Micro-grid optimal scheduling method and system based on improved electric eel foraging optimization algorithm

Abstract

The present application relates to the technical field of micro-grid optimization, and discloses a micro-grid optimization scheduling method and system based on an improved electric eel foraging optimization algorithm, which comprises constructing a target function with the minimum total operation cost of a micro-grid as the target, and establishing constraint conditions that the micro-grid needs to satisfy during operation; the micro-grid optimization scheduling model composed of the target function and the constraint conditions is solved based on the improved electric eel foraging optimization algorithm to generate an optimal scheduling scheme; the algorithm of the present application restructures the optimization mechanism in depth: in the initialization stage, an elite reverse learning strategy is adopted to mine potential high-quality solutions, significantly enhancing population diversity; in the migration and hunting stage of core evolution, a Cauchy mutation operator is introduced in combination with a tournament selection mechanism to improve the robustness of the algorithm while effectively avoiding premature convergence; in addition, a vertical and horizontal crossover strategy is fused to dynamically coordinate the algorithm behavior, achieving a precise balance between local search precision and global development capability.

Description

Technical Field

[0001] This invention relates to the field of microgrid optimization technology, specifically to a microgrid optimization scheduling method and system based on an improved electric eel foraging optimization algorithm. Background Technology

[0002] With the acceleration of global industrialization and sustained socio-economic growth, the excessive consumption of traditional fossil fuels has triggered a severe energy crisis and environmental pollution, making global warming a major challenge facing humanity. Against this backdrop, renewable energy sources, represented by wind and solar power, have gradually become the core driving force for energy transformation due to their clean and green characteristics. However, distributed power sources exhibit significant intermittency and volatility, and direct connection to the main power grid can impact grid stability. Microgrids, as independent power generation and distribution systems that integrate distributed power sources, energy storage devices, loads, and control and protection devices, can effectively achieve localized consumption and flexible management of distributed energy, becoming a key technological means to solve the grid connection challenges of renewable energy and improve energy efficiency.

[0003] In the operation of microgrid systems, optimized scheduling is a crucial aspect of ensuring their economical and reliable operation. Microgrid systems predict the output of photovoltaic and wind turbines based on meteorological data, and combine this with user load demand curves and time-of-use pricing policies. Under the premise of satisfying a series of physical and operational constraints such as power balance, equipment output limits, and ramp rates, algorithms are used to rationally allocate power from micro-turbines, fuel cells, batteries, and power interacting with the main grid, thereby achieving the goal of low-carbon and economical system operation.

[0004] The core of optimal scheduling lies in finding the optimal operating strategy that balances economy and environmental protection under complex and ever-changing constraints. However, in practical microgrid scheduling applications, traditional optimization algorithms have certain inherent defects due to the high-dimensionality, nonlinearity, and multiple constraints of the optimization model. These algorithmic shortcomings severely restrict the accuracy and stability of the solution, making it difficult for the microgrid scheduling scheme to achieve true global optimum. This results in high operating costs and an inability to effectively reduce carbon emissions during actual operation. While existing intelligent optimization algorithms can partially alleviate the solution difficulties, they still struggle to balance the breadth of the global search and the depth of local exploration when dealing with high-dimensional, nonlinear, and complex models like microgrid scheduling. They generally suffer from slow convergence speed and insufficient solution accuracy, thus affecting the accuracy of the scheduling results and restricting the economy and cleanliness of microgrid operation. Summary of the Invention

[0005] The purpose of this invention is to provide a microgrid optimization scheduling method and system based on an improved electric eel foraging optimization algorithm, so as to solve the problems mentioned in the background art.

[0006] To achieve the above objectives, the present invention provides the following technical solution:

[0007] A microgrid optimization scheduling method based on an improved electric eel foraging optimization algorithm, the method comprising:

[0008] An objective function is constructed with the goal of minimizing the total operating cost of the microgrid, and constraints that the microgrid must satisfy during operation are established. The total operating cost includes operating costs and environmental governance costs.

[0009] The microgrid optimization scheduling model consisting of the objective function and constraints is solved based on the improved electric eel foraging optimization algorithm to generate the optimal scheduling scheme;

[0010] The improved electric eel foraging optimization algorithm is based on the standard electric eel foraging optimization algorithm. It introduces an elite back learning strategy for population initialization and incorporates Cauchy mutation operator, tournament selection mechanism and cross-linking strategy during the iterative optimization process of the algorithm.

[0011] As a further aspect of the present invention, the process of solving the microgrid optimal scheduling model using the improved electric eel foraging optimization algorithm includes:

[0012] An initial population is generated based on the elite reverse learning strategy, the fitness value of each electric eel is calculated, and the initial global optimal solution is determined.

[0013] Enter the main loop and calculate the energy factor based on the current iteration number; for each individual in the population, select to enter the interaction phase, rest phase, migration phase or hunting phase to update the position based on the magnitude of the energy factor;

[0014] Specifically, during the migration phase, a hybrid mutation strategy combining differential evolution and the Cauchy mutation operator is introduced for position updates; during the hunting phase, the tournament selection mechanism is introduced for position updates.

[0015] After updating the individual position, the fitness value is recalculated, and the cross-sectional strategy is introduced to optimize the global optimal solution, and the global optimal solution is updated.

[0016] Determine if the maximum number of iterations has been reached. If so, output the global optimal solution and its corresponding fitness value.

[0017] As a further aspect of the present invention, the formula for generating the initial population using the elite reverse learning strategy is:

[0018] ;

[0019] in, It is the opposite of the solution for elite individuals; X max and Xmin These are the lower and upper bounds of the solution, respectively; X i It represents the current position of the individual.

[0020] As a further aspect of the present invention, a hybrid mutation strategy is introduced during the migration phase, and its position update formula is as follows:

[0021] ;

[0022] Among them, X i,q1 X i,q2 and X i,q3 is three distinct individual positions randomly selected from the population; cauchy is the Cauchy mutation operator; tan is the tangent function; r is a random number in the range (0,1).

[0023] As a further aspect of the present invention, the process of introducing a tournament selection mechanism for position updating during the hunting phase includes:

[0024] First, the potential new locations of the current individual are calculated based on the behavioral characteristics of the hunting phase;

[0025] Individuals are randomly selected from the remaining population to form a competition group, and the individual with the best fitness is selected as the winner through comparison.

[0026] The fitness of the potential new position is compared with that of the winner. If the fitness of the potential new position is better, the new position is retained as the updated individual position; otherwise, the winner is used as the updated individual position.

[0027] As a further aspect of this invention, a cross-sectional strategy is introduced to optimize the global optimal solution, specifically including:

[0028] Horizontal crossover: Arithmetic crossover is performed between the global optimal solution and other individuals in the population to generate new offspring individuals, while retaining individuals with better fitness.

[0029] Vertical crossover: Information is reorganized across different dimensions of the global optimal solution to generate new offspring individuals, while retaining individuals with better fitness.

[0030] As a further embodiment of the present invention, the constraints include: power balance constraints, output constraints of each power generation unit, ramp rate constraints of the controllable power generation unit, state of charge and charge / discharge power constraints of the energy storage battery, and power constraints of the interconnection line between the microgrid and the main grid.

[0031] This invention also provides a microgrid optimization scheduling system based on an improved electric eel foraging optimization algorithm, the system comprising:

[0032] The model building module is used to construct an objective function with the goal of minimizing the total operating cost of the microgrid, and to establish the constraints that the microgrid must meet during operation. The total operating cost includes operating costs and environmental governance costs.

[0033] The solution module is used to solve the microgrid optimization scheduling model composed of the objective function and constraints based on the improved electric eel foraging optimization algorithm, and generate the optimal scheduling scheme.

[0034] The improved electric eel foraging optimization algorithm is based on the standard electric eel foraging optimization algorithm. It introduces an elite back learning strategy for population initialization and incorporates Cauchy mutation operator, tournament selection mechanism and cross-linking strategy during the iterative optimization process of the algorithm.

[0035] Compared with existing technologies, the beneficial effects of this invention are as follows: To overcome the defect of traditional algorithms being prone to getting trapped in local optima when dealing with high-dimensional nonlinear scheduling models, this algorithm has undergone a deep reconstruction of the optimization mechanism: In the initialization phase, an elite reverse learning strategy is adopted to mine potential high-quality solutions, significantly enhancing population diversity; in the migration and hunting phases of core evolution, the Cauchy mutation operator combined with a tournament selection mechanism is introduced, which effectively avoids premature convergence while improving the robustness of the algorithm; in addition, the algorithm behavior is dynamically coordinated by integrating the cross-sectional and cross-sectional strategies, achieving a precise balance between local search accuracy and global development capability, providing reliable technical support and decision-making basis for microgrids to achieve low-cost, low-carbon emission, and efficient collaborative scheduling. Attached Figure Description

[0036] To more clearly illustrate the technical solutions in the embodiments of the present invention, the accompanying drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the accompanying drawings described below are only some embodiments of the present invention.

[0037] Figure 1 This is a schematic diagram of a microgrid system structure provided in an embodiment of the present invention.

[0038] Figure 2 The flowchart of the EEFO algorithm provided in the embodiment of the present invention.

[0039] Figure 3 The load demand and renewable energy output curves provided for embodiments of the present invention.

[0040] Figure 4 The purchase and sale price curve provided for embodiments of the present invention.

[0041] Figure 5 The microgrid power balance diagram obtained by the IEEFO algorithm provided in this embodiment of the invention.

[0042] Figure 6Convergence curves of five algorithms provided in embodiments of the present invention. Detailed Implementation

[0043] To make the technical problems to be solved, the technical solutions, and the beneficial effects of the present invention clearer, the present invention will be further described in detail below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely illustrative of the present invention and are not intended to limit the present invention.

[0044] In this embodiment of the invention, a microgrid optimization scheduling method based on an improved electric eel foraging optimization algorithm is provided, the method comprising:

[0045] An objective function is constructed with the goal of minimizing the total operating cost of the microgrid, and constraints that the microgrid must satisfy during operation are established. The total operating cost includes operating costs and environmental governance costs.

[0046] The microgrid optimization scheduling model consisting of the objective function and constraints is solved based on the improved electric eel foraging optimization algorithm to generate the optimal scheduling scheme;

[0047] The improved electric eel foraging optimization algorithm is based on the standard electric eel foraging optimization algorithm. It introduces an elite back learning strategy for population initialization and incorporates Cauchy mutation operator, tournament selection mechanism and cross-linking strategy during the iterative optimization process of the algorithm.

[0048] In this embodiment, the microgrid system structure configuration studied in this invention is as follows: Figure 1 As shown, this microgrid system uses photovoltaic (PV), wind turbine (WT), microturbine (MT), and fuel cell (FC) as distributed generation units, and battery (SB) as energy storage units.

[0049] The actual output power of a photovoltaic system can be calculated using the output power under conditions of light intensity, temperature, and standard test conditions. The specific formula is as follows:

[0050] ;

[0051] ;

[0052] In the formula: T c It refers to the operating temperature; T amb It refers to the ambient temperature during operation; G AC It is light intensity; NOCT is the nominal operating temperature; P PVThis is the actual output power of the photovoltaic system; P STC It is the maximum output power of photovoltaics under standard test conditions; G STC It is the light intensity under standard test conditions; k is the power temperature coefficient; T i This is a reference temperature.

[0053] The output power of a wind turbine is directly affected by the wind speed at the hub height and the aerodynamic characteristics of the turbine. The specific formula is as follows:

[0054] ;

[0055] In the formula: P WT It is the output power of the fan; P r It is the rated power of the fan; v and v r These are the actual wind speed and the rated wind speed at the hub of the wind turbine, respectively; v ci and v co These are the inlet and outlet wind speeds of the fan, respectively.

[0056] Micro turbines are a new type of small-capacity generator that converts chemical energy into kinetic energy using fuels such as natural gas. They offer advantages such as high reliability, high power generation efficiency, and low pollution. Unlike other new energy power generation units, their high flexibility allows for precise control to achieve optimal operating conditions. The relationship between the operating efficiency and output power of a micro turbine is shown below:

[0057] ;

[0058] ;

[0059] In the formula: It is the unit efficiency of the generator set; P MT It is the active power output of the unit per unit time; C MT It is the fuel cost during operation; C ng It refers to the price of natural gas; LHV ng It has the low calorific value of natural gas.

[0060] A fuel cell is a battery device that stores fuel and oxidant to generate electricity. It converts some of the chemical energy into electrical energy through a chemical reaction. Unlike traditional combustion power generation methods, it theoretically emits almost no pollutants.

[0061] Taking the natural gas-fueled proton exchange membrane fuel cell used in this study as an example, the relationship between its fuel cost and output power is shown below:

[0062] ;

[0063] In the formula: C FCThis refers to the fuel cost during fuel cell operation; It is the unit efficiency of the fuel cell per unit time; P FC It is the active power output of a fuel cell per unit time.

[0064] Energy storage batteries serve as energy buffers in microgrids, mitigating the impact of renewable energy generation on the grid and enhancing the microgrid's reliability. They store electricity during peak generation periods and release it during peak consumption periods, providing a stable power supply to the load and ensuring the safe and stable operation of the microgrid. The battery model equations characterizing the state of charge (SOC) of the energy storage battery during charging and discharging are shown below:

[0065] ;

[0066] In the formula: SOC(t) and SOC(t-1) are the states of charge of the energy storage battery at times t and t-1, respectively; and These are the charging efficiency and discharging efficiency of the energy storage battery, respectively; P SB (t) is the output power of the energy storage battery at time t; E r It refers to the capacity of the energy storage battery; It refers to a unit of time.

[0067] To balance the economic efficiency and cleanliness of microgrid operation, this invention constructs a microgrid scheduling model that uses the total operating cost of the microgrid as the objective for scheduling, including both operating costs and environmental governance costs.

[0068] ;

[0069] In the formula: C is the total cost of operating the microgrid; C1 is the operating cost; C2 is the environmental governance cost, that is, the cost of treating various pollutants.

[0070] Operating costs of microgrids:

[0071] ;

[0072] In the formula: C fuel It is the cost of fuel; C om It is the maintenance cost; C grid It is the interaction cost between the microgrid and the main grid.

[0073] The fuel costs of microgrid operation mainly include the fuel consumption costs of micro turbines and fuel cells during their operating cycle;

[0074] ;

[0075] Among them, C fuel(t) represents the fuel cost of the microgrid operation at time t, C MT (t) represents the fuel consumption cost of the micro turbine during its operating cycle at time t, C FC (t) represents the fuel consumption cost of the fuel cell during its operating cycle at time t.

[0076] The maintenance cost of microgrid operation depends on the output power of each distributed generation device during its operating cycle;

[0077] ;

[0078] In the formula: K WT K PV K MT K FC and K SB These are the maintenance cost coefficients for wind turbines, photovoltaics, micro-turbines, fuel cells, and energy storage batteries, respectively; P dis (t) and P c (t) represents the discharge and charging power of the energy storage battery at time t, respectively.

[0079] Energy exchange between microgrids and the main grid is achieved through electricity procurement and sales. In order to guide users to arrange their electricity consumption time reasonably and ensure the balance between electricity supply and demand, time-of-use pricing strategy is often adopted to charge fees based on the average marginal cost of system operation.

[0080] ;

[0081] In the formula: C buy (t) is the electricity purchase price between the microgrid and the main grid at time t; C sell (t) is the electricity sales price between the microgrid and the main grid at time t; P grid (t) represents the interaction power between the microgrid and the main grid at time t.

[0082] Environmental governance costs of microgrids:

[0083] ;

[0084] In the formula: It is the cost required to treat the nth type of pollutant in the unit's quality; This is the emission coefficient of the i-th power generation unit for the k-th type of pollutant; K is the type of pollutant, which in this invention includes CO2, SO2, and NO. x Three types of pollutants; P i (t) represents the power generation of the i-th power generation unit at time t.

[0085] As a preferred embodiment of the present invention, the constraints include: power balance constraints, output constraints of each power generation unit, ramp rate constraints of the controllable power generation unit, state of charge and charge / discharge power constraints of the energy storage battery, and power constraints of the interconnection line between the microgrid and the main grid.

[0086] In this embodiment, to ensure the stability of the microgrid, the total power generation of the system must be dynamically balanced with the total power consumption, as specified in the power balance constraint formula:

[0087] ;

[0088] In the formula: P load (t) is the load power of the system at time t; when P grid When (t)>0, the microgrid purchases electricity from the main grid, and when P grid When (t) < 0, the microgrid sells electricity to the main grid; when P SB When (t)>0, the energy storage battery discharges; when P SB When (t) < 0, the energy storage battery is charged.

[0089] The active power output constraints for the four types of power generation units—WT, PV, MT, and FC—are as follows:

[0090] ;

[0091] ;

[0092] In the formula: P i,min and P i,max is the upper and lower limits of the power of the i-th power generation unit; CG is the controllable power generation unit, namely MT and FC; and It is the downward and upward ramp rate of the controllable power generation unit.

[0093] The limitations on SB capacity and power in energy storage battery constraints are as follows:

[0094] ;

[0095] Where: SOC min and SOC max These are the upper and lower limits of the battery's state of charge; P SB,min (t) and P SB,max (t) represents the upper and lower limits of the battery output, respectively.

[0096] The power constraint between the microgrid and the main grid in the tie-line power constraint is as follows:

[0097] ;

[0098] In the formula: Pgrid,min and P grid,max These are the upper and lower limits of the transmission power of the tie line, respectively.

[0099] As a preferred embodiment of the present invention, the process of solving the microgrid optimal scheduling model using the improved electric eel foraging optimization algorithm includes:

[0100] An initial population is generated based on the elite reverse learning strategy, the fitness value of each electric eel is calculated, and the initial global optimal solution is determined.

[0101] Enter the main loop and calculate the energy factor based on the current iteration number; for each individual in the population, select to enter the interaction phase, rest phase, migration phase or hunting phase to update the position based on the magnitude of the energy factor;

[0102] Specifically, during the migration phase, a hybrid mutation strategy combining differential evolution and the Cauchy mutation operator is introduced for position updates; during the hunting phase, the tournament selection mechanism is introduced for position updates.

[0103] After updating the individual position, the fitness value is recalculated, and the cross-sectional strategy is introduced to optimize the global optimal solution, and the global optimal solution is updated.

[0104] Determine if the maximum number of iterations has been reached. If so, output the global optimal solution and its corresponding fitness value.

[0105] In this embodiment, the standard electric eel foraging optimization algorithm (EEFO) is an algorithm that simulates the collective foraging activities of electric eels. It mainly includes four stages of foraging: interaction, rest, migration, and hunting, and its flowchart is shown below. Figure 2 As shown.

[0106] During the interaction phase, electric eels interact with each other through swimming and stirring behaviors. Each electric eel represents a candidate solution, and the best candidate solution at each step is the target prey. During the interaction phase, electric eels share location information for global exploration and update their positions based on the positional differences between randomly selected electric eels and the population center. The specific process is as follows:

[0107] ;

[0108] In the formula: v i (t+1) is the new position of the i-th electric eel after the update; x i (t) is the candidate position of the i-th electric eel in the t-th iteration; x j (t) is the position of another randomly selected j-th electric eel; fit is the fitness function; It is the average position of all electric eels in the current population; xr p1 and p2 are random numbers within the population of electric eels; p1 and p2 are random numbers in (0,1).

[0109] During the resting phase, the electric eel conserves and manages energy by resting. By projecting the electric eel's position vector onto the main diagonal of the search space and normalizing the search space and the electric eel's position to the range of (0,1), the area of ​​the resting region can be calculated. The specific process is as follows:

[0110] ;

[0111] In the formula: R i It is the center of the rest area; rand is a random number in the range (0,1); round is used for rounding.

[0112] During migration, when electric eels spot potential prey, they migrate from their resting area to their hunting area. The specific process is as follows:

[0113] ;

[0114] Where: H i It can be considered any location within the hunting area; L is the Levy flight function, which is a strong flight motion established to avoid the local optimal trap in EEFO.

[0115] During the hunting phase, electric eels swim in a large circle, communicating and coordinating their actions using low-frequency electrical signals. As the interaction intensifies, the charged circle gradually tightens, driving the fish from deeper waters to shallower areas, thus creating an environment conducive to hunting. Startled prey then scatters within the area, and the electric eels update their positions as the prey moves. The coiling behavior of electric eels during hunting is described below:

[0116] ;

[0117] Where: H prey η is the location center of the prey during the hunting phase; η is the curling behavior during hunting.

[0118] The EEFO algorithm uses an energy factor to balance the electric eel's global exploration and local exploitation behaviors. When the energy factor value is greater than 1, the electric eel enters the interactive phase of global exploration; otherwise, it enters the rest, migration, and hunting phases of local exploitation.

[0119] ;

[0120] In the formula: E(t) is the energy factor at the t-th iteration; t is the current iteration number; T is the maximum iteration number.

[0121] Based on the standard Electric Eel Foraging Optimization (EEFO) algorithm, the present invention has obtained an improved Electric Eel Foraging Optimization (IEEFO) algorithm with multiple strategies. The pseudo-code of IEEFO is as follows.

[0122] Input: the number of individuals i in the population, the upper and lower bounds X max and X min 、the maximum number of iterations T, the dimension dim of the individual.

[0123] Output: the optimal position X of the electric eel best and its fitness value fit(X best ), the positions and their fitness values at each iteration.

[0124] Generate the initial population by combining the elite opposition-based learning strategy;

[0125] Calculate the fitness value of each electric eel and select the current global optimal solution X best ;

[0126] While t < T generate the energy factor E;

[0127] For x i ;

[0128] If E > 1 enter the interaction phase;

[0129] Else If rand < 1 / 3 enter the rest phase;

[0130] Else if rand > 2 / 3 combine the differential evolution algorithm and the Cauchy mutation operator to enter a new migration phase;

[0131] Else combine the tournament selection mechanism to enter a new hunting phase;

[0132] End if Update the position of the electric eel and calculate its fitness value;

[0133] Combine the crisscross strategy to select more excellent electric eel individuals;

[0134] End for;

[0135] End while.

[0136] As a preferred embodiment of the present invention, the formula for generating the initial population by the elite opposition-based learning strategy is:

[0137] ;

[0138] Where is the opposite solution of the elite individual; X max and X min are the lower and upper bounds of the solution respectively; Xi It represents the current position of the individual.

[0139] In this embodiment, the initial position of the electric eel is randomly generated in the standard EEFO algorithm, which leads to problems such as low population diversity, uneven distribution, and premature convergence.

[0140] This invention introduces an elite reverse learning strategy in the initialization phase for improvement. This strategy first generates a basic random population while simultaneously constructing a corresponding elite reverse population using a dynamic reverse formula, allowing the algorithm to explore a "mirror" region of the current solution space. Then, the original and reverse solutions are merged, and a competition mechanism selects the individual with the best fitness from the candidate solutions as the formal initial population. This modified mechanism not only enhances the initial diversity of the population but also ensures that the algorithm uses higher-quality solutions as its evolutionary starting point, thereby accelerating the convergence speed and avoiding the risk of premature convergence.

[0141] In a preferred embodiment of the present invention, the hybrid mutation strategy introduced during the migration phase has the following position update formula:

[0142] ;

[0143] Among them, X i,q1 X i,q2 and X i,q3 The positions of three distinct individuals are randomly selected from the population; cauchy is the Cauchy mutation operator; tan is the tangent function; r is a random number in the range (0,1); π is the mathematical constant pi.

[0144] In this embodiment, during the migration phase, after the electric eel individual completes the Levy flight update, to further enhance the algorithm's ability to escape local optima, this invention introduces a hybrid mutation strategy combining differential evolution and Cauchy mutation. Different individuals within the population are randomly selected to construct differential variables, and the distribution differences within the population provide directional guidance for mutation. Simultaneously, the Cauchy mutation operator replaces the scaling step in traditional differential evolution, constructing a new position update method. This improved strategy not only preserves the population's structural information but also enhances the algorithm's ability to escape local optima in the later stages of iteration and improves global optimization efficiency by leveraging the large-step perturbation generated by the Cauchy operator.

[0145] As a preferred embodiment of the present invention, the process of introducing a tournament selection mechanism for position updating during the hunting phase includes:

[0146] First, the potential new locations of the current individual are calculated based on the behavioral characteristics of the hunting phase;

[0147] Individuals are randomly selected from the remaining population to form a competition group, and the individual with the best fitness is selected as the winner through comparison.

[0148] The fitness of the potential new position is compared with that of the winner. If the fitness of the potential new position is better, the new position is retained as the updated individual position; otherwise, the winner is used as the updated individual position.

[0149] In this embodiment, during the hunting phase, a tournament selection mechanism is introduced into the generation process of new individuals to enhance the algorithm's development capabilities. The algorithm first calculates the potential new positions of the current individual based on hunting behavior characteristics. Then, it randomly selects individuals from the remaining population to form a competitive group, and selects the individual with the best fitness as the "winner" through comparison. Next, the potential new positions are compared with the tournament winner. If the newly generated hunting position has better fitness, it is retained; otherwise, the solution generated in this hunt is discarded, and the selected position is directly chosen as the "winner." The specific process is as follows:

[0150] ;

[0151] In the formula: v r It represents the position of an individual vector; Tournament Selection is the tournament selection operator.

[0152] As a preferred embodiment of the present invention, a cross-sectional strategy is introduced to optimize the global optimal solution, specifically including:

[0153] Horizontal crossover: Arithmetic crossover is performed between the global optimal solution and other individuals in the population to generate new offspring individuals, while retaining individuals with better fitness.

[0154] Vertical crossover: Information is reorganized across different dimensions of the global optimal solution to generate new offspring individuals, while retaining individuals with better fitness.

[0155] In this embodiment, the standard EEFO algorithm suffers from a single mutation pattern in the electric eel population, resulting in insufficient population diversity and limiting the algorithm's global search capability. When dealing with complex high-dimensional optimization problems, it is prone to premature convergence and getting trapped in local optima as the number of iterations increases. This invention employs a cross-cutting strategy to optimize the global optimal solution, thereby balancing the algorithm's local search capability and global optimization capability.

[0156] Horizontal crossover is very similar to the crossover operation in genetic algorithms. It enhances the algorithm's global search capability by performing arithmetic crossover on the same dimension of two different individuals. This strategy selects new parent individuals through a pairwise, non-repeating selection method, then performs arithmetic crossover on the d-th dimension of the parent individuals to generate new offspring. The offspring are then compared with the parent individuals, and the individuals with better fitness are retained. The specific process is as follows:

[0157] ;

[0158] ;

[0159] In the formula: X i,d and X j,d They are the parent individual X i and X j The d-th dimension; and r1 and r2 are the d-th dimension of the offspring generated after arithmetic crossover of the parent generation; r1 and r2 are random numbers in the range [0,1]; c1 and c2 are random numbers in the range [-1,1].

[0160] Vertical crossover is very similar to the mutation operation in genetic algorithms. It enhances the algorithm's ability to avoid getting trapped in local optima by reorganizing information across different dimensions of the global optimum. This strategy randomly selects two different dimensions of the global optimum and treats them as parents. Then, it selects new offspring through computational recombination and compares the offspring with the parents, retaining the individuals with better fitness. The specific process is as follows:

[0161] ;

[0162] In the formula: It is the globally optimal solution X best The offspring are generated by vertically crossing the d1st and d2nd dimensions; r3 is a random number in [0,1].

[0163] To verify the ability of the improved algorithm to solve single-objective optimization problems, this invention selects functions F1~F10 from the CEC2019 benchmark functions for testing. The improved electric eel foraging optimization algorithm (IEEFO) is compared with four advanced optimization algorithms: standard electric eel foraging optimization algorithm (EEFO), snake optimization algorithm (SO), particle swarm optimization algorithm (PSO), and sparrow search algorithm (SSA). The parameter settings of each algorithm are shown in Table 1.

[0164] Table 1 Algorithm Parameter Settings

[0165]

[0166] To ensure the validity and fairness of the comparative experiments, the population size of all algorithms was set to 30, and the maximum number of iterations was set to 500. To reduce the randomness of the experiments and comprehensively evaluate the convergence accuracy and stability of each algorithm under different scenarios, all algorithms were run independently 30 times, and the mean and standard deviation of each algorithm were calculated. This invention was programmed using MATLAB R2023a software, and the experimental environment was built on a computer with an Intel Core i5-10400 CPU 2.90GHz, 16.0GB of memory, and Windows 11 64-bit.

[0167] Table 2 shows the test results for each algorithm. The average values ​​of the five algorithms are ranked as follows: IEEFO > EEFO > PSO > SO > SSA. The average value obtained by the IEEFO algorithm ranks first in all cases, indicating that the IEEFO algorithm has better solution accuracy and quality. The standard deviation of the solution obtained by the IEEFO algorithm is lower in most cases, indicating that the algorithm has less volatility and better convergence stability. The experimental results show that among the five algorithms, the IEEFO algorithm has the best overall performance and can stably and accurately converge to the global optimum when solving single-objective optimization problems.

[0168] Table 2 Comparison of Experimental Results for Test Functions

[0169]

[0170] Application of the IEEFO algorithm in microgrid operation: This invention selects typical winter environmental data from a city in northern my country. Typical daily load curves and renewable energy output power curves for this region in winter are shown below. Figure 3 As shown, its dispatch cycle is set to a calendar day, with a unit time interval of 1 hour. To improve the cleanliness of microgrid operation, priority should be given to ensuring the full consumption of renewable energy. The region's electricity market adopts a tiered pricing mechanism with three price tiers. The electricity trading prices between the microgrid and the main grid at different times are as follows: Figure 4 As shown in Table 3; the emission coefficients and environmental remediation costs of the three types of pollutants are shown in Table 4 and Table 5; the relevant parameters of distributed power sources and energy storage batteries are shown in Table 4 and Table 5.

[0171] Table 3 Pollutant treatment costs and correlation coefficients

[0172]

[0173] Table 4 Distributed Power Generation Parameters

[0174]

[0175] Table 5 Energy Storage Battery Parameters

[0176]

[0177] To verify the effectiveness of the IEEFO algorithm in solving the microgrid optimal scheduling problem, this invention conducts a day-ahead optimal scheduling study on grid-connected microgrids and selects four algorithms—EEFO, SO, PSO, and SSA—for comparative analysis. The population size and maximum number of iterations for all algorithms were set to 100 and 150, respectively. All algorithms were programmed using MATLAB R2023a software, and the experimental environment was built on a computer with an Intel Core i5-10400 CPU 2.90GHz, 16.0GB of RAM, and Windows 11 64-bit.

[0178] The power balance results obtained by various algorithms show that WT and PV, due to their advantages of being pollution-free and having low maintenance costs, are prioritized by the system to achieve full absorption of renewable energy output. As the load gradually increases, the power balance requirements of each time period are met by adjusting the output of controllable distributed power sources. Taking the IEEFO algorithm as an example, ... Figure 5 As shown, during the off-peak electricity price period from 23:00 to 07:00, the photovoltaic system is not yet operational, and other generating units store excess energy in the SB (Power Storage Unit) while meeting load demand. During the peak electricity price periods from 10:00 to 14:00 and from 17:00 to 21:00, load demand gradually climbs to its peak. At this time, the MT (Power Transmission Unit) and FC (Power Fiber) units increase their output, and the SB simultaneously releases the stored energy to alleviate power supply pressure. When load demand is low, the SB also sells electricity to the main grid to generate revenue and reduce economic costs. During the stable electricity price periods from 07:00 to 10:00, 14:00 to 17:00, and 21:00 to 23:00, the SB flexibly adjusts its charging and discharging strategies according to load change trends.

[0179] Table 6 Daily Optimization Costs of Microgrids

[0180]

[0181] Table 7 Daily carbon emissions from microgrids

[0182]

[0183] Figure 6The different convergence behaviors of various optimization algorithms are shown. Except for a slight disadvantage compared to the PSO algorithm, the IEEFO algorithm outperforms the other algorithms in convergence speed, and it also shows the most outstanding performance in terms of convergence accuracy. As shown in Tables 6 and 7, when solving the optimal scheduling problem, the IEEFO algorithm achieves the lowest scheduling cost, reducing the total cost by 2.17%, 1.83%, 2.64%, and 3.29% compared to EEFO, SO, PSO, and SSA, respectively; reducing operating costs by 1.96%, 1.72%, 2.32%, and 2.24%, respectively; reducing environmental governance costs by 3.64%, 2.55%, 4.83%, and 10.47%, respectively; and reducing carbon emissions by 2.41%, 9.28%, 7.26%, and 7.99%, respectively. Experimental results show that the IEEFO algorithm has a faster convergence speed and higher convergence accuracy, and can solve the scheduling model more stably and accurately, obtaining the optimal economic and environmentally friendly scheduling scheme for the microgrid.

[0184] Addressing the challenges of economic dispatch and low-carbon operation of microgrid systems under complex operating environments, this invention focuses on the single-objective optimization dispatch problem of microgrids and proposes an IEEFO algorithm. To overcome the tendency of traditional algorithms to get trapped in local optima when handling high-dimensional nonlinear dispatch models, this algorithm deeply reconstructs the optimization mechanism: in the initialization phase, an elite back-learning strategy is employed to mine potential high-quality solutions, significantly enhancing population diversity; in the migration and hunting phases of core evolution, a Cauchy mutation operator combined with a tournament selection mechanism is introduced to improve the algorithm's robustness while effectively avoiding premature convergence; furthermore, a cross-cutting strategy is integrated to dynamically coordinate algorithm behavior, achieving a precise balance between local search accuracy and global development capability. Microgrid simulation experiments further demonstrate that this method can effectively balance the economy and cleanliness of system operation, with economic cost reductions ranging from a maximum of 3.29% to a minimum of 1.83%, and carbon emission reductions ranging from a maximum of 9.28% to a minimum of 2.41%. This invention provides reliable technical support and decision-making basis for achieving low-cost, low-carbon, and efficient collaborative dispatch of microgrids.

[0185] This invention also provides a microgrid optimization scheduling system based on an improved electric eel foraging optimization algorithm, the system comprising:

[0186] The model building module is used to construct an objective function with the goal of minimizing the total operating cost of the microgrid, and to establish the constraints that the microgrid must meet during operation. The total operating cost includes operating costs and environmental governance costs.

[0187] The solution module is used to solve the microgrid optimization scheduling model composed of the objective function and constraints based on the improved electric eel foraging optimization algorithm, and generate the optimal scheduling scheme.

[0188] The improved electric eel foraging optimization algorithm is based on the standard electric eel foraging optimization algorithm. It introduces an elite back learning strategy for population initialization and incorporates Cauchy mutation operator, tournament selection mechanism and cross-linking strategy during the iterative optimization process of the algorithm.

[0189] The above description is merely a preferred embodiment of the present invention and is not intended to limit the present invention. Any modifications, equivalent substitutions, and improvements made within the spirit and principles of the present invention should be included within the protection scope of the present invention.

Claims

1. A microgrid optimization scheduling method based on an improved electric eel foraging optimization algorithm, characterized in that, The method includes: An objective function is constructed with the goal of minimizing the total operating cost of the microgrid, and constraints that the microgrid must satisfy during operation are established. The total operating cost includes operating costs and environmental governance costs. The microgrid optimization scheduling model consisting of the objective function and constraints is solved based on the improved electric eel foraging optimization algorithm to generate the optimal scheduling scheme; The improved electric eel foraging optimization algorithm is based on the standard electric eel foraging optimization algorithm. It introduces an elite back learning strategy for population initialization and incorporates Cauchy mutation operator, tournament selection mechanism and cross-linking strategy during the iterative optimization process of the algorithm.

2. The microgrid optimization scheduling method based on the improved electric eel foraging optimization algorithm according to claim 1, characterized in that, The process of solving the microgrid optimal scheduling model using the improved electric eel foraging optimization algorithm includes: An initial population is generated based on the elite reverse learning strategy, the fitness value of each electric eel is calculated, and the initial global optimal solution is determined. Enter the main loop and calculate the energy factor based on the current iteration number; for each individual in the population, select to enter the interaction phase, rest phase, migration phase or hunting phase to update the position based on the magnitude of the energy factor; Specifically, during the migration phase, a hybrid mutation strategy combining differential evolution and the Cauchy mutation operator is introduced for position updates; during the hunting phase, the tournament selection mechanism is introduced for position updates. After updating the individual position, the fitness value is recalculated, and the cross-sectional strategy is introduced to optimize the global optimal solution, and the global optimal solution is updated. Determine if the maximum number of iterations has been reached. If so, output the global optimal solution and its corresponding fitness value.

3. The microgrid optimization scheduling method based on the improved electric eel foraging optimization algorithm according to claim 1, characterized in that, The formula for generating the initial population using the elite reverse learning strategy is: ； in, It is the opposite of the solution for elite individuals; X max and X min These are the lower and upper bounds of the solution, respectively; X i It represents the current position of the individual.

4. The microgrid optimization scheduling method based on the improved electric eel foraging optimization algorithm according to claim 1, characterized in that, The hybrid mutation strategy introduced during the migration phase has the following position update formula: ； Among them, X i,q1 X i,q2 and X i,q3 is three distinct individual positions randomly selected from the population; cauchy is the Cauchy mutation operator; tan is the tangent function; r is a random number in the range (0,1).

5. The microgrid optimization scheduling method based on the improved electric eel foraging optimization algorithm according to claim 1, characterized in that, The process of introducing a tournament selection mechanism for position updates during the hunting phase includes: First, the potential new locations of the current individual are calculated based on the behavioral characteristics of the hunting phase; Individuals are randomly selected from the remaining population to form a competition group, and the individual with the best fitness is selected as the winner through comparison. The fitness of the potential new position is compared with that of the winner. If the fitness of the potential new position is better, the new position is retained as the updated individual position; otherwise, the winner is used as the updated individual position.

6. The microgrid optimization scheduling method based on the improved electric eel foraging optimization algorithm according to claim 1, characterized in that, A cross-sectional strategy is introduced to optimize the global optimal solution, specifically including: Horizontal crossover: Arithmetic crossover is performed between the global optimal solution and other individuals in the population to generate new offspring individuals, while retaining individuals with better fitness. Vertical crossover: Information is reorganized across different dimensions of the global optimal solution to generate new offspring individuals, while retaining individuals with better fitness.

7. The microgrid optimization scheduling method based on the improved electric eel foraging optimization algorithm according to claim 1, characterized in that, The constraints include: power balance constraints, output constraints of each power generation unit, ramp rate constraints of controllable power generation units, state of charge and charge / discharge power constraints of energy storage batteries, and power constraints of the interconnection line between the microgrid and the main grid.

8. A microgrid optimization scheduling system based on an improved electric eel foraging optimization algorithm, used to implement the microgrid optimization scheduling method based on the improved electric eel foraging optimization algorithm as described in any one of claims 1-7, characterized in that, The system includes: The model building module is used to construct an objective function with the goal of minimizing the total operating cost of the microgrid, and to establish the constraints that the microgrid must meet during operation. The total operating cost includes operating costs and environmental governance costs. The solution module is used to solve the microgrid optimization scheduling model composed of the objective function and constraints based on the improved electric eel foraging optimization algorithm, and generate the optimal scheduling scheme. The improved electric eel foraging optimization algorithm is based on the standard electric eel foraging optimization algorithm. It introduces an elite back learning strategy for population initialization and incorporates Cauchy mutation operator, tournament selection mechanism and cross-linking strategy during the iterative optimization process of the algorithm.

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