Microgrid multi-objective optimization method and system based on improved SABO algorithm

Abstract

The present invention discloses a microgrid multi-objective optimization method and system based on an improved SABO algorithm, relating to the field of energy management technology for microgrids. The method comprises the following steps: establishing a microgrid multi-objective optimization scheduling model based on distributed power sources in the microgrid; introducing a chaotic mapping mechanism, an elite-guided development strategy, and a golden sine algorithm into the subtraction average optimization algorithm to obtain an improved subtraction average optimization algorithm; constructing a multi-objective improved subtraction average optimizer based on the improved subtraction average optimization, using the multi-objective improved subtraction average optimizer to solve the multi-objective optimization scheduling model, and performing energy scheduling on the microgrid based on the solution results. The present invention uses the improved multi-objective SABO to solve the microgrid multi-objective optimization scheduling model, thereby ensuring a uniform distribution of the Pareto solution set and improving the calculation speed, thereby achieving efficient multi-objective optimization scheduling of the microgrid.

Description

Technical Field

[0001] The present invention relates to the technical field of microgrid energy management, and in particular to a microgrid multi-objective optimization method and system based on an improved SABO algorithm. Background Art

[0002] The statements in this section merely provide background information related to the present invention and do not necessarily constitute prior art.

[0003] In recent years, with the increasing demands on power systems, multi-objective optimization of microgrids has become increasingly important, rather than solely focusing on economic indicators to minimize operating costs. Current multi-objective optimization scheduling models for microgrids comprehensively consider multiple factors, including power generation operating costs, carbon emissions, energy utilization, and stability. This represents a key development direction in microgrid optimization research. In multi-objective optimization problems, the solution sets generated by traditional methods are often unevenly distributed, resulting in clustering or discontinuities on the Pareto front. This unevenness results in a lack of a continuous and smooth trade-off space for decision makers when selecting the final execution strategy, making it difficult to find the truly optimal compromise.

[0004] The core concept of the Subtraction-Average-Based Optimizer (SABO) is based on mathematical concepts such as the arithmetic mean and the difference in search agent positions. This algorithm uses a unique "subtraction operation" to update the search agent position, utilizing the arithmetic mean position of all individuals in the group rather than relying solely on the best or worst individual, thereby enhancing global exploration capabilities. However, the SABO algorithm currently has many limitations in its application to multi-objective microgrid optimization. While SABO's use of the arithmetic mean position of the group to update the search agent position enhances global exploration capabilities, it may be insufficient in local exploration. Microgrid optimization scheduling problems are characterized by multiple objectives, multiple variables, nonlinearity, and high dimensionality. Relying solely on global exploration can make it difficult to find the optimal solution under complex constraints. Furthermore, while the SABO algorithm avoids the limitation of relying solely on the best or worst individual through the group average position update mechanism, it can still suffer from uneven solution distribution in multi-objective optimization. The Pareto front of multi-objective microgrid optimization requires a trade-off between multiple objectives. If the solution distribution is uneven, the optimization results of some objectives may be overly neglected.

[0005] Therefore, how to use the SABO algorithm to achieve efficient multi-objective optimization of microgrids has become a technical problem that needs to be solved urgently in existing technologies. Summary of the Invention

[0006] To address the shortcomings of existing technologies, the present invention provides a multi-objective optimization method and system for microgrids based on an improved SABO algorithm. This method uses the interaction between the microgrid and the main grid, the power generated by gas turbines, diesel generators, and batteries as decision variables, and the predicted values ​​of photovoltaic power generation, wind power generation, and load power as known variables. Minimizing the microgrid's operating costs and carbon emissions is the optimization objective. The improved multi-objective SABO algorithm is used for solution, ensuring a uniform distribution of Pareto solutions while increasing computational speed.

[0007] In order to achieve the above object, the present invention is implemented through the following technical solutions:

[0008] A first aspect of the present invention provides a microgrid multi-objective optimization method based on an improved SABO algorithm, comprising the following steps:

[0009] Establish a multi-objective optimization scheduling model for microgrid based on distributed power sources in microgrid;

[0010] The improved subtractive average optimization algorithm is obtained by introducing a chaotic mapping mechanism, an elite-guided development strategy, and a golden sine algorithm into the subtractive average optimization algorithm. The chaotic mapping mechanism is used to initialize particles, and different search strategies are generated through different combinations of the subtractive average optimization algorithm, the elite-guided development strategy, and the golden sine algorithm. Different search strategies are used in the early, middle, and late stages of the iterative process to dynamically adjust the search behavior.

[0011] Based on the improved subtraction average optimization, a multi-objective improved subtraction average optimizer is constructed. The multi-objective improved subtraction average optimizer is used to solve the multi-objective optimization scheduling model, and the energy scheduling of the microgrid is carried out according to the solution results.

[0012] Furthermore, the distributed power sources in the microgrid include photovoltaic power generation systems, wind turbines, micro gas turbines, diesel generators and batteries.

[0013] Furthermore, the constraints of the microgrid multi-objective optimization scheduling model are set, including micro gas turbine power constraint, micro gas turbine power constraint, diesel generator power constraint, battery power constraint and interactive power constraint.

[0014] Furthermore, the specific steps of initializing particles using the chaotic mapping mechanism are as follows:

[0015] By adding random perturbation terms into the Tent chaotic mapping formula, the improved Tent chaotic mapping formula is obtained.

[0016] Perform Bernoulli transform on the improved Tent chaos mapping formula;

[0017] The particle population is initialized using the transformed Tent chaos mapping formula.

[0018] Furthermore, different search strategies are generated through different combinations of the subtraction average optimization algorithm, the elite guided development strategy and the golden sine algorithm, including: a fusion strategy of the subtraction average optimization algorithm and the golden sine algorithm, a fusion strategy of the subtraction average optimization algorithm, the elite guided development strategy and the golden sine algorithm, and a fusion strategy of the subtraction average optimization algorithm and the elite guided development strategy.

[0019] Furthermore, the specific steps for dynamically adjusting the search behavior by using different search strategies in the early, middle and late stages of the iteration process are as follows:

[0020] In the early stage of iteration, with the core goal of enhancing global search capabilities, a fusion strategy combining the subtraction average optimization algorithm and the golden sine algorithm was adopted.

[0021] In the middle of the iteration, a fusion strategy combining the subtraction mean optimization algorithm, the elite-guided development strategy, and the golden sine algorithm is adopted. The subtraction mean optimization algorithm, the elite-guided development strategy, and the golden sine algorithm run in parallel, and the probability of collaborative search decays linearly with the number of iterations.

[0022] In the later stage of iteration, we focus on the refined mining of the neighborhood of high-quality solutions and adopt a fusion strategy of the subtraction average optimization algorithm and the elite guided development strategy to make the Pareto frontier solution set converge quickly.

[0023] Furthermore, a multi-objective improved subtraction average optimizer is constructed based on the improved subtraction average optimization. The specific steps of using the multi-objective improved subtraction average optimizer to solve the multi-objective optimization scheduling model are as follows:

[0024] The improved subtraction average optimizer is used to maintain the Pareto solution set based on the crowding distance to select the top The solution with the largest crowding distance is taken as the optimal solution for the archive library;

[0025] When the number of feasible solutions in the archive library falls below the preset minimum diversity threshold, the solution enhancement strategy is automatically triggered.

[0026] A second aspect of the present invention provides a microgrid multi-objective optimization system based on an improved SABO algorithm, comprising:

[0027] A model building module is configured to establish a microgrid multi-objective optimization scheduling model according to distributed power sources in the microgrid;

[0028] An algorithm improvement module is configured to introduce a chaotic mapping mechanism, an elite-guided development strategy, and a golden sine algorithm into the subtractive average optimization algorithm to obtain an improved subtractive average optimization algorithm. The improved algorithm uses the chaotic mapping mechanism to initialize particles, generates different search strategies through different combinations of the subtractive average optimization algorithm, the elite-guided development strategy, and the golden sine algorithm, and dynamically adjusts the search behavior by using different search strategies at the early, mid, and late stages of the iterative process.

[0029] The energy scheduling module is configured to construct a multi-objective improved subtraction average optimizer based on the improved subtraction average optimization, use the multi-objective improved subtraction average optimizer to solve the multi-objective optimization scheduling model, and perform energy scheduling on the microgrid based on the solution results.

[0030] A third aspect of the present invention provides a medium having a program stored thereon, which, when executed by a processor, implements the steps of the microgrid multi-objective optimization method based on the improved SABO algorithm as described in the first aspect of the present invention.

[0031] The fourth aspect of the present invention provides a device comprising a memory, a processor, and a program stored in the memory and executable on the processor. When the processor executes the program, the steps in the multi-objective optimization method for a microgrid based on the improved SABO algorithm as described in the first aspect of the present invention are implemented.

[0032] One or more of the above technical solutions have the following beneficial effects:

[0033] The present invention discloses a microgrid multi-objective optimization method and system based on an improved SABO algorithm. The invention combines the Tent chaos map, the golden sine algorithm and the elite-guided development strategy, and proposes a three-stage progressive search strategy. By dynamically adjusting the search behavior of the algorithm, an organic balance between global exploration and local development is achieved.

[0034] The present invention first constructs a multi-objective mathematical optimization model for microgrids. This model uses the output power of distributed generation (DGs) as the decision variable and simultaneously considers two conflicting optimization objectives: power generation operating costs and carbon emissions. Specifically, the operating cost objective function incorporates economic indicators such as fuel costs and maintenance expenses, while the carbon emissions objective function quantitatively assesses the environmental impact of system operation. The resulting Pareto front encompasses a range of optimal decision combinations under different priorities.

[0035] Advantages of additional aspects of the present invention will be given in part in the following description and in part will be obvious from the following description, or will be learned through practice of the present invention. BRIEF DESCRIPTION OF THE DRAWINGS

[0036] The accompanying drawings, which constitute a part of the present invention, are used to provide a further understanding of the present invention. The exemplary embodiments of the present invention and their descriptions are used to explain the present invention and do not constitute improper limitations on the present invention.

[0037] Figure 1 Flowchart of a multi-objective optimization method for a microgrid based on an improved SABO algorithm in Embodiment 1 of the present invention;

[0038] Figure 2 The image of the F5 function in the CEC2005 test function in the first embodiment of the present invention;

[0039] Figure 3 This is a comparison chart of the convergence curves of various algorithms in the F5 test function in Example 1 of the present invention;

[0040] Figure 4 The image of the F8 function in the CEC2005 test function in the first embodiment of the present invention;

[0041] Figure 5 This is a comparison chart of the convergence curves of various algorithms in the F8 test function in Example 1 of the present invention;

[0042] Figure 6 This is a performance diagram of the improved SABO algorithm in Example 1 of the present invention on the ZDT test function. DETAILED DESCRIPTION

[0043] It should be noted that the following detailed descriptions are exemplary and intended to provide further explanation of the present invention. Unless otherwise specified, all technical and scientific terms used herein have the same meaning as commonly understood by those skilled in the art to which the present invention belongs.

[0044] It should be noted that the terms used herein are only for describing specific embodiments and are not intended to limit the exemplary embodiments according to the present invention. As used herein, unless the context clearly indicates otherwise, the singular form is intended to include the plural form. In addition, it should be understood that when the terms "comprise" and / or "include" are used in this specification, they indicate the presence of features, steps, operations, devices, components and / or their combinations;

[0045] Example 1:

[0046] The first embodiment of the present invention provides a microgrid multi-objective optimization method based on an improved SABO algorithm, comprising the following steps:

[0047] Step 1: Establish a multi-objective optimization scheduling model for the microgrid based on the distributed power sources in the microgrid.

[0048] In this embodiment, the distributed power sources in the microgrid include a photovoltaic system, wind turbines, micro gas turbines, diesel generators, and batteries. With minimizing the microgrid's operating costs and carbon emissions as the optimization goals, a multi-objective optimization scheduling model for the microgrid is established by setting output constraints.

[0049] Step 1.1: Establish a multi-objective optimization scheduling model for microgrids.

[0050] The microgrid multi-objective optimization model proposed in this embodiment is as follows:

[0051] (1).

[0052] in, is the microgrid operating cost, is the carbon emissions of the microgrid, and represent inequality constraints and equality constraints, respectively.

[0053] Step 1.1.1: Mathematical model of microgrid operation cost.

[0054] (2),

[0055] (3),

[0056] (4),

[0057] (5),

[0058] (6),

[0059] (7).

[0060] Where, Indicates the scheduling period, for Fuel costs during the period, including fuel costs for micro gas turbines, diesel generators, etc. for The operation and maintenance costs of each distributed power source in the microgrid during this period, for The interaction cost between the microgrid and the large grid during the period, for The electricity purchase cost of the microgrid during the period, for The electricity sales revenue of the microgrid during the period, for The power purchased by the microgrid from the large grid during the period, for The power sold by the microgrid to the large grid during the period, is the number of time periods contained in the daily scheduling cycle, is the discrete time variable in the microgrid scheduling scheme, and its upper limit is .

[0061] Fuel cost of microturbine during the period :

[0062] (8).

[0063] Where, is the fuel price (yuan / m 3 ), is the power generation efficiency of the micro gas turbine, is the lower calorific value of natural gas (kW·h / m 3 ), for Output power of the micro gas turbine during this period.

[0064] Fuel cost of diesel generators during the period :

[0065] (9).

[0066] Where, for The fuel cost of the diesel generator during the period is a quadratic function obtained by fitting. 、 、 are the coefficients of the quadratic function, for The output power of the diesel generator during the period.

[0067] Operation and maintenance costs of each micro power source:

[0068] (10).

[0069] Where, Indicates the first Micro power supply, , For the Operation and maintenance coefficient of micro power source, for Time period Output power of micro power supply.

[0070] Step 1.1.2: Mathematical model of microgrid carbon emissions.

[0071] The carbon trading mechanism uses the purchase and sale of carbon emissions in the form of quotas to achieve low-carbon emission reductions. Standard carbon trading mechanism models mainly include carbon emission quota models, actual carbon emission models, and tiered carbon price trading models.

[0072] (11),

[0073] (12),

[0074] (13).

[0075] Where, Indicates the duration of the scheduling period, which is 1 hour in this invention. is the share of microgrid participating in carbon trading, 、 are the carbon emission quota and actual carbon emissions of the microgrid respectively. represents the daily scheduling cycle, 、 、 are the unit carbon emission quota, 、 、 are the actual carbon emissions per unit.

[0076] (14).

[0077] Where, is the cost of tiered carbon trading, is the basic price for carbon trading. The length of the carbon emission interval is divided into two parts. is the price growth rate.

[0078] Step 1.2: Set the constraints of the microgrid multi-objective optimization scheduling model, including micro gas turbine power constraint, micro gas turbine power constraint, diesel generator power constraint, battery power constraint and interactive power constraint.

[0079] Step 1.2.1: Power balance constraints:

[0080] (15).

[0081] Where, for Photovoltaic output power during the period, for The fan output power during the period, for Battery output power during the time period (discharge is positive, charge is negative), for Load power during the period.

[0082] Step 1.2.2: The power constraints of the micro gas turbine are divided into output constraints and ramp constraints.

[0083] Its mathematical model is as follows:

[0084] (16).

[0085] Where, and are the upper and lower limits of the micro gas turbine output power, It is the upper limit of the micro gas turbine climbing power.

[0086] Step 1.2.3: The diesel generator power constraints are divided into output constraints and ramp constraints.

[0087] Its mathematical model is as follows:

[0088] (17).

[0089] Where, and are the upper and lower limits of the diesel generator output power, It is the upper limit of the diesel generator's climbing power.

[0090] Step 1.2.4: Battery power constraints.

[0091] (18).

[0092] Where, 、 are the upper and lower limits of the battery output power, 、 The upper and lower limits of battery capacity.

[0093] Step 1.2.5: Interaction power constraints.

[0094] (19).

[0095] Where, 、 are the maximum power purchase and sale of the microgrid and the large power grid respectively.

[0096] Step 2: Introduce the chaos mapping mechanism, elite guided development strategy and golden sine algorithm into the subtraction average optimization algorithm to obtain the improved subtraction-average-based optimizer (ISABO), as shown in Figure 1 shown.

[0097] In a specific implementation, this embodiment improves the Subtraction Average Optimizer (SABO) algorithm by introducing the Tent chaos mapping mechanism, the elite-guided development strategy, and the golden sine algorithm to achieve a balance between exploration and development.

[0098] Subtractive Average Optimizer (SABO) algorithm.

[0099] Every optimization problem has a solution space, called the search space. This search space is a subset of the dimensional space, with a dimension equal to the number of decision variables in the given problem. The algorithm's search agents (i.e., individuals in the population) determine the values ​​of the decision variables based on their position in the search space. Therefore, each search agent contains information about the decision variables and is mathematically modeled as a vector. The collection of all search agents together constitutes the algorithm's population. Mathematically, this population can be represented by the following matrix:

[0100] (20).

[0101] in, is the SABO population matrix, Indicates the search agents (population members), The first Dimension (i.e. decision variables), is the population size, is the total number of decision variables.

[0102] Each search agent represents a candidate solution to the problem and provides a value for the decision variable. The objective function is evaluated based on the decision variable values ​​of each search agent, and the results are stored in the vector middle.

[0103] (twenty one).

[0104] During the search agent update iteration, the SABO algorithm defines ' operation, so that the position update of each search agent depends on the positions of other agents in the current iteration:

[0105] (twenty two).

[0106] in, is an m-dimensional vector whose components are drawn from the set Random numbers generated in, operations represents the Hadamard product of two vectors, Represents a symbolic function.

[0107] Search Agent The position is updated as follows:

[0108] (twenty three).

[0109] Indicates the current search agent The latest location, Represents the position of other search agents in the current generation, is the total number of search agents. is a vector whose dimensions are related to the problem space, and each component follows a normal distribution in the interval [0, 1]. Position updates are based on the following conditional formula:

[0110] (twenty four).

[0111] Step 2.1: Initialize particles using the chaos mapping mechanism.

[0112] The original SABO algorithm uses random initialization within the upper and lower bounds of the search space to generate initial search agents. However, this randomization approach can lead to uneven distribution of search agents, making it difficult to ensure population diversity, which in turn affects the algorithm's ability to perform global optimization later in the algorithm. Chaos, a quasi-random nonlinear behavior generated by deterministic systems, exhibits characteristics such as randomness and ergodicity, which can enhance the diversity of the initial population. The Tent chaos map is widely used due to its uniform distribution and computational efficiency.

[0113] Step 2.1.1: Add the random perturbation term to the Tent chaos mapping formula to obtain the improved Tent chaos mapping formula.

[0114] This embodiment uses the improved Tent chaotic map to initialize the population, and its expression is as follows:

[0115] (25).

[0116] Research has found that small periods and unstable periodic points may exist in the Tent chaotic iterative sequence. To eliminate these phenomena, a random perturbation term can be added to the original Tent chaotic map expression. The improved Tent chaotic map formula is as follows:

[0117] (26).

[0118] Step 2.1.2: Perform Bernoulli transform on the improved Tent chaos mapping formula.

[0119] The expression after Bernoulli transformation is as follows:

[0120] (27).

[0121] Step 2.1.3: Initialize the particle population using the transformed Tent chaos mapping formula. A chaotic sequence ( is the population size), each sequence length is .

[0122] in, is the number of decision variables. In the multi-objective optimization scheduling of microgrids, Pick .

[0123] Then the chaotic sequence is mapped to the decision variable space:

[0124] (28).

[0125] Where, Indicates the The particle in The value of the dimension, 、 Represents the particle The upper and lower bounds of the dimension.

[0126] In multi-objective optimization scheduling for microgrids, after particle initialization based on the improved Tent chaotic map, the system must ensure that it meets multiple practical operational constraints, such as power balance constraints, ramp-up constraints, and battery charge and discharge constraints. For particles that fail to meet the constraints during initialization, a boundary correction strategy is used to address them until all constraints are met.

[0127] Step 2.2: Generate different search strategies through different combinations of the subtractive mean optimization algorithm, the elite guided development strategy, and the golden sine algorithm. Use different search strategies in the early, middle, and late stages of the iteration process to dynamically adjust the search behavior.

[0128] Golden sine algorithm.

[0129] The Golden Sine Algorithm (GSA) is an intelligent optimization algorithm based on the sine function and the golden ratio. It updates the search agent's position by simulating the periodicity of the sine wave and the balance mechanism of the golden ratio, thereby efficiently exploring the solution space. The GSA algorithm can be combined with the SABO algorithm to enhance global exploration capabilities. Its position update expression is as follows:

[0130] (29).

[0131] in, Represents the new position after this iteration, Indicates the current iteration position. and are random numbers in the range of [0, 2π] and [0, π] respectively, Indicates the The optimal position of the particle in the current iteration. and They are the golden ratio coefficients respectively. and The initial values ​​are as follows:

[0132] (30).

[0133] During the iteration of the optimization algorithm, the golden ratio coefficient and The value of will be dynamically adjusted according to the feedback information of the objective function. The pseudo code is as follows:

[0134]

[0135] Elite-led development strategy.

[0136] During the iterative process of intelligent optimization algorithms, the coordinated balance between exploration and exploitation is the core issue in optimizing algorithm performance. Exploration refers to the algorithm's ability to conduct a global search within the solution space, aiming to discover potential optimal regions; while exploitation involves a detailed local search within already discovered high-quality regions to improve solution accuracy.

[0137] Therefore, in the later stages of algorithm iteration, an elite-guided local development strategy can be added to strengthen local search and speed up convergence. Its position is updated as follows:

[0138] (31).

[0139] in, represents the optimal search agent in the current iteration, and Denote two search agents randomly selected from the population.

[0140] In this embodiment, to address the problem of balancing exploration and development during the iterative process of the optimization algorithm, a three-stage progressive hybrid search strategy based on iterative process adaptation is proposed, including a fusion strategy of the subtractive average optimization algorithm and the golden sine algorithm, a fusion strategy of the subtractive average optimization algorithm, the elite-guided development strategy and the golden sine algorithm, and a fusion strategy of the subtractive average optimization algorithm and the elite-guided development strategy.

[0141] in, and They are two iterative process nodes, and are defined At the beginning of the iteration, In the middle of the iteration, For the late iteration.

[0142] Step 2.2.1: At the beginning of the iteration, When optimizing the microgrid, the core goal is to enhance the global search capability. A fusion strategy combining the subtraction average optimization algorithm and the golden sine algorithm is adopted to ensure extensive exploration of potential high-quality areas for microgrid optimization scheduling.

[0143] Specifically, define the mixing weight coefficient , represents the weight of the golden sine algorithm and the subtraction average optimization algorithm, It decreases linearly with the number of iterations, that is, in the early stage of iteration, the algorithm is mainly based on golden sine search; as the iteration proceeds, Linearly decreasing, gradually enhancing the dominant role of subtractive average optimization.

[0144] Step 2.2.2: In the middle of the iteration, When using the fusion strategy of subtractive mean optimization algorithm, elite guided development strategy and golden sine algorithm, the collaborative search probability is defined. The subtractive mean optimization algorithm, the elite-guided development strategy, and the golden sine algorithm run in parallel, and the probability of collaborative search decays linearly with the number of iterations, reflecting the dynamic balance between exploration and development in the microgrid's optimal scheduling space. Specifically, the global search intensity gradually decreases, while the weight of local development based on elite solutions increases accordingly, promoting a smooth transition from coarse-grained exploration to fine-grained development.

[0145] Step 2.2.3: At the end of the iteration, When focusing on the neighborhood refinement mining of high-quality solutions in the microgrid optimization dispatch space, a fusion strategy combining the subtraction average optimization algorithm and the elite guided development strategy is adopted to make the Pareto frontier solution set converge quickly. Specifically, the hybrid weight coefficient is defined as , represents the weights of the subtractive mean optimization algorithm and the elite guided development strategy, It decreases linearly with the number of iterations, that is, when it just enters the late stage of iteration, the algorithm is mainly based on the subtraction average optimization algorithm; as the iteration proceeds, Linearly decreasing, gradually enhancing the leading role of the elite-guided development strategy, so that the algorithm can converge quickly.

[0146] The present invention proposes a three-stage progressive search strategy, which achieves an organic balance between global exploration and local development by dynamically adjusting the search behavior of the algorithm. For complex problems such as microgrid multi-objective optimization scheduling with high dimensionality, strong constraints and multi-objective characteristics, the algorithm can effectively adapt to its nonlinear characteristics, while ensuring the quality of the solution and significantly improving the computational efficiency. The search focus is automatically adjusted according to the iterative process: the initial focus is on global exploration to avoid falling into local optimality, the mid-term balance of exploration and development, and the later focus on local development to ensure convergence accuracy. The ISABO algorithm flow chart is as follows: Figure 1 shown.

[0147] The Improved Subtraction-Average-Based Optimizer (ISABO) is compared with SABO, DBO, GWO, WOA, SSA, GMO, GRO, PSO, and DE optimization algorithms on the CEC2005 test function. Figure 2 shown.

[0148] Experimental results demonstrate that the improved mean subtraction optimization algorithm (ISABO) exhibits significant performance advantages on both unimodal and multimodal benchmark functions. Notably, the algorithm demonstrates exceptional optimization capabilities in the optimization tests for F5 (unimodal functions) and F8 (high-dimensional multimodal functions), with particularly strong global convergence and local extremum escape capabilities. This superior performance is primarily attributed to the algorithm's innovative search mechanism, which significantly improves search efficiency by dynamically balancing exploration and exploitation. In optimizing the complex F8 function, ISABO demonstrates enhanced global exploration capabilities, effectively overcoming the premature convergence problem common in traditional optimization algorithms. These experimental results fully demonstrate ISABO's distinct algorithmic advantages in tackling complex, high-dimensional optimization problems.

[0149] Step 3: According to the characteristics of multi-objective optimization problems, a multi-objective improved subtraction-average-based optimizer (MO_ISABO) is constructed based on the improved subtraction average optimization. The multi-objective improved subtraction-average-based optimizer is used to solve the multi-objective optimization scheduling model, and the energy scheduling of the microgrid is performed according to the solution results.

[0150] Step 3.1: Use the Pareto solution set maintenance mechanism based on the crowding distance of the improved subtraction average optimizer to select the top The solution with the largest crowding distance is selected as the optimal solution of the archive library, which can achieve a uniform distribution of the solution set in the target space.

[0151] In single-objective optimization problems, the evaluation criteria for the quality of solutions are relatively simple and direct. By comparing the values ​​of the objective function, the relative quality of the decision variables can be clearly judged. Specifically, for two given solutions and ,like , then it can be determined Better than This scalar comparison-based evaluation mechanism gives the search process a clear optimization direction.

[0152] In multi-objective optimization problems, the solution evaluation mechanism is more complicated. Since there are multiple conflicting optimization objectives at the same time, the relationship between the decision variables needs to be determined by the Pareto dominance criterion. Specifically, for two solutions and :If for all objective functions there is , and there is at least one target Make , then it is called Dominate There is a Pareto optimal solution set in the solution space, rather than a single optimal solution. The optimization goal is to find as many non-dominated solutions as possible that are evenly distributed in the feasible solution set.

[0153] In a specific implementation, in the process of maintaining the Pareto optimal solution set, crowding distance and roulette wheel selection are two key mechanisms in this embodiment.

[0154] The crowding distance mechanism is used to assess the distribution density of individuals in a solution set. It quantifies the degree of solution congestion by calculating the sum of the distances between each solution and its neighbors in each objective space. This mechanism prioritizes solutions with larger crowding distances, thereby ensuring uniformity and diversity in the Pareto front and preventing excessive clustering of solutions. In microgrid optimization and scheduling, this mechanism can effectively maintain a balanced distribution across multiple objectives, such as power generation operating costs and carbon emissions, providing decision makers with a more comprehensive range of options.

[0155] The roulette wheel selection method is a fitness-proportional selection strategy. By assigning a selection probability proportional to each solution's congestion distance, it increases the probability of retaining high-quality solutions while also taking into account the potential contribution of suboptimal solutions. This method promotes convergence while preserving population diversity while maintaining the Pareto solution set. It is particularly suitable for scenarios in microgrid scheduling that require balancing multiple conflicting objectives, ensuring that the algorithm does not miss potential optimal solutions.

[0156] For the The crowding distance of particles is defined as follows:

[0157] (32).

[0158] Where, It is The crowding distance of particles, is the dimension of the objective function, For the The fitness value of the objective function. The larger the crowding distance, the sparser the solutions around the particle and the better the distribution. The crowding distance of the boundary solution is set to infinity to ensure the ductility of the frontier.

[0159] After defining the crowding distance of particles, combining it with a roulette wheel method to select elite individuals can effectively guide the population toward the high-quality and evenly distributed Pareto frontier. This mechanism converts the crowding distance into a selection probability, giving individuals in sparse areas (with larger crowding distances) a higher probability of selection.

[0160] Step 3.2: When the number of feasible solutions in the archive library falls below the preset minimum diversity threshold (min_diversity), the solution enhancement strategy is automatically triggered.

[0161] In the early stages of multi-objective optimization scheduling of microgrids, due to the system's high dimensionality, strong constraints, and complex nonlinearity, it is often difficult for the algorithm to quickly obtain a sufficient number of high-quality Pareto optimal solutions. To address this problem, the present invention designs a solution enhancement strategy based on an adaptive diversity solution injection mechanism: when the number of feasible solutions in the archive library is lower than the preset minimum diversity threshold (min_diversity), the solution enhancement strategy is automatically triggered. The adaptive diversity solution injection mechanism improves population diversity by injecting two types of special solutions: (1) reverse solutions, which are generated based on the current optimal solution through a reverse learning strategy and can effectively explore potential optimal areas that have been ignored; (2) perturbation solutions, which apply Gaussian perturbations to the existing solutions to enhance the development capabilities of local areas. This dual injection strategy can not only quickly expand the solution set size, but more importantly, it can significantly improve the uniformity of the solution set distribution in the target space.

[0162] In a specific embodiment, the adaptive diversity solution injection mechanism generates high-quality diversity solutions by:

[0163] (33).

[0164] Where, It is the arithmetic mean of all solutions in the current archive solution set; is the generated inverse solution, and They are the upper and lower limits respectively; is the perturbed solution generated by applying Gaussian perturbation to the central solution, For Hadamard, is the disturbance intensity coefficient, is a random vector that follows a standard normal distribution.

[0165] By injecting reverse and perturbation solutions into the archive, we can effectively enhance the diversity of the archive. Reverse solutions explore complementary regions of the current solution set through symmetric mapping, helping to escape local optima; while perturbation solutions perform a refined search near the central solution. The two work together to balance the algorithm's exploration and development efficiency.

[0166] The ISABO algorithm and the MO_ISABO algorithm were then compared and tested in single-objective optimization problems and multi-objective optimization problems respectively. The experimental results showed that both algorithms showed excellent performance in their respective application scenarios.

[0167] In order to verify the effectiveness of the MO_ISABO algorithm, the present invention selected the classic test function set ZDT1-ZDT4 in the field of multi-objective optimization for systematic testing.

[0168] Experimental results show that the MO_ISABO algorithm exhibits excellent optimization performance on the ZDT series test functions. Figure 3 、 Figure 4 、 Figure 5 and Figure 6 As shown, on the four classic test functions ZDT1-ZDT4, the Pareto frontiers obtained by MO_ISABO (red asterisks) closely match the theoretical optimal frontier (blue solid lines), fully demonstrating the algorithm's excellent convergence performance. In particular, on the discontinuous ZDT3 function, MO_ISABO successfully finds all frontier segments and the global optimal region, with a uniformly distributed solution set that completely covers the entire Pareto frontier.

[0169] The model proposed in this example uses the interaction power between the microgrid and the main grid, the gas turbine output power, the diesel generator output power, and the battery charge and discharge power as decision variables. It also uses the predicted data for photovoltaic power generation, wind power generation, and load demand as known input parameters. The MO_ISABO algorithm is used for optimization.

[0170] Through iterative optimization of the MO_ISABO algorithm, the Pareto frontier solution set reflecting the relationship between power generation operating costs and carbon emissions is finally obtained.

[0171] Example 2:

[0172] A second embodiment of the present invention provides a microgrid multi-objective optimization system based on an improved SABO algorithm, comprising:

[0173] A model building module is configured to establish a microgrid multi-objective optimization scheduling model according to distributed power sources in the microgrid;

[0174] An algorithm improvement module is configured to introduce a chaotic mapping mechanism, an elite-guided development strategy, and a golden sine algorithm into the subtractive average optimization algorithm to obtain an improved subtractive average optimization algorithm. The improved algorithm uses the chaotic mapping mechanism to initialize particles, generates different search strategies through different combinations of the subtractive average optimization algorithm, the elite-guided development strategy, and the golden sine algorithm, and dynamically adjusts the search behavior by using different search strategies at the early, mid, and late stages of the iterative process.

[0175] The energy scheduling module is configured to construct a multi-objective improved subtraction average optimizer based on the improved subtraction average optimization, use the multi-objective improved subtraction average optimizer to solve the multi-objective optimization scheduling model, and perform energy scheduling on the microgrid based on the solution results.

[0176] Example 3:

[0177] A third embodiment of the present invention provides a medium having a program stored thereon. When the program is executed by a processor, the steps of the microgrid multi-objective optimization method based on the improved SABO algorithm as described in the first embodiment of the present invention are implemented.

[0178] Example 4:

[0179] Embodiment 4 of the present invention provides a device, including a memory, a processor, and a program stored in the memory and executable on the processor. When the processor executes the program, the steps in the microgrid multi-objective optimization method based on the improved SABO algorithm as described in Embodiment 1 of the present invention are implemented.

[0180] The steps involved in the above embodiments 2, 3 and 4 correspond to those in the method embodiment 1. For the specific implementation methods, please refer to the relevant description part of the embodiment 1.

[0181] Those skilled in the art will appreciate that the modules or steps of the present invention described above can be implemented using a general-purpose computer device. Alternatively, they can be implemented using program code executable by a computing device, which can then be stored in a storage device and executed by the computing device. Alternatively, they can be fabricated into separate integrated circuit modules, or multiple modules or steps can be fabricated into a single integrated circuit module for implementation. The present invention is not limited to any specific combination of hardware and software.

[0182] Although the above describes the specific embodiments of the present invention in conjunction with the accompanying drawings, it is not intended to limit the scope of protection of the present invention. Those skilled in the art should understand that various modifications or variations that can be made by those skilled in the art on the basis of the technical solution of the present invention without any creative work are still within the scope of protection of the present invention.

Claims

1. A microgrid multi-objective optimization method based on an improved SABO algorithm, characterized in that: The following steps are involved: Establish a multi-objective optimization scheduling model for microgrid based on distributed power sources in microgrid; The chaotic mapping mechanism, elite-guided development strategy and golden sine algorithm are introduced into the subtraction average optimization algorithm to obtain an improved subtraction average optimization algorithm. In this algorithm, the chaotic mapping mechanism is used to initialize particles. Different search strategies are generated through different combinations of the subtraction average optimization algorithm, the elite-guided development strategy and the golden sine algorithm. Different search strategies are adopted in the early, middle and late stages of the iteration process to dynamically adjust the search behavior. Specifically, in the early stage of the iteration, with the core goal of enhancing the global search capability, a fusion strategy of the subtraction average optimization algorithm and the golden sine algorithm is adopted. In the middle stage of the iteration, a fusion strategy of the subtraction average optimization algorithm, the elite-guided development strategy and the golden sine algorithm is adopted. The subtraction average optimization algorithm, the elite-guided development strategy and the golden sine algorithm run in parallel, and the probability of collaborative search decays linearly with the number of iterations. In the late stage of the iteration, the focus is on the refined mining of the neighborhood of high-quality solutions. The fusion strategy of the subtraction average optimization algorithm and the elite-guided development strategy is adopted to make the Pareto frontier solution set converge quickly. Based on the improved subtraction average optimization, a multi-objective improved subtraction average optimizer is constructed. The multi-objective improved subtraction average optimizer is used to solve the multi-objective optimization scheduling model, and the energy scheduling of the microgrid is carried out according to the solution results.

2. The microgrid multi-objective optimization method based on the improved SABO algorithm according to claim 1, characterized in that: The distributed power sources in the microgrid include photovoltaic power generation systems, wind turbines, micro gas turbines, diesel generators and batteries.

3. The microgrid multi-objective optimization method based on the improved SABO algorithm according to claim 1, characterized in that: Set the constraints of the microgrid multi-objective optimization scheduling model, including micro gas turbine power constraint, micro gas turbine power constraint, diesel generator power constraint, battery power constraint and interactive power constraint.

4. The microgrid multi-objective optimization method based on the improved SABO algorithm according to claim 1, characterized in that: The specific steps of initializing particles using the chaotic mapping mechanism are: By adding random perturbation terms into the Tent chaotic mapping formula, the improved Tent chaotic mapping formula is obtained. Perform Bernoulli transform on the improved Tent chaos mapping formula; The particle population is initialized using the transformed Tent chaos mapping formula.

5. The microgrid multi-objective optimization method based on the improved SABO algorithm according to claim 1, characterized in that: Different search strategies are generated through different combinations of the subtraction average optimization algorithm, the elite-guided development strategy and the golden sine algorithm, including: the fusion strategy of the subtraction average optimization algorithm and the golden sine algorithm, the fusion strategy of the subtraction average optimization algorithm, the elite-guided development strategy and the golden sine algorithm, and the fusion strategy of the subtraction average optimization algorithm and the elite-guided development strategy.

6. The microgrid multi-objective optimization method based on the improved SABO algorithm according to claim 5, characterized in that: The specific steps for dynamically adjusting the search behavior by using different search strategies in the early, mid, and late stages of the iteration process are as follows: In the early stages of iteration, with the core goal of enhancing global search capabilities, a fusion strategy combining the subtraction mean optimization algorithm and the golden sine algorithm was adopted; In the middle of the iteration, a fusion strategy combining the subtraction mean optimization algorithm, the elite-guided development strategy, and the golden sine algorithm is adopted. The subtraction mean optimization algorithm, the elite-guided development strategy, and the golden sine algorithm run in parallel, and the probability of collaborative search decays linearly with the number of iterations. In the later stage of iteration, we focus on the refined mining of the neighborhood of high-quality solutions and adopt a fusion strategy of the subtraction average optimization algorithm and the elite guided development strategy to make the Pareto frontier solution set converge quickly.

7. The microgrid multi-objective optimization method based on the improved SABO algorithm according to claim 1, characterized in that: Based on the improved subtraction average optimization, a multi-objective improved subtraction average optimizer is constructed. The specific steps of using the multi-objective improved subtraction average optimizer to solve the multi-objective optimization scheduling model are as follows: The improved subtraction average optimizer is used to maintain the Pareto solution set based on the crowding distance to select the top The solution with the largest crowding distance is taken as the optimal solution for the archive library; When the number of feasible solutions in the archive library falls below the preset minimum diversity threshold, the solution enhancement strategy is automatically triggered.

8. A microgrid multi-objective optimization system based on an improved SABO algorithm, characterized in that: include: A model building module is configured to establish a microgrid multi-objective optimization scheduling model according to distributed power sources in the microgrid; The algorithm improvement module is configured to introduce a chaotic mapping mechanism, an elite-guided development strategy, and a golden sine algorithm into the subtractive average optimization algorithm to obtain an improved subtractive average optimization algorithm. The chaotic mapping mechanism is used to initialize particles, and different search strategies are generated through different combinations of the subtractive average optimization algorithm, the elite-guided development strategy, and the golden sine algorithm. Different search strategies are used in the early, middle, and late stages of the iterative process to dynamically adjust the search behavior. Specifically, in the early stages of the iteration, with the core goal of enhancing global search capabilities, a fusion strategy combining the subtractive average optimization algorithm and the golden sine algorithm is adopted. In the middle stages of the iteration, a fusion strategy combining the subtractive average optimization algorithm, the elite-guided development strategy, and the golden sine algorithm is adopted. The subtractive average optimization algorithm, the elite-guided development strategy, and the golden sine algorithm run in parallel, and the probability of collaborative search decays linearly with the number of iterations. In the late stages of the iteration, the focus is on refined mining of the neighborhood of high-quality solutions, and a fusion strategy combining the subtractive average optimization algorithm and the elite-guided development strategy is adopted to enable rapid convergence of the Pareto frontier solution set. The energy scheduling module is configured to construct a multi-objective improved subtraction average optimizer based on the improved subtraction average optimization, use the multi-objective improved subtraction average optimizer to solve the multi-objective optimization scheduling model, and perform energy scheduling on the microgrid based on the solution results.

9. A computer-readable storage medium, characterized in that A plurality of instructions are stored therein, and the instructions are suitable for being loaded by a processor of a terminal device and executing the microgrid multi-objective optimization method based on the improved SABO algorithm according to any one of claims 1 to 7.

10. A terminal device, characterized in that: The invention comprises a processor and a computer-readable storage medium, wherein the processor is used to implement each instruction; the computer-readable storage medium is used to store multiple instructions, wherein the instructions are suitable for being loaded by the processor and executing the microgrid multi-objective optimization method based on the improved SABO algorithm according to any one of claims 1 to 7.

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