A robust unit commitment method for power system with wind power uncertainty

Abstract

This invention proposes a robust turbine unit combination method for power systems to address wind power uncertainties, specifically including the following steps: S1, establishing a robust turbine unit combination model considering K uncertainties; S2, establishing a robust turbine unit combination model for risk control; S3, using the C&CG algorithm, constructing and solving sub-problems and the main problem for both the robust turbine unit combination model considering K uncertainties and the robust turbine unit combination model for risk control, respectively, to obtain the robust turbine unit combination method for power systems. Based on the traditional two-stage robust turbine unit combination model, this invention considers multiple uncertainties, establishing a robust turbine unit combination model considering K uncertainties and a robust turbine unit combination model for risk control. Based on the framework of the main and sub-problems, a C&CG algorithm is constructed to solve these two new models, making the models both robust and economical.

Description

Technical Field

[0001] This invention relates to the field of power system operation and control technology, and specifically to a robust unit combination method for power systems to cope with the uncertainties of wind power. Background Technology

[0002] In power system optimal dispatch, the unit combination problem in day-ahead dispatch is crucial. Power system unit combination refers to a dispatching method that rationally formulates unit start-up and shutdown plans and rationally arranges the output of each unit within a certain dispatch cycle (usually one day) to minimize the total power generation cost of the system. The result of unit combination must meet both the electricity demand of users and the various security constraints of the power system.

[0003] In traditional power systems, uncertainty primarily stems from load fluctuations. Current technologies offer high accuracy in load forecasting, resulting in minimal deviations between forecasts and actual values; for daily load forecasts, the error typically does not exceed 5%. In day-ahead dispatching of traditional power systems, substituting forecasted load values ​​for actual load values ​​does not cause significant disruption. However, in power systems with a high proportion of wind power, in addition to load uncertainty, wind power output exhibits greater randomness and volatility. Despite extensive research on wind power output forecasting, current short-term wind power output forecasting errors remain around 20%, influenced by climate, topography, and temperature. Therefore, if traditional dispatching methods—using forecasted wind power output instead of actual output—continued after large-scale wind power grid integration, it would inevitably pose a severe challenge to the safe operation of the power system. Thus, researching power system unit combination methods that consider wind power uncertainty is of great significance.

[0004] Compared to stochastic optimization and interval optimization methods, robust optimization methods have moderate computational cost and ensure that the decisions made are feasible in any scenario, exhibiting excellent robustness and are widely used in unit combinatorial problems. However, traditional two-stage robust optimization methods suffer from excessive conservatism, often resulting in decisions that are uneconomical or fail to ensure the safe operation of the power system.

[0005] In view of this, the present invention proposes a robust unit combination method for power systems to cope with the uncertainties of wind power. Summary of the Invention

[0006] The purpose of this invention is to propose a robust unit combination method for power systems to cope with the uncertainties of wind power. Based on the traditional two-stage robust unit combination model, it considers multiple uncertainty sets and establishes a robust unit combination model that considers K uncertainty sets and a robust unit combination model that controls risks. Based on the principal-subproblem framework, a C&CG algorithm is constructed to solve the two new models, so that the model has both robustness and economy.

[0007] To achieve the above objectives, the technical solution of the present invention is: a robust turbine unit combination method for power systems to cope with wind power uncertainties, specifically including the following steps:

[0008] S1. Establish a robust unit combination model considering K uncertain sets, the model including a first stage and a second stage;

[0009] The goal of the first phase of the model is to minimize the start-up and shutdown costs of the unit; the decision variables include the unit operating state variables and the unit start-up / shutdown state variables; the constraints considered in the first phase of decision-making include the minimum operating time constraint, the minimum shutdown time constraint, and the logical constraints between the start-up / shutdown state variables and the operating state variables.

[0010] The objective of the second stage of the model is to minimize the sum of the fuel cost and the wind curtailment penalty cost of the system corresponding to the K uncertain sets, under the worst-case scenario where all uncertain parameters of the K uncertain sets are taken. The decision variables include the output of each unit. The constraints considered in the second stage decision include the output constraints of thermal power units, system power balance constraints, thermal power unit ramping constraints, wind farm output constraints, transmission line transmission capacity constraints, system reserve capacity constraints, and non-negativity constraints of decision variables.

[0011] S2. Establish a robust unit combination model for controlling risks, the model including a first stage and a second stage;

[0012] The goal of the first stage of the model is to minimize the total cost under the most likely prediction scenario. The decision variables include unit operating status variables, unit start-up / shutdown status variables, and the corresponding thermal power unit output and wind farm optimal dispatch output under the prediction scenario. The constraints are the minimum unit operation / shutdown time constraint and various power system security constraints under the prediction scenario.

[0013] The objective of the second stage of the model is to determine the performance indicators set by decision-makers based on uncertain parameters under adverse scenarios; the decision variables are the optimal dispatch output of wind farms and the output of thermal power units corresponding to each uncertainty set; and the constraints are the various safety constraints of the power system.

[0014] S3. Using the C&CG algorithm, sub-problems and main problems are constructed and solved for the robust unit combination model considering K uncertain sets and the robust unit combination model considering control risks, respectively, to obtain a robust unit combination method for power systems.

[0015] Preferably, the objective function of the robust unit combination model considering K uncertain sets is specifically:

[0016] (2)

[0017] In the formula, x, y, z, u, and ŵ represent the operating status of the thermal power unit, the output of the thermal power unit, the start-up status of the thermal power unit, the shutdown status of the thermal power unit, and the output vector of the wind turbine unit, respectively. This represents the total number of thermal power units. Total scheduling time period; The number of episodes is uncertain. For the number of wind farms; For the unit Startup costs; For the unit Downtime costs; For the unit Fuel costs; For wind farm The unit cost of wind curtailment; The weight coefficients are the values ​​corresponding to the k-th uncertain set. For the unit exist The start status of the time period; For the unit exist The downtime status during a specific period; For the unit exist Efforts during a specific time period; For wind farm exist Wind power output during specific time periods; For wind farm exist The optimal power output for the time period; the first term in equation (2) is the objective of the first stage, which is to minimize the start-up and shutdown costs of the units; the second term in equation (2) is the objective of the second stage, which is to minimize the sum of the fuel cost and the wind curtailment penalty cost of the system corresponding to the K uncertain sets, under the worst-case scenario where all the uncertain parameters of the K uncertain sets are taken; where, the first term is the objective of the second stage, which is to minimize the sum of the fuel cost and the wind curtailment penalty cost of the system corresponding to the K uncertain sets; The form of the wind power uncertainty set is as follows:

[0018] (1)

[0019] In the formula, This represents the total number of wind farms. This represents the total number of scheduling periods; For the first An uncertain centralized wind farm exist The upper limit of wind power output during a certain period For the first An uncertain centralized wind farm exist Lower limit of wind power output during a given time period; For wind farm exist Forecasted wind power output for a given period; , These are introduced auxiliary variables used to control the wind farm. Whether the wind power output reaches the boundary of the uncertain set, when When it is 1, When the value of reaches the upper limit of the interval, When it is 1, The value of reaches the lower limit of the interval; when both are 0, ... The value is the predicted value; , This is a conservative control parameter used to control the number of times the actual wind power output reaches the boundary.

[0020] Preferably, the minimum operating time constraint, the minimum downtime constraint, and the logical constraints between the start / stop state variables and the operating state variables are as follows;

[0021] Minimum operating time constraints for the unit:

[0022] (3)

[0023] In the formula, For the unit Minimum runtime; For the unit exist Operating status during a given time period;

[0024] Minimum downtime constraints for the unit:

[0025] (3)

[0026] In the formula, For the unit Minimum downtime;

[0027] Logical constraints between start / stop status variables and running status variables:

[0028] (5)

[0029] (6)

[0030] In equations (3) to (6), .

[0031] Preferably, the constraints on thermal power unit output, system power balance, thermal power unit ramping, wind farm output, transmission line capacity, system reserve capacity, and decision variable nonnegativity are as follows;

[0032] Thermal power unit output constraints:

[0033] (7)

[0034] In the formula, and The units Upper and lower limits of output;

[0035] System power balance constraints:

[0036] (8)

[0037] In the formula, This represents the total number of wind farms. for Total load during the period , The total number of load nodes. For load nodes exist Load during a given time period;

[0038] Thermal power unit ramping constraints:

[0039] (9)

[0040] (10)

[0041] In the formula, It is a generator set Maximum upward output; It is a generator set Maximum downward output;

[0042] Wind farm output constraints:

[0043] (11)

[0044] Transmission line capacity constraints:

[0045] (12)

[0046] In the formula, For the line Maximum transmission capacity; G l-i G l-j and G l-m thermal power units The node is connected to the line Generator output power transfer distribution factor, wind farm The node is connected to the line The generator output power transfer distribution factor and load node For the line The generator output power transfer distribution factor is calculated as follows:

[0047] G l-i =(X m’,i - X n’,i ) / x l G l-j =(X m’,j - X n’,j ) / x l G l-m =(X m’,m - X n’,m ) / x l ,in For the line Reactance, subscript and For the line The first and last nodes, All are elements in the impedance matrix;

[0048] System backup capacity constraints:

[0049] (13)

[0050] In the formula, Spinning reserve ratio;

[0051] Non-negativity constraint for decision variables:

[0052] (14).

[0053] Preferably, in step S3, the robust unit combination model considering K uncertain sets is solved using the C&CG algorithm, specifically as follows:

[0054] Step 1: Construct the main problem and the subproblems after KKT transformation, initialize the parameters of each model, set UB=Inf, LB=-Inf, and the initial number of iterations k0=1;

[0055] Step 2: Solve the main problem to obtain the solution for the decision variables in the first stage. At the same time, update the lower bound. ;

[0056] Step 3: Solve the Substitution subproblem Solve each subproblem;

[0057] Step 4: Determine if all subproblems have solutions. If all subproblems have solutions, return the constraints: To the main question, and update the upper bound. ;

[0058] Step 5: Return the constraints corresponding to the worst-case scenario found in each subproblem to the main problem;

[0059] Step 6: Determine if the upper bound approaches the lower bound. If so, end the iteration and obtain the optimal solution. If not, set k0 = k0 + 1, return to step 2, and proceed to the next iteration.

[0060] Preferably, the robust unit combination model considering K uncertain sets is used to construct and solve subproblems, specifically as follows:

[0061] Based on the given first-stage decision variables , define the first The sub-problems are as follows:

[0062] (36)

[0063] (37)

[0064] (38)

[0065] (8)

[0066] (39)

[0067] (40)

[0068] (11)

[0069] (12)

[0070] (41)

[0071] (14)

[0072] The above subproblem is a two-layer problem with a max-min structure. The inner-min linear programming problem is transformed into a max-structure MILP problem by removing the min sign from the KKT conditions and then using the Big M method to convert the complementary relaxation constraints in the KKT conditions into inequality constraints.

[0073] The main problem for constructing and solving a robust unit combination model considering K uncertain sets is as follows:

[0074] After solving the subproblems, the scenarios identified by the subproblems and their corresponding constraints are gradually added back to the main problem. The main problem is constructed as follows:

[0075] (42)

[0076] (43)

[0077] (44)

[0078] (45)

[0079] (46)

[0080] (47)

[0081] (48)

[0082] (49)

[0083] (50)

[0084] (51)

[0085] (52)

[0086] (53)

[0087] (54)

[0088] (55)

[0089] in, express The scenario for identifying a quilt problem; Equations (3) to (6) are constraints related to the decision variables in the first stage; in Equation (44) For the first The first uncertain set The second-stage objective function corresponding to each extreme point introduces auxiliary variables. The two-stage robust optimization model is transformed into a one-stage optimization problem; Equations (45)-(55) represent the scenarios identified by the sub-problems. The corresponding constraints, among which , For the scene Corresponding decision variables;

[0090] In each iteration, the main problem will return a scenario. The corresponding constraints must be met, and the scene must be generated simultaneously. Corresponding decision variables , As the iteration progresses, the constraints in the main problem increase, and the number of bad scenarios considered in the main problem gradually increases, making the decision in the first stage better.

[0091] Preferably, the objective function of the first stage of the robust unit combination model for controlling risk is specifically set as follows:

[0092] (17)

[0093] In the formula, For wind farm The unit cost of wind curtailment; For wind farm exist Forecast wind power output for the specified time period; In order to be in Scenario Unit exist Efforts during a specific time period; In order to be in Wind farm in the scenario exist The optimal power output for the time period; Equation (17) is to minimize the sum of start-up and shutdown costs, fuel costs and wind curtailment penalty costs when the wind power output is the predicted value.

[0094] Preferably, the constraints related to the decision variables in the first stage of the robust unit combination model for controlling risk are as follows:

[0095] (18)

[0096] (19)

[0097] (20)

[0098] (twenty one)

[0099] (twenty two)

[0100] (twenty three)

[0101] (twenty four)

[0102] (25)

[0103] (26)

[0104] Equations (3) to (6) represent the minimum operating and downtime constraints of the unit, as well as the logical constraints between the decision variables; Equations (19) to (26) represent the prediction scenarios. Various safety constraints of the power system.

[0105] Preferably, the constraints related to the second-stage decision variables and the constraints for controlling risk in the robust unit combination model for controlling risk are as follows:

[0106] Constraints related to the decision variables in the second stage:

[0107] (27)

[0108] (28)

[0109] (29)

[0110] (30)

[0111] (31)

[0112] (32)

[0113] (33)

[0114] (34)

[0115] In the formula, For the first Wind farms corresponding to an uncertain set exist Wind power output during specific time periods; For the first Units corresponding to an uncertain set exist Efforts during a specific time period; For the first Wind farms corresponding to an uncertain set exist Optimal output scheduling for each time period; Equations (27)-(34) are the first... Each unit's safe output constraints correspond to an uncertain set;

[0116] Constraints for controlling risk:

[0117] (35)

[0118] Equation (35) is the hard constraint imposed by the decision-maker on the performance indicators set for adverse scenarios: in the first... Under the worst-case scenario, the sum of the minimum operating cost of a thermal power unit and the cost of wind curtailment penalty must not exceed a given limit. .

[0119] Preferably, the robust unit combination model for controlling risk is solved using the C&CG algorithm, as follows:

[0120] Step 1: Construct the main problem and sub-problem models, and initialize the various parameters;

[0121] Step 2: Solve the initial master problem to obtain the optimal solution for the predicted scenario. ;

[0122] Step 3: Put Substitution Solve the K subproblems;

[0123] Step 4: Return the constraints corresponding to the scenarios identified in each sub-problem to the main problem;

[0124] Step 5: Determine whether each subproblem has a solution and whether the hard constraints corresponding to each subproblem are satisfied; if each subproblem has a solution and the hard constraints corresponding to each subproblem are satisfied, end the iteration and obtain the final optimal solution; otherwise, return the hard constraint conditions corresponding to the scenario identified by the subproblem to the main problem, increment the iteration count by one, return to step 2, and enter the next iteration;

[0125] The method for constructing and solving subproblems in a robust unit combination model for controlling risks is consistent with the method for constructing and solving subproblems in a robust unit combination model considering K uncertain sets.

[0126] The main problem of constructing and solving a robust unit combination model for risk control is as follows:

[0127] (56)

[0128] (57)

[0129] (58)

[0130] Equations (3) to (6) represent the constraints related to the decision variables in the first stage; Equations (18) to (25) represent the prediction scenarios. The following are the safety constraints of the power system; Equations (45)-(55) are the constraints corresponding to the scenarios identified by the sub-problem; Equation (57) is the hard constraint that the objective function of the sub-problem needs to satisfy;

[0131] Substitute the decisions of the main problem into the subproblems, and determine whether the performance indicators of each subproblem meet the requirements, which serves as the basis for whether the iteration should terminate.

[0132] Compared with the prior art, the present invention has the following beneficial effects:

[0133] This invention, based on the traditional two-stage robust unit combination model, proposes an improved robust unit combination model that considers multiple uncertainty sets to address the significant impact of uncertainty set selection on decision-making outcomes. By introducing K uncertainty sets, a new robust unit combination model is established, and the influence of each uncertainty set is integrated through weighting coefficients, balancing the model's conservatism and risk. This model framework is similar to the traditional two-stage robust unit combination model, but the introduction and integration of multiple uncertainty sets enhances the flexibility and accuracy of decision-making. Simultaneously, a risk-controlled robust unit combination model is constructed, adding hard constraints to the traditional prediction scenario to ensure performance index control under the worst-case scenario, further improving the system's safety and robustness. Attached Figure Description

[0134] Figure 1 The flowchart of the C&CG algorithm for the robust unit combination model considering K uncertain sets in this invention is shown below;

[0135] Figure 2 This is a flowchart of the C&CG algorithm for the robust unit combination model for risk control in this invention. Detailed Implementation

[0136] The following is in conjunction with the appendix Figure 1-2 The technical solution of the present invention will be described in detail below.

[0137] (1) Based on the traditional two-stage robust unit combination model, this invention first establishes a robust unit combination model considering K uncertainties, according to the idea of ​​selecting multiple uncertainties to balance conservatism and risk. Its basic framework is similar to that of the traditional two-stage robust unit combination model, except that the model of this invention considers more uncertainties and integrates the influence of each uncertainty set together through weight coefficients. Secondly, a robust unit combination model for controlling risk is constructed, which is similar to the basic framework of the traditional unit combination model. The target scenarios are all predicted scenarios, except that the model of this invention adds hard constraints to limit the performance indicators under the worst scenario.

[0138] (2) This invention constructs a column and constraint generation algorithm based on the master-subproblem framework to solve two new models. The subproblems of both new models are max-min structure problems, which cannot be solved directly. First, the inner min problem is transformed into a set of equations using KKT conditions, and then the complementary relaxation constraints are transformed using the Big M method, finally transforming it into a max structure MILP problem. The master problem of both models is itself a MILP problem, and MILP problems are easy to solve using existing solvers. Therefore, after transformation, both the master problem and the subproblems can be solved.

[0139] 1. Consider robust unit combination modeling with K uncertain sets.

[0140] The model considers the randomness and volatility of wind power output, meaning that the output of each wind farm fluctuates between the predicted value and the predicted boundary value. It also considers the temporal and spatial correlation of wind power output, ensuring that the number of times the same wind farm reaches the predicted boundary value at different times does not exceed a given value, and the number of times different wind farms reach the predicted boundary value at the same time does not exceed a given value. The model considers multiple uncertainty sets; the first set is given below. The form of the wind power uncertainty set is as follows:

[0141] (1)

[0142] In the formula, This represents the total number of wind farms. This represents the total number of scheduling periods; For the first An uncertain centralized wind farm exist The upper limit of wind power output during a certain period For the first An uncertain centralized wind farm exist Lower limit of wind power output during a given time period; For wind farm exist Forecasted wind power output for a given period; , These are introduced auxiliary variables used to control the wind farm. Whether the wind power output reaches the boundary of the uncertain set, when When it is 1, When the value of reaches the upper limit of the interval, When it is 1, The value of reaches the lower limit of the interval; when both are 0, ... The value is the predicted value; , This is a conservative control parameter used to control the number of times the actual wind power output reaches the boundary.

[0143] For the first-stage model, the objective is to minimize the unit start-up and shutdown costs. The decision variables are 0-1 variables and must be made before the uncertain parameters are determined. These are generally unit operating state variables and unit start-up / shutdown state variables. The constraint related to the first-stage decision is the minimum unit operating / shutdown time constraint.

[0144] For the second-stage model, since it considers a high proportion of wind power integration and the possibility that not all wind power may be absorbed, a curtailment penalty cost needs to be included. Therefore, the objective of the second stage is to minimize the sum of the system's fuel cost and curtailment penalty cost, assuming the worst-case scenario for all uncertain parameters in the K uncertain sets. The decision variables in the second stage are continuous variables, determined after the first-stage decision variables and the second-stage uncertain parameters are finalized; these are typically the output of each generating unit. The constraints related to the second-stage decision are the various security constraints of the power system. Because the improved model considers multiple uncertain sets, the uncertainties are described more fully, and the decision-making better balances risk and conservatism.

[0145] 1.1 Objective Function

[0146] (2)

[0147] In the formula, x, y, z, u, and ŵ represent the operating status of the thermal power unit, the output of the thermal power unit, the start-up status of the thermal power unit, the shutdown status of the thermal power unit, and the output vector of the wind turbine unit, respectively. This represents the total number of thermal power units. Total scheduling time period; The number of episodes is uncertain. For the number of wind farms; For the unit Startup costs; For the unit Downtime costs; For the unit Fuel costs; For wind farm The unit cost of wind curtailment; The weight coefficients are the values ​​corresponding to the k-th uncertain set. For the unit exist The start status of the time period; For the unit exist The downtime status during a specific period; For the unit exist Efforts during a specific time period; For wind farm exist Wind power output during specific time periods; For wind farm exist Optimal power output scheduling during specific time periods. Equation (2) essentially combines the objectives of the first and second stages of the model for joint optimization. The first term of the equation represents the objective of the first stage, and the second term represents the objective of the second stage, ensuring that the overall objective function is minimized even when the uncertain parameters are in their worst-case scenario. That is, the sum of start-up and shutdown costs, fuel costs, and wind curtailment penalty costs is minimized.

[0148] 1.2 Constraints Considered in the First Stage of Decision-Making

[0149] (a) Minimum operating time constraints of the unit

[0150] Due to thermal inertia, thermal power units must remain running for a period of time after startup before being shut down. This constraint can be expressed in the following form:

[0151] (3)

[0152] In the formula, For the unit Minimum runtime; For the unit exist The operational status of a given time period.

[0153] (b) Minimum downtime constraints of the unit

[0154] Also due to the influence of thermal inertia, thermal power units need sufficient time to cool down after shutdown before they can be started up again. This constraint can be written in the following form:

[0155] (4)

[0156] In the formula, For the unit Minimum downtime.

[0157] (c) Logical constraints between start / stop state variables and running state variables

[0158] These three variables do not exist independently; they are mutually determined and satisfy certain logical relationships:

[0159] (5)

[0160] (6)

[0161] In equations (3) to (6), .

[0162] 1.3 Constraints to be considered in the second stage of decision-making

[0163] (a) Output constraints of thermal power units

[0164] The output range of thermal power units is strictly limited; its upper limit is usually the rated power of the thermal power unit; its lower limit is the minimum output value that must be guaranteed when the unit is in operation, usually to keep the boiler from shutting down.

[0165] (7)

[0166] In the formula, and The units The upper and lower limits of output.

[0167] (b) System power balance constraints

[0168] When power system network losses are ignored, according to Kirchhoff's current law, the sum of the output of each thermal power unit and the output of each wind power unit in the system at any given time is equal to the load of the system.

[0169] (8)

[0170] In the formula, This represents the total number of wind farms. for Total load during the period , The total number of load nodes. For load nodes exist Load during a given time period.

[0171] (c) Gradient constraints of thermal power units

[0172] During the scheduling process, the output of each thermal power unit needs to be adjusted according to the load of the system at different times. Within a certain period of time during the adjustment process, the adjustment range of the output of each thermal power unit must not exceed a certain value. In addition, the output during the unit's start-up period and the output during the period before the unit is shut down must not exceed the unit's minimum output value.

[0173] (9)

[0174] (10)

[0175] In the formula, It is a generator set Maximum upward output; It is a generator set The maximum downward output.

[0176] (d) Wind farm output constraints

[0177] At any given time, the optimal dispatch output of each wind farm should be greater than or equal to 0, and not greater than the wind power output of that wind farm.

[0178] (11)

[0179] (e) Transmission line capacity constraints

[0180] Each line in the system has its maximum permissible active power limit. The Generation Transfer Distribution Factor (GTDF) is typically used to describe the changes in active power flow in the lines caused by variations in generator active power output. When the output of each thermal power unit changes, the power flow in the lines also changes, and it is necessary to consider whether the active power transmitted in the lines exceeds the limit.

[0181] (12)

[0182] In the formula, G l-i G l-j and G l-m thermal power units The node is connected to the line Generator output power transfer distribution factor, wind farm The node is connected to the line The generator output power transfer distribution factor and load node For the line The generator output power transfer distribution factor, in order to For example, the calculation method is as follows: G l-i =(X m,i - X n,i ) / x l ,in For the line Reactance, and For the line The first and last nodes, and These are elements in the impedance matrix; For the line Maximum transmission capacity.

[0183] (f) System reserve capacity constraints

[0184] The system's backup capacity ensures the system's ability to continue supplying power in the event of a fault. It is typically the difference between the maximum output of all operating thermal power units and the sum of the output of wind power units in the system and the actual load of the system.

[0185] (13)

[0186] In the formula, The spinning reserve rate is determined by operational experience.

[0187] (g) Nonnegativity constraint of decision variables

[0188] The output of each thermal power unit should be greater than or equal to 0 at any given time.

[0189] (14)

[0190] 1.4 Further Explanation of the Model

[0191] First, we consider only the case with two uncertain sets. Similar to the fundamental lemma presented in this section, we take uncertain sets... Included in the uncertain set ,set up The corresponding weighting coefficient is , The corresponding weighting coefficient is And there are , This is the optimal value for the model. By the fundamental lemma, we obtain:

[0192] (15)

[0193] In the formula, when or The equality holds when the value is 0.

[0194] From this formula, we can deduce that the decision obtained by considering a robust unit combination model with two uncertain sets is better than that obtained by considering only two uncertain sets. Decisions made in a shorter timeframe are more reliable. This is because decisions made within a smaller scope... It may not encompass the most severe actual scenarios, but after considering two uncertain sets, through The impact of this makes up for the deficiency. At the same time, the decisions made by the new model are better than those considering only... The decisions made at that time were less conservative. An excessively large range increases uncertainty, while considering two uncertain sets can reduce this effect, thus reducing the model's conservatism and improving the system's economy.

[0195] Admittedly, the above conclusions can be generalized to the case of K uncertain sets.

[0196] There are K uncertain sets, where the k-th uncertain set is... The corresponding weighting coefficient is And there are , Let this be the optimal value for the model. Then we have:

[0197] (16)

[0198] In a robust turbine unit combination model considering K uncertainties, the selection of weighting coefficients is crucial. It reflects the decision-maker's risk preference. If the probability of wind power output falling within a certain uncertainty set is higher, a larger weighting coefficient can be assigned to that uncertainty set.

[0199] 2. Robust unit combination model for risk control

[0200] The robust unit combination model for controlling risks also considers the impact of multiple uncertainties. However, unlike the robust unit combination model that considers K uncertainties, this model solves for the optimal value under a certain scenario that the decision-maker wants to consider. It adds constraints to the performance indicators that need to be considered under the worst scenario as constraints to the model.

[0201] For the first stage of the model, the decision variables include unit operating state variables, unit start-up / shutdown state variables, and the corresponding thermal power unit output and wind farm optimal dispatch output under the predicted scenario. The objective function considers minimizing the total cost under the most likely scenario (the predicted scenario), which is also the overall objective function of the model; the constraints are the minimum unit operation / shutdown time constraint and various power system security constraints under the predicted scenario.

[0202] For the second stage of the model, the decision variables are the optimal dispatch output of wind farms and the output of thermal power units corresponding to each uncertainty set. The objective function is the performance indicator that the decision-maker wants to consider under the worst-case scenario, which can be wind curtailment, wind curtailment penalty cost, load reduction, etc., and is formulated by the decision-maker based on the uncertainty parameters. The constraints are the various security constraints of the power system.

[0203] The model's decision minimizes the total cost in the most probable scenario (predicted scenario) while remaining feasible in the worst-case scenario, thus ensuring the model's robustness. Because the model imposes hard constraints on performance metrics in the worst-case scenario, as long as a solution exists, the given decision guarantees that its expected performance metrics in the worst-case scenario will not exceed the set value.

[0204] 2.1 Objective Function

[0205] (17)

[0206] In the formula, For wind farm The unit cost of wind curtailment; For wind farm exist Forecast wind power output for the specified time period; In order to be in Scenario Unit exist Efforts during a specific time period; In order to be in Wind farm in the scenario exist Optimal power output scheduling during specific time periods. Equation (17) essentially aims to minimize the overall objective function when the wind power output is the predicted value. That is, to minimize the sum of start-up and shutdown costs, fuel costs, and wind curtailment penalty costs.

[0207] 2.2 Constraints related to the decision variables in the first stage

[0208] (18)

[0209] (19)

[0210] (20)

[0211] (twenty one)

[0212] (twenty two)

[0213] (twenty three)

[0214] (twenty four)

[0215] (25)

[0216] (26)

[0217] Equations (3) to (6) represent the minimum operating and downtime constraints of the unit, as well as the logical constraints between the decision variables; Equations (19) to (26) represent the prediction scenarios. The power system is subject to various security constraints. These constraints ensure the feasibility of the given decisions under the predicted scenario.

[0218] 2.3 Constraints related to the decision variables in the second stage

[0219] (27)

[0220] (28)

[0221] (29)

[0222] (30)

[0223] (31)

[0224] (32)

[0225] (33)

[0226] (34)

[0227] In the formula, For the first Wind farms corresponding to an uncertain set exist Wind power output during specific time periods; For the first Units corresponding to an uncertain set exist Efforts during a specific time period; For the first Wind farms corresponding to an uncertain set exist Optimal power output scheduling for each time period. Equations (27)-(34) are the first... The constraints on the safe output of each unit corresponding to the uncertain set ensure that the given decision is feasible under the worst-case scenario.

[0228] 2.4 Constraints for Risk Control

[0229] (35)

[0230] Equation (35) is the hard constraint imposed by the decision-maker on the performance indicators to be considered in the worst-case scenario. The hard constraint considered in this invention patent is in the first... In the worst-case scenario, the sum of the operating cost and the wind curtailment penalty cost of the smallest thermal power unit must not exceed a given limit. By adding this constraint, as long as the model has a solution, the cost in the worst-case scenario is guaranteed not to be too high.

[0231] 2.5 Further Explanation of the Model

[0232] The robust unit combination model for risk control follows the approach of considering multiple uncertainty sets. The model does not include weighting coefficients; each uncertainty set has a corresponding hard constraint coefficient. Hard constraint coefficients also reflect the decision-maker's judgment on the selected uncertainty set. Generally, larger hard constraint coefficients should be set for uncertainty sets with larger ranges. If a larger hard constraint coefficient is set for a small uncertainty set, then the constraint effectively loses its meaning. This is because the model imposes stricter constraints on more severe scenarios, and looser constraints can be omitted.

[0233] The core objective of this model has shifted; it no longer seeks the optimal decision under the worst-case scenario, but rather the optimal decision under the most likely scenario, consistent with traditional unit combination models. However, the model imposes a hard constraint on a certain performance metric under the worst-case scenario, ensuring its robustness and that the decisions it provides meet the decision-maker's expectations. Furthermore, the model can detect whether the system can adequately handle uncertainty. When decision-makers expect a certain performance metric to meet a requirement under the worst-case scenario, but the model has no solution, it indicates that the system is no longer adequately able to cope with the challenges of uncertainty. This provides strong support for decision-makers to consider whether to expand or modify the system to address uncertainty.

[0234] In summary, the robust unit combination model for risk control is suitable when decision-makers prioritize the benefits under predicted scenarios and can accept that a certain performance index under the worst-case scenario does not exceed a preset value. This model is also suitable for systems with a low probability of uncertain events, such as unexpected events like unit failures and outages. If decision-makers are more concerned with the magnitude of load shedding during unit failures and outages, then a hard constraint on the load shedding during sudden events can be added to the model.

[0235] 3. C&CG algorithm for solving robust unit combination models considering K uncertain sets.

[0236] 3.1 Construction and solution of subproblems

[0237] In a robust unit combination model considering K uncertainties, it is assumed that the first-stage decision variables in the subproblems are given. The objective of the subproblems is to allocate the output of thermal power units and the optimal dispatch output of each wind farm under a given unit combination, so as to minimize the sum of unit operating costs and wind curtailment penalty costs in the worst-case scenario. The model considers K uncertainties and has K subproblems. Given the first-stage decision variables... , define the first The sub-problems are as follows:

[0238] (36)

[0239] (37)

[0240] (38) (8)

[0242] (39)

[0243] (40)

[0244] (11)-(12)

[0245] (41) (14)

[0247] It can be seen that solving the th This sub-problem corresponds to the second stage of solving the model. In the second stage, the decision variables and constraints from the first stage have been determined. The value is known in the subproblem. The second stage solves a max-min problem, seeking the optimal value under the worst-case scenario given the unit configuration. However, this "worst-case scenario" may not be the worst-case scenario for the entire problem, because the given unit configuration may not be the optimal solution for the entire problem. Furthermore, the given unit configuration may contain subproblems that have no solution.

[0248] Although the "worst-case scenario" may not be the worst-case scenario for the entire problem, we can add its corresponding constraints back to the main problem. With more worst-case scenarios considered in the main problem and stricter constraints, the given unit combination will be improved, making it more likely that the next "worst-case scenario" identification will be closer to the worst-case scenario for the entire problem.

[0249] Observing the above formula, this subproblem is a two-layer problem with a max-min structure, the inner layer being a linear programming problem with a min structure. First, the min structure linear programming problem is transformed by removing the min sign from the KKT conditions. Second, the complementary relaxation constraints (nonlinear constraints) in the KKT conditions are converted into inequality constraints using the Big M method. Finally, the max-min problem is transformed into a MILP problem with a max structure.

[0250] 3.2 Construction and Solution of the Main Problem

[0251] The influence of uncertain sets is initially ignored in the main problem. After solving the subproblems, the scenarios identified by the subproblems and their corresponding constraints are gradually added back to the main problem. The main problem is constructed as follows:

[0252] (42)

[0253] (43)

[0254] (44)

[0255] (45)

[0256] (46)

[0257] (47)

[0258] (48)

[0259] (49)

[0260] (50)

[0261] (51)

[0262] (52)

[0263] (53)

[0264] (54)

[0265] (55)

[0266] in, express The scenario for identifying a quilt problem; Equations (3) to (6) are constraints related to the decision variables in the first stage; in Equation (44) For the first The first uncertain set The second-stage objective function corresponding to each extreme point introduces auxiliary variables. The two-stage robust optimization model is transformed into a one-stage optimization problem; Equations (45)-(55) represent the scenarios identified by the sub-problems. The corresponding constraints, among which , For the scene The corresponding decision variables.

[0267] It can be seen that in each iteration, the main problem will return a scenario. The corresponding constraints must be met, and the scene must be generated simultaneously. Corresponding decision variables , Therefore, as the number of iterations increases, the number of constraints and decision variables in the main problem will gradually increase, that is, the number of rows and columns in the main problem increases with the iteration. Hence, this algorithm is called the column and constraint generation algorithm.

[0268] As the iterations proceed, the constraints in the returning master problem increase, and the number of bad scenarios considered in the master problem gradually increases, leading to better decisions in the first stage. Furthermore, the master problem is clearly a MILP problem, which is quite easy to solve.

[0269] 4. Solving the robust unit combination model for risk control using the C&CG algorithm.

[0270] 4.1 Construction and solution of subproblems

[0271] In the robust unit combination model for risk control, since the hard constraints considered in the second stage are in the first stage... In the worst-case scenario, the sum of the operating cost and the wind curtailment penalty cost of the smallest thermal power unit must not exceed a given limit. Therefore, the objective function and constraints in the second stage are consistent with those in Model 1. The construction and solution methods of the subproblems in Model 1 have been described above, and will not be repeated here.

[0272] It is worth noting that the above results are only obtained when the objective functions of the two models in the second stage of this invention are consistent. As mentioned earlier, in the robust unit combination model for risk control, decision-makers determine the performance indicators to be controlled under the worst-case scenario based on the form of the uncertainty set. If this performance indicator is changed, then when constructing the sub-problems of Model Two, only the following modifications are needed. The objective function and equations (36)-(37) are given, and the remaining constraints do not need to be modified.

[0273] 4.2 Construction and Solution of the Main Problem

[0274] The main problem of a robust unit combination model for risk control is constructed as follows:

[0275] (56)

[0276] (57)

[0277] (58)

[0278] Equations (3) to (6) represent the constraints related to the decision variables in the first stage; Equations (18) to (25) represent the prediction scenarios. The power system safety constraints are as follows: Equations (45)-(55) are the constraints corresponding to the scenarios identified by the subproblems; Equation (57) is the hard constraint that the objective function of the subproblems needs to satisfy.

[0279] In summary, the objective function of the main problem is consistent with the objective function of the first stage, therefore no auxiliary variables need to be constructed. Furthermore, the model focuses on whether a certain performance metric meets the requirements under the worst-case scenario. Since solving the subproblems is to determine whether the performance metric meets the requirements, and does not concern itself with the specific value of that performance metric, the entire model does not need to update the upper and lower bounds to achieve convergence. It only needs to substitute the decisions of the main problem into the subproblems and determine whether the performance metric of each subproblem meets the requirements, serving as the basis for whether the iteration terminates. Additionally, it is worth noting that this main problem is also a MILP problem, which can be easily solved using solvers like CPLEX.

[0280] The detailed flowchart of the C&CG algorithm for a robust unit combination model considering K uncertain sets is as follows: Figure 1 As shown:

[0281] Step 1: Construct the main problem mentioned above and the subproblems after KKT transformation, initialize the parameters of each model, set UB=Inf, LB=-Inf, and the initial number of iterations k=1;

[0282] Step 2: Solve the main problem to obtain the solution for the decision variables in the first stage. At the same time, update the lower bound. ;

[0283] Step 3: Solve the Substitution Solve each subproblem;

[0284] Step 4: Determine if all subproblems have solutions. If all subproblems have solutions, return the constraints: To the main question, and update the upper bound. ;

[0285] Step 5: Return the constraints corresponding to the "worst-case scenario" found in each subproblem to the main problem;

[0286] Step 6: Determine if the upper bound approaches the lower bound. If yes, end the iteration and obtain the optimal solution. If not, set k = k + 1, return to step 2, and proceed to the next iteration.

[0287] The detailed flowchart of the C&CG algorithm for the robust unit combination model for risk control is as follows: Figure 2 As shown:

[0288] Step 1: Construct the main problem and sub-problem models, and initialize the various parameters;

[0289] Step 2: Solve the initial master problem to obtain the optimal solution for the predicted scenario. ;

[0290] Step 3: Put Substitution Solve the K subproblems;

[0291] Step 4: Return the constraints corresponding to the scenarios identified in each sub-problem to the main problem;

[0292] Step 5: Determine if each subproblem has a solution and if the hard constraints corresponding to each subproblem are satisfied. If all subproblems have solutions and the hard constraints corresponding to each subproblem are satisfied, end the iteration and obtain the final optimal solution. Otherwise, return the hard constraints corresponding to the scenario identified in the subproblem to the main problem, increment the iteration count by one, return to Step 2, and proceed to the next iteration.

[0293] The above are preferred embodiments of the present invention. Any changes made to the technical solution of the present invention that do not exceed the scope of the technical solution of the present invention shall fall within the protection scope of the present invention.

Claims

1. A method for robust unit commitment of power system against wind power uncertainty, characterized in that, Specifically, the following steps are included: S1. Establish a robust unit combination model considering K uncertain sets, the model including a first stage and a second stage; The goal of the first phase of the model is to minimize the start-up and shutdown costs of the unit; the decision variables include the unit operating state variables and the unit start-up / shutdown state variables; the constraints considered in the first phase of decision-making include the minimum operating time constraint, the minimum shutdown time constraint, and the logical constraints between the start-up / shutdown state variables and the operating state variables. The objective of the second stage of the model is to minimize the sum of the fuel cost and the wind curtailment penalty cost of the system corresponding to the K uncertain sets, under the worst-case scenario where all uncertain parameters of the K uncertain sets are taken. The decision variables include the output of each unit. The constraints considered in the second stage decision include thermal power unit output constraints, system power balance constraints, thermal power unit ramping constraints, wind farm output constraints, transmission line transmission capacity constraints, system reserve capacity constraints, and non-negativity constraints of decision variables. S2. Establish a robust unit combination model for controlling risks, the model including a first stage and a second stage; The goal of the first stage of the model is to minimize the total cost under the most likely prediction scenario. The decision variables include unit operating status variables, unit start-up / shutdown status variables, and the corresponding thermal power unit output and wind farm optimal dispatch output under the prediction scenario. The constraints are the minimum unit operation / shutdown time constraint and various power system security constraints under the prediction scenario. The objective of the second stage of the model is to determine the performance indicators set by decision-makers based on uncertain parameters under adverse scenarios; the decision variables are the optimal dispatch output of wind farms and the output of thermal power units corresponding to each uncertainty set; and the constraints are the various safety constraints of the power system. S3. Solve the robust unit combination model considering K uncertain sets and the robust unit combination model considering control risks using the C&CG algorithm to obtain the robust unit combination method for the power system. The objective function of the robust unit combination model considering K uncertain sets is specifically: （2） In the formula, x, y, z, u, and ŵ represent the operating status of the thermal power unit, the output of the thermal power unit, the start-up status of the thermal power unit, the shutdown status of the thermal power unit, and the output vector of the wind turbine unit, respectively. This represents the total number of thermal power units. Total scheduling time period; The number of episodes is uncertain. For the number of wind farms; For the unit Startup costs; For the unit Downtime costs; For the unit Fuel costs; For wind farm The unit cost of wind curtailment; The weight coefficients are the values ​​corresponding to the k-th uncertain set. For the unit exist The start status of the time period; For the unit exist The downtime status during a specific period; For the unit exist Efforts during a specific time period; For wind farm exist Wind power output during specific time periods; For wind farm exist The optimal power output during the time period; the first term in equation (2) is the objective of the first stage, which is to minimize the start-up and shutdown costs of the units; the second term in equation (2) is the objective of the second stage, which is to minimize the sum of the fuel cost and the wind curtailment penalty cost of the system corresponding to the K uncertain sets when all the uncertain parameters of the K uncertain sets are in the worst case.

2. The robust turbine configuration method for power systems to address wind power uncertainties according to claim 1, characterized in that, The form of the first uncertain set is as follows: The form of the second uncertain set is as follows: （1） In the formula, This represents the total number of wind farms. This represents the total number of scheduling periods; For the first An uncertain centralized wind farm exist The upper limit of wind power output during a certain period For the first An uncertain centralized wind farm exist Lower limit of wind power output during a given time period; For wind farm exist Forecasted wind power output for a given period; , These are introduced auxiliary variables used to control the wind farm. Whether the wind power output reaches the boundary of the uncertain set, when When it is 1, When the value of reaches the upper limit of the interval, When it is 1, The value of reaches the lower limit of the interval; when both are 0, ... The value is the predicted value; , This is a conservative control parameter used to control the number of times the actual wind power output reaches the boundary. 3.The method of claim 2, wherein, The minimum operating time constraint, minimum downtime constraint, and logical constraints between start / stop state variables and operating state variables are as follows; Minimum operating time constraints for the unit: （3） In the formula, For the unit Minimum runtime; For the unit exist Operating status during a given time period; Minimum downtime constraints for the unit: （4） In the formula, is a machine set Minimum downtime Logical constraints between start / stop status variables and running status variables: （5） （6） In formula (3) - formula (6), . 4.The method of claim 3, wherein, The constraints on thermal power unit output, system power balance, thermal power unit ramping, wind farm output, transmission line capacity, system reserve capacity, and decision variable non-negativity are as follows; Thermal power unit output constraints: （7） wherein and are the upper and lower limits of the unit output, respectively. System power balance constraints: （8） In the formula, This represents the total number of wind farms. for Total load during the period , The total number of load nodes. For load nodes exist Load during a given time period; Thermal power unit ramping constraints: （9） （10） wherein is the maximum up-regulated power of the unit ; and is the maximum down-regulated power of the unit ; and Wind farm output constraints: （11） Transmission line capacity constraints: （12） In the formula, For the line Maximum transmission capacity; G l-i G l-j and G l-m thermal power units The node is connected to the line Generator output power transfer distribution factor, wind farm The node is connected to the line The generator output power transfer distribution factor and load node For the line The generator output power transfer distribution factor is calculated as follows: G l-i =(X m’,i - X n’,i ) / x l G l-j =(X m’,j - X n’,j ) / x l G l-m =(X m’,m - X n’,m ) / x l ,in For the line Reactance, subscript and For the line The first and last nodes, All are elements in the impedance matrix; System backup capacity constraints: （13） In the formula, Spinning reserve ratio; Non-negativity constraint for decision variables: （14）。 5. The method of claim 4, wherein, In S3, the robust unit combination model considering K uncertain sets is solved using the C&CG algorithm, specifically as follows: Step 1: Construct the main problem and the subproblems after KKT transformation, initialize the parameters of each model, set the upper bound UB=Inf, the lower bound LB=-Inf, and the initial number of iterations k0=1; Step 2: Solve the main problem to obtain the solution for the decision variables in the first stage. At the same time, update the lower bound. ; Step 3: Solve the Substitution subproblem Solve each subproblem; Step 4: Determine if all subproblems have solutions. If all subproblems have solutions, return the constraints: To the main question, and update the upper bound. ; Step 5: Return the constraints corresponding to the worst-case scenario found in each subproblem to the main problem; Step 6: Determine if the upper bound is close to the lower bound. If so, end the process and obtain the optimal solution; otherwise, k0 = k0 + 1, return to step 2, and proceed to the next iteration.

6. A robust turbine configuration method for power systems to address wind power uncertainties according to claim 5, characterized in that, The subproblems and the main problem of a robust unit combination model considering K uncertain sets are constructed and solved as follows: Based on the given first-stage decision variables , define the first The sub-problems are as follows: （36） （37） （38） (8) （39） （40） (11) (12) （41） (14) The above subproblem is a two-layer problem with a max-min structure. The inner-min linear programming problem is transformed into a max-structure MILP problem by removing the min sign from the KKT conditions and then using the Big M method to convert the complementary relaxation constraints in the KKT conditions into inequality constraints. The main problem for constructing and solving a robust unit combination model considering K uncertain sets is as follows: After solving the subproblems, the scenarios identified by the subproblems and their corresponding constraints are gradually added back to the main problem. The main problem is constructed as follows: （42） （43） （44） （45） （46） （47） （48） （49） （50） （51） （52） （53） （54） （55） in, express The scenario for identifying a quilt problem; Equations (3) to (6) are constraints related to the decision variables in the first stage; in Equation (44) For the first The first uncertain set The second-stage objective function corresponding to each extreme point introduces auxiliary variables. The two-stage robust optimization model is transformed into a one-stage optimization problem; Equations (45)-(55) represent the scenarios identified by the sub-problems. The corresponding constraints, among which , For the scene Corresponding decision variables; In each iteration, the main problem will return a scenario. The corresponding constraints must be met, and the scene must be generated simultaneously. Corresponding decision variables , As the iteration progresses, the constraints in the main problem increase, and the number of bad scenarios considered in the main problem gradually increases, making the decision in the first stage better.

7. A robust turbine configuration method for power systems to address wind power uncertainties according to claim 6, characterized in that, The first-stage objective function of the robust unit combination model for risk control is specifically set as follows: （17） In the formula, For wind farm The unit cost of wind curtailment; For wind farm exist Forecast wind power output for the specified time period; In order to be in Scenario Unit exist Efforts during a specific time period; In order to be in Wind farm in the scenario exist The optimal power output for the time period; Equation (17) is to minimize the sum of start-up and shutdown costs, fuel costs and wind curtailment penalty costs when the wind power output is the predicted value.

8. A robust turbine configuration method for power systems to address wind power uncertainties according to claim 7, characterized in that, The specific constraints related to the first-stage decision variables in the robust unit combination model for controlling risk are as follows: （18） （19） （20） （21） （22） （23） （24） （25） （26） Equations (3) to (6) represent the minimum operating and downtime constraints of the unit, as well as the logical constraints between the decision variables; Equations (19) to (26) represent the prediction scenarios. Various safety constraints of the power system.

9. A robust turbine configuration method for power systems to address wind power uncertainties according to claim 8, characterized in that, The constraints related to the second-stage decision variables and the constraints for controlling risk in the robust unit combination model for risk control are as follows: Constraints related to the decision variables in the second stage: （27） （28） （29） （30） （31） （32） （33） （34） In the formula, For the first Wind farms corresponding to an uncertain set exist Wind power output during specific time periods; For the first Units corresponding to an uncertain set exist Efforts during a specific time period; For the first Wind farms corresponding to an uncertain set exist Optimal output scheduling for each time period; Equations (27)-(34) are the first... Each unit's safe output constraints correspond to an uncertain set; Constraints for controlling risk: （35） Equation (35) is the hard constraint imposed by the decision-maker on the performance indicators set for adverse scenarios: in the first... Under the worst-case scenario, the sum of the minimum operating cost of a thermal power unit and the cost of wind curtailment penalty must not exceed a given limit. .

10. A robust turbine configuration method for power systems to address wind power uncertainties according to claim 9, characterized in that, The robust unit combination model for risk control is solved using the C&CG algorithm, as detailed below: Step 1: Construct the main problem and sub-problem models, and initialize the various parameters; Step 2: Solve the initial master problem to obtain the optimal solution for the predicted scenario. ; Step 3: Put Substitution Solve the K subproblems; Step 4: Return the constraints corresponding to the scenarios identified in each sub-problem to the main problem; Step 5: Determine whether each subproblem has a solution and whether the hard constraints corresponding to each subproblem are satisfied; if each subproblem has a solution and the hard constraints corresponding to each subproblem are satisfied, end the iteration and obtain the final optimal solution; otherwise, return the hard constraint conditions corresponding to the scenario identified by the subproblem to the main problem, increment the iteration count by one, return to step 2, and enter the next iteration; The method for constructing and solving subproblems in a robust unit combination model for controlling risks is consistent with the method for constructing and solving subproblems in a robust unit combination model considering K uncertain sets. The main problem of constructing and solving a robust unit combination model for risk control is as follows: （56） （57） （58） Equations (3) to (6) represent the constraints related to the decision variables in the first stage; Equations (18) to (25) represent the prediction scenarios. The following are the safety constraints of the power system; Equations (45)-(55) are the constraints corresponding to the scenarios identified by the sub-problem; Equation (57) is the hard constraint that the objective function of the sub-problem needs to satisfy; Substitute the decisions of the main problem into the subproblems, and determine whether the performance indicators of each subproblem meet the requirements, which serves as the basis for whether the iteration should terminate.

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