Parallel accelerated solution method for unit commitment problem of power system and its application

Abstract

The application discloses a parallel accelerated solving method for a unit commitment problem of a power system and application thereof, and the method comprises the following steps: reading a mathematical model file of the unit commitment problem; analyzing the mathematical model and identifying inequality constraints meeting preset conditions in the mathematical model; generating at least one enhanced cut plane based on the identified inequality constraints meeting the preset conditions, adding the enhanced cut plane to the mathematical model, and obtaining a strengthened mathematical model; starting a first solving process and a second solving process in parallel, and allocating CPU core sets not overlapping with each other to the two processes; monitoring a solving state of the second solving process, terminating the second solving process when a preset termination condition is met, and releasing and reallocating CPU core resources occupied by the second solving process to the first solving process; and the first solving process continues to solve until a convergence condition is met, and finally outputs an optimal solution. The application significantly improves the solving efficiency of a large-scale unit commitment problem.

Description

Technical Field

[0001] This invention relates to the field of power system optimization scheduling technology, and in particular to a parallel accelerated solution method for power system unit combination problems and its application. Background Technology

[0002] Solving the unit combination problem is a core aspect of the economic operation of the power system. Its purpose is to minimize the system operating costs while satisfying the power balance and other physical constraints of the power system. It is the basis for carrying out economic dispatch and market clearing of the power system.

[0003] Because the unit operating state variables need to be modeled as integer variables, they are typically modeled as mixed-integer linear programming problems. This makes the unit combination problem an NP-hard problem, making it difficult to solve large-scale unit combination models quickly and with high accuracy. Furthermore, in practical modeling, for reasons of physical information confidentiality, the unit combination problem is usually exported as an MPS file in mathematical problem format. This mathematical format no longer explicitly contains the physical information of the unit combination problem, but only retains its basic characteristics. That is, the minimum start-up and shutdown time of a thermal power unit can be characterized by a single state variable in a single time period, or by two or three variables; regardless of the method, it includes the unit state variables. In addition, thermal power units include minimum / maximum technical output constraints. For the remaining constraints of the unit combination problem, there are modeling strategies adapted to different system requirements, which are difficult to analyze based on the mathematical format.

[0004] For unit combination problems, the commonly used exact solution strategy is the branch-and-cut algorithm, which is employed by popular commercial solvers such as GUROBI and COPT. The most critical steps in the branch-and-cut algorithm are the generation of the cutting plane and feasible solutions. The former helps improve the objective function value of the relaxed solution (lower bound), while the latter helps generate feasible decision results and promotes algorithm convergence. However, existing general-purpose solvers may not have optimal built-in cutting plane generation and feasible solution search strategies when facing unit combination problems with specific structures, leaving room for improvement in solution efficiency. Therefore, it is urgent to study cutting plane and feasible solution generation methods with general applicability to unit combination problems, and to design efficient parallel solution frameworks to fully utilize computational resources.

[0005] It should be noted that the information disclosed in the background section above is only for understanding the background of this application, and therefore may include information that does not constitute prior art known to those skilled in the art. Summary of the Invention

[0006] The purpose of this invention is to solve the technical problem of low solution efficiency of existing power system unit combination problems, and to propose a parallel accelerated solution method for power system unit combination problems and its application.

[0007] To achieve the above objectives, the present invention adopts the following technical solution: A parallel accelerated solution method for power system unit combination problems includes the following steps: S1: Reading the mathematical model file of the unit combination problem, wherein the mathematical model is a mixed integer linear programming model; S2: Parsing the mathematical model and identifying inequality constraints that satisfy preset conditions; the preset conditions include: the constant term on the right-hand side of the inequality is not an integer, and the expression on the left-hand side contains binary variables and continuous variables with negative coefficients; S3: Based on the identified inequality constraints that satisfy the preset conditions, generating at least one enhanced cutting plane and adding the enhanced cutting plane to the mathematical model to obtain an enhanced mathematical model; S4: Starting a first solution process and a second solution process in parallel, and allocating non-overlapping CPU core sets to the two processes; the first solution process is used to complete the enhanced mathematical model. The solution is performed within the entire feasible region; the second solution process is used to solve within a subset of the feasible region of the enhanced mathematical model; S5: In the second solution process, a warm-start strategy is executed to obtain an initial feasible solution, and based on the initial feasible solution, some integer variables are fixed to construct the subset of the feasible region; S6: During the parallel solution process, when the second solution process finds a feasible solution that is better than the current global upper bound, the feasible solution is transmitted to the first solution process through inter-process communication; S7: The solution status of the second solution process is monitored, and when the preset termination condition is met, the second solution process is terminated, and the CPU core resources it occupies are released and reallocated to the first solution process; S8: The first solution process continues to solve until the convergence condition is met, and outputs the final optimal solution.

[0008] In some embodiments, step S3, generating at least one enhanced cutting plane, includes: for identified inequality constraints that satisfy preset conditions, generating enhanced cutting planes based on the Chvátal–Gomory cutting plane principle and using Chvátal–Gomory multipliers; the inequality constraints that satisfy preset conditions are:

[0009] Among them, V con V bin These are the sets of indices for continuous variables and binary variables, respectively. j and i They are V con V bin The serial number in; cj , x j They are the first j The coefficients of the nth continuous variable and the nth j One continuous variable; a i , y i They are the first i The coefficient of the first binary variable and the first... i One binary variable; b It is a constant term on the right-hand side of the inequality and is not an integer; R + Given the set of positive real numbers, define the function. f ( r )= r- , Its meaning is to indicate r The decimal part, R It is the set of real numbers. It is the floor function; The enhanced cutting plane is:

[0010] in, f ( b’ )>0 and let k ≥1 is a unique condition. Integers; define N as the set of all integer variable indices in the inequality constraints, and partition it into... k Set N 0, , N k ,make , ,in p =1, , k ;make and They represent the first i The coefficients of the integer variables and the constant term on the right-hand side of the inequality sign, i.e. and , The Chvátal–Gomory multiplier takes values ​​from the set of positive real numbers, and its values ​​are set as follows: If f ( b’ )<0.5 and t It is a positive integer satisfying 0.5 ≤ tf ( b’ )<1, use f ( t )replace The generated inequalities are at least no weaker than the Chvátal–Gomory cutting plane.

[0011] In some embodiments, after generating the enhanced cutting plane, the method further includes: determining whether the newly generated enhanced cutting plane is parallel to the enhanced cutting plane added in step S3; if they are parallel, the newly generated enhanced cutting plane is discarded; if they are not parallel, the newly generated enhanced cutting plane is added.

[0012] In some embodiments, step S5, the execution of the warm-start strategy includes: S51: linearly relaxing the integer variables in the enhanced mathematical model to obtain a linearly relaxed model, and solving the linearly relaxed model to obtain a linearly relaxed solution; S52: fixing the values ​​of some integer variables according to the linearly relaxed solution and a preset discrimination margin; S53: solving the model after fixing some integer variables to obtain the initial feasible solution.

[0013] In some embodiments, when the unit combination problem includes an energy storage system, step S5 further includes: after fixing other integer variables except for the energy storage system operating state variables, restoring the energy storage system operating state variables to integer variables and performing optimization solution; if the model with some integer variables fixed is not feasible, then adjusting the discrimination margin and re-executing step S52 with fixed variables.

[0014] In some embodiments, in step S6, the inter-process communication is implemented through shared memory; the shared memory is used to store feasible solutions generated by the first solving process and the second solving process, and is managed using a first-in-first-out queue; when accessing the shared memory, process synchronization locks are used to ensure data consistency.

[0015] In some embodiments, in step S7, the preset termination condition includes at least one of the following: the absolute difference between the upper and lower bounds of the second solving process is less than a preset threshold; the first solving process has reached a preset relative gap convergence criterion.

[0016] The present invention also provides a data processing device for power system optimization scheduling, comprising: a processor; a memory coupled to the processor and storing a computer program; when the computer program is executed by the processor, the data processing device performs the parallel accelerated solution method as described in any of the above.

[0017] The present invention also provides a computer-readable storage medium having a computer program / instruction stored thereon, which, when executed by a processor, implements the parallel accelerated solution method as described in any of the above.

[0018] The present invention also provides a data stream of the solution results of the unit combination problem generated by the parallel accelerated solution method described in any one of the above claims, wherein the data stream contains information on the optimal solution scheme obtained by the parallel accelerated solution method.

[0019] The present invention also provides a method for solving a data stream of solution results for a storage unit combinatorial problem, comprising: executing the parallel accelerated solution method described in any one of the above to generate the data stream of solution results; and storing the data stream of solution results in a non-volatile storage medium.

[0020] The present invention also provides a method for transmitting a data stream of the solution result of a unit combination problem, comprising: generating the solution result data stream by performing any of the methods described above; and transmitting the data stream to a client or another computing node via a network.

[0021] The present invention also provides an economic dispatch system for a power system, comprising: a data processing device as described above, used to solve a generator combination problem to obtain a power generation plan; and a dispatch execution unit used to control the start-up, shutdown, and output of generator units in the power system according to the power generation plan.

[0022] The present invention also provides a power market clearing system, comprising: a data processing device as described above, used for rapidly solving a market clearing model, the market clearing model being constructed based on a unit combination problem; and a clearing result publishing unit, used for publishing the market clearing price and winning bid quantity determined based on the solution results.

[0023] The beneficial effects of this invention compared to the prior art include: This invention analyzes the mathematical model of the unit combinatorial problem, identifies inequality constraints that satisfy preset conditions, and pre-generates enhanced cutting planes, effectively tightening the linearly relaxed feasible region of the problem, thereby raising the lower bound and creating conditions for pruning in the subsequent branch and bound process. Furthermore, by initiating a dual-process parallel solution and utilizing a warm-start strategy, a high-quality subset of the feasible region is quickly constructed for the second solution process, allowing it to focus on searching for high-quality feasible solutions. The two solution processes communicate with each other to promptly transmit the new upper bound discovered by the second solution process to the first solution process, enabling the first solution process to perform pruning earlier and avoid invalid searches. Simultaneously, CPU resource allocation is dynamically adjusted according to the solution status of the second solution process, and the second solution process is terminated in a timely manner when it meets the preset termination conditions, and its resources are reclaimed to the first solution process, achieving optimized allocation of computing resources. The above-mentioned technical solutions work together to overcome the shortcomings of single general-purpose solvers in finding high-quality feasible solutions and rigid resource utilization in the early stages of the solution process by "tightening the lower bound" and "providing the upper bound". They realize the intelligent allocation of computing resources at different stages of the solution process, thereby minimizing the overall solution time and ultimately achieving a significant improvement in the efficiency of solving large-scale unit combination problems.

[0024] In some embodiments, the present invention also has the following beneficial effects: By generating an enhanced cutting plane based on the Chvátal–Gomory cutting plane principle and optimizing the multiplier selection, we can generate more efficient inequalities than the standard cutting plane without cutting out integer feasible solutions, thus more effectively improving the lower bound.

[0025] By identifying and discarding parallel cutting planes, the unnecessary expansion of the model size is avoided, reducing the computational burden on the solver.

[0026] By using a hot-start strategy that fixes integer variables through linear relaxation and preset discrimination margin, we can quickly obtain an initial feasible solution and construct a high-quality subset of the feasible domain, laying the foundation for efficient search in the second solution process.

[0027] The hot-start strategy was adjusted to address issues involving energy storage systems, enhancing the applicability and robustness of the method to complex power system models.

[0028] Inter-process communication is achieved through shared memory and process synchronization locks, ensuring both the efficiency and security of data exchange.

[0029] By monitoring the difference between the upper and lower bounds and the relative gap as termination conditions, intelligent management of the resource consumption of the second solution process is achieved, ensuring the overall solution efficiency.

[0030] Other beneficial effects of the embodiments of the present invention will be further described below. Attached Figure Description

[0031] Figure 1 This is an overall flowchart of the parallel accelerated solution method in this embodiment of the invention. Detailed Implementation

[0032] The present invention will be further described below with reference to the accompanying drawings and preferred embodiments. It should be noted that, unless otherwise specified, the embodiments and features described in this application can be combined with each other.

[0033] It should be noted that the directional terms such as left, right, up, down, top, and bottom used in this embodiment are only relative concepts or are based on the normal use of the product, and should not be considered as restrictive.

[0034] To improve the efficiency of solving the unit combination problem, this invention proposes a parallel accelerated solution method that integrates a pre-generation strategy for cutting planes. Its core innovation lies in the following: after parsing the MPS-formatted UC (unit combination) model and adaptively adding cutting planes, the complete UC model (first solution process) and the accompanying sub-model during a warm start (second solution process) are solved in parallel. This fully utilizes the solver's characteristic that while it significantly improves the objective function value of relaxed solutions during root node solving, its ability to find feasible solutions is relatively weak. The second solution process uses this time to search for feasible solutions based on the warm start process, and in subsequent solving processes, it transmits high-quality feasible solutions to the first solution process via inter-process communication. Specifically, shared memory is used for updating signals that trigger feasible solution interaction, terminate the second solution process, and store the decision solutions generated by both processes. When either process uses shared memory, a process synchronization lock ensures data safety. For the transmission of feasible solutions during interaction, feasible solutions are first stored in a list and then implemented using a first-in-first-out queue. This promotes pruning in the computation process of the first solution process to accelerate the solution. The two processes are pre-allocated a specified set of CPU cores to avoid process conflicts. In addition, after the sub-model is solved, the remaining CPU cores are restored to the first solving process to give it more flexibility in allocating CPU core resources.

[0035] The acceleration principle of this method is based on the characteristics of mixed-integer programming solvers: 1) the cutting plane rapidly raises the lower bound by tightening the feasible region of the relaxation problem, assisting in pruning; 2) the solver's ability to find feasible solutions (upper bounds) is weak in the early stages of the search. This embodiment of the invention separates the time-consuming high-quality feasible solution search task (the second solving process) from the main solving process (the first solving process) through dual-process parallelism. The second solving process focuses on feasible solution search during the intervals when the main process is solving the relaxation problem, and provides immediate feedback of the new upper bound to the first solving process through inter-process communication, enabling it to perform pruning earlier. This optimizes the allocation of time resources from the search strategy perspective, achieving an acceleration effect.

[0036] This invention provides a parallel accelerated solution method for power system unit combination problems, comprising the following steps: S1: Read the mathematical model file of the unit combination problem. The mathematical model is a mixed integer linear programming model.

[0037] S2: Analyze the mathematical model and identify the inequality constraints that satisfy the preset conditions. The preset conditions include: the constant term on the right side of the inequality is not an integer, and the expression on the left side contains binary variables and continuous variables with negative coefficients.

[0038] S3: Based on the identified inequality constraints that satisfy the preset conditions, generate at least one enhanced cutting plane and add the enhanced cutting plane to the mathematical model to obtain the enhanced mathematical model.

[0039] In step S3, generating at least one enhanced cutting plane includes: for the identified inequality constraints that satisfy preset conditions, generating enhanced cutting planes based on the Chvátal–Gomory (CG) cutting plane principle and using Chvátal–Gomory multipliers (CG multipliers); the inequality constraints that satisfy the preset conditions are:

[0040] Among them, V con V bin These are the sets of indices for continuous variables and binary variables, respectively. j and i They are V con V bin The serial number in; c j , x j They are the first j The coefficients of the nth continuous variable and the nth j One continuous variable; a i , y i They are the first i The coefficient of the first binary variable and the first... i One binary variable; b It is a constant term on the right-hand side of the inequality and is not an integer; R + Given the set of positive real numbers, define the function. f ( r )= r- , r R Its meaning is to indicate r The decimal part, R It is the set of real numbers. It is the floor function; The enhanced cutting plane is:

[0041] in, f ( b’ )>0 and let k ≥1 is a unique condition. Integers; define N as the set of all integer variable indices in the inequality constraints, and partition it into... k Set N 0, , N k ,make , ,in p =1, , k ;make and They represent the first i The coefficients of the integer variables and the constant term on the right-hand side of the inequality sign, i.e. and , The CG multiplier takes values ​​from the set of positive real numbers, and its values ​​are set as follows: If f ( b’ )<0.5 and t It is a positive integer satisfying 0.5 ≤ tf ( b’ )<1, use f ( t )replace The generated inequalities are at least no weaker than the Chvátal–Gomory cutting plane.

[0042] After generating the enhanced cutting plane, the method further includes: determining whether the newly generated enhanced cutting plane is parallel to the enhanced cutting plane added in step S3. If they are parallel, the newly generated enhanced cutting plane is discarded; if they are not parallel, the newly generated enhanced cutting plane is added.

[0043] S4: Start the first and second solver processes in parallel and allocate non-overlapping sets of CPU cores to the two processes; the first solver process is used to solve within the complete feasible region of the enhanced mathematical model; the second solver process is used to solve within a subset of the feasible region of the enhanced mathematical model.

[0044] S5: In the second solution process, a hot start strategy is executed to obtain an initial feasible solution, and a subset of integer variables is fixed based on the initial feasible solution to construct a subset of the feasible domain.

[0045] Implementing a warm start strategy includes: S51: Linearly relax the integer variables in the enhanced mathematical model to obtain a linearly relaxed model, and solve the linearly relaxed model to obtain a linearly relaxed solution; S52: Based on the linear relaxation solution and the preset discrimination margin, fix the values ​​of some integer variables; S53: Solve the model with some integer variables fixed to obtain an initial feasible solution.

[0046] When the unit combination problem includes an energy storage system, it also includes: after fixing other integer variables except for the energy storage system operating state variables, restoring the energy storage system operating state variables to integer variables and performing optimization solution; if the model with some integer variables fixed is not feasible, then after adjusting the discrimination margin, step S52 of fixing variables is re-executed.

[0047] S6: During parallel solving, when the second solving process finds a feasible solution that is better than the current global upper bound, it transmits the feasible solution to the first solving process via inter-process communication. Inter-process communication is implemented through shared memory; shared memory is used to store feasible solutions generated by the first and second solving processes and is managed using a first-in, first-out queue; process synchronization locks are used to ensure data consistency when accessing shared memory.

[0048] S7: Monitor the solution status of the second solving process. When the preset termination condition is met, terminate the second solving process and release the CPU core resources it occupies and reallocate them to the first solving process. The preset termination condition includes at least one of the following: the absolute difference between the upper and lower bounds of the second solving process is less than a preset threshold; the first solving process has reached the preset relative gap convergence criterion (convergence condition in step S8).

[0049] S8: The first solution process continues to solve until the convergence condition is met, and the final optimal solution is output.

[0050] The specific algorithm for generating the cutting plane in the embodiments of the present invention (such as choosing CG or enhanced MIR) and the CPU core allocation strategy for parallel processes (such as average allocation or dynamic allocation) are optimizable and replaceable.

[0051] This invention also provides a data processing device for power system optimization scheduling, comprising: a processor; a memory coupled to the processor and storing a computer program; when the computer program is executed by the processor, the data processing device executes the parallel accelerated solution method as described in any of the above embodiments.

[0052] This invention also provides a computer-readable storage medium storing a computer program / instructions thereon, which, when executed by a processor, implements the parallel accelerated solution method described in any of the above embodiments.

[0053] This invention also provides a data stream of the solution results for the unit combination problem generated by any of the above-described parallel accelerated solution methods, the data stream containing information on the optimal solution scheme obtained by the parallel accelerated solution method.

[0054] This invention also provides a method for solving a data stream of the solution result of a storage unit combinatorial problem, comprising: executing the parallel accelerated solution method described in any one of the above to generate a data stream of the solution result; and storing the data stream of the solution result in a non-volatile storage medium.

[0055] This invention also provides a method for transmitting a data stream of solution results for a unit combination problem, comprising: executing the parallel accelerated solution method described in any of the above to generate a data stream of solution results; and transmitting the data stream of solution results to a client or another computing node via a network.

[0056] This invention also provides an economic dispatch system for a power system, comprising: a data processing device as described above, used to solve the unit combination problem to obtain a power generation plan; and a dispatch execution unit, used to control the start-up, shutdown, and output of generator units in the power system according to the power generation plan.

[0057] This invention also provides a power market clearing system, comprising: a data processing device as described above, used for rapidly solving a market clearing model, the market clearing model being constructed based on a unit combination problem; and a clearing result publishing unit, used for publishing the market clearing price and winning bid quantity determined based on the solution results.

[0058] The following describes specific embodiments of the present invention.

[0059] Figure 1 This is a flowchart illustrating a parallel accelerated solution method based on a fusion cutting plane pre-generation strategy provided in this embodiment. The specific steps are as follows: (1) Input the unit combination problem model in mps format.

[0060] (2) Constraints that meet the following characteristics: 1) The constant term on the right side of the inequality sign is not an integer; 2) The expression on the left side of the inequality sign is formed by binary variables and continuous variables through four arithmetic operations; 3) The coefficient of the continuous variable is negative.

[0061] For example, a system backup constraint modeled in this form satisfies the above conditions: (1) in, It is the set of serial numbers of all thermal power units; It is the first i Taiwanese crew during the period t A binary variable indicating whether the device is in a running state; a value of 1 indicates that it is running. and Representing the first i The maximum active power output limit of the Taiwanese generator set and during the time period t The actual output value; represents the system's reserve coefficient, with a value ranging from approximately 10%, which is taken as 10% in the example; D is the set of all node numbers. It is the first k Each node in the time period t The active load; T is the set of all scheduling periods.

[0062] For ease of explanation, the inequality signs in the above-described inequality constraints are uniformly rewritten as less than or equal to signs. The general mixed-integer inequality constraints can be written as: (2) Among them, V con V bin It is a set of ordinal numbers for continuous and binary variables; j and i They are V con V bin The serial number in; c j , x j It is the first j The coefficient of the nth continuous variable (which is negative) and the nth j One continuous variable; a i , y i It is the first i The coefficient of the first binary variable and the first... i One binary variable; b It is a constant term on the right-hand side of the inequality and is not an integer; R + It is the set of positive real numbers.

[0063] For ease of explanation, a function is defined. f ( r )= r- , Its meaning is to indicate r The decimal part, R It is the set of real numbers. This is the floor function.

[0064] The above inequalities contain non-integer terms. Based on these constraints, mixed integer rounding (MIR) inequalities can be generated. Such inequalities are convex hulls for generating mixed integer programming problems and do not eliminate any integer feasible solutions. (3) in, This indicates rounding up.

[0065] When the continuous variables in the inequality constraint do not have positive coefficients, equation (2) is a constraint consisting entirely of integer variables: (4) The Chvátal–Gomory (CG) cutting plane proves that for an inequality system defining a bounded polyhedron, its closure (obtained through linear combination and integer rounding) precisely describes the integer convex hull without cutting away integer feasible points. In this embodiment of the invention, such a cutting plane can be generated based on equation (3) as follows: (5) in, The value can be set by the user, and its range is the set of positive real numbers. It is the multiplier coefficient on both sides of the inequality. For simplicity, it is called the CG multiplier. However, in order for the multiplier to play the role of enhancing the cutting plane, its value needs to be set based on the following proposition 1.

[0066] make and Represent the first of equations (5) i The coefficients of the integer variables and the constant term on the right-hand side of the inequality sign, i.e. and .

[0067] Proposition 1: If f ( b’ )<0.5 and t It is a positive integer satisfying 0.5 ≤ tf ( b’ )<1, use f ( t )replace The generated inequalities are at least as strong as those generated by the CG cutting plane.

[0068] Equation (5) can be further refined by classifying the coefficients and multiplying them by integer factors to generate a stronger efficient inequality, expressed as: (6) in, f ( b’ )>0 and let k ≥1 is a unique condition. Integers. Define the set of all integer variable indices in the inequality constraints as N, and partition it into... k Set N 0, , N k The index of each set is: , ,in p =1, , k Equation (6) can be generated according to the mathematical relationship above.

[0069] In practical applications, CG multipliers are selected. Based on proposition 1, select And assume once Therefore, inequality (5) is not added. Furthermore, when the ratios of coefficients of different enhancement cut planes are found to be equal, this means that the enhancement cut plane is parallel to the previously added enhancement cut plane, and adding it to the model is invalid. In this case, the newly generated enhancement cut plane is discarded. If they are not parallel, a newly generated enhancement cut plane is added. Since the added cut plane is an enhancement of the MIR cut plane, the inequalities generated in this way will not cut off integer feasible solutions. For simplicity, this will be referred to as the enhancement cut plane addition process. The following is the pseudocode for the enhancement cut plane addition process: Algorithm 1: Enhanced cutting plane addition process Input the completed UC model Output the UC model after the enhanced cutting plane addition process. 1: Traverse the constraints of the UC model to obtain the set of constraints that satisfy equation (2). 2: For the constraints satisfying equation (2), an enhanced cutting plane is generated based on equation (6) and added to the UC model.

[0070] It should be noted that not all unit combination models necessarily contain constraints that satisfy the conditions of this step. After this step is completed, the number of enhanced cutting planes added may be 0. Therefore, the embodiments of the present invention are only for UC models containing such constraints.

[0071] (3) Parallel induced accelerated solution method

[0072] First, two processes are started. After both processes resolve and identify constraints to which cutting planes can be added and add the cutting planes, process 1 (the first solver) searches for feasible solutions within the entire feasible region of the UC problem, while process 2 (the second solver) searches for feasible solutions within a subset of the feasible region of the UC problem. Process 2 first executes a warm-start strategy to generate an initial feasible solution. This strategy is as follows: Step 0: Initialize the integer down (close to 0) and up discrimination margins. and (Set as follows:) , Set the maximum number of feasible solutions to be found. N max,sol (set as) N max,sol =3); Step 1: Remove the 0 / 1 integer variables from the original model (the enhanced mathematical model). y Linear relaxation is Solving this linear relaxation model yields a linear relaxation solution. At this point, restore the integer variables in the model; Step 2: If linear relaxation solution middle If the corresponding variable in the original model is fixed at 1, then the linear relaxation solution... middle Then, the corresponding variables in the original model are fixed to 0. After fixing most of the variables, the original model is solved to quickly obtain feasible solutions. When the number of feasible solutions... N sol > N max,sol If the solution fails, proceed to step 4; if the original model becomes infeasible after fixing the variables, proceed to step 3. Step 3: Update the upward discriminant margin (set as) If linear relaxation solution middle Since this variable is a unit operating state variable, the corresponding variable in the original model is fixed at 1, while the other integer variables are not fixed. The number of feasible solutions obtained by the solver... N sol > N max,sol If the condition is met, the solution process stops, and the process proceeds to step 4. Step 4: Output the initial feasible solution .

[0073] For the UC problem involving energy storage systems, the revised hot-start strategy adds two steps between steps 3 and 4 of the original strategy. In step 1, restoring integer variables is replaced with restoring integer variables other than those related to the energy storage system's operating state; the remaining steps remain unchanged. Step 4 in the original strategy is now numbered step 6. The two added steps are as follows: Step 4: Fix the current integer variable decision results except for the energy storage system's operating state, restore the integer variables of the energy storage system's operating state, and optimize the current model (the model with some integer variables fixed). If the model has a feasible solution, then the initial feasible solution is obtained. Proceed to step 6; if, after restoring the integer variables of the actual energy storage, the energy storage devices configured in the system are of poorer performance than the "virtual energy storage system," and their ability to participate in power supply such as ramping is weakened, making the model infeasible, then proceed to step 5. Step 5: Reduce the upward discrimination margin (Usually, the step size can be reduced to 0 in increments of 0.7). The integer variables of the energy storage system's operating state are linearly relaxed in the model, and other integer variables are no longer fixed. Return to step 3.

[0074] To bring the feasible region subset closer to the optimal solution, process 2 first uses the hot-start strategy to obtain an initial feasible solution. Then, it compares the variable values ​​of the linearly relaxed solution and the initial feasible solution. If all the state variables for the thermal power unit are 1, it means that the unit is likely to need to be started even in the optimal solution. All variables satisfying this condition are fixed, and then the solution process begins.

[0075] It should be noted that a process is the basic unit of operating system resource allocation. Although each process has its own independent memory space, the allocation of CPU cores in the embodiments of this invention is based on the computer's CPU configuration and is evenly distributed (e.g., 6 cores per process for 12 cores). In addition, since processes are isolated from each other, the crash of one process will not affect the operation of the remaining processes, which also improves the robustness of the solver.

[0076] During parallel processing, once process 2 finds a better feasible solution, it transmits that solution to process 1 via inter-process communication. The second solution process is monitored continuously. N In each iteration (e.g., 2 iterations), the decrease in the absolute difference between the upper and lower bounds is less than the threshold. ε If the threshold value is too high, it is determined that the search efficiency has significantly decreased (the changes in the upper and lower bounds tend to stagnate), where the threshold value is not high. ε This can be set to 0.01% of the current best upper bound. When process 2 reaches the relative gap or its upper and lower bounds stagnate, or when process 1 has reached the set relative gap, process 2 terminates, and the remaining CPU cores are allocated to process 1. Because process 2 terminates early during the solution process, the transfer of feasible solutions will not continue throughout the entire solution process, thus not affecting the solution speed. The overall flowchart is as follows. Figure 1 As shown.

[0077] (4) Set appropriate solution accuracy and maximum solution time as needed. Usually, the solution accuracy is a positive number in (0, 0.003] and the solution time is at most 1 hour. Input the completed unit combination model into the mixed integer linear programming solver for solution.

[0078] (5) Save the better solution with the smaller objective function value among the feasible solutions obtained by the two processes, and output the solution result.

[0079] This invention first constructs an enhanced cutting plane based on some special constraints of the unit combination problem. The entire model is a mixed-integer linear programming model. Then, a dual-process approach is initiated, setting the solver's accuracy and maximum solution time. The process employs direct solver invocation (process 1) and a hot-start strategy (process 2) respectively. During the solution process, the two processes interact to reach optimal upper bounds. When the changes in upper and lower bounds stagnate, process 2 is terminated. The model is then input into the solver for further processing. The cutting plane generation and parallel interaction method proposed in this invention have certain versatility, facilitating faster solutions to unit combination models without compromising the feasibility of the decision results.

[0080] Experimental example: Several large-scale simulation examples generated from actual system modeling are analyzed. The examples have been exported as .mps format mathematical models, and their sizes are listed in Table 1. The commercial solver GUROBI (version 11.0.1) was used for solving the system. No parameters other than the solution accuracy were set during the solution process. A Python program read and parsed the data, calling the corresponding interfaces of the GUROBI solver for parsing and solving. The solution results can be exported as .sol files by variable name. The parsing and solving time can be handled using timing functions in the Python program. All simulation examples were performed on a computer with a Windows operating system, an AMD Ryzen Threadripper PRO 5995WX 64-Core CPU, and 220GB of total memory. 32 threads were allocated to each process for parallel processing. The relative gap between the upper and lower convergence bounds of the solver was set to 0.3%. All other solver settings were default (the default solver settings include enabling pre-solution, cutting plane generation, multi-threaded parallelism, etc.). Table 1 shows the size of the different examples.

[0081] Table 1. Case Size

[0082] For ease of description, the combination of the parallel induced solution method in this embodiment with the addition of the enhanced cut plane generation process is called Algorithm 1, and the combination without the addition of the enhanced cut plane generation process is called Algorithm 2. The two are compared with simply using the warm start strategy (Algorithm 3) and directly calling the solver to solve (Algorithm 4).

[0083] Since the GUROBI solver performs calculations on the same hardware device with the same parameter settings, uses the same heuristic method, and has the same calculation process and final objective function value each time, in order to avoid fluctuations in solution time caused by computer performance, the calculation time is obtained by calculating the same model three times and then taking the average value.

[0084] Table 2 shows the solution time for different examples. It can be seen that Algorithm 1 has the shortest computation time. At the same time, Algorithm 1 is more robust in terms of computation time. In contrast, Algorithm 2, which does not add the enhanced cutting plane, has a long computation time in example 1. This reflects the importance of the proposed enhanced cutting plane for accelerating the solution.

[0085] Table 2 Solution Time

[0086] Table 3 shows the number of cutting planes added. It can be seen that the number of cutting planes is small and has little impact on the model size.

[0087] Table 3 Number of cutting surfaces generated after the enhanced cutting surface process

[0088] The embodiments of the present invention have a certain degree of universality for solving the problem of accelerating unit combination in actual power systems with specific constraint structures.

[0089] The above description, in conjunction with specific preferred embodiments, provides a further detailed explanation of the present invention. It should not be construed that the specific implementation of the present invention is limited to these descriptions. For those skilled in the art, several equivalent substitutions or obvious modifications can be made without departing from the concept of the present invention, and all such modifications, achieving the same performance or purpose, should be considered within the scope of protection of the present invention.

Claims

1. A parallel accelerated solution method for power system unit combination problems, characterized in that, Includes the following steps: S1: Read the mathematical model file of the unit combination problem. The mathematical model is a mixed-integer linear programming model. S2: Analyze the mathematical model and identify the inequality constraints that satisfy preset conditions; the preset conditions include: the constant term on the right side of the inequality is not an integer, and the expression on the left side contains binary variables and continuous variables with negative coefficients; S3: Based on the identified inequality constraints that satisfy the preset conditions, generate at least one enhanced cutting plane, and add the enhanced cutting plane to the mathematical model to obtain the enhanced mathematical model; S4: Start the first and second solving processes in parallel and allocate non-overlapping sets of CPU cores to the two processes; the first solving process is used to solve within the complete feasible region of the enhanced mathematical model; the second solving process is used to solve within a subset of the feasible region of the enhanced mathematical model. S5: In the second solution process, a hot start strategy is executed to obtain an initial feasible solution, and based on the initial feasible solution, some integer variables are fixed to construct the feasible domain subset; S6: During the parallel solution process, when the second solution process finds a feasible solution that is better than the current global upper bound, the feasible solution is transmitted to the first solution process through inter-process communication; S7: Monitor the solution status of the second solution process. When the preset termination condition is met, terminate the second solution process and release the CPU core resources it occupies and reallocate them to the first solution process. S8: The first solution process continues to solve until the convergence condition is met, and the final optimal solution is output.

2. The parallel accelerated solution method according to claim 1, characterized in that, In step S3, generating at least one enhanced cutting plane includes: for the identified inequality constraints that satisfy preset conditions, generating enhanced cutting planes based on the Chvátal–Gomory cutting plane principle and using Chvátal–Gomory multipliers; the inequality constraints that satisfy preset conditions are: Among them, V con V bin These are the sets of indices for continuous variables and binary variables, respectively. j and i They are V con V bin The serial number in; c j , x j They are the first j The coefficients of the nth continuous variable and the nth j One continuous variable; a i , y i They are the first i The coefficient of the first binary variable and the first... i One binary variable; b It is a constant term on the right-hand side of the inequality and is not an integer; R + Given the set of positive real numbers, define the function. f ( r )= r- , r R Its meaning is to indicate r The decimal part, R It is the set of real numbers. It is the floor function; The enhanced cutting plane is: in, f ( b’ )>0 and let k ≥1 is a unique condition. Integers; define N as the set of all integer variable indices in the inequality constraints, and partition it into... k Set N 0, , N k ,make , ,in p =1, , k ;make and They represent the first i The coefficients of the integer variables and the constant term on the right-hand side of the inequality sign, i.e. and , The Chvátal–Gomory multiplier takes values ​​from the set of positive real numbers, and its values ​​are set as follows: If f ( b’ )<0.5 and t It is a positive integer satisfying 0.5 ≤ tf ( b’ )<1, use f ( t )replace The generated inequalities are at least no weaker than the Chvátal–Gomory cutting plane.

3. The parallel accelerated solution method according to claim 2, characterized in that, After generating the enhanced cutting plane, the method further includes: determining whether the newly generated enhanced cutting plane is parallel to the enhanced cutting plane added in step S3. If they are parallel, the newly generated enhanced cutting plane is discarded; if they are not parallel, the newly generated enhanced cutting plane is added.

4. The parallel accelerated solution method according to claim 1, characterized in that, In step S5, the execution of the warm start strategy includes: S51: Perform linear relaxation on the integer variables in the enhanced mathematical model to obtain a linear relaxation model, and solve the linear relaxation model to obtain a linear relaxation solution; S52: Based on the linear relaxation solution and the preset discrimination margin, fix the values ​​of some integer variables; S53: Solve the model with some integer variables fixed to obtain the initial feasible solution.

5. The parallel accelerated solution method according to claim 4, characterized in that, When the unit combination problem includes an energy storage system, step S5 further includes: after fixing other integer variables except for the energy storage system operating state variables, restoring the energy storage system operating state variables to integer variables and performing optimization solution; if the model with some integer variables fixed is not feasible, then after adjusting the discrimination margin, step S52 of fixing variables is re-executed.

6. The parallel accelerated solution method according to claim 1, characterized in that, In step S6, the inter-process communication is implemented through shared memory; the shared memory is used to store feasible solutions generated by the first solving process and the second solving process, and is managed using a first-in-first-out queue; when accessing the shared memory, process synchronization locks are used to ensure data consistency.

7. The parallel accelerated solution method according to claim 1, characterized in that, In step S7, the preset termination condition includes at least one of the following: the absolute difference between the upper and lower bounds of the second solution process is less than a preset threshold; the first solution process has reached the preset relative gap convergence criterion.

8. A data processing device for optimized dispatching of power systems, characterized in that, include: processor; A memory, coupled to the processor and storing a computer program; when the computer program is executed by the processor, the data processing device causes the data processing device to perform the parallel accelerated solution method as described in any one of claims 1 to 7.

9. A computer-readable storage medium having a computer program / instructions stored thereon, characterized in that, When the computer program / instruction is executed by the processor, it implements the parallel accelerated solution method as described in any one of claims 1 to 7.

10. A data stream of solution results for a unit combination problem generated by the parallel accelerated solution method according to any one of claims 1 to 7, characterized in that, The data stream contains information about the optimal solution obtained through the parallel accelerated solution method.

11. A method for solving a storage unit combinatorial problem and providing a data stream of the solution, characterized in that, include: The parallel accelerated solution method according to any one of claims 1 to 7 is used to generate a solution result data stream; The solution result data stream is stored in a non-volatile storage medium.

12. A method for solving a data stream of transmission unit combination problems, characterized in that, include: The parallel accelerated solution method according to any one of claims 1 to 7 is used to generate a solution result data stream; And transmit the solution result data stream to the client or another computing node via the network.

13. An economic dispatch system for a power system, characterized in that, include: The data processing apparatus as described in claim 8 is used to solve the unit combination problem to obtain a power generation plan; The scheduling execution unit is used to control the start-up, shutdown, and power output of generator units in the power system according to the power generation plan.

14. A power market clearing system, characterized in that, include: The data processing apparatus as described in claim 8 is used to quickly solve a market clearing model, wherein the market clearing model is constructed based on the unit combination problem; The clearing result release unit is used to release the market clearing price and winning bid volume determined based on the solution results.

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