A Distributionally Robust Scheduling Method for Grid-Connected Traffic Systems Based on Potential Games

Abstract

The present invention discloses a day-ahead distributionally robust scheduling method for a power grid transportation system based on potential game, which relates to the field of energy transportation. The method includes the following steps: Step 1, respectively establish the system models and optimization problems of the power grid and the transportation network; Step 2, respectively establish the uncertainty sets and fuzzy sets of traffic demand and photovoltaic output; Step 3, construct a centralized optimization problem based on the potential game function, and propose a reconstruction method and a solution algorithm for the distributionally robust optimization problem; Step 4, conduct a case analysis of the day-ahead optimal scheduling of the power grid transportation coupling system. The present invention proposes a distributionally robust optimization method based on the potential game framework for the day-ahead scheduling optimization problem of the power grid transportation coupling system, which can effectively reduce the conservativeness of the optimization decision and improve the safety and economy of the operation of the power system.

Description

Technical Field

[0001] The present invention relates to the field of energy transportation, and particularly to a day-ahead distributionally robust scheduling method for a power grid transportation system based on potential game. Background Art

[0002] In recent years, the rapid development and popularization of electric vehicles have effectively alleviated the pollution of transportation to the urban environment. At the same time, the charging demand of electric vehicles has increased year by year, and public fast charging stations have become the main power source for electric vehicles. The spatio-temporal distribution characteristics of the electric vehicle flow in the transportation network will lead to the uncertainty of the power load distribution of the power grid, which will directly affect the power system scheduling strategy. In addition, with the large-scale application of photovoltaic power generation, its power generation is affected by various factors such as meteorological environment, making the photovoltaic output show randomness and volatility, which brings severe challenges to the safe and economic operation of the power grid. Against this background, starting from analyzing the complex coupling characteristics of the two networks, the present invention considers the multiple uncertainties of the power grid transportation coupling system and performs day-ahead scheduling of the power grid while ensuring the optimal individual decision-making of the coupling system. Obviously, accurate day-ahead scheduling of the power grid can effectively reduce the system operation cost and ensure the orderly and stable operation of the power grid transportation coupling system within a day.

[0003] There is an interaction and a close connection between the transportation network and the power grid. The traffic congestion time and the electricity price strategy of fast charging stations will affect the driving and charging plans of electric vehicles. The change in the electric vehicle path selection will redistribute the traffic flow. Furthermore, the charging loads of each power grid node will also fluctuate in time and space, redistributing the power grid power flow. Therefore, the coupling system realizes the dynamic balance of supply and demand through electricity price decision-making. In the related research on the power grid transportation coupling system, considering the interaction between the two networks, establishing a system balance framework, and considering the spatio-temporal changes of the travel time and charging electricity price of electric vehicles, an optimal scheduling scheme to achieve the optimal social benefits of the coupling system has been proposed. However, in the coupling system, electric vehicles are not only the recipients of electricity prices but also the formulators of strategies. Therefore, it is necessary to introduce game theory to study the coupling relationship between traffic flow distribution and power grid scheduling. In the game theory method, there is a special game relationship called potential game. Based on the potential game theory, an optimization model with the goal of maximizing the benefits of all parties can be established, and a corresponding potential function can be constructed. Transforming the solution of the Nash equilibrium of the system into an optimization problem constructed based on the potential function, the mechanism of all individuals in the system formulating strategies can be mapped to the global function composed of this potential function. Therefore, the optimal scheduling strategy of the system can be obtained by solving the Nash equilibrium of the potential function through a centralized optimization algorithm and the individual optimum can be achieved.

[0004] Some existing inventions have used potential game methods to model and analyze the optimal scheduling problem of the power grid - traffic coupling system, achieving the collaborative optimization of the two networks. However, most of them are applied to the real - time scheduling or pricing strategy research of daily traffic and power grid. However, the electric energy of the power grid is not generated instantaneously and requires day - ahead planning to meet the random demands of fast charging stations during the day and ensure the balance between supply and demand. However, there are uncertainties in renewable energy and traffic demand within the power grid - traffic coupling system, which need to be fully considered during day - ahead scheduling.

[0005] To handle the uncertainties in system decision - making optimization problems, according to different uncertainty parameter models, existing inventions can be roughly divided into two categories, namely stochastic optimization and robust optimization. Among them, stochastic optimization presupposes the probability distribution of uncertain parameters in advance and uses precise probability information to optimize the mathematical expectation of the objective function. However, in stochastic optimization, it usually involves calculating complex high - dimensional integrals, making the problem - solving very difficult, and in practical applications, the probability distribution of uncertain parameters is often difficult to obtain accurately. Robust optimization does not assume the probability distribution of uncertain parameters, but constructs an uncertainty set for its variation region and then seeks a robust decision that optimizes the objective function in the worst - case scenario. Since robust optimization usually has the advantage of being computationally tractable, it is widely used in inventions related to day - ahead optimal scheduling of power systems. However, since the probability distribution information of uncertain variables is not included in the robust optimization problem, robust decisions often show strong conservatism.

[0006] In the day - ahead decision - making process of the actual power grid - traffic coupling system, it is often difficult to accurately obtain the probability distribution of uncertain parameters, and decision - makers can only infer partial information of the probability distribution from limited data. To meet this practical need, some inventions have proposed the distributionally robust optimization method. This method draws on the idea of traditional robust optimization to construct a fuzzy set of probability distributions and seeks a system decision that optimizes the expectation of the objective function in the worst - case probability distribution. Compared with traditional stochastic optimization, the distributionally robust optimization method no longer assumes a single probability distribution of uncertain parameters, but constructs an uncertainty set of probability distributions through statistical inference and big - data analysis from uncertain data. On the other hand, compared with robust optimization, distributionally robust optimization effectively reduces the conservatism of system decisions by introducing useful probability information on the basis of the uncertainty set.

[0007] At the same time, although existing inventions have used the distributionally robust framework to study the scheduling problem of the power grid - traffic coupling system, they have ignored the in - depth characterization of the coupling relationship between the two networks, that is, conducting day - ahead power scheduling while ensuring the individual selfishness within the day. Therefore, based on the above analysis, in the power grid - traffic coupling system, there is an urgent need for a method to construct an optimization model that ensures individual optimality within the day in the day - ahead optimization scheduling problem considering multiple uncertainties. At the same time, an effective solution to solve this distributionally robust optimization problem needs to be proposed.

[0008] Therefore, those skilled in the art are committed to developing a day-ahead power optimization scheduling method for a new power grid-traffic coupling system based on game theory, effectively reducing the conservatism of day-ahead scheduling decisions, improving the economic performance of the system on the premise that the interests of users are not damaged, and at the same time ensuring that individuals can schedule according to individual optimal decisions during the day, which is of great significance for improving the safety and stability of the power grid. Summary of the Invention

[0009] In view of the above-mentioned defects of the prior art, the technical problem to be solved by the present invention is the day-ahead distributionally robust optimization scheduling problem considering the game relationship between the power grid-traffic network coupling systems, while reducing the decision-making conservatism and ensuring that the coupling systems reach individual optimality.

[0010] To achieve the above object, the present invention provides a day-ahead distributionally robust scheduling method for a power grid-traffic system based on potential game, and the method includes the following steps:

[0011] Step 1: Establish power grid and traffic network system models and optimization problems respectively;

[0012] Step 2: Establish uncertainty sets and fuzzy sets of traffic demand and photovoltaic output respectively;

[0013] Step 3: Construct a centralized optimization problem based on the potential game function, and propose a reconstruction method and a solution algorithm for the distributionally robust optimization problem;

[0014] Step 4: Case analysis of day-ahead optimization scheduling of the power grid-traffic coupling system.

[0015] Further, the step 1 further includes:

[0016] Step 1.1: Establish a traffic flow allocation model and a traffic-side optimization problem;

[0017] Step 1.2: Establish a distribution network and a microgrid system model, and construct a grid-side optimization problem;

[0018] Step 1.3: Construct a non-cooperative game relationship between the power grid and the traffic sides;

[0019] Step 1.4: Establish a potential game function for the coupling system.

[0020] Further, the step 1.1 further includes:

[0021] Assume that in a traffic network within a finite range, there are multiple origins o and multiple destinations d, and there are multiple paths p for electric vehicles to travel from the origin o to the destination d. Each path p consists of multiple links l, and establish the relationship model between the link flow x l,t and the path flow at each moment in the traffic network:

[0022]

[0023]

[0024]

[0025] In the formula, is the total traffic demand from the starting point o to the ending point d at time t, represents the matrix relationship between the link and the path;

[0026] To ensure that each electric vehicle charges once when passing through this traffic network, the following constraint is added, indicating the flow x on the link at the fast charging station connected to the power grid node j j,t and the path flow relationship model:

[0027]

[0028]

[0029]

[0030] In the formula, is the matrix relationship between the fast charging station location and the path;

[0031] The electric vehicle selects the driving route and charging decision according to the congestion degree of each route and the charging price of the fast charging station. According to the function of the US Road Administration, the relationship between the driving time of the vehicle on link l and the link flow is:

[0032]

[0033] x l,t ≤C l (8)

[0034] In the formula, is the free driving time of the vehicle on link l, and C l is the capacity of link l;

[0035] The congestion time of the vehicle on link l is:

[0036]

[0037] Assume that the charging price of the fast charging station at the power grid node j is λ j,t , then the total cost for a single vehicle to travel from the starting point o to the ending point d is:

[0038]

[0039] In the formula, e t$W$ is the charging amount of each electric vehicle, and $\omega$ is the equivalent cost of time; according to the Wardrop user equilibrium principle, a traffic management problem (TAP) is constructed. When the optimal decision is obtained in this optimization problem, no vehicle in the traffic network can make its total cost lower by changing its driving decision. The TAP is described as:

[0040]

[0041] s.t. (1)-(10)

[0042] Meanwhile, the optimization problem (11) is equivalent to the following Karush-Kuhn-Tucker (KKT) conditions:

[0043]

[0044] The big M method and the piecewise linearization method are used to linearize equations (12) and (9) respectively, and they are replaced with equations (13) and (14) respectively.

[0045]

[0046]

[0047] where is the minimum cost from the starting point $o$ to the ending point $d$, is a binary variable, and $H$, $g$ l,h and $\Delta x$ l,h,t represent the number of divided line segments, the line segment slope, and the link flow of line segment $h$ respectively; based on the above constraints, a traffic-side linear optimization problem is constructed:

[0048]

[0049] s.t. (1)-(6), (8), (13), (14)

[0050] Furthermore, step 1.2 further includes:

[0051] The grid-side optimization objective is to maximize the operation benefit, and the cost function is expressed as:

[0052]

[0053] In the formula, represents the DG operation cost; represents the ES operation cost; represents the demand response cost; represents the cost of purchasing electricity from the main grid; is the electricity purchase amount of microgrid $j$ from the main grid is the electricity amount sold to the main grid is the DG power generation Energy storage discharge Energy storage charge and load constitute a vector;

[0054] The constraint conditions include: microgrid-main grid transaction constraints, DG constraints, ES charge-discharge constraints, flexible load demand response constraints, and power grid power flow constraints.

[0055] Furthermore, the microgrid-main grid transaction constraints include a transaction cost function and a limit on the transaction power of the main grid per unit time, as follows:

[0056]

[0057]

[0058]

[0059] In the formula, λ t G is the day-ahead electricity trading price of the main grid, is the upper limit of the electricity trading between the microgrid and the main grid, and u j,t is a binary variable representing their buying and selling status;

[0060] The DG constraints include a DG operating cost function and a limit on the DG power generation per unit time, as described below:

[0061]

[0062]

[0063] In the formula, a, b, and c are the cost coefficients of DG power generation, and are the upper and lower limits of DG power generation respectively;

[0064] The ES charge-discharge constraints include an ES operating cost function, an ES charge constraint for adjacent time periods, a limit on the charge-discharge amount per unit time, and an SOC constraint, which are expressed as follows:

[0065]

[0066]

[0067]

[0068]

[0069] E j,0 = E j,T (26)

[0070] SOC j,min ≤E j,t / E L ≤SOC j,max (27)

[0071] Where λ ES 、η C 、η D are the unit cost generated by ES charge and discharge, the charge and discharge efficiency of ES respectively; is the upper limit of the charge and discharge amount of ES in each period, v j,t is a binary variable representing the charge and discharge state of ES. E L is the rated capacity of ES;

[0072] The flexible load demand response constraint includes the demand response cost function, the upper and lower limits of the flexible load in each period, and the total daily limit of the flexible load, which are expressed as follows:

[0073]

[0074]

[0075]

[0076] Where λ DR is the unit scheduling cost of the load demand response, and are the demand response loads actually satisfied by the microgrid and the expected values of the loads respectively, is the total demand of the demand response load at node j in one day;

[0077] The non - linear constraint (28) can be linearized into (31)-(33):

[0078]

[0079]

[0080]

[0081] The power grid power flow constraint includes the power conservation of the power grid nodes and the line loss constraint, which are expressed as follows:

[0082]

[0083]

[0084] p ji,t =b ji (θ j -θ i ) (36)

[0085]

[0086] where θ j -θ i is the voltage phase angle difference between transmission lines ji, calculated in radians, and b ji is the line susceptance.

[0087] Furthermore, step 1.3 further includes:

[0088] In steps 1.1 and 1.2, when the charging price is given, the electric vehicles on the transportation side attempt to minimize the total cost by changing their driving route decisions, and the decision-makers of each microgrid attempt to maximize the operating revenue by changing their day-ahead scheduling and operation decisions. At the same time, the supply-demand balance is maintained between the two networks, and a non-cooperative game relationship is formed between the two networks;

[0089] For the transportation side, its participants are all electric vehicles, represented by the set The strategy set is all the alternative paths between the starting point o and the ending point d of vehicle v. According to the transportation network constraints, the strategy set can be replaced by the flow of each path, that is Each electric vehicle attempts to maximize its individual revenue, and the revenue function is

[0090] For the power grid side, its participants are all microgrid decision-makers, represented by the set The strategy set consists of the operation decisions of each microgrid, denoted as Each microgrid attempts to maximize its individual revenue, and the revenue function is

[0091] Thus, a game model is constructed where the transportation-side strategy set is subject to the constraint of uncertain traffic demand. At the same time, the power grid-side strategy set is subject to the uncertainty of photovoltaic power output.

[0092] Furthermore, step 1.4 further includes:

[0093] Under the theoretical framework of steps 1.1 - 1.3 above, seek the Nash equilibrium of the coupled system and make the day-ahead scheduling decision for the power grid; this Nash equilibrium is obtained through the potential game function of equation (38) where the variables satisfy all the constraint conditions of optimization problems (15) and (16):

[0094]

[0095] Introduce Lagrange multipliers to prove that the potential game function is a potential game function for both the transportation and power grid sides, specifically as follows:

[0096] First, the Lagrangian functions \(L\) of \(-\varPhi\) with respect to constraints (1) and (34) are established respectively T-P , the Lagrangian function \(L\) of the optimization problem (15) with respect to constraint (1) T and the Lagrangian function \(L\) of the optimization problem (16) with respect to constraint (34) P , \(\lambda\) j,t and are Lagrange multipliers:

[0097]

[0098]

[0099]

[0100] Secondly, it can be obtained through calculation that equations (42) and (43) hold:

[0101]

[0102]

[0103] Finally, equations (42) and (43) show that in the potential game \(\varXi\), the utility and payoff functions of each player are mapped to the potential game function ; the Nash equilibrium of the game \(\varXi\) is equivalent to the optimal solution set of the potential function (38), where the feasible set of decision variables is defined by the constraints of the optimization problems (15) and (16); the optimal strategy of the coupled system is determined by finding the local optimum of the potential function (38).

[0104] Furthermore, step 2 further includes:

[0105] There are two uncertain quantities in the day-ahead traffic-grid coupled system scheduling problem, namely traffic demand and PV output; for the handling of uncertain quantities, the following process is included:

[0106] Step 2.1, construct an uncertainty set. The upper and lower limits of the traffic flow per hour from the origin \(o\) to the destination \(d\) within 24 hours of a day can be observed from historical data, and are represented by the following box-type uncertainty set:

[0107]

[0108] Furthermore, since the convex optimization problem TAP has a unique solution and constraint (3) is monotonically increasing, the uncertainty set of the charging demand at the microgrid \(j\) can be obtained from (44):

[0109]

[0110] Similarly, the upper and lower limits of the PV output at each microgrid per hour within 24 hours of a day can be observed from historical data and represented by the following box - type uncertainty set:

[0111]

[0112] Step 2.2: Calculate the means \(e\) of the charging demand and PV output based on historical data j,t,pr and and calculate the fluctuation value \(e\) according to Equation (47) j,t,pr and

[0113]

[0114] Introduce vectors and where all elements take values in the interval [-1, 1], and according to Equation (48), convert the charging demand and PV output into vector forms and represented, and define the vector

[0115]

[0116] Step 2.3: Divide the uncertain quantities into \(M\) 0 confidence intervals, each confidence interval is expressed as (49), where and calculate the probability values \(P\) that the uncertain quantities fall into each confidence interval based on historical data m,t , and further construct the fuzzy set (50):

[0117]

[0118]

[0119] The fuzzy set (50) characterizes the joint probability distribution of the two uncertain quantities and contains the finite probability distribution information extracted from the finite historical data. The robust optimization using the fuzzy set composed of the finite probability information is the distributionally robust optimization method.

[0120] Furthermore, Step 3 further includes:

[0121] The Nash equilibrium state of the potential function (39) can be obtained through the equivalent optimization problem (51) to ensure the individual optimality of the participants:

[0122]

[0123] s.t. (1)-(6),(8),(13),(14),(17)-(37)

[0124] Model Reconstruction Method and Solving Algorithm:

[0125] Step 3.1. Equivalent the formula (51) into a compact matrix form:

[0126]

[0127] In the formula, the vector is the first-stage decision, is the second-stage recourse decision;

[0128] Step 3.2. Discretize and perform dual transformation on the second-stage optimization problem , introduce the dual variable γ mt and the dual vectors η t and v mt , and the equivalent reconstruction can be obtained:

[0129]

[0130]

[0131] b = (C t ) T v t (53)

[0132] Since there is a bilinear term in (53), take the vectors σ 1,t and σ 2,t satisfying 0 ≤ σ 1,t , σ 2,t ≤ 1, σ 1,t , and let σ t = σ 1,t - σ 2,t . Combine (53) and the original optimization problem (52), and after dual transformation and linearization by the big M method, obtain the sub-problem (54), Benders cut (55) and the master problem (56) of the optimization problem (52):

[0133]

[0134]

[0135]

[0136] Step 3.3. Establish the Benders iterative optimization algorithm.

[0137] Furthermore, the said Step 3.3 further includes:

[0138] Step 3.3.1. Convert the variables in the optimization problem (52) into the compact form shown in (53) and initialize them. Set the upper and lower limits of the optimal cost to UB = +∞ and LB = -∞, respectively. Set the number of iterations k = 0, and set the tolerance coefficient ξ>0. Select a feasible solution to the main problem.

[0139] Step 3.3.2, solve Subproblem when fixed, obtain the target value of Benders cut and optimized solution

[0140] Step 3.3.3. Solve the main problem about x *k and Target value And set UB = min{OB,UB};

[0141] Step 3.3.4, Update The Benders cut under the problem is solved, and the optimal solution and objective value of the problem are updated. and z *(k+1) , and set LB = z *(k+1) ;

[0142] 5) If If true, the algorithm terminates and outputs the optimal solution x *k , otherwise, set k=k+1 and return to step 3.3.2.

[0143] Compared with the prior art, the present invention has at least the following beneficial technical effects:

[0144] 1. The spatiotemporal distribution models of the power grid and the transportation network were constructed respectively, and it was proved that the interaction between the coupled systems conforms to the potential game relationship and the existence of Nash equilibrium under multiple uncertainties;

[0145] 2. A two-stage optimization distribution robust optimization model based on potential game function is proposed to carry out day-ahead power dispatching under the premise of ensuring individual optimality;

[0146] 3. Through duality theory and robust equivalent form conversion method, the distributed robust optimization model is converted into a master-subproblem framework and solved by Benders decomposition method;

[0147] 4. According to the simulation analysis and results, the proposed day-ahead optimization scheduling method has lower conservatism and better economic performance, and can adapt to the optimal travel and charging strategies of individuals on the traffic side. At the same time, the proposed method can improve the flexibility of system energy scheduling and is more suitable for practical applications.

[0148] The concept, specific structure and technical effects of the present invention will be further described below in conjunction with the accompanying drawings to fully understand the purpose, features and effects of the present invention. Description of the Drawings

[0149] Figure 1 is a flowchart of a preferred embodiment of the present invention;

[0150] Figure 2 is a microgrid topology diagram of a preferred embodiment of the present invention;

[0151] Figure 3 is a microgrid topology diagram of a preferred embodiment of the present invention;

[0152] Figure 4 is a power grid topology diagram of a preferred embodiment of the present invention;

[0153] Figure 5 is a schematic diagram of the day-ahead trading electricity price of a preferred embodiment of the present invention;

[0154] Figure 6 is a schematic diagram of the scheduling decision of the distributionally robust optimization method MG1 of a preferred embodiment of the present invention;

[0155] Figure 7 is a schematic diagram of the expected load and actual satisfied load of the demand response of the distributionally robust optimization method MG1 of a preferred embodiment of the present invention;

[0156] Figure 8 is a schematic diagram of the scheduling decision of the distributionally robust optimization method MG4 of a preferred embodiment of the present invention;

[0157] Figure 9 is a schematic diagram of the expected load and actual satisfied load of the demand response of the distributionally robust optimization method MG4 of a preferred embodiment of the present invention;

[0158] Figure 10 is a schematic diagram of the comparison of the trading decisions of the three methods MG1 with the main grid of a preferred embodiment of the present invention;

[0159] Figure 11 is a schematic diagram of the comparison of the trading decisions of the three methods MG4 with the main grid of a preferred embodiment of the present invention. Detailed Embodiments

[0160] The following introduces multiple preferred embodiments of the present invention with reference to the accompanying drawings of the specification to make its technical content clearer and easier to understand. The present invention can be embodied in many different forms of embodiments, and the protection scope of the present invention is not limited to the embodiments mentioned in the text.

[0161] In the drawings, components with the same structure are denoted by the same numeral, and components with similar structures or functions are denoted by similar numerals. The dimensions and thicknesses of each component shown in the drawings are arbitrarily illustrated, and the present invention does not limit the dimensions and thicknesses of each component. To make the illustration clearer, the thicknesses of some components in the drawings are appropriately exaggerated in some places.

[0162] As Figure 1 shown, it is a flowchart of a preferred embodiment of the present invention, including the following steps:

[0163] Step 1: Respectively establish the system models and optimization problems of the power grid and the transportation network;

[0164] Step 1.1: Establish the traffic flow allocation model and the optimization problem on the transportation side

[0165] Assume that in a traffic network within a limited range, there are multiple origins o and multiple destinations d, and there are multiple paths p for electric vehicles to travel from the origin o to the destination d. Each path p consists of multiple links l. Establish the relationship model between the link flow x l,t and the path flow at each moment in the traffic network:

[0166]

[0167]

[0168]

[0169] In the formula, is the total traffic demand from the origin o to the destination d at time t, and it is also one of the uncertain factors to be considered in this embodiment. represents the matrix relationship between the link and the path;

[0170] To ensure that each electric vehicle charges once when passing through this traffic network, add the following constraint, which represents the relationship model between the flow x j,t on the link connected to the fast charging station at the power grid node j and the path flow:

[0171]

[0172]

[0173]

[0174] In the formula, is the matrix relationship between the location of the fast charging station and the path;

[0175] An electric vehicle selects a driving route and a charging decision based on the congestion level of each route and the charging price of fast charging stations. According to the American Road Bureau function, the relationship between the driving time of a vehicle on link l and the link flow is:

[0176]

[0177] x l,t ≤C l (8)

[0178] In the formula, is the free driving time of the vehicle on link l, and C l is the capacity of link l. Furthermore, the congestion time of the vehicle on link l is:

[0179]

[0180] Assume that the charging price of the fast charging station at the power grid node j is λ j,t , then the total cost of a single vehicle from the starting point o to the ending point d is:

[0181]

[0182] In the formula, e t is the charging amount of each electric vehicle, and ω is the equivalent cost of time; According to the Wardrop user equilibrium principle, in this embodiment, a traffic management problem (TAP) is constructed. When the optimal decision is obtained for this optimization problem, no vehicle in the traffic network can make its total cost lower by changing its own driving decision. This TAP is described as:

[0183]

[0184] s.t.(1)-(10)

[0185] At the same time, the optimization problem (11) is equivalent to the following Karush-Kuhn-Tucker (KKT) conditions:

[0186]

[0187] The big M method and the piecewise linearization method are used to linearize equations (12) and (9) respectively, and they are replaced with equations (13) and (14) respectively.

[0188]

[0189]

[0190] Among them, is the minimum cost from the starting point o to the ending point d, is a binary variable, and H, g l,hand Δx l,h,t respectively represent the number of divided line segments, the line segment slope, and the link flow of line segment h. Based on the above constraints, a traffic-side linear optimization problem can be constructed:

[0191]

[0192] s.t. (1)-(6), (8), (13), (14)

[0193] Step 1.2: Establish a distribution network and microgrid system model, and construct a grid-side optimization problem;

[0194] As Figure 2 shown, in this embodiment, it is assumed that each fast charging station is connected to a dispatchable generator (DG), an energy storage unit (ES), and a photovoltaic power generation (PV) unit. Their overall can be regarded as a small microgrid, and it is assumed that each microgrid is connected to a distribution network node. The demands of each microgrid include flexible demand response load and electric vehicle user charging load. The grid-side optimization goal is to maximize the operating benefit, and its cost function includes four parts, namely the DG operating cost ES charge and discharge cost demand response cost and the cost of purchasing electricity from the main grid which is expressed as:

[0195]

[0196] In the formula, is the electricity purchased by microgrid j from the main grid the electricity sold to the main grid DG power generation energy storage discharge energy storage charge and the load constitute a vector;

[0197] The constraint conditions of the optimization problem (16) include the following five aspects:

[0198] 1) Microgrid-main grid transaction constraints, including the transaction cost function and the limit of the electricity transaction volume per unit time with the main grid:

[0199]

[0200]

[0201]

[0202] In the formula, λ t G is the day-ahead electricity trading price of the main grid, is the upper limit of the electricity transaction between the microgrid and the main grid, uj,t is a binary variable representing the buying and selling status of the two parties;

[0203] 2) DG constraints, including the DG operating cost function and the DG power generation limit per unit time:

[0204]

[0205]

[0206] In the formula, a, b, and c are the cost coefficients of DG power generation, and are the upper and lower limits of DG power generation respectively;

[0207] 3) ES charge and discharge constraints, including the ES operating cost function, the ES charge state constraint in adjacent time periods, the charge and discharge amount limit per unit time, and the SOC constraint:

[0208]

[0209]

[0210]

[0211]

[0212] E j,0 = E j,T (26)

[0213] SOC j,min ≤ E j,t / E L ≤ SOC j,max (27)

[0214] In the formula, λ ES , η C , η D are the unit costs generated by ES charge and discharge, the charging and discharging efficiencies of ES respectively; is the upper limit of the charge and discharge amount of ES in each time period, v j,t is a binary variable representing the charge and discharge status of ES. E L is the rated capacity of ES;

[0215] 4) Flexible load demand response constraints, including the demand response cost function, the upper and lower limits of flexible load in each time period, and the total flexible load limit for the whole day:

[0216]

[0217]

[0218]

[0219] In the formula, λ DR is the unit scheduling cost of the load demand response, and are the demand response load actually satisfied by the microgrid and the expected value of the load respectively, is the total demand of the demand response load at node j in one day. The non - linear constraint (28) can be linearized into (31)-(33)

[0220]

[0221]

[0222]

[0223] 5) Grid power flow constraints, including grid node power conservation and line loss constraints, are respectively expressed as follows:

[0224]

[0225]

[0226] p ji,t =b ji (θ j -θ i ) (36)

[0227]

[0228] This embodiment uses the DC power flow to represent the grid node power conservation and line loss limitations.

[0229] In the formula, θ j -θ i is the voltage phase angle difference between transmission lines ji, calculated in radians, and b ji is the line susceptance. Note that in the optimization problem (16), the photovoltaic power generation cost is ignored.

[0230] Step 1.3: Construct the non - cooperative game relationship between the power grid and the transportation side;

[0231] In Steps 1.2 and 1.3, when the charging price is given, on the transportation side, electric vehicles try to minimize the total cost by changing the driving route decision, and on the microgrid side, each microgrid decision - maker tries to maximize the operation revenue by changing the day - ahead scheduling and operation decisions. At the same time, the supply - demand balance is maintained between the two networks, and a non - cooperative game relationship is formed between the two networks.

[0232] For the transportation side, its participants are all electric vehicles, represented by the set It is shown that the strategy set is all the alternative paths for vehicle v between the starting point o and the ending point d. According to the traffic network constraints, the strategy set can be replaced by the traffic flow of each path, that is Each electric vehicle attempts to maximize its individual benefit, and the benefit function is

[0233] For the power grid side, its participants are all the microgrid decision-makers, represented by the set The strategy set consists of the operation decisions of each microgrid, denoted as Each microgrid attempts to maximize its individual benefit, and the benefit function is

[0234] Thus, a game model is constructed Among them, the traffic side strategy set is restricted by the uncertain traffic demand. At the same time, the power grid side strategy set is restricted by the uncertainty of photovoltaic output. Therefore, the game model constructed in this embodiment contains uncertain quantities.

[0235] Step 1.4: Establish the potential game function of the coupled system;

[0236] The purpose of this embodiment is to seek the Nash equilibrium of the coupled system under the theoretical framework of the above steps 1.1 - 1.3, and at the same time make the day-ahead power grid scheduling decision. At this Nash equilibrium, for a fixed charging price, no electric vehicle driver on the traffic side can unilaterally change the driving route to improve its utility. At the same time, no microgrid decision-maker can make the system obtain more benefits by adopting other strategies except the optimal scheduling strategy. This embodiment proposes that this Nash equilibrium can be obtained through the potential game function in formula (38) where the variables satisfy all the constraint conditions of optimization problems (15) and (16).

[0237]

[0238] This embodiment proves that the potential game function is a potential game function for both the traffic and power grid sides, specifically as follows:

[0239] First, establish the Lagrangian functions L T-P of -Φ with respect to constraints (1) and (34), the Lagrangian function L T of optimization problem (15) with respect to constraint (1), and the Lagrangian function L P of optimization problem (16) with respect to constraint (34) respectively, where λ j,t and are Lagrange multipliers:

[0240]

[0241]

[0242]

[0243] Secondly, it can be obtained by calculation that equations (42) and (43) hold.

[0244]

[0245]

[0246] Finally, equations (42) and (43) show that in the potential game Ξ, the utility and payoff functions of each participant can be mapped to the potential game function above. The Nash equilibrium of game Ξ is equivalent to the optimal solution set of the potential function (38), where the feasible set of decision variables can be defined by the constraints of optimization problems (15) and (16). Note that the potential function is concave with respect to the decision variables, which guarantees the existence and uniqueness of this Nash equilibrium. Therefore, we can determine the optimal strategy of the coupled system by finding the local optimum of the potential function (38).

[0247] Step 2: Establish the uncertainty set and fuzzy set of traffic demand and photovoltaic output respectively;

[0248] In the day-ahead traffic-grid coupled system scheduling problem studied in this embodiment, there are two uncertain quantities, namely traffic demand and photovoltaic output. The processing of uncertain quantities includes the following processes:

[0249] Step 2.1: Construct the uncertainty set. The upper and lower limits of the traffic flow from the starting point o to the ending point d per hour within 24 hours of a day can be observed from historical data and are represented by the following box uncertainty set:

[0250]

[0251] Furthermore, since the convex optimization problem TAP has a unique solution and the constraint (3) is monotonically increasing, the uncertainty set of the charging demand at the microgrid j can be obtained from (44):

[0252]

[0253] Similarly, the upper and lower limits of the photovoltaic output at each microgrid per hour within 24 hours of a day can be observed from historical data and are represented by the following box uncertainty set:

[0254]

[0255] Step 2.2: Calculate the mean values e j,t,pr and of the charging demand and photovoltaic output according to historical data, and calculate the fluctuation values e j,t,pr and

[0256]

[0257] Introduce vectors and where all elements take values in the interval [-1, 1], and according to Equation (48), convert the charging demand and PV output into vector forms and denote, and define the vector

[0258]

[0259] Step 2.3: Divide the uncertainties into M 0 confidence intervals, each confidence interval is expressed as (49), where and calculate the probability value P that the uncertainties fall into each confidence interval according to historical data m,t , and then construct the fuzzy set (50).

[0260]

[0261]

[0262] Note that the fuzzy set (50) characterizes the joint probability distribution of two uncertainties and contains the finite probability distribution information extracted from the finite historical data. The robust optimization using the fuzzy set composed of the finite probability information is the distributionally robust optimization method applied in this embodiment.

[0263] Step 3: Construct a centralized optimization problem based on the potential game function, and propose a reconstruction method and a solution algorithm for the distributionally robust optimization problem;

[0264] In this embodiment, a centralized optimization problem (51) is constructed based on the potential game theory framework to optimize the generation cost from the perspective of the power grid, and at the same time achieve the optimal social benefits, that is, ensure the optimality of the intraday traffic dispatch. At the same time, the Nash equilibrium state of the potential function (39) can be obtained through the equivalent optimization problem (51) to ensure the individual optimality of the participants.

[0265]

[0266] s.t.(1)-(6),(8),(13),(14),(17)-(37)

[0267] Since the uncertainties in the distributionally robust optimization problem (51) follow the fuzzy set solving this optimization problem is an NP-hard problem. This embodiment proposes the following model reconstruction method and solution algorithm:

[0268] Step 3.1. Equivalent the formula (51) into a compact matrix form:

[0269]

[0270] In the formula, the vector is the first-stage decision, is the second-stage recourse decision;

[0271] Step 3.2. Discretize and perform dual transformation on the second-stage optimization problem , introduce the dual variable γ mt and the dual vectors η t and v mt , and the equivalent reconstruction can be obtained:

[0272]

[0273]

[0274] b = (C t ) T v t (53)

[0275] Since there is a bilinear term in (53), take the vectors σ 1,t and σ 2,t satisfying 0 ≤ σ 1,t , σ 2,t ≤ 1, σ 1,t , and let σ t = σ 1,t - σ 2,t . Combine (53) and the original optimization problem (52), and through dual transformation and linearization by the big M method, obtain the sub-problem (54), Benders cut (55) and the master problem (56) of the optimization problem (52).

[0276]

[0277]

[0278]

[0279] Step 3.3. Establish the Benders iterative optimization algorithm.

[0280] Step 3.3.1. Convert the variables in the optimization problem (52) into the compact form shown in (53), and perform initialization. Set the upper and lower limits of the optimal cost to UB = +∞ and LB = -∞ respectively, the iteration number k = 0, and set the tolerance coefficient ξ > 0. Select a feasible solution of the master problem

[0281] Step 3.3.2, solve the sub-problem when is fixed, and obtain the objective value of the Benders cut and the optimal solution

[0282] Step 3.3.3, solve the objective value of the master problem with respect to x *k and and set UB = min{OB, UB};

[0283] Step 3.3.4, update the Benders cut under and solve the master problem, update the optimal solution and objective value of the master problem to and z *(k+1) and set LB = z *(k+1) ;

[0284] 5) If holds, the algorithm terminates and outputs the optimal solution x *k , otherwise, set k = k + 1 and return to Step 3.3.2.

[0285] Step 4, Case analysis of the day-ahead optimal scheduling of the grid-traffic coupled system;

[0286] In a grid-traffic coupled system with a fixed topology, obtain the historical traffic demand data of the traffic network and the historical photovoltaic output data in the power grid, and use the theoretical framework proposed in this embodiment for modeling and the algorithm for solving, a less conservative day-ahead scheduling plan of the power grid can be obtained, and under this scheduling decision, the decision-makers of electric vehicles and microgrids can all operate according to their individual optimal decisions.

[0287] In Embodiment 2, a double-layer ring traffic system topology as Figure 3 shown and an IEEE-33 node power grid topology as Figure 4 shown are considered. Eight microgrids are set in the power grid system and supply power to eight fast charging stations in the traffic system respectively. The relevant parameters of the traffic system links are listed in Tables 1 and 2, and the power grid relevant parameters are listed in Table 3. The method of this embodiment has scalability and can be applied to the traffic network and power grid coupling systems with other forms of topologies. The day-ahead trading electricity price of the power grid adopts the residential electricity ladder price in Tianjin as Figure 5 shown. The total duration in the simulation is 24 hours, and it is assumed that each electric vehicle charges 0.015 MWh. This embodiment uses three optimization examples to verify the superiority of the method, namely deterministic optimization (DM), robust optimization based on column and constraint generation algorithm (RO), and distributionally robust optimization (DRO) based on the potential game theory framework proposed in this embodiment.

[0288] Table 1 20 Link Parameters in the Transportation Network

[0289]

[0290] Table 2 Traffic Flow Parameters of Three Sets of Origin-Destination

[0291]

[0292] Table 3 Operating Parameters of Each Component in the Microgrid

[0293]

[0294] Next, the performance of the method in this embodiment is analyzed. First, taking MG1 and MG4 as examples, let's take a look at the electricity purchase from the main grid by MG1 and MG4 in the next day and the corresponding power system dispatching strategies. Figure 6 and Figure 8 are the energy dispatching optimization results of MG1 and MG4 based on the DRO method, including DG output, the exchange power between the microgrid and the main power grid, PV output, and ES charge and discharge power. When the microgrid purchases electricity from the main grid, the power value is positive, otherwise it is negative. Similarly, when the ES is charging, the power value is negative, otherwise it is positive. Figure 6 and Figure 8 show that the output power of PV is 0 from 1h to 6h and from 19h to 24h. At this time, the load in the microgrid is completely provided by DG, ES, and the electricity purchased from the main grid. At this time, the main grid trading price is lower than the DG generation cost, and DG operates at the minimum output power point to reduce the system cost. In the remaining periods, the main grid trading price is higher than the DG generation cost, and DG operates at the maximum power point to increase the electric energy sold to the main grid. Under the time-of-use electricity price mechanism, ES stores the electric energy during the valley electricity price period and sells it during the peak electricity price period to achieve peak shaving and valley filling. In addition, Figure 7 and Figure 9 show the actual demand response load and the expected load dispatching decisions. The expected electricity consumption plan of the demand response load is similar to that of the conventional load, mainly concentrated in the peak electricity price period. On the premise of meeting the total electricity consumption demand and the minimum electricity consumption in each period, the microgrid distributes the electricity consumption demand from 9h to 11h and from 19h to 21h to 2h to 7h, thereby reducing the electric energy that the microgrid needs to purchase during the peak electricity price period.

[0295] Secondly, the trading situations of MG1 and MG4 with the main grid under the three optimization methods are as shown in Figure 10 、 11As shown, at the same time, Table 4 gives the total cost, total power purchase, and total power sold to the main grid under three optimization methods. When formulating the day-ahead scheduling plan, the more uncertainties faced by the microgrid are considered, the more conservative the obtained solution is, and the corresponding operating cost is also higher. The increase in operating cost mainly comes from the increase in the power purchased by the microgrid from the main grid and the decrease in the power sold. In the DRO model proposed in this paper, partial probability information of uncertain parameters can be obtained based on historical data, while the RO model uses the boundary information of the box-type uncertainty set to obtain the optimal solution in the worst case, increasing the conservatism of the strategy. Moreover, the DRO method proposed in this embodiment can avoid selling more surplus power to the main grid. The operating cost of the scheduling solution obtained by the DM method is lower than that of the RO method, but the scheduling solutions obtained by the RO and DRO methods have stronger robustness and the ability to resist the risk of real-time market electricity price fluctuations. At the same time, uncertain factors will indirectly change the route selection of vehicles, thus changing the game result between electric vehicles and microgrid operators, which is ignored in DM. Similarly, we can also observe that compared with the RO method, the method proposed in this embodiment can obtain a more economical and less conservative scheduling strategy.

[0296] Table 4 Total power transaction volume and total operating cost between the microgrid and the main grid under three methods

[0297]

[0298] The preferred specific embodiments of the present invention have been described in detail above. It should be understood that those of ordinary skill in the art can make many modifications and variations based on the concept of the present invention without creative labor. Therefore, all technical solutions that can be obtained by those skilled in the art in the technical field of the present invention through logical analysis, reasoning, or limited experiments based on the concept of the present invention on the basis of the prior art should fall within the protection scope determined by the claims.

Claims

1. A day-ahead distributionally robust scheduling method for power grid transportation systems based on potential game, characterized in that, the method comprises the following steps: Step 1, establish power grid and transportation network system models and optimization problems respectively; Step 2, establish uncertainty sets and fuzzy sets of traffic demand and photovoltaic power output respectively; Step 3, construct a centralized optimization problem based on the potential game function, and propose a reconstruction method and a solution algorithm for the distributionally robust optimization problem; Step 4, conduct a case analysis of the day-ahead optimal scheduling of the power grid transportation coupling system; The said Step 1 further includes: Step 1.1, establish a traffic flow allocation model and a traffic-side optimization problem; Step 1.2, establish a distribution network and microgrid system model, and construct a power grid-side optimization problem; Step 1.3, construct a non-cooperative game relationship between the power grid and the traffic sides; Step 1.4, establish a potential game function for the coupling system; The said Step 1.1 further includes: Assume that in a traffic network with a limited scope, there are multiple origins o and multiple destinations d, and there are multiple paths p that enable an electric vehicle to travel from the origin o to the destination d. Each path p consists of multiple links l, and the link flow x at each moment in the traffic network is established. l,t And the relationship model with the path flow is as follows: In the formula, is the total traffic demand from the origin o to the destination d at time t, represents the matrix relationship between the link and the path; To ensure that each electric vehicle charges once when passing through this transportation network, the following constraint is added, representing the flow x on the link at the fast charging station connected to grid node j j,t and the path flow relationship model: In the formula, is the matrix relationship between the positions and paths of fast charging stations; Electric vehicles select driving routes and charging decisions according to the congestion degree of each route and the charging price of fast charging stations. According to the American Road Bureau function, the relationship between the driving time of vehicles on link l and the link flow is: x l,t ≤ C l (8) In the formula, is the free driving time of the vehicle on link l, and C l is the capacity of link l; The congestion time of vehicles on link l is: Assume that the charging price of the fast charging station at grid node j is λ j,t , then the total cost for a single vehicle from the starting point o to the ending point d is: where, e t is the charging amount of each electric vehicle, and ω is the equivalent cost of time; according to the Wardrop user equilibrium principle, a traffic management problem is constructed. When the optimal decision is obtained in this optimization problem, no vehicle in the traffic network can make its total cost lower by changing its own driving decision. The traffic management problem is described as follows: Meanwhile, the optimization problem (11) is equivalent to the following Karush-Kuhn-Tucker conditions: Use the big M method and the piecewise linearization method to linearize equations (12) and (9) respectively, and replace them with equations (13) and (14) respectively: wherein, is the minimum cost from the starting point o to the end point d, is a binary variable, H, g l,h and Δx l,h,t respectively represent the number of divided line segments, the line segment slope, and the link flow of line segment h; based on the above constraints, a traffic-side linear optimization problem is constructed: s.t.(1)-(6),(8),(13),(14); The said Step 1.2 further includes: The power grid-side optimization goal is to maximize the operation benefit, and the cost function is expressed as: In the formula, represents the DG operating cost; represents the ES operating cost; represents the demand response cost; represents the cost of purchasing electricity from the main grid; is the electricity purchase volume of microgrid j from the main grid the electricity volume sold to the main grid DG power generation volume ES discharge volume ES charge volume and the load constitute a vector; The constraint conditions include: microgrid-main grid transaction constraints, DG constraints, ES charge and discharge constraints, flexible load demand response constraints, power grid power flow constraints; The said microgrid-main grid transaction constraints include a transaction cost function and a limit on the transaction power per unit time with the main grid, as follows: Wherein, is the main grid's day-ahead electricity trading price, is the upper limit of the electricity trading between the microgrid and the main grid, u j,t is a binary variable representing the buying and selling status between the two; The said DG constraints include a DG operation cost function and a limit on the DG power generation per unit time, as follows: where a, b, and c are the cost coefficients of DG power generation, and are the upper and lower limits of DG power generation, respectively; The said ES charge and discharge constraints include an ES operation cost function, an ES charge level constraint for adjacent time periods, a limit on the charge and discharge amount per unit time, and an SOC constraint, which are respectively expressed as follows: E j,0 = E j,T (26) SOC j,min ≤E j,t / E L ≤SOC j,max (27) where λ ES , η C , η D are the unit cost generated by ES charge and discharge, the charge and discharge efficiency of ES, respectively; is the upper limit of the charge and discharge amount of ES in each period, v j,t is a binary variable representing the charge and discharge state of ES; E L is the rated capacity of ES; The said flexible load demand response constraints include a demand response cost function, upper and lower limits of flexible loads for each time period, and a limit on the total amount of flexible loads throughout the day, which are respectively expressed as follows: where λ DR is the unit scheduling cost of the load demand response, and are the demand response loads actually satisfied by the microgrid and the expected values of the loads, respectively, is the total demand of the demand response load at node j in one day The non-linear constraint (28) can be linearized into (31)-(33) The said power grid power flow constraints include power conservation at power grid nodes and line loss constraints, which are respectively expressed as follows: p ji,t = b ji (θ j - θ i )(36) where θ j -θ i is the voltage phase angle difference between transmission lines ji, calculated in radians, and b ji is the line susceptance; The said Step 1.3 further includes: In the said Step 1.1 and the said Step 1.2, when the charging price is given, electric vehicles on the traffic side try to minimize the total cost by changing their driving route decisions, and each microgrid decision maker tries to maximize the operation revenue by changing the day-ahead scheduling and operation decisions. Meanwhile, the supply and demand are balanced between the two networks, and a non-cooperative game relationship is formed between the two networks; For the traffic side, its participants are all electric vehicles, represented by the set The strategy set is all the alternative paths for vehicle v between the starting point o and the ending point d. According to the traffic network constraints, the strategy set can be replaced by the flow of each path, that is Each electric vehicle attempts to maximize its individual benefit, so the benefit function is For the grid side, its participants are all microgrid decision-makers, represented by the set , and the strategy set consists of the operation decisions of each microgrid, denoted as Each microgrid attempts to maximize its individual profit, so the profit function is Thus, a game model is constructed Among them, the traffic side strategy set is constrained by the uncertain traffic demand. At the same time, the power grid side strategy set is constrained by the uncertainty of photovoltaic output; The said Step 1.4 further includes: Under the theoretical framework of the above steps 1.1 - 1.3, seek the Nash equilibrium of the coupled system and make the day-ahead scheduling decision of the power grid simultaneously; this Nash equilibrium is obtained through the potential game function in Equation (38), and the variables therein satisfy all the constraints of optimization problems (15) and (16): obtained, where the variables satisfy all the constraints of optimization problems (15) and (16): Introducing Lagrange multipliers to prove the potential game function Both sides of the traffic power grid are potential game functions, specifically as follows: First, establish the Lagrangian functions \(L\) of \(-\varPhi\) with respect to constraints (1) and (34) respectively T-P , the Lagrangian function \(L\) of optimization problem (15) with respect to constraint (1) T and the Lagrangian function \(L\) of optimization problem (16) with respect to constraint (34) P , \(\lambda\) j,t and are Lagrange multipliers: Secondly, it can be calculated that equations (42) and (43) hold: Finally, Eqs. (42) and (43) show that in the potential game Ξ, the utility and payoff functions of each player are mapped to the potential game function ; the Nash equilibrium of game Ξ is equivalent to the optimal solution set of the potential function (38), where the feasible set of decision variables is defined by the constraints of optimization problems (15) and (16); the optimal strategy of the coupled system is determined by finding the local optimum of the potential function (38); The said Step 3 further includes: The Nash equilibrium state of the potential function (39) can be obtained through the equivalent optimization problem (51) to ensure the individual optimality of the participants: s.t. (1)-(6), (8), (13), (14), (17)-(37) Model reconstruction method and solution algorithm: Step 3.1: Equivalent formula (51) to a compact matrix form: In the formula, the vector is the decision-making in the first stage, is the recourse decision-making in the second stage; Step 3.

2. Discretize and perform dual transformation on the optimization problem in the second stage and introduce dual variables γ mt and dual vectors η t and ν mt , and the equivalent reconstruction can be obtained: Due to the existence of bilinear terms in (53), take vectors σ 1,t and σ 2,t satisfying 0 ≤ σ 1,t , σ 2,t ≤ 1, σ 1,t , and let σ t = σ 1,t - σ 2,t . Combining (53) and the original optimization problem (52), after dual transformation and linearization by the big M method, the sub-problem (54), Benders cut (55) and master problem (56) of the optimization problem (52) are obtained: Step 3.3: Establish a Benders iterative optimization algorithm.

2. The day-ahead distributionally robust scheduling method for a power grid traffic system based on potential game as claimed in claim 1, characterized in that said step 2 further includes: There are two uncertain quantities in the day-ahead traffic power grid coupled system scheduling problem, namely traffic demand and photovoltaic output; the processing of the uncertain quantities includes the following process: Step 2.1: Construct an uncertainty set. The upper and lower limits of the traffic flow from the origin o to the destination d per hour within 24 hours of a day can be observed from historical data, and are represented by the following box uncertainty set: Furthermore, since the convex optimization problem TAP has a unique solution and constraint (3) is monotonically increasing, the uncertainty set of the charging demand at microgrid j can be obtained from (44): Similarly, the upper and lower limits of the photovoltaic output at each microgrid per hour within 24 hours of a day can be observed from historical data, and are represented by the following box uncertainty set: Step 2.2: Calculate the mean values e of the charging demand and the PV output according to the historical data j,t,pr and and calculate the fluctuation value e according to Equation (47) j,t,de and Introduce vectors and where all element values belong to the interval [-1, 1], and according to Equation (48), convert the charging demand and PV output into vector form Step 2.3: Divide the uncertainty into M 0 confidence intervals, each confidence interval is expressed as (49), where and calculate the probability value P of the uncertainty falling within each confidence interval based on historical data m,t , and then construct a fuzzy set (50): The fuzzy set (50) characterizes the joint probability distribution of the two uncertain quantities and contains the extraction of finite probability distribution information from finite historical data. The robust optimization using the fuzzy set composed of finite probability information is the distributionally robust optimization method.

3. The day-ahead distributionally robust scheduling method for a power grid traffic system based on potential game as claimed in claim 2, characterized in that said step 3.3 further includes: Step 3.3.

1. Convert the variables in the optimization problem (52) into the compact form shown in (53), and perform initialization. Set the upper and lower limits of the optimal cost to UB = +∞ and LB = -∞ respectively, the iteration number k = 0, and set the tolerance coefficient ξ > 0. Select a feasible solution of the master problem Step 3.3.2, solve the sub-problem when is fixed, and obtain the objective value of the Benders cut and the optimal solution Step 3.3.3, solve the objective value of the master problem with respect to x *k and and set UB = min{OB, UB}; and set UB = min{OB, UB}; Step 3.3.4, update the Benders cut under, and solve the master problem, update the optimal solution and objective value of the master problem to and z *(k+1) , and set LB = z *(k+1) ; 5) If holds, the algorithm terminates and outputs the optimal solution x *k , otherwise, set k = k + 1 and return to step 3.3.2.

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