Parallel Variable Parameter Simulated Annealing Optimization Method for Optimal Scheduling of Cascade Reservoir Groups

Abstract

This invention relates to the field of cascade reservoir group optimization scheduling technology, and discloses a parallel variable parameter simulated annealing optimization method for cascade reservoir group optimization scheduling, comprising the following steps: determining initial calculation conditions, including the objective function and constraints of cascade reservoir group optimization scheduling; setting calculation parameters; generating initial trajectories for each reservoir that satisfy the constraints using conventional dynamic programming methods or manual experience-based decision-making; starting iterative calculation, using simulated annealing for multi-core parallel computation search, and selecting different annealing control parameters in each thread to perform different forms of annealing search, iteratively optimizing to successively approach the global optimum, and outputting the final optimal trajectory. This invention's parallel variable parameter simulated annealing optimization method for cascade reservoir group optimization scheduling effectively solves the problems of insufficient search capability and low computational speed in DDDP (Digital Directed Programming) for large-scale hydropower system optimization scheduling.

Description

Technical Field

[0001] This invention relates to the field of optimized scheduling technology for cascade reservoir groups, specifically to a parallel variable parameter simulated annealing optimization method for optimized scheduling of cascade reservoir groups. Background Technology

[0002] Hydropower, as a renewable and clean energy source, occupies an extremely important position in my country's energy development history, strongly supporting the sustainable development of the economy and society. In recent years, my country's hydropower industry has developed rapidly, with large-scale development and utilization of water resources in major river basins, gradually realizing the cascade rolling development of hydropower basins and the optimal allocation of water resources. Optimal scheduling of cascade reservoir groups has significant comprehensive benefits in terms of society, economy, and ecology, effectively promoting the efficient utilization of water resources in river basins and ensuring the safe, stable, and reliable operation of the power grid system. It has always been an important engineering practice and theoretical research topic in the field of hydropower energy systems. However, with the increasingly large scale of cascade reservoir group systems, the scheduling problem has become increasingly complex, leading to an exponential increase in computation time and memory usage during the optimization scheduling process. The curse of dimensionality has become an inevitable scientific challenge for the optimal scheduling of reservoir groups. Therefore, actively developing efficient and practical methods that can adapt to the current situation in solving the joint optimal scheduling problem of cascade reservoir groups, and narrowing the gap with the actual scheduling situation, has important engineering practical value for the scheduling, operation, and management of cascade reservoir groups.

[0003] From a mathematical perspective, the optimal scheduling problem of cascade reservoir groups is a large-scale, high-dimensional, multi-stage, strongly constrained, and nonlinear optimization problem. Traditional dynamic programming (DP) methods can solve single-reservoir optimal scheduling problems well, but when dealing with the optimal scheduling problem of cascade reservoir groups, they are unable to avoid the curse of dimensionality. While intelligent optimization algorithms such as genetic algorithms, differential evolution algorithms, and particle swarm optimization algorithms differ in their operational methods, they all suffer from low computational efficiency, high computational overhead, and insufficient convergence ability when solving reservoir group optimal scheduling problems. Therefore, it is urgent to develop new and effective optimization methods that combine the latest achievements in computational science to simultaneously reduce memory consumption and computation time, effectively alleviate the curse of dimensionality, and ensure the computational efficiency and solution accuracy of large-scale reservoir group optimal scheduling.

[0004] Discrete Differential Dynamic Programming (DDDP) is an improved dynamic programming method based on successive asymptotic approximation theory. Its basic idea is as follows: First, an initial trajectory satisfying various complex constraints is obtained based on experience or other methods. Then, the state variables of each reservoir at different time periods are discretized within the neighborhood of this trajectory to form corridors. Second, optimization is performed among the discrete state combinations at each time period using conventional dynamic programming methods to find a new optimal trajectory as the experimental trajectory for the next iteration, iterating repeatedly until convergence conditions are met. However, DDDP still suffers from drawbacks such as the curse of dimensionality, premature convergence, and limited search capability when dealing with large-scale reservoir group optimal scheduling problems. Therefore, it is necessary to improve the computational mechanism of DDDP by incorporating new technologies to enhance the computational efficiency and accuracy of solving reservoir group optimal scheduling problems.

[0005] Simulated annealing is a stochastic optimization algorithm based on Monte Carlo stochastic simulation iterative solution strategy. Its basic idea is to start from a relatively high initial temperature and, as the temperature parameter decreases, randomly search for a global optimum in the feasible space using probabilistic jump characteristics. It has the advantages of escaping local optima and strong search capabilities. It has been successfully applied in fields such as control engineering, neural networks, and signal processing. Parallel computing is a novel computer technology that has emerged in recent years. Its essence is to fully utilize the computing resources of multi-core processors and execute given computational operations in parallel on different threads through reasonable and feasible parallel computing models. Summary of the Invention

[0006] The purpose of this invention is to address the shortcomings of the aforementioned technologies by providing a parallel variable parameter simulated annealing optimization method for the optimal scheduling of cascade reservoir groups, effectively solving the problems of insufficient search capability and low computational speed in DDDP when solving the optimal scheduling of large-scale hydropower systems.

[0007] To achieve the above objectives, the parallel variable parameter simulated annealing optimization method for the optimal scheduling of cascade reservoir groups designed in this invention includes the following steps:

[0008] 1) Determine the initial calculation conditions, including the objective function and constraints for the optimal scheduling of the cascade reservoir group;

[0009] 2) Set the calculation parameters;

[0010] 3) Using conventional dynamic programming methods or human experience-based decision-making, generate the initial trajectories of each reservoir that satisfy all constraints;

[0011] 4) Start iterative calculation, use simulated annealing method for multi-core parallel computing search, and select different annealing control parameters in each thread to perform different forms of annealing search, iterate repeatedly to find the best solution, and output the final optimal trajectory.

[0012] Preferably, in step 2), the calculation parameters include the number of reservoirs N, the number of scheduling stages T, the maximum number of iterations M, the maximum number of annealing searches K, the number of parallel computing threads C, the convergence accuracy ε, and the initial temperature parameter T of thread c. 0,c and annealing control parameters y 0,c , where c (1≤c≤C).

[0013] Preferably, in step 3), conventional dynamic programming methods or human experience-based decision-making are used to generate the initial trajectories of each reservoir that satisfy all constraints. And calculate the initial distance step length Δ = (Δ) for each reservoir. i,j ) N×T The calculation formula is as follows:

[0014]

[0015] in, Denotes the initial trajectory of reservoir i in stage j, Δ i,j This represents the initial distance of reservoir i from the target area in stage j. This represents the upper limit of the water level of reservoir i in stage j. Z i,j Let L represent the lower limit of the water level of reservoir i in stage j, and L be the initial number of discrete points.

[0016] Preferably, step 4) includes the following steps:

[0017] 4.1) Set the iteration count m = 1,

[0018] 4.2) Set the stage number j = 1;

[0019] 4.3) The current temperature parameter of thread c is T. m,c =T 0,c ×(y 0,c ) m Parallel simulated annealing search is performed to obtain the optimal trajectory;

[0020] 4.4) Calculate the water level difference between two adjacent optimal trajectories at different time periods. This indicates that the current trajectory is optimal, so we end the current iteration, shrink all outlier walk lengths, and let... Proceed to step 45), otherwise proceed to step 42) and continue based on... Perform parallel variable-parameter simulated annealing search;

[0021] 4.5) Let m = m + 1. If m > M, then go to step 46); otherwise, go to step 42.

[0022] 4.6) Stop the calculation and output the final optimal trajectory.

[0023] Preferably, step 4.3) involves the following steps for performing parallel simulated annealing search:

[0024] 4.3.1) Set the current trajectory The algorithm is copied C times and distributed to various threads for computation. The current trajectory of thread c is...

[0025] 4.3.2) Set the number of annealing operations k for thread c. c =1;

[0026] 4.3.3) Combine the current trajectory of thread c Randomly generate new annealing trajectories The calculation formula is as follows:

[0027]

[0028] In the formula, η is the disturbance amplitude control parameter, and λ is a random number between -1 and 1;

[0029] 4.3.4) Calculate the current trajectory respectively And new trajectory The scheduling results are obtained. and Handle according to the following three situations:

[0030] if Indicating a new trajectory Better than the current trajectory Then the new trajectory replaces the current trajectory, that is...

[0031] if and In the formula, r is a random number between 0 and 1. To maintain the diversity of the annealing search, the current trajectory is replaced with a new trajectory, i.e.

[0032] If neither of the above two conditions is met, then for No action taken;

[0033] 4.3.5) Let k c =k c +1, if k c If K ≤ K, proceed to step 4.3.3); otherwise, proceed to step 4.3.6.

[0034] 4.3.6) After all threads have completed their calculations, start from the trajectories of all C threads. The optimal trajectory is selected through comparison. have Then the current trajectory is replaced with the optimal trajectory obtained by parallel variable parameter simulated annealing in stage j, i.e.

[0035] 4.3.7) Let j = j + 1. If j ≤ T, go to step 4.3); otherwise, go to step 4.4.

[0036] Preferably, in step 4.3.3), η is 0.5.

[0037] Compared with the prior art, the present invention has the following advantages:

[0038] 1. It is simple and easy to operate, has natural parallel computing capabilities, good optimization ability, and strong robustness;

[0039] 2. Based on the simulated annealing strategy, the optimal trajectory is found by simulating the cooling process of annealing, which effectively avoids the comprehensive combination of discrete states of each reservoir at each stage, overcomes the dimensionality curse problem of traditional methods, and improves the global search capability.

[0040] 3. Based on parallel computing, the simulated annealing and cooling process with different parameters is implemented in multiple threads to reduce the uncertainty of the parameter settings of a single simulated annealing operation. This ingeniously realizes the parallel coupled calculation of different simulated annealing parameters, further improving the calculation accuracy. Attached Figure Description

[0041] Figure 1 The flowchart shows the parallel variable parameter simulated annealing optimization method for optimizing the scheduling of cascade reservoir groups according to the present invention.

[0042] Figure 2 This is a diagram showing the calculation results of the WDD reservoir under high-water year water conditions in the embodiment;

[0043] Figure 3 This is a diagram showing the calculation results of the BHT reservoir under high-water year water conditions in the embodiment;

[0044] Figure 4 This is a diagram showing the calculation results of the XLD reservoir under high-water year water conditions in the embodiment;

[0045] Figure 5 This is a diagram showing the calculation results of the XJB reservoir under high-water year water conditions in the embodiment. Detailed Implementation

[0046] The present invention will now be described in further detail with reference to the accompanying drawings and specific embodiments.

[0047] like Figure 1 As shown, a parallel variable parameter simulated annealing optimization method for the optimal scheduling of a cascade reservoir group includes the following steps:

[0048] 1) Determine the initial calculation conditions, including the objective function and constraints for the optimal scheduling of the cascade reservoir group. The optimal scheduling model for the cascade reservoir group can be described as follows: Given the initial water level, final water level, inflow process, and interval runoff process of each reservoir during the scheduling period, and under the condition of satisfying various complex constraints such as water level, flow rate, and power output of the reservoir group, the optimal stage water level operation process of the reservoir group is determined to maximize the utilization of water energy resources and achieve the maximum total power generation of the reservoir group during the scheduling period. The objective function for the optimal scheduling of the cascade reservoir group is as follows:

[0049]

[0050] In the formula: F is the total power generation during the scheduling period, N is the number of reservoirs, and i is the reservoir number, where i = 1. , 2,…,N,T are the total number of scheduling phases, j is the phase number, and j=1,2,…,T,A i Let Q be the output coefficient of reservoir i. i,j The power generation flow (m³) of reservoir i in stage j 3 / s), H i,j Let Δj be the average generating head (m) of reservoir i in stage j after deducting head loss, and let Δj be the stage length (h). To ensure the feasibility and availability of the optimization results, the hydropower scheduling problem needs to consider a large number of complex constraints, mainly including:

[0051] Hydraulic constraints:

[0052] Water balance constraints:

[0053] Time-based water level constraints:

[0054] Outbound flow constraints:

[0055] Power plant output constraints:

[0056] Initial and final water level constraints: Z i,start =Z i,end

[0057] System output constraints:

[0058] Non-negativity constraint: All variables must be non-negative.

[0059] In the formula: I i,j and R i,j The inflow rate (m³) of reservoir i in stage j is respectively. 3 / s) and interval inflow (m 3 / s), S i-1,jLet m be the discharge flow of the (i-1)th reservoir in stage j. 3 / s), V i,j The reservoir capacity (m) at the end of stage j. 3 Z min i,j and Z max i,j Let Q be the lowest and highest upstream water level (m) of reservoir i in stage j. min i,j and Q max i,j The minimum power generation flow (m³) of reservoir i in stage j are respectively. 3 / s) and maximum power generation flow (m 3 / s), P min i,j and P max i,j Z represents the minimum output (kW) and maximum output (kW) of reservoir i in stage j, respectively. i,start and Z i,end Let NP be the initial reservoir water level (m) and the final control water level (m) of reservoir i during the scheduling period, respectively. j Let be the minimum output power (kW) of the system in stage j;

[0060] Analysis of the objective function and constraints reveals that the optimal scheduling of cascade reservoir groups involves numerous complex constraints such as water level, capacity, and flow rate of each reservoir. It is a large-scale, high-dimensional, multi-stage, strongly constrained, and nonlinear complex coupled optimal control problem. When using DDDP optimization to solve this problem, the computational load increases exponentially with the number of reservoirs and discrete reservoirs, resulting in the curse of dimensionality and a tendency to get trapped in local convergence.

[0061] 2) Set the calculation parameters, including the number of reservoirs N, the number of scheduling stages T, the maximum number of iterations M, the maximum number of annealing searches K, the number of parallel computing threads C, the convergence accuracy ε, and the initial temperature parameter T of thread c. 0,c and annealing control parameters y 0,c Where c (1≤c≤C);

[0062] 3) Using conventional dynamic programming methods or manual experience-based decision-making, generate the initial trajectories of each reservoir that satisfy all constraints. And calculate the initial distance step length Δ = (Δ) for each reservoir. i,j ) N×T The calculation formula is as follows:

[0063]

[0064] in, Denotes the initial trajectory of reservoir i in stage j, Δi,j This represents the initial distance of reservoir i from the target area in stage j. This represents the upper limit of the water level of reservoir i in stage j. Z i,j Let L represent the lower limit of the water level of reservoir i in stage j, and L be the initial number of discrete points.

[0065] 4) Begin iterative computation, employing simulated annealing for multi-core parallel computation and search. Different annealing control parameters are selected for each thread to perform different forms of annealing search. This iterative optimization process is repeated to approximate the global optimum, ultimately outputting the final optimal trajectory. The specific steps are as follows:

[0066] 4.1) Set the iteration count m = 1,

[0067] 4.2) Set the stage number j = 1;

[0068] 4.3) The current temperature parameter of thread c is T. m,c =T 0,c ×(y 0,c ) m To obtain the optimal trajectory, a parallel simulated annealing search is performed. The parallel simulated annealing search includes the following steps:

[0069] 4.3.1) Set the current trajectory The algorithm is copied C times and distributed to various threads for computation. The current trajectory of thread c is...

[0070] 4.3.2) Set the number of annealing operations k for thread c. c =1;

[0071] 4.3.3) Combine the current trajectory of thread c Randomly generate new annealing trajectories The calculation formula is as follows:

[0072]

[0073] In the formula, η is the disturbance amplitude control parameter, which is generally taken as 0.5, and λ is a random number between -1 and 1;

[0074] 4.3.4) Calculate the current trajectory respectively And new trajectory The scheduling results are obtained. and Handle according to the following three situations:

[0075] if Indicating a new trajectory Better than the current trajectory Then the new trajectory replaces the current trajectory, that is...

[0076] if and In the formula, r is a random number between 0 and 1. To maintain the diversity of the annealing search, the current trajectory is replaced with a new trajectory, i.e.

[0077] If neither of the above two conditions is met, then for No action taken;

[0078] 4.3.5) Let k c =k c +1, if k c If K ≤ K, proceed to step 4.3.3); otherwise, proceed to step 4.3.6.

[0079] 4.3.6) After all threads have completed their calculations, start from the trajectories of all C threads. The optimal trajectory is selected through comparison. have Then the current trajectory is replaced with the optimal trajectory obtained by parallel variable parameter simulated annealing in stage j, i.e.

[0080] 4.3.7) Let j = j + 1. If j ≤ T, go to step 4.3); otherwise, go to step 4.4.

[0081] 4.4) Calculate the water level difference between two adjacent optimal trajectories at different time periods. This indicates that the current trajectory is optimal, so we end the current iteration, shrink all outlier walk lengths, and let... Proceed to step 45), otherwise proceed to step 42) and continue based on... Perform parallel variable-parameter simulated annealing search;

[0082] 4.5) Let m = m + 1. If m > M, then go to step 46); otherwise, go to step 42.

[0083] 4.6) Stop the calculation and output the final optimal trajectory.

[0084] This invention, based on a clear understanding of the optimal scheduling problem of cascade reservoir groups and the DDDP solution process, employs a combination of simulated annealing, parallel computing, and DDDP. Using DDDP as the basic execution framework, it first obtains the initial scheduling state that satisfies the constraints. Then, during the iterative process, for each stage of the optimal scheduling problem, the simulated annealing method is used for multi-core parallel computation search, with different annealing control parameters selected for each thread to perform different forms of annealing search. Finally, it iterates repeatedly to find the optimal solution, gradually approaching the global optimum. This invention fully utilizes the dual advantages of simulated annealing's ability to quickly escape local searches and parallel computing's ability to implement different computational modes. By executing parallel variable-parameter simulated annealing searches at each stage and continuously seeking optimization trajectories for iterative updates, it effectively overcomes the limitations of DDDP's search capabilities.

[0085] This study takes the optimal scheduling of a cascade reservoir group in the upper reaches of the Yangtze River as an example. This basin is rich in hydropower resources and is a strategic water source and major hydropower development base for my country's water resource allocation, significantly influencing flood control and water resource utilization patterns in the Sichuan-Chongqing section of the upper Yangtze River and the middle and lower reaches. Four large reservoirs—WDD, BHT, XLD, and XJB—have been built in this basin, undertaking comprehensive water resource utilization tasks including flood control, power generation, navigation, water supply, and ecological functions. The total regulating capacity of the four reservoirs is 20.821 billion m³. 3 The total installed capacity is 46,400 MW. In response to the national call for energy conservation and emission reduction, and to fully leverage the scale benefits and cascade compensation benefits of the river basin reservoir group, it is crucial to implement optimized scheduling of the cascade reservoir group.

[0086] Therefore, three different water inflows—dry year (frequency 75%), normal year (frequency 50%), and wet year (frequency 25%)—were selected to apply the method of this invention to the optimized scheduling of this cascade reservoir group, in order to verify the rational feasibility and high efficiency of the method in practical engineering applications.

[0087] Table 1 Comparison of the method of the present invention and the calculation results of DDDP.

[0088]

[0089]

[0090] As shown in Table 1, the computational advantages of the method of the present invention compared with DDDP are as follows:

[0091] 1. From the comparison of power generation, both the method of this invention and DDDP continuously approach the global optimal solution, and the power generation of the method of this invention is greater than that of DDDP, indicating that the search capability is stronger. Moreover, as the scale of computation increases, its advantage in avoiding the curse of dimensionality and escaping local optima becomes more significant.

[0092] 2. The computation time of the method in this invention is significantly less than that of DDDP, only about 4% of the computation time of DDDP. Furthermore, the computational performance advantage becomes more pronounced as the scale of the reservoir group and the computation stage increase. Therefore, compared with DDDP, this invention significantly reduces computation time and greatly improves computational efficiency, both in terms of computational results and computation time. It possesses excellent characteristics such as high computational efficiency and high computational accuracy, providing an effective method for the optimal scheduling of giant cascade reservoir groups.

[0093] Figures 2-5 Schematic diagrams of the changes in water level and output of each reservoir during a normal water year are provided. The optimized scheduling results of each reservoir meet all constraints, effectively realizing the full-cycle scheduling process, including flood control and security during the flood season, rapid filling during the water storage period, and gradual drawdown during the dry season. This fully leverages the comprehensive benefits of the reservoir group's head and volume, demonstrating that the calculation results of the method of this invention are reasonable and effective, and can provide technical support for the actual scheduling, operation, and management of cascade reservoir groups.

[0094] This invention presents a parallel variable-parameter simulated annealing optimization method for the optimal scheduling of cascade reservoir groups. It is simple and convenient to operate, possesses inherent parallel computing capabilities, exhibits good optimization ability, and strong robustness. Based on the simulated annealing strategy, it finds the optimization trajectory through the cooling process of simulated annealing, effectively avoiding the comprehensive combination of discrete states of each reservoir at each stage, overcoming the dimensionality curse problem of traditional methods, and improving global search capability. Based on parallel computing, it implements the simulated annealing cooling process with different parameters in multiple threads to reduce the uncertainty of setting parameters for a single simulated annealing operation, cleverly realizing parallel coupled computation of different simulated annealing parameters, further improving computational accuracy.

[0095] Those skilled in the art will readily understand that the above description is merely a preferred embodiment of the present invention and is not intended to limit the present invention. Any modifications, equivalent substitutions, and improvements made within the spirit and principles of the present invention should be included within the scope of protection of the present invention.

Claims

1. A parallel variable parameter simulated annealing optimization method for optimal scheduling of a cascade reservoir group, characterized in that: Includes the following steps: 1) Determine the initial calculation conditions, including the objective function and constraints for the optimal scheduling of the cascade reservoir group; 2) Set the calculation parameters, including the number of reservoirs. Number of scheduling phases Maximum number of iterations Maximum number of annealing searches Number of parallel computing threads Convergence accuracy and threads initial temperature parameters and annealing control parameters ,in, ; 3) Using conventional dynamic programming methods or human experience-based decision-making, generate the initial trajectories of each reservoir that satisfy all constraints. And calculate the initial distance step length of each reservoir. The calculation formula is as follows: in, Reservoir In the stage The initial trajectory, Reservoir In the stage The initial distance from the walk was long. Reservoir In the stage The upper limit of the water level, Reservoir In the stage The lower limit of the water level The initial number of discrete elements; 4) Begin iterative computation, employing simulated annealing for multi-core parallel computation and search. Different annealing control parameters are selected for each thread to perform different forms of annealing search. Repeated iterations are used to optimize and approximate the global optimum, outputting the final optimal trajectory. This includes the following steps: 4.1) Set the iteration count , ; 4.2) Set the number of stages ; 4.3) Threads The current temperature parameter is Parallel simulated annealing search is performed to obtain the optimal trajectory; 4.4) Calculate the water level difference between two adjacent optimal trajectories at different time periods. This indicates that the current trajectory is optimal, so we end the current iteration, shrink all outlier walk lengths, and let... If the condition is met, proceed to step 4.5; otherwise, proceed to step 4.2 and continue based on... Perform parallel variable-parameter simulated annealing search; 4.5) Let ,like If so, proceed to step 4.6); otherwise, proceed to step 4.2). 4.6) Stop the calculation and output the final optimal trajectory; In step 4.3), the parallel simulated annealing search includes the following steps: 4.3.1) Set the current trajectory copy Then, the computation is assigned to each thread for execution. The current trajectory is ; 4.3.2) Set thread Number of annealing operations ; 4.3.3) Combining threads Current trajectory Randomly generate new annealing trajectories The calculation formula is as follows: In the formula, For disturbance amplitude control parameters, A random number between -1 and 1; 4.3.4) Calculate the current trajectory respectively And new trajectory The scheduling results are obtained. and The following three situations should be handled accordingly: if This indicates a new trajectory. Better than the current trajectory Then the new trajectory replaces the current trajectory, that is... ; if and In the formula A random number between 0 and 1 is used to maintain the diversity of the annealing search, replacing the current trajectory with a new one. ; If neither of the above two conditions is met, then for No action taken; 4.3.5) Order ,if If the condition is met, proceed to step 4.3.3; otherwise, proceed to step 4.3.

6. 4.3.6) After all threads have finished calculating, from all... The trajectory of each thread The optimal trajectory is selected through comparison. ,have Then by stage The optimal trajectory obtained by performing parallel variable parameter simulated annealing replaces the current trajectory, i.e. ; 4.3.7) Order ,if If the condition is met, proceed to step 4.3; otherwise, proceed to step 4.

4.

2. The parallel variable parameter simulated annealing optimization method for optimal scheduling of cascade reservoir groups as described in claim 1, characterized in that: In step 4.3.3), The value is 0.5.

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