Micro-grid scheduling method based on improved multi-target firefly algorithm

Abstract

The invention provides a micro-grid dispatching method based on an improved multi-target firefly algorithm, and relates to the technical field of micro-grid operation. The method provided by the invention comprises the following steps: constructing a micro-grid system model, a micro-grid objective function and micro-grid constraint conditions; constructing a micro-grid dispatching model according to the micro-grid system model, the micro-grid objective function and the micro-grid constraint conditions; and solving the microgrid scheduling model based on an improved multi-target firefly algorithm to obtain an optimal scheduling scheme. According to the method, efficient optimization of the micro-grid dispatching model is realized by adopting the improved multi-target firefly algorithm.

Description

Technical Field

[0001] This invention relates to the field of microgrid operation technology, and in particular to a microgrid scheduling method based on an improved multi-objective firefly algorithm. Background Technology

[0002] Microgrids (MGs), as a crucial component of power systems, integrate distributed energy resources, energy storage devices, loads, and related control devices. Their optimal scheduling aims to coordinate various distributed energy resources, energy storage devices, and user demands while meeting constraints, thereby achieving goals such as reducing energy consumption and environmental pollution. This is vital for promoting sustainable energy development and improving power system efficiency. Therefore, solving microgrid scheduling models is an important research direction in optimization theory and application.

[0003] The multi-objective firefly algorithm simulates the bioluminescent attraction behavior of fireflies in nature, guiding the exploration direction and step size through brightness values, and is highly efficient in solving multi-objective optimization problems. However, existing multi-objective firefly algorithms still suffer from problems such as low solution accuracy, weak global exploration capability, and poor solution feasibility when solving microgrid scheduling models. Therefore, there is an urgent need to provide a solution to improve these problems. Summary of the Invention

[0004] The purpose of this invention is to provide a microgrid scheduling method based on an improved multi-objective firefly algorithm, which can improve the problems of low solution accuracy, weak global exploration capability and poor solution feasibility of existing methods.

[0005] This invention provides a microgrid scheduling method based on an improved multi-objective firefly algorithm, comprising:

[0006] Construct a microgrid system model, microgrid objective function, and microgrid constraints;

[0007] A microgrid scheduling model is constructed based on the microgrid system model, the microgrid objective function, and the microgrid constraints.

[0008] The optimal scheduling scheme is obtained by solving the microgrid scheduling model based on the improved multi-objective firefly algorithm.

[0009] This invention provides a microgrid scheduling method based on an improved multi-objective firefly algorithm. By constructing a microgrid system model, a microgrid objective function, and microgrid constraints, a microgrid scheduling model is further constructed. Finally, the optimal scheduling scheme is obtained by solving the microgrid scheduling model based on the improved multi-objective firefly algorithm, thus achieving efficient optimization of microgrid scheduling schemes.

[0010] Optionally, when solving the microgrid scheduling model based on the improved multi-objective firefly algorithm to obtain the optimal scheduling scheme, the following steps are included:

[0011] Initialize the firefly population and the output power scheme of distributed energy devices, set the microgrid scheduling model parameters and the improved multi-objective firefly algorithm parameters, and calculate the objective function value of individual fireflies in the firefly population based on the microgrid objective function;

[0012] Based on the objective function value, the firefly population is divided into non-dominant firefly individuals and dominant firefly individuals using non-dominant sorting. The angle between the dominant firefly individuals and the non-dominant firefly individuals is calculated, and the leader of the dominant firefly individual is determined according to the angle.

[0013] Dominant firefly individuals learn to move from the guide according to the position update formula, while non-dominant firefly individuals undergo random differential evolution according to the movement update formula.

[0014] The firefly population after the position is updated is sorted by dominance, and the proportion of non-dominant firefly individuals is calculated. A mutation strategy is selected based on the proportion of non-dominant firefly individuals.

[0015] Construct multi-performance evaluation constraint dominance conditions, merge the updated firefly population and the previous generation firefly population to form a new population, constrain and dominate the new population based on the multi-performance evaluation constraint conditions, select non-dominated firefly individuals that meet the minimum constraint conditions, and retain the optimal scheduling scheme.

[0016] Repeat the process until the maximum number of iterations is reached, and then output the optimal scheduling scheme.

[0017] Optionally, the objective function value is calculated based on the microgrid objective function; the microgrid scheduling model parameters include key parameters of each distributed energy device, pollutant emission coefficient, unit price of pollutant treatment cost, real-time electricity price, and energy storage battery parameters; the improved multi-objective firefly algorithm parameters include decision variables, maximum number of iterations, light attraction coefficient, and maximum attraction force.

[0018] Optionally, when calculating the angle between the dominant firefly individual and the non-dominant firefly individuals, and determining the guide of the dominant firefly individual based on the angle, the method includes: calculating the angle between each dominant firefly individual in the firefly population and all non-dominant firefly individuals, and selecting the non-dominant firefly individual with the largest angle to the currently dominant firefly individual as the guide of that dominant firefly individual.

[0019] Optionally, the position update formula and the movement update formula are defined as follows:

[0020] x i (t+1)=x i (t)+β1(Leader i -xi (t))+αε

[0021] x j (t+1)=x j (t)+F(x r1 (t)-x r2 (t)+x r3 (t)-x r4 (t))

[0022] Where, x i (t+1) represents the dominant firefly individual after its position is updated, x i (t) represents the dominant firefly individual before the position update, and β1 represents the dominant firefly individual x. i With the Leader i The attraction between them, where α is the step size factor, and ε i x is a random vector; j (t+1) represents the non-dominant firefly individual after its position is updated, x j (t) represents the non-dominant firefly individual before the position update, x r1 x r2 x r3 and x r4 Let F represent four firefly individuals randomly selected from the non-dominated firefly individuals, and F is the scaling factor.

[0023] Optionally, when selecting a mutation strategy based on the proportion of non-dominant firefly individuals, the strategy includes: if the proportion of non-dominant firefly individuals in the firefly population is greater than 0.5, the firefly individuals in the firefly population choose the Cauchy mutation for renewal and evolution; if the proportion of non-dominant firefly individuals in the firefly population is less than 0.5, the firefly individuals in the firefly population choose the simulated binary crossover operator for renewal and evolution.

[0024] Optionally, when constructing the multi-performance evaluation constraint dominance conditions, the following steps are included: constructing the multi-performance evaluation constraint dominance conditions based on the convergence index, the convergence index, and the feasibility index; the convergence index is used to evaluate the degree to which a firefly individual approaches the Pareto front by using the normalized objective function value of the individual firefly; the diversity index is used to calculate the widespread distribution of the firefly population in the target space by using the Euclidean distance value between each individual firefly; and the feasibility index is used to quantify the degree to which a firefly individual satisfies the constraint conditions by using the normalized constraint violation value of the individual firefly.

[0025] Optionally, for any individual firefly x i and individual fireflies x j If the multi-performance evaluation constraint dominance condition is satisfied simultaneously, then it means that individual firefly x... i Constraint and Domination of individual firefly x jThe governing conditions of the multi-performance evaluation constraints are defined as follows:

[0026]

[0027] Where F(i) and F(j) are the individual firefly x i and individual fireflies x j The convergence indices are D(i) and D(j), which represent the convergence indices of individual firefly x. i and individual fireflies x j The diversity indicators, C(i) and C(j), represent the number of firefly individuals x, respectively. i and individual fireflies x j Feasibility indicators.

[0028] Optionally, when selecting non-dominant firefly individuals that meet the minimum constraint condition, the process includes: merging the updated firefly population and the previous generation firefly population to form a new population with a size of 2N; sorting the new population according to the constraint dominance condition; selecting r non-dominant firefly individuals; if r ≤ N, removing r non-dominant firefly individuals from the new population; calculating the crowding distance of the remaining firefly individuals and sorting them in descending order according to the crowding distance; selecting the top Nr firefly individuals with the largest crowding distance and merging them with the r non-dominant firefly individuals to form the offspring firefly population; if r > N, calculating the crowding distance of the remaining firefly individuals and sorting them in descending order according to the crowding distance; selecting the top N firefly individuals with the largest crowding distance as the offspring firefly population.

[0029] Optionally, the microgrid system model includes a photovoltaic power generation system, a wind power generation system, a micro turbine power generation system, a diesel engine power generation system, and an energy storage battery system; the microgrid objective function includes an economic objective function for operating costs and an environmental objective function; the microgrid constraints include micro turbine operating constraints, diesel engine operating constraints, power interaction constraints between the microgrid and the external power grid, energy storage battery device constraints, and microgrid power balance constraints. Attached Figure Description

[0030] Figure 1 A flowchart illustrating a microgrid scheduling method based on an improved multi-objective firefly algorithm, provided as an embodiment of the present invention;

[0031] Figure 2 Initialize the target space for the firefly population;

[0032] Figure 3 The Pareto front distribution is obtained using the traditional multi-objective firefly algorithm;

[0033] Figure 4The Pareto front distribution obtained by the improved guided learning update mechanism in a microgrid scheduling method based on the improved multi-objective firefly algorithm provided in this embodiment of the invention;

[0034] Figure 5 The distribution of the traditional multi-objective firefly algorithm in the decision space is shown;

[0035] Figure 6 The distribution of the fusion mutation strategy in the decision space in a microgrid scheduling method based on an improved multi-objective firefly algorithm provided in an embodiment of the present invention;

[0036] Figure 7 A schematic diagram illustrating the environment selection process of a microgrid invocation method based on an improved multi-objective firefly algorithm, provided in an embodiment of the present invention;

[0037] Figure 8 Pareto fronts for six algorithms on the MW1 benchmark problem;

[0038] Figure 9 Pareto frontiers for 6 algorithms on the MW3 benchmark problem;

[0039] Figure 10 Pareto frontiers for six algorithms on the MW9 benchmark problem;

[0040] Figure 11 Pareto frontiers for six algorithms on the MW14 benchmark problem;

[0041] Figure 12 This is a predicted value of photovoltaic and wind power output based on historical data;

[0042] Figure 13 The diesel generator output power under the optimal scheduling scheme in a microgrid scheduling method based on an improved multi-objective firefly algorithm provided in this embodiment of the invention;

[0043] Figure 14 This invention provides an embodiment of a microgrid scheduling method based on an improved multi-objective firefly algorithm, which includes the optimal scheduling scheme for battery output power.

[0044] Figure 15 This invention provides an embodiment of a microgrid scheduling method based on an improved multi-objective firefly algorithm, which includes the output power of a micro turbine under the optimal scheduling scheme.

[0045] Figure 16 This invention provides an embodiment of a microgrid scheduling method based on an improved multi-objective firefly algorithm, which includes the optimal scheduling scheme for the power output interacting with the external power grid.

[0046] Figure 17 This invention provides an embodiment of the overall output power of a microgrid under the optimal scheduling scheme in a microgrid scheduling method based on an improved multi-objective firefly algorithm.

[0047] Figure 18 Seven algorithms are presented at the Pareto front of the microgrid scheduling model. Detailed Implementation

[0048] To make the objectives, technical solutions, and advantages of the embodiments of the present invention clearer, the technical solutions in the embodiments of the present invention will be clearly and completely described below. Obviously, the described embodiments are only some embodiments of the present invention, not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention. Unless otherwise defined, the technical or scientific terms used herein should have the ordinary meaning understood by those skilled in the art to which this invention pertains.

[0049] refer to Figure 1 This invention provides an improved microgrid scheduling method based on the multi-objective firefly algorithm, comprising the following steps:

[0050] S1. Construct the microgrid system model, microgrid objective function, and microgrid constraints;

[0051] S2. Construct a microgrid scheduling model based on the microgrid system model, the microgrid objective function, and the microgrid constraints;

[0052] S3. Solve the microgrid scheduling model based on the improved multi-objective firefly algorithm to obtain the optimal scheduling scheme;

[0053] In fact, the microgrid scheduling method provided by this invention generates a microgrid scheduling model by constructing a microgrid system model, a microgrid objective function, and microgrid constraints. By using an improved multi-objective firefly algorithm to solve the microgrid scheduling model, the solution efficiency of the microgrid scheduling model can be improved, thus achieving the goal of efficiently obtaining the optimal solution of the microgrid scheduling model.

[0054] In some embodiments, the microgrid system model in step S1 includes a photovoltaic power generation system, a wind power generation system, a micro turbine power generation system, a diesel engine power generation system, and an energy storage battery system.

[0055] Specifically, photovoltaic (PV) power generation converts solar radiation energy into direct current (DC) electricity through the photovoltaic effect of solar panels, which is then converted into usable alternating current (AC) electricity by an inverter. The formula for calculating the output power of PV power generation is as follows:

[0056]

[0057] Among them, P PV P represents the output power of photovoltaic power generation. STC I represents the maximum output power of the solar power generator under standard conditions; I represents the current solar radiation intensity; I STC The solar radiation intensity under standard conditions is typically taken as 1000 W / m². 2 k is the temperature coefficient of the solar panel; T c Let T be the temperature of the solar panel at time t; STC This represents the temperature of the solar panel under standard conditions.

[0058] Specifically, wind power generation involves capturing wind energy through a rotor, which then drives a generator via a transmission system to convert the wind energy into mechanical energy, and finally into usable electrical energy. The formula for calculating the output power of wind power generation is as follows:

[0059]

[0060] Among them, P WT v is the output power of the wind turbine; v is the wind speed at time t; v ci For the cut-in wind speed; v co To cut off the wind speed; v μ Rated wind speed; P T denoted as rated power; a, b, c, and d are polynomial coefficients.

[0061] Among them, micro turbine power generation uses high-temperature, high-pressure steam generated by burning natural gas to drive the micro turbine impeller to rotate, which in turn drives a generator to convert mechanical energy into electrical energy. The calculation formulas for its operation and maintenance costs, fuel costs, and pollutant gas treatment costs are as follows:

[0062]

[0063] Among them, C MT.OM (t) represents the operation and maintenance cost of the micro turbine; K MT.OM P represents the operating and maintenance cost coefficient for a micro steam turbine. MT (t) represents the output power of the micro turbine; C MT.F (t) represents the fuel cost of the micro turbine; C represents the fuel price of the micro turbine vehicle; LHV represents the lower heating value of the fuel; η MT (t) represents the power generation efficiency at time t; C MT.EN (t) represents the cost of treating pollutants from the micro turbine; C k γ is the treatment cost coefficient for the k-th type of pollutant gas; MT.k denoted as k, representing the emissions of the kth type of pollutant gas from the micro turbine; n represents the number of types of pollutant gases emitted by the micro turbine.

[0064] Specifically, diesel generators generate power by burning diesel fuel in a diesel engine, which drives a generator to convert mechanical energy into electrical energy, which is then converted into usable alternating current by control equipment. The formulas for calculating the operating and maintenance costs, fuel costs, and pollutant treatment costs during the operation process are as follows:

[0065]

[0066] Among them, C DE.OM (t) represents the operating and maintenance cost of the diesel generator; K DE.OM P represents the operating and maintenance cost coefficient for diesel generators. DE (t) represents the output power of the diesel generator; C DE.F (t) represents the fuel cost of the diesel generator; C DE.EN (t) represents the cost of treating pollutants from the diesel generator; γ DE.k C represents the emissions of Class k pollutants from a diesel generator. k α represents the cost coefficient for pollutant class k; α, β, and γ represent fuel cost coefficients.

[0067] Specifically, in a microgrid, energy storage batteries convert electrical energy into chemical energy for storage through the charging and discharging mechanism of battery packs, and then convert it back into electrical energy via an inverter; the formula for calculating battery energy storage capacity is as follows:

[0068]

[0069] Where SOC(t) is the energy storage capacity of the energy storage battery; P BESS (t) represents the charging and discharging power of the energy storage battery, P BESS (t) > 0 indicates that the energy storage battery is being charged, P BESS (t)≤0 indicates that the energy storage battery is discharging; η + The charging power of the energy storage battery; η - This refers to the discharge efficiency of the energy storage battery.

[0070] In some embodiments, the microgrid objective function in step S1 is the core of the microgrid dispatch model, used to evaluate the comprehensive performance of the dispatch strategy. Its design should be closely integrated with the microgrid's operating characteristics and actual needs, typically including an economic objective function for operating costs and an environmental objective function. In the grid-connected operation mode with external grid participation, the operating costs of the microgrid include the operation and maintenance costs of the micro turbine generator system, diesel generator system, energy storage battery system, and interaction with the external grid. The micro turbine, diesel generator, energy storage battery, and interaction with the external grid will emit air pollutants, mainly CO2, SO2, and NO. x Polluting gases, etc.

[0071] Specifically, the formula for calculating the economic objective function of microgrid operating costs is as follows:

[0072]

[0073] Where f1 is the economic objective function for the operating cost of the microgrid; C MT (t) represents the operation and maintenance cost of the micro steam turbine power generation system; C DE (t) represents the operation and maintenance cost of the diesel generator system; C BESS (t) represents the operation and maintenance cost of the energy storage battery system; C GRID (t) represents the operation and maintenance costs of the microgrid and the external power grid; K BESS.OM C represents the operation and maintenance cost coefficient for energy storage batteries. BUY (t) represents the electricity purchase cost between the microgrid and the external power grid; C SELL (t) represents the electricity sales revenue between the microgrid and the external power grid; c BUY (t) represents the real-time electricity purchase price between the microgrid and the external power grid; P BUY (t) represents the power purchased by the microgrid from the external power grid; c SELL (t) represents the real-time electricity price between the microgrid and the external power grid; P SELL (t) represents the electricity sold by the microgrid and the external power grid.

[0074] Specifically, the environmental protection objective function is defined as the sum of the products of the emission amounts of various pollutants and the unit environmental cost coefficient, and the calculation formula is as follows:

[0075]

[0076] Where f2 is the environmental impact objective function of the microgrid; C GRID.EN (t) represents the cost of pollutant treatment during the interaction between the microgrid and the external power grid; γ GRID.k It represents the emission of type k pollutant gas during the interaction between the microgrid and the external power grid; C k It is the cost coefficient for the k-th type of pollutant.

[0077] In some embodiments, the microgrid constraints in step S1 mainly include equipment operation constraints and power balance constraints. Equipment operation constraints ensure that distributed power sources, energy storage devices, and other equipment can operate within physical characteristics and safety criteria; power balance constraints maintain the real-time energy balance and operational stability of the microgrid. Specifically, equipment operation constraints can be micro turbine operation constraints, diesel engine operation constraints, and energy storage battery device constraints; power balance constraints can be power interaction constraints between the microgrid and the external power grid, and microgrid power balance constraints.

[0078] Specifically, the operating constraints of micro turbines mainly include rated power limits and dynamic adjustment constraints. The rated power limit defines the safe operating range of the equipment's active and reactive power, preventing generator overload / underload and ensuring equipment lifespan. The dynamic adjustment constraint limits the power ramp-up rate to avoid equipment damage or system instability caused by drastic power fluctuations. The expression for this constraint is as follows:

[0079]

[0080] in, This represents the lower limit of the output power of a micro steam turbine. This represents the upper limit of the output power of the micro turbine; r MT This is the threshold for the increase or decrease in power of a micro gas turbine per unit time.

[0081] Specifically, diesel engine operating constraints mainly include rated power limits and dynamic adjustment constraints. Rated power limits define the safe boundary of active power output to prevent equipment overload; dynamic adjustment constraints limit the power ramp-up rate to avoid unit vibration, increased wear, or excessive system frequency fluctuations caused by rapid load changes. The expression for these constraints is as follows:

[0082]

[0083] in, This is the lower limit of the diesel engine's output power; This represents the upper limit of the diesel engine's output power; r DE This is the threshold for the increase or decrease in power of a diesel engine per unit time.

[0084] Specifically, constraints on energy storage battery equipment mainly include charge / discharge power constraints and capacity limits. Charge / discharge power constraints limit the upper and lower limits of the battery's charge / discharge power per unit time, ensuring it does not exceed the equipment's rated power and safe operating thresholds. Capacity limits maintain the battery's remaining charge within a reasonable range, preventing equipment damage due to overcharging or over-discharging. The expression for these constraints is as follows:

[0085]

[0086] in, This represents the lower limit of the charging and discharging power of energy storage batteries. The upper limit of the charge and discharge power of energy storage batteries; SOC min (t) represents the lower limit of the energy storage capacity in the energy storage battery; SOC max (t) represents the upper limit of the energy storage capacity in the energy storage battery.

[0087] Specifically, the power constraint for the interaction between the microgrid and the external power grid must ensure that the active and reactive power injected by the microgrid into or drawn from the external power grid does not exceed the safe threshold of line transmission power. The constraint expression is as follows:

[0088]

[0089] in, This represents the lower limit of the power transmitted during the interaction between the microgrid and the external power grid. This represents the upper limit of the power transmitted during the interaction between the microgrid and the external power grid.

[0090] Specifically, the power balance constraint of a microgrid requires that, during operation, the microgrid system maintain a dynamic balance between the active and reactive power of distributed generation sources, the power consumed by loads, and the power interacting with the mains grid to ensure system frequency and voltage stability. The expression for this constraint is as follows:

[0091] P PV (t)+P WT (t)+P GRID (t)+P DE (t)+P MT (t)+P BESS (t)=P L (t)

[0092] Among them, P L (t) represents the total load of the microgrid's output power.

[0093] In some embodiments, in step S31, the firefly population size N, decision variable D, maximum number of iterations MaxIt, light attraction coefficient γ, and maximum attraction β0 are set.

[0094] Specifically, for any two fireflies i and j, their attraction β ij The calculation formula is as follows:

[0095]

[0096] Where β0 is the attractive force at the light source r = 0, usually taken as 1; γ is the light absorption coefficient, with a value in the range of γ∈[0.01,100]; r ij Let be the Euclidean distance from firefly i to firefly j.

[0097] In some embodiments, in step S3, the objective function value is calculated based on the microgrid objective function to determine the operation and maintenance cost objective function value and the environmental protection cost objective function value for each individual firefly in the firefly population, thereby evaluating the operation and maintenance cost and environmental protection cost for all microgrid scheduling schemes.

[0098] In some embodiments, in step S3 of the multi-target firefly algorithm (MOFA), each firefly traverses other fireflies before moving, comparing their luminous intensity. If the luminous intensity is stronger, it moves towards that firefly; otherwise, it continues traversing other fireflies until all traversals are completed. This firefly learning and updating mechanism is called the full attraction model. However, under this updating mechanism, fireflies with weaker luminous intensity need to frequently move towards those with stronger luminous intensity, which can easily cause oscillations and hinder algorithm convergence. Therefore, the improved multi-target firefly algorithm adopts a guided learning and updating mechanism. This mechanism uses non-dominated sorting to divide the firefly population into non-dominated and dominant fireflies, and calculates the angle j between each dominant firefly i and all non-dominated fireflies in the population. The non-dominant firefly with the largest angle to the currently dominant firefly is selected as the Leader for that dominant firefly. This reduces oscillations during the firefly's evolution and improves convergence. The formula for calculating the angle is as follows:

[0099]

[0100] in, Let be the angle between the i-th dominant firefly individual and the j-th non-dominant firefly individual; The dot product of the i-th dominant firefly individual and the j-th non-dominant firefly individual; Let be the target space vector of the i-th dominant firefly individual; Let be the target space vector of the j-th non-dominant firefly individual.

[0101] In some embodiments, in step S3, the firefly population is traversed cyclically, and the dominant firefly individual i learns to move from the guide according to the position update formula; the non-dominant firefly individual j undergoes random differential evolution (DE / rand / 2) according to the movement update formula to improve the global exploration ability of the non-dominant firefly individual.

[0102] Specifically, the position update formula is as follows:

[0103] x i (t+1)=x i (t)+β1(Leader i -x i (t))+αε

[0104] Where, x i (t+1) represents the dominant firefly individual after its position is updated; x i (t) represents the dominant firefly individual before the position update; β1 represents the dominant firefly individual x. iWith the Leader i The attraction between them; α is the step size factor, with a value range of α∈[0,1]; ε i It is a random vector.

[0105] Specifically, the move update formula is as follows:

[0106] x j (t+1)=x j (t)+F(x r1 (t)-x r2 (t)+x r3 (t)-x r4 (t))

[0107] Where, x j (t+1) represents the non-dominant firefly individual after its position is updated; x j (t) represents the non-dominant firefly individual before the position update; x r1 x r2 x r3 and x r4 , representing 4 firefly individuals randomly selected from non-dominant firefly individuals; F is the scaling factor, with a value range of F∈[0.4,0.95].

[0108] refer to Figures 2-4 The paper shows the Pareto front distribution of the algorithm before and after adopting the guided learning update mechanism on the ZDT1 test problem. The black dots represent the positions of the fireflies in the target space, and the black lines represent the optimal front surface of the test problem. Figure 2 The initial target space representing the firefly population; Figure 3 This indicates that individual fireflies using the traditional multi-objective firefly algorithm converge too early in the target space, indicating insufficient optimization accuracy. Figure 4 The results show that the firefly individuals using the guided learning update mechanism can effectively converge to the optimal Pareto front with a wider coverage. In summary, the improved multi-objective firefly algorithm effectively suppresses premature convergence and significantly improves the optimization accuracy.

[0109] In some embodiments, during the firefly individual update process in step S3, the non-dominant firefly individual guides the dominant firefly individual's movement. This can cause the dominant firefly individual to become overly dependent on the non-dominant firefly individual during its movement, thus easily getting trapped in a local optimum. Therefore, to avoid the algorithm getting trapped in a local optimum, the improved multi-objective firefly algorithm integrates Cauchy mutation and simulated binary crossover operator to enhance the local escape ability of firefly individuals. Specifically, the firefly population after the update position is sorted by non-dominant individuals, and the proportion of non-dominant firefly individuals in the firefly population is calculated. If the proportion of non-dominant firefly individuals in the firefly population is greater than 0.5, the firefly individuals in the population choose Cauchy mutation to update and evolve, improving the global search ability of the firefly individuals; if the proportion of non-dominant firefly individuals in the firefly population is less than 0.5, the firefly individuals in the population choose simulated binary crossover operator to update and evolve, improving the overall quality of the firefly individuals.

[0110] Specifically, Cauchy mutation leverages the long-tail characteristic of the Cauchy distribution to enhance population diversity, significantly improving the algorithm's ability to escape local optima in global search. The formula used is as follows:

[0111] x i (t+1)=x i (t)+x i (t)·cauchy(0,1)

[0112]

[0113] Where r is a random number that follows a normal distribution in the interval [0,1].

[0114] Specifically, the simulated binary crossover operator generates new individuals by combining two or more partial attributes of individuals in the population, thereby improving population diversity and convergence accuracy. The formula used is as follows:

[0115]

[0116] Where x1 and x2 represent two firefly individuals randomly selected from the firefly population; and denoted as , where is the decision variable value of the parent firefly individual at time t; j is the j-th dimension of the firefly's decision variables; β is the cross-distribution coefficient; rand is a uniformly distributed random number, ranging from [0,1]; η is the cross-distribution factor, the larger its value, the closer the cross-generated firefly will be to the parent firefly.

[0117] Specifically, the formula for calculating the proportion of non-dominant fireflies is as follows:

[0118]

[0119] Where R is the proportion of non-dominant fireflies; P is the set of non-dominant fireflies; sum(P) is the number of non-dominant fireflies; and N is the firefly population size.

[0120] refer to Figures 5-6 The algorithm improved by adopting the fusion mutation strategy is shown to compare the performance of the algorithm with the traditional multi-objective firefly algorithm in the decision space of the ZDT1 test problem. The black × represents the position of the firefly individual in the decision space. Figure 5 This indicates that the distribution range of individual fireflies in the decision space is limited by the traditional multi-objective firefly algorithm, indicating insufficient exploration ability and a tendency to get trapped in local optima; Figure 6 The results show that the fireflies covered the entire decision space after adopting the fusion mutation strategy, verifying the significant improvement in global exploration capability. In summary, the fusion mutation strategy can significantly improve the algorithm's exploration capability and avoid getting trapped in local optima.

[0121] In some embodiments, in step S3, the traditional constraint dominance principle prioritizes screening feasible solutions based on constraint violation degree in constrained multi-objective optimization, and then retains offspring based on Pareto dominance. Although this feasibility-first strategy can guide the search for feasible regions, it is prone to causing the population to converge prematurely to local feasible regions when faced with discrete or complex feasible region structures, neglecting the synergistic optimization of convergence and diversity. Therefore, to select and retain offspring fireflies with good convergence, diversity, and feasibility, the improved multi-objective firefly algorithm constructs multi-performance evaluation constraint dominance conditions based on the location advantages and disadvantages of individual fireflies, the distribution of firefly diversity, and the constraints of the microgrid scheduling model. The updated firefly population is merged with the previous generation to form a new population of size 2N. The new population is then ranked according to the multi-performance evaluation constraint dominance conditions, and r non-dominated firefly individuals are selected. If r ≤ N, the r non-dominated firefly individuals are removed from the new population. The crowding distance of the remaining firefly individuals is calculated and sorted in descending order based on the crowding distance. The top Nr firefly individuals with the largest crowding distance are merged with the r non-dominated firefly individuals to form the offspring firefly population. If r > N, the crowding distance of the remaining firefly individuals is calculated and sorted in descending order based on the crowding distance. The top N firefly individuals with the largest crowding distance are selected as the offspring firefly population. Among them, the quality of individual firefly locations is determined based on convergence indices; the diversity distribution of fireflies is determined based on diversity indices; and the constraints of the microgrid scheduling model are determined based on feasibility indices.

[0122] Specifically, the convergence metric assesses how close a firefly is to the Pareto front using the normalized objective function value of the individual firefly. The calculation formula is as follows:

[0123]

[0124] Where F(i) represents the individual firefly x i Convergence index; It's Firefly X i The normalized value of the j-th objective function; f j (x i (x) represents an individual firefly. i The original function value of the j-th objective function; Let be the minimum value of the objective function for the j-th individual firefly; Let be the maximum value of the j-th objective function among all firefly individuals; M is the number of objective functions; i is the number of firefly individuals; and j is the number of objective functions.

[0125] Specifically, the diversity index is calculated by determining the distribution of the firefly population in the target space using the Euclidean distance between each individual firefly. The calculation formula is as follows:

[0126]

[0127] Where D(i) represents the individual firefly x i diversity index; dis(x) i ,x n (For fireflies x) i Firefly X n Euclidean distance in the normalized target space; It is a firefly x n The normalized value of the j-th objective function.

[0128] Specifically, the feasibility index quantifies the degree to which individual fireflies satisfy the constraints by using their normalized constraint violation scores. The calculation formula is as follows:

[0129]

[0130] Where C(i) represents the individual firefly x i Feasibility indicators; For Firefly X i The normalized constraint violation value for the k-th constraint; It is the minimum value of the constraint violation degree of the k-th individual firefly; is the maximum value of the constraint violation degree of the k-th individual firefly; k is the constraint number; L is the total number of constraints.

[0131] Furthermore, for any individual firefly x i and individual fireflies x j If the constraint dominance conditions are met simultaneously, then it means that individual firefly x iConstraint and Domination of individual firefly x j The constraint dominance condition is defined as follows:

[0132]

[0133] refer to Figure 7 This diagram illustrates the selection process for individual fireflies in the target space. The shaded area represents the feasible region within the target space, white circles represent retained fireflies, and black circles represent rejected fireflies. Specifically, according to the feasibility index formula, the constraint violation degree of firefly samples within the feasible region is less than that outside the feasible region. Therefore, firefly individuals A, B, G, H, and I located outside the feasible region are rejected. According to the diversity index formula, the Euclidean distance of firefly individuals C, D, E, and F is closer to the Euclidean distance of other firefly individuals, resulting in a higher calculated diversity index value. Therefore, firefly individuals C, D, E, and F are also rejected. The final selected fireflies are evenly distributed within the feasible region.

[0134] To evaluate the effectiveness of the proposed microgrid scheduling method (GLMOFA-MG) based on the improved multi-objective firefly algorithm, a dual-dimensional verification was conducted using a MW benchmark problem and a practical application of microgrid optimal scheduling. The method was also compared with five existing novel optimization algorithms for solving constrained multi-objective optimization problems: C3M, TriP, MSCEA, MOEADLCDP, and DRLOSEMCMO. To ensure experimental fairness, the population size for all algorithms was set to 100, the maximum number of iterations was set to 10,000, and the experiment was repeated 30 times.

[0135] In the MW benchmark problem, the MW series of constrained multi-objective optimization benchmark problems were selected for evaluation. This series contains 14 test problems, characterized by high decision space dimensionality, relatively narrow feasible regions, and complex constraints, which can comprehensively test the algorithm's ability to handle such problems. The experiments were conducted on the evolutionary multi-objective optimization platform PlatEMO, and all comparison algorithms were implemented using Matlab2022b. The algorithm parameters adopted the default settings of the PlatEMO platform, and the source information of each comparison algorithm is shown in Table 1. Among them, the maximum gravity β0 of GLMOFA-MG is 1 and the light attraction coefficient γ is 1. Next, the inverse generational distance (IGD) and hypervolume (HV) indices were used to evaluate the algorithm performance, and the Friedman test was used to rank the various algorithms. The IGD index is calculated by calculating the average distance from the Pareto front approximate solution set to each point in the real Pareto front set, which comprehensively evaluates the convergence and diversity of the algorithm's solution set. The lower the value of this index, the closer the approximate solution set is to the true Pareto front and the more evenly distributed it is. This directly reflects the algorithm's ability to approximate the Pareto optimal solution and the quality of the solution set's coverage. The calculation formula is as follows:

[0136]

[0137] Where P is the optimal solution obtained by the algorithm; P * For a set of points uniformly distributed on the true Pareto front; |P * | represents the number of points uniformly distributed on the true Pareto front; dist(z,P) is the minimum Euclidean distance from the solution of P to the solution of z.

[0138] Table 1. Publications and years of each comparison algorithm.

[0139]

[0140] Table 2 shows the mean and standard deviation of GLMOFA-MG and five other optimization algorithms on IGD, and also counts the number of times each algorithm achieved its best result on the test problems. The Friedman test was used to rank the algorithms comprehensively, with bolded data representing the best results on each test problem. As shown in Table 1, GLMOFA-MG achieved the best mean IGD on 7 test problems, DRLOSEMCMO on 3 test problems, TriP on 2 test problems, and MSCEA and MOEADLCDP on 1 test problem each.

[0141] Table 2 shows the IGD results of different algorithms on 14 MW benchmark problems.

[0142]

[0143] refer to Figures 8-11 The figure shows the Pareto front approximation solution sets of six comparative algorithms on test problems MW1, MW3, MW9, and MW14. The horizontal and vertical axes represent the ranges of the two objective functions, respectively. Gray circles represent the Pareto front approximation solution sets obtained by each algorithm, and gray areas represent the feasible regions of the test problems. As can be seen from the figure, GLMOFA-MG can obtain a uniformly distributed and relatively diverse Pareto front approximation solution set within the feasible region.

[0144] Microgrid systems integrate various distributed energy devices, specifically including solar photovoltaic panels, wind turbines, diesel generators, micro gas turbines, and energy storage batteries. In practical applications of microgrid optimized dispatching, a 24-hour dispatching cycle is set, and microgrid dispatching solutions are recorded at hourly intervals. Each dispatchable unit of distributed energy is defined as a 24-dimensional decision variable. To evaluate the optimal dispatching efficiency of a local microgrid, the predicted output power of local photovoltaic and wind power is used as input data into the microgrid dispatching model. The GLMOFA-MG algorithm is used to solve the model to obtain the optimal dispatching scheme. Table 3 shows the key operating parameters of distributed energy devices; Table 4 shows the pollutant emission coefficients and treatment costs of distributed energy devices; Table 5 shows the parameters of energy storage batteries; and Table 6 shows real-time electricity price data.

[0145] Table 3 Key Operating Parameters of Distributed Energy Equipment

[0146]

[0147] Table 4 Pollutant emission coefficients and treatment costs of distributed energy equipment

[0148]

[0149] Table 5 Energy Storage Battery Parameters

[0150]

[0151]

[0152] Table 6 Real-time Electricity Prices

[0153]

[0154] refer to Figure 12 It displays historical data and predicted values ​​for photovoltaic and wind power output in the area.

[0155] refer to Figures 13-16This paper demonstrates the output power interaction between the diesel generator, battery, micro turbine, and external power grid under the optimal dispatch scheme. It can be seen that the diesel generator and micro turbine maintain continuous power supply throughout the 24-hour dispatch cycle; the battery charging power gradually decreases between 6:00 and 12:00, primarily selling excess electricity from the microgrid to the external grid during this period; the battery continuously charges between 13:00 and 24:00 to meet the microgrid's own subsequent power demand, thereby significantly reducing the cost of purchasing electricity from the external grid. The battery charging and discharging strategy effectively regulates the power exchange between the microgrid and the external grid.

[0156] refer to Figure 17 This displays the output power of each distributed energy source in a microgrid over 24 hours under the optimal scheduling scheme, where different colored blocks represent different distributed energy source output power. Figure 17 It can be seen that the various distributed energy sources work together to maintain the stable operation of the microgrid system, demonstrating the effectiveness of the scheduling scheme proposed by GLMOFA-MG in maintaining the stable operation of the system.

[0157] refer to Figure 18 This paper presents the Pareto front approximate solution sets obtained by GLMOFA-MG and six other comparative algorithms for solving the microgrid scheduling problem. The bolded data represents the environmental protection cost of the microgrid on the horizontal axis and the operating cost on the vertical axis. Figure 18 It can be seen that GLMOFA-MG achieves a better Pareto front compared to the other 6 comparison algorithms.

[0158] Table 7 shows the environmental protection cost and operation and maintenance cost of the microgrid under the optimal scheduling scheme compared with six other algorithms. The bolded data represents the lowest environmental protection cost and the lowest operation and maintenance cost. As can be seen from Table 7, the optimal scheduling scheme achieved by GLMOFA-MG achieves the lowest environmental protection cost and the lowest operation and maintenance cost. Furthermore, compared with the MOFA algorithm's scheduling scheme, GLMOFA-MG effectively reduces both environmental protection cost and operation and maintenance cost.

[0159] Table 7. Environmental protection costs and operation and maintenance costs of different algorithms in microgrid dispatching models.

[0160]

[0161] While embodiments of the present invention have been described in detail above, it will be apparent to those skilled in the art that various modifications and variations can be made to these embodiments. However, it should be understood that such modifications and variations fall within the scope and spirit of the invention as set forth in the claims. Furthermore, the invention described herein may have other embodiments and can be implemented or carried out in various ways.

Claims

1. A microgrid scheduling model based on an improved multi-objective firefly algorithm, characterized in that, include: Construct a microgrid system model, microgrid objective function, and microgrid constraints; A microgrid scheduling model is constructed based on the microgrid system model, the microgrid objective function, and the microgrid constraints. The optimal scheduling scheme is obtained by solving the microgrid scheduling model based on the improved multi-objective firefly algorithm.

2. The method as described in claim 1, characterized in that, When solving the microgrid scheduling model using the improved multi-objective firefly algorithm to obtain the optimal scheduling scheme, the following steps are included: Initialize the firefly population and the output power scheme of distributed energy devices, set the parameters of the microgrid scheduling model and the parameters of the improved multi-objective firefly algorithm, and calculate the objective function value of each individual firefly in the firefly population based on the objective function of the microgrid. Based on the objective function value, the firefly population is divided into non-dominant firefly individuals and dominant firefly individuals using non-dominant sorting. The angle between the dominant firefly individuals and the non-dominant firefly individuals is calculated, and the leader of the dominant firefly individual is determined according to the angle. Dominant firefly individuals learn to move from the guide according to the position update formula, while non-dominant firefly individuals undergo random differential evolution according to the movement update formula. The firefly population after the position is updated is sorted by dominance, and the proportion of non-dominant firefly individuals is calculated. A mutation strategy is selected based on the proportion of non-dominant firefly individuals. Construct multi-performance evaluation constraint dominance conditions, merge the updated firefly population and the previous generation firefly population to form a new population, constrain and dominate the new population based on the multi-performance evaluation constraint conditions, select non-dominated firefly individuals that meet the minimum constraint conditions, and retain the optimal scheduling scheme. Repeat the process until the maximum number of iterations is reached, and then output the optimal scheduling scheme.

3. The method as described in claim 2, characterized in that, include: The objective function value is calculated based on the microgrid objective function; the microgrid scheduling model parameters include key parameters of each distributed energy device, pollutant emission coefficient, unit price of pollutant treatment cost, real-time electricity price, and energy storage battery parameters; the improved multi-objective firefly algorithm parameters include decision variables, maximum number of iterations, light attraction coefficient, and maximum attraction force.

4. The method as described in claim 2, characterized in that, Calculating the angle between the dominant firefly individual and the non-dominant firefly individuals, and determining the guide of the dominant firefly individual based on the angle, includes: calculating the angle between each dominant firefly individual in the firefly population and all non-dominant firefly individuals, and selecting the non-dominant firefly individual with the largest angle to the currently dominant firefly individual as the guide of that dominant firefly individual.

5. The method as described in claim 2, characterized in that, The location update formula and the movement update formula are defined as follows: x i (t+1)=x i (t)+β1(Leader i -x i (t))+αε x j (t+1)=x j (t)+F(x r1 (t)-x r2 (t)+x r3 (t)-x r4 (t)) Where, x i (t+1) represents the dominant firefly individual after its position is updated, x i (t) represents the dominant firefly individual before the position update, and β1 represents the dominant firefly individual x. i With the Leader i The attraction between them, where α is the step size factor, and ε i x is a random vector; j (t+1) represents the non-dominant firefly individual after its position is updated, x j (t) represents the non-dominant firefly individual before the position update, x r1 x r2 x r3 and x r4 Let F represent four firefly individuals randomly selected from the non-dominated firefly individuals, and F is the scaling factor.

6. The method as described in claim 2, characterized in that, When selecting a mutation strategy based on the proportion of non-dominant firefly individuals, the strategy includes: if the proportion of non-dominant firefly individuals in the firefly population is greater than 0.5, the firefly individuals in the firefly population choose the Cauchy mutation for renewal and evolution; if the proportion of non-dominant firefly individuals in the firefly population is less than 0.5, the firefly individuals in the firefly population choose the simulated binary crossover operator for renewal and evolution.

7. The method as described in claim 2, characterized in that, When constructing the multi-performance evaluation constraint dominance conditions, the following steps are taken: Constructing multi-performance evaluation constraint dominance conditions based on convergence indices, feasibility indices, etc.; the convergence indices assess the degree to which individual fireflies approach the Pareto front using the normalized objective function value of each individual firefly; the diversity indices calculate the widespread distribution of the firefly population in the target space using the Euclidean distance between each individual firefly; and the feasibility indices quantify the degree to which individual fireflies satisfy the constraint conditions using the normalized constraint violation value of each individual firefly.

8. The method as described in claim 7, characterized in that, For any individual firefly x i and individual fireflies x j If the multi-performance evaluation constraint dominance condition is satisfied simultaneously, then it means that individual firefly x... i Constraint and Domination of individual firefly x j The governing conditions of the multi-performance evaluation constraints are defined as follows: Where F(i) and F(j) are the individual firefly x i and individual fireflies x j The convergence indices are D(i) and D(j), which represent the convergence indices of individual firefly x. i and individual fireflies x j The diversity indicators, C(i) and C(j), represent the number of firefly individuals x, respectively. i and individual fireflies x j Feasibility indicators.

9. The method as described in claim 2, characterized in that, When selecting non-dominant firefly individuals that meet the minimum constraint condition, the process includes: merging the updated firefly population and the previous generation firefly population to form a new population with a size of 2N; sorting the new population according to the constraint dominance condition; selecting r non-dominant firefly individuals; if r ≤ N, removing r non-dominant firefly individuals from the new population; calculating the crowding distance of the remaining firefly individuals and sorting them in descending order according to the crowding distance; merging the Nr firefly individuals with the largest crowding distance with the r non-dominant firefly individuals to form the offspring firefly population; if r > N, calculating the crowding distance of the remaining firefly individuals and sorting them in descending order according to the crowding distance; and selecting the N firefly individuals with the largest crowding distance as the offspring firefly population.

10. The method as described in claim 1, characterized in that, The microgrid system model includes a photovoltaic power generation system, a wind power generation system, a micro turbine power generation system, a diesel engine power generation system, and an energy storage battery system; the microgrid objective function includes an economic objective function for operating costs and an environmental objective function; the microgrid constraints include micro turbine operating constraints, diesel engine operating constraints, power interaction constraints between the microgrid and the external power grid, energy storage battery device constraints, and microgrid power balance constraints.

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