A power distribution network optimization scheduling method considering schedulable capacity of electric vehicle cluster

Abstract

The application discloses a power distribution network optimal dispatching method considering schedulable capacity of electric vehicle cluster, and belongs to the field of power system optimal dispatching. The method comprises the following steps: a virtual energy storage operation domain of the electric vehicle cluster is established; a collaborative optimal dispatching model is established by taking the lowest operation cost of a power distribution network operator and an electric vehicle aggregator as a target respectively according to the virtual energy storage operation domain of the electric vehicle cluster; the uncertainty of new energy output and electric vehicle response energy prediction is described, and an uncertainty set based on Wasserstein distance is established; a distribution robust optimal dispatching model based on Wasserstein distance is established according to the collaborative optimal dispatching model and the uncertainty set based on Wasserstein distance, and is converted into a mixed integer linear programming problem for solving, and the power distribution network optimal dispatching is completed. The application solves the flexible dispatching and economic operation problems of the power distribution network after large-scale electric vehicles and distributed energy are connected to the grid.

Description

TECHNICAL FIELD

[0001] The application belongs to the field of power system optimal dispatching, and particularly relates to a distribution network optimal dispatching method considering the dispatchable capacity of an electric vehicle cluster. BACKGROUND

[0002] With the promotion of the double carbon target, the coordinated development of a new power system mainly based on new energy and electric vehicles has become an inevitable trend. However, the randomness and volatility of new energy output and the randomness of electric vehicle charging bring burdens to the flexible dispatching and safe and economic operation of the distribution network. Therefore, it is necessary to reasonably utilize the dispatching flexibility of electric vehicles to enable them to participate in the dispatching plan of the distribution network.

[0003] Electric vehicles, on the one hand, are connected to the distribution network as transportation loads, and on the other hand, can be regarded as distributed energy storage to provide flexible resources for the distribution network and participate in the dispatching management of the distribution network. Since electric vehicles are numerous, widely distributed and small in individual capacity, they need to be managed by an electric vehicle aggregator and participate in the dispatching of the distribution network in the form of an energy cluster. Existing researches mainly consider the influence of new energy and basic load prediction errors, and ignore the uncertainty of electric vehicle charging behavior. With the continuous expansion of the scale of electric vehicles connected to the network, the accurate evaluation of the dispatchable capacity of the electric vehicle cluster will greatly affect the formulation of the system dispatching plan. SUMMARY

[0004] In view of the above problems in the prior art, the distribution network optimal dispatching method considering the dispatchable capacity of an electric vehicle cluster provided by the application solves the flexible dispatching and economic operation problems of the distribution network after large-scale electric vehicles and distributed energy are connected to the network.

[0005] In order to achieve the above-mentioned application purposes, the technical scheme adopted by the application is as follows: a distribution network optimal dispatching method considering the dispatchable capacity of an electric vehicle cluster, comprising:

[0006] An electric vehicle individual charging and discharging model is established, and based on the power boundary and energy boundary of a single electric vehicle, a virtual energy storage operating domain of an electric vehicle cluster is established by using Minkowski summation according to the electric vehicle individual charging and discharging model;

[0007] A collaborative optimization dispatching model is established by taking the minimum operation cost of the distribution network operator and the electric vehicle aggregator as the target respectively according to the virtual energy storage operating domain of the electric vehicle cluster;

[0008] The prediction uncertainty of new energy output and electric vehicle response energy is depicted, and an uncertain set based on the Wasserstein distance is established;

[0009] According to the cooperative optimization scheduling model and the uncertain set based on the Wasserstein distance, a distribution robust optimization scheduling model based on the Wasserstein distance is established and converted into a mixed integer linear programming problem for solving, and the optimal scheduling of the distribution network is completed.

[0010] Further, the individual charging and discharging model of the electric vehicle is established, and based on the power boundary and energy boundary of a single electric vehicle, the virtual energy storage operation domain of the electric vehicle cluster is established by using Minkowski summation according to the individual charging and discharging model of the electric vehicle.

[0011] The individual charging and discharging model of the electric vehicle is established.

[0012]

[0013] wherein, is the charging power of the nth electric vehicle at time t; P n cm is the rated charging power of the nth electric vehicle; t is time; t ar is the time when the electric vehicle is connected to the network; t eq is the time when the electric vehicle is disconnected from the network; is the discharging power of the nth electric vehicle at time t; P n dm is the rated discharging power of the nth electric vehicle; E n,t is the electric quantity of the nth electric vehicle at time t; E n,t-1 is the electric quantity of the nth electric vehicle at time t-1; η c is the charging efficiency of the electric vehicle; Δt is the time step; η d is the discharging efficiency of the electric vehicle; is the minimum electric quantity of the nth electric vehicle; is the maximum electric quantity of the nth electric vehicle; E n,t＝0 is the electric quantity of the nth electric vehicle at time t=0; E n,0 is the electric quantity of the nth electric vehicle when connected to the network; E n,T is the electric quantity of the nth electric vehicle at time T; T is the time when the electric vehicle is disconnected from the network; E n,e is the expected electric quantity of the nth electric vehicle when disconnected from the network;

[0014] According to the individual charging and discharging model of the electric vehicle, the power boundary and energy boundary of a single electric vehicle are calculated:

[0015]

[0016] wherein, is the upper energy boundary of the electric vehicle at time t; E0 is the electric quantity of the electric vehicle when connected to the network; Et-1 is the electricity amount of the electric vehicle at time t-1; P cm is the rated charging power of the electric vehicle; E e is the expected electricity amount of the electric vehicle when off-grid; P dm is the rated discharging power of the electric vehicle; S max is the maximum electricity amount of the electric vehicle; is the lower energy boundary of the electric vehicle at time t; S min is the minimum electricity amount of the electric vehicle; P t max is the upper power limit of the electric vehicle at time t; P t min is the lower power limit of the electric vehicle at time t;

[0017] According to the power boundary and the energy boundary of a single electric vehicle, a virtual energy storage operation domain of an electric vehicle cluster is obtained by superimposing the energy and power boundaries of the electric vehicles in each charging station by using Minkowski summation, taking each charging station as an electric vehicle cluster:

[0018]

[0019] wherein, is the maximum charging power of the electric vehicle cluster w at time t; w is an electric vehicle cluster; u n,t is a Boolean variable, which is 0 when the electric vehicle is off-grid and is 1 when the electric vehicle is on-grid; is the maximum discharging power of the electric vehicle cluster w at time t; are the upper energy boundary and the lower energy boundary of the electric vehicle cluster w at time t, respectively; are the upper energy boundary and the lower energy boundary of the nth electric vehicle at time t, respectively.

[0020] Further, the objective function of the collaborative optimization scheduling model is:

[0021]

[0022] wherein, is the upper distribution network optimization objective; x is a decision variable; X U is the set of decision variables of the upper model; C G is the generation cost of the distribution network; is the generation power of the mth generator at time t; C MG is the purchase cost of the distribution network; is the purchase power of the purchase node k at time t; C EVA is the energy consumption cost of the electric vehicle cluster; is the charging or discharging power of the electric vehicle cluster w at time t; Optimize the target for the lower-level electric vehicle cluster; X L The set of decision variables for the lower-level model; T is the time when the electric vehicle leaves the grid; N a For electric vehicle clusters; Let be the electricity price for charging the electric vehicle at time t; Let w be the charging power of the electric vehicle cluster at time t; Let be the discharge electricity price of the electric vehicle at time t; N represents the discharge power of the electric vehicle cluster w at time t. G For a collection of generators; a m b m and c m All are the power generation cost coefficients of the m-th generator unit; N k For the set of electricity purchase nodes; The electricity purchase price at time t; P represents the reactive power of the m-th generator unit at time t. t PV P represents the photovoltaic power generation capacity in the distribution network at time t. t WT Let t be the wind power generation capacity in the distribution network at time t.

[0023] Furthermore, the constraints of the collaborative optimization scheduling model include power flow balance constraints, security constraints, power generation constraints, power purchase constraints, renewable energy output constraints, electric vehicle electricity price constraints, and electric vehicle charging and discharging power constraints.

[0024]

[0025]

[0026] Among them, P j,t P represents the active power injected at node j at time t. jq,t Let be the active power flowing from i to q in branch iq at time t; h(j) be the set of terminal nodes of the branch with node j as the starting node; e(j) be the set of starting nodes of the branch with node j as the ending node; P ij,t Let r be the active power flowing from i to j in branch ij at time t; ij Let I be the resistance of branch ij at time t; ij,t Q is the square of the current magnitude flowing from i to j in branch ij at time t; j,t Q represents the reactive power injected at node j at time t; jq,t Let Q be the reactive power flowing from i to q in branch iq at time t; ij,t Let x be the reactive power flowing from i to j in branch ij at time t; ij Let be the reactance of branch ij at time t; Active power generated by generator j at time t; Purchased power of node j at time t; Photovoltaic power generation of node j at time t; Wind power generation of node j at time t; Charging and discharging power of electric vehicle cluster at node j at time t; Conventional active load at node j at time t; Reactive power generated by generator j at time t; Conventional reactive load at node j at time t;V j,t Voltage amplitude square at node j at time t;V i,t Voltage amplitude square at node i at time t;U i,min Lower limit of node voltage amplitude;U i,max Upper limit of node voltage amplitude;I ij,max Branch current amplitude upper limit; Minimum active output of generator j; Maximum active output of generator j; Minimum reactive output of generator j; Maximum reactive output of generator j; Lower ramp rate of generator; Active power generated by generator j at time t-1; Upper ramp rate of generator; Purchased power limit of node j at time t; Maximum output prediction value of photovoltaic; Maximum output prediction value of wind power; Purchased power price at time t; Charging price of electric vehicle at time t; Discharging price of electric vehicle at time t; Charging power of electric vehicle cluster w at time t; Maximum charging power of electric vehicle cluster w at time t; Discharging power of electric vehicle cluster w at time t;u w,t Boolean variable indicating that electric vehicle cluster w only has charging or discharging behavior at any time; Maximum discharging power of electric vehicle cluster w at time t;E w,t Total energy of electric vehicle cluster w at time t;E w,t-1 Total energy of electric vehicle cluster w at time t-1;η c Charging efficiency of electric vehicle;η d Discharging efficiency of electric vehicle; The upper energy boundary of the electric vehicle cluster w at time t; The lower energy boundary of the electric vehicle cluster w at time t; w,T The total energy of the electric vehicle cluster w at time T; The expected electricity amount when the cluster w is off-grid; The lower energy boundary of the electric vehicle cluster w at time T.

[0027] Further, the expression of the uncertainty set based on the Wasserstein distance is:

[0028]

[0029] Wherein, F is the new energy output prediction error uncertainty set based on the Wasserstein distance; D is the empirical distribution of the uncertainty quantity; The real distribution; The uncertainty quantity in the empirical distribution D; The uncertainty quantity in the empirical distribution D corresponding to The corresponding auxiliary variable; The expected value of the auxiliary variable; epsilon is the Wasserstein ball radius; The constraint of the upper limit of the expected value of the auxiliary variable; The support set V l of the empirical distribution D is taken out, and the uncertainty quantity also satisfies the real distribution; v is the uncertain variable; u is the auxiliary variable; V l The support set of the sample l; l is the lth sample extracted from the sample data; The distribution of the sample l extracted from the empirical distribution D; The probability of each distribution; The probability of each distribution is equal, and each is M is the total number of sample data; The sample data; v is the lower bound of the uncertainty quantity; v is the upper bound of the uncertainty quantity.

[0030] Further, the distribution robust optimization scheduling model based on the Wasserstein distance is established according to the collaborative optimization scheduling model and the uncertainty set based on the Wasserstein distance, and is converted into a mixed integer linear programming problem for solving, and the power distribution network optimization scheduling is completed, specifically:

[0031] According to the collaborative optimization scheduling model and the uncertainty set based on the Wasserstein distance, a two-stage distribution robust optimization scheduling model is proposed;

[0032] The two-stage distribution robust optimization scheduling model is converted into a mixed integer programming problem;

[0033] Solving the mixed integer programming problem, the optimal scheduling of the power distribution network is completed.

[0034] Further, the expression of the two-stage distribution robust optimization scheduling model is:

[0035]

[0036] Wherein, F is a two-stage distribution robust optimization scheduling model; is a first-stage deterministic optimization objective, that is, an objective function of the collaborative optimization scheduling model; is a second-stage optimization objective, indicating that the system makes adjustment items of the power generation, power purchase, and electric vehicle cluster charging power to cope with the influence of uncertain variables on the basis of the first-stage deterministic optimization; is an optimization decision variable x when the objective function is minimum; x is a decision variable; X is a decision variable set of the first stage, including X U and X L ; X U is a decision variable set of the upper model; X L is a decision variable set of the lower model; c T is a transpose of a coefficient vector of the decision variable x in the first-stage objective function; is to find the worst distribution of uncertain variables, so that the second-stage optimization objective function takes the maximum value; E D is to find the expectation; d T is a transpose of a coefficient variable corresponding to the decision variable y in the second-stage objective function; y is a second-stage optimization decision variable, including C u,G , C u,MG , and C u,EVA ; C u,G is an adjustment amount of the power distribution network generation cost to cope with the influence of uncertain variables; C u,MG is an adjustment amount of the power distribution network purchase cost to cope with the influence of uncertain variables; C u,EVA is an adjustment amount of the electric vehicle cluster charging cost to cope with the influence of uncertain variables; A is a coefficient matrix of the first-stage constraint condition; b is a parameter vector of the first-stage constraint condition; C is a coefficient matrix of the variable x in the second-stage constraint; H is a coefficient matrix of the variable y in the second-stage constraint; g(v) is a constraint related to the uncertain variable v.

[0037] Further, the expression of the mixed integer programming problem is:

[0038]

[0039] Wherein, is an optimization decision variable x, σ, to find the minimum value of the objective function; is a decision variable which has a linear relationship with the uncertain variable v after linear transformation by an affine strategy; c T is the transpose of the coefficient vector of the decision variable x in the first-stage objective function; x is the decision variable; M is the total number of sample data; m is the sample data number; β m is an auxiliary variable; σ is a dual variable; ε is the Wasserstein ball radius; d T is the transpose of the coefficient variable corresponding to the decision variable y in the second-stage objective function; d T y(·) is the second-stage objective function; is the objective function value obtained by substituting the sample data of the uncertain variable into the objective function, and the uncertain variable is the new energy output prediction error; is the objective function value obtained by substituting the upper bound of the uncertain variable into the objective function; d T y(v) is the objective function value obtained by substituting the lower bound of the uncertain variable into the objective function; is the mth sample data; A is the coefficient matrix of the first-stage constraint condition; b is the parameter vector of the first-stage constraint condition; is the decision variable when the uncertain variable v takes the upper bound ; y(v) is the decision variable when the uncertain variable v takes the lower bound v; v is the lower bound of the uncertain variable; is the upper bound of the uncertain variable; C is the coefficient matrix of the variable x in the second-stage constraint; H is the coefficient matrix of the variable y in the second-stage constraint; is the decision variable which has a linear relationship with the uncertain variable ; is the constraint g(v) into which is substituted; is the decision variable which has a linear relationship with the uncertain variable v; g(v) is the constraint g(v) into which v is substituted.

[0040] The beneficial effects of the present application are that the dispatching model can realize the maximization of the benefits of the two subjects of the power distribution network operator and the electric vehicle aggregator; the uncertain set of the new energy output and the electric vehicle cluster dispatchable energy prediction error constructed based on the Wasserstein distance fully utilizes the historical sample data, so that the formulation of the dispatching plan is more in line with the demand of the actual situation; further considering the uncertainty, the distribution robust optimization model established can realize the balance of the economy and the robustness of the dispatching model. BRIEF DESCRIPTION OF DRAWINGS

[0041] Figure 1 is the flow chart of the method of the present application.

[0042] Figure 2 is the schematic diagram of the simulation system in the embodiment of the present application.

[0043] Figure 3 A day-ahead source-load prediction curve and a power purchase market price schematic diagram in an embodiment of the present application.

[0044] Figure 4 A scheduling plan comparison result schematic diagram under various strategies in an embodiment of the present application.

[0045] Figure 5 A charging and discharging situation and power change schematic diagram of an electric vehicle cluster in an embodiment of the present application. DETAILED DESCRIPTION

[0046] The specific embodiments of the present application are described below to facilitate the understanding of the present application for those skilled in the art, but it should be clear that the present application is not limited to the scope of the specific embodiments, and for those skilled in the art, it is obvious that various changes are within the spirit and scope of the present application defined and determined by the appended claims, and all the inventions utilizing the concept of the present application are within the scope of protection.

[0047] As shown in Figure 1 ,

[0048] In an embodiment of the present application, a power distribution network optimal scheduling method considering the schedulable capacity of an electric vehicle cluster includes:

[0049] An electric vehicle individual charging and discharging model is established, and based on the power boundary and energy boundary of a single electric vehicle, a virtual energy storage operating domain of the electric vehicle cluster is established by using Minkowski summation according to the electric vehicle individual charging and discharging model;

[0050] A collaborative optimization scheduling model is established with the lowest operation cost of the power distribution network operator and the electric vehicle aggregator as the target respectively according to the virtual energy storage operating domain of the electric vehicle cluster;

[0051] The uncertainty set based on the Wasserstein distance is established by depicting the uncertainty of new energy output and electric vehicle response energy prediction;

[0052] The distribution robust optimization scheduling model based on the Wasserstein distance is established according to the collaborative optimization scheduling model and the uncertainty set based on the Wasserstein distance, and is converted into a mixed integer linear programming problem for solving to complete the power distribution network optimal scheduling.

[0053] In the embodiment, three charging stations for unified charging and discharging management by the electric vehicle aggregator are set. Three types of electric vehicles are set in each charging station to participate in the power distribution network scheduling.

[0054] The individual charging and discharging model of the electric vehicle is established, and based on the power boundary and energy boundary of a single electric vehicle, the virtual energy storage operation domain of the electric vehicle cluster is established by using Minkowski summation according to the individual charging and discharging model of the electric vehicle.

[0055] An individual charging and discharging model of an electric vehicle is established:

[0056]

[0057] Among them, is the charging power of the nth electric vehicle at time t; is the rated charging power of the nth electric vehicle; t is time; t ar is the network access time of the electric vehicle; t eq is the network exit time of the electric vehicle; is the discharging power of the nth electric vehicle at time t; is the rated discharging power of the nth electric vehicle; E n,t is the electric quantity of the nth electric vehicle at time t; E n,t-1 is the electric quantity of the nth electric vehicle at time t-1; η c is the charging efficiency of the electric vehicle; Δt is the time step; η d is the discharging efficiency of the electric vehicle; is the minimum electric quantity of the nth electric vehicle; is the maximum electric quantity of the nth electric vehicle; E n,t＝0 is the electric quantity of the nth electric vehicle at time t=0; E n,0 is the electric quantity of the nth electric vehicle when accessing the network; E n,T is the electric quantity of the nth electric vehicle at time T; T is the network exit time of the electric vehicle; E n,e is the expected electric quantity of the nth electric vehicle when exiting the network;

[0058] According to the individual charging and discharging model of the electric vehicle, the power boundary and energy boundary of a single electric vehicle are calculated:

[0059]

[0060] Among them, is the upper boundary of the energy of the electric vehicle at time t; E0 is the electric quantity of the electric vehicle when accessing the network; E t-1 is the electric quantity of the electric vehicle at time t-1; P cm is the rated charging power of the electric vehicle; E e is the expected electric quantity of the electric vehicle when exiting the network; P dm is the rated discharging power of the electric vehicle; S max is the maximum electric quantity of the electric vehicle; is the energy lower bound of the electric vehicle at time t; S min is the minimum energy of the electric vehicle; P t max is the power upper bound of the electric vehicle at time t; P t min is the power lower bound of the electric vehicle at time t;

[0061] According to the power boundary and the energy boundary of a single electric vehicle, a virtual energy storage operation domain of the electric vehicle cluster is obtained by superimposing the energy and power boundaries of the electric vehicles in each charging station by using Minkowski summation, taking each charging station as an electric vehicle cluster:

[0062]

[0063] wherein, is the maximum charging power of the electric vehicle cluster w at time t; w is the electric vehicle cluster; u n,t is a Boolean variable, which is 0 when the electric vehicle is in an off-grid state, and is 1 when the electric vehicle is in a grid-connected state; is the maximum discharging power of the electric vehicle cluster w at time t; are the energy upper bound and the energy lower bound of the electric vehicle cluster w at time t, respectively; are the energy upper bound and the energy lower bound of the nth electric vehicle at time t, respectively.

[0064] In this embodiment, the charging and discharging model of the electric vehicle is established according to the charging and discharging power constraints and the safe energy constraints of the electric vehicle.

[0065] The objective function of the collaborative optimization scheduling model is:

[0066]

[0067]

[0068] wherein, is the upper-layer power distribution network optimization objective; x is the decision variable; X U is the upper-layer model decision variable set; C G is the power distribution network power generation cost; is the power generation power of the mth power generator at time t; C MG is the power distribution network power purchase cost; is the power purchase power of the power purchase node k at time t; C EVA is the electric vehicle cluster energy cost; is the charging or discharging power of the electric vehicle cluster w at time t; is the lower-layer electric vehicle cluster optimization objective; X Lis the set of decision variables of the lower layer model; T is the off-grid time of the electric vehicle; N a is the set of electric vehicle clusters; is the charging price of the electric vehicle at time t; is the charging power of the electric vehicle cluster w at time t; is the discharging price of the electric vehicle at time t; is the discharging power of the electric vehicle cluster w at time t; N G is the set of generators; a m , b m , and c m are the generation cost coefficients of the mth generator set; N k is the set of electricity purchase nodes; λ t MG is the electricity purchase price at time t; is the reactive power of the mth generator set at time t; P t PV is the photovoltaic power in the distribution network at time t; P t WT is the wind power in the distribution network at time t.

[0069] The constraint conditions of the collaborative optimization scheduling model include power flow balance constraints, safety constraints, generation power constraints, electricity purchase power constraints, new energy output constraints, electric vehicle price constraints, and electric vehicle charging and discharging power constraints:

[0070]

[0071]

[0072] wherein, P j,t is the active power injected at node j at time t; P jq,t is the active power flowing from i to q in branch iq at time t; h(j) is the set of branch end nodes with node j as the head node; e(j) is the set of branch head nodes with node j as the end node; P ij,t is the active power flowing from i to j in branch ij at time t; r ij is the resistance of branch ij at time t; I ij,t is the square of the current amplitude flowing from i to j in branch ij at time t; Q j,t is the reactive power injected at node j at time t; Q jq,t is the reactive power flowing from i to q in branch iq at time t; Q ij,t is the reactive power flowing from i to j in branch ij at time t; x ij is the reactance of branch ij at time t; is the active power generated by the generator at node j at time t; Pj(t) is the active power purchased by node j at time t; Ppvj(t) is the photovoltaic power generated by node j at time t; Pwj(t) is the wind power generated by node j at time t; Pevj(t) is the charging / discharging power of the electric vehicle cluster at node j at time t; Pj(t) is the active power purchased by node j at time t; Qj(t) is the reactive power generated by the generator at node j at time t; Qj(t) is the reactive power generated by the generator at node j at time t; j,t Vj(t) is the voltage amplitude squared at node j at time t; i,t Vi(t) is the voltage amplitude squared at node i at time t; i,min Umin is the lower limit of the node voltage amplitude; i,max Umax is the upper limit of the node voltage amplitude; ij,max Ilim is the branch current amplitude limit; Pjmin is the minimum active output of generator j; Pjmax is the maximum active output of generator j; Qjmin is the minimum reactive output of generator j; Qjmax is the maximum reactive output of generator j; dPj is the lower ramp rate of the generator; Pj(t-1) is the active power generated by the generator at node j at time t-1; dQj is the upper ramp rate of the generator; Pjlim(t) is the purchased power limit of node j at time t; Ppvmax(t) is the maximum output prediction value of photovoltaic; Pwmax(t) is the maximum output prediction value of wind power; P(t) is the electricity purchase price at time t; Pev(t) is the charging price of electric vehicles at time t; Pev(t) is the charging price of electric vehicles at time t; Pevw(t) is the charging power of electric vehicle cluster w at time t; Pevwmax(t) is the maximum charging power of electric vehicle cluster w at time t; Pevw(t) is the discharging power of electric vehicle cluster w at time t; w,t B is a Boolean variable indicating that the electric vehicle cluster w only has charging or discharging behavior at any time; Pevwmin(t) is the maximum discharging power of electric vehicle cluster w at time t; E w,t Ew(t) is the total energy of electric vehicle cluster w at time t; E w,t-1 Ew(t-1) is the total energy of electric vehicle cluster w at time t-1; η c ηev is the charging efficiency of electric vehicles; η d ηev is the discharging efficiency of electric vehicles; Ewmax(t) is the energy upper limit of electric vehicle cluster w at time t; is the lower bound of the energy of the electric vehicle cluster w at time t; w,T is the total energy of the electric vehicle cluster w at time T; is the expected amount of electricity when the cluster w is off-grid; is the lower bound of the energy of the electric vehicle cluster w at time T.

[0073] The expression of the uncertainty set based on the Wasserstein distance is:

[0074]

[0075] Where F is the new energy output prediction error uncertainty set based on the Wasserstein distance; D is the empirical distribution of the uncertainty quantity; is the true distribution; is the uncertainty quantity in the empirical distribution D; is the uncertainty quantity in the empirical distribution D corresponding to the corresponding auxiliary variable; is the expected value of the auxiliary variable; ε is the Wasserstein ball radius; is the constraint on the upper bound of the expected value of the auxiliary variable; is the support set V l of the empirical distribution D, and any D and the corresponding u are also satisfied. The true distribution of the uncertainty quantity; v is the uncertain variable; u is the auxiliary variable; V l is the support set of the sample l; l is the lth sample extracted from the sample data; is the distribution of sample l extracted from the empirical distribution D; is the probability of each distribution; is the probability of each distribution, which is equal to M is the total number of sample data; is the sample data; v is the lower bound of the uncertainty quantity; is the upper bound of the uncertainty quantity.

[0076] In this embodiment, the support set V l On the one hand, it captures the distance between the true distribution and the empirical distribution, and on the other hand, it limits the fluctuation range of the uncertainty quantity.

[0077] According to the collaborative optimization scheduling model and the uncertainty set based on the Wasserstein distance, a distribution robust optimization scheduling model based on the Wasserstein distance is established and converted into a mixed integer linear programming problem for solving, and the power distribution network optimization scheduling is completed, specifically:

[0078] According to the collaborative optimization scheduling model and the uncertainty set based on the Wasserstein distance, a two-stage distribution robust optimization scheduling model is proposed;

[0079] transforming the two-stage distribution robust optimization scheduling model into a mixed integer programming problem;

[0080] solving the mixed integer programming problem to complete the optimal scheduling of the power distribution network.

[0081] The expression of the two-stage distribution robust optimization scheduling model is:

[0082]

[0083] wherein F is the two-stage distribution robust optimization scheduling model; is the first-stage deterministic optimization objective, i.e., the objective function of the collaborative optimization scheduling model; is the second-stage optimization objective, indicating that the system makes adjustment to the generation, power purchase and charging power of the electric vehicle cluster on the basis of the first-stage deterministic optimization to cope with the influence of uncertain variables; is the optimization decision variable x when the objective function is minimized; x is the decision variable; X is the decision variable set of the first stage, including X U and X L ; X U is the decision variable set of the upper model; X L is the decision variable set of the lower model; c T is the transpose of the coefficient vector of the decision variable x in the first-stage objective function; is to find the worst distribution of uncertain variables, so that the second-stage optimization objective function takes the maximum value; E D is to find the expectation; d T is the transpose of the coefficient variable corresponding to the decision variable y in the second-stage objective function; y is the second-stage optimization decision variable, including C u,G , C u,MG and C u,EVA ; C u,G is the adjustment amount of the generation cost of the power distribution network to cope with the influence of uncertain variables; C u,MG is the adjustment amount of the power purchase cost of the power distribution network to cope with the influence of uncertain variables; C u,EVA is the adjustment amount of the charging cost of the electric vehicle cluster to cope with the influence of uncertain variables; A is the coefficient matrix of the first-stage constraint condition; b is the parameter vector of the first-stage constraint condition; C is the coefficient matrix of the variable x in the second-stage constraint; H is the coefficient matrix of the variable y in the second-stage constraint; g(v) is the constraint related to the uncertain variable v.

[0084] In this embodiment, based on the collaborative optimization scheduling model, and considering the uncertainty of the prediction error of the lower limit of energy output of new energy sources and electric vehicle clusters, a two-stage sub-Blu-ray optimization scheduling model is proposed. The goal of the second stage optimization is to minimize the adjustment cost of rescheduling system resources under the worst-case distribution of uncertainties in order to mitigate the impact of system uncertainties.

[0085] The expression for the mixed integer programming problem is:

[0086]

[0087] in, To optimize decision variable x, σ, find the minimum value of the objective function; Let y be the decision variable that has a linear relationship with the uncertainty v after the affine policy linear transformation; c T This is the transpose of the coefficient vector of the decision variable x in the first-stage objective function; x is the decision variable; M is the total number of sample data; m is the sample data number; β m σ is the auxiliary variable; ε is the dual variable; ε is the radius of the Wasserstein sphere; d T This refers to the transpose of the coefficient variables corresponding to the decision variable y in the second-stage objective function; d T y(·) is the objective function for the second stage; To obtain the objective function value by substituting the sample data with uncertainties into the objective function, the uncertainties are the prediction errors of new energy output. To substitute the upper bound of the uncertainty into the objective function, we can obtain the value of the objective function at this point; d T y(v) is the objective function value obtained by substituting the lower bound of the uncertainty into the objective function; Let be the m-th sample data; A is the coefficient matrix of the first-stage constraints; b is the parameter vector of the first-stage constraints. Take the upper bound value for the uncertain variable v The decision variable is defined as follows: y(v) is the decision variable when the uncertain variable v takes the lower bound value v; v is the lower bound of the uncertainty. is the upper bound of the uncertainty; C is the coefficient matrix of variable x in the second-stage constraint; H is the coefficient matrix of variable y in the second-stage constraint; For uncertain variables Decision variables that exhibit a linear relationship; To be Substitute the constraint g(v); Let v be the decision variable that has a linear relationship with the uncertain variable v; g(v) is the constraint g(v) formed by substituting v into the constraint equation.

[0088] In this embodiment, asFigure 2 as shown in FIG. 1. Node 1 is selected as the balancing node, the system rated voltage level is 12.66 kV, and the power base value is 100 MVA. One photovoltaic node, one wind power node, one distributed generator node and three charging station nodes managed by an electric vehicle aggregator are set in the system. The new energy output prediction value, the basic load prediction value and the electricity purchase market price are shown in FIG. 2. The new energy output prediction error and the electric vehicle cluster energy lower limit prediction error sample data are generated by Latin hypercube sampling and are obtained by typical scene reduction. Three types of electric vehicles are set to participate in the dispatch management of the distribution network, and the parameters of each type of electric vehicle and the distribution in each charging station are shown in Table 1. Figure 3

[0089] Table 1

[0090]

[0091] wherein, t st is the time of entering the network; N(·) is a normal distribution; U(·) is a uniform distribution.

[0092] The following four scenarios are set to compare and analyze the dispatch results of each scenario:

[0093] ① Scenario 1: Electric vehicle cluster unordered charging;

[0094] ② Scenario 2: Only the maximum benefit of the distribution network is taken as the target, and the electric vehicle cluster participates in the charging and discharging dispatch;

[0095] ③ Scenario 3: The maximum benefit of the distribution network-electric vehicle cluster two main bodies is taken as the target, and the electric vehicle cluster does not perform discharging dispatch;

[0096] ④ Scenario 4: The maximum benefit of the distribution network-electric vehicle cluster two main bodies is taken as the target, and the electric vehicle cluster participates in the charging and discharging dispatch.

[0097] Scenario 4 is the method proposed in the present application, the simulation of the four scenarios is performed, and the dispatch plans of different scenarios are shown in FIG. 3. The dispatch results are shown in Table 2. Figure 4

[0098] Table 2

[0099] Scenario Power distribution network benefit / ten thousand yuan System total power generation and purchase cost / ten thousand yuan Electric vehicle charging cost / ten thousand yuan 1 11.9991 8.6422 3.0793 2 13.2018 7.3769 3.0167 3 12.0985 6.8462 1.3827 4 12.1160 6.7395 1.2935

[0100] The distribution network income in Table 2 refers to the difference between the conventional load energy cost and the distribution network cost. The electricity price of the conventional load is 1.1 times the electricity purchase market price.

[0101] From Figure 4 ​​It can be seen that in scenarios 1 and 2, the electric vehicle cluster charges a large amount of electricity in the peak period, at this time the electricity price is high, so the electric vehicle cluster energy cost is also high. At the same time, in order to meet the system load demand, the generator output in scenarios 1 and 2 also reaches the upper limit value in multiple periods, so the system generation cost is also high. In addition, in scenario 1, before and after 19:00 in the evening, the electric vehicle cluster charging demand is large, a large number of disordered charging loads are superimposed on the peak period of the basic load, so that the system generation capacity reaches the upper limit, additional electricity purchase amount from the main network is generated, and the system generation and purchase cost is further increased. Scenarios 3 and 4 consider the maximization of the interests of the distribution network and the electric vehicle cluster, the electric vehicle cluster chooses to charge a large amount of electricity in the valley period, so the energy cost of the electric vehicle cluster and the system generation and purchase cost are low. In addition, scenario 4 considers the discharging scheduling of the electric vehicle cluster, in the peak period of electricity consumption, the electric vehicle cluster discharges appropriately, further reducing the energy cost of the electric vehicle cluster and the system generation and purchase cost.

[0102] In the four scenarios, the distribution network in scenario 2 has the maximum income, because in the case of only considering the maximization of the interests of the distribution network, the electric vehicle cluster charges in the peak period of electricity price, and the distribution network obtains high charging cost income. However, this situation is not realistic, if the distribution network only considers its own interests and sacrifices the interests of the electric vehicle cluster, the cooperation between the electric vehicle cluster and the distribution network will be broken, and the charging strategy of the electric vehicle cluster will no longer be jointly formulated by the distribution network and the electric vehicle cluster. In summary, scenario 4, i.e. the strategy proposed in the present application, can maximize the interests of the distribution network and the electric vehicle cluster, and to some extent, can realize peak shaving and valley filling.

[0103] The electric vehicle cluster charging and discharging strategy formulated by the method proposed in the present application is as shown in Figure 5 In order to ensure the interests of the distribution network and the electric vehicle cluster, the electric vehicle cluster as a whole chooses to charge in the valley period of electricity consumption, and does not charge or discharges appropriately in the peak period of electricity consumption. The energy of the three clusters is always in the operating domain, indicating that the scheduling strategy can meet the charging demand of the electric vehicle in each period, including the minimum electricity requirement of the electric vehicle on the network in each period and the charging demand of the vehicle off the network in the period.

[0104] The charging station CS1 is located near the node with high photovoltaic output in the noon period, so although it is the peak period of electricity consumption, it still supports the charging service of cluster 1. Cluster 1 reaches the upper limit of cluster energy before the evening, then discharges a large amount of electricity in the evening peak period, and charges a large amount of electricity in the night valley period to meet the charging demand of cluster 1.

[0105] The charging station CS2 is located at the leaf node of the power distribution network, and the voltage amplitude is sensitive to active power injection, so it is discharged during the noon peak period and remains silent during the evening peak period to avoid under-voltage problems.

[0106] The charging station CS3 has a large growth trend in the energy lower limit of cluster 3 during the 11:00-17:00 period, indicating that cluster 3 has a higher charging demand during this period.

[0107] Random optimization (SO), robust optimization (RO) and distribution robust optimization (DRO) based on Wasserstein distance are used for comparative analysis, and the optimization results of different methods are shown in Table 3.

[0108] Table 3

[0109]

[0110]

[0111] As can be seen from Table 3, the SO optimization has the maximum power distribution network income, but the SO optimization result is too large related to the selected typical scene of uncertain quantity and the scene probability distribution, and is not representative, so it cannot well cope with system uncertainty; the RO optimization is always optimized in the worst scene, ignoring the probability distribution characteristics of each scene, so that the decision result is too conservative; the DRO optimization is optimized in the worst scene distribution of uncertain quantity, and combines the characteristics of SO and RO. As can be seen from Table 3, the DRO optimization result based on the Wasserstein distance is between the two, and the result becomes worse as the Wasserstein ball radius increases, so setting different ball radii can change the conservatism of the optimization result. At the same time, this method makes full use of historical sample data, so that the optimization result conforms to the historical statistical law, rather than blindly seeking the worst case of uncertain influence, so that the optimization result is too conservative.

[0112] In summary, the method proposed in the application comprehensively considers the uncertainty of new energy output and electric vehicle cluster adjustable energy, and can maximize the benefits of the power distribution network and the electric vehicle cluster. Compared with the traditional SO and RO optimization methods, the scheduling model realizes the balance between economy and robustness.

Claims

1. A power distribution network optimal scheduling method considering schedulable capacity of an electric vehicle cluster, characterized in that, include: Establish an individual charging and discharging model for electric vehicles, and based on the individual charging and discharging model, establish a virtual energy storage operation domain for electric vehicle clusters using Minkowski summation based on the power boundary and energy boundary of a single electric vehicle. Based on the virtual energy storage operation domain of electric vehicle clusters, a collaborative optimization scheduling model is established with the goal of minimizing the operating costs of both the distribution network operator and the electric vehicle aggregator; the objective function of the collaborative optimization scheduling model is: in, The goal is to optimize the upper-level distribution network; For decision variables; This is the set of decision variables for the upper-level model; For the cost of power generation in the distribution network; For the first The generator set is Power generation at any given moment; For the cost of purchasing electricity for the distribution network; Electricity purchase nodes exist The amount of electricity purchased at any given time; Energy costs for electric vehicle clusters; For electric vehicle clusters exist The charging or discharging power at any given time; Optimize the target for the lower-level electric vehicle cluster; This is the set of decision variables for the lower-level model; The time when electric vehicles are taken off the grid; For electric vehicle clusters; for The electricity price for charging electric vehicles at all times; For electric vehicle clusters exist The charging power at any given time; for The electricity price for electric vehicles at any given time; For electric vehicle clusters exist Discharge power at any given moment; For generator sets; , and All are the first The power generation cost coefficient of a generator set; For the set of electricity purchase nodes; for The electricity price at any given time; For the first The generator set is Reactive power at any given moment; for Photovoltaic power generation in the power distribution network at all times; for Wind power generation capacity in the power distribution network at all times; To characterize the uncertainty in predicting the output of new energy sources and the response energy of electric vehicles, an uncertainty set based on Wasserstein distance is established; Based on the collaborative optimization scheduling model and the uncertainty set based on Wasserstein distance, a partial Bruker optimal scheduling model based on Wasserstein distance is established and transformed into a mixed integer linear programming problem for solution, thus completing the optimal scheduling of the distribution network. 2.The optimal scheduling method of power distribution network considering dispatchable capability of electric vehicle cluster according to claim 1, wherein, The establishment of an individual electric vehicle charging and discharging model, and based on this model, using the Minkowski summation method to establish a virtual energy storage operating domain for an electric vehicle cluster, based on the power and energy boundaries of a single electric vehicle, is as follows: Establish an individual charging and discharging model for electric vehicles: in, For the first electric vehicles t The charging power at any given time; For the first The rated charging power of an electric vehicle; For time; The time for electric vehicles to be registered in the network; The off-grid time for electric vehicles; For the first electric vehicles Discharge power at any given moment; For the first The rated discharge power of an electric vehicle; For the first electric vehicles Battery level at any given moment; For the first electric vehicles Battery level at any given moment; For electric vehicle charging efficiency; For time step; For the discharge efficiency of electric vehicles; For the first The minimum battery capacity of an electric vehicle; For the first The maximum battery capacity of an electric vehicle; For the first electric vehicles The battery level at any given moment; For the first The battery level of an electric vehicle when it is registered with the grid; For the first electric vehicles Battery level at any given moment; The time when electric vehicles are taken off the grid; For the first The expected battery level of an electric vehicle when it is disconnected from the grid; Based on the individual charging and discharging model of electric vehicles, the power boundary and energy boundary of a single electric vehicle are calculated: in, For electric vehicles The upper boundary of energy at any given moment; The battery level of the electric vehicle when it is registered with the grid; For electric vehicles Battery level at any given moment; The rated charging power for electric vehicles; The expected charge level of the electric vehicle when it is off-grid; The rated discharge power of the electric vehicle; This refers to the maximum battery capacity of the electric vehicle. For electric vehicles The lower boundary of energy at time; This is the minimum charge capacity for an electric vehicle; For electric vehicles The power limit at any given time; For electric vehicles The lower limit of power at any given time; Based on the power and energy boundaries of a single electric vehicle, and taking each charging station as an electric vehicle cluster, the virtual energy storage operating domain of the electric vehicle cluster is obtained by superimposing the energy and power boundaries of the electric vehicles within the charging station using the Minkowski summation: in, For electric vehicle clusters exist Maximum charging power at any given time; For electric vehicle clusters; This is a Boolean variable; a value of 0 indicates that the electric vehicle is in an off-grid state, and a value of 1 indicates that the electric vehicle is in a grid-connected state. For electric vehicle clusters exist The maximum discharge power at any given moment; , electric vehicle clusters exist The upper and lower energy boundaries at any given moment; , The first electric vehicles The upper and lower bounds of energy at any given moment.

3. The optimal dispatching method of power distribution network considering dispatchable capability of electric vehicle cluster according to claim 1, characterized in that, The constraints of the collaborative optimization scheduling model include power flow balance constraints, security constraints, power generation constraints, power purchase constraints, renewable energy output constraints, electric vehicle electricity price constraints, and electric vehicle charging and discharging power constraints. in, for Time Node Active power injection at the location; for Time Branch Zhong Cong Flow direction The active power; For nodes It is the set of branch end nodes of the first node; For nodes The set of the starting nodes of the branches of the terminal nodes; for Time Branch Zhong Cong Flow direction The active power; for Time Branch The resistance; for Time Branch Zhong Cong Flow direction The square of the current amplitude; for Time Node reactive power injection at the location; for Time Branch Zhong Cong Flow direction q reactive power; for Time Branch Zhong Cong Flow direction reactive power; for Time Branch The reactance; for Time Node The active power generated by the generator at the location; for Time Node The power consumption of electricity purchased; for Time Node The photovoltaic power generation capacity; for Time Node The wind power generation capacity; for Time Node The charging and discharging power of the electric vehicle cluster; for Time Node The normal active load at the location; for Time Node The reactive power generated by the generator at that location; for Time Node The normal reactive load at the location; for Time Node Square of voltage amplitude at point; for Time Node Square of voltage amplitude at point; This is the lower limit of the node voltage amplitude; This represents the upper limit of the node voltage amplitude. This represents the upper limit of the branch current amplitude. For generator The minimum active power output; For generator Maximum active power output; For generator The minimum reactive power output; For generator The maximum reactive power output; This represents the generator's downhill ramp rate; for -1 time node The active power generated by the generator at the location; The uphill ramp rate of the generator; for time Electricity purchase limits for nodes; This is the predicted maximum output value for photovoltaic power. This is the predicted maximum output value of wind power. for The electricity price at any given time; for The electricity price for charging electric vehicles at all times; for The electricity price for electric vehicles at any given time; For electric vehicle clusters exist The charging power at any given time; For electric vehicle clusters exist Maximum charging power at any given time; For electric vehicle clusters exist Discharge power at any given moment; This is a Boolean variable representing a cluster of electric vehicles. At any given moment, there is only one behavior: charging or discharging. For electric vehicle clusters exist The maximum discharge power at any given moment; for Electric vehicle cluster Total energy; for electric vehicle cluster at -1 time Total energy; For electric vehicle charging efficiency; For the discharge efficiency of electric vehicles; For electric vehicle clusters exist The upper boundary of energy at any given moment; For electric vehicle clusters exist The lower boundary of energy at time; for Electric vehicle cluster Total energy; For cluster Expected battery capacity when offline; For electric vehicle clusters exist The lower boundary of energy at time.

4. The optimal dispatching method of power distribution network considering dispatchable capability of electric vehicle cluster according to claim 1, characterized in that, The expression for the uncertain set based on Wasserstein distance is: wherein, is the new energy output prediction error uncertainty set based on the Wasserstein distance; is the empirical distribution of the uncertainty quantity; is the true distribution; is the empirical distribution of the uncertainty quantity in ; is the auxiliary variable corresponding to in the empirical distribution ; is the expected value of the auxiliary variable; is the Wasserstein ball radius; is the constraint on the upper bound of the expected value of the auxiliary variable; is any from the support set of the empirical distribution , and the corresponding also satisfies the true distribution of the uncertainty quantity; is the uncertain variable; is the auxiliary variable; is the support set of the sample ; is the i-th sample extracted from the sample data; is the distribution of the sample extracted from the empirical distribution ; is the probability of each distribution; is that the probability of each distribution is equal, and each is ; is the total number of sample data; is the sample data; is the lower bound of the uncertainty quantity; is the upper bound of the uncertainty quantity.

5. The optimal dispatching method of power distribution network considering dispatchable capability of electric vehicle cluster according to claim 1, characterized in that, The process involves establishing a distributed bar optimization scheduling model based on Wasserstein distance, using a collaborative optimization scheduling model and an uncertainty set based on Wasserstein distance. This model is then transformed into a mixed-integer linear programming problem for solution, thereby completing the optimal scheduling of the distribution network. Specifically: Based on the collaborative optimization scheduling model and the uncertainty set based on Wasserstein distance, a two-stage partial Bruker optimization scheduling model is proposed. The two-stage bibliometric scheduling model is transformed into a mixed integer programming problem. Solve the mixed integer programming problem to achieve optimal scheduling of the power distribution network.

6. The optimal dispatching method of power distribution network considering dispatchable capability of electric vehicle cluster according to claim 5, characterized in that, The expression for the two-stage split-bar optimization scheduling model is: wherein, is a two-stage distribution robust optimization scheduling model; is the first-stage deterministic optimization objective, i.e., the objective function of the collaborative optimization scheduling model; is the second-stage optimization objective, representing the adjustment of the generation, power purchase, and electric vehicle cluster charging power made by the system to cope with the impact of uncertain variables on the basis of the first-stage deterministic optimization; is the optimization decision variable when the objective function is minimized x ; is the decision variable; X is the first-stage decision variable set, including and ; is the upper model decision variable set; is the lower model decision variable set; is the transpose of the coefficient vector of the decision variable x in the first-stage objective function; is to find the worst distribution of uncertain variables, so that the second-stage optimization objective function takes the maximum value; is to find the expectation; is the transpose of the coefficient variable corresponding to the decision variable in the second-stage objective function; is the second-stage optimization decision variable, including , and ; is the adjustment amount of the distribution network generation cost to cope with the impact of uncertain variables; is the adjustment amount of the distribution network power purchase cost to cope with the impact of uncertain variables; is the adjustment amount of the electric vehicle cluster charging cost to cope with the impact of uncertain variables; is the coefficient matrix of the first-stage constraint condition; is the parameter vector of the first-stage constraint condition; is the coefficient matrix of the variable in the second-stage constraint; is the coefficient matrix of the variable in the second-stage constraint; is the constraint related to the uncertain variable v .

7. The optimal dispatching method of power distribution network considering dispatchable capability of electric vehicle cluster according to claim 5, characterized in that, The expression for the mixed integer programming problem is: in, To optimize decision variables , , Find the minimum value of the objective function; For variables y After linear transformation by affine strategy, and the uncertainty v Decision variables with a linear relationship; Decision variables in the first-stage objective function x The transpose of the coefficient vector; The total number of sample data; Number the sample data; As an auxiliary variable; As dual variables; The radius of the Wasserstein sphere; For the second stage objective function and decision variables The transpose of the corresponding coefficient variable; This is the objective function for the second stage; To obtain the objective function value by substituting the sample data with uncertainties into the objective function, the uncertainties are the prediction errors of new energy output. To substitute the upper bound of the uncertainty into the objective function, we can obtain the value of the objective function at this point; To obtain the objective function value by substituting the lower bound of the uncertainty into the objective function; For the first Sample data; This is the coefficient matrix of the first-stage constraints; This is the parameter vector for the first-stage constraints; Uncertain variables v Take the upper bound value Decision variables at that time; Uncertain variables v Take the lower bound value Decision variables at that time; This is the lower bound of the uncertainty. This is the upper bound of the uncertainty. Variables in the second stage constraints The coefficient matrix; Variables in the second stage constraints The coefficient matrix; For uncertain variables Decision variables that exhibit a linear relationship; To be Substitute constraints ; For uncertain variables Decision variables that exhibit a linear relationship; To be with the constraint .

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