A fixed-recursive power system unit commitment determination method and system

Abstract

The application discloses a fixed-recursion type power system unit combination determination method and system, and relates to the field of power system economic dispatching.The method comprises the following steps: acquiring basic data; constructing a mixed integer programming model according to the basic data; solving the relaxed mixed integer programming model to obtain a relaxed solution and acquiring an initial feasible solution; fixing the unit start-stop state 0-1 variable meeting the to-be-fixed condition at the lower limit of the value range; calculating the importance index of the non-unit start-stop state 0-1 variable and sorting the non-unit start-stop state 0-1 variable according to the importance index; fixing the preset number of non-unit start-stop state 0-1 variables meeting the to-be-fixed condition at the lower limit of the value range according to the sorting order; and finally solving the sub-mixed integer programming model obtained after fixing the variables to obtain a unit combination optimization result.The application improves the solving efficiency of the power system unit combination and guarantees the safe and stable operation of the power system.

Description

Technical Field

[0001] This invention relates to the field of economic dispatch of power systems, and in particular to a fixed-recursive method and system for determining the combination of power system units. Background Technology

[0002] The power system unit combination problem is a significant optimization challenge in the field of power system economic dispatch. This problem aims to minimize the total power generation cost by determining the start-up and shutdown status and output scheme of each unit at different times, without violating constraints on the units, transmission lines, and the system itself. Mathematically, this is a high-dimensional, non-convex, discrete optimization problem, belonging to the NP-hard category, making it very difficult to find a theoretically optimal solution.

[0003] The power system unit combination problem is a core computational issue in the power spot market clearing process, and its results profoundly impact the fairness of power trading and the security of the power system. Given the limited timeframe and multiple rounds of current market clearing, each round requires the rapid and accurate acquisition of optimized unit combination results. Failure to optimize unit combination in a timely manner will disrupt subsequent processes in the power spot market and pose a significant threat to the safe and stable operation of the power system.

[0004] Currently, power system unit combination problems typically require consideration of numerous security constraints, which result in massive model sizes and increased difficulty in solving them. For a day-ahead unit combination model with 548 units and a 24-hour timeframe, the number of integer and continuous variables exceeds 52,600, and the constraints number over 290,000. Achieving rapid solutions to unit combination problems remains a significant challenge globally. Current solutions often employ branch and bound methods, which typically use heuristics to find better solutions and lower the upper bound. Finding a lower upper bound quickly is a key aspect of improving the optimization efficiency of unit combination problems.

[0005] In summary, there is an urgent need to propose a new method for accelerating the optimization of power system unit combination, which can effectively balance the feasibility and optimality of the solution during the unit combination optimization process, and obtain higher quality feasible solutions in a short time by taking into account the characteristics of the unit combination problem, so as to accelerate the solution of the unit combination problem, ensure the safe and stable operation of the power system and the normal operation of the electricity spot market. Summary of the Invention

[0006] The purpose of this invention is to provide a fixed-recursive method and system for determining the combination of power system units, so as to ensure the safe and stable operation of the power system.

[0007] To achieve the above objectives, the present invention provides the following solution:

[0008] A fixed-recursive method for determining the unit combination of a power system includes:

[0009] Acquire basic data of the power system; the basic data includes day-ahead load forecast data, unit cost data, transmission network topology data, and unit operating characteristic data; the day-ahead load forecast data includes the total load demand forecast and the load demand forecast for each node; the unit cost data includes the coefficients of the unit secondary generation cost function, the unit cold start cost, the unit hot start cost, and the unit shutdown cost; the transmission network topology data includes the transmission line starting node number, the transmission line ending node number, the transmission capacity upper limit, and the transmission line reactance; the unit operating characteristic data includes the unit power generation upper limit, the unit power generation lower limit, the unit ramp-up capability, the unit minimum start-up time, the unit minimum shutdown time, the unit cold start time, the unit initial operating status, and the unit initial output;

[0010] Based on the aforementioned basic data, a mixed integer programming model is established with the objective function of minimizing the sum of power generation cost and start-up cost, and with constraints including system power balance constraints, system spinning reserve constraints, power generation cost constraints, unit start-up cost constraints, unit output constraints, unit ramping constraints, logical constraints, minimum start-up and shutdown time constraints, and line transmission capacity constraints.

[0011] The first relaxed solution and the initial feasible solution of the mixed integer programming model are determined. The relaxed solution includes the relaxed solution vectors of the unit start-up and shutdown state 0-1 variables, the unit start-up state 0-1 variables, the unit shutdown state 0-1 variables, the unit cold start state 0-1 variables, and the relaxed solution vectors of each linear segmented output variable of each unit in each time period. The feasible solution includes the feasible solution vectors of the unit start-up and shutdown state 0-1 variables, the unit start-up state 0-1 variables, the unit shutdown state 0-1 variables, the unit cold start state 0-1 variables, and the feasible solution vectors of each linear segmented output variable of each unit in each time period. The initial feasible solution is obtained by solving the mixed integer programming model using the start-up heuristic method.

[0012] Based on the first relaxed solution and the initial feasible solution, the variables of the mixed integer programming model are fixed to obtain a sub-mixed integer programming model with fixed variables.

[0013] Solve the current feasible solution of the sub-mixed integer programming model after fixing the variables, determine whether the current feasible solution is better than the initial feasible solution, and obtain the first judgment result;

[0014] If the first judgment result is yes, then the current feasible solution is taken as the initial feasible solution, and the step of "determining the first relaxed solution and the initial feasible solution of the mixed integer programming model" is returned.

[0015] If the first judgment result is negative, then the current optimal feasible solution is taken as the power system unit combination optimization result.

[0016] Optionally, determining the first relaxed solution of the mixed-integer programming model specifically includes:

[0017] Transform the mixed integer programming model into a linear programming model;

[0018] Determine the first relaxed solution of the linear programming model.

[0019] Optionally, based on the first relaxed solution and the initial feasible solution, the mixed-integer programming model is subjected to variable fixing to obtain a sub-mixed-integer programming model with fixed variables, specifically including:

[0020] The unit start-up and shutdown state 0-1 variable, whose values ​​are consistent in the first relaxed solution and the initial feasible solution and whose values ​​are at the lower bound of the first value range, is fixed at the lower bound of the first value range; the first value range is the value range of the unit start-up and shutdown state 0-1 variable;

[0021] The 0-1 variables of the non-unit start-up and shutdown states in the current mixed integer programming model are sorted according to their importance to obtain the sorted 0-1 variables of the non-unit start-up and shutdown states.

[0022] A predetermined number of non-unit start-up / shutdown state 0-1 variables are sequentially fixed, taking values ​​that are consistent in the first relaxed solution and the initial feasible solution and whose values ​​are within the lower bound of the second value range, to obtain a sub-mixed integer programming model with fixed variables; the second value range is the value range of the sorted non-unit start-up / shutdown state 0-1 variables.

[0023] Optionally, the unit start-up / shutdown state 0-1 variables, whose values ​​are consistent in the first relaxed solution and the initial feasible solution and whose values ​​are within the lower bound of the first value range, are fixed at the lower bound of the first value range. Specifically, this includes:

[0024] Obtain the relaxed solution vector and the feasible solution vector of the 0-1 variables of the current unit start-up and shutdown status;

[0025] Determine whether the absolute value of the difference between the i-th element in the relaxed solution vector of the current unit start-up / shutdown state 0-1 variable and the i-th element in the feasible solution vector of the unit start-up / shutdown state 0-1 variable is less than the allowable error.

[0026] If so, the current unit start-up / shutdown state 0-1 variable takes the same value in the first relaxed solution and the initial feasible solution, and when the value of the i-th element in the relaxed solution vector of the current unit start-up / shutdown state 0-1 variable is at the lower bound of the first value range, the current unit start-up / shutdown state 0-1 variable is a variable to be fixed.

[0027] The variable to be fixed is fixed at the lower bound of the first value range.

[0028] Optionally, the 0-1 variables of the non-unit start-up and shutdown states in the current mixed-integer programming model are sorted according to importance to obtain the sorted 0-1 variables of the non-unit start-up and shutdown states, specifically including:

[0029] Calculate the upper and lower pseudo-costs of the 0-1 variables for the non-unit start-up and shutdown states in the current mixed integer programming model;

[0030] Calculate the number of locked and unlocked 0-1 variables for the non-unit start-up and shutdown states in the current mixed integer programming model;

[0031] Based on the transformed constraint coefficient matrix, the lower pseudo-cost, and the lower lock number, determine the importance of any non-unit start-up / shutdown state 0-1 variable;

[0032] Based on the importance, the non-unit start-up and shutdown state 0-1 variables of the current mixed integer programming model are sorted in descending order to obtain the sorted non-unit start-up and shutdown state 0-1 variables.

[0033] A fixed-recursive power system unit combination determination system, comprising:

[0034] The data acquisition module is used to acquire basic data of the power system. This basic data includes day-ahead load forecast data, unit cost data, transmission network topology data, and unit operating characteristic data. The day-ahead load forecast data includes the total load demand forecast and the load demand forecast for each node. The unit cost data includes the coefficients of the unit's secondary generation cost function, the unit's cold start cost, hot start cost, and shutdown cost. The transmission network topology data includes the transmission line's starting node number, transmission line's ending node number, transmission capacity limit, and transmission line reactance. The unit operating characteristic data includes the unit's upper and lower power generation limits, unit ramp-up capability, minimum start-up time, minimum shutdown time, cold start time, initial operating status, and initial output.

[0035] The model building module is used to establish a mixed integer programming model based on the aforementioned basic data, with the objective function being the minimum sum of power generation cost and start-up cost, and with constraints including system power balance constraints, system spinning reserve constraints, power generation cost constraints, unit start-up cost constraints, unit output constraints, unit ramping constraints, logical constraints, minimum start-up and shutdown time constraints, and line transmission capacity constraints.

[0036] The first relaxation solution determination module is used to determine the first relaxation solution and the initial feasible solution of the mixed integer programming model. The relaxation solution includes the relaxation solution vectors of the unit start-up and shutdown state 0-1 variables, the unit start-up state 0-1 variables, the unit shutdown state 0-1 variables, the unit cold start state 0-1 variables, and the relaxation solution vectors of each linear segmented output variable of each unit in each time period. The feasible solution includes the feasible solution vectors of the unit start-up and shutdown state 0-1 variables, the unit start-up state 0-1 variables, the unit shutdown state 0-1 variables, the unit cold start state 0-1 variables, and the feasible solution vectors of each linear segmented output variable of each unit in each time period. The initial feasible solution is obtained by solving the mixed integer programming model using the start-up heuristic method.

[0037] The variable fixing module is used to fix the variables of the mixed integer programming model according to the first relaxed solution and the initial feasible solution, so as to obtain a sub-mixed integer programming model with fixed variables.

[0038] The judgment module is used to solve the current feasible solution of the sub-mixed integer programming model after fixing the variables, and to determine whether the current feasible solution is better than the initial feasible solution, so as to obtain a first judgment result;

[0039] The first execution module is used to take the current feasible solution as the initial feasible solution and return to the "first relaxation solution determination module" if the first judgment result is yes.

[0040] The second execution module is used to take the initial feasible solution as the power system unit combination optimization result if the first judgment result is negative.

[0041] An electronic device includes a memory and a processor, the memory storing a computer program, and the processor running the computer program to cause the electronic device to perform the above-described fixed-recursive power system unit combination determination method.

[0042] A computer-readable storage medium storing a computer program that, when executed by a processor, implements the above-described fixed-recursive method for determining the combination of power system units.

[0043] According to specific embodiments provided by the present invention, the present invention discloses the following technical effects:

[0044] This invention discloses a fixed-recursive method and system for determining the unit combination of a power system. First, a mixed-integer programming model is constructed using the acquired basic data of the power system. The mixed-integer programming model is then solved to obtain relaxed solutions and initial feasible solutions. The real-valued matrix consisting of all constraint coefficients of the current mixed-integer programming model is normalized. The 0-1 variables representing the start-up and shutdown states of the units satisfying the conditions to be fixed are fixed at their lower bounds. Importance indices for the 0-1 variables representing the start-up and shutdown states of the non-units are calculated, and these variables are ranked according to their importance. Based on the ranking order, a certain number of the 0-1 variables representing the start-up and shutdown states of the non-units satisfying the conditions to be fixed are sequentially fixed at their lower bounds. Finally, the sub-mixed-integer programming model obtained after fixing the variables is solved to obtain the unit combination optimization results. This invention significantly improves the efficiency of power system unit combination optimization. It effectively balances the feasibility and optimality of solutions during the optimization process. Furthermore, it develops a comprehensive variable importance judgment method based on multiple indicators, which can quickly obtain higher-quality feasible solutions by combining the characteristics of unit combination problems, thereby accelerating the unit combination optimization process and ensuring the safe and stable operation of the power system. Attached Figure Description

[0045] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the drawings used in the embodiments will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0046] Figure 1 A flowchart of the fixed-recursive power system unit combination determination method provided by the present invention. Detailed Implementation

[0047] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0048] The purpose of this invention is to provide a fixed-recursive method and system for determining the combination of power system units, so as to ensure the safe and stable operation of the power system.

[0049] The purpose of this invention is to provide a fixed-recursive method and system for determining the power system unit combination, which significantly improves the efficiency of power system unit combination optimization. It takes into account both the feasibility and optimality of the solution during the optimization process, and can quickly obtain higher quality feasible solutions by combining the characteristics of the unit combination problem to accelerate the unit combination optimization process.

[0050] To make the above-mentioned objects, features and advantages of the present invention more apparent and understandable, the present invention will be further described in detail below with reference to the accompanying drawings and specific embodiments.

[0051] Example 1

[0052] The present invention provides a fixed-recursive method for determining the unit combination of a power system, which significantly improves the efficiency of solving the unit combination problem and can quickly obtain high-quality feasible solutions by combining the characteristics of the unit combination problem, so as to quickly start the unit combination solution process.

[0053] This embodiment uses the French-2848 node power system as an example to illustrate the fixed-recursive power system unit combination determination method proposed in this invention.

[0054] like Figure 1 As shown, the fixed-recursive power system unit combination determination method provided by the present invention includes:

[0055] Step 101: Obtain basic data of the power system; the basic data includes day-ahead load forecast data, unit cost data, transmission network topology data, and unit operating characteristic data; the day-ahead load forecast data includes the total load demand forecast and the load demand forecast for each node; the unit cost data includes the coefficients of the unit secondary generation cost function, the unit cold start cost, the unit hot start cost, and the unit shutdown cost; the transmission network topology data includes the transmission line starting node number, the transmission line ending node number, the transmission capacity upper limit, and the transmission line reactance; the unit operating characteristic data includes the unit power generation upper limit, the unit power generation lower limit, the unit ramp-up capability, the unit minimum start-up time, the unit minimum shutdown time, the unit cold start time, the unit initial operating status, and the unit initial output.

[0056] The French-2848 node test system used in this embodiment has a total of 2848 nodes, 548 generating units and 3776 transmission lines. The generating unit combination in this embodiment is divided into 24 time periods. The basic data includes the cost data of each generating unit, the operating characteristic data of the generating unit, the transmission network topology data and the day-ahead load forecast data for each time period.

[0057] In practical applications, all generating units included in the basic data are sorted according to their output and economic efficiency. First, the units are sorted based on their maximum output capacity (maximum power generation) contained in the basic data; units with higher maximum output capacity are ranked higher. If the maximum output capacity of units is the same, the ranking is determined by the unit's heat rate. To sort, H R The smaller ones are listed at the beginning of the sequence, among which A is the upper limit of the output of the i-th unit in the basic data of the unit combination. i B i C i It is the coefficient of the secondary power generation cost function of the i-th unit.

[0058] Step 102: Based on the aforementioned basic data, with the objective function being the minimum sum of power generation cost and start-up cost, and with constraints including system power balance constraints, system spinning reserve constraints, power generation cost constraints, unit start-up cost constraints, unit output constraints, unit ramp-up constraints, logical constraints, minimum start-up and shutdown time constraints, and line transmission capacity constraints, a mixed integer programming model is established.

[0059] In practical applications, a hybrid integer programming model for unit combination is constructed based on the aforementioned basic data.

[0060] In step 102, the objective function expression is as follows:

[0061]

[0062] Where I and T are the total number of generating units and the total number of time periods participating in the unit optimization, respectively, and C P,i,t C U,i,t These are the power generation cost and start-up cost of unit i in time period t, respectively.

[0063] In step 102, the system constraint expressions are as follows:

[0064] System power balance constraints:

[0065]

[0066] System spin-off standby constraints:

[0067]

[0068] Among them, D t S is the load forecast value for time period t. t It is the system spin-off standby for time period t, u i,t This is a 0-1 variable representing the unit's start-up and shutdown status. A value of 0 indicates the unit is in a stopped state, and a value of 1 indicates the unit is in a started state. i,tIt is the output of unit i in time period t. It is the maximum output of unit i.

[0069] In step 102, the constraint expression is as follows:

[0070] Power generation cost constraints:

[0071]

[0072] Unit start-up cost constraints:

[0073]

[0074] Among them, u i,t This is a 0-1 variable representing the unit's start-up and shutdown status. A value of 0 indicates the unit is in a stopped state, and a value of 1 indicates the unit is in a started state. i,t p is the output of unit i in time period t. i,t,m Let A be the output of unit i in the m-th linear segment of time period t, and it is a continuous variable. i B i C i These are the coefficients of the secondary cost function for power generation of unit i. P i , These are the minimum and maximum outputs of unit i, respectively, M i F is the total output of unit i across all time periods. i,m P is the slope of unit i in the m-th linear segment. i,m It is the upper limit of the output of unit i in the m-th segment; y i,t y cold,i,t These are the startup state (0-1) and cold start state (0-1) variables, respectively. A value of 1 indicates that unit i performs a startup operation and a cold start operation in time period t, respectively; a value of 0 indicates that no operation is performed. T i cold These represent the hot start cost, cold start cost, minimum downtime, and cold start time of unit i, respectively.

[0075] Unit output constraints:

[0076]

[0077] Unit ramp-up constraints:

[0078]

[0079] Among them, z i,t The shutdown status changes from 0 to 1. A value of 1 indicates that unit i will perform a shutdown operation in time period t, while a value of 0 indicates that the operation will not be performed. iup P i start P i down P i shut These are the ramp-up power, start-up power, ramp-down power, and shutdown power of unit i.

[0080] Logical constraints:

[0081] u i,t -u i,t-1 =y i,t -z i,t .

[0082] Minimum start-stop time constraints:

[0083]

[0084] in, U is the minimum startup time for unit i. i,0 T i,0 These are the initial state and initial continuous operating time of unit i, respectively, G i L i It is the time during which unit i needs to continue operating and shutting down after the initial moment.

[0085] Line transmission capacity constraints:

[0086]

[0087] Among them, P l,max This represents the upper limit of the transmission capacity of the l-th line, matrix K is the node-to-line generator output power transfer distribution factor matrix, and P l,max This represents the upper limit of the transmission capacity of the l-th line, and matrix K is the node-to-line generator output power transfer distribution factor matrix, n i It is the node number where the i-th unit is located, n b D is the number of the b-th loaded node. b,t It is the load forecast value of the b-th node in the t-th time period.

[0088] Step 103: Determine the first relaxed solution and the initial feasible solution of the mixed integer programming model; the relaxed solution includes the relaxed solution vectors of the unit start-up and shutdown state 0-1 variables, the relaxed solution vectors of the unit start-up state 0-1 variables, the relaxed solution vectors of the unit shutdown state 0-1 variables, the relaxed solution vectors of the unit cold start state 0-1 variables, and the relaxed solution vectors of the linear segmented output variables of each unit in each time period; the feasible solution includes the feasible solution vectors of the unit start-up and shutdown state 0-1 variables, the feasible solution vectors of the unit start-up state 0-1 variables, the feasible solution vectors of the unit shutdown state 0-1 variables, the feasible solution vectors of the unit cold start state 0-1 variables, and the feasible solution vectors of the linear segmented output variables of each unit in each time period; the initial feasible solution is obtained by solving the mixed integer programming model using the start-up heuristic method.

[0089] As an optional implementation, determining the first relaxed solution of the mixed-integer programming model specifically includes:

[0090] The mixed integer programming model is transformed into a linear programming model.

[0091] Determine the first relaxed solution of the linear programming model.

[0092] In practical applications, the relaxed mixed-integer programming model is solved to obtain the relaxed solution, and the currently known optimal feasible solution (initial feasible solution) is obtained or updated.

[0093] The so-called "relaxed mixed-integer programming model" means that the range of values ​​for all integer variables in the original mixed-integer programming model is changed from discrete to continuous. Specifically, a linear programming solver is used to relax the four types of 0-1 variables in the constructed mixed-integer programming model into continuous variables with a value range of 0-1, thus forming a linear programming model.

[0094] Solving the linear programming model using a linear programming solver yields the first relaxed solution for power system unit combination optimization. Includes: the relaxed solution vector of 0-1 variables for unit start-up and shutdown states. Relaxed solution vector of 0-1 variables in unit startup state Relaxed solution vector of 0-1 variables in unit shutdown state Relaxed solution vector of 0-1 variables in unit cold start state Relaxation solution vectors of linear piecewise output variables for each unit at each time period

[0095] The currently known optimal feasible solution Includes: feasible solution vectors of 0-1 variables representing the unit's start-up and shutdown states. Feasible solution vector of unit startup state 0-1 variables Feasible solution vector of 0-1 variables for unit shutdown state Feasible solution vector of 0-1 variables in the cold start state of the unit Feasible solution vectors of linear segmented output variables for each unit at each time period

[0096] In practical applications, this also includes normalizing the real matrix consisting of all constraint coefficients of the current mixed integer programming model.

[0097] Using formula Determine the abstract model for the aforementioned mixed integer programming.

[0098] Where c is an n-dimensional column vector composed of the coefficients of the objective function, x is an n-dimensional column vector composed of all variables, A is an m×n real matrix composed of all constraint coefficients, b is an m-dimensional column vector composed of constants, l and h are n-dimensional column vectors composed of the upper and lower bounds of all variables, and I and C represent the sets of indices of integer variables and continuous variables, respectively.

[0099] Using formula The real matrix consisting of all constraint coefficients is normalized.

[0100] Among them, a i b is the vector in the i-th row of matrix A. i It is the i-th element of vector b, e i,j It is the j-th element of the i-th row vector.

[0101] Step 104: Based on the first relaxed solution and the initial feasible solution, fix the variables of the mixed integer programming model to obtain a sub-mixed integer programming model with fixed variables. Variable fixing means setting the upper and lower bounds of the variables to be consistent; although the value of the variable is at the lower bound of its value range, it is not fixed so that the upper bound equals the lower bound.

[0102] As an optional implementation, step 104 specifically includes:

[0103] Step 1041: Fix the unit start-up / shutdown state 0-1 variable, which has the same value in the first relaxed solution and the initial feasible solution and whose value is at the lower bound of the first value range, to the lower bound of the first value range; the first value range is the value range of the unit start-up / shutdown state 0-1 variable.

[0104] As an optional implementation, step 1041 specifically includes:

[0105] Obtain the relaxed solution vector and the feasible solution vector of the 0-1 variables of the current unit start-up and shutdown status.

[0106] Determine whether the absolute value of the difference between the i-th element in the relaxed solution vector of the current unit start-up / shutdown state 0-1 variable and the i-th element in the feasible solution vector of the unit start-up / shutdown state 0-1 variable is less than the allowable error.

[0107] If so, the current unit start-up / shutdown state 0-1 variable takes the same value in the first relaxed solution and the initial feasible solution, and when the value of the i-th element in the relaxed solution vector of the current unit start-up / shutdown state 0-1 variable is at the lower bound of the first value range, the current unit start-up / shutdown state 0-1 variable is a variable to be fixed.

[0108] The variable to be fixed is fixed at the lower bound of the first value range.

[0109] In practical applications, the 0-1 variables representing the unit's start-up and shutdown states, where the values ​​are consistent in both the relaxed and feasible solutions and fall within the lower bound of their respective ranges, are fixed at their lower bound.

[0110] Obtain the relaxed solution vector of the 0-1 variables of the unit start-up and shutdown states mentioned in step 103. and feasible solution vector

[0111] The tolerance ε is set to 10. -6 Using the formula and Perform a judgment on the variable to be fixed, if Then it can be assumed that the value of the current variable is consistent in both the relaxed solution and the feasible solution. If the current variable is at the lower bound of its range, then the current variable is considered to be a variable to be fixed.

[0112] Setting the upper bound of the range of values ​​of the variable to be fixed as the lower bound of its range achieves the fixation of the variable.

[0113] in, It is the relaxed solution vector of the 0-1 variables of the unit's start-up and shutdown states. The i-th element in It is the feasible solution vector of the 0-1 variables of the unit's start-up and shutdown states. The i-th element in.

[0114] Step 1042: Sort the 0-1 variables of the non-unit start-up and shutdown states of the current mixed integer programming model according to their importance to obtain the sorted 0-1 variables of the non-unit start-up and shutdown states.

[0115] As an optional implementation, step 1042 specifically includes:

[0116] Calculate the upper and lower pseudo-costs of the 0-1 variables for the non-unit start-up and shutdown states in the current mixed integer programming model.

[0117] In practical applications, using formulas and Calculate the j-th 0-1 variable x in the current unit combination mixed integer programming model. j The upper and lower pseudo-costs represent the increment of the objective function value corresponding to the relaxation solution when the variable changes by one unit along a certain direction. The direction corresponding to the upper pseudo-cost is the upward rounding, and the direction corresponding to the lower pseudo-cost is the downward rounding.

[0118] in, and They represent the variables x respectively j The increment of the objective function value corresponding to the relaxation solution when rounding up and down. x represents j The distance required to round up. x represents j The distance required to round down.

[0119] Calculate the number of locked and unlocked 0-1 variables for the non-unit start-up and shutdown states in the current mixed integer programming model.

[0120] In practical applications, let x be the j-th 0-1 variable in the current unit combination hybrid integer programming model. j Initial number of locks Initial number of locks The upper and lower lock numbers respectively represent the variable x j The resistance imposed by all constraints in the model when rounding up and rounding down.

[0121] Iterate through all constraints in the current unit combination mixed integer programming model and determine the type of constraint, including equality constraints, inequality constraints, and integer constraints. If the current constraint is of type equality or integer constraint, then the number of 0-1 variables involved in the current constraint that are locked is ζ. + And the number of locks ζ - Add 1. If the current constraint encountered during the iteration is an inequality constraint, then the impact of the current constraint on the number of locks needs to be determined based on the coefficients of the 0-1 variables in the current constraint. If the coefficient of the variable is greater than 0, then the number of locks ζ is increased. + Add 1, otherwise the number of locks ζ - Add 1.

[0122] Based on the transformed constraint coefficient matrix, the lower pseudo-cost, and the lower lock number, determine the importance of any non-unit start-up / shutdown state 0-1 variable.

[0123] In practical applications, using formulas Determine the importance of the 0-1 variables related to non-unit start-up and shutdown states included in the current model.

[0124] in, It is the element in the i-th row and j-th column obtained after normalizing all constraint coefficient matrices A, ||A j ||1 represents the sum of the absolute values ​​of all elements in the j-th column vector of matrix A. |A j | represents the number of all non-zero elements in the j-th column vector of matrix A.

[0125] Based on the importance, the non-unit start-up and shutdown state 0-1 variables of the current mixed integer programming model are sorted in descending order to obtain the sorted non-unit start-up and shutdown state 0-1 variables.

[0126] In practical applications, the 0-1 variables of each non-unit start-up and shutdown status are sorted in descending order according to their importance. If the importance is the same, the unit with the smaller number is placed at the front of the sequence according to the unit sorting order in step 101.

[0127] Step 1043: Sequentially fix a preset number of the sorted non-unit start-up / shutdown state 0-1 variables that have the same value in the first relaxed solution and the initial feasible solution and whose value is within the lower bound of the second value range, to obtain the sub-mixed integer programming model with fixed variables; the second value range is the value range of the sorted non-unit start-up / shutdown state 0-1 variables.

[0128] Based on the sorting order, a certain number of non-unit start-up / shutdown state 0-1 variables whose values ​​are consistent in the relaxed solution and feasible solution and are within the lower bound of their value range are fixed, as follows:

[0129] Obtain the relaxed solution vector of the unit startup state 0-1 variable. and feasible solution vector

[0130] Obtain the relaxed solution vector of the 0-1 variables of the unit shutdown state. and feasible solution vector

[0131] Obtain the relaxed solution vector of the 0-1 variables of the unit's cold start state. and feasible solution vector

[0132] The tolerance ε is set to 10. -6 The fixed proportionality coefficient δ is 0.5.

[0133] Based on the sorting order, iterate through all non-unit start-up / shutdown status 0-1 variables in sequence.

[0134] During the traversal, the formula is used and Determine whether it is a variable to be fixed. Then it can be assumed that the value of the current variable is consistent in both the relaxed solution and the feasible solution. Then the current variable can be considered to be at the lower bound of its range. If both of the above conditions are met, then the current variable is a variable to be fixed, where x i This represents the 0-1 variable representing the i-th non-unit start / stop status in the sorting order. It is x i In the relaxation solution vector The values ​​in It is x i In feasible solution vectors The value that can be taken in the range.

[0135] During the traversal, if it is determined that the variable being traversed is the variable to be fixed, then the upper bound of the value range of the variable to be fixed is set as the lower bound of its value range, thereby fixing the variable.

[0136] If the number of fixed non-unit start-up and shutdown 0-1 variables is greater than or equal to the product of the total number of 0-1 variables and the fixed proportional coefficient δ, then stop traversing.

[0137] Step 105: Solve the current feasible solution of the sub-mixed integer programming model after fixing the variables, determine whether the current feasible solution is better than the initial feasible solution, and obtain the first judgment result.

[0138] Step 106: If the first judgment result is yes, then take the current feasible solution as the initial feasible solution and return to "Step 103".

[0139] Step 107: If the first judgment result is negative, then the initial feasible solution is taken as the power system unit combination optimization result.

[0140] In practical applications, the mixed-integer programming solver is used to solve the sub-mixed-integer programming model obtained after fixing the variables. If the sub-mixed-integer programming model has a better feasible solution, the process returns to step 103 to restart the method flow. If the sub-mixed-integer programming model does not have a better feasible solution, the entire method flow ends and the current optimal feasible solution x is output. * For the unit combination optimization results, x * include:

[0141] Solution vector u of 0-1 variables for unit start-up and shutdown states * The solution vector y of the 0-1 variables of the unit startup state * The solution vector z of the 0-1 variables in the unit shutdown state * Solution vector of 0-1 variables in the cold start state of the unit Solution vectors of linear segmented output variables for each unit at each time period

[0142] In this embodiment, the solution platform is CBC 2.9.4 integrated with the method provided by this invention, and the server is a ThinkStation P620 (RAM: 128GB, CPU: AMD Ryzen ThreadripperPRO 3995WX 64-CoresCPU@2.7GHz). Directly using the mixed integer programming solver CBC 2.9.4 with the upper and lower bound gaps set to 0 takes 3162 seconds to solve. However, using CBC 2.9.4 integrated with the power system unit combination determination method provided by this invention, the solution only takes 1705 seconds, reducing the computation time by about 46% and significantly improving the solution efficiency of power system unit combination.

[0143] This invention significantly improves the efficiency of solving power system unit combination problems. It obtains a method for calculating the influence of variables by combining feasibility and optimality indicators. It can quickly obtain high-quality feasible solutions by combining the characteristics of unit combination to start the unit combination solution process more quickly. This invention can be applied to multiple scenarios such as power spot market clearing and power system safe dispatch and operation.

[0144] Example 2

[0145] In order to execute the method corresponding to Embodiment 1 above and achieve the corresponding functions and technical effects, a power system unit combination determination system is provided below, including:

[0146] The data acquisition module is used to acquire basic data of the power system. This basic data includes day-ahead load forecast data, unit cost data, transmission network topology data, and unit operating characteristic data. The day-ahead load forecast data includes the total load demand forecast and the load demand forecast for each node. The unit cost data includes the coefficients of the unit's secondary generation cost function, the unit's cold start cost, hot start cost, and shutdown cost. The transmission network topology data includes the transmission line's starting node number, transmission line's ending node number, transmission capacity limit, and transmission line reactance. The unit operating characteristic data includes the unit's upper and lower power generation limits, unit ramp-up capability, minimum start-up time, minimum shutdown time, cold start time, initial operating status, and initial output.

[0147] The model building module is used to establish a mixed integer programming model based on the aforementioned basic data, with the objective function being the minimum sum of power generation cost and start-up cost, and with constraints including system power balance constraints, system spinning reserve constraints, power generation cost constraints, unit start-up cost constraints, unit output constraints, unit ramp-up constraints, logical constraints, minimum start-up and shutdown time constraints, and line transmission capacity constraints.

[0148] The first relaxation solution determination module is used to determine the first relaxation solution and the initial feasible solution of the mixed integer programming model. The relaxation solution includes the relaxation solution vectors of the unit start-up and shutdown state 0-1 variables, the unit start-up state 0-1 variables, the unit shutdown state 0-1 variables, the unit cold start state 0-1 variables, and the relaxation solution vectors of each linear segment output variable of each unit in each time period. The feasible solution includes the feasible solution vectors of the unit start-up and shutdown state 0-1 variables, the unit start-up state 0-1 variables, the unit shutdown state 0-1 variables, the unit cold start state 0-1 variables, and the feasible solution vectors of each linear segment output variable of each unit in each time period. The initial feasible solution is obtained by solving the mixed integer programming model using the start-up heuristic method.

[0149] The variable fixing module is used to fix the variables of the mixed integer programming model based on the first relaxed solution and the initial feasible solution, so as to obtain a sub-mixed integer programming model with fixed variables.

[0150] The judgment module is used to solve the current feasible solution of the sub-mixed integer programming model after fixing the variables, and to determine whether the current feasible solution is better than the initial feasible solution, so as to obtain the first judgment result.

[0151] The first execution module is used to take the current feasible solution as the initial feasible solution and return to the "first relaxation solution determination module" if the first judgment result is yes.

[0152] The second execution module is used to take the initial feasible solution as the power system unit combination optimization result if the first judgment result is negative.

[0153] Example 3

[0154] The present invention provides an electronic device, including: a memory and a processor, wherein the memory is used to store a computer program, and the processor runs the computer program to enable the electronic device to perform the power system unit combination determination method of Embodiment 1.

[0155] Example 4

[0156] This invention provides a computer-readable storage medium storing a computer program that, when executed by a processor, implements the power system unit combination determination method of Embodiment 1.

[0157] The various embodiments in this specification are described in a progressive manner, with each embodiment focusing on its differences from other embodiments. Similar or identical parts between embodiments can be referred to interchangeably. For the systems disclosed in the embodiments, since they correspond to the methods disclosed in the embodiments, the descriptions are relatively simple; relevant parts can be referred to the method section.

[0158] This document uses specific examples to illustrate the principles and implementation methods of the present invention. The descriptions of the above embodiments are only for the purpose of helping to understand the method and core ideas of the present invention. Furthermore, those skilled in the art will recognize that, based on the ideas of the present invention, there will be changes in the specific implementation methods and application scope. Therefore, the content of this specification should not be construed as a limitation of the present invention.

Claims

1. A fixed-recursive method for determining the unit combination of a power system, characterized in that, include: Acquire basic data of the power system; the basic data includes day-ahead load forecast data, unit cost data, transmission network topology data, and unit operating characteristic data; the day-ahead load forecast data includes the total load demand forecast and the load demand forecast for each node; the unit cost data includes the coefficients of the unit secondary generation cost function, the unit cold start cost, the unit hot start cost, and the unit shutdown cost; the transmission network topology data includes the transmission line starting node number, the transmission line ending node number, the transmission capacity upper limit, and the transmission line reactance; the unit operating characteristic data includes the unit power generation upper limit, the unit power generation lower limit, the unit ramp-up capability, the unit minimum start-up time, the unit minimum shutdown time, the unit cold start time, the unit initial operating status, and the unit initial output; Based on the aforementioned basic data, a mixed integer programming model is established with the objective function of minimizing the sum of power generation cost and start-up cost, and with constraints including system power balance constraints, system spinning reserve constraints, power generation cost constraints, unit start-up cost constraints, unit output constraints, unit ramping constraints, logical constraints, minimum start-up and shutdown time constraints, and line transmission capacity constraints. Determine the first relaxed solution and the initial feasible solution of the mixed integer programming model; The relaxed solution includes the relaxed solution vectors of the unit start-up and shutdown state 0-1 variables, the relaxed solution vectors of the unit start-up state 0-1 variables, the relaxed solution vectors of the unit shutdown state 0-1 variables, the relaxed solution vectors of the unit cold start state 0-1 variables, and the relaxed solution vectors of the linear segmented output variables of each unit in each time period; the feasible solution includes the feasible solution vectors of the unit start-up and shutdown state 0-1 variables, the feasible solution vectors of the unit start-up state 0-1 variables, the feasible solution vectors of the unit shutdown state 0-1 variables, the feasible solution vectors of the unit cold start state 0-1 variables, and the feasible solution vectors of the linear segmented output variables of each unit in each time period; the initial feasible solution is obtained by solving the mixed integer programming model using the start-up heuristic method; Based on the first relaxed solution and the initial feasible solution, the variables of the mixed integer programming model are fixed to obtain a sub-mixed integer programming model with fixed variables. Solve the current feasible solution of the sub-mixed integer programming model after fixing the variables, determine whether the current feasible solution is better than the initial feasible solution, and obtain the first judgment result; If the first judgment result is yes, then the current feasible solution is taken as the initial feasible solution, and the step of "determining the first relaxed solution and the initial feasible solution of the mixed integer programming model" is returned. If the first judgment result is negative, then the initial feasible solution is taken as the power system unit combination optimization result.

2. The fixed-recursive method for determining the power system unit combination according to claim 1, characterized in that, Determining the first relaxed solution of the mixed-integer programming model specifically includes: Transform the mixed integer programming model into a linear programming model; Determine the first relaxed solution of the linear programming model.

3. The fixed-recursive method for determining the unit combination of a power system according to claim 1, characterized in that, Based on the first relaxed solution and the initial feasible solution, the variables of the mixed integer programming model are fixed to obtain a sub-mixed integer programming model with fixed variables, specifically including: The unit start-up and shutdown state 0-1 variable, whose values ​​are consistent in the first relaxed solution and the initial feasible solution and whose values ​​are at the lower bound of the first value range, is fixed at the lower bound of the first value range; the first value range is the value range of the unit start-up and shutdown state 0-1 variable; The 0-1 variables of the non-unit start-up and shutdown states in the current mixed integer programming model are sorted according to their importance to obtain the sorted 0-1 variables of the non-unit start-up and shutdown states. A predetermined number of non-unit start-up / shutdown state 0-1 variables are sequentially fixed, taking values ​​that are consistent in the first relaxed solution and the initial feasible solution and whose values ​​are within the lower bound of the second value range, to obtain a sub-mixed integer programming model with fixed variables; the second value range is the value range of the sorted non-unit start-up / shutdown state 0-1 variables.

4. The fixed-recursive method for determining the power system unit combination according to claim 3, characterized in that, The 0-1 variables representing the unit's start-up and shutdown states, which take values ​​consistent in both the first relaxed solution and the initial feasible solution and whose values ​​fall within the lower bound of the first value range, are fixed at the lower bound of the first value range. Specifically, these include: Obtain the relaxed solution vector and the feasible solution vector of the 0-1 variables of the current unit start-up and shutdown status; Determine whether the absolute value of the difference between the i-th element in the relaxed solution vector of the current unit start-up / shutdown state 0-1 variable and the i-th element in the feasible solution vector of the unit start-up / shutdown state 0-1 variable is less than the allowable error. If so, the current unit start-up / shutdown state 0-1 variable takes the same value in the first relaxed solution and the initial feasible solution, and when the value of the i-th element in the relaxed solution vector of the current unit start-up / shutdown state 0-1 variable is at the lower bound of the first value range, the current unit start-up / shutdown state 0-1 variable is a variable to be fixed. The variable to be fixed is fixed at the lower bound of the first value range.

5. The fixed-recursive method for determining the unit combination of a power system according to claim 3, characterized in that, The 0-1 variables of non-unit start-up and shutdown states in the current mixed-integer programming model are sorted according to importance to obtain the sorted 0-1 variables of non-unit start-up and shutdown states, which specifically include: Calculate the upper and lower pseudo-costs of the 0-1 variables for the non-unit start-up and shutdown states in the current mixed integer programming model; Calculate the number of locked and unlocked 0-1 variables for the non-unit start-up and shutdown states in the current mixed integer programming model; Based on the transformed constraint coefficient matrix, the lower pseudo-cost, and the lower lock number, determine the importance of any non-unit start-up / shutdown state 0-1 variable; Based on the importance, the non-unit start-up and shutdown state 0-1 variables of the current mixed integer programming model are sorted in descending order to obtain the sorted non-unit start-up and shutdown state 0-1 variables.

6. A fixed-recursive power system unit combination determination system, characterized in that, include: The data acquisition module is used to acquire basic data of the power system. This basic data includes day-ahead load forecast data, unit cost data, transmission network topology data, and unit operating characteristic data. The day-ahead load forecast data includes the total load demand forecast and the load demand forecast for each node. The unit cost data includes the coefficients of the unit's secondary generation cost function, the unit's cold start cost, hot start cost, and shutdown cost. The transmission network topology data includes the transmission line's starting node number, transmission line's ending node number, transmission capacity limit, and transmission line reactance. The unit operating characteristic data includes the unit's upper and lower power generation limits, unit ramp-up capability, minimum start-up time, minimum shutdown time, cold start time, initial operating status, and initial output. The model building module is used to establish a mixed integer programming model based on the aforementioned basic data, with the objective function being the minimum sum of power generation cost and start-up cost, and with constraints including system power balance constraints, system spinning reserve constraints, power generation cost constraints, unit start-up cost constraints, unit output constraints, unit ramping constraints, logical constraints, minimum start-up and shutdown time constraints, and line transmission capacity constraints. The first relaxation solution determination module is used to determine the first relaxation solution and the initial feasible solution of the mixed integer programming model. The relaxed solution includes the relaxed solution vectors of the unit start-up and shutdown state 0-1 variables, the relaxed solution vectors of the unit start-up state 0-1 variables, the relaxed solution vectors of the unit shutdown state 0-1 variables, the relaxed solution vectors of the unit cold start state 0-1 variables, and the relaxed solution vectors of the linear segmented output variables of each unit in each time period; the feasible solution includes the feasible solution vectors of the unit start-up and shutdown state 0-1 variables, the feasible solution vectors of the unit start-up state 0-1 variables, the feasible solution vectors of the unit shutdown state 0-1 variables, the feasible solution vectors of the unit cold start state 0-1 variables, and the feasible solution vectors of the linear segmented output variables of each unit in each time period; the initial feasible solution is obtained by solving the mixed integer programming model using the start-up heuristic method; The variable fixing module is used to fix the variables of the mixed integer programming model according to the first relaxed solution and the initial feasible solution, so as to obtain a sub-mixed integer programming model with fixed variables. The judgment module is used to solve the current feasible solution of the sub-mixed integer programming model after fixing the variables, and to determine whether the current feasible solution is better than the initial feasible solution, so as to obtain a first judgment result; The first execution module is used to, if the first judgment result is yes, take the current feasible solution as the initial feasible solution and return to the "first relaxation solution determination module"; The second execution module is used to take the initial feasible solution as the power system unit combination optimization result if the first judgment result is negative.

7. An electronic device, characterized in that, include: A memory and a processor, the memory being used to store a computer program, the processor running the computer program to cause the electronic device to perform the fixed-recursive power system unit combination determination method according to any one of claims 1-5.

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 the fixed-recursive power system unit combination determination method according to any one of claims 1-5.

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