CN115619042B

CN115619042B - Transformer substation capacity planning method combining robust optimization and opportunity constraint

Info

Publication number: CN115619042B
Application number: CN202211408404.5A
Authority: CN
Inventors: 李文升; 梁荣; 杨波; 李昭; 杨慎全; 王可欣; 刘淑莉; 赵韧; 崔灿; 綦陆杰; 王延朔; 刘钊; 杨扬; 张雯; 邓少治; 李凯; 王耀雷; 李�昊; 孙东磊; 王轶群
Original assignee: Economic and Technological Research Institute of State Grid Shandong Electric Power Co Ltd
Current assignee: Economic and Technological Research Institute of State Grid Shandong Electric Power Co Ltd
Priority date: 2022-11-10
Filing date: 2022-11-10
Publication date: 2025-08-19
Anticipated expiration: 2042-11-10
Also published as: CN115619042A

Abstract

This application proposes a substation capacity planning method that combines robust optimization with opportunity 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 opportunity 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

Transformer substation capacity planning method combining robust optimization and opportunity constraint

Technical Field

The invention belongs to the field of power distribution network planning, and relates to a method for determining the total capacity range of a transformer substation meeting the requirements of new energy consumption and load complementation in a power distribution network and converting and solving a planning model combining robust optimization and opportunity constraint.

Background

As an important link playing a role in the power distribution network planning, the electric power and electric quantity balance needs to provide an important basis for determining the power grid construction scale based on a load prediction result. Therefore, scientific and reasonable electric power and quantity balance has very important significance for guaranteeing the asset utilization efficiency and input-output benefits of the power distribution network.

However, with the gradual implementation of the dual-carbon target, the access scale of the distributed power supply and the electrification degree of the terminal in the power distribution network are greatly improved. In order to fully stabilize the influence of the distributed power supply, energy storage and demand response technologies are rapidly developed, and the energy storage and demand response technologies are also important elements in the power distribution network. Conventional distribution networks are moving towards new types of distribution systems that are primarily new energy sources. The distributed power output has strong fluctuation, the load granularity at the power distribution network side is small, the randomness is strong, the controlled characteristics of energy storage and demand response are difficult to completely determine, the traditional power and electricity balance method based on a simple arithmetic method is difficult to adapt to the change, and the power and electricity balance method considering uncertainty is needed to be researched.

Disclosure of Invention

In order to solve the defects and shortcomings in the prior art, the method for planning the capacity of the transformer substation by combining robust optimization and opportunity constraint is provided to make up for the defect that an accurate electric power and electric quantity balance result cannot be obtained under the background of large-scale access of a distributed power supply, and support is provided for the rationality of a transformer substation planning scheme.

The invention provides a transformer substation capacity planning method combining robust optimization and opportunity constraint, which specifically comprises the following steps:

Step 1, a modeling method for source load and demand response uncertainty based on random optimization and a robust interval, wherein the source load uncertainty is processed by adopting random variables, and the demand response uncertainty is described by adopting the robust interval;

Step 2, constructing an uncertainty substation capacity planning model taking the minimum total planning cost of the substation into consideration of source load and demand response;

And 3, solving a transformer substation capacity planning model by combining opportunity constraint, point estimation and dual transformation.

The specific process of the step 1 is as follows:

(1) Modeling uncertainty of photovoltaic output using random variables

The probability density function of the output of the distributed photovoltaic approximately follows the Beta distribution, expressed as follows:

Wherein, f (·) is a gamma function, alpha and beta are shape parameters, the size of which can be estimated by researching historical data, and the calculation formula is as follows:

wherein mu _PV is the average value of the photovoltaic output, Is the variance of the magnitude of the photovoltaic output.

(2) Uncertainty of modeling wind power output by adopting random variables

The probability density function obeyed by the wind speed at each moment follows the two-parameter Weibull distribution

Wherein k is a shape coefficient for describing the shape of the wind power probability density function, 1 is taken here (in this case, c is the average wind speed), c is a scale coefficient reflecting the average wind speed, and v is the actual wind speed in m/s.

The method comprises the steps of enabling P _WT to be output power, enabling P _WT,N to be rated power, enabling v _in to be cut-in wind speed (generally 10-13 m/s), enabling v _out to be cut-out wind speed, enabling v _N to be rated wind speed, and enabling parameters of Weibull distribution to be estimated through historical investigation data.

Random simulation is carried out based on Weibull distribution functions obeyed by wind speeds, v is extracted as a current wind speed value in a confidence interval of wind speed output in each time period, and the current wind speed value is brought into piecewise function expression of P _WT, so that uncertainty of current wind power output can be simulated.

(3) Modeling uncertainty of conventional loads using random variables

Assuming that the loads of the load points at a certain moment all follow normal distribution, the cumulative probability distribution function is as follows.

4) Demand side resource model

In the present application, since the uncertainty description of the demand response is complicated, modeling it as a certain distribution is not appropriate, modeling it as a robust section is here, and only load shedding is considered. A set D of uncertainty of the load reduction amount is established.

Wherein, the Actually reducing load for the ith load point; the upper and lower bounds of the load reduction robust interval are respectively; A reference value for the reduction of load, and f _t is the conservation degree.

The specific process of the step 2 is as follows:

According to the geographic distribution of the load, the power supply range of each transformer substation is divided based on a conventional Voronoi diagram. Firstly, estimating the number of substations and determining the positions of the substations, then, drawing each load point to the substation with the minimum Euclidean distance by taking each substation as a vertex, constructing a conventional Voronoi diagram, wherein the division result is shown in figure 3, and finally, considering the related geographic information and expert advice, and adjusting to obtain the following division result diagram is shown in figure 4.

Based on the power supply range of the transformer substation, a transformer substation capacity uncertainty planning model with minimum total planning cost of the transformer substation as a target is established.

(1) Objective function

Where the objective function is the worst case of demand response, the sum of the total costs is minimal, and the costs include substation cost and demand response cost. Variables to be planned are the reduction values of the transformer capacity S _substation,i and the demand response of the substation

The cost of the transformer substation is the sum of the construction cost and the operation cost:

Wherein, C _substation is the annual value of the construction cost of the transformer substation and the like; N _sub is the number of substations, k is the running cost experience coefficient;

For a transformer substation in an area to be planned, the construction cost and other annual values are as follows:

Wherein d _sub is the discount rate, and T is the operational life.

The demand response only considers the reducible load, and provides a certain amount of incentive for the load reduction of the user, so the total expected cost of the incentive type demand response is as follows:

wherein, c is the basic incentive price, Is an excitation factor; the resulting load is reduced for excitation.

The larger the load reduction of the user, the higher the final grid incentive price enjoyed, and for this purpose, the incentive factor is set as:

Where k ^t is the excitation coefficient.

(2) Constraint conditions

1) Power balance constraint

Wherein, the The power is the power of the transformer substation; is photovoltaic output; the fan is powered; Is a conventional load demand; The power is the power of the load which is required to respond, and N _PV、N_WT、N_L、N_DR is the photovoltaic quantity, the fan quantity, the load quantity and the load quantity which participates in the demand response respectively.

2) Substation capacity constraint

Wherein K _sub,i is the capacitance-to-load ratio of the transformer substation, and is generally 1.8-2.0.

The specific process of the step 3 is as follows:

(1) Converting power balance constraints using opportunistic constraints

Where α is the confidence level.

(2) Rewriting the opportunity constraint into linear constraint, and obtaining probability information of the payload by using a point estimation method

Wherein F _sum is a payload probability distribution function without consideration of demand response, i.eProbability distribution function of the payload.

The method comprises the steps of obtaining probability information of the size of a payload by adopting a three-point estimation method, and obtaining a probability density function and a probability distribution function of the size of the payload by using a Gram-Charlier expansion series method, wherein the size of the payload is the superposition of the size of the payload and a distributed power supply.

When the payload is obtained, the space distribution problem of the payload needs to be considered, the internal source-load time sequence curves in the divided areas are overlapped according to the power supply range division of the transformer substation, and meanwhile, the time sequence characteristics of the distributed power supply and the payload are considered, so that the power supply unit division considering the source-load characteristic matching is performed. Firstly, superposition of time sequence curves in areas is carried out according to division of power supply ranges of transformer substations, then matching of source load characteristics among the areas is carried out, uncertainty is brought to the size of net load in a novel power distribution system, a calculation method of probability characteristics of the net load is required to be provided, and opportunity constraint is converted into deterministic constraint.

The application adopts a three-point estimation method to obtain the probability information of the size of the net load, and then obtains a probability density function and a probability distribution function of the size of the net load by a Gram-Charlier expansion series method, wherein the size of the net load is the superposition of the size of the load and a distributed power supply.

1) The real-time output of the photovoltaic is known to be subjected to Beta distribution, the time sequence of the load is known to be subjected to normal distribution, and the random variable X comprises a photovoltaic number a, b wind powers and (n-a-b) loads.

2) In the independent standard normal distribution space y= [ Y ₁,y₂...,y_n ], calculating a sampling value Y _i,k of each point and a weight p _i,k of the corresponding point by adopting a three-point estimation method to obtain S _Y in standard normal distribution.

S_Y＝[Y_1,1,Y_1,2,Y_2,1,Y_2,2,...,Y_n,1,Y_n,2,Y_2n+1]^T

Wherein the calculation formulas of Y _i,k and Y _2n+1 are as follows:

3) And obtaining a sample matrix S _Z with normal distribution of relevant standards through matrix transformation.

S_Z＝[Z_1,1,Z_1,2,Z_2,1,Z_2,2,...,Z_n,1,Z_n,2,Z_2n+1]^T

Wherein the calculation formulas of Z _i,k and Z _2n+1 are as follows:

4) The standard normal distribution sample matrix S _Z is converted into a sample matrix S _X in the actual distribution space.

S_X＝[X_1,1,X_1,2,X_2,1,X_2,2,...,X_n,1,X_n,2,X_2n+1]^T

Wherein the calculation formulas of X _i,k and X _2n+1 are as follows:

5) And adding each row of elements in the S _X to obtain a sample matrix W= [ W ₁,W₁,...,W_2n+1]^T ] of the random variable of the payload, and calculating the mean value and the variance of the random variable of the payload by adopting a three-point estimation method.

6) According to each moment of the random variable W of the payload, the probability density function F (W) and the probability distribution function F (W) of the payload W are obtained by using a Gram-Charlier expansion series method.

Fig. 5 shows a general flow of the three-point estimation method to obtain the probability distribution function of the payload W.

(3) Converting max function in transformer substation capacity planning model into min function by utilizing dual conversion

The model is expressed as follows:

Wherein lambda _1,t is a power balance constraint pair multiplier, and lambda _2,t、λ_3,t is a conservation constraint pair multiplier.

Then, a IPOPT nonlinear solver is used for solving.

The beneficial effects are that:

The method for planning the capacity of the transformer substation by combining robust optimization and opportunity constraint solves the problem of multiple uncertainty of source load and demand response, effectively solves the problem that multiple randomness factors in a power distribution network are difficult to obtain an accurate electric power and electric quantity balance result, and provides support for the rationality of a transformer substation planning scheme.

Drawings

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 solution flow chart of a substation capacity planning method combining robust optimization and opportunity constraint of the invention;

FIG. 2 is a schematic diagram of Vonoroi of the present invention;

FIG. 3 is a diagram showing the power supply range division of a transformer substation in the invention;

FIG. 4 is a diagram showing the power supply range division result of a transformer substation taking geographic information into account in the invention;

FIG. 5 is a flow chart of the acquisition of the payload probability density function and probability distribution function of the present invention;

FIG. 6 is a diagram of geographic information in the present embodiment;

FIG. 7 is a timing diagram of various typical loads in the planned area in the present embodiment;

FIG. 8 is a graph of the net load for each zone in this embodiment;

FIG. 9 is a graph of the payload curve for the present embodiment accounting for 95% quantiles;

FIG. 10 is a diagram showing the calculation result of point estimation in the present embodiment;

FIG. 11 is a schematic diagram of the demand response configuration of each region in the present embodiment;

Fig. 12 is a diagram illustrating the payload reduction taking into account the robust interval of the demand response in the present embodiment.

Detailed Description

In order to make the structure and advantages of the present invention more apparent, the structure of the present invention will be further described with reference to the accompanying drawings.

The invention provides a transformer substation capacity planning method integrated solving flow combining robust optimization and opportunity constraint, which is described in detail by referring to fig. 1, and comprises the following specific steps:

and step1, dividing the area to be planned by using the payload to obtain the power supply range of each transformer substation.

And 2, superposing the source load time sequence curves in the power supply range of each transformer substation and obtaining the payload.

And 3, obtaining cumulative probability distribution of the net load by utilizing point estimation, solving the dividing points, and rewriting the opportunity constraint of electric power and electric quantity balance into linear constraint.

And 4, substituting the constraint into the robust optimization model and performing dual change to obtain a simple deterministic optimization model.

And 5, solving by using a solver to obtain the capacity range of each transformer substation, and superposing the capacity ranges of different transformer substations to obtain the total regional capacity range.

On an example system, the effectiveness of the method is clarified, so that reasonable assessment of the power grid construction scale is realized, and the economical and efficient operation of the power distribution network is ensured.

(1) Important parameters

The manufacturing cost of each MVA of the unit capacity of the transformer substation to be planned is 25 ten thousand yuan, the capacity-to-load ratio is set to be 1.8-2.0, the service life is 20 years, and the discount rate is 9%. The basic specification of the substation is a 2×63MVA substation.

The temperature-controlled load and the building lighting load among the normal loads are considered as the reducible load. According to statistics, the power value of the load accounts for about 29.5% of the total regulating load in the eastern China, the upper limit of the capacity of the demand response load configuration is 20% of the load amount, and the cost is 0.2 yuan/kW.

The investment and operation and maintenance costs of the transformer substation are converted into equal annual values, the annual cost is obtained by multiplying the demand response cost of a typical day by the annual days, and the operation consideration is divided into 24 time periods all the day. Solving the area to be planned total capacity range of the substation.

(2) Planning an area

FIG. 6 is a geographical distribution diagram of loads in a region of North China, wherein 460 load points are distributed in the region, the average load size is 450kW, the total photovoltaic amount is 117000kW, and the total wind power amount is 21700kW. The power supply range of the transformer substation comprises 223 street nodes and 407 street segments, and the types and the geographic positions of the street nodes, the street segments and the loads are shown in fig. 6. The load has four load types of residents, businesses, industry and administration, and the time sequence load curves of the different load types on each typical day are shown as 7.

(3) Planning results

The net load curves for the various zones are shown in fig. 8:

the total load is 61400kW, the total photovoltaic power is 37425kW, and the total wind power is 7200kW in the area 1;

The total load is 59800kW, the total photovoltaic power is 42125kW, and the total wind power is 7300kW;

The total load of the area 3 is 62500kW, the total photovoltaic power of 37500kW and the total wind power of 7200kW.

Taking area 1 as an example, a payload curve without uncertainty and a 95% payload curve are shown in FIG. 9.

It can be seen that if the capacity of the substation is configured according to the payload, the actual conditions are not met, and there is still a high probability of out-of-limit. The present application thus refers to a 95% payload curve.

The different probability density functions of the load, wind power and photovoltaic are overlapped by using a point estimation method, and by taking T=15 as an example, the net load probability density function and the accumulated probability distribution function are obtained by using the point estimation method as shown in fig. 10.

The individual area demand response configuration diagram is shown in fig. 11.

The total capacity of the built transformer substation is 43.3-48.2 MVA, and the price is 118.67-131.84 ten thousand yuan;

the total capacity of the built transformer substation is 40.2-44.7 MVA, and the price is 110.18-122.42 ten thousand yuan;

The total capacity of the built transformer substation is 45.3-50.3 MVA, and the price is 125.92-139.60 ten thousand yuan.

Table 1 accounts for cost comparison of demand response (minimum)

	Meter demand response (Wanyuan)	Does not take into account demand response (Wanyuan)
			Zone 1	118.67	200.97
Zone 2	110.20	186.61
			Zone 3	137.87	210.17

From the above table, implementation of the demand response can significantly reduce the investment cost of substation construction.

The payload curtailment taking into account the demand response robust interval is shown in fig. 12.

Taking the region 3 as an example, the total cost of the transformer substation planning without considering the robust interval is 124.08-137.87 ten thousand yuan. The total cost of the transformer substation planning considering the robust interval is 125.92-139.60 ten thousand yuan. The total cost of planning increases after taking into account the uncertainty of the demand response.

Because of the nonlinear relationship between the uncertainty variable (demand response deviation) and the objective function in the problem, it is difficult to directly judge the worst response situation. The solution was performed using a nonlinear solver, and the worst case was found to be taken at-5%. This is because when the actual reduction amount is smaller than the desired amount, the net load is higher and the cost required for the capacity of the substation is greater.

Claims

1. A method for planning capacity of a substation by combining robust optimization and opportunity constraint, the method comprising:

Modeling the uncertainty of load and distributed power supply output by using random variables, wherein the probability density function of photovoltaic output approximately follows Beta distribution, the load demand approximately follows normal distribution, random simulation is carried out based on Weibull distribution function obeyed by wind speed, v is extracted as a current wind speed value in a confidence interval of wind speed output in each time period, and the current wind speed value is brought into a piecewise function expression of P _WT, so that the uncertainty of current wind power output can be simulated;

Wherein, P _WT is output power, P _WT,N is rated power, v _in is cut-in wind speed, v _out is cut-out wind speed, and v _N is rated wind speed;

In the application, because the uncertainty description of the demand response is complex, modeling the demand response into a certain distribution is not proper, the demand response is modeled into a robust interval, and only load reduction is considered;

Wherein, the Actually reducing load for the ith load point; the upper and lower bounds of the load reduction robust interval are respectively; A reference value for a load reduction amount; r _t is the degree of conservation;

And 3, combining the opportunity constraint, the point estimation and the dual transformation to solve a substation capacity planning model, wherein the specific process of the step 3 is as follows:

(1) Converting power balance constraints using opportunistic constraints

Where α is the confidence level;

Wherein F _sum is a payload probability distribution function without consideration of demand response, i.eProbability distribution functions of the payload;

the method comprises the steps of obtaining probability information of the size of a net load by adopting a three-point estimation method, and obtaining a probability density function and a probability distribution function of the size of the net load by using a Gram-Charlier expansion series method, wherein the size of the net load is the superposition of the size of the load and a distributed power supply;

The model is expressed as follows:

Where λ _1,t is the power balance constrained pair multiplier, λ _2,t、λ_3,t is the conservation constrained pair multiplier, and then solved using a IPOPT nonlinear solver.

2. The method for planning the capacity of the transformer substation by combining robust optimization and opportunity constraint according to claim 1, wherein the specific process of the step2 is as follows:

According to the geographic distribution of the load, each load point is marked to a substation with the minimum Euclidean distance by using a conventional Voronoi diagram dividing method, and a substation capacity uncertainty planning model which aims at the minimum total planning cost of the substation is established based on the power supply range of the substation;

(1) Objective function

The objective function is that the sum of the total cost is minimum when the demand response is worst, the cost comprises the substation cost and the demand response cost, and the variables to be planned are the transformer capacity S _substation,i of the substation and the cut-down value of the demand response

Wherein d _sub is the discount rate, and T is the operational life;

wherein, c is the basic incentive price, Is an excitation factor; reducing the amount of load obtained for excitation;

wherein k ^t is the excitation coefficient;

(2) Constraint conditions

1) Power balance constraint

Wherein, the The power is the power of the transformer substation; is photovoltaic output; the fan is powered; Is a conventional load demand; N _PV、N_WT、N_L、N_DR is photovoltaic quantity, fan quantity, load quantity and load quantity participating in demand response respectively;

2) Substation capacity constraint

Wherein K _sub,i is the capacitance-to-load ratio of the transformer substation, and 1.8-2.0 is taken.