Pump station optimization scheduling method based on improved Golden Litsea Algorithm

Abstract

The invention, which belongs to the technical field of pump station scheduling, discloses a pump station optimal scheduling method based on an improved Golden Litsea rotundifolia algorithm, and the method comprises the steps: (1) constructing an objective function and constraint conditions of pump station optimal scheduling; (2) initializing a population by using Fuch chaotic mapping; (3) individual fitness values are calculated to divide male and female litsea rotundifolia, and then the positions of the litsea rotundifolia are updated according to a search stage formula; (4) calculating prey escape energy improved by using a sine and cosine strategy, if a surrounding condition is met, updating the position of the litsea rotundifolia by using a prey surrounding formula improved by an inertia weight, otherwise, updating the position of the litsea rotundifolia according to a search stage formula; and (5) if the maximum number of iterations is reached, outputting the optimized scheduling scheme and result, otherwise, returning to calculate the individual fitness to carry out the next iteration. Compared with an existing algorithm, the advantages of the Golden Litsea Optimization algorithm are fully played, and the problems of the algorithm are improved by using a series of methods, so that the pump station optimization scheduling problem can be solved more quickly and effectively.

Description

Technical Field

[0001] The present invention relates to the technical field of pump station dispatching, and in particular to a pump station optimization dispatching method based on an improved golden jackal algorithm. Background Art

[0002] With the rapid development of my country's industrial and agricultural modernization and the continuous improvement of residents' living standards, the demand for regional water resources has also increased. Pump station projects play an indispensable role in achieving the rational allocation and scheduling of water resources. Since pump station projects have many characteristics such as long water transmission distance along the line, large water flow, large head changes and high energy consumption, the research on the optimization and scheduling of pump station projects has always been an important issue of general concern in the field of water conservancy system optimization.

[0003] At present, pump station optimization scheduling technology is mainly divided into mathematical programming methods and intelligent optimization algorithms. Among them, mathematical programming methods include linear programming, dynamic programming, etc. Since the optimization scheduling problem of pump stations is relatively complex and there are many nonlinear situations, traditional mathematical programming methods face problems such as dimensionality disaster and low computational efficiency when solving such problems. Intelligent optimization algorithms have been fully developed in recent years and have been widely used to solve complex engineering optimization problems.

[0004] Many people have tried to use meta-inspiration algorithms to solve engineering optimization problems. As one of the emerging meta-inspiration algorithms in recent years, the golden jackal algorithm has the advantages of easy implementation and high stability, and has been applied in many fields. However, it still has the disadvantages of unbalanced search capabilities and easy to fall into local optimality. Therefore, it is necessary to improve it for pump station scheduling problems to achieve the optimization goal of minimizing the total operating cost of the pump station. Summary of the invention

[0005] Purpose of the invention: The purpose of the present invention is to provide a pump station optimization scheduling method based on the improved golden jackal algorithm for the pump station optimization scheduling problem, to efficiently optimize the scheduling process, reduce the time spent on scheduling strategies, and achieve the optimization goal of minimizing the total operating cost of the pump station.

[0006] Technical solution: To achieve the above-mentioned invention object, the present invention adopts the following technical solution:

[0007] (1) Construct the objective function of pump station optimization scheduling with the lowest total operating cost:

[0008]

[0009] Where F is the electricity cost of the pumping station unit, i represents the time period, i = 1, 2, ..., TN (the total number of time periods in a day); ρ is the density of water, the unit is kg / m 3 ; g is the acceleration due to gravity, the unit is m / s 2;n i is the speed of the ith time period, in r / min; Q i (n i ) is the water flow rate at the rotation speed in the i-th time period, in m 3 / s;H i is the average head in the ith time period, in meters; T i is the power-on time of the ith time period, in hours; M i is the time-of-use electricity price in the i-th time period, in yuan / (kWh); η z (n i ) is the mechanical efficiency at the speed in the i-th time period; η f is the efficiency of the frequency conversion device; η d is the transmission efficiency; η m is the motor efficiency; p is the loss during operation, in kw;

[0010] (2) Constructing the constraints for optimizing the dispatch of pump stations with the lowest total operating cost:

[0011] 1): Traffic constraints:

[0012] Q i，min ≤Q i ≤Q i，max

[0013]

[0014] Where Q i，min , Q i，max are the minimum and maximum water flow rates of the pump respectively; Q min The minimum total amount of water transfer required in a single day;

[0015] 2): Lift constraint:

[0016] H min ≤H i ≤H max

[0017] Among them, H min and H max is the minimum and maximum head of the pump;

[0018] 3): Water pump speed ratio constraint:

[0019] k i =n i / n r

[0020] k i(min) ≤k i ≤1

[0021] Among them, nr is the rated speed, k i is the pump speed ratio, k i(min) It is the minimum speed ratio of the water pump, generally not less than 70%;

[0022] (3) Use Fuch chaotic mapping to initialize the population. The formula of Fuch chaotic mapping is:

[0023]

[0024] Among them, x n ≠0, n∈Z + ;

[0025] (4) Calculate the individual fitness value according to the objective function, divide the male and female golden jackals, and enter the prey search stage: The position formula of male and female golden jackals is:

[0026] Y1(t)=Y MA (t)-E*|Y MA (t)-rl*Prey(t)|

[0027] Y2(t)=Y FM (t)-E*|Y FM (t)-rl*Prey(t)|

[0028] Among them, Y1(t) and Y2(t) represent the positions of male and female golden jackals; Y MA (t), Y FM (t) represents the updated position of male and female golden jackals relative to the prey; Prey(t) is the position vector of the prey; t represents the number of iterations; rl represents the random number of Levy distribution in Levy motion; E represents the energy of the prey being hunted, which is calculated as:

[0029] E=E0*E1

[0030] Among them, E0 represents the initial state of prey energy, the formula is:

[0031] E0=2*rod+1

[0032] Among them, rod is a random number in the interval (0,1);

[0033] E1 represents the energy decline of the prey. Here, sine and cosine optimization is used to speed up the algorithm's decrease rate in the early stage to enhance the global search capability, and slow down the decrease rate in the later stage to enhance the local search capability. The optimized formula is:

[0034]

[0035] Among them, t is the current iteration number, T is the maximum iteration number

[0036] The calculation formula of rl is:

[0037]

[0038] Among them, μ and v are random numbers in the interval (0,1), and β is a constant, usually 1.5;

[0039] (5) Determine whether the escape energy of the prey satisfies the encirclement condition |E| < 1. If so, enter the encirclement and capture phase and use the inertia weight to update the positions of the prey and the golden jackal:

[0040] Y1(t)=ω(Y MA (t)-E*|rl*Y MA (t)-Prey(t)|)

[0041] Y2(t)=ω(Y FM (t)-E*|rl*Y FM (t)-Prey(t)|)

[0042]

[0043] Among them, Y1(t) and Y2(t) represent the positions of male and female golden jackals after the tth iteration; Y MA (t), Y FM (t) represents the updated position of male and female golden jackals relative to the prey after the ,th iteration; Prey(t) is the position vector of the prey after the ,th iteration; t represents the number of iterations; ω fir is the initial value of the inertia weight, usually 0.9; ω las is the final value of the inertia weight, usually 0.3;

[0044] If it is not satisfied, the prey position is updated according to the search phase formula, and the golden jackal continues to search for prey;

[0045] (6) Determine whether the maximum number of iterations has been reached. If so, output the optimization scheduling result; if not, return to step (2) to continue;

[0046] Beneficial effects: Compared with the prior art, the pump station optimization scheduling method based on the improved golden jackal algorithm of the present invention aims at solving the problems of the existing golden jackal algorithm, such as unbalanced search capability and easy falling into local optimum, and utilizes the characteristics of the improved golden jackal algorithm, such as final convergence and strong global search capability, to effectively reduce the delay of scheduling strategy problems and achieve the optimization goal of minimizing the total operating cost of the pump station. It has obvious advantages and is easy to implement. BRIEF DESCRIPTION OF THE DRAWINGS

[0047] Figure 1 It is a specific flow chart for implementing the method of the present invention;

[0048] Figure 2 It is a comparison chart of optimization results of the improved golden jackal algorithm, the unimproved golden jackal algorithm and the common grey wolf optimization algorithm under different total water transfer requirements in the application scenarios of the method described in the present invention. DETAILED DESCRIPTION

[0049] The present invention is further explained below in conjunction with the accompanying drawings and specific embodiments. It should be understood that these embodiments are only used to illustrate the present invention and are not used to limit the scope of the present invention. After reading the present invention, various equivalent forms of modifications to the present invention by those skilled in the art all fall within the scope defined by the claims attached to this application.

[0050] like Figure 1 As shown, the pump station optimization scheduling method based on the improved golden jackal algorithm comprises the following steps:

[0051] (1) Construct the objective function of pump station optimization scheduling with the lowest total operating cost:

[0052]

[0053] Where F is the electricity cost of the pumping station unit, i represents the time period, i = 1, 2, ..., TN (the total number of time periods in a day); ρ is the density of water, the unit is kg / m 3 ; g is the acceleration due to gravity, the unit is m / s 2 ;n i is the speed of the ith time period, in r / min; Q i (n i ) is the water flow rate at the rotation speed in the i-th time period, in m 3 / s;H i is the average head in the ith time period, in meters; T i is the power-on time of the ith time period, in hours; M i is the time-of-use electricity price in the i-th time period, in yuan / (kWh); η z (n i ) is the mechanical efficiency at the speed in the i-th time period; η f is the efficiency of the frequency conversion device; η d is the transmission efficiency; η m is the motor efficiency; p is the loss during operation, in kw;

[0054] (2) Constructing the constraints for optimizing the dispatch of pump stations with the lowest total operating cost:

[0055] 1): Traffic constraints:

[0056] Q i,min ≤Q i ≤Q i，max

[0057] Where Q i,min , Q i,max are the minimum and maximum water flow rates of the pump respectively; Q min The minimum total amount of water transfer required in a single day;

[0058] 2): Lift constraint:

[0059] H min ≤H i ≤H max

[0060] Among them, H min and H max is the minimum and maximum head of the pump;

[0061] 3): Water pump speed ratio constraint:

[0062] k i =n i / n r

[0063] k i(min) ≤k i ≤1

[0064] Among them, n r is the rated speed, k i is the pump speed ratio, k i(min) It is the minimum speed ratio of the water pump, generally not less than 70%;

[0065] (3) Use Fuch chaotic mapping to initialize the population. The formula of Fuch chaotic mapping is:

[0066]

[0067] Among them, x n ≠0, n∈Z + ;

[0068] (4) Calculate the individual fitness value according to the objective function, divide the male and female golden jackals, and enter the prey search stage: The position formula of male and female golden jackals is:

[0069] Y1(t)=Y MA (t)-E*|Y MA (t)-rl*Prey(t)|

[0070] Y2(t)=Y FM (t)-E*|Y FM (t)-rl*Prey(t)|

[0071] Among them, Y1(t) and Y2(t) represent the positions of male and female golden jackals; Y MA (t), Y FM (t) represents the updated position of male and female golden jackals relative to the prey; Prey(t) is the position vector of the prey; t represents the number of iterations; rl represents the random number of Levy distribution in Levy motion; E represents the energy of the prey being hunted, which is calculated as:

[0072] E=E0*E1

[0073] Among them, E0 represents the initial state of prey energy, the formula is:

[0074] E0=2*rod+1

[0075] Among them, rod is a random number in the interval (0,1);

[0076] E1 represents the energy decline of the prey. Here, sine and cosine optimization is used to speed up the algorithm's decrease rate in the early stage to enhance the global search capability, and slow down the decrease rate in the later stage to enhance the local search capability. The optimized formula is:

[0077]

[0078] Among them, t is the current iteration number, T is the maximum iteration number

[0079] The calculation formula of rl is:

[0080]

[0081] Among them, μ and v are random numbers in the interval (0,1), and β is a constant, usually 1.5;

[0082] (5) Determine whether the escape energy of the prey satisfies the encirclement condition |E| < 1. If so, enter the encirclement and capture phase and use the inertia weight to update the positions of the prey and the golden jackal:

[0083] Y1(t)=ω(Y MA (t)-E*|rl*Y MA (t)-Prey(t)|)

[0084] Y2(t)=ω(Y FM (t)-E*|rl*Y FM (t)-Prey(t)|)

[0085]

[0086] Among them, Y1(t) and Y2(t) represent the positions of male and female golden jackals after the t,th iteration; Y MA (t), YFM (t) represents the updated position of male and female golden jackals relative to the prey after the tth iteration; Prey(t) is the position vector of the prey after the tth iteration; t represents the number of iterations; ω fir is the initial value of the inertia weight, usually 0.9; ω las is the final value of the inertia weight, usually 0.3;

[0087] If it is not satisfied, the prey position is updated according to the search phase formula, and the golden jackal continues to search for prey;

[0088] (6) Determine whether the maximum number of iterations has been reached. If so, output the optimization scheduling result; if not, return to step (2) to continue;

[0089] In order to verify the feasibility of the pump station optimization scheduling method based on the improved golden jackal algorithm proposed in this invention, a MARLAB simulation experiment was conducted on the indicator with the lowest total operating cost, and compared with the unimproved golden jackal algorithm and the gray wolf algorithm. This simulation experiment simulates the actual situation to set up a single pump station unit and optimize the scheduling for different water diversion situations.

[0090] Figure 2 The total water transfer volume of the present invention is 1.18 million m 3 , 1.2 million m 3 and 1.22 million m 3 The following is a bar chart comparing the changes in the total operating cost objective function values ​​obtained after optimization by the three different algorithms. It can be seen from the figure that after the optimization of the three algorithms, the total operating cost objective function value increases with the increase in the total water transfer volume. This is because when the total water transfer volume increases, the pump station needs to operate at more time nodes and the average speed during operation will increase, resulting in an increase in power and operating time, which is finally reflected in the increase in the total operating cost. From the height of the three algorithms in the figure, it can be seen that under the same total water transfer volume, the operation plan obtained by the improved golden jackal algorithm is compared with the operation plan obtained by the unimproved golden jackal algorithm and the gray wolf algorithm. The objective function, that is, the total operating cost, has been reduced. The simulation experiment results prove that the scheduling plan optimized by the improved golden jackal algorithm can effectively reduce the operating cost while meeting the total water transfer demand, which is of profound significance.

Claims

1. A pump station optimization scheduling method based on improved golden jackal algorithm, characterized in that: The method comprises the following steps: (1) Construct the objective function and constraints for optimizing the dispatch of pump stations with the lowest total operating cost; (2) Initialize the population using Fuch chaotic map; (3) Calculate the individual fitness value (i.e., the objective function value), divide the male and female golden jackals according to the fitness value, and enter the prey search stage; (4) Using the improved formula of the sine-cosine strategy to calculate the escape energy of the prey and determine whether the escape energy meets the encirclement condition. If so, the prey capture phase is entered, and the positions of the prey and the golden jackal are updated using the encirclement formula improved by the inertia weight; if not, the prey search phase is continued; (5) Determine whether the maximum number of iterations has been reached. If so, output the optimized scheduling plan. Otherwise, return to step (3) and continue the next iteration until the maximum number of iterations has been reached.

2. The pump station optimization scheduling method based on the improved golden jackal algorithm according to claim 1 is characterized in that: The objective function and constraint conditions for the optimal scheduling of the pump station with the lowest total operating cost in step (1) are: (1) Objective function: Where F is the electricity cost of the pumping station unit, i represents the time period, i = 1, 2, ..., TN (the total number of time periods in a day); ρ is the density of water, the unit is kg / m 3 ; g is the acceleration due to gravity, in m / s 2 ; n i is the speed of the ith time period, in r / min; Q i (n i ) is the water flow rate at the rotation speed in the i-th time period, in m 3 / s;H i is the average head in the ith time period, in m; T i is the power-on time of the ith time period, in hours; M i is the time-of-use electricity price in the i-th time period, in yuan / (kWh); η z (n i ) is the mechanical efficiency at the speed in the i-th time period; η f is the frequency conversion device efficiency; η d is the transmission efficiency; η m is the motor efficiency; p is the loss during operation, in kw; (2) Constraints: 1): Traffic constraints: Q i,min ≤Q i ≤Q i，max Where Q i，min , Q i，max are the minimum and maximum water flow rates of the pump respectively; Q min The minimum total amount of water transfer required in a single day; 2): Lift constraint: H min ≤H i ≤H max Among them, H min and H max is the minimum and maximum head of the pump; 3): Water pump speed ratio constraint: k i =n i / n r k i(min) ≤k i ≤1 Among them, n r is the rated speed, k i is the pump speed ratio, k i(min) It is the minimum speed ratio of the water pump, generally not less than 70%.

3. The pump station optimization scheduling method based on the improved golden jackal algorithm according to claim 1 is characterized in that: The Fuch chaotic mapping formula in step (2) is: Among them, x n ≠0, n∈Z + .

4. The pump station optimization scheduling method based on the improved golden jackal algorithm according to claim 1 is characterized in that: The position formula of male and female golden jackals in the stage of searching for prey, the energy formula of prey escape improved by sine and cosine strategy, the encirclement condition, and the improved formula of inertia weight in the stage of encirclement and capture in the steps (3)-(4) are as follows: (1) Position formula of male and female golden jackals in the stage of searching for prey: Y1(t)=Y MA (t)-E*|Y MA (t)-rl*Prey(t)| Y2(t)=Y FM (t)-E*|Y FM (t)-rl*Prey(t)| Among them, Y1(t) and Y2(t) represent the positions of male and female golden jackals; Y MA (t), Y FM (t) represents the updated position of male and female golden jackals relative to the prey; Prey(t) is the position vector of the prey; t represents the number of iterations; rl represents the random number of Levy distribution in Levy motion; E represents the energy of the prey being hunted, which is calculated as: E=E0*E1 Among them, E0 represents the initial state of prey energy, the formula is: E0=2*rod+1 Among them, rod is a random number in the interval (0, 1); E1 indicates the energy decline of the prey, and sine-cosine optimization is used here, so that the algorithm decreases faster in the early stage to enhance the global search ability, and slows down in the later stage to enhance the local search ability; (2) The escape energy formula after sine-cosine optimization is: Among them, t is the current iteration number, T is the maximum iteration number The calculation formula of rl is: Among them, μ and v are random numbers in the interval (0,1), and β is a constant, usually 1.5; (3) Encirclement condition: Is |E| greater than 1? If it is greater than 1, the search phase continues; otherwise, the encirclement phase begins. (4) The position update formula of the golden jackal in the stage of hunting prey improved by inertia weight is: Y1(t)=ω(Y MA (t)-E*|rl*Y MA (t)-Prey(t)|) Y2(t)=ω(Y FM (t)-E*|rl*Y FM (t)-Prey(t)|) Among them, Y1(t) and Y2(t) represent the positions of male and female golden jackals after the t,th iteration; Y MA (t), Y FM (t) represents the updated position of male and female golden jackals relative to the prey after the tth iteration; Prey(t) is the position vector of the prey after the tth iteration; t represents the number of iterations; ω fir is the initial value of the inertia weight, usually 0.9; ω las is the final value of the inertia weight, usually 0.3.

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