Mobile energy storage and power distribution network cooperative power supply recovery method based on KKT master-slave game

Abstract

The invention discloses a mobile energy storage and power distribution network cooperative power supply recovery method based on a KKT master-slave game. The method comprises the following steps: firstly, constructing a power distribution network operator model and a mobile energy storage operator model; then, introducing a KKT condition, converting an objective function of the power distribution network operator model, and further converting a double-layer optimization problem of the master-slave game into a single-layer optimization problem; and finally, considering the KKT condition and the constraint condition of the power distribution network operator model, solving the target function obtained by converting the power distribution network operator model, and obtaining a game equilibrium solution. The game equilibrium solution at least comprises an optimal electricity price strategy of a power distribution network operator, an optimal charging and discharging and moving strategy of a mobile energy storage operator, and a recovery state of each power distribution network node load. The power distribution network operator is used as a leader to guide the mobile energy storage to participate in power supply recovery, and the mobile energy storage operator is used as a follower to maximize own revenue, so that the enthusiasm of the mobile energy storage to participate in power supply recovery is improved, and the power supply recovery speed and efficiency are improved.

Description

Technical Field

[0001] The present invention belongs to the technical field of emergency recovery of power system disasters, and specifically relates to a method for collaborative power supply restoration of mobile energy storage and distribution network based on KKT master-slave game, which is suitable for rapid power supply restoration of distribution network containing a high proportion of distributed power sources. Background Art

[0002] In a high-penetration environment, distributed generation (DG), due to its decentralized nature, can quickly form local microgrids after a distribution network failure, significantly improving the distribution network's power recovery capabilities. However, when the distribution network architecture is damaged, relying solely on DG often leads to a dilemma of being able to operate without a network. Mobile Energy Storage System (MESS), as a new energy storage technology, can effectively compensate for the temporal and spatial limitations of DG with its unique energy migration characteristics, providing strong support for the rapid restoration of power to the distribution network after a disaster.

[0003] With the breakthrough development of electric vehicle technology, large-scale electric vehicle clusters are evolving into a new type of mobile energy storage carrier. By dispatching and utilizing electric vehicle clusters, they can coordinate with distribution networks to restore power supply. As an emerging market player, mobile energy storage operators play a key role in fault recovery. They have a multi-dimensional interest game with distribution network operators in terms of service pricing, dispatching rights, and benefit distribution. Existing research mostly focuses on the single-agent optimization model, in which the distribution network directly determines the dispatch of mobile energy storage, without considering the interests of mobile energy storage operators, resulting in the absence of a profit distribution mechanism, which in turn affects the motivation for participation in mobile energy storage. To this end, the present invention proposes a method for coordinated power supply restoration of mobile energy storage and distribution networks based on KKT master-slave game, aiming to use the master-slave game idea to resolve the interest conflicts between distribution network operators and mobile energy storage operators, achieve joint optimization scheduling and benefit distribution between the two, and significantly improve power supply restoration capabilities. Summary of the Invention

[0004] In view of the shortcomings of the existing technology, the technical problem to be solved by the present invention is to propose a method for collaborative power supply restoration of mobile energy storage and distribution network based on KKT master-slave game.

[0005] The present invention solves the technical problem by adopting the following technical solutions:

[0006] A method for collaborative power supply restoration between mobile energy storage and distribution network based on KKT master-slave game, characterized by comprising the following steps:

[0007] S1: Establish a distribution network operator model with the objective function as follows:

[0008]

[0009] Where T represents the total number of time periods included in the fault period; N represents the number of distribution network nodes; ω i is the power loss cost coefficient of distribution network node i; τ i,t represents the load picking status at node i in the distribution network during period t; is the active power demand of the load at node i in the distribution network during period t; is the active power of the diesel generator at node i in the distribution network during period t; is the power generation cost coefficient of the diesel generator set; and are the charging and discharging power of the kth mobile energy storage vehicle in period t; N k is the number of mobile energy storage vehicles; and are the charging and discharging prices of the kth mobile energy storage vehicle in period t; c fuel is the unit moving cost of the mobile energy storage vehicle; k,t is the moving distance of the kth mobile energy storage vehicle in period t;

[0010] S2: Establish a mobile energy storage operator model with the objective function:

[0011]

[0012] Where cpre is the unit electricity cost of mobile energy storage;

[0013] S3: Introducing the KKT condition, the objective function of the distribution network operator model is transformed into:

[0014]

[0015] Where μ 2,k,t 、μ 4,k,t 、μ 5,k,t and μ 6,k,t is the dual variable corresponding to the corresponding inequality constraint in the mobile energy storage operator model; and are the maximum charging and discharging power of the kth mobile energy storage vehicle respectively; and are the minimum and maximum charge states of the kth mobile energy storage vehicle respectively; λ k,t is the dual variable corresponding to the corresponding equality constraint in the mobile energy storage operator model; is the initial state of charge of the kth mobile energy storage vehicle;

[0016] S4: Taking into account the KKT conditions and the constraints of the distribution network operator model, the objective function obtained by transforming the distribution network operator model is solved to obtain a game equilibrium solution. The game equilibrium solution at least includes the optimal electricity price strategy of the distribution network operator, the optimal charging, discharging and mobility strategy of the mobile energy storage operator, and the recovery status of the load at each distribution network node.

[0017] Furthermore, the KKT conditions include:

[0018] Equality conditions:

[0019]

[0020] Gradient conditions:

[0021]

[0022] Complementary slack conditions:

[0023]

[0024] Where, is the state of charge of the kth mobile energy storage vehicle at time t-1 and t; η c and η d The charging and discharging efficiency of mobile energy storage vehicles; is the Lagrange function of the kth mobile energy storage vehicle; μ 1,k,t 、μ 3,k,t is the dual variable corresponding to the corresponding inequality constraint in the mobile energy storage operator model; 0≤A⊥B≥0 means that at most one of A and B is strictly greater than 0.

[0025] Furthermore, the moving distance of the kth mobile energy storage vehicle in period t is expressed as:

[0026]

[0027] Where y mn,t ∈Y t Y is the shortest calculated distance from traffic network node m to traffic network node n during period t, t is the shortest reduced distance matrix during period t, z mn,k,t ∈Z k,t is the dispatching state of the kth mobile energy storage vehicle in period t, Z k,t is the dispatch matrix of mobile energy storage vehicle k in period t, and w is the number of nodes in the transportation network.

[0028] Compared with the prior art, the present invention has the following beneficial effects:

[0029] 1. Existing approaches to power restoration involving mobile energy storage often employ a single-agent optimization model. The dispatch of mobile energy storage is directly determined by the distribution network, without considering the benefits of mobile energy storage operators as stakeholders. This fails to effectively coordinate the interests of distribution network operators and mobile energy storage operators, resulting in a lack of a profit distribution mechanism and insufficient incentives for mobile energy storage to participate in scheduling. Therefore, a master-slave game approach is adopted. Distribution network operators, as leaders, set incentivized charging and discharging prices to guide mobile energy storage's participation in power restoration, dynamically adjusting to match supply and demand in fault scenarios. Mobile energy storage operators, as followers, maximize their own profits. This effectively addresses the issue of multi-agent interest distribution in power restoration, increases mobile energy storage's enthusiasm for participating in power restoration, and ultimately improves the speed and efficiency of power restoration.

[0030] 2. Traditional models of mobile energy storage dispatch often assume fixed paths and idealized travel times, ignoring the coupled effects of the dynamic congestion characteristics of the transportation network and energy migration efficiency, resulting in a disconnect between dispatch plans and actual road conditions and grid status. This invention, however, considers the spatiotemporal synergy of mobile energy storage, combining it with distributed power sources. This approach uses mobile energy storage to compensate for the spatiotemporal limitations of distributed power sources, effectively addressing the challenges of uneven spatiotemporal energy distribution and the transfer of power between power-deprived and non-powered areas after a disaster. BRIEF DESCRIPTION OF THE DRAWINGS

[0031] Figure 1 This is a schematic diagram of the coupling between the distribution network and the transportation network;

[0032] Figure 2 IEEE-33 node distribution network topology diagram of an embodiment;

[0033] Figure 3 Schematic diagram of various load curves;

[0034] Figure 4 Provide maintenance plans and network reconstruction solutions;

[0035] Figure 5 is the charging and discharging power and moving path of the first mobile energy storage vehicle in scheme 1;

[0036] Figure 6 is the charging and discharging power and moving path of the second mobile energy storage vehicle in scheme 1;

[0037] Figure 7 is the charging and discharging power and moving path of the third mobile energy storage vehicle in Scheme 1. DETAILED DESCRIPTION

[0038] Specific embodiments are given below in conjunction with the accompanying drawings. The specific embodiments are only used to introduce the technical solutions of the present invention in detail and are not intended to limit the scope of protection of the present application.

[0039] The present invention proposes a method for collaborative power supply restoration between mobile energy storage and distribution network based on KKT master-slave game, comprising the following steps:

[0040] S1: Establish a distribution network operator model;

[0041] As the leader in the master-slave game, distribution network operators incentivize mobile energy storage to provide power support services in power-out areas by issuing dynamic electricity prices and movement path instructions, thereby ensuring the power supply of critical loads.

[0042] The objective function of the distribution network operator model is:

[0043]

[0044] Where T represents the total number of time periods included in the fault period; N represents the number of distribution network nodes; ω i is the power loss cost coefficient of distribution network node i; Boolean variable τ i,t Indicates the load pickup status at the distribution network node i during period t, 1 indicates load pickup, and 0 indicates load shedding; is the active power demand of the load at node i in the distribution network during period t; is the active power of the diesel generator at node i in the distribution network during period t; is the power generation cost coefficient of the diesel generator set; and are the charging and discharging power of the kth mobile energy storage vehicle in period t; N k is the number of mobile energy storage vehicles; and are the charging and discharging prices of the kth mobile energy storage vehicle in period t; c fuel is the unit moving cost of the mobile energy storage vehicle; k,t is the moving distance of the kth mobile energy storage vehicle in period t.

[0045] The constraints of the distribution network operator model include: diesel generator output constraints, distributed photovoltaic output constraints, distribution network power flow constraints, distribution network radial topology constraints, distribution network safe operation constraints, charging and discharging price constraints, and mobile energy storage spatiotemporal constraints.

[0046] (1) Diesel generator output constraints

[0047]

[0048] Where, The upper and lower limits of the active power of the diesel generator; Boolean variable The start and stop status of the diesel generator; is the active and reactive power of the diesel generator at node i in the distribution network during period t; It is the upper limit of reactive power of diesel generator.

[0049] (2) Distributed photovoltaic output constraints

[0050]

[0051] Where, is the active power reduction of photovoltaic power generation at node i in the distribution network during period t; and is the active and reactive power output of the photovoltaic power plant at node i in the distribution network during period t; is the photovoltaic grid-connected capacity at node i in the distribution network during period t; δ PV is the maximum power factor angle of photovoltaic output.

[0052] (3) Distribution network flow constraints

[0053] Considering a three-phase symmetrical radial distribution network, the linearization method of second-order cone relaxation and large M relaxation is adopted, and the power flow model is obtained as follows:

[0054]

[0055] Where, P ij,t and Q ij,t They represent the active and reactive power flowing from distribution network node i to distribution network node j during period t; P j,t and Q j,t is the net active and reactive load of the distribution network node j during period t; P ij,t and Q ij,t They represent the active and reactive power flowing from distribution network node i to distribution network node j in period t respectively; L ij,t represents the square of the line current flowing from distribution network node i to distribution network node j during period t; R ij and X ij are the resistance and reactance of line ij respectively; σ j U represents the set of distribution network nodes connected to distribution network node j; i,t and U j,t Respectively represent the voltage amplitude of distribution network nodes i and j during period t; M is a sufficiently large constant; α ij,t Indicates the connection status of line ij during time period t. A value of 1 indicates that the line is connected, and a value of 0 indicates that the line is disconnected. and is the reactive power demand of the load at node j in the distribution network during period t; and are the active and reactive powers of the diesel generator connected to the distribution network node j, respectively; and are the active and reactive power output of the photovoltaic power plant at node j in the distribution network during period t; ε j,k,t represents the access status of the kth mobile energy storage vehicle at the distribution network node j during period t;

[0056] (4) Radial topology constraints of distribution networks

[0057] β ij,t +β ji,t =α ij,t (10)

[0058]

[0059] Where, β ij and β ji is a binary variable associated with line ij, β ij =1 means that the distribution network node j is the parent node of i, β ji =1 means that the distribution network node i is the parent node of j; Ω s is the set of root nodes; Ω u Indicates that except Ω s The set of other nodes outside; Ω i represents the set of nodes connected to the distribution network node i; Indicates the fault status of line ij during period t. A value of 1 indicates that the line is intact, and a value of 0 indicates a line fault.

[0060] (5) Constraints on safe operation of distribution network

[0061]

[0062] Where, P ij,max and Q ij,max are the maximum values ​​of active and reactive power allowed to be transmitted by line ij; U max and U min are the upper and lower limits of the distribution network node voltage respectively; I ij,t is the current of line ij during period t; I max Indicates the maximum current allowed to be transmitted by the line; S ij,max represents the maximum transmission capacity of line ij;

[0063] The feasible region formed in formula (13) is a circular region, which can be linearized by polygonal approximation as follows:

[0064]

[0065] (6) Charge and discharge price constraints

[0066]

[0067] Where, are the upper and lower limits of the charging price respectively; are the upper and lower limits of the discharge price respectively;

[0068] Unlike the pricing strategy during conventional operation and dispatch, when a distribution network fault occurs, a more attractive incentive mechanism should be implemented to promote the participation of mobile energy storage systems. That is, in the fault state, the distribution network can build a more attractive incentive mechanism by raising the upper limit of the mobile energy storage discharge price while ensuring that its charging price is lower than the daily level.

[0069] (7) Temporal and spatial constraints of mobile energy storage

[0070] This paper uses a traffic-informed MESS spatiotemporal scheduling model, divided into a spatiotemporal transfer submodel and an energy dynamic balance submodel, to accurately describe the spatiotemporal transfer and charging / discharging processes of the MESS between isolated distribution network islands after a disaster. The leader uses the MESS spatiotemporal transfer submodel as a constraint to guide MESS movement, helping the MESS find the optimal movement route during power restoration without exposing the distribution network's privacy.

[0071] In the restoration of distribution network faults, the scheduling optimization of MESS is crucial. The scheduling of MESS depends not only on the distance, but also on its state of charge, initial location and real-time traffic conditions. Therefore, it is necessary to establish a geographical coupling relationship between the distribution network nodes and the traffic network nodes, such as Figure 1 Due to factors such as road direction and road conditions, the MESS dispatch path is not completely positively correlated with the route length. Multiple transportation routes exist between each transportation network node, and traffic congestion may make some transportation network nodes unreachable. These factors increase the complexity of MESS scheduling and need to be fully considered in the fault recovery strategy.

[0072] Use the graph to describe the coupling relationship between the transportation network and the distribution network. Assuming that there are w transportation network nodes, considering the road traffic conditions in period t, the transportation network adjacency matrix D in period t is: t Described as:

[0073]

[0074] Where, d mn,t is the calculated distance from transportation network node m to transportation network node n during period t; l mn is the actual distance from transportation network node m to transportation network node n; δ mn,t is the road congestion coefficient from traffic network node m to traffic network node n during period t; v mn,t is the traffic flow from node m to node n in the traffic network during period t; mn It is the traffic flow threshold of the road from traffic network node m to traffic network node n.

[0075] Given that there are usually multiple accessible paths between the departure and destination nodes of the transportation network, the present invention sets the travel routes of all mobile energy storage vehicles to be the shortest paths between the corresponding transportation network nodes. The method for obtaining the shortest path adopts the Floyd algorithm, which continuously iterates the elements in the transportation network adjacency matrix to obtain the shortest reduced distance matrix Y for time period t. t ;

[0076]

[0077] Where y mn,t ∈Y t ; m,n=1,2,...,w is the shortest calculated distance from traffic network node m to traffic network node n in time period t.

[0078] According to the MESS dispatch plan, the dispatch matrix Z of mobile energy storage vehicle k in period t is k,t for:

[0079]

[0080] ε m,k,t =z mm,k,t ≤1 (23)

[0081]

[0082] In the formula, the Boolean variable z mn,k,t is the dispatching state of the kth mobile energy storage vehicle in period t. When m and n are different, z mn,k,t =1 means that the kth mobile energy storage vehicle is in the process of moving from traffic network node m to traffic network node n; when m and n are the same, z mn,k,t =1 means that the kth mobile energy storage vehicle stops at the traffic network node m during period t; ε m,k,t is the stop sign of the kth mobile energy storage vehicle at the traffic network node m during period t. When ε m,k,t =1, indicating that the kth mobile energy storage vehicle stops at the traffic network node m during period t; n,k,t+1 It is the stop flag position of the kth mobile energy storage vehicle at the traffic network node n during the t+1 period.

[0083] Formula (22) indicates that each mobile energy storage vehicle can only have one scheduling state in the same time period; Formula (23) indicates that each mobile energy storage vehicle can only stay at one traffic network node at most in the same time period; Formula (24) indicates that each mobile energy storage vehicle needs at least one time period to move from the previous traffic network node to the next traffic network node.

[0084] Therefore, according to the shortest reduced distance matrix Y t and the scheduling matrix Z t , get the moving distance s of the kth mobile energy storage vehicle in time period tk,t for:

[0085]

[0086] S2: Establish a mobile energy storage operator model;

[0087] As followers in the master-slave game, mobile energy storage operators will respond to the dynamic electricity prices and mobile path instructions issued by distribution network operators, and formulate optimal charging and discharging strategies accordingly to maximize their own profits.

[0088] The objective function of the mobile energy storage operator model is:

[0089]

[0090] Where cpre is the unit cost of mobile energy storage.

[0091] Under the premise of meeting the time and space transfer constraints, MESS uses its energy storage batteries as energy carriers to achieve energy transfer between isolated islands in the post-disaster distribution network. The constraints of the mobile energy storage operator model are the MESS energy balance constraints, which are expressed as:

[0092]

[0093] In the formula, the Boolean variable and are the charging and discharging states of the kth mobile energy storage vehicle during period t; and are the maximum charging and discharging power of the kth mobile energy storage vehicle respectively; is the state of charge of the kth mobile energy storage vehicle in period t; and are the minimum and maximum charge states of the kth mobile energy storage vehicle respectively; η c and η d They are the charging and discharging efficiency of the mobile energy storage vehicle respectively.

[0094] S3: Through the Karush-Kuhn-Tucke (KKT) condition, the two-level optimization problem of the master-slave game is converted into a single-level optimization problem;

[0095] The master-slave game between the distribution network and the mobile energy storage system can be viewed as a two-level optimization problem. By introducing the KKT condition, the mobile energy storage operator model is equivalently transformed into a set of constraints for the leader, thereby converting the two-level optimization problem into a single-level optimization problem with complementary constraints, effectively reducing the complexity of solving the model.

[0096] According to the mobile energy storage operator model, the Lagrange function of the kth mobile energy storage vehicle is obtained as:

[0097]

[0098] Where μ 1,k,t 、μ 2,k,t 、μ 3,k,t 、μ 4,k,t 、μ 5,k,t and μ 6,k,t is the dual variable corresponding to the inequality constraint in the mobile energy storage operator model; k,t ; t=1,2,...,T is the dual variable corresponding to the equation constraint in the mobile energy storage operator model.

[0099] The KKT conditions of the kth mobile energy storage vehicle are as follows:

[0100] Equality conditions:

[0101]

[0102] Gradient conditions:

[0103]

[0104] Complementary slack conditions:

[0105]

[0106] Where 0≤A⊥B≥0 is the complementary relaxation condition, which means that at most one of A and B is strictly greater than 0;

[0107] Since the complementary relaxation condition is nonlinear, the large M method is used to introduce auxiliary variables to linearize it. Therefore, the complementary relaxation condition can be expressed as:

[0108]

[0109] Where, ρ 1,k,t , ρ 2,k,t , ρ 3,k,t , ρ 4,k,t , ρ 5,k,t and ρ 6,k,t Both are Boolean variables.

[0110] because and It is in the form of variable multiplication and is difficult to solve directly. According to the strong duality theory, the optimal solution of the original problem and its dual problem is equal. Therefore, the objective function of the mobile energy storage operator model is equivalent to:

[0111]

[0112] Where, is the initial state of charge of the kth mobile energy storage vehicle;

[0113] By using the dual problem of the lower level problem, the objective function of the distribution network operator model is directly transformed into:

[0114]

[0115] At this point, the two-layer optimization problem is transformed into a single-layer optimization problem.

[0116] S4: Taking into account the KKT conditions and the constraints of the distribution network operator model, a solver (such as Gurobi, CPLEX, etc.) is used to solve the objective function obtained by transforming the distribution network operator model to obtain a game equilibrium solution; this game equilibrium solution includes the distribution network operator's optimal electricity price strategy, the mobile energy storage operator's optimal charging, discharging, and mobility strategies, and the recovery status of the load at each distribution network node.

[0117] Example

[0118] This embodiment is verified by taking the IEEE-33 node distribution network as an example. Figure 2 The topology diagram of the IEEE-33 node distribution network contains 5 tie lines. The installation information of photovoltaic and diesel generators is shown in Table 1. The node voltage of the distribution network is set to 1.03pu, and the upper and lower limits of the node voltage of the distribution network are 1.05pu and 0.95pu respectively. The distribution network is equipped with three mobile energy storage vehicles. The maximum capacity of each mobile energy storage vehicle is 300kw·h, and the maximum charging and discharging power is 150kw / h. There are 8 MESS accessible nodes in the distribution network, which can realize energy exchange between MESS and the distribution network. They are located at nodes 4, 10, 13, 18, 21, 23, 27, and 33 respectively. Node 29 is selected to connect to the transportation network to realize its coupling with the distribution network, and the unit movement cost c of MESS in the transportation network is set. fuel The unit electricity cost is 5 yuan / km, c pre The cost is 0.2 yuan / kw·h. In the initial state, all MESSs are on standby at node 33, and the initial state of charge of each MESS is set to 80%. 0.03 yuan / (kw·h) 2 , The node load of the distribution network is divided into three types: industrial load, commercial load and residential load. The various load curves are as follows: Figure 3 The load types of each node and the corresponding load power outage costs are shown in Table 2 below.

[0119] Table 1 PV and diesel generator installation information for the IEEE 33-node distribution network

[0120]

[0121] Table 2 Load types and corresponding load power outage costs

[0122]

[0123] Assume that an extreme disaster occurs at 11:00. In addition to the interruption between the upper main grid and the distribution network, it also causes multiple line faults (lines 2-3, 3-4, 6-7, 8-9, 17-18, 28-29, and tie line switch 25-29). The fault recovery time lasts for 6 hours, and the power restoration time step Δt is set to 30 minutes. To simulate the load recovery scenario more realistically, the maintenance plan and network reconstruction plan of the distribution network during the fault period are considered. The reconstruction plan for different time periods is as follows: Figure 4 shown.

[0124] To highlight the advantages of the proposed solution in terms of speed and cost-effectiveness, three schemes are provided: Scheme 1: the proposed solution; Scheme 2: only considers the dynamic coordination of fault repair and network reconstruction, without the MESS participating in post-disaster load recovery; Scheme 3: considers the dynamic coordination of fault repair and network reconstruction, while also incorporating the MESS into post-disaster recovery, but only performs a single search for the optimal access point, i.e., a single scheduling operation. All other settings are consistent with the proposed solution. The load recovery and cost-effectiveness of each scheme are shown in Table 3.

[0125] Table 3 Load recovery and economic indicators

[0126]

[0127] As shown in Table 3, the optimization results of Scheme 1 reduce the total cost by 8.8% compared to Scheme 2 and by 2.6% compared to Scheme 3, demonstrating significant economic superiority. In terms of load recovery, Scheme 1 also achieves better load recovery than both Schemes 2 and 3, demonstrating the significant advantages of the present method in both cost efficiency and recovery effectiveness.

[0128] The charging and discharging power and moving paths of the first, second and third mobile energy storage vehicles in Scheme 1 are as follows: Figure 5 、 6, 7. Taking the first mobile energy storage vehicle as an example, after the fault occurred, it departed from its initial location and headed for node 23 to provide power support. Between 12:00 and 1:30 PM, it released a total of 189 kW·h for power support. At 2:00 PM, the faults on lines 1-2 and 2-3 were resolved by maintenance personnel. Through dynamic network reconfiguration, power was restored to node 23, and the first mobile energy storage vehicle began charging at node 23. When the charge reached 76%, it departed for node 18. Upon arrival at node 18, the first mobile energy storage vehicle operated at full power until all loads were restored at 4:00 PM, at which point the first mobile energy storage vehicle concluded its power support process. The dispatching process of the first mobile energy storage vehicle demonstrates that mobile energy storage vehicles can achieve dual-dimensional coordination in time, space, and energy. Specifically, with the goal of prioritizing the restoration of critical loads, power originally allocated to low-priority loads is transferred to critical loads in the isolated area, improving overall social recovery benefits and achieving optimal spatial and temporal allocation of energy.

[0129] Table 4 Benefits of mobile energy storage operators

[0130]

[0131] Table 4 shows the benefits of mobile energy storage operators. As can be seen, through the strategy proposed in this paper, mobile energy storage operators can achieve a profit of 650.9 yuan during the power restoration period. This fully verifies the effectiveness of the master-slave game mechanism. It not only ensures that distribution network operators maximize the benefits of load restoration through mobile energy storage scheduling, but also ensures that mobile energy storage operators have the economic driving force to participate in coordinated restoration, forming a virtuous interaction that is mutually beneficial and win-win for both supply and demand sides.

[0132] Any matters not described in the present invention are applicable to the prior art.

Claims

1. A method for collaborative power supply restoration between mobile energy storage and distribution network based on KKT master-slave game, characterized in that: The following steps are involved: S1: Establish a distribution network operator model with the objective function as follows: Where T represents the total number of time periods included in the fault period; N represents the number of distribution network nodes; ω i is the power loss cost coefficient of distribution network node i; τ i,t represents the load picking status at node i in the distribution network during period t; is the active power demand of the load at node i in the distribution network during period t; is the active power of the diesel generator at node i in the distribution network during period t; is the power generation cost coefficient of the diesel generator set; and are the charging and discharging power of the kth mobile energy storage vehicle in period t; N k is the number of mobile energy storage vehicles; and are the charging and discharging prices of the kth mobile energy storage vehicle in period t; c fuel is the unit moving cost of the mobile energy storage vehicle; k,t is the moving distance of the kth mobile energy storage vehicle in period t; S2: Establish a mobile energy storage operator model with the objective function: Where cpre is the unit electricity cost of mobile energy storage; S3: Introducing the KKT condition, the objective function of the distribution network operator model is transformed into: Where μ 2,k,t 、μ 4,k,t 、μ 5,k,t and μ 6,k,t is the dual variable corresponding to the corresponding inequality constraint in the mobile energy storage operator model; and are the maximum charging and discharging power of the kth mobile energy storage vehicle respectively; and are the minimum and maximum charge states of the kth mobile energy storage vehicle respectively; λ k,t is the dual variable corresponding to the corresponding equality constraint in the mobile energy storage operator model; is the initial state of charge of the kth mobile energy storage vehicle; S4: Taking into account the KKT conditions and the constraints of the distribution network operator model, the objective function obtained by transforming the distribution network operator model is solved to obtain a game equilibrium solution. The game equilibrium solution at least includes the optimal electricity price strategy of the distribution network operator, the optimal charging, discharging and mobility strategy of the mobile energy storage operator, and the recovery status of the load at each distribution network node.

2. The method for collaborative power supply restoration between mobile energy storage and distribution network based on KKT master-slave game according to claim 1 is characterized in that: The KKT conditions include: Equality condition: Gradient conditions: Complementary slack conditions: Where, is the state of charge of the kth mobile energy storage vehicle at time t-1 and t; η c and η d The charging and discharging efficiency of mobile energy storage vehicles; is the Lagrange function of the kth mobile energy storage vehicle; μ 1,k,t 、μ 3,k,t is the dual variable corresponding to the corresponding inequality constraint in the mobile energy storage operator model; 0≤A⊥B≥0 means that at most one of A and B is strictly greater than 0.

3. The method for coordinated power supply restoration of mobile energy storage and distribution network based on KKT master-slave game according to claim 1 or 2, characterized in that: The moving distance of the kth mobile energy storage vehicle in period t is expressed as: Where y mn,t ∈Y t Y is the shortest calculated distance from traffic network node m to traffic network node n during period t, t is the shortest reduced distance matrix during period t, z mn,k,t ∈Z k,t is the dispatching state of the kth mobile energy storage vehicle in period t, Z k,t is the dispatch matrix of mobile energy storage vehicle k in period t, and w is the number of nodes in the transportation network.

4. The method for collaborative power supply restoration between mobile energy storage and distribution network based on KKT master-slave game according to claim 1 is characterized in that: The constraints of the distribution network operator model include: diesel generator output constraints, distributed photovoltaic output constraints, distribution network flow constraints, distribution network radial topology constraints, distribution network safe operation constraints, charging and discharging price constraints, and mobile energy storage spatiotemporal constraints.

Images