A unit commitment method based on competition particle swarm optimization algorithm

Abstract

The application discloses a unit combination method based on a competitive particle swarm optimization algorithm, which comprises the following steps: initializing a population of the particle swarm optimization algorithm, constructing a unit combination optimization model with the minimum total operation cost of a system as an objective, calculating the fitness value of each particle in the population according to obtained unit parameters and system parameters, updating the speed and position of each particle based on the competitive thought, and iterating until the maximum iteration number is reached to obtain the unit state in the first period of a scheduling period, then taking the unit state in the first period as an initial state and iteratively circulating to obtain the unit state in all periods of the scheduling period. The application has good search performance for complex problems such as unit combination in a power system, can accelerate convergence and generate a high-precision solution.

Description

Technical Field

[0001] This invention belongs to the field of power system dispatching, specifically relating to a unit combination method based on a competitive particle swarm optimization algorithm. Background Technology

[0002] Unit combination (UC) is one of the most critical tasks in power system operation. The UC problem requires determining the on / off state of each generator unit for each hour during the planning period and optimizing the allocation of demand and reserve capacity among the units. Unit combination is essentially a complex nonlinear mixed-integer optimization problem that optimizes the allocation of demand and reserve capacity among units by determining the on / off state of each generator unit for each hour during the planning period. The complexity of the UC problem increases exponentially with the number of generator units. UC algorithms for practical power systems need to have better search performance.

[0003] Currently, deterministic search algorithms are suitable for solving medium-sized power systems, but they are affected by convergence, solution quality, and complexity. Stochastic search algorithms can produce better results than traditional optimization techniques in a shorter time, but these algorithms are limited by accuracy, and increasing the problem size and the number of generators negatively impacts computation time and solution quality. Summary of the Invention

[0004] The purpose of this invention is to address the aforementioned problems in the existing technology by providing a unit combination method based on the competitive particle swarm optimization algorithm that can improve convergence speed and accuracy.

[0005] To achieve the above objectives, the technical solution of the present invention is as follows:

[0006] A unit combination method based on competitive particle swarm optimization algorithm includes the following steps:

[0007] Step A: Initialize the population for the particle swarm optimization algorithm;

[0008] Step B: Construct a unit combination optimization model with the goal of minimizing the total system operating cost, and calculate the fitness value of each particle in the population based on the obtained unit parameters and system parameters, wherein the fitness value is the objective function value of the unit combination optimization model;

[0009] Step C: Iterate and update the velocity and position of each particle based on the competition concept until the maximum number of iterations is reached. At this point, the unit status of the first time period within the scheduling cycle is obtained.

[0010] Step D: Using the unit status of the first time period as the initial state, repeat steps AC in a loop to obtain the unit status of all time periods within the scheduling cycle.

[0011] Step C includes the following steps in sequence:

[0012] Step C1: Perform the first iteration, taking the optimal fitness calculated in step B as the global optimum, and update the velocity and position of each particle based on the following formula:

[0013]

[0014]

[0015]

[0016] In the above formula, Let be the velocity vectors of particle i in the k-th and k+1-th iterations, respectively. Let w be the position vector of particle i in the kth and k+1th iterations, respectively. i Let c1, c2, and c3 be the inertia weight coefficients, respectively, representing the individual learning factor, the group learning factor, and the competition learning factor, where c1 + c2 ≥ 4, c3 ∈ [0.1, 1], and r1, r2, and r3 are random numbers in the range [0, 1]. Let be the optimal solution obtained by particle i after the k-th iteration. Let Δx be the optimal solution for the particle swarm after the k-th iteration. uppers x is the distance between the particle's current position and all particles with lower fitness values. j The position of the j-th particle with the smaller fitness value, where n is the number of particles with smaller fitness values;

[0017] Step C2: Determine the final new velocity and position of each particle based on the minimum particle velocity and position, and calculate the fitness value corresponding to the final new velocity and position of each particle.

[0018] Step C3: Using the optimal fitness value calculated in step C2 as the global optimum, repeat steps C1-C2 until the m-th iteration is completed;

[0019] Step C4: Perform the (m+1)th iteration, updating the velocity and position of each particle based on the following formula:

[0020]

[0021]

[0022]

[0023] In the above formula, Δx lower x is the distance between the particle's current position and the particle one position behind it. lower This represents the position of the particle that is one position behind.

[0024] Step C5: Determine the final new velocity and position of each particle based on the minimum particle velocity and position, and calculate the fitness value corresponding to the final new velocity and position of each particle.

[0025] Step C6: Repeat steps C1-C3 until the 2m+1th iteration is completed;

[0026] Step C7: Repeat steps C4-C5 to complete the 2m+2th iteration;

[0027] Step C8: Repeat steps C6-C7 until the maximum number of iterations is reached.

[0028] In step C2, the final new velocity and position of each particle are determined based on the following formula:

[0029]

[0030]

[0031] In the above formula, Let v be the final new velocity and position of particle i in the (k+1)th iteration. min v max These represent the minimum and maximum particle velocities, x. min x max These represent the positions of the smallest and largest particles, respectively.

[0032] In step B, the objective function of the unit combination optimization model is:

[0033]

[0034]

[0035]

[0036]

[0037] In the above formula, u ij Let PC be the on / off state variable of the i-th unit during time period j. i P i The generating cost and output power of the i-th unit are respectively, SC i Let a be the startup cost of the i-th unit. i b i c i Let σ be the coefficient of the quadratic function of the power generation cost of the i-th generating unit, n and t be the number of generating units and the number of time periods, respectively. i δ i These are the costs for hot and cold starts, respectively. τ iLet INS be the downtime and cooling time constant of the i-th unit, respectively. i This represents the initial state of the i-th unit. Let be the shutdown time before the i-th unit is put into operation.

[0038] The constraints of the unit combination optimization model include:

[0039] Power balance constraints:

[0040]

[0041] In the above formula, PD j PL j These represent the system load demand and total power loss for time period j, respectively.

[0042] Rotational spare constraint:

[0043]

[0044] In the above formula, PR j Let j be the rotational reserve power for time period j;

[0045] Unit operating constraints:

[0046]

[0047] In the above formula, P ij For the output of the i-th unit during time period j, These are the maximum and minimum outputs of the i-th unit, respectively.

[0048] The constraints of the unit combination optimization model also include minimum start-up and shutdown time constraints, which include:

[0049]

[0050] In the above formula, Let T be the continuous operating time of the i-th unit. up,i T down,i These are the minimum operating and downtime times for the i-th unit, respectively.

[0051] When the i-th unit is in a shutdown state before the selected time period, INS i If |INS is negative, it represents the continuous downtime of the i-th unit before the selected time period. i |≥T down,i If the selected time period is specified, the unit may be in a shutdown or operating state; otherwise, the unit must be in a shutdown state.

[0052] When the i-th unit is in operation before the selected time period, INS iA positive number represents the continuous operating time of the i-th unit before the selected time period. If |INS i |≥T up,i If the selected time period indicates that the unit is either shut down or running, then the unit must be running during the selected time period.

[0053] Compared with the prior art, the beneficial effects of the present invention are as follows:

[0054] 1. This invention discloses a unit combination method based on a competitive particle swarm optimization algorithm. First, it initializes the particle swarm optimization population, constructs a unit combination optimization model with the objective of minimizing the total system operating cost, and calculates the fitness value of each particle in the population based on the acquired unit parameters and system parameters. Then, it iterates, updating the velocity and position of each particle based on a competitive approach until the maximum number of iterations is reached, obtaining the unit state for the first time period within the scheduling cycle. Then, using the unit state of the first time period as the initial state, it iterates repeatedly to obtain the unit state for all time periods within the scheduling cycle. This method, based on a competitive approach, helps particles satisfy equality constraints and avoids excessive reserve allocation. It exhibits good search performance for complex problems such as unit combination in power systems, accelerates convergence, and generates high-precision solutions.

[0055] 2. The unit combination method based on the competitive particle swarm optimization algorithm of this invention uses the unit combination optimization model and its constraint condition, the minimum start-up and shutdown time constraint, which incorporates the unit initial state parameter INS. i INS i This represents the continuous operation / shutdown time of the unit before the selected time period. This design constrains the possible start-up and shutdown of the unit within the selected time period by introducing the unit operation information before the time segment, so as to avoid the occurrence of unrealistic results and ensure that the unit combination solution results have practical significance. Attached Figure Description

[0056] Figure 1 This is a flowchart of the present invention.

[0057] Figure 2 This is a topology diagram of the IEEE-39 bus system used in Example 1.

[0058] Figure 3 The simulation test convergence curves of various algorithms using the Sphere function are shown.

[0059] Figure 4 The simulation test convergence curves of various algorithms using the Rosenbrock function are shown. Detailed Implementation

[0060] The present invention will now be described in further detail with reference to specific embodiments and accompanying drawings.

[0061] This invention proposes a unit allocation method based on a competitive particle swarm optimization algorithm, specifically a swarm optimization algorithm based on the abilities of participants in a running race. In this running game, each participant utilizes information from other participants to adjust their speed. This information includes the distance between their current position and the positions of other competitors, as well as the distance between their current position and the target. Individuals attempt to adjust their next position to get closer to the leader. Furthermore, in the running race, each person occasionally uses information from lagging opponents. If someone behind gets closer, everyone tries to increase their speed so they can increase the distance between themselves and those behind. This particle swarm optimization method, considering both production and transient costs, solves and optimizes the unit allocation problem, improving the ability to utilize information from other individuals and enhancing the algorithm's accuracy and convergence.

[0062] Example 1:

[0063] like Figure 1 As shown, a unit combination method based on the competitive particle swarm optimization algorithm is proposed. Figure 2 The IEEE-39 bus system shown (containing 10 generators, with different loads every hour of the day) is the subject of this study. The parameters and load data of each unit in this system are shown in Tables 1 and 2, respectively.

[0064] Table 1 IEEE-39 bus group data

[0065]

[0066] Table 2 Load Data

[0067]

[0068] The unit combination method is carried out in the following steps:

[0069] 1. Randomly initialize the state of particles in the population of the particle swarm optimization algorithm within the specified maximum and minimum position range. The position of the particles is the unit combination sequence, and the maximum and minimum velocities of all particles are used as the particle constraints.

[0070] 2. Construct a unit combination optimization model with the objective of minimizing the total system operating cost, and calculate the fitness value of each particle in the population based on the obtained unit parameters and system parameters. The fitness value is the objective function value of the unit combination optimization model, and the objective function of the unit combination optimization model is:

[0071]

[0072]

[0073]

[0074]

[0075] In the above formula, u ij Let PC be the on / off state variable of the i-th unit during time period j. i P i The generating cost and output power of the i-th unit are respectively, SC i Let a be the startup cost of the i-th unit. i b i c i Let σ be the coefficient of the quadratic function of the power generation cost of the i-th generating unit, n and t be the number of generating units and the number of time periods, respectively. i δ i These are the costs for hot and cold starts, respectively. τ i Let INS be the downtime and cooling time constant of the i-th unit, respectively. i This represents the initial state of the i-th unit, which is its on / off state, denoted by 1 / 0. 1 indicates the unit is in operation, and 0 indicates the unit is in shutdown. Let be the shutdown time before the i-th unit is put into operation.

[0076] The constraints of the unit combination optimization model include:

[0077] Power balance constraints:

[0078]

[0079] In the above formula, PD j PL j These represent the system load demand and total power loss for time period j, respectively.

[0080] Rotational spare constraint:

[0081]

[0082] In the above formula, PR j Let j be the rotational reserve power for time period j;

[0083] Unit operating constraints:

[0084]

[0085] In the above formula, P ij For the output of the i-th unit during time period j, These are the maximum and minimum outputs of the i-th unit, respectively;

[0086] Minimum start-stop time constraints:

[0087]

[0088] In the above formula, Let T be the continuous operating time of the i-th unit. up,i T down,i These are the minimum operating and downtime times for the i-th unit, respectively.

[0089] When the i-th unit is in a shutdown state before the selected time period, INS i If |INS is negative, it represents the continuous downtime of the i-th unit before the selected time period. i |≥T down,i If the selected time period indicates that the unit is either shut down or running, then the unit must be shut down, such as INS. i = -2, and minimum downtime T down,i If it is 3 hours, then |INS i |<T down,i For the first hour, the system will remain shut down.

[0090] When the i-th unit is in operation before the selected time period, INS i A positive number represents the continuous operating time of the i-th unit before the selected time period. If |INS i |≥T up,i If the selected time period indicates that the unit is either shut down or running, then the unit must be running during the selected time period.

[0091] 3. Perform the first iteration, using the calculated optimal fitness as the global optimum, and update the velocity and position of each particle based on the following formula:

[0092]

[0093]

[0094]

[0095] In the above formula Let be the velocity vectors of particle i in the k-th and k+1-th iterations, respectively. Let w be the position vector of particle i in the kth and k+1th iterations, respectively. i Here, c1, c2, and c3 are the inertia weight coefficients, representing the individual learning factor, the group learning factor, and the competition learning factor, respectively, with c1 + c2 ≥ 4 and c3 ∈ [0.1, 1]. r1, r2, and r3 are random numbers within the range [0, 1] to increase the randomness of the search. Let be the optimal solution obtained by particle i after the k-th iteration. Let Δx be the optimal solution for the particle swarm after the k-th iteration. uppersx is the distance between the particle's current position and all particles with lower fitness values. j Let n be the position of the j-th particle with the smaller fitness value, and n be the number of particles with smaller fitness values.

[0096] 4. Determine the final new velocity and position of each particle based on the minimum particle velocity and position:

[0097]

[0098]

[0099] In the above formula, Let v be the final new velocity and position of particle i in the (k+1)th iteration. min v max These represent the minimum and maximum particle velocities, x. min x max These represent the positions of the smallest and largest particles, respectively.

[0100] 5. Calculate the fitness value corresponding to the final new velocity and position of each particle.

[0101] 6. Using the calculated best fitness value as the global optimum, repeat steps 3-5 until the 5th iteration is completed.

[0102] 7. Perform the 6th iteration, using the calculated best fitness value as the global optimum, and update the velocity and position of each particle based on the following formula:

[0103]

[0104] Δx lower =xx lower

[0105]

[0106] In the above formula, Δx lower x is the distance between the particle's current position and the particle one position behind it. lower This represents the position of the particle that is one position behind.

[0107] 8. Repeat steps 4-5.

[0108] 9. Repeat steps 3-6 until the 11th iteration is completed.

[0109] 10. Repeat steps 7-8 to complete the 12th iteration.

[0110] 11. Repeat steps 9-10 until the maximum number of iterations is reached. At this point, the unit status for the first hour within the scheduling cycle is obtained.

[0111] 12. Using the unit status of the first hour as the initial state, repeat steps 3-11 to obtain the unit status and corresponding total system operating cost for each hour within the scheduling cycle, as shown in Table 3.

[0112] Table 3 Status Results of Each Unit in the IEEE-39 Bus System

[0113] 1 111111111111111111111111 2 111111111111111111111111 3 000000111111110000011000 4 000001111111111000011100 5 000000000111111111111100 6 000111001111100001110000 7 000000000000000000000000 8 000010011011000000100000 9 000000000001000000000000 10 000000000000000000000000 Total system operating cost (RMB) 555571.5266 .

[0114] The total system operating cost calculated in Example 1 is compared with the total system operating cost obtained using other algorithms. The results are shown in Table 4.

[0115]

[0116] As can be seen from Table 4, the method described in Example 1 results in the lowest total system operating cost under the unit combination state.

[0117] Two standard test functions are selected, with a dimension of 10 and a population size of 400. f1 is used to test the convergence speed and accuracy of the algorithm; f2 is mainly used to test the algorithm's ability to escape local optima and perform global search, and can also test its convergence speed and accuracy.

[0118] f1 function (Sphere function): x∈[-5.12,5.12]

[0119]

[0120] The global optimum of the f1 function is always: when x i =0 (i=1,2,,,n), f1(x)=0.

[0121] f2 function (Rosenbrock function): x∈[-2.048,2.048]

[0122]

[0123] The global optimality of the f2 function is: when x i =1((i=1,2,,,n), f2(x)=0.

[0124] To eliminate the impact of randomness on algorithm performance, each test function was subjected to 100 independent computations using different PSO algorithms. The fitness values ​​of each test function after iteration were obtained. The mean and variance of the 100 fitness values ​​were used as evaluation metrics, as the mean most directly reflects the quality of the optimization results and verifies the algorithm's convergence speed and accuracy. See the results below. Figure 3 , Figure 4 .

[0125] Depend on Figure 3 , Figure 4 It can be seen that the competitive PSO algorithm used in this invention has significant advantages over APSO, MOPSO and GA algorithms in terms of convergence speed, accuracy and global search capability.

Claims

1. A unit combination method based on competitive particle swarm optimization algorithm, characterized in that: The method includes the following steps in sequence: Step A: Initialize the population for the particle swarm optimization algorithm; Step B: Construct a unit combination optimization model with the goal of minimizing the total system operating cost, and calculate the fitness value of each particle in the population based on the obtained unit parameters and system parameters, wherein the fitness value is the objective function value of the unit combination optimization model; Step C: Iterate, updating the velocity and position of each particle based on the competition concept until the maximum number of iterations is reached. At this point, the unit state for the first time period within the scheduling cycle is obtained, which includes the following steps: Step C1: Perform the first iteration, taking the optimal fitness calculated in step B as the global optimum, and update the velocity and position of each particle based on the following formula: ； ； ； In the above formula, , Let be the velocity vectors of particle i in the k-th and k+1-th iterations, respectively. , Let be the position vectors of particle i in the k-th and k+1-th iterations, respectively. This is the inertia weighting coefficient. , , These are individual learning factors, group learning factors, and competition learning factors, respectively. , , , , A random number in the range [0,1]. Let be the optimal solution obtained by particle i after the k-th iteration. This is the optimal solution for the particle swarm after the k-th iteration. This represents the distance between the particle's current position and all particles with lower fitness values. The position of the j-th particle with the smaller fitness value, where n is the number of particles with smaller fitness values; Step C2: Determine the final new velocity and position of each particle based on the minimum particle velocity and position, and calculate the fitness value corresponding to the final new velocity and position of each particle. Step C3: Using the optimal fitness value calculated in step C2 as the global optimum, repeat steps C1-C2 until the m-th iteration is completed; Step C4: Perform the (m+1)th iteration, updating the velocity and position of each particle based on the following formula: ； ； ； In the above formula, This represents the distance between the particle's current position and the particle one position behind it. This represents the position of the particle that is one position behind. Step C5: Determine the final new velocity and position of each particle based on the minimum particle velocity and position, and calculate the fitness value corresponding to the final new velocity and position of each particle. Step C6: Repeat steps C1-C3 until the 2m+1th iteration is completed; Step C7: Repeat steps C4-C5 to complete the 2m+2th iteration; Step C8: Repeat steps C6-C7 until the maximum number of iterations is reached; Step D: Using the unit status of the first time period as the initial state, repeat steps AC in a loop to obtain the unit status of all time periods within the scheduling cycle.

2. The unit combination method based on competitive particle swarm optimization algorithm according to claim 1, characterized in that: In step C2, the final new velocity and position of each particle are determined based on the following formula: ； ； In the above formula, , Let be the final new velocity and position of particle i in the (k+1)th iteration, respectively. , These are the minimum and maximum particle velocities, respectively. , These represent the positions of the smallest and largest particles, respectively.

3. The unit combination method based on competitive particle swarm optimization algorithm according to claim 1, characterized in that: In step B, the objective function of the unit combination optimization model is: ； ； ； ； In the above formula, Let be the on / off state variable of the i-th unit during time period j. , Let $i$ be the power generation cost and $i$ of the i-th generating unit, respectively. Let i be the startup cost of the i-th unit. , , Let be the coefficient of the quadratic function of the power generation cost of the i-th generating unit, and n and t be the number of generating units and the number of time periods, respectively. , These are the costs of hot and cold start, respectively. , Let be the shutdown time and cooling time constant of the i-th unit, respectively. This represents the initial state of the i-th unit. Let be the shutdown time before the i-th unit is put into operation.

4. The unit combination method based on competitive particle swarm optimization algorithm according to claim 3, characterized in that: The constraints of the unit combination optimization model include: Power balance constraints: ； In the above formula, , These represent the system load demand and total power loss for time period j, respectively. Rotational spare constraint: ； In the above formula, Let j be the rotational reserve power for time period j; Unit operating constraints: ； In the above formula, For the output of the i-th unit during time period j, , These are the maximum and minimum outputs of the i-th unit, respectively.

5. The unit combination method based on competitive particle swarm optimization algorithm according to claim 4, characterized in that: The constraints of the unit combination optimization model also include minimum start-up and shutdown time constraints, which include: ； In the above formula, Let i be the continuous operating time of the i-th unit. , These are the minimum operating and downtime times for the i-th unit, respectively. When the i-th unit is in a shutdown state before the selected time period, A negative number represents the continuous downtime of the i-th unit before the selected time period. If the selected time period is specified, the unit may be in a shutdown or operating state; otherwise, the unit must be in a shutdown state. When the i-th unit is in operation before the selected time period, A positive number represents the continuous operating time of the i-th unit before the selected time period. If the selected time period indicates that the unit is either shut down or running, then the unit must be running during the selected time period.

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