A distribution network optimal load carrying capacity evaluation method considering load response and development

Abstract

The application discloses a kind of optimal load carrying capacity evaluation method of distribution network considering load response and development, which comprises the following steps: S1, the influence of demand response on load curve and power supply reliability under normal / fault two kinds of scenarios is considered, and a load carrying capacity interval model is constructed;S2, considering the uncertainty of load development, a load carrying capacity optimization model with economic optimization as the target is constructed;S3, the outer model is solved by genetic algorithm, to improve the solving speed, a linearization processing method based on the inner model of large M method is proposed and solved by CPLEX, so as to obtain the optimal load carrying capacity of distribution network and the corresponding demand response strategy.The application provides a solid support for the judgment and determination of distribution network planning scheme.

Description

Technical Field

[0001] This invention relates to the field of power system distribution network planning, and specifically to an economically optimal load carrying capacity assessment method that considers the distribution network's supply capacity to different types of loads, takes into account the impact of demand response on load supply capacity during normal / fault operation, and the uncertainty of load development. Background Technology

[0002] The power distribution network is responsible for the safe, reliable, and continuous distribution of electrical energy to users within a region, constantly impacting people's lives and socio-economic development. Distribution network planning is a crucial link in distribution network construction and an important guide for its development; therefore, it is necessary to formulate scientific and effective distribution network planning schemes. The load-carrying capacity of the distribution network reflects its ability to supply various loads under certain safety constraints. This indicator is of guiding significance for distribution network planning; assessing the load-carrying capacity of the distribution network can identify power supply bottlenecks and verify the feasibility of planning schemes.

[0003] However, as traditional distribution networks gradually evolve into smart distribution networks, advanced communication and control technologies enable the effective implementation of demand response (DR). This necessitates a proper assessment of the impact of demand response on the distribution network's load-carrying capacity to avoid insufficient or excessive capacity in planning schemes. Demand response provides flexible load regulation resources for the distribution network and can be categorized into price-based demand response and incentive-based demand response based on the different methods of guiding retailers. Compared to price-based demand response, incentive-based demand response is more flexible and has therefore received widespread attention. Existing literature has conducted in-depth research on user response volume, optimization decisions, and cost-benefit aspects of incentive-based DR, but it has not comprehensively considered the impact of demand response on load-carrying capacity during normal and fault operations. Demand response during normal operation alters the load curve through peak shaving and valley filling, while demand response during fault operation can improve power supply reliability. Both the load curve and power supply reliability directly affect the distribution network's load-carrying capacity. Including demand response complicates load-carrying capacity assessment; therefore, it is necessary to find a method that can quantify the impact of demand response on load-carrying capacity under both normal and fault scenarios.

[0004] Implementing demand response can improve the load-carrying capacity of a distribution network and increase its revenue, but it also incurs corresponding demand response costs. Finding the optimal load-carrying capacity and corresponding demand response strategy is crucial for distribution network planning. Furthermore, load-carrying capacity benefits are calculated based on the maximum available loads of various types within the system. However, during the development of the existing system, the various load types may not grow in a balanced manner according to current proportions. Therefore, the uncertainty of load development needs to be considered in the calculation of load-carrying capacity benefits.

[0005] Existing research on power supply capacity calculations with reliability as a security constraint for the aforementioned problems often employs a combination of genetic algorithms and Monte Carlo simulations. However, Monte Carlo simulations are time-consuming to calculate reliability, which would consume a significant amount of computation time to solve these problems. Therefore, it is necessary to find a method that can significantly shorten the reliability calculation process to improve computational efficiency.

[0006] In summary, it is necessary to propose an economically optimal load carrying capacity assessment method that considers the distribution network's supply capacity to different types of loads, takes into account the impact of demand response on load supply capacity during normal / fault operation, and the uncertainty of load development. Summary of the Invention

[0007] To address the shortcomings and deficiencies of existing technologies, this patent proposes a method for evaluating the optimal load carrying capacity of distribution networks that considers load response and development. It assesses the economically optimal load carrying capacity of the distribution network while taking into account demand response and load development uncertainties.

[0008] Specifically, the optimal load carrying capacity assessment method for distribution networks that considers load response and development proposed in this application includes:

[0009] S1: Considering the impact of demand response on load curves and power supply reliability under both normal and fault scenarios, a load carrying capacity range model is constructed:

[0010] Because the load curves of each feeder are different, and their loads are superimposed in different proportions, the peak value of the total load curve of the interconnected system may occur at different times. Total load curve array L curv for:

[0011]

[0012] When α i When L changes from 0 to 1, the corresponding L curv Different peak times may occur, and set H records the s peak load times:

[0013] H={t|L curv (t)=1}(2)

[0014] The timing of all possible load spikes is determined by the changes in the load ratio between feeders. All peak load ratios are grouped according to their corresponding peak times t, resulting in s intervals. Each interval Z... (i) The peak load ratio in all cases is at the same time t. i Since they all reach their peak values, their load curves after reduction at peak time are the same. A total of s sets of load curves after reduction for each feeder can be obtained. Matrix Z represents the peak load ratio range for each feeder.

[0015] Z = [Z (1) Z (2) …Z (s) ] T (3)

[0016] After normalizing the load curves of each group, the maximum load supply capacity of each group of load curves under the same reliability constraints can be calculated. Furthermore, the load supply capacity at a certain peak time t can be determined. j The load-bearing capacity boundary that satisfies reliability constraints:

[0017]

[0018] In the formula, To maximize load capacity, For each feeder load curve at the peak time t of the total load j The load curve normalized after demand response reduction, y i This indicates the load on feeder i.

[0019] Each element in H defines a load carrying capacity boundary. Based on the division of the load proportion group Z during peak hours, the range of each load carrying capacity boundary is determined, ultimately forming a complete load carrying capacity boundary B that considers the uncertainty of load development. This boundary, together with the capacity constraints of each feeder, forms the load carrying capacity interval Ω. C,REDR .

[0020]

[0021]

[0022] S2: Taking into account the uncertainty of load development, a nested load carrying capacity optimization model with the goal of optimal economic efficiency is constructed.

[0023] 201) Based on the characteristic that load development follows a normal distribution, the uncertainty of load development is described by the probability density function of the multivariate normal distribution. The expectation and variance of the probability density function are calculated by the maximum likelihood estimation method in parameter estimation. Then, a load carrying capacity benefit calculation model considering the uncertainty of load development is constructed.

[0024] Power system load development typically follows a normal distribution; therefore, the normal distribution can be used to characterize the uncertainty of feeder load. For a system with n interconnected feeders, the probability density function of a multivariate normal distribution is used to describe the uncertainty of load development.

[0025] According to the definition of the multivariate normal distribution, if the random vector is a p-dimensional normal random vector, X ~ N P (μ, Σ), X=[X1, X2,...,X P ]T Then the joint probability density function of X is:

[0026]

[0027] In the formula, μ is the expected vector; Σ is the covariance matrix.

[0028] For n interconnected feeders, the points on their load-bearing capacity boundary can be represented as Y = [Y1, Y2, ..., Y]. n ] T A sample data matrix D is constructed by collecting the load values ​​of each feeder corresponding to m historical peak times.

[0029] D (i) =[d i1 , ..., d in ] T (i = 1, ..., m), use the maximum likelihood estimation method in parameter estimation to determine μ and Σ of f(Y).

[0030]

[0031] in, Let A be the sample mean and A be the sample deviation matrix.

[0032]

[0033] Due to Ω C,REDR Given an n-dimensional bounded interval, the sum of the integrals of the existing probability density function f(Y) over B is less than 1. Therefore, the probability density function needs to be modified.

[0034]

[0035] Furthermore, the overall load-bearing capacity benefit was calculated:

[0036] C inc =∮ B f'(Y)·S(Y) (11)

[0037] In the formula, S(Y) represents the electricity sales revenue corresponding to each feeder load.

[0038] 202) A nested load-bearing capacity optimization model with the goal of optimal economic efficiency. The outer layer of the model determines the demand response scheme that achieves the optimal load-bearing capacity, while the inner layer calculates the load-bearing capacity benefits corresponding to each scheme and feeds them back to the outer layer to calculate the total revenue. The specific model is as follows:

[0039] Since users who have signed DR contracts only receive notifications of load reduction incentives from the power grid company, and are unaware of whether the grid is operating at its peak or during a fault, the fault-based DR strategy is the same as the normal-operational DR strategy. The objective function of the outer model is to optimize the distribution network economy, i.e., maximize the power company's revenue. The optimization variable is the demand response incentive cost for various load types. The inner model calculates the maximum load carrying capacity based on the incentive cost output by the outer model, its corresponding participation ratio, and the load curve after peak load reduction. The optimization variable is the load of each feeder, i.e., evaluating the reliability under different feeder load combinations, considering only the participation of demand response during fault operation. Finding the optimization variable that satisfies the reliability constraint and maximizes the total load, based on the method for determining the load carrying capacity boundary, under a set of optimization variables in the outer layer, the maximum load carrying capacity must be calculated once for each peak moment in set H, and the corresponding load carrying capacity boundary must be determined. The inner layer integrates the load carrying capacity boundaries for each peak moment and returns the benefit corresponding to the entire boundary B to the outer layer to calculate the economy. The model framework is attached. Figure 1 As shown.

[0040] Total Revenue Calculation Layer

[0041] The objective function of the outer model is the load-bearing capacity benefit C. inc Normal operation demand response cost C nDR Fault operation demand response cost C fDR Power supply loss C loss Overall optimal:

[0042] F = max(C) inc -C nDR -C fDR -C loss (7)

[0043] In the formula, the load-bearing capacity benefit C inc Fault operation demand response cost C fDR and power supply loss C loss Calculated from the inner layer; Normal operation demand response cost C nDR The calculation method is as follows.

[0044] C nDR =∮ B f'(Y)P real (Y)(I(Y)+p sell (Y)-p buy )-∮ B f'(Y)(P ndr (Y)-P real (Y))p pun (Y)(8)

[0045] Pndr (Y)=λ(Y)P(Y) (9)

[0046] P real (Y)=k we (Y)P ndr (Y) (10)

[0047] In the formula, I(Y) represents the various load incentive costs corresponding to points on the boundary of the load carrying capacity interval; p sell (Y) represents the electricity sales fees charged by the electricity retailers to various loads; p buy The electricity purchase fee from the upstream power grid for the electricity retailer; P(Y) represents the load of each feeder corresponding to each point on the boundary; P ndr (Y) represents the load scale of each feeder participating in demand response; k we (Y) represents the willingness of each feeder to respond to load demands, indicating that some users may not participate in the response as per their contracts; P real (Y) represents the actual load scale of each feeder in response to the system's load shedding command; p pun λ(Y) represents the penalty price for each feeder load that fails to respond to load shedding instructions according to the contract, and λ(Y) represents the user participation rate, which is determined by the demand response contract.

[0048] The constraint is that the excitation cost of each type of load lies in the linear region of its response characteristic curve.

[0049] b1(Y)≤I(Y)≤b2(Y) (11)

[0050] When the incentive cost is less than the lower limit b1(Y), users will basically not respond; when it is greater than the upper limit b2(Y), users will no longer have more load to reduce, and the response capacity will approach saturation.

[0051] Load bearing benefit calculation layer

[0052] The objective function of the load carrying capacity benefit calculation model is to maximize the power supply capacity. The load carrying capacity boundary is determined based on the available power supply capacity, and the load carrying capacity benefit is calculated.

[0053]

[0054]

[0055]

[0056] In the formula, f i The load of each feeder is the lower-level optimization variable; p pen,j The penalty price for the lack of supply of feeder j.

[0057] Load carrying capacity benefit C inc The calculation method has been introduced in 201.

[0058] C can be determined during the inner layer calculation. fDR C loss C inc It is then passed to the upper layer to calculate the total revenue.

[0059] The constraint is the expected power supply requirement:

[0060]

[0061] δ EENS ≤δ EENS0 (twenty one)

[0062] In the formula, M is the number of equipment components in the fault set; N is the number of load points in the system; P j L represents the probability of component j failing; i,j The load at load point i when component j fails; U i,j δ represents the power outage time at load point i when component j fails; EENS0 Given the expected constraint value for power shortage.

[0063] S3: For the proposed optimal load-bearing capacity nested optimization model, the outer model is solved using a genetic algorithm, and to improve the solution speed, a linearization method based on the Big M method is proposed for the inner model, and CPLEX is used for the solution.

[0064] Because reliability assessment involves determining whether load needs to be transferred or reduced, it cannot be solved directly using a solver. Therefore, the Big M method is proposed. This method linearizes the nonlinear process of determining load transfer and reduction in the inner model, introducing Boolean variables for solution, where M is a large, artificially defined number. For example, let 'a' be the load that needs to be transferred from the faulty feeder, and 'b' be the available capacity of the tie feeder. When ab > 0, complete transfer is not possible, and the power shortage is c = (ab); when ab ≤ 0, complete transfer is possible, and c = 0. The model is as follows:

[0065] (z-1)M≤ab≤zM (22)

[0066] (z-1)M+(ab)≤c≤(1-z)M+(ab) (23)

[0067] -zM+0≤c≤zM+0 (24)

[0068] In the formula, z∈{0,1}. If z=1, it means that the transfer cannot be completely completed. Since M is a sufficiently large number, the third formula above is relaxed and has no effect in the calculation process. At this time, the equality sign is taken on both sides of the second formula above, c=ab; if z=0, the analysis method is the same, and will not be repeated.

[0069] After linearizing the lower layer, the CPLEX solver is used to solve it.

[0070] Beneficial effects:

[0071] (1) Taking into account the impact of demand response on load curves and power supply reliability under normal / fault scenarios, a load carrying capacity range modeling method is proposed, which is conducive to quantitatively reflecting the improvement effect of load carrying capacity after considering demand response, and accurately assessing the supply capacity of the distribution network to loads with different power consumption characteristics.

[0072] (2) Taking into account the uncertainty of load development, a load carrying capacity optimization model construction method with the goal of economic optimization is proposed, so that the load carrying capacity benefit calculation results are more in line with reality and it is conducive to finding the economically optimal load carrying capacity that meets reliability constraints.

[0073] (3) The lower-level model is linearized based on the Big M method, the upper-level model is solved by the genetic algorithm, and the lower-level model is solved by the CPLEX solver, thus realizing the fast solution of the two-level model. Attached Figure Description

[0074] To more clearly illustrate the technical solution of the present invention, the accompanying drawings used in the description of the embodiments will be briefly introduced below. Obviously, the accompanying drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0075] Figure 1 A flowchart of the overall optimization process for the optimal load carrying capacity assessment model of a distribution network;

[0076] Figure 2 This is a flowchart of a distribution network optimal load carrying capacity assessment method considering load response and development according to the present invention;

[0077] Figure 3 This is a diagram of the power distribution system used in this implementation case. Detailed Implementation

[0078] To make the structure and advantages of the present invention clearer, the structure of the present invention will be further described below with reference to the accompanying drawings.

[0079] Combination Figure 2 The overall process of the distribution network optimal load carrying capacity assessment method considering load response and development proposed in this invention is described in detail below, with specific steps as follows:

[0080] Step 1: Input the example information;

[0081] Step 2: When the iteration count i = 0, randomly generate the load demand response incentive cost to produce the initial population A. i ;

[0082] Step 3: Input the load demand response incentive cost into the lower-level model. The lower-level model calculates the maximum load carrying capacity benefit and demand response cost of the system under the condition of considering the uncertainty of load development, and returns it to the upper-level model.

[0083] Step 4: The upper layer calculates the sum of load carrying capacity benefits, demand response costs, and power shortage losses to obtain the fitness function of each individual in the initial population, and sorts the population according to the fitness function;

[0084] Step 5: Use a binary tournament model to generate the parent population, select parent individuals, perform crossover and mutation, and generate offspring individuals B. i ;

[0085] Step 6: Merge Ai and B i Based on the fitness function, the individuals are sorted, and an elite retention strategy is adopted to select the top N individuals to generate the offspring population A. i+1 ;

[0086] Step 7: Determine if the iteration count has been reached. If not, increment the iteration count i by 1 and return to step 5. If yes, the optimization algorithm ends, and the optimal load carrying capacity and corresponding demand response incentive cost are obtained.

[0087] The distribution network used in this embodiment consists of two 110kV substations, four main transformers, and seven 10kV feeders, as shown in the attached diagram. Figure 3 As shown in the diagram. Feeders F1, F3, and F4 are located in residential areas; feeders F2 and F5 are located in commercial areas; and feeders F6 and F7 are located in industrial areas. Based on actual conditions, demand response to reduce load peaks is implemented in summer and winter, but not in spring and autumn. Fault-based demand response is implemented year-round; that is, after equipment failure, load transfer pressure can be alleviated by incentivizing users to participate in demand response. The willingness to respond is 0.8 for residential users, 0.75 for commercial users, and 0.65 for industrial users. The energy price for residential users is 0.5 CNY / kWh, and the energy price for industrial and commercial users is 0.7 CNY / kWh, with an energy cost of 0.3 CNY / kWh. A penalty of 1 CNY / kWh is imposed for failure to respond as required. The penalty for load shortage is 20 times the electricity price.

[0088] Table 1 Demand response strategies under different reliability constraints

[0089]

[0090] Table 2. Annual Costs and Benefits under Different Reliability Constraints

[0091]

[0092] As shown in Table 2, with the relaxation of power shortage constraints, the system can carry more load, thereby increasing total revenue. When the allowable power shortage is 30 MWh / a, the incentive cost should be increased and the participation rate of various user DR (Resource Deployment) systems should be increased to improve load carrying capacity. However, the incentive cost obtained from optimization in Table 1 is not high, and the corresponding DR ratio is also small. The reason for this is that during normal operation, load reduction at peak times causes the overall load curve to shift upwards after normalization. The more peaks are reduced, the harder it is to meet reliability constraints. Even if DR can reduce transfer pressure and decrease power loss load during a fault, the stringent reliability constraints lead lower-level optimization to choose smaller feeder load values ​​that will not cause power loss in non-faulty areas after DR. Smaller feeder load values ​​leave a larger transfer margin, rendering the role of DR ineffective. Therefore, a higher DR participation rate is actually detrimental to increasing feeder load; the power shortage constraint is what affects load carrying capacity at this point.

[0093] When the power supply shortage constraint is relaxed to a certain extent, increasing the DR participation ratio during peak hours shifts the overall load curve upward. During optimization, although the load on each feeder increases, increasing the transfer pressure and causing power outages in non-faulty areas, the power supply shortage constraint is large, allowing for partial load outages. At the same time, a larger DR participation ratio can reduce the outage load. Therefore, at this point, the DR participation ratio, i.e., the incentive cost, is what affects the power supply capacity.

[0094] The serial numbers in the above embodiments are for descriptive purposes only and do not represent the order in which the components are assembled or used.

[0095] The above description is merely an embodiment of the present invention and is not intended to limit the present invention. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention should be included within the protection scope of the present invention.

Claims

1. A method for evaluating the optimal load carrying capacity of a distribution network considering load response and development, characterized in that, The method includes: S1, considering the impact of demand response on load curves and power supply reliability under both normal and fault scenarios, constructs a load carrying capacity range model; total load curve array. L curv for: (1) when α i When changing from 0 to 1, the corresponding L curv Different peak times may occur, collection H The record appeared s Peak load moments: (2) By determining the changes in the load ratio between feeders, all possible peak times are identified, and the load ratios of all peak loads are then assigned to their corresponding peak times. t Grouping can be divided into s Each interval Z (i) The peak load ratio in the data is all at the same time. t i Since they reach their peak values, their load curves after reduction at peak time are the same, and a total of [number] loads can be obtained. s Load curves and matrices of each feeder after group reduction Z Indicates the range of peak load proportions: (3) After normalizing each group of load curves, the maximum load supply capacity of each group of load curves under the same reliability constraints can be calculated, and the load supply capacity at a certain peak moment can be further determined. t j The load-bearing capacity boundary that satisfies reliability constraints: (4) In the formula, To ensure the maximum load supply capacity with reliability as a safety constraint, For each feeder load curve at the peak of total load t j Normalized load curve after demand response reduction y i Indicates feeder i The load, H Each element in the equation can define a load carrying capacity boundary, based on the load ratio group at peak times. Z Based on the division of load capacity boundaries, the boundary range of each load carrying capacity is determined, ultimately forming a complete load carrying capacity boundary that takes into account the uncertainty of load development. B Together with the capacity constraints of each feeder, they form the load-bearing capacity range Ω. C,REDR (5) (6)； S2, taking into account the uncertainty of load development, constructs an inner and outer nested load carrying capacity optimization model with the goal of optimal economy; S3. For the proposed optimal load-bearing capacity optimization model, the outer layer model is solved using a genetic algorithm, and the inner layer model is linearized based on the Big M method and solved using CPLEX to improve the solution speed.

2. The method for evaluating the optimal load carrying capacity of a distribution network considering load response and development, as described in claim 1, is characterized in that... In step S3, during power supply reliability calculations, a linearization method for the nonlinear processes of load transfer and load shedding based on the Big M method is proposed to improve the solution speed of the inner model. Specifically, this includes: The Big M method is proposed, which introduces Boolean variables for solving the problem. M is a very large number defined by the user. The model is as follows: (12) (13) (14) In the formula, ,like z =1 indicates that the transfer cannot be completely completed. Since M is a sufficiently large number, equation (14) is relaxed and has no effect during the calculation. At this time, the equality sign is taken on both sides of the second equation above. c = a - b ;like z =0, after linearizing the lower layer, the CPLEX solver is used to solve it.

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