CN116862068A - Transformer substation planning distribution robust optimization method and system considering excitation type response uncertainty - Google Patents

Abstract

The invention provides a robust optimization method and a robust optimization system for transformer substation planning distribution, which are used for considering excitation type response uncertainty. Firstly, comprehensively considering subscription cost, response cost and punishment income of excitation type demand response, and establishing a substation site selection and volume fixation mixed integer linear programming model. And secondly, constructing a response power uncertainty fuzzy set based on the 1-norm and the ++norm, and establishing a transformer substation planning distribution robust optimization model considering excitation type response uncertainty on the basis of improving the mixed integer linear programming model. And finally, decomposing the model into a main problem and a sub problem, and providing a distributed robust optimization model iterative solving method generated based on the columns and the constraints. The method provided by the invention uses the distributed robust optimization model, can fully consider the randomness of the user demand response, calculates and matches the load characteristics in the model, effectively reduces the peak value of the load curve of the transformer substation, and ensures the economy and the robustness of the planning scheme.

Description

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

Technical Field

The present invention belongs to the field of distribution network planning, and relates to a robust optimization method and system for substation planning taking into account incentive response uncertainty.

Background Art

In recent years, my country's energy transformation strategy has been rapidly promoted, and the electrification degree of terminal energy has been continuously improved, resulting in the peak load of the distribution network rising year by year, which has brought huge pressure on the planning and investment of substations. Demand response is an effective means to solve this problem. However, although demand response can reduce the load peak to a certain extent, its response has certain uncertainties due to the influence of human decision-making factors. How to carefully consider demand response and its uncertainty in substation planning is an important issue that needs to be solved urgently.

Substation planning involves the site selection, capacity determination and power supply range division of substations. It is a large-scale nonlinear optimization problem involving multiple types of decision variables. Early planning methods mainly include heuristic methods and hierarchical decoupling methods. Heuristic method algorithms can obtain optimal solutions or approximate optimal solutions when solving large-scale problems, but are prone to fall into local optimality. In addition, the power supply range division often adopts the nearest allocation, resulting in unreasonable planning and problems such as too low or too high load rate. The essence of the hierarchical decoupling method is to decouple large-scale nonlinear problems into two layers of sub-problems, and realize site selection and power supply range division for each candidate capacity combination scheme generated by the upper layer. There is a possibility that the capacity combination schemes generated by this method cannot be fully listed.

Many studies have taken demand response into account in substation planning, which can improve the comprehensive load characteristics of substations and reduce the investment cost of substation planning. However, the uncertainty of demand response has not been considered, which may lead to insufficient investment in the target year planning scheme. Considering the uncertainty factors in substation planning, some studies have modeled the uncertainty of the location and size of the target year load forecast and the uncertainty of photovoltaic output based on stochastic optimization methods. However, this method requires the known probability distribution of uncertain factors, which is difficult to obtain in practical applications, thus leading to insufficient investment in the target year planning. Some studies have used robust optimization methods to deal with uncertainty, that is, considering the probability distribution of uncertain factors under the worst scenario, and the resulting planning scheme is conservative. In recent years, the advantages of the distributed robust optimization method in dealing with uncertainty have gradually attracted the attention of scholars. It combines the characteristics of stochastic optimization and robust optimization, and the optimization results show good performance in terms of economy and conservatism.

Summary of the invention

The technical problem to be solved by the present invention is how to establish a mathematical model for substation planning that takes into account demand response and its uncertainty, and adopt mathematical programming methods to solve it, so as to overcome the problem that traditional substation planning methods are prone to fall into local optimality while ensuring the economy and robustness of the resulting planning scheme.

The present invention solves the above-mentioned problems through the following technical means.

A distributed robust optimization method for substation planning taking into account the uncertainty of incentive-type response is characterized by: the specific steps are as follows:

Step 1: Comprehensively consider the contract cost, response cost and penalty benefit of demand response, and establish a mixed integer linear programming model for substation location and sizing taking into account incentive-based demand response;

Step 2: Construct uncertain fuzzy sets of response power based on 1-norm and ∞-norm, and establish a two-stage three-layer distributed robust optimization model based on multiple discrete scenarios on the basis of improving the mixed integer linear programming model;

Step 3: For this distributed robust optimization model, an iterative algorithm for the main problem and subproblems based on column and constraint generation is proposed.

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

The power supply and user first sign a contract to stipulate the maximum power that the user can respond to during the contract period, the contract capacity P ₁ , and generate contract costs; during the operation of the distribution network, the user is given a response instruction in advance during the peak power consumption period, and the user responds to the power P _t according to the instruction, and the response cost is accumulated; the part of the user's response power that is less than the instruction requirement is the default power P _t,f , and the penalty income is accumulated. The demand response cost calculation formula paid by the power grid company to a single user each year is as follows:

Among them, C _DR is the demand response fee that the power grid company needs to pay to the user every year; σ ₁ , σ ₂ , σ ₃ are the unit prices of contract cost, response cost and penalty benefit respectively; P is the maximum load of the user; λ is the ratio of the user's maximum contractable capacity to its maximum load, which represents the ability of the load to participate in demand response;

2) Substation planning model considering demand response

The purpose of substation planning is to reduce the investment and construction costs of substations and trunk lines as much as possible under the premise of meeting the target annual load power demand and various planning constraints. At the same time, various costs related to demand response should also be considered;

a) Decision variables: Decision variables include substation location and capacity selection, load and substation connection relationship, demand response contract capacity and response power in each time period. x _is a Boolean variable, indicating whether the ith substation location selects the sth substation type. Each substation type to be selected corresponds to a different substation capacity. An option with a capacity of 0 is added to the substation types to be selected. If a substation location selects the 0 capacity type, it means that the location is not selected for substation construction. The two variables of location selection and capacity selection are unified, which solves the nonlinear problem caused by the need to multiply these two variables in the calculation of substation construction cost; y _ij is a Boolean variable, indicating whether the ith substation location has a connection relationship with the jth load; is a continuous variable, indicating the demand response contract capacity of the jth load; is a continuous variable, indicating the response power of the jth load in period t;

b) Objective function:

minC＝ _CS + _CL + _CDR1 + _CDR2

Where: C is the total cost; _CS , _CL , _CDR1 and _CDR2 are the annual cost of substation construction, annual cost of line construction, demand response contract cost and response cost respectively; _r0 is the discount rate; ms is the depreciation period of the transformer; _NP is the number of substation locations to be selected; _NS is the number of substation types to be selected; _CSs is the construction cost of the sth substation type to be selected; β is the line unit cost coefficient; ml is the line depreciation period; _NL is the number of load points; _dij is the distance from substation i to load j; _Pj is the maximum load of the jth load point; σj _,1 and σj _,2 are the unit prices of the demand response contract cost and response cost of the jth load respectively;

c) Constraints:

Substation capacity selection uniqueness constraint. Only one substation type can be selected for a substation construction location:

Load point ownership uniqueness constraint. When dividing the power supply range, there is only one upper-level substation corresponding to a load point:

Maximum power supply radius constraint, r _max is the maximum value of the power supply radius of the medium voltage line specified in the power supply and distribution design specification:

y _i,j d _ij ≤r _max i∈[1,N _P ],j∈[1,N _L ]

Substation N-1 safety constraint, based on the principle of safe operation of the power grid, after any transformer in the substation fails, the remaining transformers must meet the requirements of operating with all loads within the power supply range for 2 hours. The maximum load rate of the substation during normal operation, e _s , has the following inequality constraints:

Where, _Ji is the load set within the power supply range of the i-th substation; _Pj,t is the power of the j-th load in the t-th period; is the power factor of the jth load; S _s is the capacity of the sth substation type to be selected;

Demand response constraints: the demand response contract capacity of each load point shall not be greater than its maximum response capacity, and the user response capacity during operation shall not be greater than the contract capacity:

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

1) Constructing uncertain fuzzy sets for demand response

Considering the uncertainty of user willingness, there is a deviation between the actual response result _Pt and the grid demand response instruction, and _Pt fluctuates within a certain range. The fuzzy set of its uncertainty is modeled:

First, we obtain multiple actual scenarios through historical data, and then screen N _k finite discrete scenarios and the probability distribution p _k,0 under each scenario by means of scenario clustering. Thirdly, considering that these scenarios cannot represent the actual probability distribution, we construct a confidence set based on the 1-norm and ∞-norm to limit the fluctuation of the probability distribution:

Where Ψ ₁ and Ψ _∞ represent the confidence intervals restricted by 1-norm and ∞-norm respectively; P is the vector form of the scenario probability p _k ; P ₀ is the vector form of the initial probability p _k,0 of each scenario; is a vector of N _k positive real numbers corresponding to P; K is the number of sample scenarios; α ₁ and α _∞ are the confidence levels for Ψ ₁ and Ψ _∞ respectively. Therefore, the probability distribution confidence set is restricted by both the 1-norm and the ∞-norm, avoiding extreme situations, Ψ = Ψ ₁ ∩Ψ _∞ , that is:

2) Two-stage distributed robust optimization model considering response power uncertainty

The uncertainty of demand response considered is that users cannot fully meet their response requirements when receiving response instructions, and there is uncertainty in the response power, which results in default power. Therefore, the calculation formula of demand response cost C _DR2 in the operation stage should be rewritten as follows:

At the same time, the uncertainty of demand response will change the actual response power, causing the load curve within the power supply range of the substation to fluctuate, which in turn affects the N-1 safety constraint of the substation. The constraint formula should be rewritten as follows:

The uncertainty of user demand response will affect the planning stage in the operation stage. Therefore, the planning model can be decomposed into two stages after taking into account the uncertainty. The first stage is the planning stage. The decision variables include the relationship between substation location and capacity selection, the connection relationship between load and substation, and the demand response contract capacity. The second stage is the operation stage. The decision variable is the user's response power, and the actual response power is uncertain. The decision variables in the first stage include x _is , y _ij and The second stage decision variables are represented by vector x. It is represented by vector d. Therefore, the distributed robustness model based on discrete scenarios can be expressed as follows:

Where: a ^T is the linear coefficient matrix of the objective function of the first stage; b ^T is the linear coefficient matrix of the objective function of the second stage; N _k represents the total number of discrete scenarios of the probability distribution, k is the number of each scenario, p _k represents the probability in the k scenario, and the constraint condition form is transformed as follows:

Among them: C, E, F, G, H, m, n, u, v represent the corresponding matrix or vector form of the variables mentioned above. The first two formulas correspond to the equality constraints and inequality constraints of the first-stage variables; the third inequality constraint is the capacity coupling inequality of the first-stage variables and the second-stage variables; the last inequality constraint corresponds to the demand response inequality constraint of the second stage.

Furthermore, the iterative algorithm described in Step 3 includes:

Based on the constraint generation algorithm, the model is decomposed into the main problem MP and the sub-problem SP, and then the optimal solution is obtained through iteration. The purpose of MP solution is to obtain the optimal planning solution that satisfies the known probability distribution constraints under the conditions of finite discrete scenarios. The objective function and constraint conditions of MP are described as follows:

Where L is the lower-level demand response operating cost, the superscript r indicates the rth iteration, and except for the first iteration, the probability distribution of each iteration is obtained by SP solution. The MP problem is solved to obtain a global optimal solution C ^* and the corresponding planning decision variable x ^* _;

The purpose of SP solution is to match the load timing characteristics and demand response characteristics based on the optimization result x ^* of MP, when the substation capacity, power supply range and demand response contract capacity are known, to find the worst probability distribution P _k of the response power, and then provide this distribution to MP for the next iterative calculation, and update the global optimal solution according to the obtained L(x ^* ). The objective function of SP can be described as follows:

It can be seen from the above formula that the min problem in each scenario is independent and is calculated simultaneously using a parallel method. For example, the internal optimization result of the kth scenario is Then the objective function of SP can be converted to:

The above MP and SP problems are solved using the MILP model and linear programming model respectively, and the optimization result _Pk of SP is passed to MP for iterative calculation until the difference between the global optimal solution C ^* of the two consecutive iterations is less than the specified threshold, and the iteration is stopped to obtain the optimal planning cost and decision variable value.

A distributed robust optimization system for substation planning taking into account incentive response uncertainty, characterized in that the system comprises:

(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-level decision variables that satisfy the known probability distribution constraints under the conditions of finite discrete scenarios;

(3) The sub-problem solving module fixes the decision variables of the planning layer obtained by the main problem solving module, solves the decision variables of the operation layer with the goal of minimizing the operation cost, and finds the worst probability distribution of the response power.

Furthermore, the system further comprises the following modules:

The initialization module is used to iteratively solve the initialization settings of parameters and intervene in the algorithm through known scene probabilities to find the corresponding robust scene probabilities to form iterations;

The judgment module is used to determine whether the planning results have converged and whether the iterative solution can be stopped;

Output module, outputs planning schemes and decision variables.

A non-transitory computer-readable storage medium, characterized in that the non-transitory computer-readable storage medium stores computer instructions, and the computer instructions enable the computer to execute the method according to any one of claims 1 to 4.

A computer program product, characterized in that the computer program product comprises a computer program stored on a non-transitory computer-readable storage medium, the computer program comprising program instructions, and when the program instructions are executed by a computer, the computer executes the method as described in any one of claims 1 to 4.

The advantages of the present invention are:

(1) The model established and the solution method adopted by the present invention are based on mathematical programming, which effectively solves the problem that traditional substation planning is prone to fall into local optimality.

(2) Because the transformer capacity is a fixed value, that is, the planned substation capacity is discontinuous, the substation planning taking 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.

(3) Considering the time series power of load and demand response, the corresponding matrix model is established, which can fully consider the matching of 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.

(4) In dealing with the uncertainty of response power, a distributed robust optimization method based on multiple discrete scenarios is adopted. This 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.

Additional aspects and advantages of the present invention will be given in part in the following description and in part will be obvious from the following description, or will be learned through practice of the present invention.

BRIEF DESCRIPTION OF THE DRAWINGS

In order to more clearly illustrate the technical solution of the present invention, the accompanying drawings required for use 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 ordinary technicians in this field, other accompanying drawings can be obtained based on these accompanying drawings without paying creative work.

FIG1 is a flow chart of a distributed robust optimization method for substation planning taking into account uncertainty of incentive-type response according to the present invention;

FIG2 is a flowchart of the operation of the substation planning distribution blue stick optimization system taking into account the uncertainty of the incentive-type response of the present invention;

FIG3 is a typical daily 24-hour load curve of various loads in the embodiment;

FIG4 is a diagram showing the distribution of loads and candidate sites within the planning area in an embodiment;

FIG5 is a power supply range division result of case 1 in the embodiment;

FIG. 6 is a result of dividing the power supply range of Case 2 in the embodiment.

FIG7 is a power supply range division result of case 3 in the embodiment;

FIG8 shows the variation trend of planning cost of Case 3 with the number of sample scenarios in the embodiment.

DETAILED DESCRIPTION

In order to make the purpose, technical solution and advantages of the embodiments of the present invention clearer, the technical solution in the embodiments of the present invention will be clearly and completely described in combination with the embodiments of the present invention. Obviously, the described embodiments are part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of the present invention.

In conjunction with FIG1 , a substation planning distributed robust optimization method and an overall solution process considering the uncertainty of the incentive-type response proposed by the present invention are described in detail, and the specific steps are as follows:

Step 1: Considering the contracting cost, response cost and penalty benefit of demand response, a mixed integer linear programming model for substation site selection and sizing considering incentive-based demand response is established.

Step 2: Construct uncertain fuzzy sets of response power based on 1-norm and ∞-norm, and establish a two-stage three-layer distributed robust optimization model based on multiple discrete scenarios on the basis of improving the mixed integer linear programming model.

Step 3: For this distributed robust model, an iterative algorithm for the main problem and subproblems based on column and constraint generation is proposed.

The effectiveness of the proposed model and method is illustrated on the example system. The present invention uses a regional example covering an area of 97.56km2 for testing. According to the land use planning, it is divided into 351 communities for target year spatial load forecasting, among which the peak power of the residential load curve is 616.56MW, the peak power of the commercial load curve is 434.73MW, and the peak power of the industrial load curve is 625.23MW. After the three types of load sequence matching, the total peak power is 1385.66MW. There is a certain proportion of load that can be reduced in each of the three types of loads. The detailed load sequence is shown in Figure 3, and the distribution of load and substation location is shown in Figure 4. There are 22 optional substation construction locations in the planning area. The detailed substation location information is shown in Appendix Table A2. The capacity of the substations to be selected includes 2×40, 2×50, 3×40, and 3×50MVA, and the construction costs are 22 million, 25 million, 32 million, and 36 million yuan respectively. The service life of the substation and line is 30 years, the line cost is 0.025 million yuan/(km·kW), and the discount rate is 0.045. The contract price, response price, and penalty price of various load demand response are detailed in Table 1. In terms of uncertainty parameter setting, the confidence levels and adopted by the DRO model are 50% and 99% respectively, and 20 uncertainty scenarios of residential, commercial, and industrial loads are selected as samples.

Table 1 Demand response cost parameters

(1) Case comparative analysis

In order to analyze the impact of demand response and its uncertainty on planning results, the following three cases are set for planning comparison. Case 1 is substation planning without considering demand response; Case 2 is substation planning considering demand response but ignoring its uncertainty; Case 3 is substation planning considering demand response and its uncertainty. The planning costs of the three cases are shown in Table 2, the planned capacity of the substation and the load rate of each substation are shown in Table 3, and the power supply range division results of Cases 1-3 are shown in Figures 5-7 respectively.

Table 2 Annual planning costs for three cases

Table 3 Planned substation capacity and load rate for three cases

Note: Considering the N-1 safety principle of the substation, the upper limit of the load rate of the two main transformers in the calculation example is 65%, and the upper limit of the load rate of the three main transformers is 86%. Case 2-3 does not plan to build a substation at the 2# position.

The planning results of the three cases are analyzed. Case 2 can plan one less substation than Case 1. Although it needs to bear a demand response cost of 1.165 million yuan per year, it can save 3.377 million yuan in construction investment costs per year. Case 3 considers the uncertainty of demand response more than Case 2. Its planning cost and demand response cost have increased significantly. In the substation investment, a 40×3MVA substation was changed to a 50×3MVA substation, which increased the planning capacity and effectively coped with the impact of demand response uncertainty. The contract cost and response cost of demand response increased by 138,500 yuan in total, but because of the penalty income of 93,400 yuan, the total demand response cost increased by only 45,100 yuan. The increase in demand response cost is because the response intensity needs to be increased after considering uncertainty, which can cope with the excessive peak of the load curve caused by the uncertainty of demand response. The total cost of Case 3 increased by 196,900 yuan per year compared with Case 2, but it is still significantly lower than the planning cost of Case 1 without considering demand response.

(2) Analysis of Demand Response Effect

The substation planning method proposed in the present invention fully considers the matching of load timing characteristics, effectively reduces the peak value of the load curve within the power supply range, and considers the discontinuity of the planned substation capacity. According to the load curve characteristics within the power supply range of each substation, a reasonable demand response strategy is configured, which can effectively improve the utilization efficiency of the substation. By analyzing the load rates of each substation in Table 3, it can be found that the load rate of the substation planned by the method proposed in the present invention is significantly higher than the calculation result of the traditional planning method, that is, the utilization efficiency of the substation is significantly improved compared with the traditional planning method.

The load rates of substations in Case 2 and Case 3 considering demand response are significantly improved compared with those in Case 1 without considering demand response. After considering the uncertainty of demand response in Case 3, the load rates of most substations are lower than those in Case 2. The reason is that the substation has reserved a certain capacity margin, and the substation can still meet the N-1 safety constraint when the actual demand response deviates.

In addition, Case 2 did not take into account the uncertainty of demand response, and the load rates of most substations reached the upper limit, but the load rates of the four substations 1#, 13#, 21# and 22# did not reach the upper limit, and the load rates were slightly increased in Scheme 3. The reason for the analysis is that the peak value of the load curve within the power supply range of these four substations is lower than the planned substation capacity, and there is no need to adopt a demand response strategy; while other substations have higher peak values and adopt demand response. At the peak of the load curve, the power grid can send a response instruction to the user to reduce the peak power to the upper limit of the substation's power supply capacity, and the uncertainty is not considered, so their load rates can all reach the upper limit of the substation's load rate.

(3) Uncertainty model analysis

1) Comparison of uncertainty methods

Three methods, namely, random optimization, robust optimization and the distributed robust optimization proposed by the present invention, are used to plan Case 3. The planning cost and substation capacity selection results are as follows.

Table 4 Annual planning costs of three methods

Table 5 Substation capacity planned by three methods

Analysis of the planning results of the three methods shows that there are differences in construction investment costs and demand response costs. The planning cost obtained by using the distributed robust optimization model proposed in the present invention is between the random optimization model and the robust optimization model. It 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.

2) Impact of confidence level and number of sample scenarios on planning

In order to verify the rationality and effectiveness of the proposed distributed robust optimization model, different confidence levels and uncertain sample scenario numbers are set for testing. The annual planning costs under different confidence levels are shown in Table 6; the changing trend of planning costs with the number of sample scenarios is shown in Figure 8.

Table 6 Annual cost of DRO model planning under different confidence levels

Note: The cost unit is ten thousand yuan.

Combining the allowable deviation value formula to analyze the planning results, as the confidence level and the number of uncertainty samples increase, the allowable deviation range is larger when DRO is solved, which is conducive to finding worse uncertainty scenarios, and the planning cost is also rising. As can be seen from Figure 8, as the total number of uncertain samples increases, the planning cost increases significantly when the number of sample scenarios is small, but the growth rate tends to slow down when the number of sample scenarios reaches about 60, and increasing the number of sample scenarios has little effect on the planning results.

On the one hand, the present invention proposes a robust optimization method for substation planning taking into account the uncertainty of incentive response, the method comprising the following steps:

(1) Establish a deterministic substation planning model that takes into account incentive-based demand response. Taking into account the contracting cost, response cost, and penalty benefits of demand response, mathematical modeling is conducted on the peak shaving capacity and response cost of incentive-based demand response. Combined with the substation construction investment and line investment, a mixed integer linear programming model is established with the goal of minimizing the total grid investment cost.

(2) Construct a distributed robust model for substation planning considering the uncertainty of demand response. Considering the uncertainty of response power caused by user subjective decision-making, an uncertain fuzzy set based on 1-norm and ∞-norm is constructed; based on the improvement of the mixed integer linear programming model, a two-stage three-layer distributed robust optimization model based on multiple discrete scenarios is established.

(3) Propose a solution algorithm for the distributed robust model. Decompose the model into sub-problems and a main problem, and propose an iterative algorithm based on column and constraint generation.

The step (1) establishes a deterministic model for substation planning taking into account incentive-based demand response, including:

1) Demand response cost model of power grid companies

Incentive-based demand response, the response object is the load that can be reduced in the planning area, and it is an incentive-based demand response technology based on contractual agreements. The power supply and user parties first sign a contract to stipulate the maximum power that the user can respond to during the contract period, that is, the contract capacity _P1 , and generate contract costs; during the operation of the distribution network, the user is given a response instruction in advance during the peak power consumption period, and the user responds to the power _Pt according to the instruction, and the response cost is accumulated; the part of the user's response power that is less than the instruction requirement is the default power _Pt,f , and the penalty income is accumulated. The demand response cost calculation formula paid by the power grid company to a single user each year is as follows:

Among them, C _DR is the demand response fee that the power grid company needs to pay to the user every year; σ ₁ , σ ₂ , and σ ₃ are the unit prices of contract cost, response cost, and penalty benefit respectively; P is the maximum load of the user; λ is the ratio of the user's maximum contractable capacity to its maximum load, which represents the ability of the load to participate in demand response.

2) Substation planning model considering demand response

The purpose of substation planning is to reduce the investment and construction costs of substations and trunk lines as much as possible while meeting the target annual load electricity demand and various planning constraints. At the same time, various costs related to demand response should also be considered.

a) Decision variables: Decision variables include substation location and capacity selection, load and substation connection relationship, demand response contract capacity and response power in each time period. x _is a Boolean variable, indicating whether the ith substation location selects the sth substation type. Each substation type to be selected corresponds to a different substation capacity. An option with a capacity of 0 is added to the substation type to be selected. If a substation location selects the 0 capacity type, it means that the location has not been selected to build a substation. In this way, the two variables of location selection and capacity selection can be unified, solving the nonlinear problem caused by the need to multiply these two variables in the calculation of substation construction cost; y _ij is a Boolean variable, indicating whether the ith substation location has a connection relationship with the jth load; is a continuous variable, indicating the demand response contract capacity of the jth load; is a continuous variable, representing the response power of the jth load in period t.

b) Objective function:

minC＝ _CS + _CL + _CDR1 + _CDR2

Where: C is the total cost; _CS , _CL , _CDR1 and _CDR2 are the annual cost of substation construction, annual cost of line construction, demand response contract cost and response cost respectively; _r0 is the discount rate; ms is the depreciation period of the transformer; _NP is the number of substation locations to be selected; _NS is the number of substation types to be selected; _CSs is the construction cost of the sth substation type to be selected; β is the line unit cost coefficient; ml is the line depreciation period; _NL is the number of load points; _dij is the distance from substation i to load j; _Pj is the maximum load of the jth load point; σj _,1 and σj _,2 are the unit prices of the demand response contract cost and response cost of the jth load respectively.

c) Constraints:

Substation capacity selection uniqueness constraint: Only one substation type can be selected for a substation construction location.

Load point ownership uniqueness constraint: When dividing the power supply range, there is only one upper-level substation corresponding to a load point.

Maximum power supply radius constraint. _{r max} is the maximum value of the power supply radius of the medium voltage line specified in the power supply and distribution design specifications. It can also be designed according to actual conditions during planning, but in principle it is not allowed to be greater than the specified value.

y _i,j d _ij ≤r _max i∈[1,N _P ],j∈[1,N _L ]

Substation N-1 safety constraint. Based on the principle of safe operation of the power grid, after any transformer in the substation fails, the remaining transformers must meet the requirements of operating with all loads within the power supply range for 2 hours. This can be used to derive the maximum load rate e _s of the substation during normal operation. There are the following inequality constraints:

Where, _Ji is the load set within the power supply range of the i-th substation; _Pj,t is the power of the j-th load in the t-th period; is the power factor of the jth load; S _s is the capacity of the sth substation type to be selected.

Demand response constraints: The demand response contract capacity of each load point shall not be greater than its maximum response capacity, and the user response capacity during operation shall not be greater than the contract capacity.

The step (2) constructs a robust model for substation planning considering uncertainty in demand response, including:

1) Constructing uncertain fuzzy sets for demand response

Considering the uncertainty of user willingness, the actual response result _Pt deviates from the grid demand response instruction, and _Pt fluctuates within a certain range. Due to the limitations of historical data information, it is difficult to obtain a complete and accurate scenario probability distribution, but the fuzzy set of its uncertainty can be modeled. First, multiple actual scenarios are obtained through historical data, and then _Nk finite discrete scenarios and the probability distribution _pk,0 under each scenario are screened through scenario clustering; thirdly, considering that these scenarios cannot represent the actual probability distribution, a confidence set based on the 1-norm and ∞-norm can be constructed to limit the fluctuation of the probability distribution.

Where Ψ ₁ and Ψ _∞ represent the confidence intervals restricted by 1-norm and ∞-norm respectively; P is the vector form of the scenario probability p _k ; P ₀ is the vector form of the initial probability p _k,0 of each scenario; is a vector of N _k positive real numbers corresponding to P; K is the number of sample scenarios; α ₁ and α _∞ are the confidence levels for Ψ ₁ and Ψ _∞ respectively. Therefore, the probability distribution confidence set is restricted by both the 1-norm and the ∞-norm, avoiding extreme situations, Ψ = Ψ ₁ ∩Ψ _∞ , that is:

2) Two-stage distributed robust optimization model considering response power uncertainty

The uncertainty of demand response considered is that users cannot fully meet their response requirements when receiving response instructions, that is, there is uncertainty in the response power, which results in default power, and the power grid company can punish them according to the contract. Therefore, the calculation formula of demand response cost C _DR2 in the operation stage should be rewritten as follows:

At the same time, the uncertainty of demand response will change the actual response power, causing the load curve within the power supply range of the substation to fluctuate, which in turn affects the N-1 safety constraint of the substation. The constraint formula should be rewritten as follows:

The uncertainty of user demand response will affect the planning stage in the operation stage. Therefore, the planning model can be decomposed into two stages after taking into account the uncertainty. The first stage is the planning stage, and the decision variables include the relationship between the substation location and capacity selection, the connection relationship between the load and the substation, and the demand response contract capacity. The second stage is the operation stage, and the decision variable is the user's response power, and the actual response power is uncertain. The present invention divides the first stage decision variables into x _is , y _ij and The second stage decision variables are represented by vector x. It is represented by vector d. Therefore, the distributed robustness model based on discrete scenarios can be expressed as follows:

Among them: a ^T is the linear coefficient matrix of the objective function of the first stage; b ^T is the linear coefficient matrix of the objective function of the second stage; N _k represents the total number of discrete scenarios of probability distribution, k is the number of each scenario, and p _k represents the probability in the k scenario. The constraint condition form is transformed as follows:

Among them: C, E, F, G, H, m, n, u, v represent the corresponding matrix or vector form of the variables mentioned above. The first two formulas correspond to the equality constraints and inequality constraints of the first-stage variables; the third inequality constraint is the capacity coupling inequality of the first-stage variables and the second-stage variables; the last inequality constraint corresponds to the demand response inequality constraint of the second stage.

The step (3) proposes a solution algorithm for the distributed robust model, including:

The objective function and constraints in the above two-stage robust model are linear. Based on the constraint generation algorithm, the model can be decomposed into the main problem (MP) and sub-problems (SP), and then the optimal solution is obtained through iteration.

The purpose of MP solution is to obtain the optimal planning solution that satisfies the known probability distribution constraints under the conditions of finite discrete scenarios. The objective function and constraints of MP can be described as follows:

Where L is the lower-level demand response operating cost, the superscript r indicates the rth iteration, and the probability distribution of each iteration except the first iteration is obtained by SP solution. The MP problem can be solved to obtain a global optimal solution C ^* and the corresponding planning decision variable x ^* .

The purpose of SP solution is to match the load timing characteristics and demand response characteristics based on the optimization result x ^* of MP, when the substation capacity, power supply range and demand response contract capacity are known, to find the worst probability distribution P _k of the response power, and then provide the distribution to MP for the next iterative calculation, and update the global optimal solution according to the obtained L(x ^* ). The objective function of SP can be described as follows:

It can be seen from the above formula that the min problem in each scenario is independent, so it can be calculated simultaneously using a parallel method. For example, the internal optimization result of the kth scenario is Then the objective function of SP can be converted to:

The above MP and SP problems can be solved using the MILP model and linear programming model respectively, and can be quickly solved using commercial solvers. The optimization result _Pk of SP is passed to MP for iterative calculation until the difference between the global optimal solution C ^* of the two consecutive iterations is less than the specified threshold, and the iteration is stopped to obtain the optimal planning cost and decision variable value.

On the other hand, the present invention also provides a robust optimization system for substation planning taking into account the uncertainty of incentive-type response, the system comprising:

(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 finite discrete scenario conditions (known distribution or probability distribution obtained by the sub-problem solving module).

(3) The sub-problem solving module fixes the decision variables of the planning layer obtained by the main problem solving module, solves the decision variables of the operation layer with the goal of minimizing the operation cost, and finds the worst probability distribution of the response power.

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

The initialization module is used to iteratively solve the initialization settings of parameters, and to intervene in the algorithm through known scene probabilities to obtain the corresponding robust scene probabilities to form iterations.

The judgment module is used to determine whether the planning results have converged and whether the iterative solution can be stopped.

Output module, outputs planning schemes and decision variables.

In a third aspect, the present invention provides a non-transitory computer-readable storage medium, wherein the non-transitory computer-readable storage medium stores computer instructions, and the computer instructions enable the computer to execute the above method.

In a fourth aspect, the present invention provides a computer program product, comprising a computer program stored on a non-transitory computer-readable storage medium, wherein the computer program comprises program instructions, and when the program instructions are executed by a computer, the computer executes the above method.

Although the embodiments of the present invention have been shown and described above, it is to be understood that the above embodiments are exemplary and are not to be construed as limitations of the present invention. A person skilled in the art may change, modify, replace and vary the above embodiments within the scope of the present invention.

Claims (8)

1. A robust optimization method for substation planning considering incentive response uncertainty, characterized in that the specific steps are as follows: Step 1: Comprehensively consider the contract cost, response cost and penalty benefit of demand response, and establish a mixed integer linear programming model for substation location and sizing taking into account incentive-based demand response; Step 2: Construct uncertain fuzzy sets of response power based on 1-norm and ∞-norm, and establish a two-stage three-layer distributed robust optimization model based on multiple discrete scenarios on the basis of improving the mixed integer linear programming model; Step 3: For this distributed robust optimization model, an iterative algorithm for the main problem and subproblems based on column and constraint generation is proposed. 2. According to the method for optimizing substation planning based on incentive response uncertainty in claim 1, the method is characterized in that the establishment of the mixed integer linear programming model in Step 1 comprises: 1) Demand response cost model of power grid companies The power supply and user first sign a contract to stipulate the maximum power that the user can respond to during the contract period, the contract capacity P ₁ , and generate contract costs; during the operation of the distribution network, the user is given a response instruction in advance during the peak power consumption period, and the user responds to the power P _t according to the instruction, and the response cost is accumulated; the part of the user's response power that is less than the instruction requirement is the default power P _t,f , and the penalty income is accumulated. The demand response cost calculation formula paid by the power grid company to a single user each year is as follows: Among them, C _DR is the demand response fee that the power grid company needs to pay to the user every year; σ ₁ , σ ₂ , σ ₃ are the unit prices of contract cost, response cost and penalty benefit respectively; P is the maximum load of the user; λ is the ratio of the user's maximum contractable capacity to its maximum load, which represents the ability of the load to participate in demand response; 2) Substation planning model considering demand response The purpose of substation planning is to reduce the investment and construction costs of substations and trunk lines as much as possible under the premise of meeting the target annual load power demand and various planning constraints. At the same time, various costs related to demand response should also be considered; a) Decision variables: Decision variables include substation location and capacity selection, load and substation connection relationship, demand response contract capacity and response power in each time period. x _is a Boolean variable, indicating whether the ith substation location selects the sth substation type. Each substation type to be selected corresponds to a different substation capacity. An option with a capacity of 0 is added to the substation types to be selected. If a substation location selects the 0 capacity type, it means that the location is not selected for substation construction. The two variables of location selection and capacity selection are unified, which solves the nonlinear problem caused by the need to multiply these two variables in the calculation of substation construction cost; y _ij is a Boolean variable, indicating whether the ith substation location has a connection relationship with the jth load; is a continuous variable, indicating the demand response contract capacity of the jth load; is a continuous variable, indicating the response power of the jth load in period t; b) Objective function: minC＝ _CS + _CL + _CDR1 + _CDR2 Where: C is the total cost; _CS , _CL , _CDR1 and _CDR2 are the annual cost of substation construction, annual cost of line construction, demand response contract cost and response cost respectively; _r0 is the discount rate; ms is the depreciation period of the transformer; _NP is the number of substation locations to be selected; _NS is the number of substation types to be selected; _CSs is the construction cost of the sth substation type to be selected; β is the line unit cost coefficient; ml is the line depreciation period; _NL is the number of load points; _dij is the distance from substation i to load j; _Pj is the maximum load of the jth load point; σj _,1 and _σj,2 are the unit prices of the demand response contract cost and response cost of the jth load respectively; c) Constraints: Substation capacity selection uniqueness constraint. Only one substation type can be selected for a substation construction location: Load point ownership uniqueness constraint. When dividing the power supply range, there is only one upper-level substation corresponding to a load point: Maximum power supply radius constraint, r _max is the maximum value of the power supply radius of the medium voltage line specified in the power supply and distribution design specification: y _i,j d _ij ≤r _max i∈[1,N _P ],j∈[1,N _L ] Substation N-1 safety constraint, based on the principle of safe operation of the power grid, after any transformer in the substation fails, the remaining transformers must meet the requirements of operating with all loads within the power supply range for 2 hours. The maximum load rate of the substation during normal operation, e _s , has the following inequality constraints: Where, _Ji is the load set within the power supply range of the i-th substation; _Pj,t is the power of the j-th load in the t-th period; is the power factor of the jth load; S _s is the capacity of the sth substation type to be selected; Demand response constraints: the demand response contract capacity of each load point shall not be greater than its maximum response capacity, and the user response capacity during operation shall not be greater than the contract capacity: 3. According to the robust optimization method for substation planning considering the uncertainty of incentive-based response according to claim 1, it is characterized in that the step of constructing the robust optimization model in Step 2 comprises: 1) Constructing uncertain fuzzy sets for demand response Considering the uncertainty of user willingness, there is a deviation between the actual response result _Pt and the grid demand response instruction, and _Pt fluctuates within a certain range. The fuzzy set of its uncertainty is modeled: First, we obtain multiple actual scenarios through historical data, and then screen N _k finite discrete scenarios and the probability distribution p _k,0 under each scenario by means of scenario clustering. Thirdly, considering that these scenarios cannot represent the actual probability distribution, we construct a confidence set based on the 1-norm and ∞-norm to limit the fluctuation of the probability distribution: Where Ψ ₁ and Ψ _∞ represent the confidence intervals restricted by 1-norm and ∞-norm respectively; P is the vector form of the scenario probability p _k ; P ₀ is the vector form of the initial probability p _k,0 of each scenario; is a vector of N _k positive real numbers corresponding to P; K is the number of sample scenarios; α ₁ and α _∞ are the confidence levels for Ψ ₁ and Ψ _∞ respectively. Therefore, the probability distribution confidence set is restricted by both the 1-norm and the ∞-norm, avoiding extreme situations, Ψ = Ψ ₁ ∩Ψ _∞ , that is: 2) Two-stage distributed robust optimization model considering response power uncertainty The uncertainty of demand response considered is that users cannot fully meet their response requirements when receiving response instructions, and there is uncertainty in the response power, which results in default power. Therefore, the calculation formula of demand response cost C _DR2 in the operation stage should be rewritten as follows: At the same time, the uncertainty of demand response will change the actual response power, causing the load curve within the power supply range of the substation to fluctuate, which in turn affects the N-1 safety constraint of the substation. The constraint formula should be rewritten as follows: The uncertainty of user demand response will affect the planning stage in the operation stage. Therefore, the planning model can be decomposed into two stages after taking into account the uncertainty. The first stage is the planning stage. The decision variables include the relationship between substation location and capacity selection, the connection relationship between load and substation, and the demand response contract capacity. The second stage is the operation stage. The decision variable is the user's response power, and the actual response power is uncertain. The decision variables in the first stage include x _is , y _ij and The second stage decision variables are represented by vector x. It is represented by vector d. Therefore, the distributed robustness model based on discrete scenarios can be expressed as follows: Where: a ^T is the linear coefficient matrix of the objective function of the first stage; b ^T is the linear coefficient matrix of the objective function of the second stage; N _k represents the total number of discrete scenarios of the probability distribution, k is the number of each scenario, p _k represents the probability in the k scenario, and the constraint condition form is transformed as follows: Among them: C, E, F, G, H, m, n, u, v represent the corresponding matrix or vector form of the variables mentioned above. The first two formulas correspond to the equality constraints and inequality constraints of the first-stage variables; the third inequality constraint is the capacity coupling inequality of the first-stage variables and the second-stage variables; the last inequality constraint corresponds to the demand response inequality constraint of the second stage. 4. According to claim 1, a robust optimization method for substation planning considering incentive response uncertainty is characterized in that the iterative algorithm in Step 3 comprises: Based on the constraint generation algorithm, the model is decomposed into the main problem MP and the sub-problem SP, and then the optimal solution is obtained through iteration. The purpose of MP solution is to obtain the optimal planning solution that satisfies the known probability distribution constraints under the conditions of finite discrete scenarios. The objective function and constraint conditions of MP are described as follows: Where L is the lower-level demand response operating cost, the superscript r indicates the rth iteration, and except for the first iteration, the probability distribution of each iteration is obtained by SP solution. The MP problem is solved to obtain a global optimal solution C ^* and the corresponding planning decision variable x ^* ; The purpose of SP solution is to match the load timing characteristics and demand response characteristics based on the optimization result x ^* of MP, when the substation capacity, power supply range and demand response contract capacity are known, to find the worst probability distribution P _k of the response power, and then provide this distribution to MP for the next iterative calculation, and update the global optimal solution according to the obtained L(x ^* ). The objective function of SP can be described as follows: It can be seen from the above formula that the min problem in each scenario is independent and is calculated simultaneously using a parallel method. For example, the internal optimization result of the kth scenario is Then the objective function of SP can be converted to: The above MP and SP problems are solved using the MILP model and linear programming model respectively, and the optimization result _Pk of SP is passed to MP for iterative calculation until the difference between the global optimal solution C ^* of the two consecutive iterations is less than the specified threshold, and the iteration is stopped to obtain the optimal planning cost and decision variable value. 5. A robust optimization system for substation planning considering incentive response uncertainty, characterized in that the system comprises: (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-level decision variables that satisfy the known probability distribution constraints under the conditions of finite discrete scenarios; (3) The sub-problem solving module fixes the decision variables of the planning layer obtained by the main problem solving module, solves the decision variables of the operation layer with the goal of minimizing the operation cost, and finds the worst probability distribution of the response power. 6. A robust optimization system for substation planning considering incentive-based response uncertainty according to claim 5, characterized in that the system further comprises the following modules: The initialization module is used to iteratively solve the initialization settings of parameters and intervene in the algorithm through known scene probabilities to find the corresponding robust scene probabilities to form iterations; The judgment module is used to determine whether the planning results have converged and whether the iterative solution can be stopped; Output module, outputs planning schemes and decision variables. 7. A non-transitory computer-readable storage medium, characterized in that the non-transitory computer-readable storage medium stores computer instructions, and the computer instructions enable the computer to execute the method according to any one of claims 1 to 4. 8. A computer program product, characterized in that the computer program product comprises a computer program stored on a non-transitory computer-readable storage medium, the computer program comprising program instructions, and when the program instructions are executed by a computer, the computer executes the method according to any one of claims 1 to 4.