer programming as described in Embodiment 1.

[0107] In summary, the power distribution network planning method and apparatus based on mixed integer programming provided by this invention have the following advantages compared with traditional investment decision-making methods, which often can only deal with single-period static problems and are difficult to fully consider multi-period, dynamic, and uncertain factors:

[0108] 1. It combines mixed integer programming, optimal control theory and stochastic programming ideas, and can comprehensively and dynamically formulate multi-period investment strategies and make adjustments under uncertain conditions, considering investment decisions from an overall and long-term perspective.

[0109] 2. By introducing optimal control theory and heuristic solutions, optimal investment strategies can be formulated based on multi-period dynamic information, improving the scientific nature and robustness of decision-making. At the same time, by using stochastic programming to handle uncertainties, the risk control capability of investment decisions can be further improved, ensuring the reliability and effectiveness of decisions.

[0110] 3. Introducing heuristic solutions and optimization algorithms can effectively improve the efficiency of problem solving, shorten decision-making time, and reduce decision-making costs. In particular, for large-scale and complex problems, this technical solution has higher feasibility and practicality, and helps to achieve fast and effective investment decisions.

[0111] 4. With scientific and comprehensive investment decision support, distribution network managers can better optimize network operation, improve efficiency, and achieve sustainable network development. Based on multi-phase dynamic investment planning, the distribution network can better adapt to future development needs, ensuring stable network operation and maximizing profits.

[0112] The above description is merely an embodiment of the present invention and does not limit the patent scope of the present invention. Any equivalent modifications made based on the content of the present invention specification and drawings, or direct or indirect applications in related technical fields, are similarly included within the patent protection scope of the present invention.

Claims

1. A method of power distribution network planning based on mixed integer programming, characterized in that, The method comprises: acquiring a topology structure, device information and load characteristics of a power distribution network; taking an investment mode as an input parameter and constructing a mixed model according to the topology structure, device information and load characteristics; acquiring a preset problem matrix and obtaining an optimal investment objective function by combining the preset problem matrix on the basis of the mixed model; constructing an uncertainty function according to uncertainty of power distribution network planning; adjusting variables in the optimal investment objective function according to the uncertainty function to obtain a mixed integer optimization model; solving the mixed integer optimization model by a greedy algorithm to obtain an optimal investment mode and a corresponding best profit; the taking of the investment mode as the input parameter and the constructing of the mixed model according to the topology structure, device information and load characteristics comprise: ； wherein, is a set of time periods, denotes a time period index; determines consecutive inputs , denotes the funds invested for maintenance in each region , is a finite set of distribution network regions; is a binary input denoting the decision whether a network upgrade has to be implemented or not; denotes the funds invested in the local improvement of region in the first years; binary state denotes whether the line upgrade has been completed before time period ; is a logical OR; denotes a set of investment problems; the method further comprises determining the investment problem set: ； ； ； wherein, denotes i the user minute loss value in the time period under consideration, the subscript 0 denotes the initial loss; j denotes the quality increase in the region under consideration, the subscript 0 denotes the initial quality; j denotes the quality increase in the region f under consideration, the subscript 0 denotes the initial quality; , , , denotes the function coefficient; , , , is the investment fund in the segment, is the specific value of , the subscript j denotes the region, the superscripts 1, 2, 3, 4 denote the number of segments of the piecewise function; denotes the cost of the investment l ; U max is the maximum amount that can be invested per i year; the acquiring of the preset problem matrix and the obtaining of the optimal investment objective function by combining the preset problem matrix on the basis of the mixed model comprise: ； wherein, c , f , A , b , W , h , T denote different pre-set problem matrices; u is the decision variable, including all ; z is an auxiliary variable; the adjusting of the variables in the optimal investment objective function according to the uncertainty function to obtain the mixed integer optimization model; ； wherein, , , , represents a function form related to uncertainty E i ; Q represents the uncertain variable probability number; z i is the auxiliary variable for the i th uncertain scenario.

2. A method of power distribution network planning based on mixed integer programming according to claim 1, characterized in that, constructing an uncertainty function according to uncertainty of power distribution network planning: acquiring random variables, the random variables being associated with uncertainty of a relationship between the investment mode and user minute cost; sampling each random variable to obtain a possible value number corresponding to each random variable; obtaining the uncertainty variable probability number according to a product of the possible value number corresponding to each random variable.

3. The method of claim 1, wherein, the solving of the mixed integer optimization model by the greedy algorithm to obtain the optimal investment mode and the corresponding best profit comprise: obtaining an optimality index according to a ratio between profit and investment cost, and generating additional investment according to the optimality index; adding the additional investment to a current solution in each iteration of the greedy algorithm and subtracting a cost of the additional investment from a remaining budget; solving the mixed integer optimization model based on investment constraints until the solution is no longer optimized.

4. A method of power distribution network planning based on mixed integer programming according to claim 3, characterized in that, the investment constraints comprise: ； wherein is a region index.

5. A method of power distribution network planning based on mixed integer programming according to claim 3, characterized in that, the obtaining of the optimality index according to the ratio between the profit and the investment cost comprises: ； wherein, represents the optimality index; represents the profit of the optimal investment that can be completed by the kth iteration of the kth region; j r is the discount rate.​ 6. A power distribution network planning apparatus based on mixed integer programming, comprising a memory, a processor, and a computer program stored on the memory and executable on the processor, characterized in that, the processor implements each step of the power distribution network planning method based on mixed integer programming according to any one of claims 1-5 when executing the computer program.

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