A substation capacity planning method combining robust optimization and chance constraints

Abstract

This application proposes a substation capacity planning method that combines robust optimization with chance constraints, providing an important basis for determining the scale of power grid construction. First, a source-load and demand response uncertainty modeling method based on stochastic optimization and robust intervals is proposed; then, based on the substation power supply range obtained from the conventional Voronoi diagram, a substation capacity planning model that considers source-load and demand response uncertainty with the goal of minimizing the total planning cost of the substation is constructed; finally, a solution method for the substation capacity planning model that combines chance constraints, point estimation, and dual transformation is proposed, and the effectiveness of the method proposed in this application is verified through case analysis, so as to achieve a reasonable assessment of the scale of power grid construction and ensure the economic and efficient operation of the distribution network.

Description

Technical Field

[0001] The present invention belongs to the field of distribution network planning, and relates to determining the total capacity range of substations in the distribution network that meet the requirements of new energy consumption and load complementarity, and a transformation and solution method of a planning model combining robust optimization and chance constraints. Background Art

[0002] As a crucial link in distribution network planning, power and energy balance, based on load forecasts, provides a crucial basis for determining grid construction scale. Therefore, a scientific and rational power and energy balance is crucial for ensuring efficient asset utilization and input-output benefits of distribution networks.

[0003] However, with the gradual implementation of the dual carbon goals, the scale of distributed power generation (DGs) in distribution networks and the degree of terminal electrification will increase significantly. To fully mitigate the impact of DGs, energy storage and demand response technologies are rapidly developing and will become important elements of distribution networks. Traditional distribution networks are transitioning to new distribution systems based primarily on renewable energy. Distributed power generation output is highly volatile, and load granularity on the distribution network side is small and highly random. The controllable characteristics of energy storage and demand response are also difficult to fully determine. Traditional power and energy balancing methods based on simple arithmetic methods are unable to adapt to these changes, and research on power and energy balancing methods that account for uncertainty is urgently needed. Summary of the Invention

[0004] In order to address the shortcomings and deficiencies in the existing technology, a substation capacity planning method combining robust optimization with opportunity constraints is provided to make up for the inability to obtain accurate power balance results in the context of large-scale access of distributed power sources, and to provide support for the rationality of substation planning schemes.

[0005] The present invention provides a substation capacity planning method combining robust optimization with chance constraints, which specifically includes:

[0006] Step 1: Modeling the uncertainty of source load and demand response based on stochastic optimization and robust intervals, where source load uncertainty is handled by random variables and demand response uncertainty is described by robust intervals.

[0007] Step 2: Constructing a substation capacity planning model with uncertainty considering source load and demand response with the goal of minimizing the total planning cost of the substation;

[0008] Step 3: A solution method for the substation capacity planning model combining chance constraints, point estimation and dual transformation.

[0009] The specific process of step 1 is as follows:

[0010] (1) Modeling the uncertainty of photovoltaic output using random variables

[0011] The probability density function of distributed photovoltaic output approximately follows the Beta distribution, which is expressed as follows:

[0012]

[0013] Where Г(·) is the gamma function; α and β are shape parameters, whose sizes can be estimated by investigating historical data. The calculation formula is as follows:

[0014]

[0015]

[0016] Among them, μ PV is the average value of photovoltaic output, is the variance of photovoltaic output.

[0017] (2) Using random variables to model the uncertainty of wind power output

[0018] The probability density function of the wind speed at each moment follows the two-parameter Weibull distribution

[0019]

[0020] Where k is the shape coefficient, which is used to describe the shape of the wind power probability density function and is taken as 1 here (in this case, c is the average wind speed); c is the scale coefficient, which reflects the average wind speed; and v is the actual wind speed, in m / s.

[0021]

[0022] Among them, P WT is the output power; P WT,N is the rated power; v in is the cut-in wind speed (generally 10-13 m / s); v out is the cut-out wind speed; v N is the rated wind speed; the parameters of the Weibull distribution can be estimated using historical survey data.

[0023]

[0024]

[0025] Based on the Weibull distribution function obeyed by the wind speed, random simulation is performed, and v is extracted as the current wind speed value in the confidence interval of the wind speed output in each time period, and it is brought into P WT The uncertainty of the current wind power output can be simulated by expressing it as a piecewise function.

[0026] (3) Modeling the uncertainty of conventional loads using random variables

[0027] Assuming that the loads at the load points at a certain moment all obey the normal distribution, the cumulative probability distribution function is as follows.

[0028]

[0029] 4) Demand-side resource model

[0030] In this application, since the uncertainty description of demand response is relatively complex, it is not appropriate to model it as a certain distribution. Here, it is modeled as a robust interval and only considers the load that can be reduced. The uncertainty set D of the load reduction amount is established.

[0031]

[0032]

[0033] in, is the actual load reduction at the i-th load point; are the upper and lower bounds of the robust range of load reduction respectively; is the reference value of load reduction; t For conservative degree.

[0034] The specific process of step 2 is as follows:

[0035] Based on the geographical distribution of load, the power supply range of each substation is divided based on the conventional Voronoi diagram. First, the number of substations is estimated and the substation locations are determined; then, with each substation as a vertex, each load point is assigned to the substation with the smallest Euclidean distance, and a conventional Voronoi diagram is constructed. The division result is as follows: Figure 3 Finally, considering the relevant geographical information and expert suggestions, the following division results are obtained. Figure 4 shown.

[0036] Based on the power supply range of substations, a substation capacity uncertainty planning model is established with the goal of minimizing the total planning cost of substations.

[0037] (1) Objective function

[0038] The objective function is to minimize the total cost under the worst demand response conditions, which includes substation cost and demand response cost. The variable to be planned is the substation transformer capacity S substation,i and demand response reduction values

[0039]

[0040] The substation cost is the sum of construction cost and operation cost:

[0041]

[0042] Among them, C substation The annual value of the substation construction cost is equal to; is the price per unit capacity of the substation; N sub is the number of substations; k is the empirical coefficient of operating cost;

[0043] For the substation in the planned area, the annual construction cost is:

[0044]

[0045] Among them, d sub is the discount rate, and T is the operating life.

[0046] Demand response only considers the load that can be reduced and provides a certain amount of incentive for users to reduce their load. Therefore, the total expected cost of incentive-based demand response is:

[0047]

[0048] Among them, c is the basic incentive price, is the motivating factor; is the load reduction amount obtained by incentive.

[0049] The greater the load reduction of the user, the higher the final grid incentive price will be. Therefore, the incentive factor is set as:

[0050]

[0051] Among them, k t is the incentive coefficient.

[0052] (2) Constraints

[0053] 1) Power balance constraints

[0054]

[0055] in, The power delivered to the substation; Producing power for photovoltaics; Provide power for the fan; For normal load demand; is the demand response load power; N PV 、N WT 、N L 、N DR They are the number of photovoltaics, the number of wind turbines, the number of loads, and the number of loads participating in demand response.

[0056] 2) Substation capacity constraints

[0057]

[0058] Among them, K sub,i It is the capacity load ratio of the substation, which is generally 1.8 to 2.0.

[0059] The specific process of step 3 is as follows:

[0060] (1) Using opportunity constraints to transform power balance constraints

[0061]

[0062] Here, α is the confidence level.

[0063] (2) Rewrite the chance constraint into a linear constraint and use the point estimation method to obtain the probability information of the net load

[0064]

[0065] Among them, F sum is the net load probability distribution function without considering demand response, that is Probability distribution function of the payload.

[0066] Among them, the three-point estimation method is used to obtain the probability information of the net load size, and then the probability density function and probability distribution function of the net load size are obtained through the Gram-Charlier expansion series method, where the net load size is the superposition of the load size and the distributed power source.

[0067] When calculating the net load, it is necessary to consider the spatial distribution of the load. Based on the division of the substation power supply range, the internal source-load timing curves within the divided area are superimposed. At the same time, the timing characteristics of the distributed power supply and load are taken into account to divide the power supply unit into power supply units that consider the matching of source-load characteristics. First, it is necessary to superimpose the internal timing curves of the area based on the division of the substation power supply range, and then match the source-load characteristics between areas. The net load size in the new distribution system is uncertain, so it is necessary to propose a calculation method for the probabilistic characteristics of the net load and convert the opportunity constraints into deterministic constraints.

[0068] This application adopts the three-point estimation method to obtain the probability information of the net load size, and then obtains the probability density function and probability distribution function of the net load size through the Gram-Charlier expansion series method, where the net load size is the superposition of the load size and the distributed power supply.

[0069] 1) It is known that the real-time output of photovoltaic power follows the Beta distribution, and the time series of load follows the normal distribution; the random variable X contains a photovoltaic power plants, b wind power plants, and (nab) loads.

[0070] 2) In the independent standard normal distribution space Y=[y1,y2...,y n ], the three-point estimation method is used to calculate the sampling value y of each point i,k and the weight p of the corresponding point i,k , we get S in the standard normal distribution Y .

[0071] S Y =[Y 1,1 ,Y 1,2 ,Y 2,1 ,Y 2,2 ,...,Y n,1 ,Y n,2 ,Y 2n+1 ] T

[0072] where Y i,k With Y 2n+1 The calculation formula is as follows:

[0073]

[0074] 3) Through matrix transformation, the sample matrix S of the relevant standard normal distribution is obtained Z .

[0075] S Z =[Z 1,1 ,Z 1,2 ,Z 2,1 ,Z 2,2 ,...,Z n,1 ,Z n,2 ,Z 2n+1 ] T

[0076] where Z i,k With Z 2n+1 The calculation formula is as follows:

[0077]

[0078] 4) The sample matrix S of the standard normal distribution Z , converted to the sample matrix S in the actual distribution space X .

[0079] S X =[X 1,1 ,X 1,2 ,X 2,1 ,X 2,2 ,...,Xn,1 ,X n,2 ,X 2n+1 ] T

[0080] where X i,k With X 2n+1 The calculation formula is as follows:

[0081]

[0082] 5) For S X Add up each row of elements in and get the sample matrix W=[W1,W1,...,W 2n+1 ] T , using the three-point estimation method, the mean and variance of the net load random variable can be calculated.

[0083] 6) According to the moments of the net load random variable W, the Gram-Charlier series expansion method is used to obtain the probability density function f(W) and probability distribution function F(W) of the net load W.

[0084] Figure 5 The general process of obtaining the probability distribution function of the net load W using the three-point estimation method is shown.

[0085] (3) Use dual transformation to convert the max function in the substation capacity planning model into a min function

[0086] The standard expression of the model is as follows:

[0087]

[0088] Among them, λ 1,t is the dual multiplier of the power balance constraint; 2,t ,λ 3,t is the dual multiplier of the conservative degree constraint.

[0089] Then, the IPOPT nonlinear solver is used to solve the problem.

[0090] Beneficial effects:

[0091] A substation capacity planning method combining robust optimization and chance constraints is proposed, which properly solves the multiple uncertainty problems of source load and demand response, and effectively addresses the problem that it is difficult to obtain accurate power balance results due to various random factors in the distribution network, providing support for the rationality of substation planning schemes. BRIEF DESCRIPTION OF THE DRAWINGS

[0092] In order to more clearly illustrate the technical solution of the present invention, the following is a brief introduction to the drawings required for use in the description of the embodiments. Obviously, the drawings described below are only some embodiments of the present invention. For ordinary technicians in this field, other drawings can be obtained based on these drawings without paying any creative work.

[0093] Figure 1 A flowchart of a substation capacity planning method combining robust optimization with opportunity constraints according to the present invention;

[0094] Figure 2 This is a schematic diagram of Vonoroi in the present invention;

[0095] Figure 3 This is a diagram showing the division of the power supply range of the substation in the present invention;

[0096] Figure 4 This is a diagram showing the division of power supply range of substations taking geographic information into account in the present invention;

[0097] Figure 5 This is a flow chart for obtaining the net load probability density function and the probability distribution function in the present invention;

[0098] Figure 6 This is the geographic information map used in this implementation case;

[0099] Figure 7 The following are the timing curves of various typical loads in the planning area of this implementation case;

[0100] Figure 8 is the net load curve of each area in this implementation case;

[0101] Figure 9 is the net load curve taking into account the 95% quantile in this implementation case;

[0102] Figure 10 This is a schematic diagram of the midpoint estimation calculation results of this implementation case;

[0103] Figure 11 This is a schematic diagram of the demand response configuration in each area in this implementation case;

[0104] Figure 12 Schematic diagram of net load reduction considering the robust interval of demand response in this implementation case. DETAILED DESCRIPTION

[0105] To make the structure and advantages of the present invention more clear, the structure of the present invention will be further described below with reference to the accompanying drawings.

[0106] Combine Figure 1The overall solution process of the substation capacity planning method combining robust optimization and chance constraints proposed in this invention is described in detail. The specific steps are as follows:

[0107] Step 1: Divide the planning area by net load to obtain the power supply range of each substation.

[0108] Step 2: Superimpose the source-load time series curves within the power supply range of each substation and obtain the net load.

[0109] Step 3: Use point estimation to obtain the cumulative probability distribution of net load, and find the quantiles to rewrite the opportunity constraint of power balance into a linear constraint.

[0110] Step 4: Substitute the above constraints into the robust optimization model and perform dual transformation to obtain a simple deterministic optimization model.

[0111] Step 5: Use the solver to obtain the capacity range of each substation, and superimpose the capacity ranges of different substations to obtain the total regional capacity range.

[0112] The effectiveness of the proposed method is demonstrated on a case study system to achieve a reasonable assessment of the grid construction scale and ensure the economical and efficient operation of the distribution network.

[0113] (1) Important parameters

[0114] The planned substation has a construction cost of RMB 250,000 per MVA, a load factor of 1.8 to 2.0, a 20-year lifespan, and a 9% discount rate. The basic substation specification is a 2 x 63 MVA substation.

[0115] Consider temperature control loads and building lighting loads within conventional loads as curtailable loads. According to statistics, the power of these loads accounts for approximately 29.5% of the total dispatching load in East China. The upper limit for demand response load configuration is 20% of this load, with a cost of 0.2 yuan / kW.

[0116] Convert the substation investment and O&M costs to their equivalent annual values. Multiply the demand response cost for a typical day by the number of days in a year to get the annual cost. Consider dividing the day into 24 time periods. Calculate the total capacity range of the substations in the planned area.

[0117] (2) Planning area

[0118] Figure 6 This is a load distribution map for a region in North China. There are 460 load points in the region, with an average load of 450kW, a total photovoltaic capacity of 117,000kW, and a total wind capacity of 21,700kW. The substation's power supply area contains 223 street nodes and 407 street segments. The types and geographical locations of each street node, street segment, and load are shown in the figure below. Figure 6 There are four types of loads: residential, commercial, industrial, and administrative. The time series load curves of different types of loads on typical days are shown in Figure 7.

[0119] (3) Planning results

[0120] The net load curves of each area are as follows: Figure 8 As shown:

[0121] Region 1: Total load is 61,400kW, total photovoltaic power is 37,425kW, and total wind power is 7,200kW;

[0122] Region 2: Total load is 59,800kW, total photovoltaic power is 42,125kW, and total wind power is 7,300kW;

[0123] Region 3: The total load is 62,500kW, the total photovoltaic power is 37,500kW, and the total wind power is 7,200kW.

[0124] Take area 1 as an example: the net load curve without considering uncertainty and the 95% net load curve are as follows: Figure 9 shown.

[0125] It can be seen that if the capacity of the substation is configured according to the net load, it does not meet the actual conditions and there is still a high probability of exceeding the limit. Therefore, this application refers to the 95% net load curve.

[0126] The point estimation method is used to superimpose the different probability density functions of load, wind power and photovoltaic power. Taking T = 15 as an example, the point estimation method is used to obtain the net load probability density function and the cumulative probability distribution function as shown in the following figure: Figure 10 shown.

[0127] The demand response configuration diagram for each region is as follows: Figure 11 shown.

[0128] Area 1: The total capacity of the substation to be built is 43.3 to 48.2 MVA, and the construction cost is RMB 1.1867 million to RMB 1.3184 million;

[0129] Area 2: The total capacity of the substation to be built is 40.2 to 44.7 MVA, and the construction cost is RMB 1.1018 million to RMB 1.2242 million;

[0130] Area 3: The total capacity of the substation to be built is 45.3 to 50.3 MVA, and the construction cost is RMB 1.2592 million to RMB 1.396 million.

[0131] Table 1 Comparison of costs including demand response (minimum value)

[0132] Including demand response (10,000 yuan) Excluding demand response (10,000 yuan) Area 1 118.67 200.97 Area 2 110.20 186.61 Area 3 137.87 210.17

[0133] It can be seen from the above table that the implementation of demand response can significantly reduce the investment cost of substation construction.

[0134] Considering the net load reduction in the robust interval of demand response, Figure 12 shown.

[0135] Taking Region 3 as an example, the total cost of substation planning without considering the robust interval ranges from 1.2408 million to 1.3787 million yuan. The total cost of substation planning with the robust interval ranges from 1.2592 million to 1.3960 million yuan. After accounting for the uncertainty of demand response, the total planning cost increases.

[0136] Due to the nonlinear relationship between the uncertain variable (demand response deviation) and the objective function in this problem, it is difficult to directly determine the worst-case response scenario. Using a nonlinear solver, we found that the worst-case scenario is at -5%. This is because when the actual curtailment is smaller than the expected amount, the net load is higher, resulting in higher substation capacity costs.

Claims

1. A substation capacity planning method combining robust optimization with chance constraints, characterized in that: The method comprises: Step 1: Modeling the uncertainty of source load and demand response based on stochastic optimization and robust intervals, where source load uncertainty is handled by random variables and demand response uncertainty is described by robust intervals. The specific process of step 1 is as follows: use random variables to model the uncertainty of load and distributed power output. The probability density function of photovoltaic output approximately follows the Beta distribution, and the load demand follows the normal distribution. Random simulation is performed based on the Weibull distribution function obeyed by wind speed. In each time period, v is extracted as the current wind speed value in the confidence interval of wind speed output and substituted into P WT The piecewise function expression of can simulate the uncertainty of current wind power output; Among them, P WT is the output power; P WT,N is the rated power; v in is the cut-in wind speed; v out is the cut-out wind speed; v N is the rated wind speed; In this application, since the uncertainty description of demand response is relatively complex, it is not appropriate to model it as a certain distribution. Here, it is modeled as a robust interval and only considers the load that can be reduced. The uncertainty set D of the load reduction amount is established; in, is the actual load reduction at the i-th load point; are the upper and lower bounds of the robust range of load reduction respectively; is the reference value of load reduction; t is conservative; Step 2: Constructing a substation capacity planning model with uncertainty considering source load and demand response with the goal of minimizing the total planning cost of the substation; Step 3: A method for solving the substation capacity planning model that combines chance constraints, point estimation, and dual transformation. The specific process of Step 3 is as follows: (1) Using opportunity constraints to transform power balance constraints Where α is the confidence level; (2) Rewrite the chance constraint into a linear constraint and use the point estimation method to obtain the probability information of the net load Among them, F sum is the net load probability distribution function without considering demand response, that is Probability distribution function of the net load; The three-point estimation method is used to obtain the probability information of the net load size, and then the Gram-Charlier expansion series method is used to obtain the probability density function and probability distribution function of the net load size, where the net load size is the superposition of the load size and the distributed power source; (3) Use dual transformation to convert the max function in the substation capacity planning model into a min function The standard expression of the model is as follows: Among them, λ 1,t is the dual multiplier of the power balance constraint; 2,t ,λ 3,t is the dual multiplier of the conservative constraint; then, the IPOPT nonlinear solver is used to solve it.

2. The substation capacity planning method combining robust optimization and chance constraints according to claim 1 is characterized in that: The specific process of step 2 is as follows: Based on the geographical distribution of loads, the conventional Voronoi diagram partitioning method is used to assign each load point to the substation with the smallest Euclidean distance. Based on the power supply range of the substation, a substation capacity uncertainty planning model is established with the goal of minimizing the total planning cost of the substation. (1) Objective function The objective function is to minimize the sum of total costs under the worst demand response conditions, which includes substation costs and demand response costs; The variable to be planned is the substation transformer capacity S substation,i and demand response reduction values Among them, the substation cost is the sum of construction cost and operation cost: Among them, C substation The annual value of the substation construction cost is equal to; is the price per unit capacity of the substation; N sub is the number of substations; k is the empirical coefficient of operating cost; For the substation in the planned area, the annual construction cost is: Among them, d sub is the discount rate, T is the operating life; Demand response only considers the load that can be reduced and provides a certain amount of incentive for users to reduce their load. Therefore, the total expected cost of incentive-based demand response is: Among them, c is the basic incentive price, is the motivating factor; is the load reduction amount obtained by incentive; The greater the load reduction of the user, the higher the final grid incentive price will be. Therefore, the incentive factor is set as: Among them, k t is the incentive coefficient; (2) Constraints 1) Power balance constraints in, The power delivered to the substation; Producing power for photovoltaics; Provide power for the fan; For normal load demand; is the demand response load power; N PV 、N WT 、N L 、N DR They are the number of photovoltaics, the number of wind turbines, the number of loads, and the number of loads participating in demand response; 2) Substation capacity constraints Among them, K sub,i is the substation capacity ratio, which is taken as 1.8~2.0.

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