Two-stage robust optimization method for flexible interconnected power distribution system

Abstract

The present application relates to a kind of flexible interconnection power distribution system two-stage robust optimization method, comprising the following steps: step 1, considering the dynamic reconstruction of FDS, energy storage, tie switch and the multiple control means of DG reduction, construct flexible interconnection power distribution system coordinated optimization model;Step 2, according to the flexible interconnection power distribution system coordinated optimization model established in step 1, establish the corresponding two-stage robust optimization model, and solve the corresponding mathematical model based on improved CCG algorithm, realize the coordinated optimization operation of flexible interconnection power distribution system.The present application can greatly improve the calculation speed.

Description

TECHNICAL FIELD

[0001] The application belongs to the technical field of power distribution network dispatching, and particularly relates to a two-stage robust optimization method for a flexible interconnected power distribution system. BACKGROUND

[0002] The large-scale access of strong fluctuation distributed generation (DG) effectively improves the energy structure of the power distribution network, which is of great significance for promoting China's energy transformation and achieving the carbon neutralization goal. At the same time, the fluctuation characteristics of wind and light DG output have brought problems such as increased operation cost and frequent voltage out-of-limit of the power distribution system, which urgently requires the power distribution network to have flexible and rapid response capability and accurate and efficient regulation capability.

[0003] In recent years, the flexible distribution switch (FDS) based on back-to-back voltage source converter (VSC) has attracted widespread attention. The FDS is installed at the associated feeder to replace the mechanical tie switch, and through the implementation of appropriate control strategies, it can realize the flexible and accurate control of power flow, effectively improve the voltage distribution, balance the three-phase load, save energy, and realize the rapid recovery from faults.

[0004] Due to the high investment and operation cost of the current FDS, it is temporarily difficult to replace all mechanical tie switches, so it is of great significance to fully utilize the FDS and network reconstruction to improve the economic efficiency and DG accommodation capacity of the current flexible interconnected power distribution system. However, the existing static reconstruction scheme considering tie switches and FDS does not consider the coupling of tie switch action sequence in time, and is only a local optimal solution. At the same time, since the static reconstruction is based on the separate solution of each time period, it cannot be applied to the optimal dispatching of power distribution networks with energy storage and other time sequence devices.

[0005] In addition, robust optimization is an important means to deal with DG output, which only needs to search for the worst scenario in a given uncertainty set to ensure the reliability of the decision scheme, and usually uses the column and constraint generation (CCG) algorithm to solve the model.

[0006] However, for the robust dispatching model of the flexible interconnected power distribution system with dynamic reconstruction, since it considers the large-scale access of DG and network dynamic reconstruction, it is a complex mixed integer nonlinear model, so the calculation efficiency of the model also needs to be considered. SUMMARY

[0007] The present application aims at overcoming the deficiencies of the prior art, and provides a two-stage robust optimization method for a flexible interconnected power distribution system, which can consider the coordination of flexible power distribution switches, energy storage and dynamic reconstruction, and greatly improve the solving speed.

[0008] The present application solves its practical problems by adopting the following technical solutions:

[0009] A two-stage robust optimization method for a flexible interconnected power distribution system, comprising the following steps:

[0010] Step 1: comprehensively considering various control means of FDS, energy storage, tie switch dynamic reconstruction and DG reduction, a coordinated optimization model of the flexible interconnected power distribution system is constructed;

[0011] Step 2: according to the coordinated optimization model of the flexible interconnected power distribution system established in step 1, a corresponding two-stage robust optimization model is established, and the corresponding mathematical model is solved based on the improved CCG algorithm, so as to realize the coordinated optimization operation of the flexible interconnected power distribution system.

[0012] Moreover, the specific steps of step 1 include:

[0013] (1) taking the minimum system operation cost and the maximum DG accommodation capacity as the objective function, and constructing a coordinated optimization model of the flexible interconnected power distribution system according to the parameters of the power distribution network, load, DG, energy storage, tie switch and FDS:

[0014]

[0015] Among them, f loss is the total daily power loss of the system; f V is the voltage out-of-limit cost; f act is the switch action cost; f cut is the wind and light abandonment cost;

[0016] System power loss f loss : including line loss, energy storage charging and discharging loss, FDS transmission loss; P i,t is the injected active power of node i at time t; is the internal power loss of the VSC close to node i at time t; is the energy storage charging and discharging loss of node i at time t; Ω T is the set of all time periods; Ω b is the set of all nodes; Ω FDS is the set of all FDS; Ω ESS is the set of all energy storages;

[0017] Voltage out-of-limit cost f V : V i,t is the voltage amplitude of node i at time t; V These are the upper and lower limits of the voltage, respectively; C V This is the voltage over-limit penalty coefficient;

[0018] Switching operation cost f act :S act Number of times the interlock switch has been activated; C act Cost coefficient for the operation of the interconnecting switch;

[0019] Cost of curtailing wind and solar power f cut : C represents the curtailed wind and solar power output at node i; cut This refers to the penalty coefficient for curtailing solar and wind power.

[0020] (2) Establish the constraints of the flexible interconnected power distribution system coordination optimization model, including: FDS constraints, energy storage charging and discharging constraints, power flow balance constraints, radial structure constraints, tie switch operation frequency constraints, current carrying capacity constraints and DG reduction constraints.

[0021] Furthermore, the specific steps in step 2 include:

[0022] (1) The coordinated optimization model of the flexible interconnected power distribution system established in step 1 is linearized by using Big-M and second-order cone relaxation techniques, and control strategies for different stages are formulated according to the characteristics of various control methods, so as to establish a corresponding two-stage robust optimization model.

[0023] Among them: network topology and energy storage output are the first-stage control variables, which need to be decided before the uncertain parameters of DG output in each time period of the second day are known; FDS transmission power is the second-stage control variable, which can be adjusted according to the real-time prediction of the uncertain parameters;

[0024] (2) The two-stage robust model is decomposed into a main-subproblem based on the CCG algorithm; the dual model of the subproblem is constructed by the Lagrange multiplier method; and finally, the coordinated and optimized operation of the flexible interconnected power distribution system is achieved by iteratively solving the problem using the improved CCG algorithm.

[0025] Furthermore, the specific method of step (1) in step 2 is as follows:

[0026] First, the original mixed-integer nonlinear model is transformed into an easier-to-solve MISOCP model using the Big M method and second-order cone relaxation, and an auxiliary variable l is introduced. ij,t u i,t replace Equation (4) can be rearranged as follows:

[0027]

[0028] At the same time, the FDS capacity constraint in equation (2) is relaxed:

[0029]

[0030] Then, by introducing auxiliary variable A to punish the node voltage beyond the operating range, the absolute value term in the objective function is eliminated, and the voltage out-of-limit cost is rearranged as:

[0031]

[0032] Thus, the model is transformed into a MISOCP problem, which can be solved efficiently by mature solvers. For the sake of clear expression, the first-stage decision variable x, the second-stage control variable y and the scenario variable d are introduced, and the following compact form robust model is constructed:

[0033]

[0034] In the formula, L(x, d) is the objective function under the first-stage decision scheme x and the scenario d; X is the set of all feasible day-ahead decision schemes x; Y(x, d) is the set of all variables y under the decision x and the scenario d, which is specifically described as formula (13); D is the box type uncertainty set of all DG output scenarios, which is specifically described as formula (14):

[0035]

[0036] Wherein: x, y, d are vectors representing the first-stage and second-stage decisions and DG output; A, D, C, G are the corresponding coefficient matrices; formula (a) represents all inequality constraints in formulas (2)-(3), (5)-(11); formula (b) represents all equality constraints therein; formula (c) represents all cone constraints therein.

[0037]

[0038] Wherein: is the DG output prediction value; ΔP i,DG is the absolute value of the upper and lower fluctuations; B i and is a 0-1 variable representing the DG output scenario, is 1, indicating that the current node DG output reaches the upper limit; at the same time, the uncertainty parameter Г introduced to balance the economy and conservatism.

[0039] Moreover, the specific steps of the step (2) of the step 2 comprise:

[0040] ① Based on the CCG algorithm, the model is divided into a main problem and sub-problems: the main problem considers the adverse scenario constraints returned by a finite number of sub-problems, solves the first-stage decision, and updates the lower bound of the objective function; the sub-problems solve the worst-case scenario under the decision of the main problem and feed it back to the main problem, and update the upper bound of the objective function.

[0041] The main problem is:

[0042]

[0043] In the formula: s is the number of worst-case scenarios selected from the subproblem, and its value is also used to represent the number of iterations;

[0044] After the main problem is solved, the lower bound of the objective function is updated, and the network topology and energy storage decisions are passed to the sub-problems. The objective function of the sub-problems is the sum of the objectives of each time period, and the only control variable is the FDS transmission power. Therefore, the time periods are no longer temporally coupled and can be computed in parallel. The specific form is as follows:

[0045]

[0046] In the formula: π, λ, σ, μ are the Lagrange multiplier vectors (dual variables) corresponding to the constraints.

[0047] By constructing the Lagrange equality, the min problem is transformed into the dual max problem, and the transformed model is as follows:

[0048]

[0049] After the subproblem is solved, the lower bound of the objective function is updated, and it is determined whether the iteration has converged. If the iteration termination condition is not met, the worst-case scenario selected is passed to the main problem, and variables and constraints are added to the main problem.

[0050] ② Decompose the subproblems of each time period into easily solvable integer linear programming and second-order cone programming problems, and accelerate the solution of subproblems by alternating between auxiliary and dual variables:

[0051] The solution process for the main problem remains unchanged using the improved CCG algorithm; the specific calculation process for the subproblems is as follows:

[0052] (1) Taking the predicted scenario as the initial state, set the initial value d of the integer variable representing the scenario. * =d0, and simultaneously set a large number as the upper bound UB for the inner iteration of the subproblem. Sub =∞;

[0053] (2) Let the auxiliary variable d be fixed, solve the following inner SOCP problem, and use the optimal objective function value as the lower bound of the inner iteration of the subproblem. Then, pass the obtained dual variable (π,λ,δ,μ) to the inner ILP problem:

[0054]

[0055] (3) Fixing the dual variables (π, λ, δ, μ), solve the following inner ILP problem, update the upper bound of the inner iteration of the sub-problem, and pass the obtained auxiliary variable d to the inner SOCP problem:

[0056]

[0057] s.t.D T λ * +C T π * +∑(G T y+gμ * )=b

[0058] (4) Determine whether the inner problem converges, if the inner iteration of the sub-problem in the period is stopped, solve the sub-problem in other periods, otherwise, return to step (2).

[0059] (5) The 24 time points without coupling relationship can be independently calculated in parallel, if all time periods are calculated, the calculation results are accumulated, the upper bound of the outer main-sub problem iteration is updated, and the worst scenario obtained is passed to the main problem for outer iteration.

[0060] The advantages and beneficial effects of the present application are:

[0061] 1. The present application comprehensively considers the coordination of FDS, energy storage and tie switch, and proposes a two-stage robust optimization method for flexible interconnected distribution system, first, a two-stage robust optimization scheduling mathematical model of flexible interconnected distribution system is established, the prediction uncertainty of DG output in the first stage is considered, the network topology and energy storage output are globally optimized, in the second stage, the real-time scheduling of FDS is carried out in each period of the day based on the decision scheme determined in the first stage and real-time prediction information, secondly, an improved column and constraint generation algorithm CC&G is used to solve the robust model, the auxiliary variable and the dual variable are iterated alternately to accelerate the solution of the sub-problem, finally, the effectiveness of the proposed scheduling model and solving algorithm is verified by testing 33 and 69 node systems.

[0062] 2、The application proposes a multi-means coordination strategy considering FDS, energy storage, and dynamic network reconstruction, which is divided into two stages for coordination by considering the characteristics of various control means. In the first stage, the action sequence of the tie switch and the time coupling of the energy storage device are considered to realize dynamic reconstruction and search for the global optimal solution. In the second stage, the FDS scheduling strategy of each time period without time coupling is calculated independently in parallel to reduce the solving time. At the same time, the existing CC&G algorithm is optimized, which can greatly improve the calculation speed on the basis of sacrificing part of the solution accuracy. BRIEF DESCRIPTION OF DRAWINGS

[0063] Figure 1 An improved column constraint generation algorithm flowchart is provided for the application.

[0064] Figure 2 A 33-node power distribution system schematic diagram is provided for the application.

[0065] Figure 3 A DG output fluctuation interval schematic diagram is provided for the application.

[0066] Figure 4 A real-time state of charge curve of energy storage is provided for the application.

[0067] Figure 5 A node voltage curve based on day-ahead deterministic optimization is provided for the application.

[0068] Figure 6 A node voltage curve based on day-ahead robust scheduling is provided for the application.

[0069] Figure 7 A node voltage curve based on two-stage robust scheduling is provided for the application. DETAILED DESCRIPTION

[0070] The embodiments of the application are further described in detail below with reference to the accompanying drawings:

[0071] A two-stage robust optimization method for a flexible interconnected power distribution system, as shown in Figure 1 , includes the following steps:

[0072] Step 1: comprehensively consider various control means such as FDS, energy storage, tie switch dynamic reconstruction, and DG reduction, and construct a coordinated optimization model of the flexible interconnected power distribution system.

[0073] The specific steps of step 1 include:

[0074] (1) Taking the minimum system operation cost and the maximum DG accommodation capacity as the objective function, considering the power distribution network optimization control means such as DG reduction, energy storage, tie switch, and FDS, and constructing a coordinated optimization model of the flexible interconnected power distribution system:

[0075]

[0076] wherein f loss is the total system daily energy loss; f V is the voltage out-of-limit cost; f act is the switching action cost; f cut is the wind and light curtailment cost;

[0077] System energy loss f loss : mainly contains line loss, energy storage charging and discharging loss, FDS transmission loss; P i,t is the injected active power of node i at t time; is the internal power loss of VSC close to node i at t time; is the energy storage charging and discharging loss installed at node i at t time; Ω T is the set of all time periods; Ω b is the set of all nodes; Ω FDS is the set of all FDSs; Ω ESS is the set of all energy storages; through multi-means coordination, the system operation efficiency is improved as much as possible.

[0078] Voltage out-of-limit cost f V : V i,t is the voltage amplitude of node i at t time; V are the upper and lower voltage limits respectively; C V is the voltage out-of-limit penalty coefficient, in order to improve power supply reliability, the voltage operation range constraint is converted into a soft constraint by applying a larger voltage penalty, so as to avoid the infeasibility of the two-stage robust sub-problem.

[0079] Switching action cost f act : S act is the number of tie switch actions; C act is the tie switch action cost coefficient; in order to prolong the service life of the tie switch, it is not suitable to frequently open and close.

[0080] Wind and light curtailment cost f cut : is the wind and light active power of node i; C cut is the wind and light penalty coefficient, and the value is the ratio of wind and light on-grid price to real-time price.

[0081] (2) The constraint conditions of the coordination optimization model of the flexible interconnected distribution system are established:

[0082] The coordination optimization model established by the application needs to meet the FDS constraint, the energy storage charging and discharging constraint, the power flow balance constraint, the radial structure constraint, the tie switch action number constraint, the current carrying capacity constraint, the DG reduction constraint and the system safe operation constraint, and the specific description is as follows:

[0083] 1) FDS related constraints:

[0084] Multi-terminal FDS consists of multiple VSCs, and the control variables in normal operation mode are the active and reactive power transmitted by each VSC. Assuming that the power injection of FDS into the grid is in the positive direction, the FDS operation needs to satisfy the following constraints:

[0085]

[0086] In the formula: P i,t,FDS , Q i,t,FDS are the active and reactive power injected by FDS at node i at time t; A loss,FDS is the VSC loss coefficient; Q min,FDS , Q max,FDS are the upper and lower limits of FDS reactive power; S max,FDS is the maximum apparent power allowed by FDS. Equation (b) makes the sum of the active power injected by FDS into all associated feeder lines and the internal active loss of all VSCs zero; equation (c) makes the reactive power compensated by FDS not exceed its adjustable reactive power limit; equation (d) makes the apparent power of FDS not exceed its transmission capacity.

[0087] 2) Energy storage charging and discharging constraints:

[0088] The energy storage device connected to the distribution system should satisfy the following constraints when charging and discharging:

[0089]

[0090] In the formula: are the charging and discharging power of the energy storage at node i at time t; are the maximum charging and discharging power of the energy storage at node i; E i,t is the energy storage at node i at time t; and are the charging and discharging efficiencies of the energy storage at node i. Equations (a)-(b) make the charging and discharging power at any time not exceed the maximum charging and discharging power; equation (c) makes the energy storage meet the continuity constraint; equation (d) makes the energy storage free from deep charging or discharging; equation (e) makes the energy storage at the end of each day equal to the initial energy of that day, so as to ensure that the total charging energy of each day is equal to the total discharging energy.

[0091] 3) Power flow balance constraints:

[0092] The present application adopts DisFlow power flow model, and the active and reactive power injected by each node at each time should be equal to the difference between the power generation and the load at that time. The power flow balance constraint is as follows:

[0093]

[0094] In the formula: P ij,t Q ij,t I ij,t These represent the active power, reactive power, and current amplitude of branch ij at time t; P i,t,DG P i,t,FDS P i,t,L Let Q represent the active power injected by the DG, the active power injected by the FDS, and the active power extracted by the load at node i at time t, respectively. i,t,DG Q i,t,FDS Q i,t,L These represent the reactive power injected by the DG, the reactive power injected by the FDS, and the reactive power extracted by the load at node i at time t, respectively; r ij x ij These are the resistance and reactance of branch ij, respectively; Ω l For the set of all lines; Ω REF This is the set of all substation nodes.

[0095] 4) Radial structural constraints:

[0096] To ensure the radiating structure meets the following constraints:

[0097]

[0098] Where: β ij It is a 0-1 variable, where 1 indicates that node j is the parent node of node i; α ij Let N(i) be the connectivity state of line ij; N(i) be the set of neighboring nodes of node i; Ω b \Ω REF Let be the set of all nodes except the root node. Equation (b) guarantees that each node has only one parent node; Equation (c) guarantees that the root node has no parent node.

[0099] 5) Limitation on the number of times the interlock switch can be activated:

[0100] Frequent switching actions during dynamic reconfiguration can reduce the switch's lifespan; therefore, the following constraint on the number of switch actions is set:

[0101]

[0102] In the formula: and As a 0-1 auxiliary variable, when When the value is 1, it indicates that the connection switch between node i and node j changes from closed to open at that moment. A value of 1 indicates that the contact switch is open at this moment; if both are 0, it indicates that the switch state is the same as the previous moment; S ij,max S represents the maximum number of communication switching actions between node i and node j; maxAn upper limit of the sum of all the number of contact switch operations.

[0103] 6) Current flow constraint:

[0104] The current flowing through each line should satisfy the current flow constraint:

[0105] 0≤(I ij,t ) 2 ≤α ij (I ij,max ) 2 (7) where: I ij,max is the current flow of branch i-j.

[0106] 7) DG constraint

[0107] DGs connected to the distribution system should satisfy the power and capacity constraints when operating, and the DG curtailment should be less than the product of the installed capacity and the maximum rejection ratio. The power factor of the AC regional PV model of the present invention is constant, and the constraint condition is shown in (8).

[0108]

[0109] where: μ cut is the maximum wind and light rejection ratio. P i,t,DG,max is the maximum value of DG output; is the power factor angle of the DG.

[0110] Step 2, based on the flexible interconnected distribution system coordination optimization model established in step 1, a corresponding two-stage robust optimization model is established, and the corresponding mathematical model is solved based on the improved CCG algorithm, to realize the coordinated optimization operation of the flexible interconnected distribution system.

[0111] The specific steps in the step 2 include:

[0112] (1) linearize the flexible interconnected distribution system coordination optimization model established in step 1 by using Big-M and second-order cone relaxation techniques, and formulate different stages of control strategies according to the characteristics of various control means, to establish a corresponding two-stage robust optimization model;

[0113] Among them: the network topology and the energy storage output are the first stage control variables, which need to be decided before the second day of each time period DG output uncertainty parameter is known; the FDS transmission power is the second stage control variable, which can be adjusted according to the real-time prediction of the uncertain parameter;

[0114] (2) based on the CCG algorithm, the two-stage robust model is decomposed into master-sub problems; and the dual model of the sub-problems is constructed through the Lagrange multiplier method; finally, the improved CCG algorithm is iterated to solve, to realize the coordinated optimization operation of the flexible interconnected distribution system.

[0115] The specific method of step (1) in step 2 is:

[0116] Since the optimization model established in step 1 is a mixed integer nonlinear programming problem, it is difficult to achieve fast solution, and the model needs to be transformed for solution.

[0117] Firstly, the original mixed integer nonlinear model is transformed into an MISOCP model which is easy to solve by using the big M method and the second-order cone relaxation, and auxiliary variables l ij,t 、u i,t are introduced to replace Equation (4) is rearranged as:

[0118]

[0119] At the same time, the FDS capacity constraint of equation (2) is relaxed:

[0120]

[0121] Then, auxiliary variables A are introduced to punish the node voltage that exceeds the operating range, so as to eliminate the absolute value term in the objective function. The voltage out-of-limit cost is rearranged as:

[0122]

[0123]

[0124]

[0125] A t,i ≥0

[0126] Thus, the model is transformed into a MISOCP problem, which can be efficiently solved by using mature solvers. In order to express clearly, the first-stage decision variable x, the second-stage control variable y and the scenario variable d are introduced, and the following compact form robust model is constructed:

[0127]

[0128] In the formula: L(x,d) is the objective function under the first-stage decision scheme x and scenario d; X is the set of all feasible day-ahead decision schemes x; Y(x,d) is the set of all variables y under the decision x and scenario d, which is described as formula (13); D is the box type uncertainty set of all DG output scenarios, which is described as formula (14):

[0129]

[0130] Where: x, y, d are vectors representing the first-stage and second-stage decisions and DG output; A, D, C, G are the corresponding coefficient matrices; then equation (a) represents all inequality constraints in equations (2)-(3), (5)-(11); equation (b) represents all equality constraints in equations (4), (12)-(14); equation (c) represents all cone constraints in equation (15).

[0131]

[0132] Where: is the predicted value of DG output; ΔP i,DG is the absolute value of the upper and lower fluctuations; B i and is a 0-1 variable representing the DG output scenario, is 1, indicating that the current node DG output reaches the upper limit; at the same time, is an uncertainty parameter introduced to balance the economy and conservatism.

[0133] The specific method of step (2) in step 2 is:

[0134] Based on the CCG algorithm, the model is divided into a main problem and a sub-problem: the main problem considers the worst-case scenario constraints returned by a finite number of sub-problems, solves the first-stage decision, and updates the lower bound of the objective function; the sub-problem solves the worst-case scenario feedback to the main problem under the decision of the main problem, and updates the upper bound of the objective function. The main problem is:

[0135]

[0136] In the formula: s is the number of worst-case scenarios selected by the sub-problem, which is also used to represent the number of iterations.

[0137] After the main problem is solved, the lower bound of the objective function is updated, and the network topology and energy storage decision are passed to the sub-problem. The objective function of the sub-problem is the sum of the objectives of each period, and the control variable is only the FDS transmission power, so each period no longer has temporal coupling and can be calculated in parallel. The specific form is as follows:

[0138]

[0139] In the formula: π, λ, σ, μ are the Lagrange multiplier vectors (dual variables) corresponding to the constraints.

[0140] Since the sub-problem is a max-min problem, it is necessary to construct a Lagrange equation to convert the min problem into a dual max problem. The transformed model is as follows:

[0141]

[0142] After the sub-problem is solved, the lower bound of the objective function is updated, and it is determined whether the iteration converges. If the iteration termination condition is not met, the worst-case scenario selected is passed to the main problem, and variables and constraints are added to the main problem.

[0143] In addition, since the original CCG algorithm is a MISOCP model, the solving time is relatively long, therefore, the sub-problems of each period are decomposed into an integer linear programming (ILP) and a second-order cone programming (SOCP) which are easy to solve, and the sub-problems are solved by alternately iterating auxiliary variables and dual variables. The overall process of the improved CCG algorithm is shown in Figure 1 The solving process of the main problem is consistent with the original algorithm, and the specific calculation process of the sub-problem in the dashed box is as follows:

[0144] (1) Taking the predicted scenario as the initial state, setting the initial value d * of the integer variable representing the scenario to d Sub = d 0, and setting a large number as the upper bound UB Sub of the inner iteration of the sub-problem to ∞;

[0145] (2) fixing the auxiliary variable d, solving the following inner SOCP problem, taking the optimal objective function value as the lower bound of the inner iteration of the sub-problem, and passing the obtained dual variables (π, λ, δ, μ) to the inner ILP problem:

[0146]

[0147] (3) fixing the dual variables (π, λ, δ, μ), solving the following inner ILP problem, updating the upper bound of the inner iteration of the sub-problem, and passing the obtained auxiliary variable d to the inner SOCP problem:

[0148]

[0149] s.t.D T λ * +C T π * +∑(G T y+gμ * )=b

[0150] (4) determining whether the inner problem converges, if the inner problem converges, the inner iteration of the sub-problem at this period stops, and the sub-problem at other times is solved; otherwise, returning to step (2).

[0151] (5) 24 time points without coupling relationship can be independently and parallelly calculated, if all time periods are calculated, the calculation results are accumulated, the upper limit of the outer main-sub problem iteration is updated, and the worst scenario obtained is transmitted to the main problem to perform outer iteration.

[0152] The improved algorithm and the two-stage robust scheduling strategy considering reconstruction of the application are verified through a specific example as follows:

[0153] 1. Example setting

[0154] The example of the application is an improved IEEE33 node power distribution system, the reference voltage is 12.66 kV, the node voltage safety range is [0.95, 1.05] p.u, and the configuration of photovoltaic, wind turbine, energy storage and FDS is as shown in the table. Figure 2 Among them, the end nodes 18, 22 and 33 are flexibly interconnected through a three-terminal FDS, the capacity is 1.5 MVA, and the transmission efficiency is 98%; the capacity of the energy storage device is 1.0 MW, the initial electric quantity is 50%, and the charging and discharging efficiency is 95%; the installed capacity of a single photovoltaic and wind turbine is 600 kVA and 300 kVA respectively. In addition, the penalty factor C act = 18, C cut = 1.5 and are set, and the output of photovoltaic and wind turbine is allowed to fluctuate by 20% and 30% respectively based on the predicted value. The active power output of DG and the load curve at each time point are as shown in the table. Figure 3

[0155] 2. Simulation analysis

[0156] Simulation example one

[0157] In order to verify the feasibility of the improved algorithm, Г = 4 is set, and the improved CCG method of the application is compared with the deterministic optimization without considering the output fluctuation of DG and the robust optimization based on the CCG algorithm. The network topology decision of the three methods is as shown in the table. Figure 4

[0158] Table 1 Network topology decision scheme

[0159]

[0160] In order to further verify the reliability of the method, 500 groups of Monte Carlo sampling verification are performed on the decisions generated by different calculation methods, and the verification results are as shown in the table.

[0161] Table 2 Monte Carlo sampling test results​​

[0162]

[0163] From Table 2, it can be seen that the day-ahead decision generated by the method of the application sacrifices a small amount of average active power loss compared to deterministic optimization, greatly reduces the maximum active power loss, ensures that the voltage does not exceed the limit, and can better cope with the more severe fluctuation scenarios. Compared with the original CC&G algorithm, the decision generated by the method of the application also ensures the power supply reliability, and has a smaller average cost. At the same time, the calculation method of the application greatly improves the solving speed of the two-stage robust model, and this advantage will be highlighted with the increase of the system size and the proportion of distributed energy access. When the number of DG access is set to 6, the method of the application is tested by using different size systems, and the calculation time is shown in Table 3.

[0164] Table 3 Comparison of calculation time of different systems

[0165]

[0166] From the above table, it can be seen that the method of the application has good convergence in different test systems, and greatly improves the solving speed of the dual sub-problem. In addition, with the increase of the number of DGs, the number of integer variables in the corresponding robust model is also increasing, and the increase of the calculation time required by the method of the application is smaller than that of the original CC&G algorithm, and the calculation time of each scenario is shown in Table 4.

[0167] Table 4 Comparison of calculation time under different DG quantities

[0168]

[0169] Simulation Example 2

[0170] Example 1 verifies the reliability and efficiency of the improved algorithm of the application. In order to further verify the economy and reliability of the two-stage robust scheduling strategy of the application, the following three comparison schemes are made.

[0171] Case 1, without considering the DG output uncertainty, based on the predicted scene, using reconstruction, energy storage and FDS and other regulation means to optimize the distribution system.

[0172] Case 2, considering the DG output uncertainty, using reconstruction, energy storage and FDS and other regulation means to optimize the distribution system.

[0173] Case 3, based on robust optimization, according to the characteristics of reconstruction, energy storage and FDS and other means, the distribution system is optimized in two stages.

[0174] For the above three schemes, the simulation example 1 is selected in the Monte Carlo test of the maximum voltage deviation scene for 24 hours a day simulation. The simulation results are shown in Figures 5-7 In this scenario, the scheme three adopted by the application can achieve the power supply reliability requirements. The scheme one does not consider the uncertainty of DG output, and the voltage exceeds the upper limit at 12 and 13 o'clock when the photovoltaic output is large. At 20 o'clock when the load is large, the voltage exceeds the lower limit. The voltage at 12 and 20 o'clock reaches the safe operation range after considering the uncertainty of DG output in the scheme two. But at 13 o'clock, although the voltage peak is slightly reduced, it still cannot reach the safe operation range due to the limitation of FDS transmission capacity, which reflects the limitations of not considering FDS real-time optimization in some adverse scenarios, and verifies the necessity of two-stage robust scheduling.

[0175] Simulation example 3

[0176] The two-stage robust scheduling strategy and the improved CCG algorithm are adopted to verify the improvement effect of various control means on the DG accommodation capacity under the premise of ensuring the robustness of the voltage. Seven test schemes are designed as shown in Table 5, schemes 2-4 use energy storage, FDS and reconstruction respectively for testing; schemes 5-6 compare static reconstruction and dynamic reconstruction strategies; scheme 7 is a multi-means coordination scheme based on the two-stage scheduling framework of the application. The specific test results are shown in Table 6.

[0177] Table 5 test scheme

[0178]

[0179] Table 6 example operation results

[0180]

[0181] As can be seen from Table 6, the application of FDS, energy storage, dynamic reconstruction joint scheduling can effectively reduce the system comprehensive cost and realize full consumption of wind and light. Comparing schemes 2-4, compared with energy storage which is limited by installation location and traditional mechanical switch which needs to act frequently, FDS can better balance the voltage of each feeder and effectively improve the DG accommodation capacity by adjusting the power flow transfer and reactive power compensation capacity. In addition, scheme 5 adopts a static network reconstruction scheme that divides the reconstruction period in advance to solve the local optimal scheduling scheme in each period; on the contrary, the dynamic reconstruction scheme of scheme 6 gets a global optimal solution with smaller system energy loss under the same number of tie switch actions.

[0182] In summary, the optimal control strategy considering the coordination of reconstruction, energy storage and FDS combines traditional and new power electronic equipment, improves the power quality of the power grid, reduces the operation cost of the power grid, and improves the accommodation capacity of distributed power supply of the system.

[0183] The computer program instructions can also be loaded onto a computer or other programmable data processing apparatus to cause a series of operational steps to be performed on the computer or other programmable apparatus to produce a computer-implemented process such that the instructions which execute on the computer or other programmable apparatus provide steps for implementing the functions specified in the flowchart block or blocks. Figure One one or more flowcharts and / or blocks Figure One means for functionally implementing the steps listed in the flowchart block or blocks.

[0184] These computer program instructions can also be stored in a computer-readable memory that can direct a computer or other programmable data processing apparatus to function in a particular manner, such that the instructions stored in the computer-readable memory produce an article of manufacture including instructions which implement the function specified in the flowchart block or blocks. Figure One one or more flowcharts and / or blocks Figure One means for functionally implementing the steps listed in the flowchart block or blocks.

[0185] The computer program instructions can also be loaded onto a computer or other programmable data processing apparatus to cause a series of operational steps to be performed on the computer or other programmable apparatus to produce a computer-implemented process such that the instructions which execute on the computer or other programmable apparatus provide steps for implementing the functions specified in the flowchart block or blocks. Figure One one or more flowcharts and / or blocks Figure One means for functionally implementing the steps listed in the flowchart block or blocks.

Claims

1. A two-stage robust optimization method for a flexible interconnected power distribution system, characterized in that: The method comprises the following steps: Step 1, considering multiple control means of FDS, energy storage, tie switch dynamic reconstruction and DG reduction, a coordinated optimization model of the flexible interconnected distribution system is established with the minimum system operation cost and the maximum DG accommodation capacity as objective functions; Step 2, according to the coordinated optimization model of the flexible interconnected distribution system established in step 1, a corresponding two-stage robust optimization model is established, and the corresponding mathematical model is solved based on an improved CCG algorithm to realize the coordinated optimization operation of the flexible interconnected distribution system; The specific steps in step 2 comprise: (1) the flexible interconnected distribution system coordinated optimization model established in step 1 is linearized by using Big-M and second-order cone relaxation technology, and different control strategies in different stages are formulated according to the characteristics of various control means to establish a corresponding two-stage robust optimization model; Wherein: the network topology and the energy storage output are the first-stage control variables, which need to be decided before the DG output uncertainty parameter in each time period of the next day is known; and the FDS transmission power is the second-stage control variable, which is adjusted according to the real-time prediction of the uncertain parameter; (2) the two-stage robust model is decomposed into a master problem and a sub-problem based on the CCG algorithm; a dual model of the sub-problem is constructed by using the Lagrange multiplier method; and finally, the improved CCG algorithm is iterated to solve, so that the coordinated optimization operation of the flexible interconnected distribution system is realized. 2.The two-stage robust optimization method for a flexible interconnected power distribution system according to claim 1, wherein: The specific steps of step 1 comprise: (1) a coordinated optimization model of the flexible interconnected distribution system is established with the minimum system operation cost and the maximum DG accommodation capacity as objective functions according to the parameters of the distribution network, the load, the DG, the energy storage, the tie switch and the FDS: Wherein, f loss is the total power loss of the system within a day; f V is the voltage out-of-limit cost; f act is the switching action cost; f cut is the wind and light curtailment cost; System power loss f loss : including line loss, energy storage charging and discharging loss, FDS transmission loss; P i,t is the injected active power of node i at time t; is the internal power loss of VSC close to node i at time t; is the energy storage charging and discharging loss installed at node i at time t; Ω T is the set of all time periods; Ω b is the set of all nodes; Ω b(v) is the set of nodes associated with the vth FDS; Ω FDS is the set of all FDSs; Ω ESS is the set of all energy storages; Voltage excursion cost f V : V i,t is the voltage amplitude of node i at time t; V are the upper and lower voltage limits, respectively; V is the voltage excursion penalty coefficient; Switching action cost f act : S act is the number of tie switch actions; C act is the tie switch action cost coefficient; Cost of curtailment of wind and solar power f cut : Pci is the curtailment of wind and solar power for node i; C cut is the penalty coefficient of curtailment of wind and solar power; (2) the constraint conditions of the flexible interconnected distribution system coordinated optimization model are established, including: FDS constraint, energy storage charging and discharging constraint, power flow balance constraint, radial structure constraint, tie switch action frequency constraint, current-carrying capacity constraint and DG reduction constraint. 3.The two-stage robust optimization method for a flexible interconnected power distribution system according to claim 1, wherein: The specific method of step (1) in step 2 is: Firstly, the original MINLP model is transformed into a MISOCP model by big M method and second order cone relaxation, and auxiliary variables l ij,t 、 i,t are introduced Equation (4) is rearranged as: At the same time, the FDS capacity constraint of formula (2) is relaxed: Then, the auxiliary variable A is introduced to punish the node voltage exceeding the operation range, so as to eliminate the absolute value term in the objective function, and the voltage out-of-limit cost is arranged as: Therefore, the model is converted into a MISOCP problem, which can be efficiently solved by using a mature solver. In order to express clearly, the first-stage decision variable x, the second-stage control variable y and the scenario variable d are introduced to construct the following compact form robust model: where L(x, d) is the objective function under the first stage decision x and scenario d; X is the set of all feasible day-ahead decision x; Y (x, d) is the set of all variables y under decision x and scenario d, which is described as (13); D is the box uncertainty set of all DG output scenarios, which is described as (14). Wherein: x, y and d are vectors representing the first-stage and second-stage decisions and the DG output; A, D, C and G are corresponding coefficient matrices; then formula (a) represents all inequality constraints in formula (2)-(3), formula (5)-(11); formula (b) represents all equality constraints; and formula (c) represents all cone constraints; where: is the DG power forecast value; ΔP i,DG is the absolute value of the up and down fluctuation; B i and is a 0-1 variable representing the DG power scenario, is 1 if the current node DG power reaches the upper limit; meanwhile, is the uncertainty parameter introduced to balance the economy and conservatism. 4.The two-stage robust optimization method for a flexible interconnected power distribution system according to claim 1, wherein: The specific steps of step (2) in step 2 comprise: ① based on the CCG algorithm, the model is divided into a master problem and a sub-problem: the master problem considers the worst scenario constraints returned by a limited number of sub-problems, solves the first-stage decision and updates the lower bound of the objective function; and the sub-problem feeds back the worst scenario under the decision of the master problem to the master problem and updates the upper bound of the objective function; Where, the main problem is: In the formula: s is the number of the worst selected scenarios of the sub-problem, which is also used to represent the number of iterations; After the main problem is solved, the lower bound of the objective function is updated, and the network topology and energy storage decision is passed to the sub-problem. The objective function of the sub-problem is the sum of the target of each period, and the control variable is only the transmission power of the FDS. Therefore, each period no longer has time coupling and can be calculated in parallel. The specific form is as follows: In the formula: π, λ, σ, μ are the Lagrange multiplier vectors corresponding to the constraints; By constructing the Lagrange equivalence, the min problem is converted into a dual max problem. The transformed model is as follows: After the sub-problem is solved, the lower bound of the objective function is updated, and it is judged whether the iteration converges. If the iteration termination condition is not met, the worst scenario selected is passed to the main problem, and the variables and constraints of the main problem are increased; ②The sub-problem of each period is decomposed into an integer linear programming and a second-order cone programming problem that is easy to solve. Through the alternate iteration of auxiliary variables and dual variables, the solution of the sub-problem is accelerated: The main problem solving process of the improved CCG algorithm is unchanged, and the specific calculation process of the sub-problem is as follows: (1) Set the initial state as the predicted scenario, set the initial value of the integer variable d representing the scenario as d0 * = d0, and set a large number as the upper bound UB of the inner iteration of the subproblem Sub = ∞; (2) Fix the auxiliary variable d, solve the following inner SOCP problem, and the optimal objective function value is the lower bound of the inner iteration of the sub-problem. The dual variable(π, λ, δ, μ) obtained by the solution is passed to the inner ILP problem: (3) Fix the dual variable(π, λ, δ, μ), solve the following inner ILP problem, update the upper bound of the inner iteration of the sub-problem, and pass the auxiliary variable d obtained by the solution to the inner SOCP problem: s.t.D T λ * +C T π * +∑(G T y+gμ * )=b (4)Judge whether the inner problem converges. If it converges, the inner iteration of the sub-problem in this period stops, and the other time of the sub-problem is solved. Otherwise, return to step (2); (5)The 24 time periods with no coupling relationship can be calculated independently in parallel. If all the periods are calculated, the calculation results are accumulated, the upper bound of the outer main-sub problem iteration is updated, and the worst scenario obtained by the solution is passed to the main problem for outer iteration.

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