Power system unit commitment model solving method based on improved simulated annealing algorithm

Abstract

The invention discloses a power system unit commitment model solving method based on an improved simulated annealing algorithm, and the method comprises the steps: carrying out the optimization solving of a model objective function through employing the improved simulated annealing algorithm on the basis of a standard simulated annealing algorithm, and carrying out the optimization solving of a model objective function through adaptive temperature control and a multi-starting point strategy. And the global search capability and the convergence speed are improved when the unit commitment optimization problem of the power system is solved. Through the improvement of the invention, the algorithm can more effectively avoid falling into local optimum during solving, and the solving process is accelerated.

Description

Technical Field

[0001] The invention relates to the field of unit combination optimization scheduling, and in particular to a method for solving a power system unit combination model. Background Art

[0002] Unit Commitment (UC) not only needs to consider the on / off status of the generator set, but also needs to optimize the power generation cost while meeting the power demand, technical and environmental constraints. Due to its multi-constraint and nonlinear characteristics, it is considered a typical NP-hard problem. Traditional optimization methods, such as dynamic programming and mixed integer linear programming, can provide relatively accurate solutions when solving unit commitment problems, but they usually rely on large-scale computing resources, and often perform poorly when dealing with complex and nonlinear constraints, and are prone to falling into local optimal solutions. For this reason, heuristic algorithms have become a powerful tool for solving unit commitment problems due to their flexibility and strong global search capabilities.

[0003] The simulated annealing algorithm (SA) in the heuristic algorithm solves the optimization problem by simulating the annealing process in physics. It can jump out of the local optimal solution and find the global optimal solution. It is particularly suitable for solving complex optimization problems. The simulated annealing algorithm can simulate the thermodynamic principles of the physical annealing process, effectively search in a large range of solution space, accept suboptimal solutions with a certain probability, allow larger solution space jumps in the early stage, and gradually converge to the global optimal solution. Therefore, it has been widely used in solving unit combination problems.

[0004] The unit commitment problem is usually accompanied by nonlinear constraints (such as the cost and operation restrictions of the start and stop of the generator set), making it difficult to solve the problem efficiently through traditional linear or integer programming methods. The simulated annealing algorithm does not require strict linearity on the mathematical structure of the problem and can handle a variety of complex constraints on the unit, such as: start and stop costs, load demand constraints, start and stop time restrictions for each generator set, upper and lower limits of power output, etc. SA can reasonably handle and optimize these constraints through appropriate neighborhood operation design and annealing strategies.

[0005] The solution space of the unit commitment problem is very large, especially when considering multiple generators and long-term scheduling, the number of combinations grows exponentially. The simulated annealing algorithm can flexibly define the neighborhood of the solution and regulate the search process through probability functions, so that effective search and optimization can be performed in the solution space. This adaptability to large-scale combination spaces makes simulated annealing very suitable for solving unit commitment problems.

[0006] Although the convergence speed of the simulated annealing algorithm is relatively slow, the solution time can be controlled by adjusting parameters such as cooling rate, initial temperature and stop condition. For unit commitment problems, since the scheduling cycle is usually long (e.g., 24 hours or longer), the progressive optimization characteristics of the simulated annealing algorithm can provide a better solution within an acceptable time.

[0007] Nevertheless, the classic simulated annealing algorithm still has problems such as slow convergence and easy to fall into local optimality in practical applications. Summary of the invention

[0008] Purpose of the invention: In view of the above-mentioned prior art, a method for solving the power system unit combination model based on an improved simulated annealing algorithm is proposed to improve the convergence speed and global search capability of the solution algorithm, thereby effectively improving the accuracy and efficiency of solving the unit combination model.

[0009] Technical solution: A method for solving the power system unit commitment model based on an improved simulated annealing algorithm, including:

[0010] Step 1: Establish a power system unit combination model with the goal of minimizing economic cost;

[0011] Step 2: Establish power balance constraints, operation constraints, ramp rate constraints, and start / stop time constraints respectively;

[0012] Step 3: Introduce an adaptive temperature control strategy and a multiple starting point strategy, and solve the model based on an improved simulated annealing algorithm.

[0013] Furthermore, the model established in step 1 is expressed as:

[0014]

[0015] Among them, F1 is the target value, t is the time, n is the number of units, C i is the power cost function, P i,t is the cost coefficient of the power value of the i-th unit at time t;

[0016]

[0017] a i 、b i 、c i They are The cost coefficient, P i,t Cost coefficient, constant cost coefficient, e i is the cost coefficient of the sine function, f i is the cost coefficient of power increment, P i min is the minimum power of unit i.

[0018] Furthermore, in step 2, the power balance constraint is: t=1,2,...,24,where D t is the total load of the unit at time t;

[0019] The operating constraints are: P i min ≤P i,t ≤P i max , i=1,2,...,n,t=1,2,...,24,where P i max is the maximum power of unit i;

[0020] The climbing rate constraint is: i=1,2,...,n,t=1,2,...,24,where UR i is the upward climbing rate, DR i is the downward climbing rate;

[0021] The start and stop time constraints are: i∈n,t∈T, where and are the maximum on and off durations of unit i respectively; and are the number of time periods that unit u has been continuously turned on and off until time period t; u i,t is the on / off status of unit i at time t, with on being 1 and off being 0; T is the total time.

[0022] Furthermore, in step 3, the adaptive temperature control strategy is dynamically adjusted according to the quality of the current solution and the search progress, which is specifically expressed as:

[0023]

[0024] Among them, T k is the temperature of the kth iteration, α is the basic cooling rate, β is the adaptive adjustment parameter, f(S k ) is the objective function value of the current solution, f(S best ) is the objective function value of the current optimal solution;

[0025] Combined with the model established in step 1, we get:

[0026]

[0027] Among them, the objective function value of the current solution The optimal solution to be solved is the minimum value of the objective function, that is,

[0028] During the iteration process, the temperature is dynamically adjusted according to the quality of the current solution. If the current solution is far away from the optimal solution, the temperature drops faster and the search range is increased; if the current solution is close to the optimal solution, the temperature drops slower and the local search capability is enhanced.

[0029] Furthermore, in step 3, the multiple starting point strategy is to start searching from multiple random initial points simultaneously, specifically including:

[0030] In the initialization phase, multiple random initial solutions P are generated. i,t , each initial solution P i,t Corresponding to an independent search path R i,t ;

[0031] For each initial solution P i,t Simultaneously perform simulated annealing search, all search paths R i,t Share global optimal solution information;

[0032] During the search process, the paths R are regularly compared. i,t The current solution P i,t , the optimal solution P best The information is fed back to all paths to enhance the global search capability of the algorithm.

[0033] Beneficial effects: The present invention provides a new method for the optimization problem of power system unit combination. On the basis of the standard simulated annealing algorithm, the improved simulated annealing algorithm improves the global search capability and convergence speed when solving the optimization problem of power system unit combination through adaptive temperature control and multiple starting point strategy. Through the improvement of the present invention, the algorithm can more effectively avoid falling into the local optimum when solving the problem and accelerate the solution process. BRIEF DESCRIPTION OF THE DRAWINGS

[0034] Figure 1 It is a solution flow chart based on the improved simulated annealing algorithm in the method of the present invention;

[0035] Figure 2 It is the simulation result of the classic simulated annealing algorithm in the embodiment;

[0036] Figure 3 The simulation results of the improved simulated annealing algorithm of the present invention in the embodiment;

[0037] Figure 4 It is the simulation result of the particle swarm algorithm in the embodiment. DETAILED DESCRIPTION

[0038] The present invention will be further explained below in conjunction with the accompanying drawings.

[0039] The unit commitment problem is a key issue in power system scheduling. The main goal is to meet the load demand at the lowest operating cost by determining the generator units that should be operated in a given time period, while complying with various constraints, such as unit start and stop restrictions, power output restrictions, etc.

[0040] A method for solving a power system unit combination model based on an improved simulated annealing algorithm of the present invention takes a unit combination model of 6 units as an example, and the process is as follows:

[0041] Step 1: With the goal of minimizing economic cost, establish a power system unit combination model, expressed as:

[0042]

[0043] Among them, F1 is the target value, t is the time, C i is the power cost function, P i,t is the cost coefficient of the power value of the i-th unit at time t.

[0044]

[0045] a i 、b i 、c i They are The cost coefficient, P i,t Cost coefficient, constant cost coefficient, e i is the cost coefficient of the sine function, f i is the cost coefficient of power increment, P i min is the minimum power of unit i.

[0046] Step 2: Establish power balance constraints, operation constraints, ramp rate constraints, and start / stop time constraints respectively.

[0047] The power balance constraint is: t=1,2,...,24,where D t is the total load of the unit at time t.

[0048] The operating constraints are: P i min ≤P i,t ≤P i max , i=1,2,...,6,t=1,2,...,24,where P i max is the maximum power of unit i.

[0049] The climbing rate constraint is: i=1,2,...,6,t=1,2,...,24,where URi is the upward climbing rate, DR i is the downward climbing rate.

[0050] The start and stop time constraints are: i∈n,t∈T, where and are the maximum on and off durations of unit i respectively; and are the number of time periods that unit i has been continuously turned on and off until time period t; u i,t is the on / off state of unit i at time t, where on is 1 and off is 0; n is the total number of units, and T is the total time. In this embodiment, n is 6 and T is 24.

[0051] Step 3: Introduce the adaptive temperature control strategy and the multiple starting point strategy, and solve the unit commitment model based on the improved simulated annealing algorithm.

[0052] Adaptive temperature control strategy: When the traditional simulated annealing algorithm performs a global search, the temperature parameters are pre-set and gradually reduced according to a fixed cooling strategy. This fixed strategy may cause the algorithm to converge too early or converge too slowly in practical applications. In order to improve the adaptability of the algorithm, the present invention proposes an adaptive temperature control strategy. The temperature update no longer depends solely on a fixed cooling rate, but is dynamically adjusted according to the quality of the current solution and the search progress. The update formula is specifically expressed as:

[0053]

[0054] Among them, T k is the temperature of the kth iteration, α is the basic cooling rate, β is the adaptive adjustment parameter, f(S k ) is the objective function value of the current solution, f(S best ) is the objective function value of the current optimal solution.

[0055] Taking the unit combination model of 6 units as an example, after substituting into the temperature update formula, we get:

[0056]

[0057] In the 6-unit combination model, the objective function value of the current solution is The optimal solution to be solved is the minimum value of the objective function, that is,

[0058] During the iterative solution process, the algorithm will i,t The quality of the dynamic adjustment temperature T k , if the current solution P i,t Distance optimal solution P bestIf the temperature of the algorithm is farther away, the temperature drop rate of the algorithm will become faster, thereby increasing the global search range of the algorithm for the solution; if the current solution P i,t The optimal solution P required for the distance best As the distance is shortened, the algorithm's temperature drop rate will slow down, thereby enhancing the algorithm's local search capability.

[0059] Multiple starting point strategy: Traditional simulated annealing algorithm starts searching from a single starting point and is prone to fall into a local optimal solution. The present invention introduces a multiple starting point strategy, which starts searching from multiple random starting points at the same time, including multiple starting point generation, parallel search, and path fusion process.

[0060] Multiple starting point generation: In the initialization phase, multiple random initial solutions P are generated i,t , each initial solution P i,t Corresponding to an independent search path R i,t .

[0061] Parallel search: For each initial solution P i,t Simultaneously perform simulated annealing search, all search paths R i,t Share the global optimal solution information.

[0062] Path fusion: During the search process, the paths R are periodically compared. i,t The current solution P i,t , the optimal solution P best The information is fed back to all paths to enhance the global search capability of the algorithm.

[0063] Taking the unit combination model of 6 units as an example, the specific execution process of this step is as shown in the attached Figure 1 As shown, including:

[0064] 1. Initialization: Generate multiple random initial solutions P i,t , set the initial temperature T0 and the basic cooling rate α.

[0065] 2. Parallel search: For each initial solution P i,t Simultaneous simulated annealing search.

[0066] 3. State transition: Generate a new solution P' according to the state transition rule i,t .

[0067] 4. Acceptance criterion: Use the Metropolis criterion to decide whether to accept the new solution P' i,t .

[0068] 5. Temperature update: Update the temperature T according to the adaptive temperature control strategy k .

[0069] 6. Path fusion: Regularly integrate search information from multiple starting points.

[0070] 7. Termination condition: meet the temperature threshold or the maximum number of iterations n, and output the global optimal solution P best .

[0071] In the above process, the state transition rule is that in each iteration, a new partitioning scheme is generated according to the current solution. The specific state transition method includes operations such as node reallocation, edge addition or deletion, etc.

[0072] Acceptance criteria: The Metropolis criterion is used to decide whether to accept the new solution. The acceptance probability calculation formula is:

[0073]

[0074] Among them, ΔE is the difference in the objective function value between the new and old solutions, T k is the current temperature.

[0075] Taking the 6-unit combination model as an example, substituting the Metropolis criterion into it, we can get:

[0076]

[0077] Among them, P' i,t The algorithm solves P i,t Combined with the acceptance criterion of adaptive temperature control, under the adaptive temperature control strategy, the acceptance criterion will dynamically adjust the temperature parameter T k , to balance the relationship between global search and local optimization.

[0078] In this embodiment, the unit combination model parameters of the 6 units and the load data of the units are shown in Table 1 and Table 2 respectively.

[0079] Table 1

[0080] unit 1 2 3 4 5 6 <![CDATA[P i min ]]> 100 50 80 50 50 50 <![CDATA[P i max ]]> 500 200 300 150 200 120 <![CDATA[a i ]]> 0.0070 0.0095 0.0090 0.0090 0.0080 0.0075 <![CDATA[b i ]]> 7 10 8.5 11 10.5 12 <![CDATA[c i ]]> 240 200 220 200 220 190 <![CDATA[e i ]]> 130 110 120 110 120 100 <![CDATA[f i ]]> 0.0315 0.0300 0.0450 0.0300 0.0400 0.0052 <![CDATA[UR i ]]> 80 50 65 50 50 50 <![CDATA[DR i ]]> 120 90 100 90 90 90

[0081] Table 2

[0082]

[0083] The simulation results are as follows Figure 2 , Figure 3 , Figure 4 As shown, the minimum cost obtained after optimizing the unit combination model of this embodiment by using the classical simulated annealing algorithm, the improved simulated annealing algorithm of the present invention, and the particle swarm algorithm is shown in Table 3 below.

[0084] Table 3

[0085] algorithm Simulated annealing algorithm Improved simulated annealing algorithm Particle Swarm Optimization Minimum cost ($) 31436.8723 31381.1762 32029.2386

[0086] From the above results, it can be seen that the cost of the unit commitment problem calculated by the improved simulated annealing algorithm is the smallest, which is a significant improvement compared with the simulated annealing algorithm.

[0087] The above is only a preferred embodiment of the present invention. It should be pointed out that for ordinary technicians in this technical field, several improvements and modifications can be made without departing from the principle of the present invention. These improvements and modifications should also be regarded as the scope of protection of the present invention.

Claims

1. A method for solving the power system unit commitment model based on an improved simulated annealing algorithm, characterized in that: include: Step 1: Establish a power system unit combination model with the goal of minimizing economic cost; Step 2: Establish power balance constraints, operation constraints, ramp rate constraints, and start / stop time constraints respectively; Step 3: Introduce an adaptive temperature control strategy and a multiple starting point strategy, and solve the model based on an improved simulated annealing algorithm.

2. The method for solving the power system unit combination model according to claim 1, characterized in that: The model established in step 1 is expressed as: Among them, F1 is the target value, t is the time, n is the number of units, C i is the power cost function, P i,t is the cost coefficient of the power value of the i-th unit at time t; a i 、b i 、c i They are The cost coefficient, P i,t Cost coefficient, constant cost coefficient, e i is the cost coefficient of the sine function, f i is the cost coefficient of power increment, P i min is the minimum power of unit i.

3. The method for solving the power system unit combination model according to claim 2, characterized in that: In step 2, the power balance constraint is: t=1,2,...,24,where D t is the total load of the unit at time t; The operating constraints are: P i min ≤P i,t ≤P i max , i=1,2,...,n,t=1,2,...,24,where P i max is the maximum power of unit i; The climbing rate constraint is: Among them UR i is the upward climbing rate, DR i is the downward climbing rate; The start and stop time constraints are: in and are the maximum on and off durations of unit i respectively; and are the number of time periods that unit i has been continuously turned on and off until time period t; u i,t is the on / off status of unit i at time t, with on being 1 and off being 0; T is the total time.

4. The method for solving the power system unit combination model according to claim 2 or 3, characterized in that: In step 3, the adaptive temperature control strategy is dynamically adjusted according to the quality of the current solution and the search progress, which is specifically expressed as: Among them, T k is the temperature of the kth iteration, α is the basic cooling rate, β is the adaptive adjustment parameter, f(S k ) is the objective function value of the current solution, f(S best ) is the objective function value of the current optimal solution; Combined with the model established in step 1, we get: Among them, the objective function value of the current solution The optimal solution to be solved is the minimum value of the objective function, that is, During the iteration process, the temperature is dynamically adjusted according to the quality of the current solution. If the current solution is far away from the optimal solution, the temperature drops faster and the search range is increased; if the current solution is close to the optimal solution, the temperature drops slower and the local search capability is enhanced.

5. The method for solving the power system unit combination model according to claim 4, characterized in that: In step 3, the multiple starting point strategy is to start searching from multiple random initial points simultaneously, specifically including: In the initialization phase, multiple random initial solutions P are generated. i,t , each initial solution P i,t Corresponding to an independent search path R i,t ; For each initial solution P i,t Simultaneously perform simulated annealing search, all search paths R i,t Share global optimal solution information; During the search process, the paths R are regularly compared. i,t The current solution P i,t , the optimal solution P best The information is fed back to all paths to enhance the global search capability of the algorithm.

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