Multi-virtual power plant-containing power system collaborative optimization method based on feasible region equivalent projection theory

Abstract

The invention discloses a collaborative optimization method for a power system containing multiple virtual power plants based on a feasible region equivalent projection theory. The method comprises the following steps: establishing a main network operation model; modeling wind and light uncertainty by adopting an opportunity constraint optimization method and establishing a virtual power plant operation model; the chance constraint is converted into a deterministic constraint through quantiles; giving an objective function of virtual power plant-main network collaborative optimization, and establishing an integrated dispatching model of a power system containing multiple virtual power plants; eliminating internal variables of the virtual power plant in the target function by using an upper mirror graph theory; describing a multi-period power-cost feasible region projection of the virtual power plant at the common coupling point based on a feasible region equivalent projection theory and a vertex projection convex hull search method; and establishing a VPP-major network collaborative optimization model based on feasible region equivalent projection, and calling a GUROBI solver for solving in a Matlab2021a environment. According to the method, the virtual power plant-main network collaborative optimization model in multiple periods is solved in a non-iterative mode, the solving time is greatly shortened compared with a traditional iterative method, and the method has the same optimality as the traditional method.

Description

Technical Field

[0001] The present invention relates to the field of virtual power plant (VPP)-main grid collaborative optimization, and specifically relates to a collaborative optimization method for a power system with multiple virtual power plants based on the theory of equivalent projection of the feasible region. Background Technique

[0002] Distributed energy resources (DERs) represented by wind power and solar power have been increasingly valued globally due to their stability, economic efficiency, flexibility, and environmental friendliness. Although DERs have obvious advantages, there are also some problems. Due to the small scale and wide distribution of DERs, new challenges have been brought to the dispatching management of the power system. To address this challenge, virtual power plant technology has emerged. The virtual power plant (VPP) integrates various distributed energy resources using advanced communication and measurement technologies and participates in the transmission grid dispatching as a unified virtual entity.

[0003] Most of the existing studies on VPP-main grid collaborative optimization are based on the idea of unified optimization. For example, the literature (Jiang T, Wu C, Huang T, et al. Optimal market participation of VPPs in TSO-DSO coordinated energy and flexibility markets[J]. APPLIED ENERGY, 2024, 360.) proposed an optimal market model for VPPs to participate in the clearing of the transmission-level market and used the alternating direction method of multipliers with adaptive penalty parameters for solution. The alternating direction method of multipliers with adaptive penalty parameters used in this literature for solving the proposed market model requires multiple iterations, highly depends on computing power, and there may be problems such as non-convergence in the calculation results.

[0004] The literature (Zhang G, Wang X, Jiang C W, et al. Economic analysis of virtual power plants using two-layer optimal dispatching[J]. Power System Technology, 2016, 40(8): 2295-2301.) established a two-layer optimal dispatching model for the main grid and VPP, analyzed from the perspective of different capacity ratios of the VPP in the system, and provided support for the dispatching of the main grid and VPP. Solving the VPP-main grid collaborative optimization problem with the idea of unified optimization requires the use of iterative solution methods, but problems such as non-convergence or oscillation may occur during the solution process.

[0005] To solve the above problems, some studies have proposed non-iterative VPP-main grid collaborative optimization methods. For example, the literature (Ren J, Zeng Y, Qin C, et al. Characterization and application of flexible operation region of virtual power plant[J]. APPLIED ENERGY, 2024, DOI: 10.1016 / j.apenergy.2024.123733.) proposed a method for characterizing the scheduling boundary of VPP based on the concept of flexible operation region, characterized the flexible operation feasible region of VPP, and finally projected it onto the point of common coupling to support the scheduling of the transmission grid. However, such non-iterative methods still have problems such as high algorithm complexity or excessive computational burden. Summary of the Invention

[0006] To solve the problem that the traditional solution method for virtual power plant-main grid collaborative optimization may have problems of non-convergence or oscillation in solving. The present invention proposes a collaborative optimization method for a power system with multiple virtual power plants based on the theory of equivalent projection of feasible regions. This method solves the virtual power plant-main grid collaborative optimization model in multiple time periods in a non-iterative manner, and the solving time is significantly reduced compared with the traditional iterative method, and it has the same optimality as the traditional method.

[0007] The technical solution adopted by the present invention is as follows:

[0008] A collaborative optimization method for a power system with multiple virtual power plants based on the theory of equivalent projection of feasible regions, comprising the following steps:

[0009] Step 1: Considering the constraints of the main grid power network and transmission capacity constraints, establish a main grid operation model; considering the uncertainties of wind power and photovoltaic power outputs, establish a virtual power plant operation model;

[0010] Step 2: Convert the wind power and photovoltaic chance constraints into deterministic constraints through quantile transformation;

[0011] Step 3: Establish an objective function for virtual power plant-main grid collaborative optimization, and based on Step 1 and Step 2, establish an integrated scheduling model for a power system with multiple virtual power plants;

[0012] Step 4: Use the epigraph theory to eliminate the internal variables of the virtual power plant in the objective function, and describe the multi-time period power-cost feasible region projection of the virtual power plant at the point of common coupling based on the theory of equivalent projection of feasible regions and the vertex projection convex hull search method;

[0013] Step 5: Establish a VPP-main grid collaborative optimization model based on the equivalent projection of the feasible region, and solve the model.

[0014] In the above-mentioned step 1, the main grid operation model includes generator output constraint, generator ramp rate constraint, interchange power injection constraint, node power balance constraint, main grid branch power flow constraint, and line transmission capacity constraint;

[0015] 1) Generator output constraint:

[0016]

[0017] In formula (1), represents the active power output of the generator at node b in the main grid at time t; are respectively the upper and lower limits of the active power output of the main grid generator at node b.

[0018] 2) Generator ramp rate constraint:

[0019]

[0020] In formula (2), is the generator ramp rate at node b in the main grid at time t; represents the active power output of the generator at node b in the main grid at time t + 1;

[0021] 3) Interchange power injection constraint:

[0022]

[0023] In formula (3), represents the upper limit of the power injected by the i-th VPP into the main grid; represents the active power injected by the i-th virtual power plant into the point of common coupling of the main grid at time t.

[0024] 4) Node power balance constraint:

[0025]

[0026] In formula (4), is the active power of the generator at node b in the main grid at time t; is the active power of the line between node b and q in the main grid at time t; is the active power injected by the i-th virtual power plant into the point of common coupling at time t; is the active load of node b in the main grid at time t; χ b represents the set of nodes connected to node b in the main grid; e VPP is the incidence matrix of the virtual power plant access node and the main grid node; N VPP represents the total number of virtual power plants; i represents the virtual power plant number index.

[0027] 5) Main grid branch power flow constraint:

[0028]

[0029] In formula (5), are the active and reactive powers of the line between nodes b and q in the main grid at time period t; b bq , g bq are the susceptance and conductance values of the line between nodes b and q in the main grid at time period t; and are the voltage amplitudes of nodes b and q in the main grid at time period t; and are the voltage phase angles of nodes b and q in the main grid at time period t; Z is the number of segments for piecewise linearization; z is the index number of the segment; are the upper and lower limit values of the main grid voltage amplitude; are the upper and lower limit values of the main grid voltage phase angle; represents the capacity of the line between nodes b and q in the main grid at time period t.

[0030] 6) Line transmission capacity constraint:

[0031]

[0032] In formula (6), is the power transmission distribution factor from the main grid node b to branch l; is the power transmission distribution factor from the i-th virtual power plant to the main grid branch l; is the capacity of the main grid branch l; N Main represents the number of main grid nodes; t represents the scheduling time index; T represents the total scheduling time.

[0033] In step 1, the virtual power plant operation model includes power network constraints, gas turbine output constraints, photovoltaic output constraints, wind power output constraints, node power balance constraints, and exchange power constraints;

[0034] 1). Power network constraints:

[0035] The power network constraints include linearized virtual power plant power flow constraints and power system operation constraints. Formulas (7) to (8) are the linearized virtual power plant power flow constraints; formula (9) is the linearized form of the virtual power plant branch power flow constraint, and formulas (10) to (11) are the power system operation constraints.

[0036]

[0037] In the above formula, i is the virtual power plant number index; are the active and reactive powers of the line between nodes m and n in the i-th virtual power plant at time period t; b i,mn , g i,mnThey are the susceptance and conductance values of the line between the m-th and n-th nodes of the i-th virtual power plant, respectively; and They are the voltage amplitudes of the m-th and n-th nodes of the i-th virtual power plant at time t, respectively; and They are the voltage phase angles of the m-th and n-th nodes of the i-th virtual power plant at time t, respectively; G is the number of segments for piecewise linearization; g is the index number of the segment; V max , V min They are the upper and lower limit values of the voltage amplitude, respectively; θ max , θ min They are the upper and lower limit values of the voltage phase angle, respectively; It represents the capacity of the line between the m-th and n-th nodes of the i-th virtual power plant.

[0038] 2) Gas turbine output constraint:

[0039]

[0040] In the above formula, P max , P min They are the upper and lower limits of the active power output of the gas turbine, respectively; Q max , Q min They are the upper and lower limits of the reactive power output of the gas turbine, respectively; is the active power output of the gas turbine at the m-th node of the i-th virtual power plant at time t; is the reactive power output of the gas turbine at the m-th node of the i-th virtual power plant at time t.

[0041] 3) Photovoltaic power generation constraint:

[0042] The uncertainty of photovoltaic power generation is modeled using chance constraints, as shown in Equation (14),

[0043]

[0044] In Equation (14), represents the probability of event ; is the active power output of the photovoltaic at the m-th node of the i-th virtual power plant at time t; is the predicted value of the active power output of the photovoltaic at the m-th node of the i-th virtual power plant at time t; η PV is the confidence level.

[0045] 4) Wind power generation constraint:

[0046] The wind power generation constraint is the same as the photovoltaic power generation constraint. The wind power generation constraint is as follows:

[0047]

[0048] In Equation (15), Represents the probability of an event ; is the active power output of wind power at node m of the i-th virtual power plant at time t; is the predicted value of the active power output of wind power at node m of the i-th virtual power plant at time t; η W is the confidence level.

[0049] 5) Node power balance constraint:

[0050]

[0051] In the formula, is the active load at node m of the i-th virtual power plant at time t; is the reactive load at node m of the i-th virtual power plant at time t; χ m is the set of nodes connected to node m; n represents the index of the termination node of a branch in each virtual power plant.

[0052] 6) Exchange power constraint:

[0053]

[0054] In formula (18), is the active power injected into the common connection point by the i-th virtual power plant at time t; is the active power of the branch connected to the common connection point in the i-th virtual power plant; χ pcc is the set of nodes connected to the common connection point. m represents the index of the starting node of a branch in each virtual power plant.

[0055] In step 2, taking photovoltaic power generation as an example, the process of converting the chance constraint into a deterministic constraint through quantile transformation is as follows:

[0056]

[0057]

[0058] In the above formula, Represents the probability of an event ; represents the average value of the photovoltaic predicted output at node m of the i-th virtual power plant at time t; Φ(·) represents the distribution cumulative function; represents the inverse distribution cumulative function of the standard normal distribution N(0,1); is the standard deviation of the photovoltaic predicted output at node m of the i-th virtual power plant at time t; η PV represents the confidence level of photovoltaic.

[0059] After the above transformation, the photovoltaic chance constraint formula (14) is transformed into the deterministic constraint formula (22).

[0060] The steps of converting the wind power generator constraints into deterministic constraints are the same as those of the photovoltaic power generation, as shown in Equation (23);

[0061]

[0062] In Equation (23), represents the average value of the predicted wind power output at node m in the t-th period of the i-th virtual power plant; is the standard deviation of the predicted wind power output at node m in the t-th period of the i-th virtual power plant; η W represents the confidence level of the wind power.

[0063] In Step 3, the optimization objective is to minimize the sum of the main grid operation cost and the operation costs of each virtual power plant, ignoring the investment costs of each energy device. The main grid only considers the power generation cost of conventional units, and each VPP only considers the power generation cost of gas turbines, the operation and maintenance costs of new energy devices. As shown in Equation (24):

[0064]

[0065] In Equation (24), min Cost represents minimizing the total operation cost of the system; are the cost functions of the gas turbine, photovoltaic, and wind power in the t-th period of the i-th virtual power plant, respectively; are the active power outputs of the gas turbine, photovoltaic, and wind power at node m in the t-th period of the i-th virtual power plant, respectively; C b,t (·) is the generator cost function at node b in the t-th period of the main grid; is the active power output of the generator at node b in the t-th period of the main grid; i is the virtual power plant index; N VPP is the total number of virtual power plants; m is the internal node index of the virtual power plant; is the number of internal nodes of each virtual power plant; b is the main grid node index; N main is the total number of main grid nodes; t is the period index; T is the total number of periods.

[0066] The established integrated dispatching model of the power system with multiple virtual power plants is as follows:

[0067] Objective function:

[0068] The objective function is Equation (24);

[0069] Constraint conditions:

[0070] Main grid operation constraints: Equations (1) to (26);

[0071] VPP operation constraints: Equations (7) to (13), Equations (16) to (18), Equation (22), Equation (23).

[0072] In step 4, first, the objective function is transformed based on the epigraph theory. The epigraph describes the upper region of the range of a function within a given domain. For a general function f(x), its epigraph refers to the set composed of the graph of the function and all the points above it. Formally, the epigraph of f(x) is defined as:

[0073] epi(f(x)) = {(x, o) ∈ R n ×R | f(x) ≤ epi(f(x)) ≤ N} (25);

[0074] In equation (25), epi(f(x)) represents the epigraph of the function f(x); (x, o) represents the input of the function f(x); R n represents the dimension of x; R represents the dimension of o; N is a real number, and its value can be any number greater than f(x). Essentially, the epigraph represents the region between the function f(x) and N.

[0075] Based on equation (25), the operating cost part of the virtual power plant in equation (24) is transformed. The transformed objective function is as follows:

[0076]

[0077] In the above formula, is the introduced auxiliary variable, representing the cost function corresponding to the i-th virtual power plant at time t;

[0078] respectively represent the operating costs of the gas turbine, photovoltaic, and wind power generation at node m of the i-th virtual power plant at time t; respectively represent the quadratic term coefficient, linear term coefficient, and constant term coefficient of the main grid cost function. For its epigraph has the specific form:

[0079]

[0080] In the above formula, represents the gas turbine operating cost coefficient at node m of the i-th virtual power plant at time t;

[0081] represents the photovoltaic power generation operating cost coefficient at node m of the i-th virtual power plant at time t; represents the wind power generation operating cost coefficient at node m of the i-th virtual power plant at time t;

[0082] is an arbitrary constant greater than ;

[0083] So far, the internal variables of each virtual power plant in the original objective function have been eliminated, and the objective function is replaced by Equation (26). Equations (29) and (30) are used as the operation constraints of the virtual power plant to participate in the system operation.

[0084] In Step 4, the operation feasible region of the virtual power plant is an irregular polyhedron. The first step of projection is to determine the projection plane.

[0085] In the present invention, the variables constituting the projection plane are called projection variables. For the i-th virtual power plant, the projection variables are taken as as follows: The dimensionality reduction model will be the equivalent projection of the operation feasible region of the virtual power plant onto the plane and its internal variables are Based on the vertex projection convex hull search method for solving the feasible region, the equivalent projection of the multi-virtual power plant multi-period feasible region is characterized. According to geometric principles, each vertex of the projection polygon is an extreme point, and solving the optimization problem can obtain the feasible region of the projection variables ;

[0086]

[0087] s.t. Equations (7)-(13), (16)-(18), (23), (24), (29), (30)

[0088] In Equation (31), μ T is the vertex search direction; Vertex represents the objective function of vertex search; among them, the distance between the two points connected by the line corresponding to the new vertex and the new search direction is as follows:

[0089]

[0090] In Equation (32), is the abscissa of the new vertex obtained in the λ-th new vertex search for the i-th virtual power plant at time t; is the ordinate of the new vertex obtained in the λ-th new vertex search for the i-th virtual power plant at time t; respectively represent the coefficients of the straight line equation of the line connecting two adjacent points in the convex hull corresponding to the search direction in the λ-th new vertex search for the i-th virtual power plant at time t.

[0091] Based on the characterization of the equivalent projection of the virtual power plant feasible region in Step 4, the internal variables are eliminated from the operation models of each virtual power plant, realizing the equivalent dimensionality reduction of the VPP model.

[0092] In Step 5 described above, the mathematical model of the equivalent projection of the VPP operation feasible region is expressed as follows:

[0093]

[0094] In formula (33), are respectively the switching power at the common connection point of the i-th virtual power plant at time t the lower limit value and the upper limit value in the equivalent projection area; are respectively the cost of the i-th virtual power plant at time t the lower limit value and the upper limit value in the equivalent projection area; are respectively the coefficients of the straight line equations of the projection polygon boundary of the i-th virtual power plant at time t.

[0095] The multi-VPP-main grid collaborative optimization model based on the equivalent projection of the feasible region is shown as follows:

[0096]

[0097] Call the Gurobi solver in Matlab to first solve problem (34) to obtain the optimal value represents the optimal value of the active power injected into the common connection point by the i-th virtual power plant at time t; represents the optimal value of the operating cost of the i-th virtual power plant at time t.

[0098] The main grid distributes it to the virtual power plant VPP; secondly, each virtual power plant VPP uses as the boundary condition to perform optimal dispatching by solving problem (35).

[0099] A collaborative optimization method for a power system with multiple virtual power plants based on the theory of equivalent projection of the feasible region of the present invention has the following beneficial effects:

[0100] 1), Step 1 of the present invention considers the main grid power network constraints and transmission capacity constraints to establish the main grid operation model, and considers the uncertainty of wind power and photovoltaic output to establish the virtual power plant operation model, improving the reliability and stability of the power system. At the same time, it provides accurate system states and parameters for subsequent optimization, laying a solid foundation for achieving more efficient resource allocation and dispatching.

[0101] 2), Step 2 of the present invention converts the chance constraints of wind power and photovoltaic power into deterministic constraints through quantile transformation, simplifies the complexity of the optimization problem, enables the originally difficult-to-handle uncertainty factors to be quantified and determined, not only improves the solvability of the model, but also makes the optimization results more robust.

[0102] 3) The step 3 of the present invention establishes an integrated dispatching model for a power system with multiple virtual power plants based on steps 1 and 2, achieving coordination and optimization between the virtual power plants and the main grid. It can more effectively utilize renewable energy, improve the economy and environmental friendliness of the system, and ensure the stability and economy of power supply at the same time.

[0103] 4) The step 4 of the present invention transforms the objective function and depicts the projection of the feasible region of the exchanged power at the point of common coupling. After the transformation of the objective function, the internal variables of the virtual power plant are eliminated, reducing the complexity of the integrated dispatching model. The depiction of the projection of the feasible region reduces the dimension of the operation model of the virtual power plant and gives the detailed data of the exchanged power at the point of common coupling, which is of great significance for the collaborative optimization of the two-level system of the virtual power plant - main grid.

[0104] 5) The step 5 of the present invention establishes a VPP - main grid collaborative optimization model based on the equivalent projection of the feasible region, realizing non - iterative solution of the VPP - main grid collaborative optimization, greatly reducing the model solution time, being conducive to making full use of various distributed energy sources, improving the management effect of distributed energy source dispatching, and protecting the VPP data privacy. Brief Description of the Drawings

[0105] The present invention will be further described below in conjunction with the drawings and embodiments:

[0106] Figure 1 It is the system structure diagram of the embodiment;

[0107] Figure 2 It is the curve graph of the predicted values of wind and light active power output.

[0108] Figure 3 It is the sliced graph of the multi - period feasible region projection of the first VPP.

[0109] Figure 4 It is the dispatching result graph of the first VPP.

[0110] Figure 5 It is the graph of the exchanged power injected by the first VPP into the main grid.

[0111] Figure 6 It is the dispatching result of the main grid. Specific Embodiments

[0112] A collaborative optimization method for a power system with multiple virtual power plants based on the theory of equivalent projection of the feasible region includes the following steps:

[0113] Step S1: Considering the power network constraints and transmission capacity constraints of the main grid, establish the main grid operation model; considering the uncertainty of wind power and photovoltaic power output, establish the virtual power plant operation model.

[0114] The main grid operation model and the virtual power plant operation model include:

[0115] The main network operation model includes generator output constraints, generator ramp rate constraints, interchange power injection constraints, nodal power balance constraints, main network branch power flow constraints, and line transmission capacity constraints.

[0116] 1) Generator output constraints:

[0117]

[0118] In the formula, represents the active power output of the generator at node b in the main network at time period t; are respectively the upper and lower limits of the active power output of the main network generator at node b.

[0119] 2) Generator ramp rate constraints:

[0120]

[0121] In the formula, is the generator ramp rate capacity at node b in the main network at time period t.

[0122] 3) Interchange power injection constraints:

[0123]

[0124] In the formula, represents the upper limit of the power injected by the i-th VPP into the main network; represents the active power injected by the i-th virtual power plant into the point of common coupling at time period t.

[0125] 4) Nodal power balance constraints:

[0126]

[0127] In the formula, is the active power of the generator at node b in the main network at time period t; is the active power of the line between node b and q in the main network at time period t; is the active power injected by the i-th virtual power plant into the point of common coupling at time period t; is the active load of node b in the main network at time period t; χ b represents the set of nodes connected to node b in the main network; e VPP is the incidence matrix of the virtual power plant access node and the main network node; N VPP represents the total number of virtual power plants.

[0128] 5) Main network branch power flow constraints:

[0129]

[0130] In the formula, The active and reactive powers of the line between nodes b and q during the t period of the main grid; b bq , g bq The susceptance and conductance values of the line between nodes b and q during the t period of the main grid respectively; and The voltage amplitudes of nodes b and q during the t period of the main grid respectively; and The voltage phase angles of nodes b and q during the t period of the main grid respectively; Z is the number of segments for piecewise linearization; z is the index number of the segment; The upper and lower limit values of the main grid voltage amplitude respectively; The upper and lower limit values of the main grid voltage phase angle respectively.

[0131] 6) Line transmission capacity constraint:

[0132]

[0133] In the formula, is the power transmission distribution factor from the main grid node b to the branch l; is the power transmission distribution factor from the i-th virtual power plant to the main grid branch l; is the capacity of the main grid branch l.

[0134] The VPP operation model includes power network constraints, gas turbine output constraints, photovoltaic output constraints, wind power output constraints, node power balance constraints, and exchange power constraints.

[0135] 1) Power network constraints:

[0136] The power network constraints include linearized virtual power plant power flow constraints and power system operation constraints. Equations (7)-(8) are the linearized virtual power plant power flow constraints, Equation (9) is the linearized form of the virtual power plant branch power flow constraints, and Equations (10)-(11) are the power system operation constraints.

[0137]

[0138] In the formula, i is the virtual power plant number index; The active and reactive powers of the line between nodes m and n during the t period of the i-th virtual power plant respectively; b i,mn , g i,mn The susceptance and conductance values of the line between nodes m and n of the i-th virtual power plant respectively; and The voltage amplitudes of nodes m and n during the t period of the i-th virtual power plant respectively; and The voltage phase angles of nodes m and n during the t period of the i-th virtual power plant respectively; G is the number of segments for piecewise linearization; g is the index number of the segment; Vmax , V min are the upper and lower limit values of the voltage amplitude respectively; θ max , θ min are the upper and lower limit values of the voltage phase angle respectively.

[0139] 2) Gas turbine output constraint:

[0140]

[0141] In the formula, P max , P min are the upper and lower limits of the active power output of the gas turbine respectively; Q max , Q min are the upper and lower limits of the reactive power output of the gas turbine respectively; is the active power output of the gas turbine at node m of the i-th virtual power plant at time t; is the reactive power output of the gas turbine at node m of the i-th virtual power plant at time t.

[0142] 3) Photovoltaic power generation constraint

[0143] The uncertainty of photovoltaic power generation is modeled using chance constraint, as shown in Equation (14),

[0144]

[0145] In the formula, represents the probability of event ; is the active power output of the photovoltaic at node m of the i-th virtual power plant at time t; is the predicted value of the active power output of the photovoltaic at node m of the i-th virtual power plant at time t; η PV is the confidence level.

[0146] 4) Wind power generation constraint

[0147] The wind power generation constraint is the same as the photovoltaic power generation constraint. The wind power generation constraint is as follows:

[0148]

[0149] In the formula, represents the probability of event ; is the active power output of the wind power at node m of the i-th virtual power plant at time t; is the predicted value of the active power output of the wind power at node m of the i-th virtual power plant at time t; η W is the confidence level.

[0150] 5) Node power balance constraint

[0151]

[0152] In the formula, is the active power load at node m of the i-th virtual power plant at time t; is the reactive power load at node m of the i-th virtual power plant at time t; χ m is the set of nodes connected to node m.

[0153] 6) Exchange power constraint

[0154]

[0155] In the formula, is the active power injected into the common connection point by the i-th virtual power plant at time t; is the active power of the branch connected to the common connection point in the i-th virtual power plant; χ pcc is the set of nodes connected to the common connection point.

[0156] Step S2: Convert the wind power and photovoltaic chance constraints into deterministic constraints through quantile transformation.

[0157] The chance constraints converted through quantile transformation include:

[0158] Taking photovoltaic power generation as an example, the process of converting the chance constraint into a deterministic constraint through quantile transformation is as follows:

[0159]

[0160] In the formula, represents the probability of event ; represents the average value of the photovoltaic predicted output at node m of the i-th virtual power plant at time t; Φ(·) represents the distribution cumulative function; represents the inverse distribution cumulative function of the standard normal distribution N(0,1); is the standard deviation of the photovoltaic predicted output at node m of the i-th virtual power plant at time t; η PV represents the confidence level of photovoltaic power generation.

[0161] After the above transformation, the photovoltaic power generation chance constraint formula (14) is transformed into the deterministic constraint formula (22). The steps of transforming the wind power generation chance constraint into a deterministic constraint are the same as those of photovoltaic power generation, as shown in formula (13), so they will not be elaborated here.

[0162]

[0163] In the formula, represents the average value of the wind power predicted output at node m of the i-th virtual power plant at time t; represents the inverse distribution cumulative function of the standard normal distribution N(0,1); is the standard deviation of the predicted output of wind power at node m of the i-th virtual power plant at time t; η W represents the confidence level of wind power.

[0164] Step S3: Establish the objective function for the coordinated optimization of the virtual power plant-main grid, and establish an integrated dispatching model for the power system with multiple virtual power plants based on Steps S1 and S2.

[0165] The coordinated optimization objective function and the integrated dispatching model include:

[0166] The present invention takes the minimum of the sum of the main grid operation cost and the operation costs of each virtual power plant as the optimization objective, ignores the investment costs of each energy device, only considers the power generation cost of conventional units for the main grid, and only considers the gas turbine power generation cost, the operation and maintenance costs of new energy devices for each VPP. As shown in the following formula:

[0167]

[0168] In the formula, are the cost functions of the gas turbine, photovoltaic, and wind power of the i-th virtual power plant at time t, respectively; are the active power outputs of the gas turbine, photovoltaic, and wind power at node m of the i-th virtual power plant at time t, respectively; C b,t (·) is the generator cost function at node b of the main grid at time t; is the active power output of the generator at node b of the main grid at time t; i is the virtual power plant index; N VPP is the total number of virtual power plants; m is the internal node index of the virtual power plant; is the number of internal nodes of each virtual power plant; b is the main grid node index; N main is the total number of main grid nodes; t is the time period index; T is the total number of time periods.

[0169] Based on the above steps, an integrated dispatching model for the power system with multiple virtual power plants is established as follows:

[0170] Objective function:

[0171] The objective function is Equation (24);

[0172] Constraint conditions:

[0173] Main grid operation constraints: Equations (1)-(6);

[0174] VPP operation constraints: Equations (7)-(14), Equations (16)-(18), Equation (22), Equation (23).

[0175] Step S4: Use the epigraph theory to eliminate the internal variables of the virtual power plant in the objective function, and characterize the projection of the multi-period power-cost feasible region of the virtual power plant at the common coupling point based on the equivalent projection theory of the feasible region and the vertex projection convex hull search method.

[0176] Eliminating the internal variables of the virtual power plant from the objective function and characterizing the projection of the VPP feasible region include:

[0177] First, the objective function is transformed based on the epigraph theory. The epigraph describes the region above the range of a function within a given domain. For a general function f(x), its epigraph is the set composed of the graph of the function and all points above it. Formally, the epigraph of f(x) is defined as:

[0178] epi(f(x)) = {(x,t) ∈ R n ×R | f(x) ≤ epi(f(x)) ≤ N} (25);

[0179] where (x,t) represents the input of the function f(x); R n represents the dimension of x; R represents the dimension of o; N is a real number whose value can be any number greater than f(x), and the epigraph essentially represents the region between the function f(x) and N.

[0180] Based on Equation (25), the operating cost part of the virtual power plant in Equation (24) is transformed, and the transformed objective function is as follows:

[0181]

[0182] where is the introduced auxiliary variable, representing the cost function corresponding to the i-th virtual power plant at time t;

[0183] respectively represent the operating costs of the gas turbine, photovoltaic, and wind power generation at node m of the i-th virtual power plant at time t; respectively represent the quadratic term coefficient, linear term coefficient, and constant term coefficient of the main grid cost function.

[0184] For its epigraph in specific form is:

[0185]

[0186] where represents the gas turbine operating cost coefficient at node m of the i-th virtual power plant at time t; represents the photovoltaic power generation operating cost coefficient at node m of the i-th virtual power plant at time t; represents the wind power generation operating cost coefficient at node m of the i-th virtual power plant at time t; is an arbitrary constant greater than .

[0187] So far, the internal variables of each virtual power plant in the original objective function have been eliminated, and the objective function is replaced by Equation (26). Equations (29) and (30) are used as the operation constraints of the virtual power plant to participate in the system operation.

[0188] The operation feasible region of the virtual power plant is an irregular polyhedron. The first step in projection is to determine the projection plane. In the present invention, the variables that make up the projection plane are called projection variables. For the i-th virtual power plant, the projection variables are taken as: The dimensionality reduction model will be the equivalent projection of the operation feasible region of the virtual power plant onto the plane and its internal variables are

[0189] Based on the vertex projection convex hull search method for solving the feasible region, the present invention simultaneously depicts the equivalent projection of the multi-virtual power plant multi-period feasible region. According to geometric principles, each vertex of the projection polygon is an extreme point. Solving the optimization problem can obtain the feasible region of the projection variables :

[0190]

[0191] s.t. Equations (7)-(13), (16)-(18), (23), (24), (29), (30)

[0192] where μ T is the vertex search direction.

[0193] Among them, the distance between the two points connected by the line corresponding to the new vertex is:

[0194]

[0195] where is the abscissa of the new vertex obtained in the λ-th new vertex search for the i-th virtual power plant at time t; is the ordinate of the new vertex obtained in the λ-th new vertex search for the i-th virtual power plant at time t; respectively represent the coefficients of the straight line equation of the line connecting two adjacent points in the convex hull corresponding to the search direction in the λ-th new vertex search for the i-th virtual power plant at time t.

[0196] Step S5: On the basis of Steps S1, S2, S3, and S4, establish a VPP-main grid collaborative optimization model based on the equivalent projection of the feasible region, and call the GUROBI solver to solve it in the Matlab2021a environment.

[0197] The VPP-main grid collaborative optimization model based on the equivalent projection of the feasible region includes:

[0198] Based on the characterization of the equivalent projection of the virtual power plant's feasible region in step S4, the internal variables are eliminated from the operation models of each virtual power plant, achieving the equivalent dimensionality reduction of the VPP model. The mathematical model of the equivalent projection of the VPP operation feasible region is expressed as follows:

[0199]

[0200] In the formula, are respectively the lower limit value and the upper limit value of the switching power at the common connection point of the i-th virtual power plant at time t in the equivalent projection region; are respectively the lower limit value and the upper limit value of the cost of the i-th virtual power plant at time t in the equivalent projection region; are respectively the coefficients of each straight-line equation of the projection polygon boundary of the i-th virtual power plant at time t.

[0201] The multi-VPP-main grid collaborative optimization model based on the equivalent projection of the feasible region is as shown in Equation (34):

[0202]

[0203] In Matlab, the Gurobi solver is called to first solve Problem (34) to obtain the optimal value The main grid distributes it to the VPP; secondly, each VPP takes as the boundary condition to perform optimal dispatching by solving Problem (35).

[0204] Example:

[0205] In this case, a multi-virtual power plant power system with 3 VPPs is built. All models and algorithms are programmed and implemented on MATLAB2021a, and Gurobi 10.0.2 is called for solution. The test environment has a CPU of the ninth-generation Intel Core i5 2.40GHz and 16GB of memory. The first virtual power plant and the second virtual power plant adopt the improved IEEE 9-node test system, the third virtual power plant adopts the improved IEEE 33-node test system, and the main grid adopts the IEEE 30-node test system. The system structure is as Figure 1 shown.

[0206] ​​The main grid has 6 conventional generators, each with a maximum active power output of 30 MW; the first virtual power plant has 2 gas turbines, each with a maximum active power output of 8 MW, 2 photovoltaic power stations with a capacity of 7 MW, and 2 wind power stations with a capacity of 3 MW; the second virtual power plant is configured basically the same as the first virtual power plant; the third virtual power plant has 7 gas turbines, each with a maximum output of 9 MW, 7 photovoltaic power stations with a capacity of 4 MW, and 7 wind power stations with a capacity of 3.5 MW. The dispatching time scale is 1 hour, the time span is 24 hours, and the prediction error of wind and light is taken as 10% of the corresponding predicted active power output value.

[0207] According to step S1, establish the main grid operation model and the VPP operation model. The relevant main grid part data is shown in Tables 1 - 2 below:

[0208] Table 1 Main grid generator parameters

[0209] Node where the generator is located Upper limit of active power output / MW Lower limit of active power output / MW 1 30 0 2 30 0 22 30 0 27 30 0 23 30 0 13 30 0

[0210] Table 2 Main grid generator cost coefficient (unit: US dollars)

[0211] Node where the generator is located Quadratic term coefficient Linear term coefficient Constant term coefficient 1 0.5 50 0 2 0.4375 43.75 0 22 1.5625 25 0 27 0.2085 81.25 0 23 0.625 75 0 13 0.625 75 0

[0212] The data of the first and second VPPs are basically the same. The relevant data of the first VPP is shown in Tables 3 - 4 below:

[0213] Table 3 First VPP gas turbine parameters

[0214] Gas turbine node Upper limit of active power output / MW Lower limit of active power output / MW 1 8 0 2 8 0 8 8 0 9 9 0

[0215] Table 4 First VPP gas turbine cost coefficient (unit: US dollars)

[0216] Gas turbine node Linear term coefficient Constant term coefficient 1 60 30 2 52.5 125 8 57.5 30 9 55 125

[0217] The relevant data of the third VPP is shown in Tables 5 - 6 below:

[0218] Table 5 Third VPP gas turbine parameters

[0219] Gas turbine node Upper limit of active power output / MW Lower limit of active power output / MW 1 9 0 14 9 0 18 9 0 22 10 0 25 9 0 30 10 0 32 9 0

[0220] Table 6 Third VPP gas turbine cost coefficient (unit: US dollars)

[0221] Gas turbine node Linear term coefficient Constant term coefficient 1 52.5 125 14 55 30 18 55.625 25 22 52.5 125 25 55 30 30 52.5 30 32 55 32.5

[0222] The branch and node parameters of the main grid operation model and the VPP operation model can be obtained in matpower7.0.

[0223] According to step S2, convert the wind power and photovoltaic chance constraints into deterministic constraints through quantile transformation. The average predicted wind power and photovoltaic output of each virtual power plant is asFigure 2 as shown

[0224] Based on steps S1 and S2, an integrated scheduling model of a power system with multiple virtual power plants is established.

[0225] According to step S4, the objective function is transformed, and the multi-period feasible region projection of the virtual power plant at the point of common coupling is characterized. The relevant processes and parameters are as follows.

[0226]

[0227] According to step S5, based on steps S1, S2, S3, and S4, a VPP-main grid collaborative optimization model based on equivalent projection of the feasible region is established, and the GUROBI solver is called to solve it in the Matlab2021a environment.

[0228] Collaborative optimization results:

[0229] (1) Results of characterizing the equivalent projection of the feasible region:

[0230] Figure 3 is the equivalent projection slice diagram of the multi-period feasible region of VPP No. 1. The selected time periods are 1:00, 5:00, 9:00, 13:00, 17:00, and 21:00, including the valley load and peak load periods within a natural day. The pink area is the equivalent projection of the multi-period feasible region of VPP No. 1. It can be seen from the figure that the equivalent projections of the feasible regions in each period are very different. From the perspective of the area of the feasible region projection, as the load increases, the area of the feasible region projection gradually decreases. This is because the selected feasible region projection in the present invention is a plane related to the exchange power and the operation cost of the VPP. The horizontal axis is the exchange power, and the vertical axis is the operation cost of the VPP. Therefore, when the load rises, the operation cost of the VPP increases accordingly, the bottom edge of the feasible region projection rises, and the projection area decreases.

[0231] The blue solid line at the bottom of the coordinate axis in the figure is the range of the exchange power injected by the VPP into the main grid in each period. When the power load level is low, the maximum active power injected by the VPP into the main grid is at a relatively high level, but the maximum active power injected by the main grid into the VPP is at a relatively low level. When the power load level is high, it is the opposite.

[0232] (2) VPP scheduling results:

[0233] For the convenience of display, taking VPP No. 1 as an example, Figure 4 and Figure 5 are the scheduling results of VPP No. 1 and its exchange power situation respectively. From Figure 4It can be seen that from 1:00 to 5:00, the load gradually decreases to the trough value, and the active power output of the gas turbine decreases accordingly. During the period from 7:00 to 13:00, the load begins to increase, and the output of the photovoltaic unit gradually rises with the increase of the light intensity. During the period from 19:00 to 20:00, the output of the photovoltaic unit is zero, and the load gradually rises from a relatively low level to the second peak. Therefore, the output of the gas turbine begins to increase significantly, from Figure 5 It can be seen that the change trend of the exchanged power between the first VPP and the main grid is opposite to that of the VPP power load.

[0234] (3) Main grid dispatching results:

[0235] The main grid dispatching results are as Figure 6 shown. It can be observed from Figure 6 that as the main grid electrical load increases or decreases, the active power of the main grid generator shows the same trend. However, the change in the power injected by the VPP into the main grid is different. This is because the change trend of the electrical load in a typical day is the same. When the main grid is at valley load or peak load, each VPP is also at valley load or peak load at the same time.

[0236] (4) Comparison with traditional methods:

[0237] The comparison of the calculation time of different solution methods for the integrated dispatching model of the power system with multiple virtual power plants proposed in the present invention is shown in Table 7. It can be seen that the method adopted in the present invention has a significant improvement in the solution time compared with traditional coordinated optimization solution methods such as Benders decomposition and multi-parameter programming methods, reducing the calculation time by about 51%-61%.

[0238] Table 7 Comparison of calculation time (seconds) of different solution methods

[0239]

[0240] The comparison of the costs of each VPP and the total system cost under different solution methods is shown in Table 8. It can be seen that the costs of each VPP and the total system cost are almost the same when different solution methods are adopted, proving that the method adopted in the present invention still has the same optimality as the traditional solution method while reducing the dimension of the original operation model, and greatly reducing the solution time while protecting the data privacy of each VPP.

[0241] Table 8 Comparison of costs (US dollars) of different solution methods

[0242]

Claims

1. A collaborative optimization method for a power system with multiple virtual power plants based on the feasible domain equivalent projection theory is characterized by The following steps are involved: Step 1: Considering the main grid power network constraints and transmission capacity constraints, establish the main grid operation model; considering the uncertainty of wind power and photovoltaic output, establish the virtual power plant operation model; Step 2: Convert wind power and photovoltaic opportunity constraints into deterministic constraints through quantiles; Step 3: Establish the objective function of virtual power plant-main grid collaborative optimization, and establish an integrated dispatching model of the power system containing multiple virtual power plants based on steps 1 and 2; Step 4: Eliminate the internal variables of the virtual power plant in the objective function using the mirror image, and describe the multi-period power-cost feasible domain projection of the virtual power plant at the common coupling point based on the feasible domain equivalent projection theory and vertex projection convex hull search method; Step 5: Establish a VPP-main network collaborative optimization model based on the equivalent projection of the feasible domain and solve the model.

2. The collaborative optimization method for a power system containing multiple virtual power plants based on the feasible domain equivalent projection theory according to claim 1 is characterized by: In step 1, the main network operation model includes generator output constraints, generator ramp constraints, exchange power injection constraints, node power balance constraints, main network branch power flow constraints and line transmission capacity constraints; 1) Generator output constraints: In formula (1), It represents the active output of the generator at node b in the main grid during period t; They are respectively the upper and lower limits of the active output of the main grid generator at node b; 2) Generator climbing constraints: In formula (2), is the ramp capacity of the generator at node b in the main grid during period t; Indicates the active output of the generator at node b in the main grid during period t+1; 3) Switching power injection constraints: In formula (3), represents the upper limit of the power injected into the main network by the i-th VPP; represents the active power injected into the main grid common connection point by the i-th virtual power plant during period t; 4) Node power balance constraints: In formula (4), is the active power of the generator at node b in the main grid during period t; is the active power of the line between nodes b and q in the main network during period t; The active power injected into the common connection point for the i-th virtual power plant during period t; is the active load of node b in the main network during period t; b Represents the set of nodes connected to node b in the main network; e VPP is the association matrix between the virtual power plant access nodes and the main network nodes; N VPP represents the total number of virtual power plants; i represents the virtual power plant number index; 5) Main network branch flow constraints: In formula (5), are respectively the active and reactive power of the line between nodes b and q in the main grid during period t; b bq ,g bq are the susceptance and conductance values ​​of the line between nodes b and q in the main network during period t, respectively; and are the voltage amplitudes of nodes b and q in the main grid during period t, respectively; and are the voltage phase angles of nodes b and q in the main grid during period t, respectively; Z is the number of segments of the piecewise linearization; z is the index number of the segment; They are the upper and lower limits of the main grid voltage amplitude respectively; They are the upper and lower limits of the main grid voltage phase angle respectively; represents the capacity of the line between nodes b and q in the main network during period t; 6) Line transmission capacity constraints: In formula (6), is the power transmission allocation factor from the main network node b to the branch l; is the power transfer allocation factor from the ith virtual power plant to the main grid branch l; is the capacity of the main network branch l; N Main represents the number of main network nodes; t represents the scheduling time index; T represents the total scheduling time.

3. The collaborative optimization method for a power system containing multiple virtual power plants based on the feasible domain equivalent projection theory according to claim 2 is characterized by: The virtual power plant operation model includes power network constraints, gas turbine output constraints, photovoltaic output constraints, wind power output constraints, node power balance constraints and exchange power constraints; 1). Power network constraints: The power network constraints include linearized virtual power plant flow constraints and power system operation constraints; equations (7) to (8) are linearized virtual power plant flow constraints; equation (9) is the linearized form of virtual power plant branch flow constraints, and equations (10) to (11) are power system operation constraints; In the above formula, i is the virtual power plant number index; are the active and reactive power of the line between nodes m and n in the ith virtual power plant during period t; b i,mn ,g i,mn are the susceptance and conductance values ​​of the line between nodes m and n of the i-th virtual power plant, respectively; and are the voltage amplitudes of nodes m and n at time period t of the i-th virtual power plant; and are the voltage phase angles of nodes m and n in the ith virtual power plant during period t; G is the number of segments of the piecewise linearization; g is the index number of the segment; V max ,V min are the upper and lower limits of the voltage amplitude respectively; θ max ,θ min are the upper and lower limits of the voltage phase angle respectively; represents the capacity of the line between nodes m and n of the ith virtual power plant; 2) Gas turbine output constraints: In the above formula, P max ,P min They are the upper and lower limits of the active output of the gas turbine; Q max ,Q min They are the upper and lower limits of reactive power output of gas turbine respectively; is the active output of the gas turbine at node m in the i-th virtual power plant during period t; is the reactive power output of the gas turbine at node m in the i-th virtual power plant during period t; 3) Constraints on photovoltaic power generation: Photovoltaic power generation uses chance constraints to model its uncertainty, as shown in formula (14): In formula (14), Indicates an event probability; is the photovoltaic active output at node m of the i-th virtual power plant during period t; is the predicted value of the photovoltaic active output at node m in the i-th virtual power plant during period t; η PV is the confidence level; 4) Wind power generation constraints: Wind power generation constraints are the same as photovoltaic power generation constraints. Wind power generation constraints are as follows: In formula (15), Indicates an event probability; is the wind power active output at node m of the i-th virtual power plant during period t; is the predicted wind power output value at node m in the i-th virtual power plant during period t; η W is the confidence level; 5) Node power balance constraints: In the formula, is the active load at node m of the i-th virtual power plant during period t; is the reactive load at node m in the ith virtual power plant during period t; m is the set of nodes connected to node m; n represents the index of the terminal node of a branch in each virtual power plant; 6) Switching power constraints: In formula (18), The active power injected into the common connection point for the i-th virtual power plant during period t; is the active power of the branch connected to the public connection point in the i-th virtual power plant; pcc is a set of nodes connected to the common connection point; m represents the index of the starting node of a branch in each virtual power plant.

4. The collaborative optimization method for a power system containing multiple virtual power plants based on the feasible domain equivalent projection theory according to claim 3 is characterized by: In step 2, for photovoltaic power generation, the process of converting the opportunity constraint into a deterministic constraint through quantiles is as follows: In the above formula, Indicates an event probability; represents the average value of the predicted photovoltaic output at node m in the ith virtual power plant during period t; Φ(·) represents the distribution cumulative function; Represents the inverse distribution cumulative function of the standard normal distribution N(0,1); is the standard deviation of the photovoltaic output prediction at node m in the i-th virtual power plant during period t; η PV represents the confidence level of photovoltaic; After the above transformation, the photovoltaic generator constraint (14) is transformed into the deterministic constraint (22).

5. The collaborative optimization method for a power system containing multiple virtual power plants based on the feasible region equivalent projection theory according to claim 4 is characterized by: The wind turbine generator constraint is transformed into a deterministic constraint, as shown in formula (23); In formula (23), represents the average value of the predicted wind power output at node m in the i-th virtual power plant during period t; is the standard deviation of wind power forecast output at node m in the ith virtual power plant during period t; η W Indicates the confidence level of wind power.

6. The collaborative optimization method for a power system containing multiple virtual power plants based on the feasible region equivalent projection theory according to claim 5 is characterized by: In step 3, the optimization goal is to minimize the sum of the main grid operation cost and the operation cost of each virtual power plant, ignoring the investment cost of each energy equipment. The main grid only considers the power generation cost of conventional units, and each VPP only considers the power generation cost of gas turbines and the operation and maintenance cost of new energy equipment; as shown in formula (24): In formula (24), min Cost represents the total operating cost of the minimized system; are the cost functions of gas turbine, photovoltaic and wind power in the i-th virtual power plant during period t, respectively; are the active outputs of the gas turbine, photovoltaic, and wind power at node m in the i-th virtual power plant during period t; C b,t (·) is the cost function of the generator at node b in the main network during period t; is the active output of the generator at node b in the main grid during period t; i is the virtual power plant index; N VPP is the total number of virtual power plants; m is the internal node index of the virtual power plant; is the number of nodes inside each virtual power plant; b is the main network node index; N main is the total number of main network nodes; t is the time period index; T is the total number of time periods.

7. The collaborative optimization method for a power system containing multiple virtual power plants based on the feasible region equivalent projection theory according to claim 6 is characterized by: The established integrated dispatch model of the power system with multiple virtual power plants is as follows: Objective function: The objective function is formula (24); Constraints: Main network operation constraints: Equation (1) to (26); VPP operation constraints: Equation (7) to (13), Equation (16) to (18), Equation (22), Equation (23).

8. The collaborative optimization method for a power system containing multiple virtual power plants based on the feasible region equivalent projection theory according to claim 7 is characterized by: In step 4, first, the objective function is transformed based on the photogram. The photogram describes the area above the range of a function in a given domain. For a general function f(x), its photogram refers to a set consisting of the image of the function and all points above it. Formally, the photogram of f(x) is defined as: epi(f(x))={(x,o)∈R n ×R|f(x)≤epi(f(x))≤N} (25); In formula (25), epi(f(x)) represents the mirror image of function f(x); (x,o) represents the input of function f(x); R n represents the dimension of x; R represents the dimension of o; N is a real number, whose value is any number greater than f(x). The mirror image essentially represents the area between the function f(x) and N. Based on formula (25), the operating cost part of the virtual power plant in formula (24) is converted, and the objective function after conversion is as follows: In the above formula, is the auxiliary variable introduced, which represents the cost function corresponding to the i-th virtual power plant in period t; They represent the gas turbine, photovoltaic and wind power generation operating costs of the i-th virtual power plant m node in time period t respectively; Respectively represent the quadratic term coefficient, linear term coefficient and constant term coefficient of the main network cost function; The specific form of the photogenic image is: In the above formula, represents the gas turbine operation cost coefficient at node m in the i-th virtual power plant during period t; represents the photovoltaic power generation operation cost coefficient at node m of the i-th virtual power plant during period t; represents the wind power operation cost coefficient at node m of the i-th virtual power plant during period t; For any value greater than The constant of At this point, the internal variables of each virtual power plant in the original objective function are eliminated, and the objective function is replaced by equation (26). Equations (29) and (30) participate in the system operation as virtual power plant operation constraints.

9. The collaborative optimization method for a power system containing multiple virtual power plants based on the feasible region equivalent projection theory according to claim 8 is characterized by: The feasible domain of the virtual power plant is an irregular polyhedron. The first step in projection is to determine the projection plane. The variables that make up the projection plane are called projection variables. For the i-th virtual power plant, take the projection variable for: The dimension reduction model converts the feasible domain of virtual power plant operation into a plane The equivalent projection of The feasible domain solution method based on vertex projection convex hull search simultaneously depicts the equivalent projection of the feasible domain of multiple virtual power plants in multiple time periods. According to the geometric principle, each vertex of the projection polygon is an extreme point, and solving the optimization problem can obtain the projection variable The feasible domain of In formula (31), μ T is the vertex search direction; Vertex represents the objective function of the vertex search; New Vertex The distance between the two points corresponding to the new search direction for: In formula (32), is the horizontal coordinate of the new vertex obtained in the λth new vertex search of the i-th virtual power plant in period t; is the ordinate of the new vertex obtained in the λth new vertex search during the tth period of the i-th virtual power plant; They respectively represent the coefficients of the straight line equation connecting two adjacent points in the convex hull corresponding to the search direction in the λth new vertex search of the i-th virtual power plant in time period t.

10. The method for collaborative optimization of a power system containing multiple virtual power plants based on the feasible region equivalent projection theory according to claim 9 is characterized in that: In step 5, the mathematical model of the equivalent projection of the VPP running feasible domain is expressed as follows: In formula (33), The exchange power of the public connection point for the i-th virtual power plant in period t is The lower and upper limits of the equivalent projection area; are the cost of the i-th virtual power plant in period t The lower and upper limits of the equivalent projection area; are the coefficients of the straight line equations of the projection polygon boundary of the i-th virtual power plant in period t; The multi-VPP-main network collaborative optimization model based on feasible domain equivalent projection is as follows: In Matlab, we call the Gurobi solver to solve equation (34) and get Optimal value represents the optimal value of active power injected into the common connection point by the i-th virtual power plant during period t; represents the optimal operating cost of the i-th virtual power plant in period t; The main network sends it to the virtual power plant VPP; secondly, each virtual power plant VPP As the boundary condition, the optimal scheduling is performed by solving equation (35).

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