An economical virtual capacity expansion method based on distributed flexible resources

Abstract

A method for economical virtual capacity increase of a substation based on distributed flexible resources can economically increase the allocation of distributed resources under the premise of not exceeding the actual capacity of the transformer in the process of optimal scheduling of the substation, thereby accommodating the load during the peak period of the substation and achieving the effect of virtual capacity increase. The main steps are as follows: establish an upper-level model for electric vehicle charging, which aims to minimize the user's cost; establish a lower-level model for economical virtual capacity increase of distributed flexible resources in the substation; solve the two-layer optimization model, and use the KKT condition to convert the two-layer optimization model into a single-layer optimization model; use the column constraint generation algorithm (C&CG) to solve the converted single-layer uncertainty model. The present invention solves the problem of economically allocating distributed flexible resources in the substation under uncertainty by establishing a two-layer optimization model for uncertainty optimization, thereby ensuring the economic charging needs of electric vehicle users and eliminating the hidden dangers of transformer over-limit.

Description

Technical Field

[0001] The invention belongs to the field of virtual capacity expansion of a transformer area, and in particular relates to an economical virtual capacity expansion method of a transformer area based on distributed flexible resources. Background Art

[0002] Improving the efficiency of existing power equipment is one of the biggest drivers for the development of smart grids. Exploring the transmission potential of power equipment, reducing the cost and reinvestment of power systems, and meeting the needs of an energy-saving and conservation-oriented society. With the widespread access to distributed resources today, the operation mode of the substation has undergone major changes. Fully tapping the distributed power generation capacity and cooperating with the substation's own potential complementary characteristics can effectively improve the operation performance of the substation, and can also bear heavier loads without physical transformation and capacity increase of the substation. Therefore, based on the existing distributed flexibility resources in the substation, it is of great practical significance to carry the maximum daily load in the optimal economic dispatching mode.

[0003] At present, traditional optimization scheduling is mainly based on deterministic models, which fail to fully consider the uncertainty of distributed resources such as photovoltaics, and fail to fully consider the uncertainty of predicted loads. Stochastic optimization overly relies on the distribution type of uncertain quantities and probability assumptions. However, this sampling-type random optimization easily ignores very severe situations, resulting in excessive loads during peak periods of transformers, causing transformers to operate overloaded for a long time, and reducing the life of transformers. In addition, the distribution functions that the uncertain quantities rely on are becoming increasingly difficult to predict as human activities and climate continue to change. Therefore, a virtual capacity increase model for distributed flexible resources in the substation area that fully considers the distribution of uncertain quantities is an urgent problem to be solved. Summary of the invention

[0004] In order to solve the deficiencies in the prior art, the purpose of the present invention is to provide an economical virtual capacity increase method for a substation based on distributed flexible resources.

[0005] The present invention adopts the following technical solution:

[0006] A method for economical virtual capacity increase of a substation based on distributed flexible resources comprises the following steps:

[0007] S1, building the upper-level model of electric vehicle charging;

[0008] S2, establish the economic virtual capacity increase lower layer model of distributed flexible resources in the substation area;

[0009] S3, solving the upper model constructed in S1, and adding the solved constraint conditions to the lower model in step 2;

[0010] S4, solve the lower model of S2 after adding constraints to obtain the capacity increase value of the transformer carrying power.

[0011] The upper-level model of electric vehicle charging satisfies the following relationship:

[0012]

[0013]

[0014] Where n represents the nth electric car; T0 n With T1 n Respectively represent the charging start and end time of the nth electric vehicle; P t n represents the charging power of the nth electric vehicle; represents the maximum charging power of the nth electric vehicle; represents the electricity price in time period t; Q n Indicates the amount of power after the nth electric car is fully charged; represents the maximum power of the nth electric vehicle when charging is completed; w n represents the charging intention of the owner of the nth electric car, w n ∈{w0,w1,...,w m}, the owner's charging intention w i Proportional to the amount of electricity that the electric vehicle can be fully charged, i = 0, 1, 2, ..., m, w m It means that the owner will definitely be able to fully charge the car.

[0015] Electricity price in time period t for: μ top , μ peak , μ flat , μ valley Represents one day T N Peak, flat and valley electricity prices during a period of time.

[0016] The lower model satisfies the following relationship:

[0017]

[0018]

[0019] Where: P t dg represents the output of distributed generators during period t; T N Indicates the total number of optimization periods; and They represent the charging and discharging power of the distributed generator energy storage during period t, with positive values ​​representing energy storage discharging and negative values ​​representing energy storage charging; P t h Indicates the power transmission size of the upper power grid; Pt pv represents the photovoltaic output during period t, P t pv,p Represents the predicted output of photovoltaic power; P t l Indicates the load size during period t, P t l,p Indicates the load forecast output; μ dg represents the electricity generation cost of distributed generators; Represents the time-of-use electricity price of the power grid; μ h Indicates the cost of purchasing electricity from the upper power grid; μ s represents the photovoltaic grid-connected electricity price; N represents the total number of electric vehicles; P cap Indicates the actual maximum capacity of the transformer; Q tol Indicates the total load size for one day; and They represent the upper and lower limits of load uncertainty fluctuation respectively; and They represent the upper and lower limits of the fluctuation of the photovoltaic uncertainty respectively; and Respectively represent the maximum charging and discharging power of energy storage; Indicates the maximum charging power. Indicates the maximum discharge power; and Respectively indicate the charging and discharging states; Indicates the state of charge (SOC) of the energy storage during time period t; represents the charging efficiency of energy storage, Indicates the discharge efficiency of energy storage; Q ess Indicates the capacity of energy storage; and Respectively represent the maximum and minimum SOC thresholds; represents the maximum output of distributed generators, Indicates the current SOC value.

[0020] The economic factor of the lower model is the time-of-use electricity price The power generation cost of distributed generators μ dg , the cost of purchasing electricity from the upper power grid μ h , Photovoltaic grid-connected electricity price μ s ; The uncertain factors are photovoltaic and load, respectively That is, the corresponding upper and lower limits of fluctuations are expressed.

[0021] The KKT conditions are used to solve the upper model and obtain the constraints on the lower model.

[0022] The Lagrangian function used in the solution process satisfies the following relationship:

[0023]

[0024] in, represents the Lagrangian function of the upper model, Q n represents the charge of the nth electric car after it is fully charged, represents the dual variable of the corresponding constraint, T1 n Table n represents the time when the nth electric car is picked up, T0 n Indicates the time when the nth electric car starts charging.

[0025] The specific constraints on the lower model are:

[0026] Stability conditions:

[0027]

[0028]

[0029] Complementary slack conditions:

[0030]

[0031]

[0032]

[0033] Feasibility conditions:

[0034]

[0035]

[0036]

[0037] Complementary conditional relaxation:

[0038]

[0039]

[0040]

[0041]

[0042]

[0043]

[0044] Where M is an arbitrarily large number, They are respectively the first logical variable, the second logical variable and the third logical variable introduced, and are used to relax the product form of the above complementary relaxation condition into a linear form.

[0045] The outer model MP used in the solution process specifically satisfies the following relationship:

[0046]

[0047]

[0048] Among them U (l*) It represents the worst uncertainty situation fed back by the inner model to the outer model. It is a constant for the outer model. (l) The inner model feeds back the newly introduced variables to the outer model.

[0049] The inner model SP satisfies the following relationship:

[0050]

[0051]

[0052] Where X = [P t n ,P t ess ],U=[P t pv ,P t l ],Y=[P t dg ], and h(·), g(·), m(·), n(·) are linear mapping groups, and l is the number of iterations.

[0053] The Lagrangian function used in solving the outer layer model SP is as follows:

[0054]

[0055] Among them, f(·) represents the mapping of the objective function, It is the dual variable corresponding to the inequality constraint and the equality constraint. X represents the optimal value of the current X solved by the outer layer, which is a constant for the inner model.

[0056] When solving the inner model SP, the corresponding stability conditions, complementary relaxation conditions, and feasibility conditions satisfy the following relationships:

[0057]

[0058] π h,i ≤s h,i M

[0059] h i (X,U,Y)≤M(s h,i -1)

[0060] h(X,U,Y)≤0

[0061] g(X,U,Y)=0

[0062] where y i , π h,i 、h i They are Y and π respectively. h , elements in h, π h , π g is the dual variable corresponding to the KKT condition, L represents the Lagrangian dual function of the SP model, s h,i is the introduced 01 slack variable, and M is an arbitrarily large number.

[0063] The specific steps for solving the outer model MP and the inner model SP are:

[0064] Step 1: Set the initial upper bound UB = +∞, the lower bound LB = -∞, the number of iterations l = 1, and U1 randomly selects a value from the uncertain set.

[0065] Step 2: Solve the MP model to obtain η, X, {Y (1) ,Y (2) , ..., Y (k+1)}, where k+1 represents the k+1th iteration, and updates LB=max{LB,η}.

[0066] Step 3: Solve the SP model to obtain U k+1 And the corresponding optimal value SP * , and update UB=min{UB,SP *}.

[0067] Step 4: Determine whether UB-LB < ε. If so, exit the loop. If not, go to step 5.

[0068] Step 5: Create new constraints and add them to the MP model, return to step 2;

[0069] η≥f(X,U (k+1) ,Y (k+1) )

[0070] h(X,U (k+1) ,Y (k+1) )≤0

[0071] g(X,U (k+1) ,Y (k+1) )=0

[0072] The beneficial effect of the present invention is that, compared with the prior art, the present invention establishes a two-layer model of economic virtual capacity increase in the substation based on the distributed flexible resources in the substation, and solves the two-layer model through KKT and C&CG, which solves the problem of being able to economically allocate the distributed flexible resources in the substation under uncertainty, guarantees the economic charging needs of electric vehicle users, and eliminates the hidden danger of over-limit of the substation. BRIEF DESCRIPTION OF THE DRAWINGS

[0073] Figure 1 It is a flow chart of the algorithm of the present invention;

[0074] Figure 2 is the electric vehicle charging strategy;

[0075] Figure 3 It is the energy storage charging and discharging strategy;

[0076] Figure 4 It is a distributed generator generation strategy;

[0077] Figure 5 It refers to the actual power that the transformer can bear, the actual load size of the substation, and the power limit of the transformer. DETAILED DESCRIPTION

[0078] The present application is further described below in conjunction with the accompanying drawings. The following embodiments are only used to more clearly illustrate the technical solution of the present invention, and cannot be used to limit the protection scope of the present application.

[0079] A method for economical virtual capacity increase of a substation based on distributed flexible resources, the prediction method comprising the following steps:

[0080] S1: Establish the upper-level model of electric vehicle charging;

[0081] Those skilled in the art should know that the upper model is a model that can express the relationship between the charging performance of electric vehicles and electricity prices, and those skilled in the art can construct it according to actual conditions; in order to improve the calculation accuracy, the model construction method proposed in the embodiment of the present invention is only a preferred embodiment, and is not an inevitable limitation for implementing the economic virtual capacity increase method of the area based on distributed flexible resources of the present invention. According to the charging characteristics of electric vehicles and electricity price information, an economic charging model of electric vehicles is established; the specific model is as follows:

[0082]

[0083]

[0084] Where: n represents the nth electric car; T0 n With T1 n Respectively represent the charging start and end time of the nth electric vehicle; Pt n represents the charging power of the nth electric vehicle; represents the electricity price in time period t; Q n Indicates the amount of power after the nth electric car is fully charged; represents the maximum power of the nth electric car after charging; w n represents the charging mode of the nth electric vehicle, w n The larger the value, the stronger the demand for charging and the weaker the demand for economy.

[0085] Furthermore, the economical charging characteristics in S1 are mainly reflected in the time-of-use electricity price. superior, μ top , μ peak , μ flat , μ valley Represents one day T N Peak, flat and valley electricity prices during the time period; n represents the charging intention of the owner of the nth electric car, w n ∈{w0,w1,…,w m}, where w n The larger the value, the stronger the owner's charging intention. In this embodiment, the owner's charging intention w i Proportional to the amount of electricity that the electric vehicle can be fully charged, i = 0, 1, 2, ..., m, w m It means that the owner will definitely be able to fully charge the car;

[0086] S2: Establishing the economic virtual capacity increase lower layer model of distributed flexible resources in the substation area;

[0087] Those of ordinary skill in the art should know that the lower-level model is capable of expressing the relationship between the charging and discharging power and the cost of energy storage and energy-consuming equipment in the substation area, and those of ordinary skill in the art can construct it according to actual conditions; in order to improve the accuracy of calculations, the model construction method proposed in the embodiment of the present invention is only a preferred embodiment, and is not an inevitable limitation for implementing the method of economic virtual capacity expansion of substations based on distributed flexible resources of the present invention. Based on the distributed flexible resources owned by the substation area: small distributed generators, substation energy storage, electric vehicles, and distributed photovoltaics, an economic virtual capacity expansion lower-level model is established, and the model is shown below.

[0088]

[0089]

[0090] Where: P t dg represents the output of distributed generators during period t; T N Indicates the total number of optimization periods; and They represent the charging power and discharging power of the energy storage in time period t, respectively. A positive value indicates energy storage discharging, and a negative value indicates energy storage charging. t h Indicates the power transmission size of the upper power grid; P t pv represents the photovoltaic output during period t, P t pv,p Represents the predicted output of photovoltaic power; P t l Indicates the load size during period t, P t l,p Indicates the load forecast output; μ dg represents the electricity generation cost of distributed generators; Represents the time-of-use electricity price of the power grid; μ h Indicates the cost of purchasing electricity from the upper power grid; μ s represents the photovoltaic grid-connected electricity price; N represents the total number of electric vehicles; P cap Indicates the actual maximum capacity of the transformer; Q tol Indicates the total load size for one day; and They represent the upper and lower limits of load uncertainty fluctuation respectively; and They represent the upper and lower limits of the fluctuation of the photovoltaic uncertainty respectively; and Respectively represent the maximum charging power and discharging power of energy storage; Indicates the maximum charging power. Indicates the maximum discharge power; and Respectively indicate the charging and discharging states; Indicates the state of charge (SOC) of the energy storage during time period t; Indicates the charging and discharging efficiency of energy storage, Indicates the charging efficiency, represents the discharge efficiency; Qess represents the energy storage capacity; and Respectively represent the maximum and minimum SOC thresholds; represents the maximum output of distributed generators, Indicates the current SOC value.

[0091] Furthermore, the economic efficiency of S2 is mainly reflected in the time-of-use electricity price. The power generation cost of distributed generators μ dg , the cost of purchasing electricity from the upper power grid μ h , Photovoltaic grid-connected electricity price μ s ; The uncertainty is mainly reflected in photovoltaic and load, respectively Indicates the upper and lower limits of load fluctuation. Indicates the upper and lower limits of fluctuation corresponding to photovoltaics.

[0092] S3: Solve the upper model constructed in S1 and add the solved constraints to the lower model in S2;

[0093] Those skilled in the art can solve the problem according to existing algorithms or using existing solution tools in the prior art. What is provided in this embodiment is only a preferred embodiment and is not an inevitable limitation for implementing the economical virtual capacity expansion method of a substation based on distributed flexible resources of the present invention.

[0094] This method solves the upper model according to KKT and obtains three types of constraints that the optimal solution of the upper model needs to meet: feasibility conditions, complementary relaxation conditions, and feasibility conditions. The complementary relaxation conditions are relaxed to obtain a set of linear constraints containing integers. Finally, the constraints are added to the lower model, and the original two-layer optimization model becomes a single-layer optimization model.

[0095] Furthermore, the three types of constraints satisfied by KKT in S3 for solving the upper model are as follows:

[0096] Stability conditions:

[0097] The Lagrangian function is shown below:

[0098]

[0099] in, represents the Lagrangian function of the upper model, Q n represents the charge of the nth electric car after it is fully charged, denote the first, second, third and fourth dual variables of the corresponding constraints, T1 n Indicates the time when the nth electric car is picked up, T0 n Indicates the time when the nth electric car starts charging

[0100] The corresponding stability conditions are as follows:

[0101]

[0102]

[0103] Complementary slack conditions:

[0104]

[0105]

[0106]

[0107] Feasibility conditions:

[0108]

[0109]

[0110]

[0111] Complementary conditional relaxation:

[0112]

[0113]

[0114]

[0115]

[0116]

[0117]

[0118] Where M is an arbitrarily large number, They are respectively the first logical variable, the second logical variable and the third logical variable introduced, and are used to relax the product form of the above complementary relaxation condition into a linear form.

[0119] S4: Solve the lower model of step 2 after adding constraints to obtain the capacity increase value of the transformer carrying power.

[0120] The column constraint generation algorithm (C&CG) is used to solve the converted single-layer uncertainty model, which is obtained by adding the constraints in step 3 to step 2. Solve the inner model to obtain a feasible solution as the upper bound of the optimal solution; solve the outer model to obtain a solution that satisfies some uncertainties as the lower bound of the optimal solution; the inner and outer layers are iterated continuously until the upper and lower bounds meet the given accuracy.

[0121] Furthermore, the column constraint generation algorithm (C&CG) in S4 is used to solve the converted single-layer uncertainty model. The included interval is discretized, and the fluctuation error unit is 1%. Therefore, the uncertainty of photovoltaic and load is as follows:

[0122]

[0123]

[0124]

[0125]

[0126] Among them, I pv Indicates the maximum number of bits used to represent photovoltaic uncertainty variables in binary format, I l Indicates the maximum number of digits used to represent the load uncertainty variable in binary, λ t pv represents the photovoltaic uncertainty using binary notation, represents the load uncertainty expressed in binary format, Represents the value of each bit of the photovoltaic binary variable, The value of each bit of the binary variable representing the load is determined according to the following formula: pv with I l Values:

[0127]

[0128]

[0129] To better illustrate the C&CG solution process, the model established in S2 is abbreviated as:

[0130]

[0131]

[0132] Where X = [P t n ,P t ess ],U=[P t pv ,P t l ],Y=[P t dg ], and h(·), g(·), m(·), and n(·) are linear mapping groups respectively.

[0133] For this, the outer model MP is as follows, where l is the number of iterations.

[0134]

[0135]

[0136] The inner model SP is as follows:

[0137]

[0138]

[0139] To solve the SP problem, KKT conditions are required, and the Lagrangian function is as follows:

[0140]

[0141] Among them, f(·) represents the mapping of the objective function, It is represented as the dual variable corresponding to the inequality constraint and the equality constraint. X represents the optimal value of the current X solved by the outer layer, which is a constant for the inner model.

[0142] The corresponding stability conditions, complementary relaxation conditions, and feasibility conditions are as follows:

[0143]

[0144] π h,i ≤s h,i M

[0145] h i (X,U,Y)≤M(s h,i -1)

[0146] h(X,U,Y)≤0

[0147] g(X,U,Y)=0

[0148] where y i , π h,i 、h i They are Y and π respectively. h , elements in h, π h , π g is the dual variable corresponding to the KKT condition, L represents the Lagrangian dual function of the SP model, s h,i is the introduced 01 slack variable, and M is an arbitrarily large number. Therefore, the solution to the SP problem can be transformed into:

[0149]

[0150]

[0151] In the formula, X represents the optimal value of the current X solved by the outer layer, which is a constant for the inner layer model.

[0152] Further, according to MP and SP, the iterative steps of solution are as follows:

[0153] Step 1: Set the initial upper bound UB = +∞, the lower bound LB = -∞, the number of iterations l = 1, and U1 randomly selects a value from the uncertainty set;

[0154] Step 2: Solve the MP model to obtain η, X, {Y (1) ,Y (2) , …, Y (k+1)}, where k+1 represents the k+1th iteration, and updates LB=max{LB,η};

[0155] Step 3: Solve the SP model to obtain U k+1 And the corresponding optimal value SP * , and update UB=min{UB,SP *};

[0156] Step 4: Determine whether UB-LB < ε. If so, exit the loop. If not, go to step 5.

[0157] Step 5: Create new constraints and add them to the MP model, return to step 2;

[0158] η≥f(X,U (k+1) ,Y (k+1) )

[0159] h(X,U (k+1) ,Y (k+1) )≤0

[0160] g(X,U (k+1) ,Y (k+1) )=0

[0161] An example of step S1 in the economical virtual capacity increase method of the substation area of ​​the present invention is as follows:

[0162] There are 3 electric cars in the area, and the charging time is from morning to evening, that is, 9 am to 5 pm. The charging willingness is w 1 =w min =1,w 2 =5,w 3 =w max =20, time-of-use electricity price μ top =1.6,μ peak =1.1,μ flat =0.6, μ valley =0.29, the time-of-use electricity price periods are as follows:

[0163] Table 1 Time-of-use electricity price period

[0164]

[0165] The upper level electricity purchase cost μ in S2 h =0.5, photovoltaic grid-connected electricity price μ s =0.7, the power generation cost of distributed generators μ dg =0.6, load / PV uncertainty fluctuation upper and lower limits

[0166] Electric vehicle charging strategy Figure 2 The remaining charge percentage is shown in Table 2.

[0167] Table 2 Remaining charge percentage of electric vehicles

[0168]

[0169] The energy storage charging and discharging strategy and distributed generator generation strategy in the substation area are as follows: Figure 3 to Figure 4 shown.

[0170] In addition, the actual load power borne by the transformer is as follows Figure 5 As shown in the figure, if there is no distributed flexible resource in the substation, the substation will be overloaded in a specific period of time, which will have a great impact on the life of the transformer. After the introduction of distributed resources, the power carried by the transformer can be reduced in the most economical way, achieving the effect of virtual capacity increase.

[0171] The applicant of the present invention has made a detailed explanation and description of the implementation examples of the present invention in conjunction with the drawings in the specification. However, those skilled in the art should understand that the above implementation examples are only preferred implementation schemes of the present invention, and the detailed description is only to help readers better understand the spirit of the present invention, but not to limit the scope of protection of the present invention. On the contrary, any improvements or modifications based on the inventive spirit of the present invention should fall within the scope of protection of the present invention.

Claims

1. A method for economical virtual capacity expansion of a substation based on distributed flexible resources, characterized in that: The economical virtual capacity increase method of the station area based on distributed flexible resources comprises the following steps: S1, building the upper-level model of electric vehicle charging; The upper-level model of electric vehicle charging satisfies the following relationship: In the formula, n represents the nth electric car; With T1 n Respectively represent the charging start and end time of the nth electric vehicle; P t n represents the charging power of the nth electric vehicle; represents the maximum charging power of the nth electric vehicle; represents the electricity price in time period t; Q n Indicates the amount of power after the nth electric car is fully charged; represents the maximum power of the nth electric vehicle when charging is completed; w n represents the charging intention of the owner of the nth electric car, w n ∈{w0,w1,…,w m }, the owner's charging intention w i Proportional to the amount of electricity that the electric vehicle can be fully charged, i = 0, 1, 2, ..., m, w m It means that the owner will definitely be able to fully charge the car; S2, establishing a lower-level model of economic virtual capacity expansion of distributed flexible resources in the substation area; the lower-level model is a model that expresses the relationship between the charging and discharging power and the consumed cost of the energy storage and energy consumption equipment in the substation area; S3, solving the upper model constructed in S1, and adding the solved constraint conditions to the lower model in step 2; S4, solving the S2 lower model after adding the constraint conditions to obtain the capacity increase value of the transformer carrying power.

2. The method for economical virtual capacity expansion of a substation based on distributed flexible resources according to claim 1, characterized in that: The electricity price for the period t for: μ top , μ peak , μ flat , μ valley Represents one day T N Peak, flat and valley electricity prices during a period of time.

3. A method for economical virtual capacity expansion of a substation based on distributed flexible resources according to claim 1 or 2, characterized in that: The lower layer model satisfies the following relationship: Where: P t dg represents the output of distributed generators during period t; T N Indicates the total number of optimization periods; and They represent the charging and discharging power of the distributed generator energy storage during period t, with positive values ​​representing energy storage discharging and negative values ​​representing energy storage charging; P t h Indicates the power transmission size of the upper power grid; P t pv represents the photovoltaic output during period t, P t pv,p Represents the predicted output of photovoltaic power; P t l Indicates the load size during period t, P t l,p Indicates load forecast output; μ dg represents the electricity generation cost of distributed generators; Represents the time-of-use electricity price of the power grid; μ h Indicates the cost of purchasing electricity from the upper power grid; μ s represents the photovoltaic grid-connected electricity price; N represents the total number of electric vehicles; P cap Indicates the actual maximum capacity of the transformer; Q tol Indicates the total load size for one day; and They represent the upper and lower limits of load uncertainty fluctuation respectively; and They represent the upper and lower limits of the fluctuation of the photovoltaic uncertainty respectively; and Respectively represent the maximum charging and discharging power of energy storage; Indicates the maximum charging power. Indicates the maximum discharge power; and Respectively indicate the charging and discharging states; Indicates the state of charge (SOC) of the energy storage during time period t; represents the charging efficiency of energy storage, Indicates the discharge efficiency of energy storage; Q ess Indicates the capacity of energy storage; and Respectively represent the maximum and minimum SOC thresholds; represents the maximum output of distributed generators, Indicates the current SOC value.

4. The method for economical virtual capacity expansion of a substation based on distributed flexible resources according to claim 1, characterized in that: The economic factor of the lower model is the time-of-use electricity price The power generation cost of distributed generators μ dg , the cost of purchasing electricity from the upper power grid μ h , Photovoltaic grid-connected electricity price μ s ; The uncertain factors are photovoltaic and load, respectively That is, the corresponding upper and lower limits of fluctuations.

5. The method for economical virtual capacity expansion of a substation based on distributed flexible resources according to claim 1, characterized in that: The KKT conditions are used to solve the upper model and obtain the constraints on the lower model.

6. The method for economical virtual capacity expansion of a substation based on distributed flexible resources according to claim 1, characterized in that: The Lagrangian function used in the solution process satisfies the following relationship: in, represents the Lagrangian function of the upper model, Q n represents the charge of the nth electric car after it is fully charged, represents the dual variable of the corresponding constraint, T1 n Indicates the time when the nth electric car is picked up, T0 n Indicates the time when the nth electric car starts charging.

7. A method for economical virtual capacity expansion of a substation based on distributed flexible resources according to claim 5 or 6, characterized in that: The specific constraints on the lower model are: Stability conditions: Complementary slack conditions: Feasibility conditions: Complementary conditional relaxation: Where M is an arbitrarily large number, They are respectively the first logical variable, the second logical variable and the third logical variable introduced, and are used to relax the product form of the above complementary relaxation condition into a linear form.

8. The method for economical virtual capacity expansion of a substation based on distributed flexible resources according to claim 7, characterized in that: The outer model MP used in the solution process specifically satisfies the following relationship: Among them U (l*) It represents the worst uncertainty situation fed back by the inner model to the outer model. It is a constant for the outer model. (l) The inner model feeds back the newly introduced variables to the outer model; The inner model SP satisfies the following relationship: Where X = [P t n ,P t ess ],U=[P t pv ,P t l ],Y=[P t dg ], and h(·), g(·), m(·), n(·) are linear mapping groups, and l is the number of iterations.

9. The method for economical virtual capacity expansion of a substation based on distributed flexible resources according to claim 8, characterized in that: The Lagrangian function used in solving the outer layer model SP is as follows: Among them, f(·) represents the mapping of the objective function, It is the dual variable corresponding to the inequality constraint and the equality constraint; X represents the optimal value of the current X solved by the outer layer, which is a constant for the inner model.

10. The method for economical virtual capacity expansion of a substation based on distributed flexible resources according to claim 9, characterized in that: When solving the inner model SP, the corresponding stability conditions, complementary relaxation conditions, and feasibility conditions satisfy the following relationships: p h,i ≤s h,i M h i (X,U,Y)≤M(s h,i -1) h(X,U,Y)≤0 g(X,U,Y)=0 where y i , π h,i 、h i They are Y and π respectively. h , elements in h, π h , π g is the dual variable corresponding to the KKT condition, L represents the Lagrangian dual function of the SP model, s h,i is the introduced 01 slack variable, and M is an arbitrarily large number.

11. A method for economical virtual capacity expansion of a substation based on distributed flexible resources according to any one of claims 8 to 10, characterized in that: The specific steps for solving the outer model MP and the inner model SP are: Step 1: Set the initial upper bound UB = +∞, the lower bound LB = -∞, the number of iterations l = 1, and U1 randomly selects a value from the uncertainty set; Step 2: Solve the MP model to obtain η, X, {Y (1) ,Y (2) , ..., Y (k+1) }, where k+1 represents the k+1th iteration, and updates LB=max{LB,η}; Step 3: Solve the SP model to obtain U k+1 And the corresponding optimal value SP * , and update UB=min{UB,SP * }; Step 4: Determine whether UB-LB < ε. If so, exit the loop. If not, go to step 5. Step 5: Create new constraints and add them to the MP model, return to step 2;

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