Improved intelligent water drop algorithm-based cascade reservoir group power generation optimal scheduling method

Abstract

The application relates to a cascade reservoir group power generation optimization scheduling method based on an improved intelligent water droplet algorithm, and the method comprises the following steps: setting parameters, a target function and constraint conditions of the improved intelligent water droplet algorithm; initializing a water droplet population; the water droplets are randomly moved, and relevant parameters of the water droplets and paths are updated after the movement; a fitness function is used to calculate the fitness value of each individual in a new generation population, meanwhile, a difference mutation operator is used to mutate the individual in the new generation population to obtain a difference mutation individual, and then a current local optimal individual is selected by calculation and comparison; the speed of the current optimal individual and the sediment content of the path are updated, and the optimal individual is selected by calculation and comparison; whether the maximum iteration number is reached is judged, if the maximum iteration number is reached, the calculation is ended, and the optimal solution, that is, an optimal scheduling scheme, is output; and the improved intelligent water droplet algorithm has better stability, is suitable for solving a cascade reservoir group power generation optimization scheduling scheme, has high solving efficiency, and can obtain a better scheduling scheme.

Description

Technical Field

[0001] This invention belongs to the field of reservoir optimization scheduling, specifically involving a method for optimizing the scheduling of power generation in a cascade reservoir group based on an improved intelligent water droplet algorithm. Background Technology

[0002] Optimal scheduling of cascade reservoir groups is a multi-stage, high-dimensional, and multi-constrained nonlinear optimization problem, and its optimization methods have become one of the research hotspots in the field of reservoir scheduling. Compared with traditional optimization methods that are prone to the "curse of dimensionality," intelligent optimization algorithms have advantages such as high efficiency, simple structure, strong global optimization performance, and strong versatility, providing a new approach for reservoir optimal scheduling. As a novel swarm intelligent optimization algorithm, the Intelligent Water Drops (IWD) algorithm simulates the path selection principle of water droplets during the scouring of the riverbed by water flow. It has many advantages such as strong self-organization ability and robustness, but it also has drawbacks such as insufficient diversity in initial population, susceptibility to local optima, and slow initial solution speed. Summary of the Invention

[0003] The purpose of this invention is to address the aforementioned problems by providing a method for optimizing the scheduling of power generation in a cascade reservoir group based on the Improved Intelligent Water Drops (IIWD) algorithm. This method uses logistic chaotic mapping as the population initialization method and introduces the differential mutation operator of the Differential Evolution (DE) algorithm to mutate the population updated initially in each iteration of IIWD to solve the problem of easily getting trapped in local optima. Furthermore, an improved neuron update method based on the Self-Organizing Map (SOM) algorithm is applied to the optimal individual update process of the IIWD algorithm, further enhancing its optimization ability.

[0004] The technical solution of this invention is a method for optimized scheduling of power generation in a cascade reservoir group based on an improved intelligent water droplet algorithm, comprising the following steps:

[0005] Step 1: Set the population size, individual dimension, crossover probability, maximum number of iterations, and objective function of the improved intelligent water droplet algorithm. The optimization objective is to maximize the total power generation of the cascade reservoir group during the scheduling period. The fitness value is the size of the total power generation of the cascade reservoir group during the scheduling period. After inputting the constraints, read the relevant data information of the reservoir, including the normal water level, the inflow and outflow of each day during the scheduling period, and the water level and reservoir capacity curve.

[0006] Step 2: Under the premise of satisfying the reservoir's own constraints, initialize the water droplet population with a population size of N and an individual dimension of D, i.e., containing D water levels. Determine whether the water level constraints are met. If not, perform water level correction.

[0007] Step 3: The water droplet selects a path to move according to the path selection probability. After the movement is completed, the relevant parameters of the water droplet and the path are updated to obtain a new generation of population.

[0008] Step 4: Calculate the fitness value of each individual in the new generation population using the fitness function, and simultaneously use the differential mutation operator to mutate the individuals in the new generation population to obtain differentially mutated individuals. Then, compare the new generation population and the differentially mutated individuals using the fitness function to select the best individual in the current generation.

[0009] Step 5: Update the velocity and sediment content of the path of the current best individual, compare the fitness function of the current best individual and the updated individual, and select the best individual.

[0010] Step 6: Determine if the maximum number of iterations has been reached. If it has, end the calculation and output the optimal solution as the final cascade reservoir optimization scheduling scheme; otherwise, proceed to step 3.

[0011] The intelligent water droplet algorithm includes:

[0012] 1) Initialization process,

[0013] The variables to be initialized include: the initial velocity v of the water droplet. ini Speed ​​update parameter a v b v c ν Update parameter a for water droplet sediment content s b s c s Local variables update parameter α, and global variables update parameter β;

[0014] The set of sediment contents along each path is denoted as W;

[0015] 2) Path selection process,

[0016] The water droplets will move to their destination in several steps. Let the current position of a water droplet in the population be i, and the next position be j. Let p(i,j) be the probability that the water droplet chooses the path (i,j), and s(i,j) be the sediment content of the path (i,j). p(i,j) and s(i,j) are inversely proportional.

[0017] The expression for the path selection probability p(i,j) is as follows:

[0018]

[0019]

[0020]

[0021] In the formula, f(s(i,j)) represents the correlation function of s(i,j); ε represents a constant greater than zero, which is used to avoid the case where the denominator is zero; g(s(i,k)) is a conversion function that ensures that s(i,j) is positive.

[0022] 3) Local variable update process,

[0023] After completing the path selection, the water droplet will move to the next position j, and the sediment content s(i,j) and the water droplet velocity v will be updated. IWD Assuming the water droplet moves from position i to position j between time t and time t+1, then v IWD The update formula for s(i,j) is as follows:

[0024]

[0025] s(i,j)=(1-α)s(i,j)-αΔs(i,j) (5)

[0026] s IWD =s IWD +Δs(i,j) (6)

[0027]

[0028] In the formula, ΔS(i,j) is the change in sediment content along path (i,j), and t(i,j) is the time it takes for a water droplet to travel along path (i,j) with t(i,j) = 1.

[0029] v IWD (t), v IWD (t+1) represent the velocities of the water droplet at times t and t+1, respectively;

[0030] 4) Global variable update process,

[0031] Calculate the fitness value of each feasible solution in each generation of the population, select the solution with the best fitness value as the optimal solution of the population, and use the set W of sediment content corresponding to the optimal solution as the initial path sediment content for the next iteration. The update formula for global path sediment content is as follows:

[0032]

[0033] In the formula N IWD This represents the total number of water droplets in the population; β is the global variable update parameter.

[0034] Preferably, in step 2, a Logistic chaotic mapping is used for population initialization, the expression of which is as follows:

[0035]

[0036] In the formula, μ is a control parameter. When μ = 4, the population is in a completely chaotic state. c(t) and c(t+1) represent the positions of individual water droplets in the initial population at times t and t+1, respectively.

[0037] Preferably, the differential mutation operator from the standard differential evolution algorithm is introduced to perform differential mutation on the local optimum after each iteration, and its expression is as follows:

[0038] v′ q，G (t)=v best，G +m·(v q，G --v q+1，G )+m·(v q+2，G --v q+3，G (10)

[0039] s′ q，G (i, j) = s best，G (i,j)+m·(s) q，G (i,j)-s q+1，G (i,j))+n·(s) q+2，G (i,j)-s q+3，G (i, j)) (11)

[0040] In the formula v q，G v q+1，G v q+2，G v q+3，G v′ represents the velocity of individuals q, q+1, q+2, and q+3 in the G-th generation population, respectively. q，G (t) represents the velocity of the q-th individual in the G-th generation population after differential mutation, v best，G s represents the velocity of the optimal individual in the Gth generation of the population. best，G (i, j) represents the sediment content of the path (i, j) after the optimal individual in the G-th generation population moves from i to j before differential mutation; s′ q，G (i,j) represents the sediment content of the path (i,j) after the qth individual in the Gth generation population moves from i to j after differential mutation, where m is the scaling factor of the mutation operation.

[0041] Preferably, the difference mutation operator employs "DE / best / 1" mutation and binomial crossover.

[0042] An improved method is introduced to update neurons using SOM (Self-Optimal Origin and Mean Time) to perform the secondary update process for the optimal individual in the IIWD algorithm. The specific steps are as follows:

[0043] 1) Treat the sediment content along the path as neurons, and denote the sediment content s(i,j) of path (i,j) as Q. i，j , record X i，j This represents the weight vector of the corresponding neuron;

[0044] 2) Select the best individual in the current population as the most matched neuron s * (i, j), where s is the worst path sediment content obtained in the (n+1)th iteration. n+1 # Using (i, j) as input, calculate the Euclidean distance between it and the sediment content of the corresponding paths of all individuals in the population obtained in the nth iteration, and select the neuron s that best matches the current one. * The neuron with the smallest Euclidean distance (i, j) is the best-matched neuron s. * (i, j), thereby updating the best-matching neuron s * (i, j);

[0045] 3) Using the current best-matching neurons s * Calculate the neighborhood radius r centered at (i, j). G And update all neurons within this neighborhood.

[0046] The specific expressions for the above three steps are as follows:

[0047] r G =r0·e -G / λ , λ=N s / lgr0 (12)

[0048]

[0049] V(G)=V0e -G / N G = 1, 2, ..., N (14)

[0050]

[0051] In the formula r G Let r0 be the initial neighborhood radius of the population in generation G, λ be a time constant, V(G) be the velocity learning factor for the population in generation G, and V0 be the initial velocity learning factor. s p is the maximum number of iterations for the population. s Represents the coordinates of neuron s(i, j); Indicates the most matching neuron s * The coordinates of (i, j); For the best matching neurons s * The Euclidean distance between (i, j) and neuron s(i, j); The most matching neurons s in the Gth generation population* (i, j) is the function for calculating the Euclidean distance between other neurons; r(G) represents the neighborhood radius of the population in generation G; λ represents the time constant; s G-1 (i, j), s G (i, j), s G+1 (i, j) represent the sediment content along path (i, j) in the populations of generations G-1, G, and G+1, respectively;

[0052] 4) Update the global variables using the following expression:

[0053]

[0054] In the formula w(s) * (i, j) is s * (i, j) constitute the population center point, a t * U represents the Euclidean distance between adjacent neurons. t * Let M(0, r) represent a unit vector. G I) represents a normally distributed noise vector.

[0055] Preferably, the population size of the improved intelligent water droplet algorithm is 50.

[0056] Compared with the prior art, the beneficial effects of the present invention include:

[0057] 1) The improved intelligent water droplet algorithm proposed in this invention enhances the optimization performance of the intelligent water droplet algorithm, and can obtain a better scheduling scheme in the power generation optimization scheduling of cascade reservoir groups. At the same time, its calculation speed is faster and the results are more stable.

[0058] 2) The present invention uses logistic chaotic mapping for population initialization, which can make the distribution of individuals in the initial population more uniform and stable, thereby reducing the possibility of the algorithm getting trapped in local optima.

[0059] 3) This invention uses a differential mutation operator to perform differential mutation on the local optimal solution, which helps the algorithm escape local optima.

[0060] 4) This invention uses a neuron update method based on the self-organizing map algorithm to update the current best individual. The mapping process of the self-organizing map algorithm has adaptive characteristics of topology preservation and distribution preservation. Based on its improved neuron update method, the structural characteristics of the population can be better preserved, and the changes in the population structural characteristics caused by the operation of the algorithm can be avoided, thus making the algorithm solution more stable. Attached Figure Description

[0061] The present invention will be further described below with reference to the accompanying drawings and embodiments.

[0062] Figure 1 This is a flowchart illustrating the optimized scheduling method for power generation in a cascade reservoir group according to an embodiment of the present invention.

[0063] Figure 2a The graph shows the water level change curve of Xiluodu Reservoir under the IIWD algorithm optimization scheduling under the water inflow conditions in 2020.

[0064] Figure 2b The graph shows the water level change curve of Xiangjiaba Reservoir under the IIWD algorithm optimization scheduling under the water inflow conditions in 2020.

[0065] Figure 2c The graph shows the water level change curve of the Three Gorges Reservoir under the IIWD algorithm optimization scheduling under the water inflow conditions in 2020.

[0066] Figure 3a The graph shows the water level change curve of Xiluodu Reservoir under the IIWD algorithm optimization scheduling under the water inflow conditions in 2015.

[0067] Figure 3b The graph shows the water level change curve of Xiangjiaba Reservoir under the IIWD algorithm optimization scheduling under the water inflow conditions in 2015.

[0068] Figure 3c The graph shows the water level change curve of the Three Gorges Reservoir under the IIWD algorithm optimization scheduling under the water inflow conditions in 2015.

[0069] Figure 4a The graph shows the water level change curve of Xiluodu Reservoir under the IIWD algorithm optimization scheduling under the water inflow conditions in 2016.

[0070] Figure 4b The graph shows the water level change curve of Xiangjiaba Reservoir under the IIWD algorithm optimization scheduling under the water inflow conditions in 2016.

[0071] Figure 4c The graph shows the water level change curve of the Three Gorges Reservoir under the IIWD algorithm optimization scheduling under the water inflow conditions in 2016. Detailed Implementation

[0072] like Figure 1 As shown, the optimized scheduling method for power generation in a cascade reservoir group based on the improved intelligent water droplet algorithm includes the following steps:

[0073] Step 1: Set the parameters of the improved intelligent water droplet algorithm: population size N, individual dimension D, crossover probability CR, maximum number of iterations, objective function / fitness function. The optimization objective is to maximize the total power generation of the cascade reservoir group during the scheduling period. The fitness value is the size of the total power generation of the cascade reservoir group during the scheduling period. After inputting the constraints, read the relevant data information of the reservoir, including normal water level, daily inflow and outflow during the scheduling period, water level and reservoir capacity curves, etc.

[0074] Step 2: Under the premise of satisfying the reservoir's own constraints, use the logistic chaotic mapping to initialize the water droplet population. The population size is N and the individual dimension is D, that is, it contains D water levels. Determine whether the water level constraint is satisfied. If it is not satisfied, perform water level correction.

[0075] Step 3: The water droplet selects a path to move based on the path selection probability. After the movement is completed, the relevant parameters of the water droplet and the path are updated to obtain a new generation of population.

[0076] Step 4: Calculate the fitness value of each individual in the new generation population using the fitness function. At the same time, use the differential mutation operator to mutate the individuals in the new generation population to obtain differentially mutated individuals. Then, compare the new generation population and the differentially mutated individuals using the fitness function to select the best individual in the current generation.

[0077] Step 5: The speed and sediment content of the current best individual are updated using a neuron update method based on the self-organizing map algorithm. The fitness function of the current best individual and the updated individual are compared and the best individual is selected.

[0078] Step 6: Determine if the maximum number of iterations has been reached. If it has, end the calculation and output the optimal solution as the final cascade reservoir optimization scheduling scheme. Otherwise, return to Step 3 and repeat the process until the iteration ends.

[0079] This implementation example uses the Xiluodu, Xiangjiaba, and Three Gorges cascade reservoirs as the subject, constructing an optimized power generation scheduling model for the cascade reservoir group with the objective of maximizing total power generation. 2020, 2015, and 2016 were selected as three typical years (high, average, and low water levels), respectively, with the scheduling period from September 1st to October 31st. Considering the hydraulic connections between the Xiluodu, Xiangjiaba, and Three Gorges reservoirs, the IIWD, IWD, and DE algorithms were used to solve the cascade reservoir group power generation scheduling model 500 times under the water conditions of the three typical years. The maximum, minimum, average, and standard deviation of the power generation corresponding to the solution obtained by the three algorithms in the 500 calculations were statistically analyzed, as well as the average time required to complete each calculation. The calculation results are shown in Tables 1-3. The population size N = 50 and the number of iterations iter = 500 were set for the three algorithms. The initial droplet velocity v in the IIWD and IWD algorithms was... ini =0.5, initial sediment content of water droplets s IWD =0, the DE algorithm uses "DE / best / 1" mutation and binomial crossover, and takes the crossover probability CR = 0.5.

[0080] The water levels of Xiluodu, Xiangjiaba, and Three Gorges Reservoirs, optimized by the IIWD algorithm of this invention under the water inflow conditions of 2020, are as follows: Figure 2a , 2b As shown in Figures 2 and 2c; under the water inflow conditions of 2015, the water levels of Xiluodu, Xiangjiaba, and Three Gorges Reservoirs optimized and scheduled by the IIWD algorithm of this invention are respectively as follows: Figure 3a , 3b As shown in Figures 3c. Under the 2016 water inflow conditions, the water levels of Xiluodu, Xiangjiaba, and Three Gorges Reservoirs optimized and scheduled by the IIWD algorithm of this invention are respectively as follows: Figure 4a , 4b As shown in 4c.

[0081] As shown in Tables 1, 2, and 3, in terms of the quality of the solution results, under the three different typical annual water conditions, the maximum, minimum, and average power generation values ​​obtained by the IIWD algorithm are all higher than those obtained by the IWD and DE algorithms. Therefore, the solution obtained by the IIWD algorithm is superior. The magnitude of the standard deviation of the solution results directly reflects the stability of the algorithm's solution; the smaller the standard deviation, the stronger the algorithm's stability. Compared to the IWD and DE algorithms, the standard deviation of the power generation obtained by the IIWD algorithm is smaller, indicating that the IIWD algorithm has better stability. In terms of solution speed, compared to the other two algorithms, the IIWD algorithm requires less time on average to complete one full calculation, making it faster.

[0082] In summary, the IIWD algorithm outperforms the IWD and DE algorithms in terms of solution quality, stability, and speed. The IIWD algorithm has better optimization performance than the IWD and DE algorithms, providing a superior optimization algorithm for the optimal scheduling of power generation in cascade reservoir groups.

[0083] Table 1 Calculation Results for 2020 (High Water Year)

[0084]

[0085] Table 2 Calculation Results for 2015 (Equal Water Year)

[0086]

[0087] Table 3 Calculation results for 2016 (dry year)

[0088]

Claims

1. A method for optimized scheduling of power generation in a cascade reservoir group based on an improved intelligent water droplet algorithm, characterized in that, Includes the following steps: Step 1: Set the population size, individual dimension, crossover probability, maximum number of iterations, and objective function of the improved intelligent water droplet algorithm. The optimization objective is to maximize the total power generation of the cascade reservoir group during the scheduling period. The fitness value is the size of the total power generation of the cascade reservoir group during the scheduling period. After inputting the constraints, read the relevant data information of the reservoir. The improved intelligent water droplet algorithm includes: 1) Initialization process, The variables to be initialized include: the initial velocity of the water droplet. Parameters update speed , , Updated parameters for water droplet sediment content , , Local variable update parameters Global variable update parameters ; The set of sediment content along each path is denoted as ; 2) Path selection process, The water droplets will move to their destination in several steps. The current position of the water droplets in the population is denoted as... The next position is Water droplet selects path The probability is denoted as ,path The sediment content is recorded as , and Inversely proportional, Path selection probability The expression is as follows: ；（1） ；（2） ；（3） In the formula express Related functions; Represents a constant greater than zero; It is to ensure The conversion function for positive numbers; 3) Local variable update process, After selecting its path, the water droplet will move to the next location. Update sediment content Water droplet speed Assuming the water droplet is at time [time] At that time From position Move to location ,but as well as The update formula is as follows: ；（4） ；（5） ；（6） ；（7） In the formula For path Changes in sediment content For water droplets on the path The time spent exercising; , These represent the water droplets at... , The speed of time; 4) Global variable update process, Calculate the fitness value of each feasible solution in each generation of the population, select the solution with the best fitness value as the optimal solution for that population, and then compile a set of sediment contents corresponding to the optimal solutions. As the initial path sediment content for the next iteration, the update formula for the global path sediment content is as follows: ；（8） In the formula This represents the total number of water droplets in the population; Update parameters for global variables; Step 2: Under the premise of satisfying the reservoir's own constraints, initialize the water droplet population, determine whether the water level constraints are met, and if not, perform water level correction. Population initialization is performed using the Logistic chaotic mapping, and its expression is as follows: ；（9） In the formula For control parameters, i ( t ), i ( t +1) represent the initialization of individual water droplets in the population. and The position at that moment; Step 3: The water droplet randomly selects a path to move. After the movement is completed, the relevant parameters of the water droplet and the path are updated to obtain a new generation of population. Step 4: Calculate the fitness value of each individual in the new generation population using the fitness function, and simultaneously use the differential mutation operator to mutate the individuals in the new generation population to obtain differentially mutated individuals. Then, compare the new generation population and the differentially mutated individuals using the fitness function to select the best individual in the current generation. The differential mutation operator from the standard differential evolution algorithm is introduced to perform differential mutation on the local optimum after each iteration. Its expression is as follows: ；（10） ；（11） In the formula , , , They represent the first Generation 1 q , q +1、 q +2、 q +3 individuals' speed; Indicates the th after difference mutation G Generation 1 q The speed of each individual Indicates the first G The speed of the best individual in the population; Before performing differential mutation, the first The optimal individual of the population from Move to Subsequent path The sediment content; Indicates the th after difference mutation Generation 1 Individuals from Move to Subsequent path The sediment content, The scaling factor for the mutation operation; Step 5: Update the velocity and sediment content of the path of the current best individual, compare the fitness function of the current best individual and the updated individual, and select the best individual. The method of updating neurons in the neural network of the self-organizing map algorithm is introduced and improved. This is used to perform a secondary update process after the differential mutation update of the optimal individual in the intelligent droplet algorithm. The specific steps are as follows: 1) Treat the sediment content along the path as neurons, and record the path. Sediment content for ,remember This represents the weight vector of the corresponding neuron; 2) Select the best individual in the current population as the best matching neuron. , will the The worst path sediment content obtained in the second iteration As input, calculate its relationship with the first... The Euclidean distance between the sediment content of each path corresponding to all individuals in the population obtained in the next iteration is used to select the neuron that best matches the current one. The neuron with the smallest Euclidean distance is selected as the best-matched neuron. This updates the best-matching neuron. ; 3) Using the currently best-matching neuron Calculate the neighborhood radius centered on the given point. And update all neurons within this neighborhood; The specific expressions for the above three steps are as follows: ；（12） ；（13） ；（14） ；（15） In the formula For the first The neighborhood radius corresponding to the generation population Let be the initial neighborhood radius of the population. It is a time constant. For the first The speed learning factor corresponding to the generation population As the initial velocity learning factor, The maximum number of iterations for the population. Represents neurons The coordinates; Represents the best-matching neuron The coordinates; For the best matching neuron With neurons The Euclidean distance between them; Indicates the first The most matched neuron in the population A function for calculating the Euclidean distance between neurons; Indicates the first The neighborhood radius of the generation population; Indicates a time constant; , , They represent the first , , Path in generation population The sediment content on the surface; 4) Update the global variables using the following expression: ；（16） In the formula for The central point that constitutes the population This represents the Euclidean distance between adjacent neurons. Represents a unit vector. Represents a noise vector that follows a normal distribution; Step 6: Determine if the maximum number of iterations has been reached. If it has, end the calculation and output the optimal solution as the final cascade reservoir optimization scheduling scheme; otherwise, proceed to step 3.

2. The cascade reservoir group power generation optimization scheduling method according to claim 1, wherein the differential mutation operator adopts "DE / best / 1" mutation and binomial crossover.

3. The optimized scheduling method for power generation of a cascade reservoir group according to claim 2, characterized in that, The population size of the improved intelligent waterdrop algorithm is 50.

4. The optimized scheduling method for power generation of a cascade reservoir group according to any one of claims 1-3, characterized in that, Reservoir-related data includes normal water level, daily inflow and outflow during the scheduling period, and water level and reservoir capacity curves.

Images