Power system economic scheduling method based on improved dung beetle optimizer algorithm

Abstract

The present invention relates to the technical field of optimizing economic scheduling of new energy power systems, and specifically to a power system economic scheduling method based on an improved dung beetle optimizer algorithm. The method comprises: establishing a wind turbine set output power mathematical model, a power system low-carbon economic unit combination optimization model, and a load-side low-carbon demand response model; and improving a raw dung beetle optimizer algorithm, processing day-ahead wind and load data, and performing optimized solving on a target function by using the improved dung beetle optimizer algorithm. The improved dung beetle optimizer algorithm used in the design of the present invention has a high search capability and high optimization precision, and by using the algorithm to perform the optimized solving on the system model on the basis of the day-ahead wind output power and the load data, the economy of the system is improved, and the economic scheduling of the system is implemented. A good point set policy is introduced to initialize a dung beetle population, a chaotic mechanism policy is used to improve the speed of the algorithm, a Gaussian mutation policy is used to solve the problems such as the precocity and the convergence precision of an algorithm, and a random walk policy is introduced to enhance an algorithm optimization capability.

Description

A method for economic dispatch of power systems based on improved dung beetle optimization algorithm Technical Field

[0001] The present invention relates to the technical field of optimized economic dispatch of new energy power systems, and in particular to a power system economic dispatch method based on an improved dung beetle optimization algorithm. Background Art

[0002] Against the backdrop of the "dual carbon" initiative, the construction of a power generation system primarily based on renewable energy has garnered widespread attention, and wind power generation has experienced rapid growth. However, the randomness, volatility, and intermittency of large-scale, centralized wind power access at a single point will exacerbate the difficulty of regional grid operation and dispatch control. For example, if the impact of random fluctuations in wind power output is not accounted for during maintenance, improper wind power control can lead to frequency and voltage over-limits, the disorderly disconnection of large numbers of wind turbines, and even regional grid disconnection. Therefore, rational economic dispatch of wind turbines is imperative.

[0003] In addition, in order to adapt to the low-carbon trend, the traditional low-carbon dispatching method of the power system only optimizes the power generation side and lacks guidance on environmentally friendly electricity use for users. Therefore, it is very important to comprehensively consider low-carbon economic dispatching on both the power generation side and the load side.

[0004] Among the many power system optimization and dispatch algorithms, metaheuristics possess a powerful ability to solve nonlinear problems. The Dung Beetle Optimizer (DBO) algorithm, proposed on November 27, 2022, is highly effective for handling complex mathematical problems with multiple constraints. The Dung Beetle Optimizer (DBO) is a biomimetic metaheuristic algorithm whose core concept and fundamental approach are inspired by the ball-rolling behavior of dung beetles. The algorithm mathematically models the ball-rolling, reproduction, foraging, and stealing behaviors of dung beetles, helping the agent explore and exploit every potential region of the search space to achieve comprehensive and accurate optimization of the proposed problem. This algorithm possesses novel concepts and highly effective strategies.

[0005] However, the original dung beetle algorithm has limited speed, problems with premature convergence, and poor convergence accuracy. Its optimization capabilities also need to be improved, making it difficult to quickly and accurately implement efficient economic dispatch of power systems. To address this, we propose a power system economic dispatch method based on an improved dung beetle optimization algorithm.

[0006] Summary of the Invention

[0007] The object of the present invention is to provide a method for economic dispatch of a power system based on an improved dung beetle optimization algorithm to solve the problems raised in the above background technology.

[0008] To solve the above technical problems, one of the objectives of the present invention is to provide a power system economic dispatch method based on an improved dung beetle optimization algorithm. First, a power system consisting of wind turbines, thermal power generators, and loads is constructed. Considering the carbon emission responsibility sharing results, the user-side carbon emission cost is used as a signal to respond to the user's low-carbon demand. A two-stage power system source-grid-load low-carbon economic dispatch model is proposed. Finally, a system operation control strategy - the improved dung beetle optimization algorithm - is set with economic optimization as the goal. The method specifically includes the following steps:

[0009] S1. Establish a mathematical model of wind turbine output power;

[0010] S2. Propose a low-carbon economic unit portfolio optimization model for the power system. The objective function includes the wind turbine operating cost, thermal power unit cost, and carbon emission cost, and considers the constraints of the system power flow equation. The specific steps include:

[0011] S2.1. The objective function of the system is obtained by integrating the operating cost of wind turbines, the cost of thermal power units, and the carbon emission cost of power generation.

[0012] S2.1. The proposed constraints include the tidal flow equation constraint and the carbon flow equation constraint;

[0013] S3. The proposed load-side low-carbon demand response model has an objective function including the load carbon emission cost and the demand response cost, and takes into account the constraints on the load side. It has the following steps:

[0014] S3.1. The proposed load-side low-carbon demand response model has an objective function including load carbon emission costs and demand response costs;

[0015] S3.2, the proposed constraints include node load variation constraints and load response balance constraints;

[0016] S4. Improve the original dung beetle optimization algorithm by introducing a good point set strategy to initialize the dung beetle population, using a chaos mechanism strategy to increase the speed of the heuristic algorithm, introducing a Gaussian mutation strategy to address issues such as premature convergence and convergence accuracy, and introducing a random walk strategy enhancement algorithm for local optimization. This results in an improved dung beetle optimization algorithm that enhances the algorithm's initialization and search capabilities.

[0017] Process the day-ahead wind and load data, recording the data at regular intervals throughout the 24-hour day. Divide the 24-hour day into T consecutive time periods, and obtain a graph of wind output power and local load. This allows the relationship between wind power generation and local load power to be determined at different time periods.

[0018] Then, the improved dung beetle optimization algorithm is used to perform coordinated control to optimize the objective function while satisfying the constraints, and the scheduling plan of wind turbines and thermal power units is obtained.

[0019] As a further improvement of the present technical solution, in step S1, establishing a mathematical model of wind turbine output power includes the following:

[0020] Establish a wind turbine model. For a given wind speed v, the output power p of the wind turbine is wt is defined as follows:

[0021] In formula (1), p wt is the output power of a single wind turbine, is the rated power, v in is the cut-in wind speed of the wind turbine, v r is the rated wind speed of the wind turbine, v out is the cut-out wind speed of the wind turbine.

[0022] As a further improvement of the present technical solution, in step S2.1, the objective function of the system is obtained by integrating the operating cost of the wind turbine set, the cost of the thermal power set, and the carbon emission cost on the power generation side. First, it is necessary to construct the objective function of the operating cost of the wind turbine set, the cost of the thermal power set, and the carbon emission cost on the power generation side; specifically, the following contents are included:

[0023] S2.1.1. The cost of wind power generation consists of three parts: the direct cost of purchasing wind power C d,wt (P l ), penalty costs caused by underestimating wind power output C ue,wt,l (P l ), the auxiliary service costs C generated by overestimating wind power output oe,wt,l (P l ); the total wind power generation cost C wt,l (P l ) is as follows: C wt,l (P l )=C d,wt (P l )+C ue,wt,l (P l )+C oe,wt,l (P l ),l=1,2,…,N l (2)

[0024] In formula (2), C d,wt (P l ) is the direct cost of purchasing wind power, C ue,wt,l (P l ) is the penalty cost caused by underestimating wind power output, Coe,wt,l (P l ) Ancillary service costs due to overestimation of wind power output; C d,wt (P l )=d wt,l p wt,l ,l=1,2,…,N l (3)

[0025] In formula (3), d wt,l is the direct cost coefficient of wind power, p wt,l is the planned output power of the first wind turbine;

[0026] In formula (4), K ue,wt,l is the underestimated coefficient of wind power, p wt,rate,l is the rated power of the first wind turbine, p wt,l is the planned output power of the first wind turbine, is the probability density function of wind speed;

[0027] In formula (5), K oe,wt,l The overestimated cost of wind power;

[0028] S2.1.2. Cost of thermal power units for:

[0029] In formula (6), is the power generation; a i 、b i 、c i is the cost coefficient of the generator set; d i 、e i is the cost coefficient taking into account the valve point effect; is the lower limit of the active power output of the i-th unit; N p is the number of power sources that generate electricity only;

[0030] S2.1.3 Carbon emission costs on the power generation side for:

[0031] In formula (7), N is the number of nodes; λ is the carbon emission cost coefficient; is the carbon emission responsibility that the generator at node i needs to bear:

[0032] In formula (8), L is the number of nodes; is the load carbon flow rate at node k,i. Since only N nodes are original nodes in the system and the last L nodes are newly added during the lossless process, k ranges from 1 to N. A two-way carbon emission responsibility sharing model is proposed. By introducing an adjustable parameter β in the range of 0-1, the β part of the network loss carbon emission is shared with the user, and the 1-β part is shared with the power generation side. The adjustable parameter β is jointly negotiated by the power generation side, the load side, and the operating organization.

[0033] S2.1.4. Total cost C total,G for:

[0034] In formula (9), C wt,l (P l ) is the total wind power generation cost, is the cost of thermal power units, is the carbon emission cost on the power generation side.

[0035] As a further improvement of this technical solution, in step 2.1, the constraints proposed include tidal flow equation constraints and carbon flow equation constraints, specifically including the following:

[0036] S2.2.1. The power flow equation constraints are:

[0037] In formula (10) and formula (11), are the reactive power and reactive load of the generator at the node at time t respectively; are the active load and reactive load of node i at time t; U i,t 、U j,t are the node voltages of node i and node j at time t; G ij 、B ij are the conductance and susceptance of branch ij (the line segment between node i and node j), respectively; θ ij,t is the phase angle difference between node j and node i at time t;

[0038] S2.2.2. The carbon flow equation constraint is:

[0039] In formula (12), ρ i,t , ρ j,t are the carbon potentials of nodes i and j at time t respectively; P ji,t is the active power of branch ij at time t; are the active power and carbon potential of the generator at node i at time t respectively.

[0040] As a further improvement of this technical solution, in step S3.1, the load-side low-carbon demand response model is proposed, and the objective function includes the load carbon emission cost and the demand response cost, and the calculation method is:

[0041] In formula (13), c diss The cost price of the unit load; D k,t is the load response at node k at time t, which is positive when the load is increased and negative when the load is decreased; is the carbon emission responsibility borne by the user at node k at time t; λ is the carbon emission cost coefficient;

[0042] In step S3.2, the constraints include the node load variation constraint and the load response balance constraint, and the calculation method is:

[0043] The node load variation constraint is:

[0044] Formula (14) ensures that the load fluctuation caused by demand response is stable within a certain range;

[0045] The load response balance constraint is:

[0046] Formula (15) ensures that each load is only shifted in different time periods.

[0047] As a further improvement of the present technical solution, in step S4, the original dung beetle optimization algorithm is improved, and the improved dung beetle optimization algorithm includes the following contents:

[0048] S4.1. Initialize algorithm parameters, including the maximum number of iterations T max , population size N, variable space dimension D, upper bound Ub and lower bound Lb of the optimization problem;

[0049] S4.2. Initial populationization: A population of dung beetles is divided into different roles according to the ratio of e:f:g:h, including e ball-rolling dung beetles for ball-rolling behavior, f female dung beetles for breeding behavior, g young dung beetles for foraging behavior, and h thief dung beetles for stealing behavior;

[0050] S4.3, the dung beetle updates its position in different ways according to its role;

[0051] S4.4, introduce the random walk strategy to enhance the local optimization ability of the algorithm, and calculate x best,t+1 , and perform random walk processing on it;

[0052] S4.5. Update the global optimal solution and the t+1 generation optimal solution;

[0053] S4.6, t=t+1, determine whether the maximum number of iterations T has been reached max If yes, then exit the loop and execute step S4.7; otherwise, return to step S4.5.

[0054] S4.7. Output the optimal solution x best And its most suitable function value F(x best );

[0055] S4.8. Utilize the dung beetle optimization algorithm to optimize and solve the objective function by executing the coordinated control of step S3 while satisfying the constraints; input relevant data on wind power, thermal power units, carbon cost, etc., substitute the objective function into the improved dung beetle optimization algorithm, and iterate to obtain the optimal cost and the scheduling plan of the wind turbine unit.

[0056] As a further improvement of this technical solution, in step S4.2, during the initial population formation, the good point set strategy is first introduced to initialize the dung beetle population. Compared with the randomly initialized population, the sequence generated by the good point set strategy is more uniform and the population covers a wider global range. The definition of the good point set is as follows:

[0057] Let GS be the S-dimensional Euclidean space unit cube. When γ∈GS, the good point set P is generated. n (k):

[0058] And the set P n (k) The deviation φ(n) between each point satisfies: φ(n)=C(γ,ε)n -1+ε (17)

[0059] In formula (16) and formula (17), C(γ,ε)n -1+ε is a constant related only to γ ​​and ε (ε is an arbitrary constant); P n (k) is the set of good points; γ is the good point; n is the number of points.

[0060] As a further improvement of the present technical solution, in step S4.3, the dung beetle updates its position in different ways according to different roles, specifically including the following steps:

[0061] S4.3.1. When the dung beetle has no obstacles in its way, it will use the sun for navigation while rolling the dung ball. During the rolling process, the position of the dung beetle is updated and can be expressed as: i (t+1)=x i (t)+a×h×x i (t-1)+bΔx (18) Δx=|x i (t)-X W| (19)

[0062] In formula (18) and formula (19), t represents the current number of iterations, x i (t) represents the position information of the i-th dung beetle at the t-th iteration, h∈(0,0.2] represents a constant, which represents the deflection coefficient, b represents a constant belonging to (0,1), a is a natural coefficient, assigned to -1 or 1, X W represents the global worst position, and Δx is used to simulate the change of light intensity;

[0063] S4.3.2. When the dung beetle encounters an obstacle and cannot move forward, it needs to dance to regain its forward direction. To simulate dancing behavior, a tangent function is used to obtain a new rolling direction. Once the dung beetle successfully determines a new direction, it should continue to roll the ball backward. Therefore, the position update of the rolling ball dung beetle is defined as follows: i (t+1)=x i (t)+tanθ|x i (t)-x i (t-1)| (20)

[0064] In formula (20), θ is the deflection angle, θ∈[0,π];

[0065] S4.3.3. For step S4.3.2, use the chaos mechanism strategy to improve the speed of the heuristic algorithm and update the deflection angle θ of the original dung beetle optimization algorithm based on the chaos mechanism: θ new =θ+δ t θ (21) δ t+1 =4δ t ×(1-δ t ) (twenty two)

[0066] In formula (21) and formula (22), δ t is the chaotic value of the t-th iteration, and the initial value δ1 is a random number between (0,1);

[0067] S4.3.4. Some grown-up dung beetles will emerge from the ground to look for food. These are called baby dung beetles. We also need to establish an optimal foraging area to guide the baby dung beetles' foraging and simulate the foraging process of these dung beetles in nature. Update the position of the baby dung beetles to: x i (t+1)=x i (t)+C1×(x i (t)-Lb b )+C2×(x i (t)-Ub b ) (23) R=1-t / T max(24) Lb b =max(X b ×(1-R),Lb) (25) Ub b =max(X b ×(1+R),Ub) (26)

[0068] In formula (23)-(26), x i (t) represents the position information of the i-th dung beetle at the n-th iteration, C1 represents a random number that obeys the normal distribution, C2 represents a random vector belonging to (0,1), X b is the global optimal position, Lb b and Ub b are the lower and upper bounds of the optimal foraging area, respectively, and Tmax represents the maximum number of iterations;

[0069] S4.3.5. In a population, there are some dung beetles that steal dung balls from other dung beetles. They are called thief dung beetles. The position update of thief dung beetles can be described as: i (t+1)=X b +S×g×(|x i (t)-X * |+|x i (t)-X b |) (27)

[0070] In formula (27), x i (t) represents the position information of the ith thief at the nth iteration, g is a random vector of size 1×D, which obeys the normal distribution, S represents a constant, X * represents the current local optimal position, X b Indicates the best place to compete for food;

[0071] S4.3.6. Use mutation strategy to improve the dung beetle algorithm:

[0072] In order to solve the problems of premature convergence and convergence accuracy of the dung beetle algorithm without changing the complexity of the original algorithm, the Gaussian mutation strategy is introduced. The corresponding Gaussian mutation operator is given to the dung beetle position iteration of Equation (18), Equation (20), Equation (23) and Equation (27), as shown in Equation (28):

[0073] In formula (28), x new (t+1) represents the position of the dung beetle in the next iteration; α is the attenuation factor; N(0,1) is the standard Gaussian distribution.

[0074] The mutation strategy can enable the dung beetle optimization algorithm to obtain sufficient disturbances in the early stage of the search to increase the global search capability of the algorithm, and reduce disturbances in the late stage of the algorithm to avoid the turbulence of the optimal solution and accelerate the convergence speed.

[0075] As a further improvement of this technical solution, in step S4.4, the random walk strategy is introduced to enhance the local optimization ability of the algorithm, and x is calculated. best,t+1 , and perform a random walk on it:

[0076] In formula (29), x′ best,t+1 is the optimal individual of the t+1 generation after the introduction of the random walk strategy; is the scaling factor, x t+1,g 、x t+1,w Generate two random solutions for t+1 generations.

[0077] As a further improvement of this technical solution, in step S4.5, the global optimal solution and the t+1 generation optimal solution are updated. The specific algorithm is:

[0078] In formula (30) and formula (31), F represents the most suitable function value.

[0079] The second object of the present invention is to provide a power system economic dispatch platform device, including a processor, a memory, and a computer program stored in the memory and running on the processor, and the processor is used to implement the steps of the above-mentioned power system economic dispatch method based on the improved dung beetle optimization algorithm when executing the computer program.

[0080] The third object of the present invention is to provide a computer-readable storage medium, which stores a computer program, and when the computer program is executed by a processor, it implements the steps of the above-mentioned power system economic dispatch method based on the improved dung beetle optimization algorithm.

[0081] Compared with the prior art, the present invention has the following beneficial effects:

[0082] 1. This power system economic dispatch method based on the improved dung beetle optimization algorithm addresses the intermittent and fluctuating characteristics of wind power generation. Therefore, a reasonable power generation plan is formulated to reduce the impact of these characteristics on power system dispatch, while also reducing a large amount of wind curtailment and improving power generation efficiency. Furthermore, considering the currently advocated "dual carbon" plan, the responsibility for power system carbon emissions is allocated to both the generation side and the user side, rather than just the generation side. This, on the one hand, can incentivize energy-saving and carbon-reduction behaviors of generators and users; on the other hand, it can balance the economic and environmental aspects of the power system and guide load-side users to use electricity in an environmentally friendly way, thereby further reducing the system's carbon emissions.

[0083] 2. This power system economic dispatch method based on the improved dung beetle optimization algorithm uses the improved dung beetle optimization algorithm to solve the system model. The improved algorithm has fast search capabilities and high optimization accuracy. Using the algorithm to optimize and solve the system model under the conditions of day-ahead wind power output power and load data can effectively improve the economic efficiency of the system, thereby achieving economic dispatch of the system.

[0084] 3. In the power system economic dispatch method based on the improved dung beetle optimization algorithm, the good point set strategy is introduced to initialize the dung beetle population, the chaos mechanism strategy is used to improve the speed of the algorithm, the Gaussian mutation strategy is used to solve problems such as algorithm premature maturity and convergence accuracy, and the random walk strategy is introduced to enhance the algorithm's optimization ability. BRIEF DESCRIPTION OF THE DRAWINGS

[0085] FIG1 is a flow chart of an exemplary method for economic dispatch of a power system according to the present invention;

[0086] FIG2 is a schematic diagram of an exemplary method for economic dispatch of a power system according to the present invention;

[0087] FIG3 is a control strategy diagram of an exemplary method for economic dispatch of a power system in the present invention;

[0088] FIG4 is a structural diagram of an exemplary electronic computer platform device in the present invention. DETAILED DESCRIPTION

[0089] The following will provide a clear and complete description of the technical solutions in the embodiments of the present invention in conjunction with the accompanying drawings. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. All other embodiments obtained by ordinary technicians in this field based on the embodiments of the present invention without making any creative efforts shall fall within the scope of protection of the present invention.

[0090] Example 1

[0091] As shown in Figures 1 to 3, this embodiment provides an economic dispatch method for a power system based on an improved dung beetle optimization algorithm. The structural diagram of the dispatch method is shown in Figure 1, which includes modeling wind turbines and establishing an economic dispatch model of wind and fire complementarity, establishing an economic indicator objective function, setting operating constraints for each unit of the system, processing day-ahead data, and solving the system model using the improved dung beetle optimization algorithm to obtain a day-ahead dispatch plan that takes economic efficiency into consideration.

[0092] Before implementing the dispatch method, a power system consisting of wind turbines, thermal power generators, and loads is constructed. Considering the results of carbon emission responsibility allocation, a two-stage source-grid-load low-carbon economic dispatch model is proposed for the power system. Finally, a system operation control strategy—an improved dung beetle optimization algorithm—is established with economic optimization as the goal. Specifically, as shown in Figure 2, a wind-thermal complementary economic dispatch model is established that considers carbon emission responsibilities on both the generation and load sides. This dispatch method considers both wind power generation (from renewable energy sources) and thermal power generation (from traditional sources), taking into account the randomness and volatility of wind power generation, and establishing a wind-thermal complementary economic dispatch model. Considering that traditional low-carbon economic dispatch of power systems only considers power plants as the sole bearer of carbon emission responsibilities, which is extremely unfair to the generation side, this approach builds on this foundation by considering both the generation and load sides' carbon emission responsibilities. In the first stage, the method optimizes the unit mix by minimizing both the generation cost and the generation-side carbon emission cost. In the second stage, the load distribution is optimized by minimizing the demand response cost and the user's carbon emission cost. Finally, the optimization model is solved using an improved dung beetle optimization algorithm. Four mechanisms are introduced to improve the original dung beetle optimization algorithm: a good point set strategy, a chaotic mechanism strategy, a mutation strategy, and a random walk strategy. Based on the above, a reasonable scheduling plan is formulated.

[0093] In this embodiment, the power system economic dispatch method specifically includes the following steps.

[0094] S1. Establish a mathematical model of wind turbine output power;

[0095] In this step, the mathematical model of wind turbine output power is established, including the following contents:

[0096] Establish a wind turbine model. For a given wind speed v, the output power p of the wind turbine is wt is defined as follows:

[0097] In formula (1), p wt is the output power of a single wind turbine, is the rated power, v in is the cut-in wind speed of the wind turbine, v ris the rated wind speed of the wind turbine, v out is the cut-out wind speed of the wind turbine.

[0098] S2. Propose a low-carbon economic unit portfolio optimization model for the power system. The objective function includes the wind turbine operating cost, thermal power unit cost, and carbon emission cost, and considers the constraints of the system power flow equation. The specific steps include:

[0099] S2.1. The objective function of the system is obtained by integrating the operating cost of wind turbines, the cost of thermal power units, and the carbon emission cost of power generation.

[0100] In this step, we first need to construct the objective functions for wind turbine operating costs, thermal power unit costs, and power generation side carbon emission costs; specifically, the following are included:

[0101] S2.1.1. The cost of wind power generation consists of three parts: the direct cost of purchasing wind power C d,wt (P l ), penalty costs caused by underestimating wind power output C ue,wt,l (P l ), the auxiliary service costs C generated by overestimating wind power output oe,wt,l (P l ); the total wind power generation cost C wt,l (P l ) is as follows: C wt,l (P l )=C d,wt (P l )+C ue,wt,l (P l )+C oe,wt,l (P l ),l=1,2,…,N l (2)

[0102] In formula (2), C d,wt (P l ) is the direct cost of purchasing wind power, C ue,wt,l (P l ) is the penalty cost caused by underestimating wind power output, C oe,wt,l (P l ) Ancillary service costs due to overestimation of wind power output; C d,wt (P l )=d wt,l p wt,l ,l=1,2,…,N l (3)

[0103] In formula (3), d wt,l is the direct cost coefficient of wind power, p wt,lis the planned output power of the first wind turbine;

[0104] In formula (4), K ue,wt,l is the underestimated coefficient of wind power, p wt,rate,l is the rated power of the first wind turbine, p wt,l is the planned output power of the first wind turbine, f pwt is the probability density function of wind speed;

[0105] In formula (5), K oe,wt,l The overestimated cost of wind power;

[0106] S2.1.2. Cost of thermal power units for:

[0107] In formula (6), is the power generation; a i 、b i 、c i is the cost coefficient of the generator set; d i 、e i is the cost coefficient taking into account the valve point effect; is the lower limit of the active power output of the i-th unit; N p is the number of power sources that generate electricity only;

[0108] S2.1.3 Carbon emission costs on the power generation side for:

[0109] In formula (7), N is the number of nodes; λ is the carbon emission cost coefficient; is the carbon emission responsibility that the generator at node i needs to bear:

[0110] In formula (8), L is the number of nodes; is the load carbon flow rate at node k,i. Since only N nodes are original nodes in the system and the last L nodes are newly added during the lossless process, k ranges from 1 to N. A two-way carbon emission responsibility sharing model is proposed. By introducing an adjustable parameter β in the range of 0-1, the β part of the network loss carbon emission is shared with the user, and the 1-β part is shared with the power generation side. The adjustable parameter β is jointly negotiated by the power generation side, the load side, and the operating organization.

[0111] S2.1.4. Total cost C total,G for:

[0112] In formula (9), C wt,l (P l) is the total wind power generation cost, is the cost of thermal power units, is the carbon emission cost on the power generation side.

[0113] S2.1. The proposed constraints include the tidal flow equation constraint and the carbon flow equation constraint;

[0114] This step specifically includes the following:

[0115] S2.2.1. The power flow equation constraints are:

[0116] In formula (10) and formula (11), are the reactive power and reactive load of the generator at the node at time t respectively; are the active load and reactive load of node i at time t; U i,t 、U j,t are the node voltages of node i and node j at time t; G ij 、B ij are the conductance and susceptance of branch ij (i.e., the line segment between node i and node j), respectively; θ ij,t is the phase angle difference between node j and node i at time t;

[0117] S2.2.2. The carbon flow equation constraint is:

[0118] In formula (12), ρ i,t , ρ j,t are the carbon potentials of nodes i and j at time t respectively; P ji,t is the active power of branch ij at time t; are the active power and carbon potential of the generator at node i at time t respectively.

[0119] S3. The proposed load-side low-carbon demand response model has an objective function including the load carbon emission cost and the demand response cost, and takes into account the constraints on the load side. It has the following steps:

[0120] S3.1. The proposed load-side low-carbon demand response model has an objective function including load carbon emission costs and demand response costs;

[0121] In this step, the calculation method is:

[0122] In formula (13), c diss The cost price of the unit load; D k,t is the load response at node k at time t, which is positive when the load is increased and negative when the load is decreased; is the carbon emission responsibility borne by the user at node k at time t; λ is the carbon emission cost coefficient;

[0123] S3.2, the proposed constraints include node load variation constraints and load response balance constraints;

[0124] In this step, the calculation method is:

[0125] The node load variation constraint is:

[0126] Formula (14) ensures that the load fluctuation caused by demand response is stable within a certain range;

[0127] The load response balance constraint is:

[0128] Formula (15) ensures that each load is only shifted in different time periods.

[0129] S4. The original dung beetle optimization algorithm is improved by introducing a good point set strategy to initialize the dung beetle population, using a chaotic mechanism strategy to improve the speed of the heuristic algorithm, introducing a Gaussian mutation strategy to solve the problems of premature maturity and convergence accuracy of the algorithm, and introducing a random walk strategy enhancement algorithm for local optimization, thereby obtaining an improved dung beetle optimization algorithm and enhancing the initialization and search capabilities of the algorithm; the control strategy diagram is shown in Figure 3;

[0130] Process the day's wind and load data, i.e., record the data every 15-20 minutes for 24 hours a day, and divide the 24 hours into T consecutive time periods. Obtain a wind output power and local load curve, and determine the relationship between wind power generation and local load power in different time periods. In this embodiment, it is preferred to record the time every 15 minutes, and divide the 24 hours a day into T (T = 96) time periods.

[0131] Then, the improved dung beetle optimization algorithm is used to perform coordinated control to optimize the objective function while satisfying the constraints, and the scheduling plan of wind turbines and thermal power units is obtained.

[0132] In this step, the original dung beetle optimization algorithm is improved. The improved dung beetle optimization algorithm includes the following contents:

[0133] S4.1. Initialize algorithm parameters, including the maximum number of iterations T max , population size N, variable space dimension D, upper bound Ub and lower bound Lb of the optimization problem;

[0134] S4.2. Initial populationization: A population of dung beetles is divided into different roles according to the ratio of e:f:g:h, including e ball-rolling dung beetles for ball-rolling, f female dung beetles for breeding, g young dung beetles for foraging, and h thief dung beetles for stealing. For example, suppose a population of dung beetles is divided into different roles according to the ratio of 6:6:7:11. That is, among 30 individuals, 6 dung beetles are used for ball-rolling, 6 dung beetles are used for breeding, 7 dung beetles are defined as young dung beetles for foraging, and the remaining 11 dung beetles are defined as thieves for stealing.

[0135] In this step, during the initial population formation, the good point set strategy is first introduced to initialize the dung beetle population. Compared with the randomly initialized population, the sequence generated by the good point set strategy is more uniform and the population covers a wider global range. The definition of the good point set is as follows:

[0136] Let GS be the S-dimensional Euclidean space unit cube. When γ∈GS, the good point set P is generated. n (k):

[0137] And the set P n (k) The deviation φ(n) between each point satisfies: φ(n)=C(γ,ε)n -1+ε (17)

[0138] In formula (16) and formula (17), C(γ,ε)n -1+ε is a constant related only to γ ​​and ε (ε is an arbitrary constant); P n (k) is the set of good points; γ is the good point; n is the number of points.

[0139] S4.3. The dung beetle updates its position in different ways according to its role. The steps are as follows:

[0140] S4.3.1. When the dung beetle has no obstacles in its way, it will use the sun for navigation while rolling the dung ball. During the rolling process, the position of the dung beetle is updated and can be expressed as: i (t+1)=x i (t)+a×h×x i (t-1)+bΔx (18) Δx=|x i (t)-X W | (19)

[0141] In formula (18) and formula (19), t represents the current number of iterations, x i(t) represents the position information of the i-th dung beetle at the t-th iteration, h∈(0,0.2] represents a constant, which represents the deflection coefficient, b represents a constant belonging to (0,1), a is a natural coefficient, assigned to -1 or 1, X W represents the global worst position, Δx is used to simulate the change of light intensity; in this case, h = 0.1, b = 0.3;

[0142] S4.3.2. When the dung beetle encounters an obstacle and cannot move forward, it needs to dance to regain its forward direction. To simulate dancing behavior, the tangent function is used to obtain a new rolling direction. It should be noted that only the value of the tangent function defined on the interval [0, π] needs to be considered. Once the dung beetle successfully determines a new direction, it should continue to roll the ball backward. Therefore, the position update of the rolling ball dung beetle is defined as follows: i (t+1)=x i (t)+tanθ|x i (t)-x i (t-1)| (20)

[0143] In formula (20), θ is the deflection angle, θ∈[0,π];

[0144] S4.3.3. For step S4.3.2, use the chaos mechanism strategy to improve the speed of the heuristic algorithm and update the deflection angle θ of the original dung beetle optimization algorithm based on the chaos mechanism: θ new =θ+δ t θ (21) δ t+1 =4δ t ×(1-δ t ) (twenty two)

[0145] In formula (21) and formula (22), δ t is the chaotic value of the t-th iteration, and the initial value δ1 is a random number between (0,1);

[0146] S4.3.4. Some grown-up dung beetles will emerge from the ground to look for food. These are called baby dung beetles. In addition, we need to establish an optimal foraging area to guide the baby dung beetles' foraging and simulate the foraging process of these dung beetles in nature. Update the position of the baby dung beetles to: x i (t+1)=x i (t)+C1×(x i (t)-Lb b )+C2×(x i (t)-Ub b ) (23) R=1-t / T max (24) Lb b=max(X b ×(1-R),Lb) (25) Ub b =max(X b ×(1+R),Ub) (26)

[0147] In formula (23)-(26), x i (t) represents the position information of the i-th dung beetle at the n-th iteration, C1 represents a random number that obeys the normal distribution, C2 represents a random vector belonging to (0,1), X b is the global optimal position, Lb b and Ub b are the lower and upper bounds of the optimal foraging area, respectively, and Tmax represents the maximum number of iterations;

[0148] S4.3.5. In a population, there are some dung beetles that steal dung balls from other dung beetles. They are called thief dung beetles. The position update of thief dung beetles can be described as: i (t+1)=X b +S×g×(|x i (t)-X * |+|x i (t)-X b |) (27)

[0149] In formula (27), x i (t) represents the position information of the ith thief at the nth iteration, g is a random vector of size 1×D, which obeys the normal distribution, S represents a constant, X * represents the current local optimal position, X b Indicates the best place to compete for food;

[0150] S4.3.6. Use mutation strategy to improve the dung beetle algorithm:

[0151] In order to solve the problems of premature convergence and convergence accuracy of the dung beetle algorithm without changing the complexity of the original algorithm, the Gaussian mutation strategy is introduced. The corresponding Gaussian mutation operator is given to the dung beetle position iteration of Equation (18), Equation (20), Equation (23) and Equation (27), as shown in Equation (28):

[0152] In formula (28), x new (t+1) represents the position of the dung beetle in the next iteration; α is the attenuation factor; N(0,1) is the standard Gaussian distribution.

[0153] The mutation strategy can enable the dung beetle optimization algorithm to obtain sufficient disturbances in the early stage of the search to increase the global search capability of the algorithm, and reduce disturbances in the late stage of the algorithm to avoid the turbulence of the optimal solution and accelerate the convergence speed.

[0154] S4.4, introduce the random walk strategy to enhance the local optimization ability of the algorithm, and calculate x best,t+1 , and perform a random walk on it:

[0155] In formula (29), x′ best,t+1 is the optimal individual of the t+1 generation after the introduction of the random walk strategy; is the scaling factor, x t+1,g 、x t+1,w Generate two random solutions for t+1 generations.

[0156] S4.5. Update the global optimal solution and the t+1 generation optimal solution. The specific algorithm is:

[0157] In formula (30) and formula (31), F represents the most suitable function value.

[0158] S4.6, t=t+1, determine whether the maximum number of iterations T has been reached max If yes, then exit the loop and execute step S4.7; otherwise, return to step S4.5.

[0159] S4.7. Output the optimal solution x best And its most suitable function value F(x best );

[0160] S4.8. Utilize the dung beetle optimization algorithm to optimize and solve the objective function by executing the coordinated control of step S3 while satisfying the constraints; input relevant data on wind power, thermal power units, carbon cost, etc., substitute the objective function into the improved dung beetle optimization algorithm, and iterate to obtain the optimal cost and the scheduling plan of the wind turbine unit.

[0161] In addition, preferably, the day-ahead wind and load data are processed, that is, the 24-hour day is divided into T (T = 96) time periods, and the data is recorded every 15 minutes to obtain the wind power load diagram and local load curve diagram. The wind power and local load curve diagrams are obtained from the wind power load diagram. From the wind power and local load curve diagrams, it can be determined whether the power in each time period is surplus or insufficient, and the relationship between the wind turbine power generation and the local load power in different time periods can be determined for the implementation of the coordinated control strategy. On this basis, considering the carbon emission responsibilities of the generation side and the load side, a two-way carbon emission responsibility allocation model is proposed. By introducing an adjustable parameter β in the range of 0-1, the β part of the network loss carbon emission is allocated to the user, and the 1-β part is allocated to the generation side. Using the improved dung beetle algorithm, the coordinated control strategy of step S4 is executed under the condition of meeting the constraint conditions to optimize and solve the objective functions in steps S2 and S3, and obtain the day-ahead scheduling plan for wind power generation.

[0162] As shown in FIG4 , this embodiment further provides a power system economic dispatch platform device, which includes a processor, a memory, and a computer program stored in the memory and running on the processor.

[0163] The processor includes one or more processing cores, and the processor is connected to the memory through a bus. The memory is used to store program instructions. When the processor executes the program instructions in the memory, the steps of the power system economic dispatch method based on the improved dung beetle optimization algorithm are implemented.

[0164] Alternatively, the memory may be implemented by any type of volatile or non-volatile memory device or a combination thereof, such as static random access memory (SRAM), electrically erasable programmable read-only memory (EEPROM), erasable programmable read-only memory (EPROM), programmable read-only memory (PROM), read-only memory (ROM), magnetic memory, flash memory, magnetic disk or optical disk.

[0165] In addition, the present invention also provides a computer-readable storage medium, which stores a computer program. When the computer program is executed by a processor, it implements the steps of the above-mentioned power system economic dispatch method based on the improved dung beetle optimization algorithm.

[0166] Optionally, the present invention also provides a computer program product comprising instructions, which, when executed on a computer, enables the computer to execute the steps of the above-mentioned power system economic dispatch method based on the improved dung beetle optimization algorithm.

[0167] Those skilled in the art will understand that the process of implementing all or part of the steps of the above embodiments can be completed by hardware, or can be completed by a program to instruct the relevant hardware. The program can be stored in a computer-readable storage medium, and the above-mentioned storage medium can be a read-only memory, a disk or an optical disk, etc.

[0168] The above shows and describes the basic principles, main features, and advantages of the present invention. Those skilled in the art should understand that the present invention is not limited to the above embodiments. The above embodiments and descriptions are merely preferred examples of the present invention and are not intended to limit the present invention. Various changes and improvements may be made to the present invention without departing from the spirit and scope of the present invention. Such changes and improvements fall within the scope of the present invention. The scope of protection claimed in the present invention is defined by the appended claims and their equivalents.

Claims

1. A method for economic dispatch of power system based on improved dung beetle optimization algorithm, characterized in that: Firstly, a power system consisting of wind turbines, thermal power generators and loads is constructed. The carbon emission responsibility sharing results are considered, and the user-side carbon emission cost is used as a signal to respond to the user's low-carbon demand. A two-stage power system source-grid-load low-carbon economic dispatch model is proposed. Finally, the system operation control strategy - the improved dung beetle optimization algorithm - is set with economic optimality as the goal. The specific steps include the following: S1. Establish a mathematical model of wind turbine output power; S2. A low-carbon economic unit portfolio optimization model for the power system is proposed. The objective function includes the wind turbine operating cost, thermal power unit cost, and carbon emission cost, and considers the constraints of the system power flow equation. The specific steps include: S2.

1. The objective function of the system is obtained by integrating the operation cost of wind turbines, the cost of thermal power units, and the carbon emission cost of the power generation side; S2.

1. The proposed constraints include tidal equation constraints and carbon flow equation constraints; S3. The proposed load-side low-carbon demand response model has an objective function including the load carbon emission cost and the demand response cost, and takes into account the constraints on the load side, and has the following steps: S3.1, the proposed load-side low-carbon demand response model, the objective function includes load carbon emission cost and demand response cost; S3.2, the proposed constraints include node load variation constraints and load response balance constraints; S4. Improve the original dung beetle optimization algorithm and introduce the best point set strategy to initialize the dung beetle population; process the day-ahead wind and load data, that is, record the data at regular intervals for 24 hours a day, divide the 24 hours a day into T continuous time periods, obtain the wind output power and local load curve, and determine the relationship between the wind power generation power and the local load power in different time periods; then use the improved dung beetle optimization algorithm to perform coordinated control under the condition of satisfying the constraints to optimize and solve the objective function, and obtain the scheduling plan of the wind turbine and thermal power unit.

2. The power system economic dispatch method based on the improved dung beetle optimization algorithm according to claim 1 is characterized in that: In step S1, establishing a mathematical model of wind turbine output power includes the following contents: Establish a wind turbine model. For a given wind speed v, the output power p of the wind turbine is wt is defined as follows: In formula (1), p wt is the output power of a single wind turbine, is the rated power, v in is the cut-in wind speed of the wind turbine, v r is the rated wind speed of the wind turbine, v out is the cut-out wind speed of the wind turbine.

3. The power system economic dispatch method based on the improved dung beetle optimization algorithm according to claim 2 is characterized in that: In step S2.1, the objective function of the system is obtained by combining the operation cost of the wind turbine set, the cost of the thermal power set, and the carbon emission cost on the power generation side. First, the objective function of the operation cost of the wind turbine set, the cost of the thermal power set, and the carbon emission cost on the power generation side needs to be constructed; specifically, the following contents are included: S2.1.

1. The cost of wind power generation consists of three parts: the direct cost of purchasing wind power C d,wt (P l ), penalty costs caused by underestimating wind power output C ue,wt,l (P l ), the auxiliary service costs C generated by overestimating wind power output oe,wt,l (P l ), then the total wind power generation cost C wt,l (P l )as follows: C wt,l (P l )=C d,wt (P l )+C ue,wt,l (P l )+C oe,wt,l (P l ),l=1,2,…,N l (2) In formula (2), C d,wt (P l ) is the direct cost of purchasing wind power, C ue,wt,l (P l ) is the penalty cost caused by underestimating wind power output, C oe,wt,l (P l ) ancillary service costs incurred to overestimate wind power output; C d,wt (P l )=d wt,l p wt,l ,l=1,2,…,N l (3) In formula (3), d wt,l is the direct cost coefficient of wind power, p wt,l is the planned output power of the first wind turbine; In formula (4), K ue,wt,l is the underestimation factor of wind power, p wt,rate,l is the rated power of the first wind turbine, p wt,l is the planned output power of the first wind turbine, is the probability density function of wind speed; In formula (5), K oe,wt,l for the overestimated costs of wind power; S2.1.

2. Cost of thermal power units for: In formula (6), is the power generation; a i 、b i 、c i is the cost coefficient of the generator set; d i 、e i is the cost coefficient taking into account the valve point effect; is the lower limit of the active output of the i-th unit; N p is the number of power sources for power generation only; S2.1.3 Carbon emission costs on the power generation side for: In formula (7), N is the number of nodes; λ is the carbon emission cost coefficient; is the carbon emission responsibility that the generator at node i needs to bear: In formula (8), L is the number of nodes; is the load carbon flow rate at node k,i. Since only N nodes are original nodes of the system and the last L nodes are newly added nodes in the lossless process, k ranges from 1 to N. A two-way carbon emission responsibility sharing model is proposed. By introducing an adjustable parameter β in the range of 0-1, the β part of the network loss carbon emission is shared by the user, and the 1-β part is shared by the power generation side. The adjustable parameter β is jointly negotiated by the power generation side, the load side and the operating organization. S2.1.

4. Total cost C total,G for: In formula (9), C wt,l (P l ) is the total wind power generation cost, is the cost of thermal power unit, is the carbon emission cost on the power generation side.

4. The power system economic dispatch method based on the improved dung beetle optimization algorithm according to claim 3 is characterized in that: In step 2.1, the constraints proposed include the tidal equation constraints and the carbon flow equation constraints, which specifically include the following: S2.2.1, the power flow equation constraints are: In formula (10) and formula (11), are the reactive power and reactive load of the generator at the node at time t respectively; are the active load and reactive load of node i at time t respectively; U i,t , U j,t are the node voltages of node i and node j at time t; G ij , B ij are the conductance and susceptance of branch ij respectively; θ ij,t is the phase angle difference between node j and node i at time t; S2.2.2, Carbon flow equation constraint condition is: In formula (12), ρ i,t , j,t are the carbon potentials of nodes i and j at time t respectively; P ji,t is the active power of branch ij at time t; are the active power and carbon potential of the generator at node i at time t respectively.

5. The power system economic dispatch method based on the improved dung beetle optimization algorithm according to claim 4 is characterized in that: In step S3.1, the proposed load-side low-carbon demand response model has an objective function including load carbon emission cost and demand response cost, and the calculation method is: In formula (13), c diss To respond to the cost price per unit load; D k,t is the load response at node k at time t, which is positive when the load is increased and negative when the load is decreased; is the carbon emission responsibility borne by the user at node k at time t; λ is the carbon emission cost coefficient; In step S3.2, the constraints include node load variation constraints and load response balance constraints, and the calculation method is: The node load variation constraint is: Formula (14) ensures that the load fluctuation caused by demand response is stable within a certain range; The load response balance constraint is: Formula (15) ensures that each load is only shifted in different time periods.

6. The power system economic dispatch method based on the improved dung beetle optimization algorithm according to claim 5 is characterized in that: In step S4, the original dung beetle optimization algorithm is improved, and the improved dung beetle optimization algorithm includes the following contents: S4.

1. Initialize algorithm parameters, including the maximum number of iterations T max , population size N, variable space dimension D, upper bound Ub and lower bound Lb of the optimization problem; S4.

2. Initial population: A population is divided into different roles according to the ratio of e:f:g:h, including e ball-rolling dung beetles for ball-rolling behavior, f female dung beetles for breeding behavior, g small dung beetles for foraging behavior, and h thief dung beetles for stealing behavior; S4.3, the dung beetle updates its position in different ways according to different roles; S4.4, introduce the random walk strategy to enhance the local optimization ability of the algorithm, and calculate x best,t+1 ,and Perform random walk treatment on it; S4.5, update the global optimal solution and the t+1 generation optimal solution; S4.6, t=t+1, determine whether the maximum number of iterations T is reached max If yes, then jump out of the loop and execute step S4.7, otherwise return to step S4.5; S4.

7. Output the optimal solution x best and its most suitable function value F(x best ); S4.

8. Utilize the dung beetle optimization algorithm to optimize and solve the objective function by executing the coordinated control of step S3 while satisfying the constraints; input the relevant data of wind, thermal power unit, and carbon cost, substitute the objective function into the improved dung beetle optimization algorithm, and iterate to obtain the optimal cost and the dispatch plan of the wind turbine.

7. The power system economic dispatch method based on the improved dung beetle optimization algorithm according to claim 6 is characterized in that: In step S4.2, during the initial population formation, the good point set strategy is first introduced to initialize the dung beetle population. The definition of the good point set is as follows: Let GS be the S-dimensional Euclidean space unit cube. When γ∈GS, the good point set P is generated. n (k): And the set P n (k) The deviation φ(n) between the points satisfies: φ(n)=C(γ,ε)n -1+ε (17) In formula (16) and formula (17), C(γ,ε)n -1+ε is a constant related only to γ ​​and ε; P n (k) is the set of good points; γ is the good point; n is the number of points.

8. The power system economic dispatch method based on the improved dung beetle optimization algorithm according to claim 7 is characterized in that: In step S4.3, the dung beetle updates its position in different ways according to different roles, which specifically includes the following steps: S4.3.

1. When the dung beetle has no obstacles to move forward, it will use the sun to navigate while rolling the dung ball. During the rolling process, the position of the rolling ball dung beetle is updated, which can be expressed as: x i (t+1)=x i (t)+a×h×x i (t-1)+bΔx (18) Δx=|x i (t)-X W | (19) In formula (18) and formula (19), t represents the current iteration number, x i (t) represents the position information of the i-th dung beetle at the t-th iteration, h∈(0,0.2] represents a constant, which represents the deflection coefficient, b represents a constant belonging to (0,1), a is a natural coefficient, assigned to -1 or 1, X W represents the global worst position, and Δx is used to simulate the change of light intensity; S4.3.

2. When the dung beetle encounters an obstacle and cannot move forward, it needs to regain its forward direction by dancing. In order to simulate dancing behavior, a tangent function is used to obtain a new rolling direction. Once the dung beetle successfully determines a new direction, it should continue to roll the ball backward. Therefore, the position update of the rolling ball dung beetle is defined as follows: x i (t+1)=x i (t)+tanθ|x i (t)-x i (t-1)| (20) In formula (20), θ is the deflection angle, θ∈[0,π]; S4.3.

3. For step S4.3.2, a chaos mechanism strategy is used to improve the speed of the heuristic algorithm, and the deflection angle θ of the original dung beetle optimization algorithm is updated based on the chaos mechanism: i new =θ+δ t i (21) d t+1 =4d t ×(1-d t ) (22) In formula (21) and formula (22), δ t is the chaotic value of the tth iteration, and the initial value δ1 is a random number between (0,1); S4.3.

4. Some grown-up dung beetles will come out of the ground to look for food. They are called small dung beetles. It is also necessary to establish the best foraging area to guide the foraging of small dung beetles and simulate the foraging process of these dung beetles in nature. Update the position of the small dung beetles to: x i (t+1)=x i (t)+C1×(x i (t)-Lb b )+C2×(x i (t)-Ub b ) (23) R=1-t / T max (24) Lb b =max (X b ×(1-R),Lb) (25) Ub b =max (X b ×(1+R),Ub) (26) In formula (23) to formula (26), x i (t) represents the position information of the i-th dung beetle at the n-th iteration, C1 represents a random number that obeys a normal distribution, C2 represents a random vector belonging to (0,1), and X b is the global optimal position, Lb b and Ub b are the lower and upper bounds of the optimal foraging area, respectively, and Tmax represents the maximum number of iterations; S4.3.

5. In a population, there are some dung beetles that steal dung balls from other dung beetles. They are called thief dung beetles. The position update of thief dung beetles can be described as: x i (t+1)=X b +S×g×(|x i (t)-X * |+|x i (t)-X b |) (27) In formula (27), x i (t) represents the position information of the ith thief at the nth iteration, g is a random vector of size 1×D, which obeys the normal distribution, S represents a constant, and X * represents the current local optimal position, X b Indicates the best place to compete for food; S4.3.

6. Use mutation strategy to improve the dung beetle algorithm: The Gaussian mutation strategy is introduced, and the corresponding Gaussian mutation operator is given to the dung beetle position iteration of equations (18), (20), (23) and (27), as shown in equation (28): In formula (28), x new (t+1) represents the position of the dung beetle in the next iteration; α is the attenuation factor; N(0,1) is the standard Gaussian distribution.

9. The power system economic dispatch method based on the improved dung beetle optimization algorithm according to claim 8 is characterized in that: In step S4.4, the random walk strategy is introduced to enhance the local optimization ability of the algorithm, and x is calculated. best,t+1 , and subject it to a random walk: In formula (29), x′ best,t+1 is the optimal individual of the t+1 generation after the introduction of the random walk strategy; To shrink Release factor, x t+1,g 、x t+1,w There are two random solutions for t+1 generations.

10. The power system economic dispatch method based on the improved dung beetle optimization algorithm according to claim 9 is characterized in that: In step S4.5, the global optimal solution and the t+1 generation optimal solution are updated. The specific algorithm is: In formula (30) and formula (31), F represents the most suitable function value.

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