Power grid dynamic partition optimization method based on two-stage robustness

Abstract

The invention relates to a power grid dynamic partition optimization method based on two-stage robustness, which comprises the following steps of: establishing a power grid dynamic partition objective function by taking the minimum weighted sum of system power failure loss, tie line power and recovery time difference of each partition in an expected scene and the minimum adjusting quantity of the system partition in the worst scene as an optimization objective; considering the uncertainty of new energy output, and constructing a system partition two-stage robust optimization model; converting the system partition two-stage robust optimization model into a two-layer optimization model comprising an upper layer model and a lower layer model; the upper-layer model is a partition optimization robust model with set partition recovery time; the lower-layer model is a partition approximate recovery model of a set partition scheme and is used for obtaining node recovery time; solving the upper-layer model by adopting a nested column and a constraint generation method algorithm; and solving the lower-layer model by adopting a column and constraint generation method. According to the method, the model solving difficulty is reduced, the optimization result is more practical, and the engineering requirements are met.

Description

Technical Field

[0001] The invention relates to the technical field of power grid partitioning, and in particular to a two-stage robust power grid dynamic partitioning optimization method. Background Art

[0002] With the increase in the number of grid-connected new energy and energy storage stations, the number of power sources with black start capabilities in the power grid is increasing. If these power sources are used as black start power sources, after a large-scale power outage in the power grid, they are first partitioned and restored in parallel, and then synchronized, which can quickly improve the recovery speed of the power grid and greatly reduce the losses caused by large-scale power outages in the power grid. The selection and zoning strategy of black start power sources are crucial to the recovery speed and stability of the power system. Through a reasonable black start power source zoning strategy, the recovery process of the power grid can be accelerated, and the power outage time and losses can be reduced. It helps to avoid excessive current shocks and voltage fluctuations in the power grid during the recovery process, thereby enhancing the stability of the power system. The capacity and characteristics of the black start power source can be better utilized to optimize the configuration and utilization efficiency of power resources. Accordingly, how to use the black start power source as the starting power source for the partition to achieve reasonable zoning of the power grid has become a research topic that has received much attention.

[0003] In the prior art, commonly used partitioning methods include: 1) partitioning methods based on complex network theory; 2) partitioning methods based on intelligent evolutionary optimization algorithms; 3) partitioning methods based on 0-1 mixed integer programming. Most methods based on complex network theory only consider power balance constraints and fail to consider constraints on safe operation of the power grid, such as partition adjustment capacity constraints, which makes the actual feasibility of the partitioning scheme low. The model built by the partitioning method based on the intelligent evolutionary optimization algorithm can meet a variety of partitioning objectives, but its disadvantage is that the solution speed is very slow and it is only suitable for smaller-scale system partitioning. The partitioning method based on 0-1 mixed integer programming has a relatively complete mathematical programming theory, but its disadvantage is that it can only construct an approximate model, and since most of the models built are mixed integer nonlinear optimization models, when the system scale is relatively large, it cannot be guaranteed that the optimal solution will be obtained within a given time. Summary of the invention

[0004] In view of the shortcomings of the prior art, the present invention provides a two-stage robust power grid dynamic partitioning optimization method, the purpose of which is to reduce the difficulty of solving the problem and make the optimization results more practical and meet engineering needs by optimizing model construction and solution methods.

[0005] The technical solution adopted by the present invention is as follows:

[0006] A two-stage robust power grid dynamic partition optimization method includes:

[0007] S1. The optimization goal is to minimize the weighted sum of the power outage loss, the tie line power and the recovery time difference of each partition under the expected scenario, and minimize the adjustment amount of the system partition under the worst scenario. The objective function of the dynamic partition of the power grid is established, the uncertainty of the output of new energy is considered, and a two-stage robust optimization model of the system partition is constructed;

[0008] The objective function of the dynamic partitioning of the power grid is:

[0009]

[0010] In the formula, x ik and lk 0-1 variables indicating whether node i and line l belong to partition k. If it is 1, it means it belongs to partition k, and if it is 0, it means it does not belong to partition k; p r is the actual output of the renewable energy unit connected to node r, T i,k represents the time required for node i to recover from partition k, T k and T m are the time required for partition k and m to complete system recovery respectively; N, N l and N A They represent the total number of nodes, the total number of lines and the number of partitions in the system, i.e. the number of black start power supplies; α1, α2, β1, β2 and γ1 are weight coefficients; P l represents the transmission power of the tie line, Represents x corresponding to the rescheduling phase ik and lk variable;

[0011] like It means that line l is a tie line; P i,d is the active load at node i;

[0012] S2, converting the system partition two-stage robust optimization model into a two-layer optimization model including an upper model and a lower model; the upper model is a partition optimization robust model for a given partition recovery time; the lower model is a partition approximate recovery model for a given partition scheme, used to obtain node recovery time;

[0013] S3, solving the upper model using a nested column and constraint generation algorithm;

[0014] S4. Solve the lower model by using the column and constraint generation method to obtain the network, load and started power source carried by each black start power source, as well as the new energy units without black start capability belonging to the partition.

[0015] Further technical solutions are:

[0016] The constraints of the two-stage robust optimization model for system partitioning include:

[0017] Partition power balance constraints:

[0018]

[0019] Among them, P unb The maximum power imbalance allowed for each partition, P i,g represents the power rating of the conventional unit connected to the bus node i, p r represents the output forecast value of the new energy unit connected to the bus node r; x rk A 0-1 variable indicating whether the rth renewable energy source is connected to partition k;

[0020] Unit starting power constraints:

[0021]

[0022] The above formula indicates that for partition k, the starting power of at least one started unit j should be less than 70% of the upper limit of the black start unit output in the partition, ensuring that at least one non-black start unit in the partition can be successfully started; Ω B represents the set of nodes connected to the black start unit, Ω NB represents the set of nodes not connected to the black start unit, P j,st represents the starting power of the jth started unit; Indicates the upper limit of conventional unit output, x jk A 0-1 variable indicating whether the jth started unit is connected to partition k;

[0023] Node and branch partition constraints, including: each node can only belong to one partition; each branch can only belong to one partition at most. When a branch does not belong to any partition, it means that the branch is a tie line branch; each area must have a black start power supply node; each partition must have at least one started unit;

[0024] The network connectivity constraints constructed based on network flow theory include: defining the black start unit node as the system source point, the unit to be started and the load node as the sink point, the virtual flow only flows on the internal lines of the partition, and there is no flow on the interconnection lines between partitions; except for the black start power supply node, the flow value consumed by other nodes is not less than 1 unit; except for the black start power supply in the partition, other nodes should have inflow flow; the outflow flow of the black start power supply node is equal to the total number of nodes in the area minus 1; the inflow flow of the black start power supply node is 0;

[0025] Uncertain set constraints:

[0026]

[0027] The above formula indicates that the uncertainty of renewable energy output satisfies the budget uncertainty set, where NW is the total number of renewable energy units; and p r are the expected value and predicted value of the output of the new energy unit r respectively; δ r represents the output fluctuation limit of the new energy unit r; Γ represents the uncertain budget value, Ω WT A node set representing a new energy unit; It represents the space composed of the output values ​​of NW new energy units;

[0028] It also includes reactive power regulation reserve capacity constraints and active power reserve capacity constraints.

[0029] The big M method is used to deal with the partition power balance constraint x rk p r Item, introduce auxiliary continuous variables The transformed partition power balance constraints are as follows:

[0030]

[0031] Wherein, M represents a large number.

[0032] The matrix form of the upper model is as follows:

[0033]

[0034] Where x = [x ik ,y lk ,F lk ], F lk represents the virtual traffic on line l in partition k; x * It means that the main problem is to find the solution of x; is a 0-1 variable, is a continuous variable; u=[p r ] is a random variable; C T and W T is the coefficient matrix of the power grid dynamic partition objective function corresponding to the 0-1 variable x, C T The time required for node i to recover from partition k is T i,k Obtained by solving the lower model, it is considered a constant when solving the upper model; A T x+B T y≤E T u+e、D T x+E T y≤d corresponds to the partition power balance constraint inequality after conversion, Represent the corresponding constraints in the rescheduling phase; A T , B T , e and E T , and DT and d are the corresponding coefficient matrices; G T x=g represents the equality constraints in the node and branch partitioning constraints and network connectivity constraints, represents the corresponding constraints in the rescheduling phase; G T and g are the corresponding coefficient matrices; H T x≤h represents an inequality constraint among other constraints except the partition power balance constraint, represents the corresponding constraints in the rescheduling phase, H T and h are the corresponding coefficient matrices.

[0035] The method of solving the upper model by using a nested column and constraint generation algorithm includes:

[0036] Decompose the upper model to get the main problem MP1:

[0037]

[0038] Among them, η is an auxiliary variable, which represents the adjustment amount of the partition decision variable under the worst scenario;

[0039] Decompose the upper model to obtain sub-problem SP1:

[0040]

[0041] Among them, x * To find the optimal solution to the main problem MP1;

[0042] Given a 0-1 variable An initial value Decompose the sub-problem SP1 to obtain the objective function of the main problem MP2 and obtain the corresponding constraints:

[0043]

[0044] Bλ1 r ≥0

[0045] Eλ1 r ≥0

[0046]

[0047] Where, γ is the estimated value of the MP2 objective function of the main problem; is the value of the integer variable x at the rth iteration; is a continuous variable at the rth iteration; λ1 r ,λ2 r are the dual variables of the corresponding Lagrange multipliers at the rth iteration; k is the total number of iterations;

[0048] Solve subproblem SP1 to obtain the objective function of subproblem SP2 and the corresponding constraints:

[0049]

[0050] In the formula, is the worst scenario obtained by solving the main problem MP2 for the rth time;

[0051] Solve the main problem MP1 and subproblem SP1 alternately and iteratively.

[0052] The alternating iterative solution of the main problem MP1 and the sub-problem SP1 includes:

[0053] S351, given the lower bound value LB1 = 0 and the upper bound value UB1 = +∞ of the subproblem SP1, initialize the number of iterations of the subproblem SP1 k1 = 1;

[0054] S352, solve the main problem MP1 and obtain the current optimal solution x * and * , update the upper bound UB1 = min{UB1, C T x * +η};

[0055] S353, main problem MP1 to obtain Substitute into subproblem SP1, solve the inner CCG loop, and find the optimal Update the Nether

[0056] S354, judge |UB1-LB1|≤ε, if the criterion is met, terminate the loop and output the optimal solution and scenario; otherwise, solve the subproblem SP1 to obtain the optimal solution. Substitute into the main problem MP1 and add the following constraints:

[0057]

[0058] k1=k1+1, return to S352.

[0059] Step S353 includes:

[0060] S3531: Given the lower bound LB2 = 0 and the upper bound UB2 = +∞ of the subproblem SP1, initialize the number of iterations k2 = 1, and give a 0-1 variable An initial value

[0061] S3532: Solve the main problem MP2 and obtain the current worst scenario Update upper bound UB2 = γ;

[0062] S3533: Solve the main problem MP2 to obtain Substitute into the subproblem, solve subproblem SP2, obtain the current optimal partition result, and update the lower bound

[0063] S3534: Determine |UB2-LB2|≤ε. If the criterion is met, terminate the loop. Return to the main problem; otherwise, k2=k2+1, and solve the subproblem to obtain the 0-1 variable solution Substitute into the main problem and create new variables λ1 r and λ2 r , and add the following constraints:

[0064]

[0065] Bλ1 r ≥0

[0066] Eλ1 r ≥0

[0067]

[0068] The objective function corresponding to the lower model is:

[0069]

[0070] The lower model divides the system recovery process into N T time periods, each time period is ΔT, and the total recovery time is N S , and assume that the black start unit and the node in the partition are restored at time 0; in the above formula, and They represent the state variables of the i-th bus node, load node and unit node in partition k in time period s, respectively. A value of 1 indicates that the node has been restored, otherwise it indicates that it has not been restored; A state variable indicating whether the line l connecting nodes i and j in partition k is restored in time period s; and represents the active and reactive output of the i-th conventional unit in partition k under the expected scenario; Indicates the actual active output of the i-th renewable energy unit in the k-th partition under the expected scenario; represents the load size that node i in partition k needs to recover; W i,d N represents the load weight coefficient of node i k,BUS Indicates the number of busbar nodes in partition k; Ω T Represents the set composed of each time period; It represents the output of the rth renewable energy unit in the zone k during the time period s;

[0071] It indicates the adjustment amount of the output of conventional units and new energy units as well as the restored load at the node during the re-dispatching stage.

[0072] The constraints of the lower model include: conventional unit output and ramp constraints; new energy unit output constraints; cold and hot start time limit constraints; safe operation constraints; transformer ratio and capacitor input group upper and lower limit constraints; node power balance constraints taking into account AC constraints; equipment recovery state constraints; new energy output uncertainty set; cold load recovery constraints; overvoltage constraints; frequency constraints; adjustment amount constraints.

[0073] The method of solving the lower model by using a column and constraint generation method comprises:

[0074] S41, decomposing the lower model into a main problem and a sub-problem, wherein the main problem determines the component recovery order and the load recovery amount under the expected scenario of new energy output, and the sub-problem seeks the minimum adjustment amount based on the decision of the main problem under the worst scenario of new energy output, so that the recovery plan after adjustment under the worst scenario is feasible;

[0075] S42. Solve the main problem and obtain the optimal solution x of a set of main problems * And the corresponding objective function value And update the iteration lower limit

[0076] S43, the optimal solution x * Substitute into the subproblem and solve the subproblem to obtain a set of optimal solutions to the subproblem And the corresponding objective function value And the worst scene collection And update the iteration limit

[0077] S44. Compare the iteration lower limit and the iteration upper limit. If |UB-LB| / |LB|≤ε, stop the iteration. Otherwise, update as well as Then go to S42 to continue iterative solution; ε is the set threshold.

[0078] The beneficial effects of the present invention are as follows:

[0079] The present invention considers the influence of approximate system recovery on partitioning, improves the two-stage robust dynamic partitioning model of power grid, and makes the model close to the actual engineering needs. The present invention decomposes the partitioning model into a two-layer linear programming problem, solves the problem that mixed integer linear programming with 0-1 variables cannot be dualized, and obtains the worst scenario of uncertainty realization.

[0080] 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

[0081] Figure 1 The figure is a flow chart of a method according to an embodiment of the present invention.

[0082] Figure 2 This is the IEEE39 node system partitioning situation of the embodiment of the present invention.

[0083] Figure 3 This is the IEEE118 node system partitioning situation of the embodiment of the present invention. DETAILED DESCRIPTION

[0084] The specific implementation of the present invention is described below with reference to the accompanying drawings.

[0085] See also Figure 1 , a two-stage robust power grid dynamic partition optimization method according to this embodiment includes:

[0086] S1. Taking the minimum weighted sum of the system power outage loss, the tie line power and the recovery time difference of each partition under the expected scenario and the minimum adjustment amount of the system partition under the worst scenario as the optimization goal, the dynamic partition objective function of the power grid is established, the uncertainty of the output of new energy is considered, and a two-stage robust optimization model of the system partition taking into account the uncertainty of the output of new energy is constructed;

[0087] The objective function of the dynamic partitioning of the power grid is:

[0088]

[0089] In the formula, x ik and lk 0-1 variables indicating whether node i and line l belong to partition k. If it is 1, it means it belongs to partition k, and if it is 0, it means it does not belong to partition k; p r is the actual output of the renewable energy unit connected to node r, T i,k represents the time required for node i to recover from partition k, T k and T m are the time required for partition k and m to complete system recovery respectively; N, N l and N A They represent the total number of nodes, the total number of lines and the number of partitions in the system respectively; α1, α2, β1, β2 and γ1 are weight coefficients; P l represents the transmission power of the tie line, Represents x corresponding to the rescheduling phase ik and lk variable;

[0090] like It means that line l is a tie line; P i,d is the active load at node i;

[0091] Among them, the number of partitions N A That is, the number of black start power supplies. In this embodiment, a partition contains only one black start power supply.

[0092] The constraints of the two-stage robust optimization model for system partitioning in this embodiment include:

[0093] (1) Partition power balance constraints:

[0094]

[0095] The above formula indicates that the power imbalance of each area must be within the threshold range. unb The maximum power imbalance allowed for each partition, P i,g represents the power rating of the conventional unit connected to the bus node i, p r represents the output forecast value of the new energy unit connected to the bus node r; x rk A 0-1 variable indicating whether the r-th renewable energy source is connected to partition k.

[0096] The big M method is used to deal with the partition power balance constraint x rk p r Item, introduce auxiliary continuous variables The transformed partition power balance constraints are as follows:

[0097]

[0098] Wherein, M represents a large number, and in this embodiment, it is 1000.

[0099] (2) Reactive power regulation reserve capacity constraints:

[0100]

[0101] The above two equations indicate that the system should have a certain reactive reserve regulation capacity for voltage control. Q i,g The upper and lower limits of reactive power output of traditional unit i connected to node i; Q i The upper and lower limits of the reactive power output of the reactive power source (comprehensive capacitor and reactor) connected to node i; is the reactive positive reserve and negative reserve capacity requirement of partition k; q i,d Represents the reactive load of node i.

[0102] (3) Active reserve capacity constraints:

[0103] Each partition should have an appropriate amount of active regulation reserve capacity, and its corresponding reserve capacity constraint is:

[0104]

[0105]

[0106] in, and P i,g Indicates the upper and lower limits of the power of unit i; N G and N d Indicates the total number of units and loads in the system; and They represent the active positive reserve and negative reserve factors in partition k, respectively, taking into account the impact of the unit output adjustment rate on the reserve capacity, and the adjustment amount is usually 0.1~0.3P i,g , can take values ​​of 0.3 and 0.1 respectively; and They represent the positive reserve and negative reserve factors of the load demand in partition k respectively. Considering that the positive reserve of the load demand is 8% of the load and the negative reserve is 2% of the load, they can be taken as 0.08 and 0.02 respectively.

[0107] (4) Unit starting power constraints:

[0108]

[0109] The above formula indicates that for partition k, the starting power of at least one started unit j should be less than 70% of the upper limit of the black start unit output in the partition, ensuring that at least one non-black start unit in the partition can be successfully started; Ω B represents the set of nodes connected to the black start unit, Ω NB represents the set of nodes not connected to the black start unit, P j,st represents the starting power of the jth started unit; Indicates the upper limit of conventional unit output, x jk A 0-1 variable indicating whether the j-th activated unit is connected to partition k.

[0110] (5) Node and branch partition constraints, which include:

[0111]

[0112] The above formula means that each node can only belong to one partition;

[0113]

[0114] The above formula indicates that each branch can belong to at most one partition. When a branch does not belong to any partition, it means that the branch is a tie line branch.

[0115]

[0116] The above formula indicates that each area must have a black start power node;

[0117]

[0118] The above formula indicates that there is at least one started unit in each partition.

[0119] (6) Network connectivity constraints based on network flow theory. This embodiment constructs subsystem connectivity constraints based on network flow theory. Traffic is injected from the source point in the system, and the traffic reaches each node through the line. All nodes consume unit traffic. When each node has traffic arriving, the connectivity of the network can be ensured. Specifically, this embodiment defines the black start unit node as the system source point, and the unit to be started and the load node as the sink point. When the network satisfies the network flow constraint, the connectivity of the resulting sub-area can be guaranteed, which is expressed by the following expression:

[0120]

[0121] The above formula indicates that the virtual traffic flows only on the lines within the partition, and there is no traffic on the contact lines between partitions; lk is a 0,1 variable, y lk =1 means F lk ≥1, that is, there is traffic on the line, y lk =0 means F lk =0, that is, there is no flow on the line; where M is a sufficiently large positive number;

[0122]

[0123] The above formula indicates that except for the black start power supply node, the flow value consumed by other nodes is not less than 1 unit; where l(m,i) represents the branch with end point i, and l(i,n) represents the branch with start point i;

[0124]

[0125] The above formula indicates that except for the black start power supply, other nodes in the partition should have inflow traffic;

[0126]

[0127] The above formula indicates that the outflow from the black start power node is equal to the total number of nodes in the area minus 1;

[0128]

[0129] The above formula indicates that the flow rate flowing into the black start power supply node is 0.

[0130] (7) Uncertain set constraints:

[0131]

[0132] The above formula indicates that the uncertainty of renewable energy output satisfies the budget uncertainty set. Among them, NW is the total number of renewable energy units; and p r are the expected value and predicted value of the output of the new energy unit r respectively; δ r represents the output fluctuation limit of the new energy unit r; Γ represents the uncertain budget value, which is usually an integer, Ω WT A node set representing a new energy unit; It represents the space formed by the output values ​​of NW new energy generating units.

[0133] S2, converting the system partition two-stage robust optimization model into a two-layer optimization model including an upper model and a lower model;

[0134] The upper model is a partition optimization robust model for a given partition recovery time, that is, the upper model is a given node power outage time (the time required for node i to recover in partition k, T i,k ) partition optimization problem:

[0135] The lower model is a partition approximate recovery model of a given partitioning scheme, which is used to obtain the node recovery time.

[0136] Among them, the matrix form of the upper model is as follows:

[0137]

[0138] Where x = [x ik ,y lk ,F lk ], F lk represents the virtual traffic on line l in partition k; x * It means that the main problem is to find the solution of x; is a 0-1 variable, is a continuous variable; u=[p r ] is a random variable; C T and W T is the coefficient matrix of the power grid dynamic partition objective function corresponding to the 0-1 variable x, C T The time required for node i to recover from partition k is T i,k Obtained by solving the lower model, it is considered a constant when solving the upper model; A T x+B T y≤E T u+e、D T x+E T y≤d corresponds to the partition power balance constraint inequality after conversion, Represent the corresponding constraints in the rescheduling phase; AT , B T , e and E T , and D T and d are the corresponding coefficient matrices; G T x=g represents the equality constraints in the node and branch partitioning constraints and network connectivity constraints, represents the corresponding constraints in the rescheduling phase; G T and g are the corresponding coefficient matrices; H T x≤h represents an inequality constraint among other constraints except the partition power balance constraint, represents the corresponding constraints in the rescheduling phase, H T and h are the corresponding coefficient matrices.

[0139] The objective function corresponding to the lower model is:

[0140]

[0141] The lower model divides the system recovery process into N T time periods, each time period is ΔT, and the total recovery time is N S , and assume that the black start unit and the node in the partition are restored at time 0; in the above formula, and They represent the state variables of the i-th bus node, load node and unit node in partition k in time period s, respectively. A value of 1 indicates that the node has been restored, otherwise it indicates that it has not been restored; A state variable indicating whether the line l connecting nodes i and j in partition k is restored in time period s; and represents the active and reactive output of the i-th conventional unit in partition k under the expected scenario; Indicates the actual active output of the i-th renewable energy unit in the k-th partition under the expected scenario; represents the load that node i in partition k needs to recover; W i,d N represents the load weight coefficient of node i k,BUS Indicates the number of busbar nodes in partition k; Ω T Represents the set composed of each time period; It represents the output of the rth renewable energy unit in the zone k during the time period s;

[0142] It indicates the adjustment amount of the output of conventional units and new energy units as well as the restored load at the node during the re-dispatching stage.

[0143] The constraints of the lower model include: conventional unit output and ramp constraints; new energy unit output constraints; hot and cold start time constraints; safe operation constraints; transformer ratio and capacitor input group upper and lower limit constraints; node power balance constraints taking into account AC constraints; equipment recovery state constraints; new energy output uncertainty set; cold load recovery constraints; overvoltage constraints; frequency constraints; adjustment constraints. The above constraints are commonly used in solving the grid system partition problem, so they will not be repeated here.

[0144] S3, using a nested column and constraint generation (NC&CG) algorithm to solve the upper model, including:

[0145] S31. Decompose the upper model to obtain the main problem MP1:

[0146]

[0147] Among them, η is an auxiliary variable, which represents the adjustment amount of the partition decision variable in the worst scenario.

[0148] The main problem MP1 is to minimize the system power outage loss, tie line transmission power, partition recovery time difference and partition adjustment amount in the worst scenario under the premise that the constraints in the expected scenario and the superimposed constraints fed back from the sub-problems are satisfied. This model is a MILP problem. Calling the solver to solve the problem can obtain the ownership of all equipment sequences in the system.

[0149] S32. Decompose the upper model to obtain sub-problem SP1:

[0150]

[0151] Among them, x * To find the optimal solution to the main problem MP1.

[0152] Subproblem SP1 contains 0-1 integer variables. This double-layer max-min subproblem cannot be directly converted into a single-layer problem using KKT conditions for solution. Therefore, the nested CC&G algorithm is used for solution, including:

[0153] S33, given 0-1 variable An initial value Decompose the sub-problem SP1 to obtain the objective function of the main problem MP2 and obtain the corresponding constraints:

[0154]

[0155] Bλ1 r ≥0

[0156] Eλ1 r ≥0

[0157]

[0158] Where, γ is the estimated value of the MP2 objective function of the main problem; is the value of the integer variable x at the rth iteration; is a continuous variable at the rth iteration; λ1 r ,λ2 r are the dual variables of the corresponding Lagrange multipliers at the rth iteration; k is the total number of iterations. From the second to sixth expressions above, and the last expression, we can know that The second to fifth equations from the last give the conditions of the complementary relaxation theorem, which ensures that is the optimal solution to the primal and dual problems.

[0159] S34. Solve subproblem SP1 to obtain the objective function of subproblem SP2 and obtain the corresponding constraint conditions:

[0160]

[0161] In the formula, is the worst scenario obtained by solving the main problem MP2 for the rth time.

[0162] Based on the severe scenario obtained from the main problem, the subproblem is solved to obtain the optimal 0-1 variable and continuous variable solution in the current scenario, and a new variable y is introduced r and λ r And add corresponding constraints to the main problem to ensure that the solution generated in the next main problem is feasible in this scenario. When enough bad uncertainty scenarios are eliminated, the solution obtained can be applied to any other scenario. The main and sub-problems are all linear programming problems, which can be solved by calling the solver to obtain the current optimal partitioning solution.

[0163] S35, alternately iteratively solving the main problem MP1 and the subproblem SP1, including:

[0164] S351, given the lower bound value LB1 = 0 and the upper bound value UB1 = +∞ of the subproblem SP1, initialize the number of iterations of the subproblem SP1 k1 = 1;

[0165] S352, solve the main problem MP1 and obtain the current optimal solution x * and * , update the upper bound UB1 = min{UB1, C T x * +η};

[0166] S353, main problem MP1 to obtain Substitute into subproblem SP1, solve the inner CCG loop, and find the optimal Update the Nether

[0167] S354, judge |UB1-LB1|≤ε, if the criterion is met, terminate the loop and output the optimal solution and scenario; otherwise, solve the subproblem SP1 to obtain the optimal solution. Substitute into the main problem MP1 and add the following constraints:

[0168]

[0169] k1=k1+1, return to S352.

[0170] Wherein, step S353 includes:

[0171] S3531: Given the lower bound LB2 = 0 and the upper bound UB2 = +∞ of the subproblem SP1, initialize the number of iterations k2 = 1, and give a 0-1 variable An initial value

[0172] S3532: Solve the main problem MP2 and obtain the current worst scenario Update upper bound UB2 = γ;

[0173] S3533: Solve the main problem MP2 to obtain Substitute into the subproblem, solve subproblem SP2, obtain the current optimal partition result, and update the lower bound

[0174] S3534: Determine |UB2-LB2|≤ε. If the criterion is met, terminate the loop. Return to the main problem; otherwise, k2=k2+1, and solve the subproblem to obtain the 0-1 variable solution Substitute into the main problem and create new variables λ1 r and λ2 r , and add the following constraints:

[0175]

[0176] Bλ1 r ≥0

[0177] Eλ1 r ≥0

[0178]

[0179] S4. The column and constraint generation method (C&CG) is used to solve the lower model to obtain the network, load and started power source carried by each black start power source, as well as the new energy units without black start capability belonging to the partition.

[0180] Specifically include:

[0181] S41, decomposing the lower model into a main problem and a sub-problem, wherein the main problem determines the component recovery order and the load recovery amount under the expected scenario of new energy output, and the sub-problem seeks the minimum adjustment amount based on the decision of the main problem under the worst scenario of new energy output, so that the recovery plan after adjustment under the worst scenario is feasible;

[0182] S42. Solve the main problem and obtain the optimal solution x of a set of main problems * And the corresponding objective function value And update the iteration lower limit

[0183] S43, the optimal solution x * Substitute into the subproblem and solve the subproblem to obtain a set of optimal solutions to the subproblem And the corresponding objective function value And the worst scene collection And update the iteration limit

[0184] S44. Compare the iteration lower limit and the iteration upper limit. If |UB-LB| / |LB|≤ε, stop the iteration. Otherwise, update as well as Then go to S42 to continue iterative solution; ε is the set threshold.

[0185] The elements in the element recovery sequence include units, loads, buses and lines.

[0186] In order to evaluate the rationality of this embodiment, a partition evaluation index system including active balance and reactive balance is constructed to evaluate the effectiveness of the partition scheme of this embodiment. The method of this embodiment obtains the IEEE39 node partition as follows Figure 2 As shown, and compared with the partition method that only considers active power balance (hereinafter referred to as method 1) and the method using the Dijkstra algorithm (hereinafter referred to as method 2), nodes 1, 31 and 34 are selected to connect to the black start units, and wind farms are connected to nodes 3, 5, 14, 16 and 17. The capacity of each wind farm is 100MW, and the uncertainty budget parameter is 5. Table 1 gives other related parameter settings.

[0187] Table 1 Basic parameters of the example

[0188]

[0189] 1) Active power imbalance index: This index is used to measure the active power distribution balance of the partition scheme. The specific expression is:

[0190]

[0191] in is the active power balance of the kth partition, P k,i,g represents the rated active output of the i-th conventional unit in the k-th partition, P k,r represents the output forecast value of the rth renewable energy unit in the kth partition; P k,i,d represents the load of the i-th node in the k-th partition, Indicates the average active power balance of the partition.

[0192] 2) Reactive power imbalance index: This index is used to measure the reactive power distribution balance of the partition scheme. The specific expression is:

[0193]

[0194]

[0195] in is the sum and reactive power balance of the kth partition. k,i,g represents the reactive reserve capacity of the kth partition; q k,i,d represents the reactive load of the ith node in the kth partition, Indicates the average reactive power balance of the partition.

[0196] Based on this, take and The weighted sum of is taken as the power imbalance evaluation index value φ, which is specifically expressed as:

[0197]

[0198] Table 2 Comparison of evaluation indicators of different partitioning schemes for 39-node system

[0199]

[0200] Table 3 Comparison of evaluation indicators of different partitioning schemes for 118-node system

[0201]

[0202] Table 4 Actual grid system partition results

[0203]

[0204]

[0205] Table 5 Evaluation indicators of actual system partitioning scheme

[0206]

[0207] Table 2 gives the comparison results of the evaluation indicators obtained by the three methods of the IEEE39 node system. It can be seen that the active imbalance and reactive imbalance of the method of this embodiment are both smaller than those of Method 1 and Method 2. The reason is that Method 1 groups nodes with close electrical distances together, but does not consider the balance of power distribution, resulting in a large power imbalance index. Method 2 considers the minimum electrical distance between units, the power of the tie line and the network loss in the objective function, but when this method adjusts the partition scheme, it only adjusts the scheme according to the active imbalance, and cannot take into account the reactive power imbalance at the same time, resulting in a large reactive imbalance. The partition optimization model of this embodiment considers both the active power imbalance constraint and the reactive capacity imbalance constraint in the constraints, so that the power imbalance index of the partition scheme obtained is significantly better than the other two methods. The effectiveness and advancement of this method are correspondingly confirmed.

[0208] IEEE118 node system partition comparison Figure 3 In this example, the generators connected to nodes 1, 55 and 69 are used as black start units, and wind turbines are connected to nodes 4, 54 and 104, with an uncertain parameter of 5.

[0209] Table 3 shows the comparison results of the evaluation indicators obtained by the three methods for the IEEE118 node system. It can be seen that the active unbalance and reactive unbalance of this method are better than those of method 1 and method 2, that is, the power distribution is uniform, which reflects the superiority of the model and algorithm of this embodiment.

[0210] The applicability of the method of this embodiment is further verified by using an actual power grid example of a certain province. Table 4 shows the ownership of nodes in each partition. The actual power grid has 419 plants, 134 generators, 275 loads and 559 lines, with voltage levels including 230kV, 525kV and 1050kV; there are 98 new energy plants. Table 5 shows the evaluation index results of the partition scheme obtained by the scheme of this embodiment. It can be seen that all indicators of the partition scheme can meet the requirements of partition recovery.

[0211] 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 two-stage robust power grid dynamic partition optimization method, characterized in that: include: S1. The optimization goal is to minimize the weighted sum of the power outage loss, the tie line power and the recovery time difference of each partition under the expected scenario, and minimize the adjustment amount of the system partition under the worst scenario. The objective function of the dynamic partition of the power grid is established, the uncertainty of the output of new energy is considered, and a two-stage robust optimization model of the system partition is constructed; The objective function of the dynamic partitioning of the power grid is: In the formula, x ik and lk 0-1 variables indicating whether node i and line l belong to partition k. If it is 1, it means it belongs to partition k, and if it is 0, it means it does not belong to partition k; p r is the actual output of the renewable energy unit connected to node r, T i,k represents the time required for node i to recover from partition k, T k and T m are the time required for partition k and m to complete system recovery respectively; N, N l and N A They represent the total number of nodes, the total number of lines and the number of partitions in the system, i.e. the number of black start power supplies; α1, α2, β1, β2 and γ1 are weight coefficients; P l represents the transmission power of the tie line, Represents x corresponding to the rescheduling phase ik and lk variable; like It means that line l is a tie line; P i,d is the active load at node i; S2, converting the system partition two-stage robust optimization model into a two-layer optimization model including an upper model and a lower model; the upper model is a partition optimization robust model for a given partition recovery time; the lower model is a partition approximate recovery model for a given partition scheme, used to obtain node recovery time; S3, solving the upper model using a nested column and constraint generation algorithm; S4. Solve the lower model by using the column and constraint generation method to obtain the network, load and started power source carried by each black start power source, as well as the new energy units without black start capability belonging to the partition.

2. The method according to claim 1, characterized in that The constraints of the two-stage robust optimization model for system partitioning include: Partition power balance constraints: Among them, P unb The maximum power imbalance allowed for each partition, P i,g represents the power rating of the conventional unit connected to the bus node i, p r represents the output forecast value of the new energy unit connected to the bus node r; x rk A 0-1 variable indicating whether the rth renewable energy source is connected to partition k; Unit starting power constraints: The above formula indicates that for partition k, the starting power of at least one started unit j should be less than 70% of the upper limit of the black start unit output in the partition, ensuring that at least one non-black start unit in the partition can be successfully started; Ω B represents the set of nodes connected to the black start unit, Ω NB represents the set of nodes not connected to the black start unit, P j,st represents the starting power of the jth started unit; Indicates the upper limit of conventional unit output, x jk A 0-1 variable indicating whether the jth started unit is connected to partition k; Node and branch partition constraints, including: each node can only belong to one partition; each branch can only belong to one partition at most. When a branch does not belong to any partition, it means that the branch is a tie line branch; each area must have a black start power supply node; each partition must have at least one started unit; The network connectivity constraints constructed based on network flow theory include: defining the black start unit node as the system source point, the unit to be started and the load node as the sink point, the virtual flow only flows on the internal lines of the partition, and there is no flow on the interconnection lines between partitions; except for the black start power supply node, the flow value consumed by other nodes is not less than 1 unit; except for the black start power supply in the partition, other nodes should have inflow flow; the outflow flow of the black start power supply node is equal to the total number of nodes in the area minus 1; the inflow flow of the black start power supply node is 0; Uncertain set constraints: The above formula indicates that the uncertainty of renewable energy output satisfies the budget uncertainty set, where NW is the total number of renewable energy units; and p r are the expected value and predicted value of the output of the new energy unit r respectively; δ r represents the output fluctuation limit of the new energy unit r; Γ represents the uncertain budget value, Ω WT A node set representing a new energy unit; It represents the space composed of the output values ​​of NW new energy units; It also includes reactive power regulation reserve capacity constraints and active power reserve capacity constraints.

3. The method according to claim 2, characterized in that The big M method is used to deal with the partition power balance constraint x rk p r Item, introduce auxiliary continuous variables The transformed partition power balance constraints are as follows: Wherein, M represents a large number.

4. The method according to claim 3, characterized in that The matrix form of the upper model is as follows: Where x = [x ik ,y lk ,F lk ],F lk represents the virtual traffic on line l in partition k; x * It means that the main problem is to find the solution of x; is a 0-1 variable, is a continuous variable; u=[p r ] is a random variable; C T and W T is the coefficient matrix of the power grid dynamic partition objective function corresponding to the 0-1 variable x, C T The time required for node i to recover from partition k is T i,k Obtained by solving the lower model, it is considered a constant when solving the upper model; A T x+B T y≤E T u+e、D T x+E T y≤d corresponds to the partition power balance constraint inequality after conversion, Represent the corresponding constraints in the rescheduling phase; A T , B T , e and E T , and D T and d are the corresponding coefficient matrices; G T x=g represents the equality constraints in the node and branch partitioning constraints and network connectivity constraints, represents the corresponding constraints in the rescheduling phase; G T and g are the corresponding coefficient matrices; H T x≤h represents an inequality constraint among other constraints except the partition power balance constraint, represents the corresponding constraints in the rescheduling phase, H T and h are the corresponding coefficient matrices.

5. The method according to claim 4, characterized in that The method of solving the upper model by using a nested column and constraint generation algorithm includes: Decompose the upper model to get the main problem MP1: Among them, η is an auxiliary variable, which represents the adjustment amount of the partition decision variable under the worst scenario; Decompose the upper model to obtain sub-problem SP1: Among them, x * To find the optimal solution to the main problem MP1; Given a 0-1 variable An initial value Decompose the sub-problem SP1 to obtain the objective function of the main problem MP2 and obtain the corresponding constraints: Bλ1 r ≥0 Eλ1 r ≥0 Where, γ is the estimated value of the MP2 objective function of the main problem; is the value of the integer variable x at the rth iteration; is a continuous variable at the rth iteration; λ1 r ,λ2 r are the dual variables of the corresponding Lagrange multipliers at the rth iteration; k is the total number of iterations; Solve subproblem SP1 to obtain the objective function of subproblem SP2 and the corresponding constraints: In the formula, is the worst scenario obtained by solving the main problem MP2 for the rth time; Solve the main problem MP1 and subproblem SP1 alternately and iteratively.

6. The method according to claim 5, characterized in that The alternating iterative solution of the main problem MP1 and the sub-problem SP1 includes: S351, given the lower bound value LB1 = 0 and the upper bound value UB1 = +∞ of the subproblem SP1, initialize the number of iterations of the subproblem SP1 k1 = 1; S352, solve the main problem MP1 and obtain the current optimal solution x * and * , update the upper bound UB1 = min{UB1, C T x * +η}; S353, main problem MP1 to obtain Substitute into subproblem SP1, solve the inner CCG loop, and find the optimal Update the Nether S354, judge |UB1-LB1|≤ε, if the criterion is met, terminate the loop and output the optimal solution and scenario; otherwise, solve the subproblem SP1 to obtain the optimal solution. Substitute into the main problem MP1 and add the following constraints: k1=k1+1, return to S352.

7. The method according to claim 6, characterized in that Step S353 includes: S3531: Given the lower bound LB2 = 0 and the upper bound UB2 = +∞ of the subproblem SP1, initialize the number of iterations k2 = 1, and give a 0-1 variable An initial value S3532: Solve the main problem MP2 and obtain the current worst scenario Update upper bound UB2 = γ; S3533: Solve the main problem MP2 to obtain Substitute into the subproblem, solve subproblem SP2, obtain the current optimal partition result, and update the lower bound S3534: Determine |UB2-LB2|≤ε. If the criterion is met, terminate the loop. Return to the main problem; otherwise, k2=k2+1, and solve the subproblem to obtain the 0-1 variable solution Substitute into the main problem and create new variables λ1 r and λ2 r , and add the following constraints: Bλ1 r ≥0 Eλ1 r ≥0 8. The method according to claim 4, characterized in that The objective function corresponding to the lower model is: The lower model divides the system recovery process into N T time periods, each time period is ΔT, and the total recovery time is N S , and assume that the black start unit and the node in the partition are restored at time 0; in the above formula, and They represent the state variables of the i-th bus node, load node and unit node in partition k in time period s, respectively. A value of 1 indicates that the node has been restored, otherwise it indicates that it has not been restored; A state variable indicating whether the line l connecting nodes i and j in partition k is restored in time period s; and represents the active and reactive output of the i-th conventional unit in partition k under the expected scenario; Indicates the actual active output of the i-th renewable energy unit in the k-th partition under the expected scenario; represents the load size that node i in partition k needs to recover; W i,d N represents the load weight coefficient of node i k,BUS Indicates the number of busbar nodes in partition k; Ω T Represents the set of time periods; It represents the output of the rth renewable energy unit in the zone k during the time period s; It indicates the adjustment amount of the output of conventional units and new energy units as well as the restored load at the node during the re-dispatching stage.

9. The method according to claim 8, characterized in that The constraints of the lower model include: conventional unit output and ramp constraints; new energy unit output constraints; cold and hot start time limit constraints; safe operation constraints; transformer ratio and capacitor input group upper and lower limit constraints; node power balance constraints taking into account AC constraints; equipment recovery state constraints; new energy output uncertainty set; cold load recovery constraints; overvoltage constraints; frequency constraints; adjustment amount constraints.

10. The method according to claim 8, characterized in that The method of solving the lower model by using a column and constraint generation method comprises: S41, decomposing the lower model into a main problem and a sub-problem, wherein the main problem determines the component recovery order and the load recovery amount under the expected scenario of new energy output, and the sub-problem seeks the minimum adjustment amount based on the decision of the main problem under the worst scenario of new energy output, so that the recovery plan after adjustment under the worst scenario is feasible; S42. Solve the main problem and obtain the optimal solution x of a set of main problems * And the corresponding objective function value And update the iteration lower limit S43, the optimal solution x * Substitute into the subproblem and solve the subproblem to obtain a set of optimal solutions to the subproblem And the corresponding objective function value And the worst scene collection And update the iteration limit S44. Compare the iteration lower limit and the iteration upper limit. If |UB-LB| / |LB|≤ε, stop the iteration. Otherwise, update as well as Then go to S42 to continue iterative solution; ε is the set threshold.

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