Method for solving micro-grid robust scheduling problem without dual transformation
By constructing an iterative search method based on a master-auxiliary model, the problem of robust scheduling in microgrids is solved, and efficient solutions to robust optimization problems of Boolean variables are achieved, reducing the complexity of the solution.
Patent Information
- Application Number
- CN202511068667.X
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- Filing Date
- 2025-07-31
- Publication Date
- 2025-12-12
AI Technical Summary
The robust scheduling problem of microgrids is difficult to solve directly due to the existence of max-min or min-max-min structures. Existing dual-solution algorithms have high complexity and cannot handle inner Boolean variables.
The robust scheduling problem of microgrids is transformed into a master model and an auxiliary model with the same constraints and decision variable set. The auxiliary model iteratively searches for the optimal scenario, while the master model selects the worst scenario, thus constructing a deterministic optimization problem to solve the robust optimization problem of Boolean variables.
It effectively solves the worst-case scenario of robust optimization problems with inner layers containing Boolean variables, reducing the solution complexity and improving the solution efficiency.
Smart Images
Figure CN121119488A_ABST
Abstract
Description
TECHNICAL FIELD
[0001] The application belongs to the technical field of two-stage robust scheduling problems of microgrids, and particularly relates to a method for solving a robust scheduling problem of a microgrid without dual transformation. BACKGROUND
[0002] Robust optimization methods are widely used to deal with uncertainty factors in microgrid operation and effectively address security and economic challenges caused by uncertainty. Due to the existence of max-min or min-max-min structure, the robust scheduling problem of a microgrid is difficult to be directly solved, and therefore it is urgent to design a simple and efficient solving method.
[0003] Existing researches usually transform the max-min and min-max-min scheduling models into classical max-max and min-max-max optimization problems based on dual theory, the former can be directly solved, and the latter needs to be solved iteratively by using C&CG algorithm or Benders decomposition algorithm. Such dual solving algorithms have high complexity, and may not be able to be solved when the inner optimization problem contains Boolean variables. SUMMARY
[0004] The application aims to provide a method for solving a robust scheduling problem of a microgrid without dual transformation, which can effectively solve the worst-case scenario of a robust optimization problem containing Boolean variables in the inner layer.
[0005] To solve the above technical problems, the application provides a method for solving a robust scheduling problem of a microgrid without dual transformation, which comprises the following steps:
[0006] transforming a two-stage robust scheduling model of a microgrid into a main model with the same constraint conditions and decision variable set;
[0007] constructing an auxiliary model of the deterministic optimization scheduling main model, wherein the sum of the related Boolean variables representing uncertainty in the main model is equal to 1;
[0008] based on the conflict of interests between the main model and the auxiliary model, searching for an optimal scenario by the auxiliary model in the front iteration, and screening the worst-case scenario from the corresponding adverse scenarios by the main model.
[0009] Preferably, the deterministic optimization scheduling main model is constructed as follows:
[0010]
[0011] wherein A, U and B represent a slow-action variable set, an uncertainty factor related variable set and a fast-action variable set respectively; F gt,start represents the start-up cost of a gas turbine; F gt / b / egThese represent the costs of gas turbine power generation, battery lifespan depletion, and grid interconnection, respectively. These represent the costs of purchasing and selling electricity; This represents the projected electricity price. Let α represent the purchase price and sales price of electricity in time period t, respectively; ep / es+ and α ep / es- These represent the upward and downward deviations of the predicted value, respectively. These represent the power purchased from and the power sold to the external power grid, respectively. These respectively indicate the upward and downward skewness of the electricity purchase and sale price forecast; and This holds true, where M is a sufficiently large positive number.
[0012] Preferably, the auxiliary model is:
[0013]
[0014] Where A', U', and B' represent the slow-motion variable set, the uncertainty factor-related variable set, and the fast-motion variable set in the auxiliary model, respectively; F gt，start′ F gt′ F b′ and F eg′ These represent the start-up cost of the gas turbine, the power generation cost of the gas turbine, the battery life loss cost, and the grid interaction cost in the auxiliary model, respectively. These represent the upper and lower skewness of the variables related to uncertainties in the power purchase and sale price, wind power, photovoltaic power generation, and power load in the auxiliary model, respectively. and T-Γ represents the up-skewness and down-skewness of the forecasts for the variables related to uncertainties in the main model, namely, electricity purchase and sale prices, wind power, photovoltaic power generation, and electricity load; ep / es / wt / pv / el The degree of conservatism in the problem is indicated by T; T represents the scheduling cycle in hours.
[0015] Preferably, the following iterative solution methods are also included:
[0016] Step 1: Solve for constraints Deterministic auxiliary model F 3 Among them, as the number of iterations k increases, the constraints This will force the auxiliary model F 3 The solution gradually transitions from the optimal scenario to the worst scenario, and the optimal solution is passed to step 2;
[0017] Step 2: Solve the master model F 2,k and according to the formula Update F 1 The values are determined, and the parameters and iteration count k are updated.
[0018] Step 3: Check the termination condition. Let K be the maximum number of iterations and k be the current number of iterations, i.e., k = 1, 2, ..., K. If k ≤ K, then return to step 2; otherwise, output the optimal solution F. 1 We obtain the worst-case solution to the robust scheduling problem of microgrids.
[0019] Preferably, the F 1 This is a two-stage robust scheduling model for microgrids, namely:
[0020]
[0021] The present invention also provides a solution system for the robust scheduling problem of microgrids without dual transformation, which performs the solution method for the robust scheduling problem of microgrids without dual transformation as described above.
[0022] The present invention also provides an electronic device, which includes a memory and a processor. The memory stores a computer program, and the processor executes the computer program to implement a solution method for a robust microgrid scheduling problem without dual transformation as described above.
[0023] The present invention also provides a computer-readable storage medium storing a computer program, which, when executed by a processor, implements a method for solving a robust microgrid scheduling problem without dual transformation as described above.
[0024] Compared with the prior art, the present invention has the following beneficial effects:
[0025] This invention proposes a novel solution method for the two-stage robust scheduling problem in microgrids without dual transformation. The method transforms the min-max-min optimization model into a conventional deterministic optimization problem with identical constraints and decision variables. To find the worst-case scenario, an auxiliary deterministic optimization problem with opposite uncertain Boolean variables is further established. Based on the conflict of interest between the two, the auxiliary model iteratively searches for its optimal scenario at the frontier, while the main model selects the worst-case scenario from the corresponding worst-case scenarios. Simulation results demonstrate that the proposed method can effectively solve the worst-case scenario of the robust optimization problem with inner Boolean variables. Attached Figure Description
[0026] Figure 1 This is a flowchart of a robust microgrid scheduling method that does not require dual transformation according to the present invention.
[0027] Figure 2 This is a schematic diagram of the microgrid structure of the present invention.
[0028] Figure 3 This is a graph showing the changes in the objective function values of F2 and F3 under uncertain scenarios according to the present invention.
[0029] Figure 4 This invention provides a graph showing renewable energy generation, load, and electricity purchase price.
[0030] Figure 5 These are performance curves of the algorithm in four scenarios according to the present invention. Detailed Implementation
[0031] The present invention will be further described in detail below with reference to the accompanying drawings and specific embodiments. The advantages and features of the present invention will become clearer from the following description. It should be noted that the drawings are all in a very simplified form and use non-precise proportions, and are only used to facilitate and clarify the illustration of the embodiments of the present invention.
[0032] like Figure 1 As shown in the figure, this invention proposes a robust microgrid scheduling method without dual transformation. First, by keeping the original problem constraints and decision variables unchanged, it is transformed into a conventional deterministic optimization model, and simultaneously an auxiliary optimization problem with opposite Boolean variables that can represent uncertainty is constructed. Second, based on the conflict of interest mechanism between the two, the auxiliary model iteratively searches for the optimal scenario at the forefront, while the main model selects the worst scenario from the corresponding adverse scenarios. Finally, simulation examples verify the effectiveness of the proposed method.
[0033] like Figure 2 The diagram shows the structure of a microgrid system. The microgrid dispatch model aims to minimize operating costs, which include gas turbine (GT) start-up and shutdown costs, external grid (EG) power purchase and sale costs, GT generation costs, and battery life depreciation costs. Furthermore, this invention employs a robust optimization method to characterize uncertainties.
[0034] The scheduling objective is fully expressed by equations (1)-(6), where equation (1) defines the objective function, equations (2)-(4) describe the constraint sets of slow-motion variables, uncertain variables and fast-motion variables respectively, and equations (5)-(6) specify the cost parameters of each unit.
[0035]
[0036] Where A, U, and B represent the slow-motion variable set, the uncertain variable set, and the fast-motion variable set, respectively. F gt,start , and These represent the gas turbine's start-up cost, power generation status indicator, and start-up status indicator, respectively. and These represent the upper and lower deviations in the forecasts for electricity purchase and sale prices, wind power, photovoltaic power generation, and electricity load, respectively. F gt / b / egThese represent the costs of gas turbine power generation, battery lifespan depletion, and grid interaction, respectively. This represents the electricity purchase price, electricity sales price, and natural gas price for time period t. This represents the wind power output, photovoltaic power output, power load, gas turbine output, battery charging power, battery discharging power, electricity purchase power, and electricity sales power during time period t. This indicates the status of electricity purchase / sale / charging / discharging during time period t. This represents the state of charge of the battery at time t. gt,start This represents the start-up cost of a gas turbine. b η and η represent the battery operating efficiency and price coefficient, respectively.
[0037] Uncertainty modeling is shown in equations (7)-(10): Equation (7) stipulates that power and price uncertainties cannot shift upwards and downwards simultaneously, Equation (8) limits the duration of the total deviation, and Equations (9)-(10) constrain the fluctuation range of actual prices and power.
[0038]
[0039] Wherein, parameter Γ ep / es / wt / pv / el α is used to characterize the conservatism of the scheduler. ep / es / wt / pv / el + and α ep / es / wt / pv / el- These represent the upper and lower deviation errors of the predicted values, respectively. and This represents the predicted values for electricity price and power.
[0040] The microgrid operation constraints are given by equations (11)-(18), where: equation (11) limits the power interaction range with the external power grid; equations (12)-(13) constrain the power generation output and operating time of the gas turbine; equations (14)-(17) limit the charging and discharging power and energy storage state of the battery; and equation (18) is the system power balance equation.
[0041]
[0042]
[0043] in, and T gt These represent the maximum / minimum output and minimum operating time of the gas turbine, respectively. This represents the maximum power purchase / sale capacity between the microgrid and the external power grid. This represents the maximum charging / discharging power of the battery; This indicates its rated energy storage capacity.
[0044] This invention embodiment is for inner layers containing Boolean variables (i.e. and For the robust scheduling problem, a novel algorithm is proposed.
[0045] (1) Scheduling model transformation
[0046] The conventional two-stage robust scheduling model can be transformed into a static robust optimization problem. To quickly identify the worst-case scenario, favorable uncertainties such as rising electricity prices are directly excluded. The equivalent problem F... 1 The statement is as follows:
[0047]
[0048] Compared with the above model F 1 In contrast, this invention also constructs a system with a conservatism of Γ. ep / es / wt / pv / el Microgrid dispatch model F 2 As shown in equations (21)-(25): where equation (21) is the objective function, and equations (22)-(25) linearize the nonlinear constraint (5). This mixed integer linear programming (MILP) problem F 2 Given the same uncertainty scenario, its optimal solution value will be the same as F. 1 Maintain consistency.
[0049]
[0050] in, and Established.
[0051] (2) Solving the scheduling problem
[0052] For model F 2 Identify the worst-case scenario (not the optimal scenario) and establish a microgrid scheduling model F. 3 As shown in equations (26)-(28), where x represents its decision variable and the conservatism T-Γ ep / es / wt / pv / el Set to 1.
[0053]
[0054] Due to the existence of constraints (27)-(28), model F 2 With F 3 There is a conflict of interest. If F is solved in order from the optimal to the worst-case scenario... 3 Its target value generally shows an upward trend, while F 2 The target value will decrease accordingly (e.g.) Figure 3 (As shown). It should be noted that F 2 The target value may fluctuate slightly depending on the scenario, and its worst-case scenario will occur in F. 3 The neighborhood of the optimal scene.
[0055] Let the maximum number of iterations and the current number of iterations be K and k (k = 1, 2, ..., K), respectively. Based on the above analysis, the following iterative solution method is designed:
[0056] Step 1: Solve the integral equation (29), which will force the system to transition from the optimal scenario to the worst scenario. Proceed to Step 2 with the optimal solution.
[0057]
[0058] Step 2: Solve equation (30) to update parameter F 2,k And the iteration count k.
[0059]
[0060] Step 3: Check the termination condition. If k ≤ K, return to step 2; otherwise, output the optimal solution F. 1 We obtain the worst-case solution to the robust scheduling problem of microgrids.
[0061] The embodiments of the present invention also include the following simulation calculations: for Figure 2 The microgrid shown is used for a case study. Figure 4 The system displays forecast curves for wind power, photovoltaic power generation, load demand, and electricity purchase price, with the grid set at 0.2 times the electricity purchase price. The maximum permissible errors for each forecast are 0.2, 0.2, 0.1, 0.1, and 0.1, respectively. The maximum and minimum operating power of the gas turbine (GT) are 200kW and 20kW, respectively, with its minimum continuous operating time and generation cost set at 3 hours and 0.6 yuan / kWh, respectively. The battery has a rated capacity of 140kWh, a rated power of 70kW, an operating efficiency of 0.9, and a life-cycle depreciation cost of 0.6 yuan / kWh. The system scheduling cycle is set to 24 hours, with a time step of 1 hour. All numerical simulations are implemented in the MATLAB environment and the calculations are completed by calling the Gurobi solver through the Yalmip interface.
[0062] Optimization Result Analysis: To verify the effectiveness of the method of this invention, four comparison schemes with different levels of conservatism were set up:
[0063] a) Option 1: Set Γ ep / es / wt / pv / el =18 / 16 / 14 / 17 / 19
[0064] b) Option 2: Set Γ ep / es / wt / pv / el =12 / 10 / 10 / 8 / 12
[0065] c) Option 3: Set Γ ep / es / wt / pv / el =10 / 8 / 8 / 6 / 10
[0066] d) Option 4: Set Γ ep / es / wt / pv / el=4 / 6 / 2 / 5 / 4
[0067] Algorithm performance in four cases as follows Figure 5 As shown, Figure 5 In the diagram, A, B, C, and D represent coordinate points related to the worst-case scenario. Figure 5 It can be seen that as the number of iterations increases, the overall trend shows F 2 Decrease and F 3 An upward trend. Despite F 2 While slight fluctuations exist, the worst-case scenario can be accurately identified from the set of adverse scenarios in all four cases. Furthermore, as the level of conservatism decreases, the operating cost of the microgrid also decreases. These results validate the effectiveness of the proposed method.
[0068] In summary, this invention proposes a novel solution method for the two-stage robust scheduling problem in microgrids. This method transforms the min-max-min optimization model into two sets of conventional deterministic optimization problems with opposing uncertain Boolean variables, enabling iterative search for the worst-case scenario. Test results show that the proposed algorithm can effectively identify the worst-case operating scenario of the robust optimization problem.
[0069] The above description is merely a description of preferred embodiments of the present invention and is not intended to limit the scope of the present invention in any way. Any changes or modifications made by those skilled in the art based on the above disclosure shall fall within the protection scope of the claims.
Claims
1. A method for solving the robust scheduling problem of microgrids without dual transformation, characterized in that, include: The two-stage microgrid robust scheduling model is transformed into a master model with the same constraints and decision variable set. Construct an auxiliary model for the deterministic optimization scheduling master model, wherein the sum of the auxiliary model and the relevant Boolean variables representing uncertainty in the master model is equal to 1; Based on the conflict of interest between the main model and the auxiliary model, the auxiliary model iteratively searches for the optimal scenario at the forefront, while the main model selects the worst scenario from the corresponding adverse scenarios.
2. The method for solving the robust scheduling problem of microgrids without dual transformation as described in claim 1, characterized in that, The constructed deterministic optimization scheduling master model is as follows: Where A, U, and B represent the slow-motion variable set, the uncertainty factor-related variable set, and the fast-motion variable set, respectively; F gt ,start This indicates the start-up cost of a gas turbine; F gt / b / eg These represent the costs of gas turbine power generation, battery lifespan depletion, and grid interconnection, respectively. These represent the costs of purchasing and selling electricity; This represents the projected electricity price. Let α represent the purchase price and sales price of electricity in time period t, respectively; ep / es+ and α ep / es- These represent the upward and downward deviations of the predicted value, respectively. These represent the power purchased from and the power sold to the external power grid, respectively. These respectively indicate the upward and downward skewness of the electricity purchase and sale price forecast; and This holds true, where M is a sufficiently large positive number.
3. The method for solving the robust scheduling problem of microgrids without dual transformation as described in claim 2, characterized in that, The auxiliary model is: Where A', U', and B' represent the slow-motion variable set, the uncertainty factor-related variable set, and the fast-motion variable set in the auxiliary model, respectively; F gt，start′ F gt′ F b′ and F eg′ These represent the start-up cost of the gas turbine, the power generation cost of the gas turbine, the battery life loss cost, and the grid interaction cost in the auxiliary model, respectively. These represent the upper and lower skewness of the variables related to uncertainties in the power purchase and sale price, wind power, photovoltaic power generation, and power load in the auxiliary model, respectively. and T-Γ represents the up-skewness and down-skewness of the forecasts for the variables related to uncertainties in the main model, namely, electricity purchase and sale prices, wind power, photovoltaic power generation, and electricity load; ep / es / wt / pv / el The degree of conservatism in the problem is indicated by T; T represents the scheduling cycle in hours.
4. The method for solving the robust scheduling problem of microgrids without dual transformation as described in claim 3, characterized in that, It also includes the following iterative solution methods: Step 1: Solve for constraints Deterministic auxiliary model F 3 Among them, as the number of iterations k increases, the constraints This will force the auxiliary model F 3 The solution gradually transitions from the optimal scenario to the worst scenario, and the optimal solution is passed to step 2; Step 2: Solve the master model F 2,k and according to the formula Update F 1 The values are determined, and the parameters and iteration count k are updated. Step 3: Check the termination condition. Let K be the maximum number of iterations and k be the current number of iterations, i.e., k = 1, 2, ..., K. If k ≤ K, then return to step 2; otherwise, output the optimal solution F. 1 We obtain the worst-case solution to the robust scheduling problem of microgrids.
5. The method for solving the robust scheduling problem of microgrids without dual transformation as described in claim 4, characterized in that, The F 1 This is a two-stage robust scheduling model for microgrids, namely:
6. A solution system for the robust scheduling problem of microgrids without dual transformation, characterized in that, The method described in any one of claims 1 to 5 for solving the robust scheduling problem of microgrids without dual transformation is employed.
7. An electronic device, characterized in that, The electronic device includes a memory and a processor. The memory stores a computer program, and when the processor executes the computer program, it implements a solution method for the robust scheduling problem of microgrids without dual transformation as described in any one of claims 1 to 5.
8. A computer-readable storage medium, characterized in that, The computer-readable storage medium stores a computer program that, when executed by a processor, implements a method for solving a robust microgrid scheduling problem without dual transformation as described in any one of claims 1 to 5.