The optimization and operation of multi-energy-coupled microgrids by the improved fireworks algorithm-shuffled frog-leaping algorithm

Comprehensive energy system architecture

The rapid growth of renewable energy underscores the significance of comprehensive energy systems, integrating diverse energy resources and technologies for sustainable energy supply. This system encompasses renewable and traditional energy sources, energy storage, and conversion equipment to ensure efficiency and reliability (Karunarathne et al., 2020; Ju, Ding & Hu, 2023; Shirvani, 2023). Illustrated in Fig. 1, the architecture of a comprehensive energy system comprises wind turbines, photovoltaics, combined heat and power (CHP) units, electric and gas boilers, and power-to-gas systems, alongside energy storage systems for electricity, heat, and gas. By harnessing a range of resources such as solar energy, wind energy, biomass, natural gas, and conventional electricity, this system caters to varied energy demands. This diversity mitigates reliance on a singular energy source, thereby bolstering system stability and reliability.

By integrating multi-energy-coupled microgrids into comprehensive energy systems, it becomes feasible to harmonize and optimize the utilization of energy resources, ensuring efficient distribution and utilization of energy within a regional scope. Microgrids operate at the micro-level, comprising small-scale generation and distribution systems that include distributed power sources and energy storage systems. Possessing both power supply and user resources, microgrids can function autonomously and are typically deployed in closed settings such as industrial parks, large facilities, residential communities, or geographically proximate areas. Multi-energy-coupled microgrids, while small in scale, are capable of independent operation and may also connect to the main power grid. This connectivity facilitates the provision of additional power supply to the microgrid when necessary or the transfer of excess energy to the main power grid (Pan et al., 2022; Farah et al., 2021).

Microsource optimization configuration in microgrids based on SFLA

In the realm of microgrid optimization, meta-heuristic optimization algorithms like the fireworks algorithm (FWA) and the SFLA are extensively employed to tackle multi-objective and constrained optimization problems. SFLA, a group intelligence algorithm, mimics the process of fireworks explosion to explore the solution space by generating sparks continuously, combining global and local search effectively. Conversely, the frog jumping algorithm emulates the foraging behavior of frog groups, employing global information sharing and local search to find optimal solutions. These algorithms are prevalent in microgrid optimization, enhancing system performance and efficiency by optimizing operation strategies. This study aims to address optimization and operational challenges in multi-energy-coupled microgrid systems by combining the IFWA with the SFLA, thereby enhancing system stability and reliability. IFWA introduces adaptive resource allocation and community inheritance strategies, dynamically adjusting explosion range and spark quantity based on individual optimization states to better meet actual needs. Moreover, utilizing a multi-objective optimization model, incorporating factors like active power network loss and static voltage, the frog jumping algorithm resolves multi-objective optimization problems. Case study simulations conducted in a typical integrated energy system validate the feasibility and superiority of the IFWA-SFLA algorithm.

This study delves into a specific radial distribution network, guided by several assumptions. Firstly, it presupposes a three-phase balanced load that absorbs active and reactive power with specific power factors from the system. Given the network’s relatively low voltage level and short distribution lines, mutual inductance between the three-phase lines is disregarded in the analysis. Additionally, the network at the substation is treated as equivalent to a voltage source (Van Tran et al., 2021; Chicco & Mazza, 2020; Tran et al., 2021). Furthermore, the study maintains a constant voltage output model, ensuring that the voltage at the system busbar end remains consistent throughout the analysis.

In microgrid planning, the determination of the location and scale of independent microgrid systems constitutes decision variables for distributed power sources. The optimization objective involves the amalgamation of active power network loss and static voltage. The calculation of active power network loss is depicted in Eqs. (1) and (2):

(1) $$P_{min}=min\sum _{k\in N}{P}_{kloss}$$

(2) $$P_{kloss}=G_{ij}\left(V_i^2+V_j^2-2V_i{V}_j\cos {\theta }_{ij}\right)$$

In Eqs. (1) and (2), $P_{min}$ refers to the active power network loss of the system, $P_{kloss}$ represents the active power network loss of branch k, $V_i$ and $V_j$ denote the voltage at nodes i and j, $G_{ij}$ signifies the conductance between nodes i and j, and ${\theta }_{ij}$ denotes the phase difference angle between nodes i and j.

The static voltage stability index is computed via Eq. (3):

(3) $$V_{stab,k}={\displaystyle \frac{4\left[{\left(X{P}_j-R{Q}_j\right)}^2+\left(X{Q}_j-R{P}_j\right)V_i^2\right]}{V_i^4}}$$

In Eq. (3), $P_j$ and $Q_j$ represent the active and reactive power at node j, $R$ and $X$ denote the resistance and reactance of branch k, and $V_{stab,k}$ signifies the static voltage index of branch k.

The weighted factor method integrates the optimization objectives of active power network loss and static voltage, formulated as shown in Eq. (4):

(4) $$f_{min}={\omega }_1{\displaystyle \frac{P_{min}}{P_0}+{\omega }_2{\displaystyle \frac{V_{stab,k}}{V_0}}}$$

In Eq. (4), $f_{min}$ represents the multi-objective function, ${\omega }_1$ and ${\omega }_2$ are the weights assigned to multi-objective allocation, and $P_0$ and $V_0$ respectively denote the initial active power network loss and static voltage of distributed power sources.

The calculation of node voltage constraints is represented by Eq. (5).

(5) $$V_{i,min}\le V_i\le V_{i,max}$$

The constraints on distributed power source power are defined by Eqs. (6) and (7):

(6) $$P_{DGmin}\le P_{DGi}\le P_{DGmax}$$

(7) $$Q_{DGmin}\le Q_{DGi}\le Q_{DGmax}$$

In Eqs. (6) and (7), $P_{DGmin}$ and $Q_{DGmin}$ represent the minimum active and reactive power at the point of distributed power generation connection; $P_{DGmax}$ and $Q_{DGmax}$ represent the maximum active and reactive power at the point of power source connection.

The strength of SFLA lies in its amalgamation of global and local searches, enabling the frog population to explore the search space for the global optimum while refining solutions through local search. SFLA comprises two primary components: global information sharing and local search, which partition the virtual frog population into distinct communities. Each community undertakes independent local searches, with individuals gradually improving alongside the community’s evolution. As communities progress, frog populations undergo mixing and recombination to form new communities, facilitating the dissemination of local information across the entire population. This iterative process continues until termination conditions are met. This dual-loop mechanism aids in overcoming local optima, bringing the population closer to the global optimum (Ma et al., 2019; Shaheen et al., 2022).

SFLA employs fitness-based sorting from high to low and utilizes a randomized balanced grouping strategy to enhance the optimization performance of different subgroups (Xu, Deng & Shen, 2020; Vinnikov et al., 2021; Osman, Sedhom & Kaddah, 2023). The operation of this random balancing strategy is as follows: initially, frogs are ranked in descending order of fitness, with individuals possessing the highest fitness assigned to the first group, followed by frogs with progressively lower fitness levels assigned to subsequent groups. This process continues until frogs with the m-th highest fitness value are allocated to the m-th group. In this approach, based on fitness ranking, (n−1) * m individuals are assigned to the m-th group, while the remaining m frogs are randomly allocated until all frogs are grouped. This strategy effectively moderates the search speed of lower fitness subgroups, thereby enhancing overall search performance and preserving population diversity.

SFLA comprises the following steps (Fig. 2):

1: Initialize parameters by setting the number of subgroups, m, the number of frogs in each subgroup, n, and determining the total population size, F.

2: Create a virtual population by generating F frogs in the space of feasible solutions, $\mathrm{\Omega }\subset R^N$, where each frog represents a potential solution, covering the search space for microgrid operational optimization.

3: Sort the frogs using the randomized balanced grouping method to ensure that high-fitness frogs are evenly distributed across different subgroups.

4: Perform optimization operations for each subgroup. All frogs within the subgroups undergo optimization and updates to move closer to the target position. $P_b$ represents the best frog, and $P_w$ represents the worst frog.

5: Conduct local search on $P_b$ to further refine the solutions.

6: Merge all subgroups into the total population X and update the global best frog by aggregating information from each subgroup.

7: Determine whether termination conditions are met. If the conditions are satisfied, output the optimal solution.

Microgrid energy storage bidirectional inverter control based on IFWA

The circuit structure of the microgrid energy storage bidirectional inverter primarily comprises two modes: grid-connected and islanded. In the grid-connected mode, the bidirectional inverter can link to the large-scale electrical system and operates in charge and discharge modes. Users have the option to select automatic or manual modes. In automatic mode, the battery’s charging and discharging process is system-regulated based on preset values. Conversely, manual mode allows users to adjust parameters such as current, voltage, and time for charging and discharging to meet specific requirements. In the islanded mode, the bidirectional inverter can detach from the large-scale electrical system and independently supply power to designated loads. This mode ensures autonomy for local loads, shielding them from external grid disturbances. The bidirectional inverter’s performance is influenced by both hardware (such as power electronic devices and energy storage units) and software (including control algorithms and protection strategies). Hence, to maximize the bidirectional inverter’s potential, appropriate hardware and software configurations should be selected according to application needs and system limitations.

This study utilizes a voltage-type three-phase bridge inverter, with the main circuit topology depicted in Fig. 3. This inverter serves both rectification and inversion functions. During rectification, energy undergoes rectification and conversion using pulsating current. Conversely, during inversion, direct current (DC) voltage is inverted and converted using semiconductor switching devices. The operation of this circuit involves modulating the pulse width modulation (PWM) output waveform, facilitating the circuit’s transition between inversion and rectification modes for bidirectional energy flow transmission. Power switches S1–S6 and freewheeling diodes D1–D6 constitute the key components. The output side connects to a series resonant filter comprising filter inductance $L_n$ and filter capacitor $C_n$, with $R_n$ representing the inductive impedance. This series resonant filter serves to absorb harmonics introduced by the inverter’s switching, preventing these harmonics from affecting power quality within the electrical grid. Additionally, a large parallel capacitor $C_n$ on the DC side is introduced to maintain stable DC voltage and effectively mitigate voltage fluctuations, while also providing a reactive current path.

The droop control characteristics of the energy storage bidirectional inverter resemble the droop characteristics curve of a synchronous generator, demonstrating a proportional correlation between active output and frequency deviation, as well as between reactive output and voltage deviation. Virtual synchronous generator control mimics the behavior of traditional generators by internally modeling a synchronous generator and adjusting active frequency and reactive voltage to meet control objectives (Naik, Dash & Bisoi, 2021; Tajjour & Chandel, 2023). Proper selection of control parameters is critical in this process. Correct parameter selection enables the control system to attain desired performance, whereas incorrect choices may degrade system performance or cause failure (Sharma et al., 2020; Iris & Lam, 2019).

Traditional FWA typically employs fixed parameters to regulate the explosion range and the number of sparks. However, in the improved version proposed in this study, an adaptive resource allocation strategy is introduced. This entails dynamically allocating resources based on the problem’s characteristics and the current state of individuals (Taherian-Fard et al., 2022; Singh et al., 2020). When a community encounters significant optimization challenges, the algorithm can automatically increase resources, such as expanding the explosion range or increasing the number of sparks, to broaden and deepen the search. Conversely, if the community is converging, the algorithm can reduce resources to finely search for the optimal solution. The community inheritance strategy allows individuals to learn and inherit information from their respective communities. This facilitates knowledge sharing, enabling individuals to benefit from each other’s discoveries without redundant searches. Consequently, individuals can communicate and collaborate, enhancing the overall efficiency of the algorithm.

In FWA, fireworks with higher fitness generally produce more sparks within a smaller explosion radius, while those with lower fitness generate fewer sparks within a larger radius (Murugan & Vijayarajan, 2023). However, allocating resources solely based on the current fireworks’ fitness may not always align with the actual optimization scenario. This is because in regions where the objective function’s variation trend is steep, fireworks close to the optimal point may exhibit lower fitness, potentially causing smaller sparks within a larger radius to miss the optimum (Yaprakdal, Baysal & Anvari-Moghaddam, 2019; Raut & Mishra, 2023; Ramalingam & Shanmugam, 2022). Conversely, fireworks trapped in local optima often display higher fitness, yet even with multiple sparks within a small radius, they are less likely to escape from local optimal points. In IFWA, an adaptive resource allocation strategy is employed, and the calculation of the i-th firework’s explosion radius and the number of sparks is as follows:

(8) $$r_i=r/4^{m_i}$$

(9) $$S_i=S+rand\left(m_{i}S/M\right)$$

In Eqs. (8) and (9), $r$ and $S$ denote the initial explosion radius and the number of sparks for fireworks, $m_i$ represents the adaptive coefficient for the i-th firework, and $rand(\cdot )$ is a rounding function.

The adaptive resource allocation strategy enables the population to dynamically adjust the explosion radius and the number of sparks based on their evolutionary status. Initially, the population employs a larger explosion radius and fewer sparks to roughly identify potential optimal locations across a wide range. If a superior location is not discovered after an explosion, the algorithm gradually decreases the radius and increases the number of sparks to conduct a more precise search. This iterative process continues, ensuring that each population converges toward the extremum relatively swiftly.

Another crucial strategy involves promptly eliminating individuals trapped in local optima. This not only prevents resource wastage but also enhances population diversity through suitable mapping strategies. As Gaussian distribution tends to cluster around the original position and exhibits relatively poor exploratory performance, IFWA utilizes the tent chaotic mapping with uniform distribution characteristics to alter the positions of fireworks ensnared in local optima. The fireworks entangled in local optima undergo transformation into the chaotic space across any dimension. The calculation for each dimension k is as depicted in Eq. (10):

(10) $$C_k^1=\left(x_k-a\right)/\left(b-a\right)$$

Through multiple iterations using the tent chaotic mapping, the calculation is as shown in Eq. (11):

(11) $$C_k^{l+1}=\{\begin{array}{c}2\times C_k^1,0\le C_k^1\le 0.5\hfill \\ 2\times \left(1-C_k^1\right),0.5<C_k^1\le 1\hfill \end{array}$$

In Eq. (11), $l$ represents the number of iterations.

The final new position of fireworks is obtained, and its transformation is as described in Eq. (12):

(12) $$x_k=a+C_k^{l+1}\times \left(b-a\right)$$

Chaos mapping demonstrates high sensitivity to initial conditions, signifying that even two fireworks confined within the same local optimum area will map to entirely different locations. In contrast, tent chaotic mapping exhibits more uniform distribution characteristics, ensuring coverage of every possible area. The structure of the multi-objective optimization model for multi-energy-coupled microgrids is depicted in Fig. 4. This model encompasses various energy resources such as solar energy, wind energy, battery energy, etc., along with loads. Through intelligent control and optimization operations, it achieves synergistic operation and optimal configuration among energy sources. The improved IFWA algorithm, integrated with adaptive resource allocation strategies and community inheritance strategies, dynamically adjusts the range of explosions and the number of sparks based on the optimization status of individuals to meet their actual needs. The construction of the multi-objective optimization model considers active power network losses and static voltage as optimization objectives and utilizes a constrained multi-objective optimization problem-solving approach. SFLA combines global search and local search by optimizing through a virtual frog population. The adoption of a random balanced grouping strategy enhances optimization performance and population diversity.

The pseudocode for the IFWA-SFLA algorithm is presented in Table 1:

The steps of the IFWA-SFLA algorithm are outlined as follows:

1) Initialization of parameters: The algorithm begins with setting parameters such as the initial explosion range, initial number of sparks, maximum step size, overall scale, number of subgroups, and number of frogs in each subgroup. Additionally, the maximum number of iterations (max_iterations) is determined to regulate the algorithm’s execution duration.

2) Iterative optimization process: During each iteration, the algorithm conducts optimization operations on each subgroup. This involves sorting the frogs within each subgroup based on their fitness and distributing them using the random balanced grouping strategy. Subsequently, each frog undergoes optimization to approach the target positions. Following this, local search is performed on the best frog to further refine the solution.

3) Merging and updating: After completing the optimization operations, the algorithm merges all subgroups and updates the global best frog. This step consolidates information from each subgroup into the overall population, ensuring progress towards the global optimum.

4) Termination evaluation: After each iteration, the algorithm evaluates whether the termination condition is met. If so, the optimal solution is outputted, and the algorithm terminates. Otherwise, it proceeds to the next iteration until the maximum number of iterations is reached.

Simulation of IFWA-SFLA

To ensure the reliability and reproducibility of these research findings, meticulous calibration of the hyperparameters of metaheuristic algorithms is conducted, with careful documentation of the utilized values. As highlighted by Velasco, Guerrero & Hospitaler (2022), theoretical limitations within algorithms like genetic algorithms and evolutionary strategies may lead to inaccurate estimations of the global optimal position. The study noted substantial disparities in the landscapes generated by the operators of these metaheuristic algorithms within the solution space, potentially yielding incongruent outcomes when employing extremum theory. To address this concern, the calibration process involved several steps: Firstly, a comprehensive theoretical analysis of the metaheuristic algorithms under consideration is conducted, focusing on the influence of their operators on the solution space and potential theoretical deficiencies. Drawing on this analysis and prior experimental insights, a metaheuristic algorithm well-suited for addressing multi-energy-coupled microgrid optimization problems is identified, and pertinent hyperparameters, such as the crossover and mutation rates for genetic algorithms and the mutation strategy for evolutionary strategies, are delineated. Subsequently, a series of experiments are devised to assess the impact of various hyperparameter combinations on algorithm performance, encompassing diverse problem instances and scales to comprehensively evaluate algorithmic efficacy. Based on the experimental findings, iterative adjustments to the hyperparameters are made, refining their numerical values to enhance algorithmic performance and stability across different settings. Finally, validation experiments using the optimized parameter configurations are conducted to ascertain the algorithm’s robustness and efficacy in solving multi-energy-coupled microgrid optimization problems. Through meticulous analysis of the experimental outcomes, the optimal hyperparameter combinations are identified, and conclusive insights are derived. Aligned with the rigorous approach advocated by Velasco, Guerrero & Hospitaler (2022), the diligent hyperparameter calibration process underscores the reliability and replicability of the research outcomes. In the case study, a typical integrated energy system located in northern China with a scheduling period of T = 24 is considered. The system consists of two CHP units, each with output power limits of 2,000 kW and 100 kW, as detailed in Table 2. Additionally, Table 3 provides the parameters for the energy storage units. In the IFWA algorithm, the parameters are configured as follows: R = 300, M = 100, and L = 60. The population size (F) is set to 150, with 30 subpopulations (m) and five frogs in each subpopulation (n). The maximum number of iterations is capped at 50, while the maximum step size is restricted to 488. Notably, the system’s main bus voltage registers at 10 kV, accompanied by active power losses totaling 322.17 kW and a static voltage stability index of 0.113.

To validate the feasibility and efficacy of the IFWA-SFLA algorithm, several alternative algorithms, namely PSO, FWA, and GA-FWA, are employed for comparison. These algorithms undergo testing on the Sphere and Schaffer nonlinear functions, with subsequent analysis of their performance based on experimental outcomes. The Sphere function serves as a classical optimization test function frequently utilized to assess the performance of optimization algorithms. Its mathematical expression is delineated in Eq. (13):

(13) $$f(x)=\sum _{i=1}^n{x}_i^2$$

In Eq. (13), $x$ represents an n-dimensional vector. Moreover, the Schaffer function is a renowned optimization test function characterized by multiple local minima and one global minimum. Its mathematical expression is portrayed in Eq. (14):

(14) $$f(x)=0.5+{\displaystyle \frac{{\sin }^2(\sqrt{x_1^2+x_2^2}-0.5}{1+0.001(x_1^2+x_2^2)}}$$

In Eq. (14), $x$ denotes a two-dimensional vector.

This study employs the Power Data from the Microgrid dataset (Bashir et al., 2023), which encompasses electrical power data collected from the Mesa Del Sol microgrid situated in Albuquerque, New Mexico. The dataset encompasses measurements of voltage, current, power, and energy from microgrid components. It comprises 18 features gathered over the span of 15 months, spanning from May 2022 to July 2023. For experimental training, data from May 2022 to January 2023 is utilized, while data from February 2023 to July 2023 is employed for experimental testing. This dataset holds significance for machine learning applications and holds potential for enhancing microgrid operation and management. The algorithm parameter settings are detailed in Table 4.

Performance evaluation

To comprehensively evaluate the performance of the IFWA-SFLA algorithm, this study defines and computes the following key metrics. The optimal solution value refers to the numerical value of the best solution found by the algorithm during the iteration process, typically representing the minimum or maximum value of the objective function. Its mathematical expression is shown in Eq. (15):

(15) $${\mathrm{V}}_{best}={min}_{i=1}^N{V}_i$$

In Eq. (15), $V_i$ is the optimal solution value at the $i$-th iteration, and $N$ is the number of iterations. The average best solution value represents the average of all best solution values obtained after multiple runs of the algorithm, reflecting the stability and consistency of the algorithm across repeated experiments. Its mathematical expression is shown in Eq. (16):

(16) $${\mathrm{V}}_{avg}={\displaystyle \frac{1}{M}\sum _{j=1}^M{V}_{best,j}}$$

In Eq. (16), $V_{best,j}$ represents the best solution value for the j-th run, and M signifies the number of runs. The convergence rate indicates the speed at which the algorithm finds the optimal solution and can be assessed by comparing the number of iterations required for the algorithm to reach the best solution. Its mathematical expression is shown in Eq. (17):

(17) $$C\mathrm{R}={\displaystyle \frac{t_{end}-t_{start}}{t_{total}}}$$

In Eq. (17), $t_{start}$ is the time when the algorithm starts iterating, $t_{end}$ is the time when the algorithm finds the optimal solution, and $t_{total}$ is the total iteration time of the algorithm. The computation time represents the total time required by the algorithm from start to finish, which is crucial for evaluating the feasibility of the algorithm in practical applications. Its mathematical expression is shown in Eq. (18):

(18) $$T=t_{end}-t_{start}$$

Algorithm stability refers to the consistency of the results generated by the algorithm across multiple runs and can be evaluated by comparing the variation in the best solution values among different runs. Its mathematical expression is shown in Eq. (19):

(19) $$S={\displaystyle \frac{1}{M}\sum _{j=1}^M{\displaystyle \frac{1}{st{d}_j}}}$$

In Eq. (19), $st{d}_j$ represents the standard deviation of the best solution values for the j-th run, and M is the number of runs. Diversity measures the degree of variation among the solutions in the population, which is crucial for preventing the algorithm from prematurely converging to local optima. Its mathematical expression is shown in Eq. (20):

(20) $$D={\displaystyle \frac{1}{N}\sum _{i=1}^N{\displaystyle \frac{1}{d_i}}}$$

In Eq. (20), $d_i$ represents the diversity measure of solutions in the i-th iteration, and N is the number of iterations. Standard deviation is the standard deviation of the best solution values, reflecting the range of fluctuation in the algorithm results. Its mathematical expression is shown in Eq. (21):

(21) $$SD=\sqrt{{\displaystyle \frac{\sum _{j=1}^M{(V_{best,j}-V_{avg})}^2}{M-1}}}$$

In Eq. (21), $V_{best,j}$ represents the best solution value for the j-th run, and $V_{avg}$ is the average best solution value. Success rate is the proportion of successful attempts in finding the optimal solution across multiple runs, which is a key metric for assessing algorithm performance. Its mathematical expression is shown in Eq. (22):

(22) $$SR={\displaystyle \frac{C}{M}\times 100\mathrm{\%}}$$

In Eq. (22), C represents the number of times the algorithm successfully finds the optimal solution.

Computational analysis of the IFWA-SFLA algorithm

Figures 5 and 6 present the results of various algorithms on the Sphere and Schaffer functions. For the Sphere function (2,500 iterations, 30 dimensions), the IFWA-SFLA algorithm attained an average best solution value of 2.96 × 10⁻¹⁰². On the Schaffer function (50 iterations, two dimensions), the IFWA-SFLA algorithm yielded an average best solution value of 3.01 × 10⁻⁴. Among the compared algorithms, the IFWA-SFLA algorithm demonstrated the highest precision in locating the optimal solution, underscoring its feasibility.

The measurement results of algorithm execution time are presented in Table 5. The data indicates that the IFWA-SFLA algorithm exhibits a relatively shorter total execution time compared to other algorithms, underscoring its efficiency and fast convergence characteristics.

Content and applications of green building

Figure 7 illustrates the voltage stability index waveform obtained using the IFWA-SFLA algorithm to minimize the system’s static voltage stability index as the optimization objective. The results indicate that when minimizing the static voltage stability index is the optimization objective, the optimal connection point is at Node 23. In this case, the active power network loss is 50.093 kW, and the static voltage stability index is 0.014. It is evident that connecting to Node 23 results in the minimum static voltage stability index, demonstrating the successful application of the IFWA-SFLA algorithm in a multi-objective optimal configuration model. Figure 8 presents the amplitude of node voltages. When minimizing the static voltage stability index, the static voltage stability index is minimized, but the active power network loss index is relatively high, possibly not meeting the requirements of the optimization configuration. On the other hand, when minimizing active power network loss is the optimization objective, the active power network loss can be reduced to a minimum, but at this point, the static voltage stability index is relatively high and may not meet the requirements of the optimization configuration. In the multi-objective optimization configuration discussed in this study, individual sub-objectives may not be optimal, but effective adjustments in the relationships between sub-objectives can achieve an overall optimization effect.

The IFWA-SFLA algorithm proposed in this study integrates adaptive resource allocation strategies and community genetic strategies in its design, ensuring efficiency and diversity in the optimization process through a random balanced grouping strategy. These strategies endow the IFWA-SFLA algorithm with powerful global search capabilities and precise local search capabilities, demonstrating unparalleled advantages over other algorithms in the optimization of multi-energy-coupled microgrid operation problems. Simulation experiment results also confirm the applicability and outstanding performance of the IFWA-SFLA algorithm in multi-objective optimization configuration models.

Limitations

Although the IFWA-SFLA algorithm proposed in this study has demonstrated noteworthy success in optimizing the economic operation of microgrids, it faces certain limitations. Chief among these is the study’s primary focus on small-scale microgrid systems, thereby leaving the validation of its applicability to large-scale microgrid systems somewhat incomplete. In future research, several promising directions warrant exploration: Firstly, there is an opportunity for a more in-depth investigation into the performance of optimization algorithms, especially their suitability for addressing the complexities of real-world microgrid systems. Fine-tuning algorithm parameters to enhance their efficacy and robustness in practical scenarios could significantly advance their utility. Secondly, a deeper exploration of control strategies for bidirectional inverters in microgrid energy storage systems, spanning both grid-connected and islanded operation modes, holds promise. Enhancing control algorithms has the potential to bolster the performance and resilience of inverters within microgrids, thereby bolstering the overall reliability and flexibility of such systems. Moreover, exploring the applicability of the IFWA-SFLA algorithm in other domains, such as smart grids and energy management systems, could yield valuable insights. Investigating its efficacy and advantages across diverse contexts may unveil its versatility and benefits beyond microgrid optimization. In summary, future research endeavors should prioritize the refinement and optimization of algorithms and control strategies tailored to multi-energy-coupled microgrid optimization and operation. Such endeavors are poised to drive advancements in microgrid technology, fostering the efficient utilization of energy and furthering sustainable development efforts.