CN116862068A - Transformer substation planning distribution robust optimization method and system considering excitation type response uncertainty - Google Patents
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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
Technical Field
The invention belongs to the field of power distribution network planning, and relates to a robust optimization method and a robust optimization system for substation planning with uncertainty of excitation response.
Background
In recent years, energy transformation strategy in China is rapidly advanced, the electrification degree of terminal energy is continuously improved, peak load of a power distribution network is increased year by year, and huge pressure is brought to planning investment of a transformer substation. Demand response is an effective means to solve this problem. However, although the demand response can reduce the load peak to some extent, there is some uncertainty in the response due to the influence of human decision-making factors. How to finely consider the demand response and the uncertainty thereof in the transformer substation planning is an important problem to be solved currently.
The transformer substation planning relates to site selection, volume fixing and power supply range division of a transformer substation, is a large-scale nonlinear optimization problem comprising multiple types of decision variables, and an early planning method mainly comprises two types of heuristic methods and a layered decoupling method. The heuristic algorithm can obtain an optimal solution or an approximate optimal solution when solving a large-scale problem, is easy to sink into local optimum, and the power supply range is divided by adopting nearby distribution, so that the problems of unreasonable planning, too low or too high load rate and the like are caused; the essence of the layered decoupling method is that the large-scale nonlinear problem is decoupled into an upper layer sub-problem and a lower layer sub-problem, address selection and power supply range division are realized aiming at each capacity combination scheme to be selected generated by the upper layer, and the capacity combination scheme generated by the method has the possibility of being incapable of enumerating completely.
Many studies have considered demand responses in substation planning, which can improve the comprehensive load characteristics of the substation and reduce the investment cost of substation planning, but all have not considered the uncertainty of the demand responses, so that the planning scheme may have insufficient planning investment of the target year. In consideration of uncertainty factors in transformer substation planning, some researches model uncertainty of the position and the size of target annual load prediction, uncertainty of photovoltaic output and the like based on a random optimization method, but the method needs known uncertainty factor probability distribution and is difficult to acquire in practical application, so that the investment of the target annual planning is insufficient; still other studies use robust optimization to deal with uncertainty, i.e., consider the probability distribution of uncertainty factors in the worst scenario, and the resulting planning scheme is also biased to be conservative. In recent years, the advantages of the distributed robust optimization method in terms of uncertainty treatment are gradually paid attention to by students, the characteristics of random optimization and robust optimization are combined, and the optimization result shows good performance in terms of economy and conservation.
Disclosure of Invention
The technical problem to be solved by the invention is how to establish a substation planning mathematical model considering the demand response and the uncertainty thereof, solve the problem that the traditional substation planning method is easy to fall into local optimum, and ensure the economy and the robustness of the obtained planning scheme.
The present invention solves the above problems by the following means.
A robust optimization method for transformer substation planning distribution considering excitation type response uncertainty is characterized by comprising the following steps of: the method comprises the following specific steps:
step1: comprehensively considering the signing cost, response cost and punishment income of the demand response, and establishing a substation site selection and volume fixation mixed integer linear programming model considering the incentive type demand response;
step2: the response power uncertain fuzzy set based on 1-norm and ≡norm is constructed, and a two-stage three-layer distribution robust optimization model based on a multi-discrete scene is built on the basis of improving the mixed integer linear programming model;
step3: aiming at the distributed robust optimization model, a main problem and sub-problem iterative algorithm generated based on columns and constraints is provided.
Furthermore, the building of the mixed integer linear programming model described in Step1 includes: 1) Demand response cost model of power grid company
The power supply and the power utilization parties firstly contract, the maximum power which can be responded by the user in the good signing period is regulated,subscription capacity P 1 Generating signing cost; the method comprises the steps that response instructions during power consumption peak are sent to users in advance during operation of the power distribution network, and the users respond to power P according to the instructions t Accumulating to generate response cost; the part of the user response power less than the instruction requirement is the default power P t，f And accumulating to generate punishment benefits. The demand response cost for a single customer paid annually by the grid company is calculated as follows:
wherein C is DR A demand response fee per year paid to the user for the grid company; sigma (sigma) 1 、σ 2 、σ 3 The price per unit is subscription cost, response cost and punishment income respectively; p is the maximum value of the load of the user; lambda is the ratio of the maximum signable capacity of the user to the maximum load capacity of the user, and represents the capacity of the load to participate in demand response;
2) Transformer substation planning model considering demand response
The transformer substation planning aims to reduce the investment construction cost of the transformer substation and the main line as much as possible on the premise of meeting the load electricity demand of a target year and various planning constraints, and meanwhile, various costs related to demand response are considered;
a) Decision variables: the decision variables comprise the position and capacity selection of the transformer substation, the connection relation between the load and the transformer substation, the demand response subscription capacity and the response power of each period, and x is For Boolean variables, representing whether the ith transformer substation position selects the ith transformer substation type, each type of transformer substation to be selected corresponds to different transformer substation capacity, adding a capacity 0 option in the type of transformer substation to be selected, if a certain transformer substation position selects the type of 0 capacity, representing that the position is not selected for constructing the transformer substation, unifying two variables of position selection and capacity selection, and solving the nonlinear problem caused by multiplication of the two variables in the calculation of the construction cost of the transformer substation; y is ij The position of the ith transformer substation is a Boolean variable, and whether a connection relation exists between the position of the ith transformer substation and the jth load is indicated;the continuous variable represents the demand response subscription capacity of the jth load;As a continuous variable, representing the response power of the j-th load in the t period;
b) Objective function:
minC＝C S +C L +C DR1 +C DR2
wherein: c is the total cost; c (C) S 、C L 、C DR1 And C DR2 The method comprises the steps of respectively determining construction annual cost, line construction annual cost, demand response signing cost and response cost of the transformer substation; r is (r) 0 Is the discount rate; ms is the depreciation age of the transformer; n (N) P The number of the positions to be selected is the number of the positions to be selected of the transformer substation; n (N) S The number of types of substations to be selected is; c (C) Ss The construction cost for the type of the s-th transformer substation to be selected; beta is the line unit cost coefficient; ml is the depreciation age of the line; n (N) L The number of load points; d, d ij Distance from the transformer station i to the load j; p (P) j Maximum load amount for the j-th load point; sigma (sigma) j,1 Sum sigma j,2 Demand response subscription cost and response costs for the jth load, respectivelyThe unit price of the book;
c) Constraint conditions:
substation capacity selects a unique constraint. Only one substation type can be selected for one substation construction location:
the load points are attributed to a unique constraint. When the power supply range is divided, one upper-level transformer station corresponding to one load point is provided with only one:
Maximum power supply radius constraint, r max Maximum value of the radius of supply for medium voltage lines specified in the power supply and distribution design specification:
y i,j d ij ≤r max i∈[1,N P ],j∈[1,N L ]
the N-1 safety constraint of the transformer substation is based on the power grid safety operation principle, after any transformer in the transformer substation fails, the residual transformer needs to meet the maximum load rate e of the transformer substation in normal operation after all loads in the power supply range are operated for 2 hours s There are the following inequality constraints:
wherein J is i A load set in the power supply range of the ith transformer substation; p (P) j,t Power for the j-th load in the t period;the power factor for the j-th load; s is S s The capacity of the type of the s-th transformer substation to be selected;
and (3) demand response constraint, wherein the demand response subscription capacity of each load point is not more than the maximum response capacity of each load point, and the user response capacity is not more than the subscription capacity in running:
moreover, the Step of constructing the robust optimization model in Step2 includes:
1) Building an uncertainty fuzzy set of demand responses
Taking into account uncertainty of user will, actual response result P t Deviation from the grid demand response command, and P t Fluctuation is carried out within a certain range, and the fuzzy set of uncertainty is modeled:
firstly, obtaining a plurality of actual scenes through historical data, and then screening to obtain N through a scene clustering means k A finite discrete scene and probability distribution p under each scene k,0 The method comprises the steps of carrying out a first treatment on the surface of the Again, considering that these scenarios do not represent the actual probability distribution, a confidence set based on 1-norm and + -norm is constructed to limit the fluctuating variation of the probability distribution:
wherein ψ is 1 And psi is ∞ Respectively represent 1-normsAnd a confidence interval of +_norm constraint; p is scene probability P k Vector form of (a); p (P) 0 Initial probability p for each scene k,0 Vector form of (a);is N corresponding to P k A vector of positive real numbers; k is the number of sample scenes; alpha 1 And alpha ∞ Respectively is psi 1 And psi is ∞ Confidence of establishment. The confidence coefficient set of probability distribution is limited by 1-norm and infinity-norm at the same time, so that the situation of extreme is avoided, ψ=ψ 1 ∩Ψ ∞ The method comprises the following steps:
2) Two-stage distributed robust optimization model considering response power uncertainty
The uncertainty of the demand response is that the user can not fully meet the response requirement when receiving the response instruction, and the uncertainty exists in the response power, so that the default power is generated, and the demand response cost C of the operation stage is calculated DR2 The calculation formula should be rewritten as follows:
meanwhile, the actual response power can be changed due to the uncertainty of the demand response, so that load curve fluctuation in the power supply range of the transformer substation is caused, and the N-1 safety constraint of the transformer substation is influenced, and the constraint formula is rewritten as follows:
The uncertainty of the user demand response in the operation stage affects the planning stage, so that the planning model can be decomposed into two stages after the uncertainty is taken into account, the first stage is the planning stage, and the decision variables comprise power transformationStation position and capacity selection relation, connection relation between load and transformer substation and demand response subscription capacity; the second stage is an operation stage, the decision variable is the response power of the user, and the actual response power has uncertainty; the first stage decision variables include x is 、y ij Andrepresented by vector x, second stage decision variable +.>Represented by vector d. The distributed robust model based on discrete scenes can be expressed as follows:
wherein: a, a T A linear coefficient matrix for the first stage objective function; b T A linear coefficient matrix for the second stage objective function; n (N) k The total number of discrete scenes representing the probability distribution, k being the number of each scene, p k Representing the probability at k scenes, the constraint form transforms as follows:
wherein: c, E, F, G, H, m, n, u, v represent the matrix or vector form corresponding to the variables above, the first two formulas corresponding to the equality constraint and inequality constraint of the first stage variables; the third inequality constraint is a capacity coupling inequality of the first stage variable and the second stage variable; the last inequality constraint corresponds to the second stage demand response inequality constraint.
Furthermore, the iterative algorithm described in Step3 includes:
based on a constraint generation algorithm, decomposing a model into a main problem MP and a sub problem SP, and then solving an optimal solution through iteration, wherein the purpose of MP solving is to obtain an optimal planning scheme meeting the constraint of a known probability distribution under the condition of a limited discrete scene, and the objective function and constraint condition of MP are described as follows:
l is lower-layer demand response running cost, the upper corner mark r represents the r-th iteration, and probability distribution of each iteration except the 1 st iteration is obtained by solving by the SP. MP problem solving to obtain a global optimal solution C * And corresponding planning decision variable x * ；
SP solution purpose is MP-based optimization result x * Under the condition that the capacity, the power supply range and the demand response signing capacity of the transformer substation are known, the load time sequence characteristic and the demand response characteristic are matched, and the worst probability distribution P of the response power is found k The distribution is then provided to MP for further iterative computation while being based on the resulting L (x * ) Updating the globally optimal solution, the objective function of the SP may be described as follows:
as can be seen from the above equation, the min problem in each scene is independent, and the parallel method is used for simultaneous calculation, for example, the internal optimization result of the kth scene is that The objective function of the SP may be converted to:
the MP and SP problems are respectively carried out by using an MILP model and a linear programming modelSolving the rows and optimizing the result P of the SP k Transmitting to MP for iterative calculation until the global optimal solution C of two adjacent iterations * And stopping iteration when the difference value is smaller than a specified threshold value, and obtaining the optimal planning cost and the decision variable value.
A substation planning distribution robust optimization system accounting for excitation type response uncertainty, the system comprising:
(1) The data input and processing module is used for carrying out matrixing processing on input load prediction data and various planning parameter information;
(2) The main problem solving module obtains an optimal planning scheme and planning layer decision variables meeting the known probability distribution constraint under the condition of a limited discrete scene;
(3) And the sub-problem solving module is used for fixing the decision variables of the planning layer obtained by the main problem solving module, solving the decision variables of the operation layer by taking the minimum operation cost as a target, and finding out the worst probability distribution of the response power.
Moreover, the system further comprises the following modules:
the initialization module is used for initializing and setting iteration solving parameters, and solving corresponding robustness scene probability through a known scene probability intervention algorithm so as to form iteration;
The judging module is used for judging whether the planning result is converged or not and stopping iterative solution;
and the output module is used for outputting the planning scheme and the decision variables.
A non-transitory computer readable storage medium storing computer instructions that cause the computer to perform the method of any one of claims 1 to 4.
A computer program product comprising a computer program stored on a non-transitory computer readable storage medium, the computer program comprising program instructions which, when executed by a computer, cause the computer to perform the method of any of claims 1 to 4.
The invention has the advantages that:
(1) The model built by the invention and the solving method adopted by the invention are both based on a mathematical programming method, and effectively solve the problem that the traditional transformer substation programming is easy to fall into local optimum.
(2) Because the transformer capacity is a fixed value, namely the planned transformer substation capacity has discontinuity, the transformer substation planning taking the demand response into account can configure a reasonable demand response strategy according to the load curve characteristic in the power supply range of each transformer substation, and the utilization efficiency of the transformer substation is effectively improved.
(3) The time sequence power of the load and the demand response is considered, a corresponding matrix model is established, the time sequence characteristic matching of the load and the demand response can be fully considered, the peak value of a load curve in a power supply range is effectively reduced, and the capacity cost of transformer substation planning is reduced.
(4) On the aspect of the processing of response power uncertainty, a distributed robust optimization method based on multiple discrete scenes is adopted, so that the defect that the random optimization depends on known probability distribution and is easy to cause insufficient planning is overcome, and meanwhile, the conservation of a planning result is effectively reduced.
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.
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In order to more clearly illustrate the technical solutions of the present invention, the drawings that are needed in the description of the embodiments will be briefly described below, it being obvious that the drawings in the following description are only some embodiments of the present invention, and that other drawings may be obtained according to these drawings without inventive effort for a person skilled in the art.
FIG. 1 is a flow chart of a substation planning distribution robust optimization method accounting for excitation type response uncertainty of the present invention;
FIG. 2 is a flow chart of a substation planning distribution robust optimization system operation taking excitation response uncertainty into account;
FIG. 3 is a typical daily 24h load profile for various types of loads in the examples;
FIG. 4 is a diagram of load and candidate site distribution in a planned area in an embodiment;
fig. 5 is a power supply range division result of case 1 in the embodiment;
fig. 6 is a power supply range division result of case 2 in the embodiment.
FIG. 7 is a power supply range division result of case 3 in the embodiment;
fig. 8 is a plot of case 3 planning cost versus the number of sample scenarios in an embodiment.
Detailed Description
For the purpose of making the objects, technical solutions and advantages of the embodiments of the present invention more apparent, the technical solutions in the embodiments of the present invention will be clearly and completely described in the following in conjunction with the embodiments of the present invention, and it is apparent that the described embodiments are some embodiments of the present invention, but not all embodiments. All other embodiments, which can be made by those skilled in the art based on the embodiments of the invention without making any inventive effort, are intended to be within the scope of the invention.
The invention provides a robust optimization method for transformer substation planning distribution and an overall solving flow, which are used for considering excitation type response uncertainty, and specifically comprises the following steps of:
Step1: and comprehensively considering the signing cost, the response cost and the punishment income of the demand response, and establishing a substation site selection and volume fixation mixed integer linear programming model considering the incentive type demand response.
Step2: and (3) constructing a response power uncertain fuzzy set based on 1-norm and + -norm, and constructing a two-stage three-layer distribution robust optimization model based on a multi-discrete scene on the basis of improving the mixed integer linear programming model.
Step3: and aiming at the distributed robust model, a main problem and sub-problem iterative algorithm generated based on columns and constraints is provided.
On an example system, the effectiveness of the proposed model and method is elucidated. The invention selects a regional example with a certain occupied area of 97.56km2 for testing. The method comprises the steps of dividing the system into 351 cells according to land planning to conduct target annual space load prediction, wherein the peak power of a residential load curve is 616.56MW, the peak power of a commercial load curve is 434.73MW, the peak power of an industrial load curve is 625.23MW, and the total peak power after three types of load time sequence matching is 1385.66MW. The three types of loads have a certain proportion of load reduction, the detailed load time sequence is shown in fig. 3, and the load and substation position distribution is shown in fig. 4. 22 optional transformer substation construction positions are arranged in the planning area, and detailed transformer substation position information is shown in an annex table A2. The capacity of the transformer substation to be selected comprises four types of 2X 40, 2X 50, 3X 40 and 3X 50MVA, and the construction cost is 2200, 2500, 3200 and 3600 ten thousand yuan respectively. The service life of the transformer substation and the circuit is 30 years, the cost of the circuit is 0.025 ten thousand yuan/(km.kW), and the discount rate is 0.045. The various load demands respond to the subscription prices, the response prices and the punishment prices are shown in table 1 in detail. In the aspect of uncertainty parameter setting, the confidence level adopted by the DRO model and 50% and 99% of the confidence level are respectively taken, and 20 uncertainty scenes of three loads of residents, businesses and industries are respectively selected as samples.
TABLE 1 demand response cost parameters
(1) Case contrast analysis
In order to facilitate analysis and consideration of the influence of the demand response and uncertainty thereof on the planning result, the following 3 cases are set for planning comparison. Respectively planning the transformer substations without considering the demand response for the case 1; case 2 considers the demand response, but does not account for the uncertain substation planning; case 3 considers the substation planning of the demand response and its uncertainty. The planning cost of the 3 cases is shown in table 2, the planning capacity of the transformer substation and the load factor of each transformer substation are shown in table 3, and the power supply range division results of the cases 1-3 are shown in fig. 5-7 respectively.
Table 2 annual cost of planning for three cases
Table 3 three cases plan substation capacity and load factor
Note that: considering the N-1 safety principle of the transformer substation, the upper limit of the load rate of two main transformers is 65% and the upper limit of the load rate of three main transformers is 86% in the calculation example. Cases 2-3 did not plan the build substation at position # 2.
The planning results of the 3 cases were analyzed. Case 2 can plan 1 substation less than case 1, and can save construction investment cost 337.7 ten thousand yuan each year although the requirement response cost of 116.5 ten thousand yuan is born each year. The uncertainty of demand response is considered in case 3 more than in case 2, the planning cost and the demand response cost are obviously increased, a 40X 3MVA transformer substation is changed into a 50X 3MVA transformer substation in transformer substation investment, the planning capacity is improved, and the influence on the uncertainty of demand response can be effectively caused; the signing cost and the response cost of the demand response are increased by 13.85 ten thousand yuan, but the total demand response cost is increased by 4.51 ten thousand yuan because of punishment income of 9.34 ten thousand yuan, and the demand response cost is increased because the response strength is required to be increased after the uncertainty is considered, so that the peak value of a load curve caused by the uncertainty of the demand response can be dealt with. The overall cost of case 3 over case 2 increases by 19.69 ten thousand yen per year, but still is significantly lower than the planning cost of case 1 without considering demand response.
(2) Demand response effect analysis
According to the transformer substation planning method provided by the invention, load time sequence characteristic matching is fully considered, the peak value of a load curve in a power supply range is effectively reduced, meanwhile, the discontinuity of the capacity of the planned transformer substation is considered, and a reasonable demand response strategy is configured according to the load curve characteristic in the power supply range of each transformer substation, so that the utilization efficiency of the transformer substation can be effectively improved. As can be seen by analyzing the variable load rates in table 3, the load rate of the transformer substation planned by the method provided by the invention is obviously higher than the example result of the traditional planning method, namely, the utilization efficiency of the transformer substation is obviously improved compared with that of the traditional planning method.
The transformer substation load rate of the case 2 and the case 3 considering the demand response is obviously improved compared with that of the case 1 without considering the demand response, and most transformer substation load rates are reduced compared with that of the case 2 after the case 3 considering the uncertainty of the demand response, because a certain capacity margin is reserved for the transformer substation, and the power station can still meet the safety constraint of N-1 when the actual demand response deviates.
In addition, case 2 does not account for the uncertainty of the demand response, most of the transformer substation load rates reach the upper limit, but the load rates of the transformer substations # 1, # 13, # 21 and # 22 do not reach the upper limit, and the load rate is slightly increased in scheme 3. The analysis reason is that the peak value of the load curve in the power supply range of the four transformer substations is lower than the planned transformer substation capacity, and a demand response strategy is not needed; the peak value of other substations adopts demand response, a response instruction can be issued to a user at the peak value of the load curve, the peak power is reduced to the upper limit value of the power supply capacity of the substation, and uncertainty is not considered, so that the load rate of the power supply system can reach the upper limit of the load rate of the substation.
(3) Uncertainty model analysis
1) Uncertainty method comparison
And planning the case 3 by adopting three methods of random optimization, robust optimization and distributed robust optimization. The planning cost and the substation capacity selection result are as follows.
Table 4 annual cost of planning for three methods
Table 5 three method planned substation capacities
The planning results of the three methods are analyzed, and differences exist in construction investment cost and demand response cost, and the planning cost obtained by adopting the distributed robust optimization model is between the random optimization model and the robust optimization model, so that the defect that the random optimization depends on the known probability distribution and is easy to cause insufficient planning is overcome, and meanwhile, the conservation of the planning result is effectively reduced.
2) Influence of confidence level and number of sample scenes on planning
In order to verify the rationality and effectiveness of the distributed robust optimization model, different confidence levels and uncertain sample scene numbers are set for testing. Annual cost of planning at different confidence levels is shown in table 6; the variation trend of the planning cost with the number of sample scenes is shown in fig. 8.
TABLE 6 annual cost of DRO model planning at different confidence levels
Note that: the cost unit is ten thousand yuan.
And the planning result is analyzed by combining an allowable deviation value formula, and along with the increase of the confidence level and the uncertainty sample number, the larger the allowable deviation range is when the DRO is solved, the worse uncertainty scene is found, and the planning cost is also continuously increased. As can be seen from fig. 8, as the total number of uncertain samples increases, the planning cost increases significantly when the number of sample scenes is small, but increases gradually when the number of sample scenes reaches about 60, and the effect of increasing the number of sample scenes on the planning result is not great.
On one hand, the invention provides a robust optimization method for transformer substation planning distribution considering excitation type response uncertainty, which comprises the following steps:
(1) And establishing a substation planning deterministic model considering the excitation type demand response. Comprehensively considering the signing cost, the response cost and the punishment income of the demand response, and carrying out mathematical modeling on the peak clipping capacity and the response cost of the incentive type demand response; and then, combining the construction investment and the line investment of the transformer substation, and establishing a mixed integer linear programming model with the minimum total cost of the power grid investment as a target.
(2) And constructing a substation planning distribution robust model considering the uncertainty of the demand response. The response power uncertainty caused by subjective decision of a user is considered, and an uncertainty fuzzy set based on 1-norm and ++norm is constructed; on the basis of improving the mixed integer linear programming model, a two-stage three-layer distribution robust optimization model based on a multi-discrete scene is established.
(3) And a solving algorithm of the distributed robust model is provided. The model is decomposed into sub-problems and main problems, and an iterative algorithm generated based on columns and constraints is provided.
The step (1) is to build a substation planning deterministic model considering excitation type demand response, and comprises the following steps:
1) Demand response cost model of power grid company
Based on the stimulated demand response, the response object is a reducible load in a planning area, and is a stimulated demand response technology based on contract agreement. The power supply and use parties firstly sign contracts, and the maximum power which can be responded by the user in the good signing period is regulated, namely the signing capacity P 1 Generating signing cost; the method comprises the steps that response instructions during power consumption peak are sent to users in advance during operation of the power distribution network, and the users respond to power P according to the instructions t Accumulating to generate response cost; the part of the user response power less than the instruction requirement is the default power P t，f And accumulating to generate punishment benefits. The demand response cost for a single customer paid annually by the grid company is calculated as follows:
wherein C is DR A demand response fee per year paid to the user for the grid company; sigma (sigma) 1 、σ 2 、σ 3 The price per unit is subscription cost, response cost and punishment income respectively; p is the maximum value of the load of the user; lambda is the ratio of the maximum signable capacity of the user to the maximum load capacity of the user and represents the load participation demand response Capability of the application.
2) Transformer substation planning model considering demand response
The transformer substation planning aims to reduce the investment and construction costs of the transformer substation and the main line as much as possible on the premise of meeting the load electricity demand of a target year and various planning constraints, and meanwhile, various costs related to demand response are considered.
a) Decision variables: the decision variables comprise the position and capacity selection of the transformer substation, the connection relation between the load and the transformer substation, the demand response subscription capacity and the response power of each period. X is x is For Boolean variables, representing whether the ith transformer substation position selects the ith transformer substation type, each type of transformer substation to be selected corresponds to different transformer substation capacity, adding a capacity 0 option in the type of transformer substation to be selected, and if a certain transformer substation position selects the type of 0 capacity, representing that the position is not selected for constructing the transformer substation, so that two variables of position selection and capacity selection can be unified, and the nonlinear problem caused by multiplication of the two variables in transformer substation construction cost calculation is solved; y is ij The position of the ith transformer substation is a Boolean variable, and whether a connection relation exists between the position of the ith transformer substation and the jth load is indicated;the continuous variable represents the demand response subscription capacity of the jth load; / >As a continuous variable, the response power of the j-th load in the t period is represented.
b) Objective function:
minC＝C S +C L +C DR1 +C DR2
wherein: c is the total cost; c (C) S 、C L 、C DR1 And C DR2 The method comprises the steps of respectively determining construction annual cost, line construction annual cost, demand response signing cost and response cost of the transformer substation; r is (r) 0 Is the discount rate; ms is the depreciation age of the transformer; n (N) P The number of the positions to be selected is the number of the positions to be selected of the transformer substation; n (N) S The number of types of substations to be selected is; c (C) Ss The construction cost for the type of the s-th transformer substation to be selected; beta is the line unit cost coefficient; ml is the depreciation age of the line; n (N) L The number of load points; d, d ij Distance from the transformer station i to the load j; p (P) j Maximum load amount for the j-th load point; sigma (sigma) j,1 Sum sigma j,2 The demand response contract cost and the unit price of the response cost for the j-th load, respectively.
c) Constraint conditions:
substation capacity selects a unique constraint. Only one substation type can be selected for one substation construction location.
The load points are attributed to a unique constraint. When the power supply range is divided, there is only one upper-level substation corresponding to one load point.
Maximum supply radius constraint. r is (r) max The maximum value of the power supply radius of the medium-voltage line specified in the power supply and distribution design specification can also be calculated according to actual conditions during planningThe row design, however, is in principle not allowed to be greater than the specification value.
y i,j d ij ≤r max i∈[1,N P ],j∈[1,N L ]
Substation N-1 security constraints. Based on the principle of safe operation of the power grid, after any transformer in the transformer substation fails, the residual transformer needs to meet the requirement that all loads in the power supply range are operated for 2 hours, so that the maximum load rate e of the transformer substation in normal operation can be deduced s . There are the following inequality constraints:
wherein J is i A load set in the power supply range of the ith transformer substation; p (P) j,t Power for the j-th load in the t period;the power factor for the j-th load; s is S s And the capacity of the type of the s-th to-be-selected substation.
Demand response constraints. The demand response subscription capacity of each load point is not more than the maximum response capacity of each load point, and the response capacity of a user in running is not more than the subscription capacity.
The step (2) of constructing a substation planning distribution robust model considering the uncertainty of the demand response comprises the following steps:
1) Building an uncertainty fuzzy set of demand responses
Taking into account uncertainty of user will, actual response result P t Deviation from the grid demand response command, and P t Fluctuating within a certain range. Due to historical data informationWe have difficulty in obtaining a complete and accurate scene probability distribution, but can model the fuzzy set of its uncertainties. Firstly, obtaining a plurality of actual scenes through historical data, and then screening to obtain N through a scene clustering means k A finite discrete scene and probability distribution p under each scene k,0 The method comprises the steps of carrying out a first treatment on the surface of the Again, considering that these scenarios do not represent the actual probability distribution, a confidence set based on the 1-norm and the + -norm can be constructed to limit the fluctuating variation of the probability distribution.
Wherein ψ is 1 And psi is ∞ Respectively represent 1-norm and ≡ -confidence interval of norm limitation; p is scene probability P k Vector form of (a); p (P) 0 Initial probability p for each scene k,0 Vector form of (a);is N corresponding to P k A vector of positive real numbers; k is the number of sample scenes; alpha 1 And alpha ∞ Respectively is psi 1 And psi is ∞ Confidence of establishment. The confidence coefficient set of probability distribution is limited by 1-norm and infinity-norm at the same time, so that the situation of extreme is avoided, ψ=ψ 1 ∩Ψ ∞ The method comprises the following steps:
2) Two-stage distributed robust optimization model considering response power uncertainty
The uncertainty of the demand response is considered that the user cannot fully meet the response requirement when receiving the response command, namely, the uncertainty exists in the response power, so that the default power is generated, and the grid company can punish the uncertainty according to contracts. So the demand response cost C of the operation stage DR2 The calculation formula should be rewritten as follows:
meanwhile, the actual response power can be changed due to the uncertainty of the demand response, so that load curve fluctuation in the power supply range of the transformer substation is caused, and the N-1 safety constraint of the transformer substation is influenced, and the constraint formula is rewritten as follows:
The uncertainty of the user demand response is in the run phase and can affect the planning phase. Thus, taking into account uncertainty, the planning model may be decomposed into two phases. The first stage is a planning stage, and the decision variables comprise a relation between the position and capacity selection of the transformer substation, a connection relation between the load and the transformer substation and a demand response subscription capacity. The second stage is a running stage, the decision variable is the response power of the user, and the actual response power has uncertainty. The invention includes the first stage decision variable including x is 、y ij Andrepresented by vector x, second stage decision variable +.>Represented by vector d. Therefore, the distributed robust model based on discrete scene can be expressedThe following are provided:
wherein: a, a T A linear coefficient matrix for the first stage objective function; b T A linear coefficient matrix for the second stage objective function; n (N) k The total number of discrete scenes representing the probability distribution, k being the number of each scene, p k Representing the probability of being in a k scene. The constraint form transformation is as follows:
wherein: c, E, F, G, H, m, n, u, v represent the matrix or vector form corresponding to the variables above. The first two formulas correspond to the equality constraint and the inequality constraint of the first stage variable; the third inequality constraint is a capacity coupling inequality of the first stage variable and the second stage variable; the last inequality constraint corresponds to the second stage demand response inequality constraint.
The step (3) provides a solving algorithm of the distributed robust model, which comprises the following steps:
the objective function and constraint conditions in the two-stage distributed robust model are linear. Based on the listed constraint generation algorithm, the model can be decomposed into a Main Problem (MP) and a sub-problem (SP), and then an optimal solution can be obtained through iteration.
The MP solving purpose is to obtain an optimal planning scheme meeting the constraint of the known probability distribution under the condition of limited discrete scenes. The objective function and constraints of MP can be described as follows:
l is lower-layer demand response running cost, the upper corner mark r represents the r-th iteration, and probability distribution of each iteration except the 1 st iteration is obtained by solving by the SP. MP problem solving can obtain a global optimal solution C * And corresponding planning decision variable x * 。
SP solution purpose is MP-based optimization result x * Under the condition that the capacity, the power supply range and the demand response signing capacity of the transformer substation are known, the load time sequence characteristic and the demand response characteristic are matched, and the worst probability distribution P of the response power is found k The distribution is then provided to MP for further iterative computation while being based on the resulting L (x * ) And updating the globally optimal solution. The objective function of the SP may be described as follows:
As can be seen from the above equation, the min problem in each scene is independent, so that parallel methods can be used to calculate simultaneously, such as the internal optimization result of the kth scene is thatThe objective function of the SP may be converted to:
the MP and SP problems can be solved by an MILP model and a linear programming model respectively, can be quickly solved by a commercial solver, and the optimization result P of the SP is obtained k Transmitting to MP for iterative calculation until the global optimal solution C of two adjacent iterations * And stopping iteration when the difference value is smaller than a specified threshold value, and obtaining the optimal planning cost and the decision variable value.
On the other hand, the invention also provides a transformer substation planning distribution robust optimization system considering excitation type response uncertainty, which comprises the following steps:
(1) And the data input and processing module is used for carrying out matrixing processing on the input load prediction data and various planning parameter information.
(2) And the main problem solving module is used for obtaining an optimal planning scheme and planning layer decision variables which meet the constraint of the known probability distribution under the condition of a limited discrete scene (the known distribution or the probability distribution obtained by the sub-problem solving module).
(3) And the sub-problem solving module is used for fixing the decision variables of the planning layer obtained by the main problem solving module, solving the decision variables of the operation layer by taking the minimum operation cost as a target, and finding out the worst probability distribution of the response power.
Further, the complete planning system should also include the following modules:
the initialization module is used for initializing and setting iteration solving parameters, and solving corresponding robustness scene probability through a known scene probability intervention algorithm so as to form iteration.
And the judging module is used for judging whether the planning result is converged or not and stopping iterative solution.
And the output module is used for outputting the planning scheme and the decision variables.
In a third aspect the present invention provides a non-transitory computer readable storage medium storing computer instructions that cause a computer to perform the above-described method.
A fourth aspect 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 which, when executed by a computer, cause the computer to perform the above method.
While embodiments of the present invention have been shown and described above, it will be understood that the above embodiments are illustrative and not to be construed as limiting the invention, and that variations, modifications, alternatives and variations may be made to the above embodiments by one of ordinary skill in the art within the scope of the invention.
Claims (8)
1. A robust optimization method for transformer substation planning distribution considering excitation type response uncertainty is characterized by comprising the following steps of: the method comprises the following specific steps:
step1: comprehensively considering the signing cost, response cost and punishment income of the demand response, and establishing a substation site selection and volume fixation mixed integer linear programming model considering the incentive type demand response;
step2: the response power uncertain fuzzy set based on 1-norm and ≡norm is constructed, and a two-stage three-layer distribution robust optimization model based on a multi-discrete scene is built on the basis of improving the mixed integer linear programming model;
step3: aiming at the distributed robust optimization model, a main problem and sub-problem iterative algorithm generated based on columns and constraints is provided.
2. The method for robust optimization of a substation planning distribution taking account of uncertainty in excitation-type response of claim 1, wherein the building of the mixed integer linear programming model in Step1 comprises:
1) Demand response cost model of power grid company
The power supply and use parties firstly sign contracts, define the maximum power which can be responded by users in the good signing period and sign up the capacity P 1 Generating signing cost; the method comprises the steps that response instructions during power consumption peak are sent to users in advance during operation of the power distribution network, and the users respond to power P according to the instructions t Accumulating to generate response cost; the part of the user response power less than the instruction requirement is the default power P t，f And accumulating to generate punishment benefits. The demand response cost for a single customer paid annually by the grid company is calculated as follows:
wherein C is DR A demand response fee per year paid to the user for the grid company; sigma (sigma) 1 、σ 2 、σ 3 The price per unit is subscription cost, response cost and punishment income respectively; p is the maximum value of the load of the user; lambda (lambda)The ratio of the maximum signable capacity of the user to the maximum load capacity of the user represents the capacity of the load to participate in the demand response;
2) Transformer substation planning model considering demand response
The transformer substation planning aims to reduce the investment construction cost of the transformer substation and the main line as much as possible on the premise of meeting the load electricity demand of a target year and various planning constraints, and meanwhile, various costs related to demand response are considered;
a) Decision variables: the decision variables comprise the position and capacity selection of the transformer substation, the connection relation between the load and the transformer substation, the demand response subscription capacity and the response power of each period, and x is For Boolean variables, representing whether the ith transformer substation position selects the ith transformer substation type, each type of transformer substation to be selected corresponds to different transformer substation capacity, adding a capacity 0 option in the type of transformer substation to be selected, if a certain transformer substation position selects the type of 0 capacity, representing that the position is not selected for constructing the transformer substation, unifying two variables of position selection and capacity selection, and solving the nonlinear problem caused by multiplication of the two variables in the calculation of the construction cost of the transformer substation; y is ij The position of the ith transformer substation is a Boolean variable, and whether a connection relation exists between the position of the ith transformer substation and the jth load is indicated;the continuous variable represents the demand response subscription capacity of the jth load;As a continuous variable, representing the response power of the j-th load in the t period;
b) Objective function:
minC＝C S +C L +C DR1 +C DR2
wherein: c is the total cost; c (C) S 、C L 、C DR1 And C DR2 The method comprises the steps of respectively determining construction annual cost, line construction annual cost, demand response signing cost and response cost of the transformer substation; r is (r) 0 Is the discount rate; ms is the depreciation age of the transformer; n (N) P The number of the positions to be selected is the number of the positions to be selected of the transformer substation; n (N) S The number of types of substations to be selected is; c (C) Ss The construction cost for the type of the s-th transformer substation to be selected; beta is the line unit cost coefficient; ml is the depreciation age of the line; n (N) L The number of load points; d, d ij Distance from the transformer station i to the load j; p (P) j Maximum load amount for the j-th load point; sigma (sigma) j,1 Sum sigma j,2 The unit price of the demand response subscription cost and the response cost of the jth load respectively;
c) Constraint conditions:
substation capacity selects a unique constraint. Only one substation type can be selected for one substation construction location:
the load points are attributed to a unique constraint. When the power supply range is divided, one upper-level transformer station corresponding to one load point is provided with only one:
Maximum power supply radius constraint, r max Maximum value of the radius of supply for medium voltage lines specified in the power supply and distribution design specification:
y i,j d ij ≤r max i∈[1,N P ],j∈[1,N L ]
the N-1 safety constraint of the transformer substation is based on the power grid safety operation principle, after any transformer in the transformer substation fails, the residual transformer needs to meet the maximum load rate e of the transformer substation in normal operation after all loads in the power supply range are operated for 2 hours s There are the following inequality constraints:
wherein J is i A load set in the power supply range of the ith transformer substation; p (P) j,t Power for the j-th load in the t period;the power factor for the j-th load; s is S s The capacity of the type of the s-th transformer substation to be selected;
and (3) demand response constraint, wherein the demand response subscription capacity of each load point is not more than the maximum response capacity of each load point, and the user response capacity is not more than the subscription capacity in running:
3. the robust optimization method for substation planning distribution considering excitation type response uncertainty as claimed in claim 1, wherein the Step of constructing the robust optimization model in Step2 comprises the steps of:
1) Building an uncertainty fuzzy set of demand responses
Taking into account uncertainty of user will, actual response result P t Deviation from the grid demand response command, and P t Fluctuation is carried out within a certain range, and the fuzzy set of uncertainty is modeled:
Firstly, obtaining a plurality of actual scenes through historical data, and then screening to obtain N through a scene clustering means k A finite discrete scene and probability distribution p under each scene k,0 The method comprises the steps of carrying out a first treatment on the surface of the Again, considering that these scenarios do not represent the actual probability distribution, a confidence set based on 1-norm and + -norm is constructed to limit the fluctuating variation of the probability distribution:
wherein ψ is 1 And psi is ∞ Respectively represent 1-norm and ≡ -confidence interval of norm limitation; p is scene probability P k Vector form of (a); p (P) 0 Initial probability p for each scene k,0 Vector form of (a);is N corresponding to P k A vector of positive real numbers; k is the number of sample scenes; alpha 1 And alpha ∞ Respectively is psi 1 And psi is ∞ Confidence of establishment. The confidence coefficient set of probability distribution is limited by 1-norm and infinity-norm at the same time, so that the situation of extreme is avoided, ψ=ψ 1 ∩Ψ ∞ The method comprises the following steps:
2) Two-stage distributed robust optimization model considering response power uncertainty
The uncertainty of the demand response is that the user can not fully meet the response requirement when receiving the response instruction, and the uncertainty exists in the response power, so that the default power is generated, and the demand response cost C of the operation stage is calculated DR2 The calculation formula should be rewritten as follows:
meanwhile, the actual response power can be changed due to the uncertainty of the demand response, so that load curve fluctuation in the power supply range of the transformer substation is caused, and the N-1 safety constraint of the transformer substation is influenced, and the constraint formula is rewritten as follows:
The uncertainty of the user demand response is in an operation stage, and the planning stage is influenced, so that the planning model can be decomposed into two stages after the uncertainty is taken into account, wherein the first stage is the planning stage, and the decision variables comprise the relation between the position and the capacity selection of the transformer substation, the connection relation between the load and the transformer substation and the demand response signing capacity; the second stage is an operation stage, the decision variable is the response power of the user, and the actual response power has uncertainty; the first stage decision variables include x is 、y ij Andrepresented by vector x, second stage decision variable +.>Represented by vector d. The distributed robust model based on discrete scenes can be expressed as follows:
wherein: a, a T A linear coefficient matrix for the first stage objective function; b T A linear coefficient matrix for the second stage objective function; n (N) k The total number of discrete scenes representing the probability distribution, k being the number of each scene, p k Representing the probability at k scenes, the constraint form transforms as follows:
wherein: c, E, F, G, H, m, n, u, v represent the matrix or vector form corresponding to the variables above, the first two formulas corresponding to the equality constraint and inequality constraint of the first stage variables; the third inequality constraint is a capacity coupling inequality of the first stage variable and the second stage variable; the last inequality constraint corresponds to the second stage demand response inequality constraint.
4. The robust optimization method of substation planning distribution taking account of excitation type response uncertainty as set forth in claim 1, wherein the iterative algorithm in Step3 includes:
based on a constraint generation algorithm, decomposing a model into a main problem MP and a sub problem SP, and then solving an optimal solution through iteration, wherein the purpose of MP solving is to obtain an optimal planning scheme meeting the constraint of a known probability distribution under the condition of a limited discrete scene, and the objective function and constraint condition of MP are described as follows:
l is lower-layer demand response running cost, the upper corner mark r represents the r-th iteration, and probability distribution of each iteration except the 1 st iteration is obtained by solving by the SP. MP problem solving to obtain a global optimal solution C * And corresponding planning decision variable x * ；
SP solution purpose is MP-based optimization result x * Under the condition that the capacity, the power supply range and the demand response signing capacity of the transformer substation are known, the load time sequence characteristic and the demand response characteristic are matched, and the worst probability distribution P of the response power is found k The distribution is then provided to MP for further iterative computation while being based on the resulting L (x * ) Updating the globally optimal solution, the objective function of the SP may be described as follows:
As can be seen from the above equation, the min problem in each scene is independent, and the parallel method is used for simultaneous calculation, for example, the internal optimization result of the kth scene is thatThe objective function of the SP may be converted to:
solving the MP and SP problems by using an MILP model and a linear programming model respectively, and solving an SP optimization result P k Transferring to MP for iterative calculation until the front and back phases are reachedGlobal optimal solution C of adjacent two iterations * And stopping iteration when the difference value is smaller than a specified threshold value, and obtaining the optimal planning cost and the decision variable value.
5. A substation planning distribution robust optimization system accounting for excitation type response uncertainty, the system comprising:
(1) The data input and processing module is used for carrying out matrixing processing on input load prediction data and various planning parameter information;
(2) The main problem solving module obtains an optimal planning scheme and planning layer decision variables meeting the known probability distribution constraint under the condition of a limited discrete scene;
(3) And the sub-problem solving module is used for fixing the decision variables of the planning layer obtained by the main problem solving module, solving the decision variables of the operation layer by taking the minimum operation cost as a target, and finding out the worst probability distribution of the response power.
6. A substation planning distribution robust optimization system taking account of excitation response uncertainty as in claim 5, further comprising the following modules:
the initialization module is used for initializing and setting iteration solving parameters, and solving corresponding robustness scene probability through a known scene probability intervention algorithm so as to form iteration;
the judging module is used for judging whether the planning result is converged or not and stopping iterative solution;
and the output module is used for outputting the planning scheme and the decision variables.
7. A non-transitory computer readable storage medium storing computer instructions that cause the computer to perform the method of any one of claims 1 to 4.
8. A computer program product comprising a computer program stored on a non-transitory computer readable storage medium, the computer program comprising program instructions which, when executed by a computer, cause the computer to perform the method of any of claims 1 to 4.
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| CN118469101A (en) * | 2024-07-12 | 2024-08-09 | 山东大学 | Supply chain toughness optimization and recovery method and system based on conditional risk value |
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| CN117726151B (en) * | 2024-02-08 | 2024-05-03 | 四川大学 | EIPSCN collaborative planning method considering decision-dependent uncertainty and flow balance |
| CN118469101A (en) * | 2024-07-12 | 2024-08-09 | 山东大学 | Supply chain toughness optimization and recovery method and system based on conditional risk value |
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