Probability feasible region characterization method for distributed resource uncertainty

Abstract

The invention discloses a probability feasible region characterization method for distributed resource uncertainty, and relates to the field of distributed resource management of a power system. In order to solve the defects that the existing distributed resource probability feasible region description is inaccurate, the uncertainty and the time-varying characteristic are strong, and an accurate adjustable capacity cannot be provided for a superior power grid operator, the method comprises the following steps: constructing a probability feasible region model of multi-type distributed resources; modeling, analyzing and solving the uncertainty of the distributed resources; and solving the probability feasible region of the distributed resources to obtain a boundary range of the probability feasible region of the distributed resources. The method is mainly used for characterizing the probability feasible region of the uncertainty of the distributed resources, the boundary range of the probability feasible region of the distributed resources is obtained, and the problem that the 0-1 variable of the distributed resources is difficult to characterize in the modeling process is solved.

Description

Technical Field

[0001] The present invention relates to the field of distributed resource management in power systems, and particularly to a method for characterizing the probabilistic feasible region of distributed resource uncertainty. Background Art

[0002] With the continuous increase in the number of distributed resources, the coupling between the power grid and a large number of distributed energy sources has gradually deepened. The disordered grid connection of various resources poses a major challenge to the safe and stable operation of the power system. Therefore, a collaborative mode in which electric vehicle aggregators aggregate a large number of distributed resources and jointly operate with the superior power grid operator has gradually emerged.

[0003] However, due to the inherent uncertainty and time-varying characteristics of distributed resources such as electric vehicles, it is difficult for the superior power grid operator to trust the adjustable capacity of various types of distributed resources provided by the electric vehicle aggregator. Considering the large number and variable parameters of distributed resources, it is unrealistic to directly provide large-scale data to the superior power grid operator.

[0004] Therefore, there is a need for a method for characterizing the probabilistic feasible region of distributed resource uncertainty that can ensure the flexible and accurate adjustable capacity provided by distributed resources at different confidence levels, reduce the amount of interaction data between electric vehicle aggregators and superior power grid operators, and accurately depict the boundary of the probabilistic feasible region of distributed resources. Summary of the Invention

[0005] In order to solve the defects of inaccurate characterization of the probabilistic feasible region of existing distributed resources, strong uncertainty and time-varying characteristics, and inability to provide accurate adjustable capacity at different confidence levels to the superior power grid operator, the present invention provides a method for characterizing the probabilistic feasible region of distributed resource uncertainty that can ensure the flexible and accurate adjustable capacity provided by distributed resources at different confidence levels, reduce the amount of interaction data between electric vehicle aggregators and superior power grid operators, and accurately depict the boundary of the probabilistic feasible region of distributed resources.

[0006] A method for characterizing the probabilistic feasible region of distributed resource uncertainty according to the present invention includes the following steps: S1. Construct a probabilistic feasible region model for different types of distributed resources; S2. Model, analyze, and solve the uncertainty of the distributed resources; S3. Solve the probabilistic feasible region of the distributed resources to obtain the boundary range of the probabilistic feasible region of the distributed resources.

[0007] Further: In S1, the specific steps for constructing the probabilistic feasible region model for different types of distributed resources are as follows: S11. Define a probabilistic feasible region model between the electric vehicle aggregator and the superior power grid; S12. Preset the operation constraints of the distribution network with electric vehicle aggregators; S13. Build the charging and discharging model of electric vehicles.

[0008] Furthermore: In S11, the probability feasible region model is: The formula of the probability feasible region model is: ; In the formula, represents the high-dimensional probability feasible region generated by the entire model, is the set of operation states of the distribution network with a large number of distributed resources, is the interactive active power, represents the interactive reactive power, represents the set of probability constraints and ordinary constraints in the operation of the distribution network. PV is photovoltaic, is the output power of the th photovoltaic PV at time t, is the output power of the micro gas turbine at time t, is the charging power of electric vehicle v at time t, is the discharging power of electric vehicle v at time t,

[0009] Furthermore: In S12, the operation constraints of the distribution network include power flow constraints of the grid, charging state constraints of electric vehicles, time-domain coupling constraints, output constraints of distributed resources, and power and energy balance constraints. The above constraints jointly form a convex hull, and the convex hull is used to represent the high-dimensional probability feasible region formed by the operation constraints of the distribution network.

[0010] Furthermore: In S13, the constraint conditions of the electric vehicle charging and discharging model include the upper limit of charging and discharging power, the representation of integer variables for charging and discharging, the time-coupled change model of SOC, the initial state of charge of the vehicle and the ideal state of charge value to be reached when starting, and the range limit of SOC.

[0011] Furthermore: In S2, the specific processes of the modeling, analysis, and solution are as follows: S21. Consider the uncertainties of distributed resources and dispatchable resources, and classify the uncertain variables; S22. Model the randomness of the errors of the uncertain variables; Assume that the probability of the prediction error follows a normal distribution using the central limit theorem, and establish a joint probability density function through a multivariate Gaussian model to characterize the uncertainty of the prediction value error; S23. Convert the constraint conditions into chance constraints at different confidence levels; S24. Through the original constraint transformed into an equivalent transformation based on the inverse function of the probability cumulative distribution function, the chance constraint containing uncertain variables is converted into a deterministic constraint under different confidence levels; S25. For the deterministic constraints under different confidence levels, for the terms involving the square root of variables among them, the piecewise linearization method is adopted to simplify the solving difficulty.

[0012] Furthermore: In S3, the specific process for solving the probabilistic feasible region of the distributed resources is as follows: S31. Characterize the probabilistic feasible region by solving the parameters under different confidence levels; S32. Use the confidence boundary deviation as the criterion for the points within the region, and transform the dual problem to solve the feasible cut corresponding to the farthest point; S33. Adopt the McCormick envelope relaxation method to transform the non-convex set composed of the complementary constraints of the charging and discharging states of electric vehicles into a convex form; S34. Through linearizing the relaxation problem, transform the non-convex constraints into a combination of multiple convex constraints, and use the block feasible region described by the convex polyhedron to characterize the original non-convex problem, thereby obtaining the boundary range of the probabilistic feasible region of the distributed resources.

[0013] The beneficial effects of the present invention are as follows: The method for characterizing the probabilistic feasible region of the uncertainty of distributed resources according to the present invention, based on the theory of probabilistic feasible region equivalence, can accurately depict the external characteristics of the distributed resources of the electric vehicle aggregator, characterize the regulation ability of the aggregator through the probabilistic feasible region under different confidence intervals, and realize the safe and efficient coordination between the electric vehicle aggregator and the superior power grid operator. By aggregating the random characteristics of a large number of distributed resources together to form an equivalent external characteristic to describe the probabilistic feasible region under different confidence intervals, it better ensures the safe coordination and interaction between the electric vehicle aggregator and the superior power grid operator. The method for equivalent characterization of the external characteristics outside the feasible region based on equivalent projection allows a large number of distributed resources to aggregate, thereby significantly reducing the amount of interaction data between the electric vehicle aggregator and the superior power grid operator.

[0014] The present invention proposes the concept of probabilistic feasible region to characterize the influence of uncertain resources with probability distribution characteristics and time coupling characteristics on the feasible region, providing a guarantee for the electric vehicle aggregator to participate in the scheduling of the superior power grid.

[0015] The method for characterizing the probabilistic feasible region according to the present invention formulates the probability density distributions of electric vehicles and renewable energy power generation as chance constraints. Using the inverse function analysis method, the chance constraints are transformed into a deterministic linearized mathematical model. The outer cutting approximation algorithm is adopted to achieve fast solution, thereby promoting the efficient description of the feasible regions under different probabilities.

[0016] On this basis, a non-convex constraint relaxation method based on probabilistic feasible region representation is proposed. Taking EV (electric vehicle) as an example, through theoretical reasoning and experiments, it is proved that under the background of probabilistic feasible region representation, complementary constraints can be relaxed by McCormick envelope (a convex relaxation method for bilinear non-linear programming problems) without affecting the convexity of the probabilistic feasible region. This solves the problem of representing the probabilistic feasible region of non-convex mathematical models involving multiple types of distributed resources such as electric vehicles, and at the same time solves the problem of difficult model solution caused by complementary constraints such as charge and discharge constraints. It also solves the problem of difficult representation of 0-1 variables of distributed resources in the modeling process. Description of the Drawings

[0017] Figure 1 is a schematic diagram of the improved 33-node distribution network; Figure 2 is a comparison chart of the number of constraints and variables before and after dimension reduction and equivalence under different scenarios; Figure 3 is a schematic diagram of the interactive power range depicting and representing the probabilistic feasible region of the distribution network under deterministic conditions within a unit time period, considering only the traditional power grid and not the uncertainties of electric vehicles, photovoltaics, and demand response; where P is the interactive active power between the electric vehicle aggregator in the distribution network and the superior power grid, and Q is the interactive reactive power between the electric vehicle aggregator in the distribution network and the superior power grid; Figure 4 is a schematic diagram of the interactive power range depicting and representing the probabilistic feasible region of the distribution network under different confidence levels within a unit time period considering the uncertainties of distributed generation resources; Figure 5 is a schematic diagram of the interactive power range depicting and representing the probabilistic feasible region of the distribution network under different confidence levels within a unit time period after establishing the coupling relationship between different time scales by considering the chance constraints of time-coupled demand response; Figure 6 is a schematic diagram of the interactive power range depicting and representing the probabilistic feasible region of the distribution network under deterministic conditions within a unit time period by simulating the scenario of the electric vehicle aggregator participating in day-ahead scheduling and considering the probability distributions of PV (photovoltaic), DR (demand response), and EV (electric vehicle) under chance constraints; Figure 7 is a schematic diagram of the combination of all cases after complementary relaxation; P1, P2, and P3 are the interactive active powers between the electric vehicle aggregator in the distribution network and the superior power grid in three time periods; Figure 8 is a schematic diagram of the feasible region of each time period by taking the output interactive power as the projection variable and plotting the feasible space of the optimal scheduling problem within three time periods; Figure 9It is a schematic diagram showing the overall feasible range under linear coupling constraints for multiple time periods. Specific Embodiment

[0018] The following are only preferred specific embodiments of the present invention, but the protection scope of the present invention is not limited thereto. Any changes or substitutions that can be easily thought of by those skilled in the art within the technical scope disclosed by the present invention should be covered within the protection scope of the present invention. The following embodiments are only used to explain the present invention and should not be construed as a limitation of the present invention. The protection scope of the present invention should be based on the protection scope of the claims. The embodiments of the present invention are described in detail below. For the convenience of describing the present invention and simplifying the description, the technical terms used in the specification of the present invention should be interpreted in a broad sense, including but not limited to conventional replacement schemes not mentioned in this application, and including both direct implementation methods and indirect implementation methods.

[0019] Embodiment 1 Combined with Figure 1 and Figure 2 to illustrate this embodiment. A method for characterizing the probabilistic feasible region of distributed resource uncertainty disclosed in this embodiment includes the following steps: S1. Construct a probabilistic feasible region model for different types of distributed resources; The probabilistic feasible region is a form of information exchange between electric vehicle aggregators and the superior power grid operator. The superior power grid operator uses electric vehicle aggregators to understand the dispatchable area of the distribution network. Its physical meaning is to ensure that for any actual scenario within the probabilistic feasible region, there exists a feasible control strategy, and the distribution network operates while satisfying all operation constraints with a certain confidence probability.

[0020] S11. Define the probabilistic feasible region model between the electric vehicle aggregator and the superior power grid; The formula of the probabilistic feasible region model is: (1) In the formula, represents the high-dimensional probabilistic feasible region generated by the entire model, is the set of operating states of the distribution network with a large number of distributed resources, is the interactive active power, represents the interactive reactive power, represents the set of probabilistic constraints and ordinary constraints in the operation of the distribution network. PV is photovoltaic, is the output power of the th photovoltaic PV at time t, is the micro gas turbine 's output power at time t, is the charging power of electric vehicle v at time t, is the discharge power of the electric vehicle v at time t, is the probability confidence parameter, and g is the affine function form of the constraint set.

[0021] Compared with the traditional feasible region representation, the probabilistic feasible region takes into account the prediction errors of distributed resources. At the same time, the probabilistic feasible region of the electric vehicle aggregator also takes into account the actual situation and state of electric vehicles, which is more complex and special than general energy storage. Therefore, considering the prediction errors of the dispatchable electric vehicle state provides a real and objective range for the upper-level power grid.

[0022] is the high-dimensional probabilistic feasible region generated by the entire model, which equivalently represents the constraints of the electric vehicle aggregator and the constraints of the power grid operation at different confidence levels; Probabilistic feasible region is defined as follows: (2) In the formula, and are the coefficient parameter matrices corresponding to the constraint conditions, y is the internal variable of the constraint at different confidence levels, represents the constant vector of the right-hand side of the constraint condition; is the projection variable at different confidence levels and usually represents variables such as the interactive power in the equivalent distribution network; S12, the operation constraints of the distribution network with an electric vehicle aggregator preset; The operation constraints of the distribution network with an electric vehicle aggregator mainly include power flow constraints of the power grid operation, electric vehicle charging state constraints, time-domain coupling constraints, distributed resource output constraints, and power and energy balance constraints. These sub-constraint sets together form a convex hull, and the convex hull is used to represent the high-dimensional probabilistic feasible region generated by the distribution network operation constraints.

[0023] The operation constraints of the distribution network of the electric vehicle aggregator mainly include the following constraints: Power flow constraints of the power grid operation; electric vehicle charging state constraints; time-domain coupling constraints; distributed resource output constraints; power and energy balance constraints, etc.; these sub-constraint sets are successively represented as , , …, ; can be calculated by the convex hull formed by the intersection of the sub-constraint sets; (3) The charge and discharge power constraint limit is expressed as Equation (2) - Equation (3); Convex hull represents the high-dimensional probabilistic feasible region generated by the entire model; S13. Build an electric vehicle charging and discharging model; The constraint conditions of the electric vehicle charging and discharging model include the upper limit of charging and discharging power, the integer variable representation of charging and discharging, the time-coupled change model of SOC (State of Charge of the electric vehicle battery), the initial state of charge of the vehicle, the ideal state of charge value to be achieved at departure, and the range limit of SOC.

[0024] An electric vehicle is equivalent to a restricted mobile energy storage system, and its state of charge (SOC) reflects the remaining capacity of the electric vehicle battery. To build an electric vehicle SOC model, the charging and discharging power of the electric vehicle must meet the following constraint conditions: (4) Equation (4) represents the time-coupled change model of SOC; (5) (6) Equations (5)-(6) are the initial state of charge of the vehicle and the ideal state of charge value that the electric vehicle needs to reach at departure; (7) Equation (7) represents the SOC range of the vehicle and the upper limit that should not be exceeded; (8) (9) Among them, is the charging power of the v-th electric vehicle at time t, is the charging power of the v-th electric vehicle at time t; is the upper limit of the charging and discharging power of the electric vehicle at time t, is the upper limit of the charging and discharging power of the electric vehicle at time t; represents an integer variable indicating whether the electric vehicle v is charging at time t, represents an integer variable indicating whether the electric vehicle v is discharging at time t, with a value of 0 or 1; is the time of the state of charge, is the maximum capacity of the on-vehicle battery; and represent the charging and discharging efficiency; is the capacity when the electric vehicle arrives at the charging station, is the time when the v-th electric vehicle arrives at the charging pile; is the minimum power that the electric vehicle must have when leaving; is the time when the v-th electric vehicle leaves; is the upper limit of SOC; The charge and discharge power constraint is expressed by Equations (2) - (3), and Equation (4) represents the time-coupled change model of SOC. Equations (5) - (6) are the initial state of charge of the vehicle and the ideal state of charge value to be achieved when the electric vehicle departs. Equation (7) represents the SOC range of the vehicle and the upper limit that should not be exceeded.

[0025] S2. Model, analyze, and solve the uncertainty of the distributed resources; S21. Consider the uncertainty of distributed resources and dispatchable resources, model the randomness of the uncertainty variables error, and convert the constraint conditions into chance constraints at different confidence levels; Since the output of a large number of distributed resources is random and the dispatchable resources also have time-varying characteristics, it is crucial to model and analyze the uncertainty of the corresponding variables. Considering the randomness of the uncertainty variables error, these constraints are converted into chance constraints at different confidence levels. For the optimal dispatch problem of the distribution network with electric vehicle aggregators, the distributed photovoltaic output, load, and adjustable electric vehicle resources are uncertain, but generally follow a certain daily distribution law. Therefore, the uncertainty error is modeled as: (10) Where is the actual value of the photovoltaic output of the th photovoltaic PV at time t, is the predicted value of the photovoltaic output of the th photovoltaic PV at time, is the photovoltaic output error of the th photovoltaic PV at time, is the actual value of the load parameter of the i-th charging station L at time t, is the predicted value of the load parameter of the i-th charging station L at time, is the load parameter error of the i-th charging station L at time, is the actual value of the number of dispatchable electric vehicles, is the predicted value at time, is the error of the number of dispatchable electric vehicles; Since the uncertainty variables have daily correlation, they can be represented by a joint probability density distribution set.

[0026] S22. Use chance constraints to convert the uncertainty variables into deterministic constraints at different confidence levels; To reduce the impact of the prediction error of the day-ahead data on the upstream grid operator, the error probability information of the historical data is taken into account and transmitted to the upstream grid operator, and the chance constraint is introduced to construct the probabilistic feasible region of the distribution network of the electric vehicle aggregator; (11) (12) Among them, represents the set of probabilistic constraints and ordinary constraints in the operation of the distribution network, is the charging power of the i-th charging station at time t, is the discharging power of the i-th charging station at time t, is the output power of the th photovoltaic PV at time t, is the output power of the micro gas turbine m at time t, is the power value of the load at time t, is the demand response deviation, is the probabilistic confidence parameter; The chance constraint established for the uncertain components has probabilistic characteristics, and it is difficult to directly solve and reduce the dimension of the constraint set through algorithms during the solution process. Therefore, a theoretical derivation method for the chance constraint is proposed. The aim is to convert the uncertain variables into deterministic constraints under different confidence levels to facilitate the solution of the model.

[0027] (13) Among them, represents the set of probabilistic constraints and ordinary constraints in the operation of the distribution network, is the decision variable, is the random variable, is the affine function, which is used to simplify the representation of the operation constraints of the distribution network, is the probabilistic confidence parameter; S23. Use the vector set to uniformly represent the deterministic constraints, assume that the probability of the prediction error follows a normal distribution by the central limit theorem, and establish the joint probability density function through the multivariate Gaussian model; Since there are a large number of constraints, but they exist in the form of linear convex functions in the system, the vector set is used for unified representation, and the constraint can be regarded as a convex function of the random variable with respect to ; In the formula, is the affine function constraint set, is the vector set of random variables, is the vector set of decision variables, c is the constant term of the affine function, is the decision variable, is the random variable; In this case, the original constraint can be transformed into: (14) Due to the influence of the central limit theorem, it is generally assumed that the probability of the prediction error follows a normal distribution. Based on multiple uncertainty variables, the joint probability density function of the entire uncertainty set is established through a multivariate Gaussian model; the variance of the error value corresponding to each uncertainty variable set is respectively expressed as (Variance of the error value of load prediction) (Variance of the error value of PV power prediction) Variance of the error value of the predicted number of electric vehicles; Since the function is an affine function, it follows a normal distribution, and the mean and variance are simplified as follows: (15) (16) Wherein, is the mean of the affine function constraint set, is the vector set of random variables, is the vector set of decision variables, is the mean of the constant term of the affine function, is the variance of the affine function constraint set, is the variance of the constant term of the affine function; is the variance term of, is the inverse function of the cumulative probability distribution at the confidence level.

[0028] S24. Transform the original constraint into an equivalent transformation based on the inverse function of the probability cumulative distribution function. For the terms involving the square root of the variable, the piecewise linearization method is adopted to simplify the solution difficulty.

[0029] Since the variable follows a normal distribution, the equivalent transformation of the constraint can be obtained by using the inverse function of its probability cumulative distribution function: (19) (20) In the formula, is the vector set of random variables, is the vector set of decision variables, c is the constant term of the affine function, is the variance of the constant term of the affine function, is the mean of the constant term of the affine function, is the inverse function of the cumulative probability distribution, is the probability confidence level parameter.

[0030] In the power grid operation scenario, the power balance constraint expression in the following form is obtained to represent the safety margin of the system under uncertainty; (21) (22) In the formula, is the variance of the vehicle number error, is the output power of the k-th PV, is the predicted value of the vehicle number of the dispatchable electric vehicle at time t, is the output power of the electric vehicle at time t, is the output power of the micro gas turbine m, is the variance of the error value of the PV, is the demand response deviation, is the variance of the error value of the load, is the output power of the i-th load, is the inverse function of the cumulative probability distribution under the confidence level.

[0031] To handle the terms involving the square root of variables, the piecewise linearization method can be used to solve the constraints; the power of the electric vehicle must be within the range; within the variable range of the variable, it is expressed in the form of a piecewise linear combination; Assume a function has linear segments, and the breakpoints , introduce to represent the variable, then there is ; the square root part to be linearized can be expressed as .

[0032] In the formula, is the piecewise linearization coefficient corresponding to the k-th breakpoint, is the k-th breakpoint, is the n-th breakpoint, is the discharge power of the v-th electric vehicle at time t.

[0033] Through linearization, the convexity of the model is ensured and the difficulty of solving is simplified.

[0034] S3. Solve the probabilistic feasible region of the distributed resources to obtain the boundary range of the probabilistic feasible region of the distributed resources; S31. Characterize the probabilistic feasible region by solving the parameters under different confidence levels; The polyhedral linear inequality representation form formed by the feasible region is as follows: (23) In the formula, is the boundary parameter matrix of the distribution network feasible region, is the projection variable, usually representing variables such as interactive power in the equivalent distribution network, is the boundary parameter vector of the probabilistic feasible region.

[0035] S32. Use the confidence boundary deviation as the criterion for in-domain points, and transform the dual problem to solve the feasible cut corresponding to the farthest point; Solving the feasible cut is to solve for different confidence levels under and . Therefore, use the confidence boundary deviation as the criterion for in-domain points.

[0036] (24) Among them, represents the positive deviation of the confidence boundary, represents the negative deviation of the confidence boundary. is the coefficient parameter matrix corresponding to the constraint conditions where the internal variables are located, is the coefficient parameter matrix corresponding to the constraint conditions where the projection variables are located, is the internal variable under different confidence levels , represents the constant vector of the right-hand side of the constraint condition, is the projection variable, usually representing variables such as interactive power in the equivalent distribution network, represents a vector with all values being 1.

[0037] Taking the minimum deviation as the optimization objective, judge the model deviation situation according to the slack variable. If , it indicates that there is a deviation at the regional point, that is, the operating point is outside the feasible boundary at this confidence level. The necessary and sufficient condition for no deviation is that the objective function value obtained by solving is 0.

[0038] Due to the strong duality principle, the optimal solutions are the same, so there is: . For the probabilistic feasible regions under different confidence levels, the farthest point of the dual problem corresponds to the feasible cut. Therefore, the problem of solving the feasible region parameters can be transformed into the problem of solving the farthest point of the dual problem.

[0039] (26) (27) In the formula, Q is the transformed dual function, v is the variable to be solved after the dual transformation, represents the constant vector of the right-hand side of the constraint condition, y is the internal variable under different confidence levels, is the boundary parameter matrix of the distribution network feasible region, is a projection variable, usually representing variables such as interactive power in the equivalent distribution network after equal value, is the boundary parameter vector of the probabilistic feasible region, and m is the dual variable of the feasible region constraint.

[0040] S33. The McCormick envelope relaxation method is adopted to transform the non-convex set formed by the complementary constraints of the charging and discharging states of electric vehicles into a convex form; On this basis, the McCormick envelope relaxation method is used to transform the above problem into a mixed-integer linear programming problem based on the complementary slackness principle and solve it. In the process of solving this problem, each solution corresponds to a feasible cut.

[0041] (28) (29) v is the variable to be solved after dual transformation, is the constant vector representing the right-hand side of the constraint condition, m is the dual variable of the feasible region constraint, is the boundary parameter vector of the probabilistic feasible region, is the boundary parameter matrix of the distribution network feasible region, and A is the coefficient parameter matrix corresponding to the constraint condition, is a projection variable, usually representing variables such as interactive power in the equivalent distribution network after equal value, and M represents an infinite real number, is the 0-1 variable introduced by relaxation.

[0042] The probabilistic feasible region forms a convex polyhedron, and its characterization method requires a linear representation of the constraint conditions. However, the charging and discharging state constraints form complementary constraints. In the process of characterizing the probabilistic feasible region of the electric vehicle optimal scheduling problem, the influence of these constraint conditions on the convex hull formation is a challenge.

[0043] Considering that electric vehicles are used as energy storage units, the charging power and discharging power cannot be positive at the same time. Therefore, at any moment, the following constraints must be satisfied: (30) is the charging power of electric vehicle v at time t, is the discharging power of electric vehicle v at time t.

[0044] Since the above charging and discharging state constraints are a kind of complementary constraints, they often form a non-convex set in most cases. In the solving process, they are usually transformed into a mixed-integer programming problem containing 0-1 variables.

[0045] ≤1(31) An integer variable indicating whether the electric vehicle v is charging at time t An integer variable indicating whether the electric vehicle v is discharging at time t, taking values of 0 or 1.

[0046] However, in the representation of the feasible region, the 0-1 variables in integer programming lack continuity and cannot be represented by a high-dimensional convex polyhedron. Complementary constraints may cause the feasible region to no longer be a single convex set. This makes it difficult for traditional methods based on convex optimization theory to directly solve the problem, especially in high-dimensional spaces involving a large number of variables. Non-convexity poses significant computational challenges.

[0047] S34. By linearizing the relaxation problem, convert non-convex constraints into a combination of multiple convex constraints, and characterize the original non-convex problem with the feasible region described by a convex polyhedron, so as to obtain the boundary range of the probabilistic feasible region of distributed resources.

[0048] To address the above problems, under sufficient conditions, relax the non-convex EV (electric vehicle) problem in the probabilistic feasible region characterization into a convex form. Through the concept of McCormick envelope relaxation, while ensuring convexity, maintain a sufficiently tight boundary, and achieve a strict conversion of the constraint of a continuous variable multiplied by a 0-1 variable into multiple linear constraints. Through the study of such problems, the probabilistic feasible region characterization depends on the boundary of the constraints. Therefore, the 0-1 relaxation does not affect the boundary of the probabilistic feasible region.

[0049] To convert this complementary constraint into a solvable convex problem, the McCormick envelope relaxation theory is adopted. Assume and are both within the interval , the complementary constraint (30) can be converted into the following four linear inequalities.

[0050] (31) (32) (33) (34) Among them, is the introduced slack variable used to approximate the non-convex variables and . is the charging power of the electric vehicle v, is the discharging power of the electric vehicle v, is the power upper limit of the electric vehicle. Through the combination of these linear inequalities, the original non-convex constraint is relaxed into a convex constraint, and then solved by convex optimization methods. The relaxation problem is no longer a singular non-convex problem but is linearized into a combination of multiple convex constraints.

[0051] By applying the McCormick envelope relaxation proposed above, the charge-discharge complementary constraint is transformed into the union of two different convex feasible regions: (35) (36) where is the charging power of the v-th electric vehicle at time t, is the discharging power of the v-th electric vehicle at time t.

[0052] According to the polyhedron theory, a polyhedron can be represented by its boundary constraints. The charging state and the discharging state each form two different convex polyhedra and . This union operation not only preserves the convexity of each state but also ensures that the feasible region of the entire problem is the union of multiple convex regions. Through the McCormick envelope relaxation, the original non-convex problem is transformed into a feasible region described by convex polyhedra. Under the above constraints, the relaxed constraints can be equivalent to the original constraints under certain specific conditions without changing the feasible region mapped to the equivalent space.

[0053] (37) To illustrate the conversion process of the complementary constraint, this embodiment adopts a simple example, taking energy storage as an example. Figure 7 Taking the interactive power output at different time periods as the projection variable, it depicts the feasible space formed by the optimal scheduling problem among three time periods.

[0054] Under the linear coupling constraints of multiple time periods, Figure 7 the union of the feasible regions in Figure 7 corresponds to the actual feasible range, and the actual solution must be within the range described in

[0055] Compared with the traditional method that treats the energy storage change as a single variable, the model of this embodiment considers the influence of the charge-discharge efficiency difference, thus more accurately predicting the feasible region.

[0056] Example 2 This example is described in combination with Example 1. A method for characterizing the probabilistic feasible region of distributed resource uncertainty disclosed in this example is as follows Figure 1 As shown, an improved IEEE-33 node test case system is used to verify the effectiveness of the proposed method and model. There are 32 lines in the distribution network grid, and 10 PVs (photovoltaic), 5 MTs (micro gas turbines) and 7 electric vehicle charging stations are installed at the same time. The installation locations and model structures are as follows Figure 1 shown. The program uses MATLAB R2021a for example running tests. The proposed method is implemented in the YALMIP optimization toolbox (a free and open-source mathematical optimization toolbox based on MATLAB), and IBM ILOG CPLEX 12.9 is used for solving

[0057] 1. Results of basic examples To compare the performance and applicability of the probabilistic feasible region, considering the uncertainties of different distributed resources, four scenarios are set, and the number of in and out times and configuration conditions of electric vehicles are kept unchanged under different circumstances

[0058] As Figures 3 - 6 shown, Scenario 1: Only consider the traditional power grid, without considering the uncertainties of electric vehicles, photovoltaics, and demand response, and characterize the interactive power range of the distribution network under deterministic conditions. Scenario 2: Consider the uncertainties of distributed generation resources. Scenario 3: Consider the chance constraints of time-coupled demand response and establish the coupling relationship between different time scales. Scenario 4: Simulate the scenario where electric vehicle aggregators participate in day-ahead scheduling, and consider the probability distributions of PV (photovoltaic), DR (Demand response), and EV (electric vehicle) under chance constraints

[0059] By comparing the above four scenarios, analyze the impact of electric vehicle aggregators on the probabilistic feasible region of the distribution network under different circumstances. In the context of power grid scheduling, prediction errors will change the feasible region range to a certain extent, thereby affecting the overall performance of the system. It can be seen from the examples that only considering the uncertainty of the photovoltaic error distribution will affect the interactive active power during the day. When the uncertainties of load and electric vehicles are considered simultaneously, due to the introduction of multi-variable uncertainties, the boundary of the probabilistic feasible region will change more significantly. When the number of electric vehicles in the station is large, the overall adjustable capacity of the system increases, especially during the peak hours at noon and in the evening. In addition, within the confidence interval range of 80% - 99%, the feasible region range gradually narrows, and due to the presence of photovoltaics and electric vehicles, the impact on the active power range is more significant

[0060] Figure 2The number of constraints and variables after dimensionality reduction for different scenarios. It can be seen that the probabilistic feasible region method shows superiority in equivalent dimensionality reduction. While maintaining information completeness, it effectively captures the key features of interaction information, improving the efficiency of cross-regional power dispatch and resource allocation. The comparison of tabular data shows that the equivalent characterization method of the probabilistic feasible region reduces the number of constraints by 92.11%. By adopting an effective dimensionality reduction strategy, it promotes the coordination between power grids while ensuring data validity and reducing computational complexity.

[0061] 3. Time coupling in the probabilistic feasible region The feasible regions of the three time periods in Scenario 4 are illustrated through the time-coupled probabilistic feasible region, and the result is an irregular three-dimensional convex polyhedron, reflecting the coupling relationship among P1, P2, and P3. Electric vehicle charging and discharging, as a special form of energy storage, responds to the dispatching demand while meeting the charging needs of vehicle owners. In addition, demand response can change the time period of load demand, enabling a certain time shift characteristic of the interactive power, but its overall regulation ability is limited. Similarly, micro gas turbines are also restricted by the unit ramp rate constraints. Figure 7 It shows the combination of all cases after complementary slackness. The outer boundary contour represents the result without slackness, indicating the consistency between the two.

[0062] Embodiment 3 This embodiment is described in combination with Embodiment 1. A method for characterizing the probabilistic feasible region of distributed resource uncertainty disclosed in this embodiment uses a simple 9-node power system as an example to more clearly illustrate the conversion process of complementary constraints and their application in actual optimization problems, and focuses on the problem of characterizing the probabilistic feasible region of the energy storage system over multiple time periods.

[0063] In Figure 8 and Figure 9 , this embodiment uses the output interactive power as the projection variable to plot the feasible space of the optimal scheduling problem over three time periods. Through this visualization method, it is possible to intuitively observe how the constraint relationships between different time periods affect the feasible solutions of the system. Specifically, Figure 8 shows the feasible regions of each time period, which are jointly determined by the physical constraints of the energy storage system (such as capacity limit, power limit, etc.) and the differences in charge and discharge efficiency. Since the operating states of the energy storage system in different time periods affect each other, Figure 9 further depicts the overall feasible range under the linear coupling constraints of multiple time periods. It can be seen that Figure 8 the union of the feasible regions of each time period in Figure 9 corresponds to the overall feasible range in Figure 9 . This means that the actual optimal solution must satisfy the constraint conditions of all time periods simultaneously, so the solution space is restricted within the range described by

[0064] Compared with traditional optimization methods, the model proposed in this embodiment has significant advantages. Traditional methods usually treat the change in energy storage as a single variable, ignoring the impact of charge-discharge efficiency differences on system operation. Although this simplification reduces the computational complexity, it may also lead to deviations in the optimization results, especially in long-term or multi-period scheduling problems. The model of this embodiment fully considers the differences in charge-discharge efficiency, that is, the different energy conversion efficiencies of the energy storage system during the charging and discharging processes. By introducing complementary constraints, the model can more accurately describe the operating characteristics of the energy storage system, thereby more precisely predicting the feasible region.

[0065] In addition, the model of this embodiment also considers the coupling constraints between multiple time periods. The operating state of the energy storage system is continuous in time, and the decisions in the current time period will affect the feasible solutions in subsequent time periods. For example, excessive discharge in the current time period may lead to insufficient energy storage capacity in subsequent time periods, thus affecting the overall operation of the system. By introducing coupling constraints, the model of this embodiment can effectively capture this temporal dependence, ensuring the feasibility and rationality of the optimization results over multiple time periods.

Claims

1. A method for characterizing the probabilistic feasible domain of distributed resource uncertainty, characterized in that: The steps include: S1. Construct probabilistic feasible domain models for different types of distributed resources; S2. Modeling, analyzing and solving the uncertainty of the distributed resources; S3. Solve the probabilistic feasible domain of the distributed resources to obtain the boundary range of the probabilistic feasible domain of the distributed resources.

2. According to claim 1, a method for characterizing the probabilistic feasible domain of distributed resource uncertainty is characterized in that: In S1, the specific steps of constructing the probabilistic feasible domain model of different types of distributed resources are: S11. Define the probabilistic feasible domain model between electric vehicle aggregators and the upper-level power grid; S12. Preset distribution network operation constraints including electric vehicle aggregators; S13. Construct an electric vehicle charging and discharging model.

3. The method for characterizing the probabilistic feasible domain of distributed resource uncertainty according to claim 2 is characterized in that: In S11, the probabilistic feasible domain model is: The formula of the probabilistic feasible domain model is: ； In the formula, Represents the high-dimensional probabilistic feasible domain generated by the entire model, is the operating status set of the distribution network containing massive distributed resources. is the interactive active power, represents the interactive reactive power, represents the set of probabilistic constraints and common constraints in the operation of the distribution network, PV is photovoltaic, For the The output power of a photovoltaic PV at time t is Micro gas turbine The output power at time t is is the charging power of electric vehicle v at time t, is the discharge power of the electric vehicle v at time t, is the probability confidence parameter, and g is the affine function form of the constraint set.

4. The method for characterizing the probabilistic feasible domain of distributed resource uncertainty according to claim 2 is characterized in that: In S12, the distribution network operation constraints include power grid operation flow constraints, electric vehicle charging status constraints, time domain coupling constraints, distributed resource output constraints and power balance constraints. The above constraints together form a convex hull, which is used to represent the high-dimensional probabilistic feasible domain formed by the distribution network operation constraints.

5. The method for characterizing the probabilistic feasible domain of distributed resource uncertainty according to claim 2 is characterized in that: In S13, the constraints of the electric vehicle charging and discharging model include the upper limit of charging and discharging power, integer variable representation of charging and discharging, time-coupled variation model of SOC, the vehicle's initial state of charge and the ideal state of charge value that needs to be achieved when setting off, and the range limit of SOC.

6. The method for characterizing the probabilistic feasible domain of distributed resource uncertainty according to claim 1 is characterized in that: In S2, the specific process of modeling, analyzing and solving the uncertainty of the distributed resources is: S21. Consider the uncertainty of distributed resources and dispatchable resources and classify the uncertain variables; S22. Model the randomness of uncertain variable errors; use the central limit theorem to assume that the probability of prediction error follows a normal distribution, and establish a joint probability density function through a multivariate Gaussian model to characterize the uncertainty of the prediction value error; S23, transform constraints into chance constraints at different confidence levels; S24, converting the original constraint into an equivalent transformation based on the inverse function of the probability cumulative distribution function, converting the chance constraint containing uncertain variables into a certain constraint under different confidence levels; S25. For the deterministic constraints under different confidence levels, for the terms involving square roots of variables, the piecewise linearization method is used to simplify the difficulty of solving.

7. The method for characterizing the probabilistic feasible domain of distributed resource uncertainty according to claim 1 is characterized in that: In S3, the specific process of solving the probabilistic feasible domain of the distributed resources is: S31, characterize the probability feasible domain by solving the parameters under different confidence levels; S32, using the confidence boundary deviation as the criterion for points within the domain, transforming the dual problem to solve the feasible cut corresponding to the farthest point; S33, using McCormick envelope relaxation method, the non-convex set consisting of complementary constraints of the charging and discharging states of electric vehicles is transformed into a convex form; S34. By linearizing the relaxation problem, the non-convex constraint is transformed into a combination of multiple convex constraints, and the block feasible region described by a convex polyhedron is used to characterize the original non-convex problem, thereby obtaining the boundary range of the probabilistic feasible domain of distributed resources.

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