Power system recovery partition stochastic optimization model solving method and system

Abstract

The invention relates to a power system recovery partition stochastic optimization model solving method and system, and the method comprises the steps: taking the maximum conventional unit power generation amount, new energy power generation amount and load recovery amount of a system in a to-be-recovered period as objective functions; constructing a stochastic optimization model for unified modeling of the system partition decision and the subsystem recovery decision under the participation of the new energy electric field; the optimal recovery decision in the system is expressed as a linear function of partition decision variables, variables of the stochastic optimization model are simplified to only contain the partition decision variables, and a decoupled system partition decision model and a decoupled system recovery decision model are obtained; solving a system recovery decision model to calculate an optimal recovery scheme under the conditions of a given new energy output scene and a partition scheme; after calculation of all scenes and all partition schemes is completed, a calculation result is substituted into the system partition decision model, and an approximate optimal system partition scheme is obtained through calculation. And on the premise of ensuring the optimality and feasibility of the partitioning scheme, the solving speed of the model is greatly improved.

Description

Technical Field

[0001] The present invention relates to the technical field of rapid restoration of electric power systems, and in particular to a method and system for solving a random optimization model of restoration partitions of an electric power system. Background Art

[0002] Black start technology is a key means to ensure that the power system can restore power after a large-scale or full-network power outage. As the penetration rate of new energy in the power system continues to increase, the uncertainty and volatility of output have brought new challenges to black start technology. Since there are multiple black start power sources in the power grid, the partition recovery strategy has become an important strategy for rapid system recovery. It divides the power system into multiple relatively independent sub-areas based on the distribution of units with black start capabilities, and each partition (i.e., sub-area) is restored independently and in parallel, thereby greatly improving the system's recovery speed. At present, there are usually two ways to model the partition recovery strategy:

[0003] The first is to model the partition and recovery separately, and add some modeling indicators that are conducive to system recovery when modeling the partition, such as black start capability, partition size, and grid compactness within the partition. However, there are certain limitations. For example, most of them only consider the balance of component distribution or the minimum mismatch power between the power generation capacity and load demand of each partition after the system is partitioned. The impact of the recovery process such as the unit startup time limit and characteristics is not considered, making it impossible for the partition scheme to ensure that the recovery time of each partition is basically the same, resulting in the overall system recovery time not being significantly improved.

[0004] The second is centralized modeling, which is to unify the modeling of system partitioning and recovery, thus taking into account the impact of each partition recovery process on the partition, and approximately ensuring the consistency of the actual recovery time of each partition. This makes the recovery of each partition subsystem more coordinated and more efficient. However, the optimization model contains a large number of partition and recovery decision variables at the same time, which greatly increases the complexity of the model and the difficulty of solving. The calculation time is often very long, so it is only suitable for solving small-scale systems. Therefore, how to improve the solution speed of this type of model still needs to be improved and explored. Summary of the invention

[0005] In view of the deficiencies in the prior art, the present invention provides a method and system for solving a random optimization model of power system restoration partitions, so as to achieve rapid and effective solution of the optimization model.

[0006] The technical solution adopted by the present invention is as follows:

[0007] The present invention relates to a method for solving a random optimization model of a power system restoration partition, comprising:

[0008] Under the system constraints, taking the maximum power generation of conventional units, new energy power generation and load recovery during the recovery period as the objective function, an optimization model for unified modeling of system partition decision and subsystem recovery decision with the participation of new energy power field is constructed;

[0009] The optimal recovery decision in the system is expressed as a linear function of the partition decision variables, thereby simplifying the variables of the stochastic optimization model to include only the partition decision variables, and obtaining a decoupled system partition decision model and a system recovery decision model;

[0010] The optimal restoration decision includes the optimal values ​​of restoration decision variables of conventional units, new energy power plants and loads at the nodes to be restored;

[0011] The objective function of the system partition decision model is the same as that of the stochastic optimization model, and the constraints include partition recovery decoupling constraints and the first part of the system constraints;

[0012] The objective function of the system recovery decision model is the same as that of the stochastic optimization model, and the constraint conditions include the remaining conditions of the system constraint conditions except the first part of conditions;

[0013] Solving the system partition decision model and the system recovery decision model includes:

[0014] Solve the system recovery decision model to calculate the optimal recovery plan for conventional units, renewable energy power plants and loads in a certain period of time under given renewable energy output scenarios and zoning plans; after completing the calculation of all scenarios and all zoning plans, substitute the calculation results into the system zoning decision model to calculate and obtain an approximately optimal system zoning plan.

[0015] Further technical solutions are:

[0016] The objective function of the stochastic optimization model is:

[0017]

[0018] Where f is the objective function value; n k is the number of new energy prediction error scenarios; n t is the number of time periods during the system recovery process; p k is the probability of new energy prediction error scenario k; n g 、n r 、n d are the number of conventional units to be restored, the number of new energy power plants to be restored, and the number of loads to be restored in the system; a1, a2, and a3 are the weight coefficients of the relative importance of the three parts when the power outage losses of conventional units, new energy power plants, and loads in the objective function are minimized during the restoration period, and a1+a2+a3=1; Pk,g,t , P k,r,t , P k,d,t is the active output of conventional unit g, renewable energy power plant r, and active demand of load d at time t under renewable energy prediction error scenario k; Δt is the duration of each recovery period.

[0019] The method of expressing the optimal recovery decision in the system as a linear function of the partition decision variables includes:

[0020] The random optimization model is simplified to obtain a simplified expression model, and the objective function expression of the simplified expression model is:

[0021]

[0022] The constraint expression of the simplified expression model includes only the constraint related to z The constraint g2(u)=0 only related to u, and and u coupling constraints in, represents the partition decision variable of the node to be restored in the system; u represents the restoration decision variable of the conventional unit, new energy power field and load on the node to be restored in the system;

[0023] According to the simplified expression model, we can obtain the given and The optimal value of u under the condition Its expression is as follows:

[0024]

[0025] Will Substituting back the simplified expression model, the equivalent model is obtained as follows:

[0026]

[0027] In the equivalent model and The implicit mapping relationship between them is simplified into an explicit mapping relationship, thereby simplifying the equivalent model, so that the recovery decision variables in the stochastic optimization model are simplified to only include the system partition decision variables;

[0028] The explicit mapping relationship is:

[0029]

[0030] in, for Optimal restoration plan for conventional units, new energy power plants and loads at mid-node i; is the given value of z when all nodes to be recovered belong to partition m, representing the partition scheme; Indicates that in a given partitioning scheme Optimal restoration plan for conventional units, new energy power plants and loads at the nodes to be restored; Indicated in The optimal restoration plan for conventional units, new energy power plants and loads at the node i to be restored; i,m A 0-1 variable indicating whether the node i to be restored belongs to partition m. A value of 1 indicates that the node i to be restored belongs to partition m, otherwise it does not belong to partition m; n i 、n m They are the number of nodes and partitions to be recovered in the system, respectively.

[0031] The partition recovery decoupling constraints include:

[0032]

[0033] Among them, u k,g,t 、u k,r,t 、u k,d,t They are the recovery plans of conventional unit g, renewable energy power plant r and load d in time period t under renewable energy output scenario k; and Respectively represent the given new energy output scenario k and partition scheme Under the condition of , the optimal recovery plan of conventional units g, new energy power field r and load d in time period t is obtained by solving the system recovery decision model; G(i), R(i), and D(i) are the sets of conventional units, new energy power fields and loads connected to node i, respectively.

[0034] The solving of the system partition decision model and the system recovery decision model specifically includes:

[0035] S1. Initialize the given new energy output scenario k=1 and partition m=1;

[0036] S2. Given a partitioning scheme Solve the system recovery decision model to calculate and

[0037] S3, let m=m+1, repeat S2 for iterative calculation until m reaches the threshold;

[0038] S4, let k = k + 1, repeat S2 for iterative calculation until k reaches the threshold, and output the calculation result;

[0039] S5. According to the calculation result, solve the system partition decision model to calculate and obtain the approximately optimal system partition solution.

[0040] The first part of the system constraints includes:

[0041] Node planning constraints:

[0042]

[0043] Among them, n i is the number of nodes to be restored in the system; n m is the number of partitions; z i,m A 0-1 variable indicating whether the node i to be restored belongs to partition m. Its value is 1 if the node i to be restored belongs to partition m, otherwise it does not belong to partition m.

[0044] Partition connectivity constraints, which use network flows to ensure grid topology connectivity.

[0045] The remaining conditions of the system constraints except the first part of the conditions include unit recovery constraints;

[0046] The unit recovery constraint includes: converting the maximum technical output curve and the minimum technical output curve in the conventional unit recovery process into linear functions of recovery time respectively, and taking the range between the maximum technical output curve and the minimum technical output curve as the value range of the unit output.

[0047] The remaining conditions in the system constraints except the first part of the conditions also include new energy recovery constraints, which include:

[0048] The electric field can only be started after the node where the new energy electric field is located is powered on, and once it is started, it will not be shut down again during the recovery period;

[0049] Relevant constraints on the active output and recovery time of renewable energy power plants;

[0050] Constraints on the regulation range of reactive power output of new energy power plants.

[0051] The remaining conditions in the system constraints except the first part of the conditions also include:

[0052] Node and line restoration constraints, which include that a branch can be restored to power if at least one of the nodes at both ends of the branch is powered on;

[0053] Load recovery constraints, including the reactive output regulation range of the load;

[0054] Node power balance constraints, including node active and reactive power balance constraints;

[0055] System standby constraints;

[0056] Branch flow constraints.

[0057] The invention also provides a system for executing the method.

[0058] The beneficial effects of the present invention are as follows:

[0059] Aiming at the optimization problem of power system partition restoration under the participation of new energy electric fields, the present invention proposes a random optimization model of system partition and restoration integration based on random planning and a corresponding solution method, which greatly improves the solution speed of the model while ensuring the optimality and feasibility of the partition scheme. It solves the shortcomings of the existing system partition and restoration integration decision model, which has a slow solution speed and can only be adapted to small-scale systems.

[0060] The present invention proposes a decoupling and coordination solution strategy, which is to approximately simplify the complex relationship between partition decisions and recovery decisions into a linear relationship to achieve the decoupling of the problem. The decoupled unified decision model is decomposed into independent partition decision and recovery decision models. Through the interactive iteration between the two models, a fast and effective solution is achieved, which greatly reduces the computational complexity. At the same time, the interactive coordination between the decoupled partition decision and the recovery decision allows the partition decision to approximately consider its impact on the subsequent recovery process, thereby improving the rationality of the partition scheme. It provides an efficient, practical and adaptable solution to the problem of partition restoration of power systems with the participation of new energy power fields, and can provide theoretical guidance and reference for the formulation of partition schemes for actual systems.

[0061] Other features and advantages of the present invention will be set forth in the following description or may be learned by practicing the present invention. BRIEF DESCRIPTION OF THE DRAWINGS

[0062] Figure 1 The figure is a flow chart of a method according to an embodiment of the present invention.

[0063] Figure 2 It is a schematic diagram of maximum and minimum technical output curves during the conventional unit recovery process involved in the unit recovery constraint in the embodiment method of the present invention.

[0064] Figure 3 The figure is a schematic diagram of a decoupling solution strategy for a partition decision model and a recovery decision model in a method according to an embodiment of the present invention.

[0065] Figure 4 The wind power and photovoltaic output curves within 24 hours simulated in the verification experiment of the embodiment of the present invention are shown. DETAILED DESCRIPTION

[0066] The specific implementation of the present invention is described below with reference to the accompanying drawings.

[0067] See also Figure 1 A method for solving a random optimization model of a power system restoration partition in this embodiment includes the following steps:

[0068] 1. Under the system constraints, taking the maximum power generation of conventional units, power generation of new energy and load recovery during the recovery period as the objective function, an optimization model for unified modeling of system partition decision and subsystem recovery decision with the participation of new energy power field is constructed;

[0069] 2. Expressing the optimal recovery decision in the system as a linear function of the partition decision variables, thereby simplifying the variables of the stochastic optimization model to include only the partition decision variables, and obtaining a decoupled system partition decision model and a system recovery decision model;

[0070] The optimal restoration decision includes the optimal values ​​of restoration decision variables of conventional units, new energy power plants and loads at the nodes to be restored;

[0071] The objective function of the system partition decision model is the same as that of the stochastic optimization model, and the constraints include partition recovery decoupling constraints and the first part of the system constraints;

[0072] The objective function of the system recovery decision model is the same as that of the stochastic optimization model, and the constraint conditions include the remaining conditions of the system constraint conditions except the first part of conditions;

[0073] 3. Solving the system partition decision model and the system recovery decision model, including:

[0074] Solve the system recovery decision model to calculate the optimal recovery plan for conventional units, renewable energy power plants and loads in a certain period of time under given renewable energy output scenarios and zoning plans; after completing the calculation of all scenarios and all zoning plans, substitute the calculation results into the system zoning decision model to calculate and obtain an approximately optimal system zoning plan.

[0075] The optimization model established in this embodiment is a stochastic optimization integrated model of system partitioning and recovery decision taking into account the uncertainty of the output of the new energy power field, which can ensure the feasibility and optimality of the partitioning scheme. In order to avoid the difficulty in solving the optimization model of unified modeling of system partitioning decision and subsystem recovery decision, a decoupling coordination solution strategy is proposed, that is, the complex relationship between the partitioning decision and the recovery decision is approximately simplified to a linear relationship, so that the partitioning decision and the recovery decision in the integrated model are decoupled, and a mutually independent partitioning decision model and recovery decision model are obtained. Through the interactive solution between the two models, the optimal recovery plan for conventional units, new energy power fields and loads in the solution period and the approximate optimal system partitioning plan are obtained, which significantly reduces the computational complexity and improves the computational efficiency.

[0076] Among them, the objective function of the stochastic optimization model is:

[0077]

[0078] Where f is the objective function value; n k is the number of new energy prediction error scenarios; n t is the number of time periods during the system recovery process; p k is the probability of new energy prediction error scenario k; n g 、n r 、n d are the number of conventional units to be restored, the number of new energy power plants to be restored, and the number of loads to be restored in the system; a1, a2, and a3 are the weight coefficients of the relative importance of the three parts when the power outage losses of conventional units, new energy power plants, and loads in the objective function are minimized during the restoration period, and a1+a2+a3=1; P k,g,t , P k,r,t , P k,d,t is the active output of conventional unit g, renewable energy power plant r, and active demand of load d at time t under renewable energy prediction error scenario k; Δt is the duration of each recovery period. It can be understood that the conventional units in this application are non-renewable energy units, including coal-fired and gas-fired units.

[0079] The system constraints include:

[0080] The first constraint is the node partition constraint:

[0081]

[0082] Among them, n i is the number of nodes to be restored in the system; n m is the number of partitions; z i,m A 0-1 variable indicating whether the node i to be restored belongs to partition m. Its value is 1 if the node i to be restored belongs to partition m, otherwise it does not belong to partition m.

[0083] Among them, formula (2) ensures that each partition contains at least one node, namely the black start power supply node; formula (3) shows that the node in the system belongs to and only belongs to one partition.

[0084] The second constraint is the partition connectivity constraint, which includes the constraints related to ensuring the topological connectivity of the power grid by using network flow. The specific principle will not be described in detail, and only the specific expression is given as follows:

[0085]

[0086] f i,j,m -Me i,j,m ≤0,l ij ,l ji =1,2,…,n l ,m=1,2,…,n m (5)

[0087] f j,i,m =0,i∈I b ,l ij ,l ji =1,2,…,n l ,m=1,2,…,n m (6)

[0088]

[0089] Among them, n l is the number of branches in the system; I b is the set of black start power supply nodes; L(i) is the set of branches connected to node i; M is a sufficiently large positive number; e i,j,m Indicates whether the directed arc from node i to node j belongs to partition m. If its value is 1, the directed arc is in partition m, otherwise it is not in partition m; f i,j,m is the size of the network flow from node i to node in partition m;

[0090] Formula (4) means that when both nodes i and j are in partition m and there is a branch l between nodes i and j ij When , the directed arc from node i to node j belongs to partition m;

[0091] Formula (5) indicates that when nodes i and j are both in partition m and there is a branch l between nodes i and j ij When , the network flow can flow between node i and node j;

[0092] Formula (6) indicates that the black start power supply node only serves as the source of network flow, only provides network flow, and does not consume network flow;

[0093] Formula (7) gives the relationship between the amount of network flow provided and consumed within a partition, that is, the size of the network flow provided by the source point is equal to the total number of nodes in the partition minus 1;

[0094] Formula (8) ensures that all nodes except the black start power supply node satisfy Kirchhoff's first law, that is, the total amount of network flow flowing into a node minus the total amount flowing out of the node is equal to the unit network flow;

[0095] Formula (9) ensures that at least one unit of network flow flows into any node in the partition.

[0096] The third constraint is node and line recovery constraint:

[0097]

[0098]

[0099] Among them, n tis the number of time periods during the system recovery process; Δt is the duration of a single time period; y i,t,m They represent the branch l in partition m respectively. ij and the power status of node i at time t, where the value is 1 if it is powered, otherwise it is not powered;

[0100] Formula (10) shows that if branch l ij At least one of the two end nodes is powered on, then branch l ij Power can be restored;

[0101] Formula (11) shows that if node i is connected to at least one energized branch, node i can be restored to power;

[0102] Equations (12) and (13) indicate that once a branch or node is powered on, it is not considered that it will lose power again;

[0103] Formula (14) shows that at the beginning of recovery, except for the black start power supply node, the other nodes are not powered;

[0104] Formula (15) shows that when node i belongs to partition m, the node can be powered on in partition m.

[0105] The fourth constraint is the unit recovery constraint, which includes converting the maximum technical output curve and the minimum technical output curve in the conventional unit recovery process into linear functions of the recovery time, and taking the range between the maximum technical output curve and the minimum technical output curve as the value range of the unit output.

[0106] See also Figure 2 , showing the schematic diagram of the minimum and maximum technical output curves. According to the unit output model, by introducing auxiliary variables that characterize the unit recovery state, the maximum and minimum technical output curves during the unit recovery process can be converted into a linear function of the recovery time. The specific derivation process will not be repeated here, and only the specific expression is given:

[0107]

[0108]

[0109] Among them, G i represents the set of conventional units g connected to node i; are the maximum technical output, minimum technical output and starting power requirement of unit g respectively; is the ramp rate of the conventional unit g; are the cold and hot start-up durations of conventional unit g respectively; G is the time it takes for the conventional unit g to change from hot state to cold state without recovery; c , G h, G b They are the collection of cold units, hot units and black start units respectively; Indicates the time that the conventional unit g waits for recovery during the entire recovery process; T g,t,1 T represents the time that the conventional unit g waits for recovery before time t; g,t,2 T represents the time from the time when the minimum technical output curve of the conventional unit g reaches the minimum technical output to the time t; g,t,3 represents the time from the moment when the maximum technical output curve of conventional unit g reaches the maximum technical output to the moment t; w g,t,1 、w g,t,2 、w g,t,3 Auxiliary state variables introduced to characterize the minimum and maximum technical output curves of the unit; w g,t,1 Indicates the grid-connected status of the conventional unit g at time t. Its value is 1, indicating that the unit has been connected to the grid, otherwise it has not been connected to the grid; w g,t,2 Indicates whether the minimum technical output curve of the conventional unit g has reached the minimum technical output point at time t. Its value is 1, indicating that the minimum technical output point has been reached, otherwise it has not been reached; w g,t,3 Indicates whether the maximum technical output curve of the conventional unit g has reached the maximum technical output point at time t. Its value is 1, indicating that it has reached the maximum technical output point, otherwise it has not reached it; v g,t,τ,1 、v g,t,τ,2 、v g,t,τ,3 Auxiliary state variables introduced to characterize the minimum and maximum technical output curves of the unit are used to calculate T g,t,1 、T g,t,2 、T g,t,3 The value range of Q k,g,t represents the reactive power output of conventional unit g at time t under the new energy prediction error scenario k; are the minimum and maximum reactive power outputs of the conventional unit g respectively;

[0110] Formula (16) indicates that the conventional unit can only be started after the node where the unit g is located is powered on, and once started, it will not be considered to be shut down again during the recovery period;

[0111] Formula (17) is the value range of the g output of conventional units;

[0112] Formula (18) is the value range of the startup time of conventional unit g;

[0113] Equations (19)-(21) are the piecewise linear representations of the minimum and maximum technical output curves of conventional unit g;

[0114] Formula (22) is the reactive output adjustment range of the conventional unit g.

[0115] The fifth constraint is the new energy recovery constraint:

[0116]

[0117] Among them, R i represents the set of new energy electric fields r connected to node i; is the predicted active output of the new energy electric field r at time t; is the prediction error of the new energy electric field r at time t under the new energy prediction error scenario k; It indicates the time that the new energy electric field r waits for recovery in the whole recovery process; Q k,r,t It represents the reactive power output of the new energy electric field r at time t under the new energy prediction error scenario k; are the minimum and maximum reactive power output of the new energy electric field r respectively;

[0118] Formula (23) indicates that the electric field can only be started after the node where the new energy electric field r is located is powered on, and once it is started, it will not be shut down again during the recovery period;

[0119] Formula (24) is the relevant constraints on the active output and recovery time of the new energy power field r;

[0120] Formula (25) is the reactive power output adjustment range of the new energy electric field r.

[0121] The sixth constraint, load recovery constraint:

[0122]

[0123] Among them, D i represents the set of loads d connected to node i; is the predicted active power demand of load d at time t; It indicates the time that load d waits for recovery during the entire recovery process; Q k,d,t represents the reactive power demand of load d under the renewable energy prediction error scenario k; is the power factor angle of load d;

[0124] Formula (26) indicates that the load can be restored only after the node where the load d is located is powered on, and once restored, it will not be considered to be removed again during the recovery period;

[0125] Formula (27) is the related constraints of load d’s active power demand and recovery time;

[0126] Formula (28) is the reactive output adjustment range of load d.

[0127] The seventh constraint is the node power balance constraint:

[0128]

[0129] Among them, Pk,i,j,t,m , Q k,i,j,t,m They represent the branch l in partition m under the new energy prediction error scenario k. ij The active power and reactive power flowing from node i to node j in time period t; Equation (29) represents the node active and reactive balance constraints.

[0130] The eighth constraint is system standby constraint:

[0131]

[0132] in, They represent respectively the active positive and negative reserve and reactive positive and negative reserve of conventional unit g at time t under the new energy prediction error scenario k; They represent respectively the active positive and negative reserve and reactive positive and negative reserve of the new energy electric field r at time t under the new energy prediction error scenario k; They are the total active positive and negative standby and reactive positive and negative standby requirements of the system respectively.

[0133] The eighth constraint is branch flow constraint:

[0134]

[0135] Among them, G ij , B ij The elements of the i-th row and j-th column in the system node admittance matrix respectively; V i min and V i max Respectively represent the minimum and maximum voltage amplitude limits of node i; For branch l ij The transmission power limit of V k,i,t,m 、V k,j,t,m They represent the voltage amplitudes of nodes i and j in partition m at time period t under the new energy prediction error scenario k; θ k,i,j,t,m It represents the voltage phase angle difference between nodes i and j in partition m in time period t under the new energy prediction error scenario k;

[0136] Formula (33) is the branch l ij and l ji The branch flow equations;

[0137] Formula (34) is the node voltage constraint in partition m;

[0138] Formula (35) is the value range of the active power flow of branch z in partition m.

[0139] The optimization model established in the first step of this embodiment couples the partition decision and the recovery decision with each other, which makes the calculation extremely difficult and it is difficult to ensure the calculation efficiency of the model in practical applications. Therefore, a decoupling coordination solution strategy is proposed, which includes the following steps:

[0140] The optimization model composed of equations (1)-(35) is simplified to obtain the simplified expression model as shown in equations (36)-(39):

[0141]

[0142] g2(u)=0 (38)

[0143]

[0144] in, Represents the partition decision variable of the node to be restored in the system, which includes z i,m ; u represents the recovery decision variables of conventional units, new energy power plants and loads at the nodes to be restored in the system, which includes u in the above text g,t 、u r,t 、u d,t ; Formula (36) is the objective function of the simplified expression model; Formula (37) is only related to The constraint condition related to u is: and the coupling constraints of u.

[0145] According to the simplified expression model, we can obtain the given The optimal value of u under the condition that g1(z)=0 Its expression is as follows:

[0146]

[0147] Substituting equation (40) back into the simplified expression model, the equivalent model is obtained as follows:

[0148]

[0149] Formula (40) reflects and There is a complex implicit mapping relationship between them. Assume and The complex implicit mapping relationship between can be approximately simplified to an explicit mapping relationship h, for example Then the optimization model (41)-(43) can be simplified to

[0150]

[0151] At this time, the recovery decision variables of the optimization module are simplified, and the model only contains system partition decision variables, and the complexity of the model will be greatly reduced.

[0152] The decoupling coordination solution strategy of this embodiment is to simplify the complex mapping relationship between the system partition decision and the optimal restoration decision of the unit, new energy power field and load at the node to be restored in each subsystem into a linear mapping relationship, that is, the explicit mapping relationship h, and the calculation expression is as follows:

[0153]

[0154] in, for Optimal restoration plan for conventional units, new energy power plants and loads at mid-node i; is the given value of z when all nodes to be recovered belong to partition m, representing the partition scheme; Indicates that in a given partitioning scheme Optimal restoration plan for conventional units, new energy power plants and loads at the nodes to be restored; Indicated in The optimal restoration plan for conventional units, new energy power plants and loads at the node i to be restored; i,m A 0-1 variable indicating whether the node i to be restored belongs to partition m. A value of 1 indicates that the node i to be restored belongs to partition m, otherwise it does not belong to partition m; n i 、n m They are the number of nodes and partitions to be recovered in the system, respectively.

[0155] The basic concept of this simplified strategy of simplifying the complex mapping relationship into a linear mapping relationship in this embodiment is that during the black start recovery process, each partition and subsystem are independent of each other, and the optimal recovery decision of any node to be recovered is only directly affected by the single black start power supply in the partition to which it belongs. Therefore, the strategy of using a single black start power supply to start all nodes to be recovered is adopted, and the optimal recovery plan of each node to be recovered is approximately calculated when the node belongs to different partitions.

[0156] Although this simplified strategy ignores the impact of partition topology changes on the optimal recovery decision of the node to be recovered, sacrificing the optimality of some results, it decouples the partition decision and recovery decision in the optimization model established in the first step. The decoupled unified decision model is decomposed into independent partition decision and recovery decision models, which greatly reduces the computational complexity. The interactive coordination between the decoupled partition decision and recovery decision allows the partition decision to approximately consider its impact on the subsequent recovery process, improving the rationality of the partition scheme.

[0157] The system partition decision model obtained after decoupling is still a random optimization model, and its objective function is still formula (1). The constraints include the black start power supply constraint within the partition, the callable power balance constraint within the partition, and the partition connectivity constraint, that is, the first constraint and the second constraint. In addition, it also includes the partition recovery decoupling constraint:

[0158]

[0159] Among them, u k,g,t 、u k,r,t 、u k,d,t They are the recovery plans of conventional unit g, renewable energy power plant r and load d in time period t under renewable energy output scenario k;

[0160] and Respectively represent the given new energy output scenario k and partition scheme Under the condition of , the optimal recovery plan of conventional unit g, new energy power plant r and load d in time period t, whose value is obtained by solving the system recovery decision model;

[0161] G(i), R(i), and D(i) are the sets of conventional units, new energy power plants, and loads connected to node i, respectively.

[0162] The system recovery decision model obtained after decoupling is a deterministic (non-random) recovery model for a given renewable energy output scenario and a partitioning scheme, and its objective function is formula (1), where the term containing the partitioning decision variable is a constant term under the condition of a given partitioning scheme. The corresponding constraints include constraints related to power transmission path reconstruction, active power constraints of partitioning subsystems, reactive power constraints of partitioning subsystems, power flow constraints of partitioning subsystems, etc., i.e., the third to ninth constraints.

[0163] See also Figure 3 , the solving of the system partition decision model and the system recovery decision model specifically includes:

[0164] S1. Initialize the given new energy output scenario k=1 and partition m=1;

[0165] S2. Given a partitioning scheme Solve the system recovery decision model to calculate and

[0166] S3, let m = m + 1, repeat S2 for iterative calculation until m reaches the threshold n m ;

[0167] S4, let k = k + 1, repeat S2 for iterative calculation until k reaches the threshold n k , output the calculation results;

[0168] S5. According to the calculation result, solve the system partition decision model to calculate and obtain the approximately optimal system partition solution.

[0169] In order to verify the effectiveness of this embodiment, the improved IEEE 39-node system is used as an example to simulate the partition recovery process of the power system after a fault. In the improved IEEE 39-node system, nodes 31 to 37 are connected to conventional units, and the conventional units connected to nodes 31, 35 and 37 are selected as black start units. Nodes 30 and 38 are respectively connected to a wind farm with a capacity of 100MW, and node 39 is connected to a photovoltaic field with a capacity of 100MW. Subsequently, an example of a real large system was used to further verify the superiority of the solution strategy. The computing environment is configured as Intel Core i7-12700K CPU@3.6GHz, 32GB memory, MATLAB programming language, and GUROBI 9.5 optimization solver.

[0170] In order to verify the superiority of the optimization model for unified modeling of system partitioning decision and subsystem recovery decision under the participation of the new energy electric field in this embodiment, this embodiment is compared with a traditional deterministic method. The deterministic method assumes that the new energy output and load demand are known and fixed, ignoring the randomness and volatility of new energy. The feasibility of the partition recovery scheme of the two methods under the condition of new energy output fluctuations is compared. By simulating different new energy output scenarios, the adaptability of the partition recovery schemes generated by the two methods in different scenarios is analyzed.

[0171] Figure 4 The curves of wind power and photovoltaic output within 24 hours are shown, where the bold black line is the predicted power generation curve of new energy, and the colored thin lines are 60 simulated actual power generation curves of new energy. 30 curves were extracted from these 60 curves as samples for building a random programming model. Based on these sample curves, the corresponding partition recovery scheme was generated using the method of this embodiment. In order to comprehensively evaluate the performance of the scheme, not only the scenarios within the sample were tested, but also the scenarios outside the sample were further investigated to verify the adaptability and robustness under the condition of unprecedented new energy output fluctuations.

[0172] Table 1 In-sample scenario evaluation results

[0173]

[0174] Table 2 Out-of-sample scenario evaluation results

[0175]

[0176] Tables 1 and 2 show the evaluation results in the in-sample scenario, including key indicators such as recovery success rate, power outage time, and power outage loss. From the evaluation results of Tables 1 and 2, it can be seen that the method of this embodiment is superior to the traditional deterministic method in key indicators such as recovery success rate, power outage time, and power outage loss, whether in the in-sample or out-of-sample scenario. This shows that the method of this embodiment not only performs well in known scenarios, but also shows stronger adaptability and robustness when facing unprecedented fluctuations in the output of new energy. This shows that the method of this embodiment can effectively deal with the uncertainty of new energy and provide a more advantageous solution to the problem of system partition recovery with the participation of new energy power fields.

[0177] In order to verify the superiority of the decoupled coordination solution strategy of this embodiment, the method of this embodiment is compared with a method of directly solving the unified decision model. The direct solution method is to optimize the partition decision and the recovery decision at the same time in the unified decision optimization model, which often faces high computational complexity when dealing with complex system partition recovery problems. By comparing the key indicators such as the calculation time of the two methods, it is shown that the method of this embodiment has significantly improved the computational efficiency.

[0178] Table 3 Comparison of calculation time and power outage loss

[0179]

[0180] Table 3 shows the comparison between the decoupled coordination solution strategy proposed in this embodiment and the direct solution method in terms of two key indicators: calculation time and power outage loss. The results show that the calculation time of this method is only about 1 / 5 of that of the direct solution method, while the power outage loss is only slightly higher than that of the direct solution method. This shows that the decoupled coordination solution strategy significantly reduces the computational complexity and greatly improves the computational efficiency through the decoupling and interactive coordination mechanism of partition decision and recovery decision, and is suitable for real-time decision-making of large-scale systems. The fast calculation of the method in this embodiment can generate an effective partition recovery plan in a short time, providing an efficient and practical solution to the partition recovery problem of complex systems.

[0181] This embodiment also provides a system for solving a random optimization model of power system restoration partitions, which is used to execute the method for solving a random optimization model of power system restoration partitions.

[0182] Those skilled in the art can understand that the above description is only a preferred embodiment of the present invention and is not intended to limit the present invention. Although the present invention is described in detail with reference to the aforementioned embodiments, those skilled in the art can still modify the technical solutions recorded in the aforementioned embodiments or replace some of the technical features therein by equivalents. Any modification, equivalent replacement, improvement, etc. made within the spirit and principle of the present invention shall be included in the protection scope of the present invention.

Claims

1. A method for solving a random optimization model for power system restoration partitions, characterized in that: include: Under the system constraints, taking the maximum power generation of conventional units, power generation of new energy and load recovery during the recovery period as the objective function, a stochastic optimization model for unified modeling of system partition decision and subsystem recovery decision with the participation of new energy power field is constructed. The optimal recovery decision in the system is expressed as a linear function of the partition decision variables, thereby simplifying the variables of the stochastic optimization model to include only the partition decision variables, and obtaining a decoupled system partition decision model and a system recovery decision model; The optimal restoration decision includes the optimal values ​​of restoration decision variables of conventional units, new energy power plants and loads at the nodes to be restored; The objective function of the system partition decision model is the same as that of the stochastic optimization model, and the constraints include partition recovery decoupling constraints and the first part of the system constraints; The system recovery decision model has the same objective function as the stochastic optimization model, and the constraint conditions include the remaining conditions in the system constraint conditions except the first part of conditions; Solving the system partition decision model and the system recovery decision model includes: Solve the system recovery decision model to calculate the optimal recovery plan for conventional units, renewable energy power plants and loads in a certain period of time under given renewable energy output scenarios and zoning plans; after completing the calculation of all scenarios and all zoning plans, substitute the calculation results into the system zoning decision model to calculate and obtain an approximately optimal system zoning plan.

2. The method according to claim 1, characterized in that The objective function of the stochastic optimization model is: Where f is the objective function value; n k is the number of new energy prediction error scenarios; n t is the number of time periods during the system recovery process; p k is the probability of new energy prediction error scenario k; n g 、n r 、n d are the number of conventional units to be restored, the number of new energy power plants to be restored, and the number of loads to be restored in the system; a1, a2, and a3 are the weight coefficients of the relative importance of the three parts when the power outage losses of conventional units, new energy power plants, and loads in the objective function are minimized during the restoration period, and a1+a2+a3=1; P k,g,t , P k,r,t , P k,d,t is the active output of conventional unit g, renewable energy power plant r, and active demand of load d at time t under renewable energy prediction error scenario k; Δt is the duration of each recovery period.

3. The method according to claim 1, characterized in that The method of expressing the optimal recovery decision in the system as a linear function of the partition decision variables includes: The random optimization model is simplified to obtain a simplified expression model, and the objective function expression of the simplified expression model is: The constraint expressions of the simplified expression model include a constraint g1(z)=0 related only to z, a constraint g2(u)=0 related only to u, and a constraint g3(z,u)=0 coupled with z and u; wherein z represents the partition decision variable of the node to be restored in the system; u represents the restoration decision variable of the conventional unit, the new energy electric field and the load at the node to be restored in the system; According to the simplified expression model, the optimal value of u under the condition of given z and g1(z)=0 is obtained Its expression is as follows: Will Substituting back the simplified expression model, the equivalent model is obtained as follows: stg1(z)=0 In the equivalent model The implicit mapping relationship between y and z is simplified to an explicit mapping relationship, thereby simplifying the equivalent model, so that the recovery decision variables in the stochastic optimization model are simplified to only include the system partition decision variables; The explicit mapping relationship is: in, for Optimal restoration plan for conventional units, new energy power plants and loads at mid-node i; is the given value of z when all nodes to be recovered belong to partition m, representing the partition scheme; Indicates that in a given partitioning scheme Optimal restoration plan for conventional units, new energy power plants and loads at the nodes to be restored; Indicated in The optimal restoration plan for conventional units, new energy power plants and loads at the node i to be restored; i,m A 0-1 variable indicating whether the node i to be restored belongs to partition m. A value of 1 indicates that the node i to be restored belongs to partition m, otherwise it does not belong to partition m; n i 、n m They are the number of nodes and partitions to be recovered in the system, respectively.

4. The method according to claim 3, characterized in that The partition recovery decoupling constraints include: Among them, u k,g,t 、u k,r,t 、u k,d,t They are the recovery plans of conventional unit g, renewable energy power plant r and load d in time period t under renewable energy output scenario k; and Respectively represent the given new energy output scenario k and partition scheme Under the condition of , the optimal recovery plan of conventional units g, new energy power field r and load d in time period t is obtained by solving the system recovery decision model; G(i), R(i), and D(i) are the sets of conventional units, new energy power fields and loads connected to node i, respectively.

5. The method according to claim 4, characterized in that The solving of the system partition decision model and the system recovery decision model specifically includes: S1. Initialize the given new energy output scenario k=1 and partition m=1; S2. Given a partitioning scheme Solve the system recovery decision model to calculate S3, let m=m+1, repeat S2 for iterative calculation until m reaches the threshold; S4, let k = k + 1, repeat S2 for iterative calculation until k reaches the threshold, and output the calculation result; S5. According to the calculation result, solve the system partition decision model to calculate and obtain the approximately optimal system partition solution.

6. The method according to claim 1, characterized in that The first part of the system constraints includes: Node planning constraints: Among them, n i is the number of nodes to be restored in the system; n m is the number of partitions; z i,m A 0-1 variable indicating whether the node i to be restored belongs to partition m. Its value is 1 if the node i to be restored belongs to partition m, otherwise it does not belong to partition m. Partition connectivity constraints, which use network flows to ensure grid topology connectivity.

7. The method according to claim 1, characterized in that The remaining conditions of the system constraints except the first part of the conditions include unit recovery constraints; The unit recovery constraint includes: converting the maximum technical output curve and the minimum technical output curve in the conventional unit recovery process into linear functions of recovery time respectively, and taking the range between the maximum technical output curve and the minimum technical output curve as the value range of the unit output.

8. The method according to claim 7, characterized in that The remaining conditions in the system constraints except the first part of the conditions also include new energy recovery constraints, which include: The electric field can only be started after the node where the new energy electric field is located is powered on, and once it is started, it will not be shut down again during the recovery period; Relevant constraints on the active output and recovery time of renewable energy power plants; Constraints on the regulation range of reactive power output of new energy power plants.

9. The method according to claim 7, characterized in that: The remaining conditions in the system constraints except the first part of the conditions also include: Node and line restoration constraints, which include that a branch can be restored to power if at least one of the nodes at both ends of the branch is powered on; Load recovery constraints, including the reactive output regulation range of the load; Node power balance constraints, including node active and reactive power balance constraints; System standby constraints; Branch flow constraints.

10. A system for performing the method according to any one of claims 1 to 9.

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