A substation planning distributed robust optimization method and system considering incentive response uncertainty

Abstract

The application provides a substation planning distribution robust optimization method and system considering incentive response uncertainty. First, the signing cost, response cost and penalty income of the incentive demand response are comprehensively considered, and a substation site selection and capacity determination mixed integer linear programming model is established. Second, the response power uncertainty fuzzy set based on 1-norm and infinity-norm is constructed, and on the basis of improvement of the mixed integer linear programming model, a substation planning distribution robust optimization model considering the uncertainty of the incentive response is established. Finally, the model is decomposed into a main problem and a subproblem, and an iteration solving method of the distribution robust optimization model based on column and constraint generation is proposed. The method provided by the application uses the distribution robust optimization model, can fully consider the randomness of the user demand response, and can consider the load characteristic matching in the model, effectively reduces the peak value of the substation load curve, and guarantees the economy and robustness of the planning scheme.

Description

Technical Field

[0001] This invention belongs to the field of power distribution network planning and relates to a substation planning sub-bar optimization method and system that takes into account the uncertainty of excitation-type response. Background Technology

[0002] In recent years, my country's energy transition strategy has been rapidly advancing, and the electrification of end-use energy sources has been continuously improving, leading to a year-on-year increase in peak loads on distribution networks and placing enormous pressure on substation planning and investment. Demand response is an effective means to address this issue. However, while demand response can reduce peak loads to some extent, its response is subject to uncertainty due to the influence of human decision-making factors. How to meticulously consider demand response and its uncertainties in substation planning is a crucial issue that urgently needs to be addressed.

[0003] Substation planning involves substation site selection, capacity determination, and power supply range allocation. It is a large-scale nonlinear optimization problem with multiple types of decision variables. Early planning methods mainly included heuristic methods and hierarchical decoupling methods. Heuristic methods can obtain optimal or near-optimal solutions when solving large-scale problems, but they are prone to getting trapped in local optima. Furthermore, the power supply range allocation often adopts proximity allocation, leading to unreasonable planning and problems such as excessively low or high load rates. The essence of hierarchical decoupling methods is to decouple the large-scale nonlinear problem into two layers of sub-problems. For each candidate capacity combination scheme generated by the upper layer, site selection and power supply range allocation are implemented. However, the capacity combination schemes generated by this method may not be fully enumerated.

[0004] Many studies have incorporated demand response into substation planning, which can improve the overall load characteristics of substations and reduce planning investment costs. However, none of these studies have considered the uncertainty of demand response, potentially leading to insufficient investment in the target year. Regarding the consideration of uncertainties in substation planning, some studies use stochastic optimization methods to model the uncertainties in the location and magnitude of the target year's load forecast, as well as the uncertainty of photovoltaic output. However, this method requires known probability distributions of uncertainties, which are difficult to obtain in practical applications, thus leading to insufficient investment in the target year. Other studies employ robust optimization methods to handle uncertainties, considering the probability distribution of uncertainties under the worst-case scenario, but the resulting planning schemes tend to be conservative. In recent years, the advantages of distributed robust optimization in handling uncertainties have gradually attracted attention. It combines the characteristics of stochastic and robust optimization, and the optimization results show good performance in terms of both economy and conservatism. Summary of the Invention

[0005] The technical problem to be solved by this invention is how to establish a mathematical model for substation planning that takes into account demand response and its uncertainty, and solve it using mathematical programming methods. This overcomes the tendency of traditional substation planning methods to fall into local optima while ensuring the economy and robustness of the resulting planning scheme.

[0006] The present invention solves the above problems through the following technical means.

[0007] A substation planning subbulb optimization method considering the uncertainty of excitation-type response, characterized by the following specific steps:

[0008] Step 1: Taking into account the contracting cost, response cost, and penalty benefits of demand response, establish a mixed integer linear programming model for substation site selection that takes into account incentive-based demand response.

[0009] Step 2: Construct a response power uncertainty fuzzy set based on 1-norm and ∞-norm, and establish a two-stage three-layer sub-Bruker optimization model based on multiple discrete scenarios based on the improvement of the mixed integer linear programming model;

[0010] Step 3: For this sub-Bruker optimization model, we propose an iterative algorithm for the main problem and sub-problems based on column and constraint generation.

[0011] Furthermore, the establishment of the mixed-integer linear programming model described in Step 1 includes: 1) the demand response cost model of the power grid company.

[0012] The power supplier and user first sign a contract, specifying the maximum power that the user can respond to during the contract period, the contracted capacity P1, and incurring contract costs. During the operation of the distribution network, the power supplier issues a response command to the user in advance for peak electricity consumption, and the user responds with the command at a power P1. t The cumulative response cost; the portion of the user's response power that is less than the instruction requirement is the default power P. t，f This generates cumulative penalty revenue. The formula for calculating the demand response cost paid annually by the power grid company to a single user is as follows:

[0013]

[0014] Among them, C DR σ1, σ2, and σ3 are the unit prices of contract cost, response cost, and penalty revenue, respectively; P is the maximum load of the user; λ is the ratio of the user's maximum contractable capacity to its maximum load, representing the load's ability to participate in demand response.

[0015] 2) Substation planning model considering demand response

[0016] The purpose of substation planning is to minimize the investment and construction costs of substations and main lines while meeting the target annual load electricity demand and various planning constraints, and also to consider various costs related to demand response.

[0017] a) Decision variables: Decision variables include substation location and capacity selection, load-substation connection relationship, demand response contracted capacity, and response power for each time period, x is Let y be a Boolean variable representing whether the i-th substation location is selected for the s-th substation type. Each candidate substation type corresponds to a different substation capacity. An option with a capacity of 0 is added to the candidate substation types. If a substation location is selected for a 0-capacity type, it means that the location has not been chosen for substation construction. This unifies the location selection and capacity selection variables, resolving the non-linearity issue caused by the need to multiply these two variables in substation construction cost calculation; ij This is a Boolean variable indicating whether the location of the i-th substation is connected to the j-th load. Let be a continuous variable, representing the contracted demand response capacity of the j-th load. Let be a continuous variable, representing the response power of the j-th load during time period t;

[0018] b) Objective function:

[0019] minC=C S +C L +C DR1 +C DR2

[0020]

[0021]

[0022]

[0023]

[0024] Where: C represents the total cost; C S C L C DR1 and C DR2 These represent the annual construction costs of substations, annual construction costs of transmission lines, contracted demand response costs, and demand response costs, respectively; r0 is the discount rate; ms is the depreciation period of the transformer; N P N represents the number of candidate locations for the substation. S C represents the number of candidate substation types. Ss β is the construction cost of the s-th candidate substation type; β is the unit cost coefficient of the line; ml is the depreciation period of the line; N L d represents the number of load points. ijP represents the distance from substation i to load j. j σ represents the maximum load at the j-th load point; j,1 and σ j,2 These are the unit prices of the demand response contract cost and response cost for the j-th load, respectively;

[0025] c) Constraints:

[0026] Uniqueness constraint for substation capacity selection. Only one substation type can be selected for a given substation location:

[0027]

[0028] Load point attribution uniqueness constraint. When dividing the power supply area, each load point corresponds to one and only one upstream substation.

[0029]

[0030] Maximum power supply radius constraint, r max The maximum power supply radius for medium-voltage lines as specified in the power supply and distribution design code is:

[0031] y i,j d ij ≤r max i∈[1,N P ],j∈[1,N L ]

[0032] The N-1 safety constraint for substations, based on the principle of safe operation of the power grid, requires that after the failure of any transformer in the substation, the remaining transformers must be able to operate for 2 hours to supply all loads within their power supply range. The maximum load rate e of the substation during normal operation is also required. s The following inequality constraints apply:

[0033]

[0034] In the formula, J i P represents the load set within the power supply range of the i-th substation; j,t Let be the power of the j-th load during time period t; S is the power factor of the j-th load; s The capacity of the s-th candidate substation type;

[0035] Demand response constraints: The contracted demand response capacity at each load point cannot exceed its maximum response capacity, and the runtime user response capacity cannot exceed the contracted capacity.

[0036]

[0037]

[0038] Furthermore, the steps for constructing the robust optimization model described in Step 2 include:

[0039] 1) Constructing an uncertain fuzzy set of demand response

[0040] Considering the uncertainty of user intentions, the actual response result P t There is a deviation from the grid demand response command, and P t Modeling a fuzzy set whose uncertainty fluctuates within a certain range:

[0041] First, multiple real-world scenarios are obtained through historical data. Then, N scenarios are selected through scenario clustering. k A finite discrete scenario and the probability distribution p under each scenario k,0 Furthermore, considering that these scenarios do not represent the actual probability distribution, we construct confidence sets based on the 1-norm and ∞-norm to constrain the fluctuations in the probability distribution:

[0042]

[0043]

[0044]

[0045]

[0046] Among them, Ψ1 and Ψ ∞ Let P represent the confidence intervals restricted by the 1-norm and ∞-norm, respectively; P is the scenario probability p. k The vector form; P0 is the initial probability p of each scenario. k,0 The vector form; For P to correspond to N k A vector consisting of _n positive real numbers; K is the number of sample scenarios; α1 and α ∞ They are Ψ1 and Ψ respectively ∞ The confidence level is determined by the probability distribution. Therefore, the confidence set is constrained by both the 1-norm and the ∞-norm, avoiding overly extreme cases, where Ψ=Ψ1∩Ψ. ∞ ,Right now:

[0047]

[0048] 2) Two-stage sub-Brussels bar optimization model considering response power uncertainty

[0049] The demand response uncertainty considered refers to the fact that users cannot fully meet their response requirements when they receive a response instruction. The response power is uncertain, resulting in default power. Therefore, the demand response cost C during the operation phase... DR2 The calculation formula should be rewritten as follows:

[0050]

[0051] Meanwhile, demand response uncertainty will change the actual response power, causing fluctuations in the load curve within the substation's power supply range, which in turn affects the substation's N-1 safety constraint. The constraint formula should be rewritten as follows:

[0052]

[0053] Uncertainty in user demand response occurs during the operational phase and subsequently affects the planning phase. Therefore, considering uncertainty, the planning model can be decomposed into two phases: the first phase is the planning phase, where decision variables include the relationship between substation location and capacity selection, the connection relationship between load and substation, and the contracted demand response capacity; the second phase is the operational phase, where the decision variable is the user's response power, but the actual response power is uncertain. The decision variables in the first phase include x. is y ij and Let vector x represent the decision variables in the second stage. Let d represent this. Therefore, the discrete-scene-based split-bar model can be expressed as follows:

[0054]

[0055] Where: a T b is the linear coefficient matrix of the objective function in the first stage; T N is the linear coefficient matrix of the objective function in the second stage; k Let p represent the total number of discrete scenarios representing the probability distribution, k be the number of each scenario, and p be the number of the discrete scenarios. k Let represent the probability in scenario k. The constraint condition is transformed into the following form:

[0056]

[0057] Where: C, E, F, G, H, m, n, u, v represent the matrix or vector forms of the variables mentioned above; the first two formulas correspond to the equality and inequality constraints of the variables in the first stage; the third inequality constraint is the capacity coupling inequality between the variables in the first stage and the variables in the second stage; and the last inequality constraint corresponds to the demand response inequality constraint in the second stage.

[0058] Furthermore, the iterative algorithm described in Step 3 includes:

[0059] Based on the constraint generation algorithm, the model is decomposed into a main problem (MP) and a subproblem (SP). The optimal solution is then obtained iteratively. The purpose of solving MP is to obtain the optimal planning scheme that satisfies the known probability distribution constraints under finite discrete scenario conditions. The objective function and constraints of MP are described as follows:

[0060]

[0061]

[0062] Where L represents the lower-level demand response operating cost, and the superscript r indicates the r-th iteration. Except for the first iteration, the probability distribution of each subsequent iteration is obtained by solving the SP problem. Solving the MP problem yields a globally optimal solution C. * and the corresponding planning decision variable x * ；

[0063] The purpose of solving SP is to optimize the results of MP. * Given the substation capacity, power supply range, and contracted demand response capacity, the load timing characteristics and demand response characteristics are matched to find the worst-case probability distribution P of the response power. k Then, this distribution is provided to MP for the next iterative calculation, while based on the obtained L(x) * To update the global optimum, the objective function of SP can be described as follows:

[0064]

[0065] As can be seen from the above formula, the min problem in each scenario is independent and can be computed simultaneously using parallel methods. For example, the internal optimization result for the k-th scenario is... The objective function of SP can then be transformed into:

[0066]

[0067] The MP and SP problems described above are solved using the MILP model and the linear programming model, respectively, and the optimization result P of the SP problem is calculated. k The solution is passed to MP for iterative computation until the globally optimal solution C is obtained from two consecutive iterations. * The iteration stops when the difference is less than a specified threshold, and the optimal planning cost and decision variable values ​​are obtained.

[0068] A substation planning sub-Browser optimization system considering excitation-induced response uncertainty, characterized in that the system comprises:

[0069] (1) Data input and processing module, used to perform matrix processing on the input load forecast data and various planning parameter information;

[0070] (2) The main problem solving module obtains the optimal planning scheme and planning layer decision variables that satisfy the known probability distribution constraints under the condition of finite discrete scenarios;

[0071] (3) Sub-problem solving module: fix the decision variables of the planning layer obtained by the main problem solving module, solve the decision variables of the operation layer with the goal of minimizing the operating cost, and find the worst probability distribution of the response power.

[0072] Furthermore, the system also includes the following modules:

[0073] The initialization module is used to iteratively solve the initialization settings of the parameters, and to calculate the corresponding robust scene probability by intervening in the algorithm with known scene probabilities, thereby forming an iteration;

[0074] The decision module is used to determine whether the planning results have converged and whether the iterative solution can be stopped.

[0075] The output module outputs the planning scheme and decision variables.

[0076] A non-transitory computer-readable storage medium, characterized in that the non-transitory computer-readable storage medium stores computer instructions that cause the computer to perform the method as described in any one of claims 1 to 4.

[0077] A computer program product, characterized in that the computer program product includes a computer program stored on a non-transitory computer-readable storage medium, the computer program including program instructions that, when executed by a computer, cause the computer to perform the method as described in any one of claims 1 to 4.

[0078] The advantages of this invention are:

[0079] (1) The model and solution method established in this invention are both based on mathematical programming, which effectively solves the problem that traditional substation planning is prone to getting trapped in local optima.

[0080] (2) Since the transformer capacity is a fixed value, the planned substation capacity is discontinuous. Substation planning that takes demand response into account can configure a reasonable demand response strategy based on the load curve characteristics within the power supply range of each substation, thereby effectively improving the utilization efficiency of the substation.

[0081] (3) Considering the time-series power of load and demand response, a corresponding matrix model is established, which can fully consider the time-series characteristics of load and demand response, effectively reduce the peak value of the load curve within the power supply range, and reduce the capacity cost of substation planning.

[0082] (4) In dealing with the uncertainty of response power, the multi-discrete scenario-based sub-Bruker optimization method is adopted, which overcomes the problem that random optimization relies on known probability distribution and is prone to insufficient planning, while effectively reducing the conservatism of the planning results.

[0083] Additional aspects and advantages of the invention will be set forth in part in the description which follows, and in part will be obvious from the description, or may be learned by practice of the invention. Attached Figure Description

[0084] To more clearly illustrate the technical solution of the present invention, the accompanying drawings used in the description of the embodiments will be briefly introduced below. Obviously, the accompanying drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0085] Figure 1 The flowchart of the substation planning sub-Bruker optimization method considering excitation-type response uncertainty of the present invention is shown below.

[0086] Figure 2 The present invention provides a flowchart of the substation planning sub-Brow bar optimization system considering the uncertainty of excitation-type response.

[0087] Figure 3 The examples show typical 24-hour load curves for various load types.

[0088] Figure 4 This example illustrates the load and candidate site distribution within the planned area.

[0089] Figure 5 This is the power supply range division result of Case 1 in the embodiment;

[0090] Figure 6 This is the result of power supply range division in Example 2 of the embodiment.

[0091] Figure 7 This is the power supply range division result of Case 3 in the embodiment;

[0092] Figure 8 The example shows the trend of planning cost as the number of sample scenarios changes in Case 3. Detailed Implementation

[0093] To make the objectives, technical solutions, and advantages of the embodiments of the present invention clearer, the technical solutions of the embodiments of the present invention will be clearly and completely described below in conjunction with the embodiments of the present invention. Obviously, the described embodiments are only some embodiments of the present invention, not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0094] Combined with appendix Figure 1 The present invention provides a detailed explanation of a substation planning sub-Bruker optimization method considering excitation-type response uncertainty and its overall solution process. The specific steps are as follows:

[0095] Step 1: Taking into account the contracting cost, response cost, and penalty benefits of demand response, establish a mixed integer linear programming model for substation site selection that takes into account incentive-based demand response.

[0096] Step 2: Construct a response power uncertainty fuzzy set based on 1-norm and ∞-norm. Based on the improvement of the mixed integer linear programming model, establish a two-stage three-layer sub-Bruker optimization model based on multiple discrete scenarios.

[0097] Step 3: For this split bar model, we propose an iterative algorithm for the main problem and sub-problems based on column and constraint generation.

[0098] The effectiveness of the proposed model and method is demonstrated through a numerical example system. This invention uses a regional example covering an area of ​​97.56 km² for testing. Based on land use planning, the area is divided into 351 sub-regions for target year spatial load prediction. The peak power of the residential load curve is 616.56 MW, the peak power of the commercial load curve is 434.73 MW, and the peak power of the industrial load curve is 625.23 MW. After time-series matching of the three load types, the total peak power is 1385.66 MW. Each of the three load types has a certain proportion of reducible load; detailed load time series can be found in... Figure 3 For load and substation location distribution, see [link to relevant documentation]. Figure 4 There are 22 potential substation construction sites within the planning area. Detailed substation location information is provided in Appendix Table A2. The substation capacities available include four types: 2×40, 2×50, 3×40, and 3×50 MVA, with construction costs of 22 million, 25 million, 32 million, and 36 million yuan respectively. The service life of the substations and lines is 30 years, with a line cost of 0.025 million yuan / (km·kW) and a discount rate of 0.045. Details of the contracted price, response price, and penalty price for various load demand responses are provided in Table 1. Regarding uncertainty parameter settings, the DRO model uses confidence levels of 50% and 99%, respectively, and selects 20 uncertainty scenarios each for residential, commercial, and industrial loads as samples.

[0099] Table 1 Demand Response Cost Parameters

[0100]

[0101] (1) Case Comparison Analysis

[0102] To facilitate the analysis of the impact of demand response and its uncertainty on the planning results, the following three case studies are set up for planning comparison: Case 1: Substation planning without considering demand response; Case 2: Substation planning considering demand response but not its uncertainty; Case 3: Substation planning considering both demand response and its uncertainty. The planning costs for the three cases are shown in Table 2, the planned substation capacity and load factor of each substation are shown in Table 3, and the power supply area division results for Cases 1-3 are shown in Table 4. Figure 5-7 .

[0103] Table 2. Planning Annual Costs for Three Case Studies

[0104]

[0105] Table 3. Substation capacity and load factor planning for three case studies.

[0106]

[0107] Note: Considering the N-1 safety principle of substations, the upper limit of the load rate for two main transformers is set at 65% and the upper limit of the load rate for three main transformers is set at 86% in the example. Case 2-3 did not plan to build a substation at location #2.

[0108] The planning results of the three cases were analyzed. Case 2 required one fewer substation than Case 1. Although it incurred an annual demand response cost of 1.165 million yuan, it saved 3.377 million yuan in construction investment annually. Case 3, compared to Case 2, considered the uncertainty of demand response. Both its planning and demand response costs increased significantly. One 40×3MVA substation was replaced with a 50×3MVA substation, increasing the planned capacity and effectively addressing the impact of demand response uncertainty. The contract and response costs for demand response increased by 138,500 yuan, but due to a penalty benefit of 93,400 yuan, the total increase in demand response cost was only 45,100 yuan. The increased demand response cost is due to the need to increase response intensity after considering uncertainty, which can cope with excessively high load curve peaks caused by demand response uncertainty. The total cost of Case 3 increased by 196,900 yuan annually compared to Case 2, but it is still significantly lower than the planning cost of Case 1 without considering demand response.

[0109] (2) Demand Response Effect Analysis

[0110] The substation planning method proposed in this invention fully considers load timing characteristics matching, effectively reducing the peak load curve within the power supply range. Simultaneously, it considers the discontinuity of planned substation capacity and configures reasonable demand response strategies based on the load curve characteristics within the power supply range of each substation, effectively improving substation utilization efficiency. Analysis of the substation load rates in Table 3 reveals that the substation load rates planned by the method proposed in this invention are significantly higher than the results of traditional planning methods, indicating a significant improvement in substation utilization efficiency compared to traditional planning methods.

[0111] In Case 2 and Case 3, the load rate of substations considering demand response is significantly higher than that in Case 1 without considering demand response. In Case 3, after considering the uncertainty of demand response, the load rate of most substations is lower than that in Case 2. This is because the substations have a certain capacity margin, and the substations can still meet the N-1 safety constraint when the actual demand response deviates.

[0112] Furthermore, Case 2 did not account for the uncertainty of demand response. Most substations reached their maximum load rate, except for substations #1, #13, #21, and #22, whose load rates did not reach their maximums and were even slightly higher in Scheme 3. The reason for this is that the peak load curves within the power supply range of these four substations were lower than the planned substation capacity, thus eliminating the need for a demand response strategy. In contrast, other substations with higher peak loads adopted demand response. At the peak of the load curve, the grid could issue response commands to users, reducing the peak power to the substation's maximum power supply capacity. Since this did not consider uncertainty, their load rates all reached the substation's maximum load rate.

[0113] (3) Uncertainty Model Analysis

[0114] 1) Comparison of uncertainty methods

[0115] Three methods—stochastic optimization, robust optimization, and the sub-Brutal robust optimization proposed in this invention—were used to plan Case 3. The planning cost and substation capacity selection results are as follows.

[0116] Table 4. Annual Planning Costs of the Three Methods

[0117]

[0118] Table 5. Substation capacity planned using three methods

[0119]

[0120]

[0121] Analysis of the planning results of the three methods reveals differences in construction investment costs and demand response costs. The planning cost obtained by the robust optimization model proposed in this invention falls between that of the stochastic optimization model and the robust optimization model. This overcomes the problem that stochastic optimization relies on known probability distributions and is prone to under-planning, while effectively reducing the conservatism of the planning results.

[0122] 2) The impact of confidence level and number of sample scenarios on planning

[0123] To verify the rationality and effectiveness of the proposed split-bar optimization model, tests were conducted with different confidence levels and varying numbers of uncertain sample scenarios. The annual planning costs at different confidence levels are shown in Table 6; the trend of planning costs with the number of sample scenarios is shown in [Table 6]. Figure 8 .

[0124] Table 6. Annual Planning Costs of the DRO Model at Different Confidence Levels

[0125]

[0126] Note: Costs are in ten thousand yuan.

[0127] Analyzing the planning results using the allowable deviation formula reveals that as the confidence level and the number of uncertainty samples increase, the allowable deviation range in the DRO solution becomes larger, which is beneficial for finding more severe uncertainty scenarios, but also leads to a continuous increase in planning costs. Figure 8 It can be seen that as the total number of uncertain samples increases, the planning cost rises significantly when the number of sample scenarios is small, but the growth rate slows down when the number of sample scenarios reaches about 60, and further increasing the number of sample scenarios has little impact on the planning results.

[0128] On the one hand, this invention proposes a sub-Browser bar optimization method for substation planning that takes into account the uncertainty of excitation-type response. The method includes the following steps:

[0129] (1) Establish a deterministic model for substation planning that takes into account incentive-based demand response. Taking into account the contract cost, response cost and penalty benefit of demand response, mathematical modeling is performed on the peak shaving capacity and response cost of incentive-based demand response; then, combined with substation construction investment and line investment, a mixed integer linear programming model is established with the goal of minimizing the total investment cost of the power grid.

[0130] (2) Construct a substation planning subbulb bar model that considers the uncertainty of demand response. Considering the uncertainty of response power caused by users' subjective decisions, construct an uncertain fuzzy set based on the 1-norm and ∞-norm; on the basis of the improvement of the mixed integer linear programming model, establish a two-stage three-level subbulb bar optimization model based on multiple discrete scenarios.

[0131] (3) A solution algorithm for the sub-Bruker model is proposed. The model is decomposed into sub-problems and a main problem, and an iterative algorithm based on column and constraint generation is proposed.

[0132] Step (1) establishes a deterministic model for substation planning that takes into account incentive-driven demand response, including:

[0133] 1) Demand response cost model for power grid companies

[0134] Incentive-based demand response targets reduceable loads within a planned area and is an incentive-based demand response technology built on contractual agreements. First, the power supplier and user sign a contract specifying the maximum power the user can respond to during the contract period, i.e., the contracted capacity P1, thus incurring contractual costs. During the distribution network operation, the power grid issues response instructions to users in advance for peak electricity consumption periods, and users respond with the instructed power P1. t The cumulative response cost; the portion of the user's response power that is less than the instruction requirement is the default power P. t，f This generates cumulative penalty revenue. The formula for calculating the demand response cost paid annually by the power grid company to a single user is as follows:

[0135]

[0136] Among them, C DR σ1, σ2, and σ3 are the unit prices of contract cost, response cost, and penalty revenue, respectively; P is the maximum load of the user; and λ is the ratio of the user's maximum contractable capacity to its maximum load, representing the load's ability to participate in demand response.

[0137] 2) Substation planning model considering demand response

[0138] The purpose of substation planning is to minimize the investment and construction costs of substations and main lines while meeting the target annual load electricity demand and various planning constraints, and also to consider various costs related to demand response.

[0139] a) Decision variables: Decision variables include substation location and capacity selection, load-substation connection relationship, demand response contracted capacity, and response power for each time period. is Let y be a Boolean variable representing whether the i-th substation location is selected for the s-th substation type. Each candidate substation type corresponds to a different substation capacity. An option with a capacity of 0 is added to the candidate substation types. If a substation location is selected for a 0-capacity type, it means that the location has not been chosen for substation construction. This unifies the location selection and capacity selection variables, solving the non-linearity problem caused by multiplying these two variables in substation construction cost calculation; ijThis is a Boolean variable indicating whether the location of the i-th substation is connected to the j-th load. Let be a continuous variable, representing the contracted demand response capacity of the j-th load. Let be a continuous variable, representing the response power of the j-th load during time period t.

[0140] b) Objective function:

[0141] minC=C S +C L +C DR1 +C DR2

[0142]

[0143]

[0144]

[0145]

[0146] Where: C represents the total cost; C S C L C DR1 and C DR2 These represent the annual construction costs of substations, annual construction costs of transmission lines, contracted demand response costs, and demand response costs, respectively; r0 is the discount rate; ms is the depreciation period of the transformer; N P N represents the number of candidate locations for the substation. S C represents the number of candidate substation types. Ss β is the construction cost of the s-th candidate substation type; β is the unit cost coefficient of the line; ml is the depreciation period of the line; N L d represents the number of load points. ij P represents the distance from substation i to load j. j σ represents the maximum load at the j-th load point; j,1 and σ j,2 These are the unit prices of the demand response contract cost and response cost for the j-th load, respectively.

[0147] c) Constraints:

[0148] Uniqueness constraint for substation capacity selection. Only one type of substation can be selected for a given construction location.

[0149]

[0150] The uniqueness constraint of load point attribution: When dividing the power supply area, each load point has one and only one upstream substation.

[0151]

[0152] Maximum power supply radius constraint. max The maximum power supply radius for medium-voltage lines is specified in the power supply and distribution design code. It can also be designed according to the actual situation during the planning stage, but in principle, it is not allowed to exceed the specified value.

[0153] y i,j d ij ≤r max i∈[1,N P ],j∈[1,N L ]

[0154] Substation N-1 safety constraint. Based on the principle of safe operation of the power grid, if any transformer in the substation fails, the remaining transformers must be able to operate for 2 hours to supply all loads within their power supply range. From this, the maximum load factor e of the substation during normal operation can be derived. s The following inequality constraints apply:

[0155]

[0156] In the formula, J i P represents the load set within the power supply range of the i-th substation; j,t Let be the power of the j-th load during time period t; S is the power factor of the j-th load; s Let be the capacity of the s-th candidate substation type.

[0157] Demand response constraints. The contracted demand response capacity at each load point shall not exceed its maximum response capacity, and the user response capacity during operation shall not exceed the contracted capacity.

[0158]

[0159]

[0160] Step (2) involves constructing a substation planning sub-bar model that considers demand response uncertainty, including:

[0161] 1) Constructing an uncertain fuzzy set of demand response

[0162] Considering the uncertainty of user intentions, the actual response result P t There is a deviation from the grid demand response command, and P t It fluctuates within a certain range. Due to the limitations of historical data, it is difficult to obtain a complete and accurate scenario probability distribution, but we can model its uncertain fuzzy set. First, we obtain multiple actual scenarios through historical data, and then we use scenario clustering to filter out N. k A finite discrete scenario and the probability distribution p under each scenario k,0Furthermore, considering that these scenarios do not represent the actual probability distribution, confidence sets based on the 1-norm and ∞-norm can be constructed to constrain the fluctuations in the probability distribution.

[0163]

[0164]

[0165]

[0166]

[0167] Among them, Ψ1 and Ψ ∞ Let P represent the confidence intervals restricted by the 1-norm and ∞-norm, respectively; P is the scenario probability p. k The vector form; P0 is the initial probability p of each scenario. k,0 The vector form; For P to correspond to N k A vector consisting of _n positive real numbers; K is the number of sample scenarios; α1 and α ∞ They are Ψ1 and Ψ respectively ∞ The confidence level is determined by the probability distribution. Therefore, the confidence set is constrained by both the 1-norm and the ∞-norm, avoiding overly extreme cases, where Ψ=Ψ1∩Ψ. ∞ ,Right now:

[0168]

[0169] 2) Two-stage sub-Blule bar optimization model considering response power uncertainty

[0170] The demand response uncertainty considered refers to the inability of users to fully meet their response requirements upon receiving a response instruction; that is, the response power is uncertain, resulting in defaulted power, which the power grid company can penalize according to the contract. Therefore, the demand response cost C during the operation phase... DR2 The calculation formula should be rewritten as follows:

[0171]

[0172] Meanwhile, demand response uncertainty will change the actual response power, causing fluctuations in the load curve within the substation's power supply range, which in turn affects the substation's N-1 safety constraint. The constraint formula should be rewritten as follows:

[0173]

[0174] Uncertainty in user demand response occurs during the operational phase, which in turn affects the planning phase. Therefore, considering uncertainty, the planning model can be decomposed into two phases. The first phase is the planning phase, where decision variables include the relationship between substation location and capacity selection, the connection relationship between load and substation, and the contracted demand response capacity. The second phase is the operational phase, where the decision variable is the user's response power, but the actual response power is uncertain. This invention includes x as the decision variable in the first phase. is y ij and Let vector x represent the decision variables in the second stage. Let d represent this. Therefore, the discrete-scene-based split-bar model can be expressed as follows:

[0175]

[0176] Where: a T b is the linear coefficient matrix of the objective function in the first stage; T N is the linear coefficient matrix of the objective function in the second stage; k Let p represent the total number of discrete scenarios representing the probability distribution, k be the number of each scenario, and p be the number of the discrete scenarios. k This represents the probability in scenario k. The constraint condition is transformed as follows:

[0177]

[0178] Where C, E, F, G, H, m, n, u, v represent the matrix or vector forms of the variables mentioned above. The first two formulas correspond to the equality and inequality constraints of the variables in the first stage; the third inequality constraint is the capacity coupling inequality between the variables in the first and second stages; and the last inequality constraint corresponds to the demand-response inequality constraint in the second stage.

[0179] Step (3) proposes a solution algorithm for the split-bar model, including:

[0180] In the two-stage decomposed bar model described above, both the objective function and the constraints are linear. Based on the constraint generation algorithm, the model can be decomposed into a main problem (MP) and subproblems (SP), and then the optimal solution can be obtained through iteration.

[0181] The objective of MP (Maximum Probability) is to obtain the optimal planning scheme that satisfies the known probability distribution constraints under finite discrete scenario conditions. The objective function and constraints of MP can be described as follows:

[0182]

[0183]

[0184] Where L represents the lower-level demand response operating cost, and the superscript r indicates the r-th iteration. Except for the first iteration, the probability distribution of each subsequent iteration is obtained by solving the SP problem. Solving the MP problem yields a globally optimal solution C. * and the corresponding planning decision variable x * .

[0185] The purpose of solving SP is to optimize the results of MP. * Given the substation capacity, power supply range, and contracted demand response capacity, the load timing characteristics and demand response characteristics are matched to find the worst-case probability distribution P of the response power. k Then, this distribution is provided to MP for the next iterative calculation, while based on the obtained L(x) * Update the global optimum. The objective function of SP can be described as follows:

[0186]

[0187] As can be seen from the above formula, the min problem in each scenario is independent, so parallel methods can be used to compute them simultaneously. For example, the internal optimization result of the k-th scenario is... The objective function of SP can then be transformed into:

[0188]

[0189] The MP and SP problems described above can be solved using the MILP model and linear programming model, respectively. They can be solved quickly using commercial solvers, and the optimization result P of the SP problem can be used to solve these problems. k The solution is passed to MP for iterative computation until the globally optimal solution C is obtained from two consecutive iterations. * The iteration stops when the difference is less than a specified threshold, and the optimal planning cost and decision variable values ​​are obtained.

[0190] On the other hand, the present invention also provides a substation planning sub-bar optimization system that takes into account the uncertainty of excitation-type response, the system comprising:

[0191] (1) Data input and processing module, used to perform matrix processing on the input load forecast data and various planning parameter information.

[0192] (2) The main problem solving module, under the condition of finite discrete scenario (known distribution or probability distribution obtained by the sub-problem solving module), obtains the optimal planning scheme and planning layer decision variables that satisfy the known probability distribution constraints.

[0193] (3) Sub-problem solving module: fix the decision variables of the planning layer obtained by the main problem solving module, solve the decision variables of the operation layer with the goal of minimizing the operating cost, and find the worst probability distribution of the response power.

[0194] Furthermore, a complete planning system should also include the following modules:

[0195] The initialization module is used to iteratively solve the initialization settings of parameters, and to calculate the corresponding robust scene probabilities by intervening in the algorithm with known scene probabilities, thereby forming an iteration.

[0196] The decision module is used to determine whether the planning results have converged and whether the iterative solution can be stopped.

[0197] The output module outputs the planning scheme and decision variables.

[0198] In a third aspect, the present invention provides a non-transitory computer-readable storage medium storing computer instructions that cause the computer to perform the above-described method.

[0199] Fourthly, the present invention provides a computer program product comprising a computer program stored on a non-transitory computer-readable storage medium, the computer program comprising program instructions that, when executed by a computer, cause the computer to perform the above-described method.

[0200] Although embodiments of the present invention have been shown and described above, it is understood that the above embodiments are exemplary and should not be construed as limiting the present invention. Those skilled in the art can make changes, modifications, substitutions and variations to the above embodiments within the scope of the present invention.

Claims

1. A sub-Browser bar optimization method for substation planning considering excitation-type response uncertainty, characterized in that: The specific steps are as follows: Step 1: Taking into account the contracting cost, response cost, and penalty benefits of demand response, establish a mixed integer linear programming model for substation site selection that takes into account incentive-based demand response. Step 2: Construct a response power uncertainty fuzzy set based on 1-norm and ∞-norm, and establish a two-stage three-layer sub-Bruker optimization model based on multiple discrete scenarios based on the improvement of the mixed integer linear programming model; The steps for constructing the robust optimization model include: 1) Constructing an uncertain fuzzy set of demand response Considering the uncertainty of user intentions, the actual response results P t There is a deviation from the grid demand response command, and P t Modeling a fuzzy set whose uncertainty fluctuates within a certain range: First, multiple real-world scenarios are obtained through historical data. Then, scenario clustering is used to filter and select the best scenarios. N k A finite discrete scenario and its probability distribution p k,0 Furthermore, considering that these scenarios do not represent the actual probability distribution, a system based on... 1- Norm and ∞- The norm's confidence set is used to constrain fluctuations in the probability distribution. ,in, Ψ 1 and Ψ ∞ Let P represent the confidence intervals constrained by the 1-norm and ∞-norm, respectively; P is the scenario probability. p k The vector form; P0 is the initial probability of each scenario. p k,0 The vector form; To correspond with P N k A vector consisting of 1 positive real numbers; K The number of sample scenarios; α 1 and α ∞ They are respectively Ψ 1 and Ψ ∞ The confidence level is determined by the probability distribution, which is constrained by both the 1-norm and the ∞-norm, thus avoiding overly extreme cases. Ψ=Ψ 1 ∩Ψ ∞ ,Right now: , 2) Two-stage sub-Brussels bar optimization model considering response power uncertainty The uncertainty in demand response considered refers to the fact that users cannot fully meet their response requirements when they receive a response instruction. The response power is uncertain, resulting in default power. Therefore, the demand response cost during the operational phase... C DR2 The calculation formula should be rewritten as follows: Meanwhile, demand response uncertainty will change the actual response power, causing fluctuations in the load curve within the substation's power supply range, which in turn affects the substation's N-1 safety constraint. The constraint formula should be rewritten as follows: The uncertainty of user demand response occurs during the operation phase and subsequently affects the planning phase. Therefore, considering this uncertainty, the planning model can be decomposed into two phases: the first phase is the planning phase, where decision variables include the relationship between substation location and capacity selection, the connection relationship between load and substation, and the contracted demand response capacity; the second phase is the operation phase, where the decision variable is the user's response power, but the actual response power is uncertain. The decision variables in the first phase include... x is , y ij and Let vector x represent the decision variables in the second stage. Represented by vector d, the discrete-scene-based sub-Bruker model can be expressed as follows: ,in: This is the linear coefficient matrix of the objective function for the first stage; This is the linear coefficient matrix of the objective function for the second stage; N k The total number of discrete scenarios representing the probability distribution. k Number each scene. p k Indicates in k The probability of the scenario and the form of the constraints are transformed as follows: Where: C, E, F, G, H, m, n, u, v represent the matrix or vector forms of the variables mentioned above. The first two formulas correspond to the equality and inequality constraints of the variables in the first stage; the third inequality constraint is the capacity coupling inequality between the variables in the first stage and the variables in the second stage; the last inequality constraint corresponds to the demand response inequality constraint in the second stage. Step 3: For this sub-Bruker optimization model, we propose an iterative algorithm for the main problem and sub-problems based on column and constraint generation.

2. The sub-Browser optimization method for substation planning considering excitation-type response uncertainty as described in claim 1, characterized in that, The establishment of the mixed-integer linear programming model described in Step 1 includes: 1) the demand response cost model of the power grid company. The power supplier and user first sign a contract, specifying the maximum power and contracted capacity that the user can respond to during the contract period. P 1 This incurs contract costs; during the operation of the distribution network, response instructions are issued to users in advance for peak electricity consumption, and users respond with power according to the instructions. P t This results in accumulated response costs; the portion of the user's response power that is less than the instruction's requirement constitutes a breach of contract. P t，f The cumulative penalty revenue generated, and the annual demand response cost paid by the power grid company to a single user, are calculated using the following formula: ,in, C DR This is the demand response fee that the power grid company needs to pay to the user annually. σ 1 , σ 2 , σ 3 These are the unit prices for contract signing costs, response costs, and penalty benefits, respectively. P This represents the maximum user load. λ The ratio of a user's maximum contractable capacity to its maximum load represents the load's ability to participate in demand response. 2) Substation planning model considering demand response The purpose of substation planning is to minimize the investment and construction costs of substations and main lines while meeting the target annual load electricity demand and various planning constraints, and also to consider various costs related to demand response. a) Decision variables: Decision variables include the selection of substation location and capacity, the connection relationship between load and substation, the contracted capacity for demand response, and the response power for each time period. x is Let be a Boolean variable, representing the first... i Should the location of the substation be selected as the first one? s There are several types of substations, and each type of candidate substation corresponds to a different substation capacity. An option with a capacity of 0 is added to the candidate substation types. If a substation location is selected with a capacity of 0, it means that the location has not been selected for substation construction. The location selection and capacity selection variables are unified, which solves the nonlinearity problem caused by the need to multiply these two variables in the substation construction cost calculation. y ij Let be a Boolean variable, representing the first... i Is the location of the substation related to the first one? j The loads are interconnected; For continuous variables, it represents the first... j Demand response contracted capacity for each load; For continuous variables, it represents the first... j A load in t Response power over a given time period; b) Objective function: minC=C S +C L +C DR1 +C DR2 ,in: C Total cost; C S , C L , C DR1 and C DR2 These are the annual costs of substation construction, annual costs of line construction, demand response contract costs, and response costs. r 0 The discount rate; ms The depreciation period for transformers; N P The number of candidate locations for the substation; N S The number of candidate substation types; C Ss For the first s Construction costs for each of the candidate substation types; β This is the unit cost coefficient for the line; ml The depreciation period for the line; N L Number of load points; d ij For substation i to load j The distance; P j For the first j The maximum load capacity of each load point; σ j,1 and σ j,2 The first j The unit price of demand response contract cost and response cost per load; c) Constraints: The uniqueness constraint for substation capacity selection means that only one type of substation can be selected for a given construction location: The uniqueness constraint of load point attribution means that, when dividing the power supply area, a load point corresponds to one and only one upstream substation. Maximum power supply radius constraint r max The maximum power supply radius for medium-voltage lines as specified in the power supply and distribution design code is: The N-1 safety constraint for substations, based on the principle of safe operation of the power grid, requires that after any transformer in the substation fails, the remaining transformers must be able to operate for 2 hours to supply all loads within their power supply range. This is the maximum load factor of the substation during normal operation. e s The following inequality constraints apply: In the formula, J i For the first i Load clusters within the power supply range of each substation; P j,t For the first j A load in t Power during a given time period; cosφ j For the first j The power factor of each load; S s For the first s The capacity of the candidate substation types; Demand response constraints: The contracted demand response capacity at each load point cannot exceed its maximum response capacity, and the runtime user response capacity cannot exceed the contracted capacity.

3. The sub-Browser bar optimization method for substation planning considering excitation-type response uncertainty as described in claim 1, characterized in that, The iterative algorithm described in Step 3 includes: Based on the constraint generation algorithm, the model is decomposed into a main problem (MP) and a subproblem (SP). The optimal solution is then obtained iteratively. The purpose of solving MP is to obtain the optimal planning scheme that satisfies the known probability distribution constraints under finite discrete scenario conditions. The objective function and constraints of MP are described as follows: Where L represents the lower-level demand response operating cost, indicated by the superscript. r Indicates the first r In each iteration, except for the first iteration, the probability distribution is obtained by solving the SP problem, and the MP problem is solved to obtain a globally optimal solution. and corresponding planning decision variables ; The purpose of solving SP is to optimize based on the results of MP. Given the substation capacity, power supply range, and contracted demand response capacity, the load timing characteristics and demand response characteristics are matched to find the worst-case probability distribution P of the response power. k Then, this distribution is provided to MP for the next iterative calculation, while based on the obtained... The objective function for updating the global optimum, SP, can be described as follows: As can be seen from the above formula, the min problem in each scenario is independent and can be computed simultaneously using parallel methods, such as the first... k The internal optimization results for each scenario are as follows: Then the objective function of SP can be transformed into: The MP and SP problems mentioned above are solved using the MILP model and the linear programming model, respectively, and the optimization result P of SP is calculated. k The solution is passed to MP for iterative computation until the globally optimal solution is found between two consecutive iterations. The iteration stops when the difference is less than a specified threshold, and the optimal planning cost and decision variable values ​​are obtained.

4. A sub-Browser optimization system for substation planning that considers excitation-type response uncertainty, characterized in that, The system for performing the method as described in claim 1 includes: (1) Data input and processing module, used to perform matrix processing on the input load forecast data and various planning parameter information; (2) The main problem solving module obtains the optimal planning scheme and planning layer decision variables that satisfy the known probability distribution constraints under the condition of finite discrete scenarios; (3) Sub-problem solving module: fix the decision variables of the planning layer obtained by the main problem solving module, solve the decision variables of the operation layer with the goal of minimizing the operating cost, and find the worst probability distribution of the response power.

5. A substation planning sub-bar optimization system considering excitation-type response uncertainty according to claim 4, characterized in that, The system also includes the following modules: The initialization module is used to iteratively solve the initialization settings of the parameters, and to calculate the corresponding robust scene probability by intervening in the algorithm with known scene probabilities, thereby forming an iteration; The decision module is used to determine whether the planning results have converged and whether the iterative solution can be stopped. The output module outputs the planning scheme and decision variables.

6. A non-transitory computer-readable storage medium, characterized in that, The non-transitory computer-readable storage medium stores computer instructions that cause the computer to perform the method as described in any one of claims 1 to 3.

7. A computer program product, characterized in that, The computer program product includes a computer program stored on a non-transitory computer-readable storage medium, the computer program including program instructions that, when executed by a computer, cause the computer to perform the method as described in any one of claims 1 to 3.

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