Optimization scheduling of microgrid cluster based on improved moth-flame algorithm

Abstract

With the rapid development of renewable energy, microgrid cluster systems are gradually being applied. To promote the development of microgrid cluster scheduling technology, maximize economic benefits while reducing the operating cost required for microgrid scheduling, an optimized scheduling scheme is proposed by constructing a function to minimize the operating cost of microgrids. Then, chaos mutation and Gaussian mutation are applied to improve the moth-flame algorithm that easily falling into local optima. A microgrid cluster optimization scheduling model on the basis of the improved moth-flame algorithm is constructed. The experimental results showed that the operating cost in islanding mode was 4286.21 yuan after 160 iterations. After optimizing the scheduling, the operating cost was 3912.3 yuan, with a decrease of 8.7%. The improved moth-flame algorithm had a stable average loss value of 20% and an operating efficiency of 97.19% after 10–50 iterations, which was significantly higher than other intelligent algorithms. This indicates that the improved moth-flame algorithm has high reliability and effectiveness in microgrid cluster optimization scheduling. Therefore, the proposed model effectively optimizes the scheduling scheme of microgrid cluster, providing new solutions for the efficient utilization of smart grids and renewable energy in the future.

Introduction

With the development of society, human demand for electricity has also increased. However, fossil fuels are non-renewable energy sources. As mining increases, the reserve continues to decrease, posing significant challenges to the long-term supply of power systems [1]. To address these challenges, researchers have integrated distributed power generation technology into the power grid operation. Distributed power generation technology has low pollution emissions, high efficiency, and high flexibility, so its development scale is rapidly expanding [2]. The randomness and volatility of distributed power sources are uncontrollable, and their large-scale application and integration also bring huge challenges and impacts to traditional power grids [3]. Microgrid cluster scheduling can effectively address the grid connection of distributed power sources and promote the transition from traditional power grids to smart grids [4]. However, there are still some issues in its optimization scheduling. Firstly, microgrids contain various distributed energy sources, like photovoltaics, wind power, energy storage devices, etc. These energy sources have intermittent and fluctuating characteristics, leading to complex and variable scheduling problems in microgrids [5]. Secondly, the operating environment of microgrids is complex and diverse, and there are coupling and collaborative relationships between various microgrids, which increases the difficulty and cost of optimization scheduling. Therefore, optimizing microgrid cluster scheduling to reduce the cost and difficulty of energy scheduling has become an urgent problem.

The Moth-flame Optimization algorithm (MFO) has strong parallel optimization capability and global optimization performance, which is widely used by researchers in various fields. Yao et al. proposed a node deployment optimization algorithm for remote environment detection. This algorithm used an adaptive inertia strategy to improve the global search capability of MFO. The disturbance factor in MFO was utilized for path optimization to avoid local optima. The coverage was significantly improved, and its performance advantages were more obvious compared wit other algorithms [6]. Wang et al. designed an influence assessment model for evaluating social networks. This model was based on the valuation scheme of adjacent nodes and used MFO to search for the node set with maximum influence. The model could effectively identify influential individuals in social networks [7]. Wang et al. proposed a multi-level charging strategy model on the basis of fractional model and MFO. This model divided the charging process of new energy electric vehicles into different stages, with charging time, temperature changes, and other optimization objectives. The MFO algorithm was taken to optimize the charging performance. The model provided optimal guidance for the charging process of electric vehicles under different demands [8]. Xu et al. proposed a local MFO method for ship thermal energy scheduling. This method introduced MFO to enhance the exploration and development capabilities in iterative computation, A population diversity strategy was introduced to prevent algorithm stagnation. The results indicated that this method optimized energy scheduling problems, and reduced operating cost and greenhouse gas emissions [9]. Long et al. designed a power grid current model predictive control method based on MFO and sliding discrete Fourier transform. This method introduced MFO to identify and update model parameters, and iteratively solved them using an adaptive function. The experimental results showed that this method converged faster and reduced the harmonics compared with other algorithms [10]. Naji Alhasnawi and other professionals focus on efficient management of electrical energy, optimizing equipment energy and regulating load demand through improved sine cosine algorithm and MFO. The results indicate that the method is practical [11].

There is also abundant research on the optimization scheduling of microgrid cluster. Chu et al. designed a microgrid scheduling method that constrained the frequency of microgrids. This method combined system frequency dynamics with the uncertainty of renewable energy and loads. The synthetic inertia control was used to regulate the active power output of inverter-based generators. The distributionally robust formula was used to explicitly model the uncertainty of non-critical load shedding, ensuring elastic operation during islanding events. This method improved the frequency stability of power electronics [12]. Wu et al. built a mixed integer linear programming. The model first established a microgrid planning model and evaluated its reliability using sequential Monte Carlo method. The model effectively improved the supply efficiency of microgrids [13]. Aaslim et al. proposed a multi-level stochastic programming model for of microgrids such as generators and electricity. This model used stochastic dual dynamic programming and Markov chain to solve the running process. The experimental results indicated that the model improved the operational efficiency of microgrids and the allocation efficiency of renewable energy [14]. Gao et al. designed a microgrid power optimization scheduling model based on imitation learning. This model used reinforcement learning networks to learn strategies from historical data of microgrid operation, by mimicking integer linear programming solvers. This method could effectively reduce training time in the optimization scheduling of small microgrids. The operating cost tended to approach the actual operating cost [15]. Qiu et al. proposed a novel robust two-layer distribution optimization method to solve the economic dispatch in microgrids. This method was based on a robust scheduling model, which collaboratively optimized the connection line scheme according to the load reduction situation of each entity’s power generation, reducing the specific cost of the microgrid. The results indicated that this method could effectively solve the economic dispatch problem in microgrids [16]. Alhasnawi et al. proposed an improved artificial rabbit optimization algorithm to manage household devices in order to reduce energy costs and carbon emissions. The results showed that the algorithm saved 80.34% in cost [17]. Alhasnawi’s team has conceived an improved artificial intelligence algorithm to enhance the Internet of Things for real-time monitoring of photovoltaic systems. The results show that the average efficiency of the algorithm reaches 88% [18]. In addition, scholars such as Alhasnawi have utilized an improved cockroach swarm optimization algorithm combined with a power equipment scheduling framework for energy management of household appliances. The results showed that this method reduced energy costs by 46.09% [19].

In summary, the MFO algorithm has many application areas. Researchers have carried out extensive research on optimization scheduling of microgrids, while there is still relatively little research on its microgrid cluster. To optimize the efficiency and economy of optimization scheduling microgrid cluster, it is necessary to make precise scheduling of energy in the microgrid cluster. Therefore, in order to reduce energy waste and operating cost, a microgrid cluster optimization scheduling model based on Improved Moth-Flame Optimization Algorithm (IMFO) is developed, which integrates chaotic mapping and Gaussian mutation. It is expected to explore more efficient energy scheduling models, improve the utilization efficiency of renewable energy, enhance the reliability of power supply, and promote the development of microgrid clusters [20].

The innovation of the research is reflected in two aspects. (1) This study comprehensively considers multiple resource and load requirements, proposes a function with the goal of minimizing the operating cost of microgrids, and based on this, constructs an optimization scheduling model for microgrid clusters. (2) Gaussian mutation and chaos mechanisms were introduced in the optimization algorithm to improve the traditional MFO algorithm. The main contributions of the research are reflected in the following three aspects. (1) The optimized scheduling model proposed in the study can not only effectively reduce operating costs, but also improve economic benefits. (2) IMFO algorithm enhances the effectiveness and stability of optimization scheduling, and solves the problem of traditional algorithms easily getting stuck in local optima. (3) By optimizing the application of scheduling models, the utilization efficiency of renewable energy in microgrid clusters has been improved, promoting the rational allocation and use of green energy.

The summary of the literature review is shown in Table 1.

Table 1 Summary of Literature Review

The research is structured from three parts. The first section constructs a new model. The second part is the performance testing. The third part is the discussion and experimental results. The flowchart of the proposed method is shown in Fig. 1.

Fig. 1

Flowchart of the proposed method

Methods and materials

This section first introduces the scheme design for optimizing the operation and scheduling of microgrid clusters. Then the construction process of the microgrid scheduling optimization model based on IMFO is designed.

Design of optimization scheduling scheme for microgrid cluster operation

Microgrid cluster is composed of energy sources like wind turbines, fuel cells, solar photovoltaic arrays, and gas turbines. How to ensure the stable operation of new energy in microgrid clusters and minimize the operating cost of microgrids while meeting the negative charge demand of users is still an urgent problem. Therefore, the research is to improve the optimization scheduling, reduce operating cost, and reasonably allocate the power generation of each unit in the microgrid cluster. Therefore, a model for optimizing the operation scheduling of microgrid cluster is constructed. The internal structure of the microgrid cluster is displayed in Fig. 2.

Fig. 2

Microgrid cluster structure

In Fig. 2, the microgrid cluster consists of multiple microgrids. In order to achieve an optimized scheduling model for microgrid clusters, the objective function is to minimize environmental and operational costs [21]. The environmental cost includes the penalty fees for pollutant gas emissions [22]. The main pollutant gases are carbon dioxide, sulfur dioxide, and nitrites [23]. In addition, the study also aims to maximize the economic benefits generated by microgrid cluster. The constructed objective function is displayed in Eq. (1).

$$\begin{gathered} C=\sum\limits_{{i=1}}^{3} {\sum\limits_{{t=1}}^{T} {\left[ {C_{i}^{{MT}}\left( t \right)+C_{i}^{{BT}}\left( t \right)+C_{i}^{{ET}}\left( t \right)+C_{i}^{{EM}}\left( t \right)} \right]} } \hfill \\ +\sum\limits_{{i=1}}^{3} {\sum\limits_{{t=1}}^{T} {\sum\limits_{{k=1}}^{3} {\left[ {{C_k}\lambda _{k}^{{MT}}C_{i}^{{MT}}\left( t \right)+{C_k}\lambda _{k}^{{grid}}P_{i}^{{buy}}\left( t \right)} \right]} } } \hfill \\ \end{gathered}$$

(1)

In Eq. (1), $C_{i}^{{EM}}$ signifies the maintenance cost of the wind turbine. $C_{i}^{{ET}}$ is the cost of transactions between power grids. t signifies the running time of the microgrid cluster. $C_{i}^{{MT}}$ signifies the cost of generating electricity using gas turbines. $C_{i}^{{BT}}$ is the cost of purchasing energy storage systems. $\lambda _{k}^{{grid}}$ is the generation coefficient value of pollutants in the distribution network. T signifies the scheduling period. $\lambda _{k}^{{MT}}$ is the coefficient of k-class pollutants generated by gas turbines during operation. $C_{i}^{{BT}}$ is the transaction cost of the energy storage system. $P_{i}^{{buy}}$ is the pollution cost during electricity trading. To ensure the stable operation of microgrids, The internal power generation units of the microgrid cluster are subjected to power constraint balancing, and the constraint expression is displayed in Eq. (2).

$$P_{i}^{{WT}}\left( t \right)+P_{i}^{{PV}}\left( t \right)+P_{i}^{{BT}}\left( t \right)+P_{i}^{{mg}}\left( t \right)+P_{i}^{{grid}}\left( t \right)=P_{i}^{{load}}\left( t \right)$$

(2)

In Eq. (2), $P_{i}^{{load}}\left( t \right)$ signifies the microgrid load. $P_{i}^{{WT}}\left( t \right)$ signifies the installed power of the wind turbine. $P_{i}^{{PV}}\left( t \right)$ is the device power of the photovoltaic power source. $P_{i}^{{BT}}\left( t \right)$ signifies the device power of the energy storage system. $P_{i}^{{mg}}\left( t \right)$ signifies the power traded with other microgrids, with a negative value when selling electricity and a positive value when purchasing electricity. $P_{i}^{{grid}}\left( t \right)$ signifies the power traded between the distribution network and microgrid, with a negative value when selling electricity and a positive value when purchasing electricity. The uphill power constraint of the gas turbine is displayed in Eq. (3).

$$R_{{i,down}}^{{MT}}\Delta t \leqslant P_{i}^{{MT}}\left( t \right) - P_{i}^{{MT}}\left( {t - 1} \right) \leqslant R_{{i,up}}^{{MT}}\Delta t$$

(3)

In Eq. (3), $R_{{i,down}}^{{MT}}$ is the down ramp power of the gas turbine. $R_{{i,up}}^{{MT}}$ signifies the uphill power of the gas turbine. $P_{i}^{{MT}}\left( {t - 1} \right)$ signifies the installed power of the gas turbine at the previous moment at t. $P_{i}^{{MT}}\left( t \right)$ signifies the installed power of the gas turbine at The constraint expression of the energy storage device is displayed in Eq. (4).

$$SOC_{t}^{{\hbox{min} }} \leqslant SOC\left( t \right) \leqslant SOC_{t}^{{\hbox{max} }}$$

(4)

In Eq. (4), $SOC_{t}^{{\hbox{min} }}$ is the minimum charge in the energy storage unit. $SOC\left( t \right)$ is the unit charge in the energy storage unit. $SOC_{t}^{{\hbox{max} }}$ refers to the maximum charge in the energy storage unit. The expression for its discharge power is shown in Eq. (5).

$$\left\{ {\begin{array}{*{20}{l}} {0 \leqslant P_{i}^{{ch}}\left( t \right) \leqslant P_{i}^{{\hbox{max} }}} \\ {0 \leqslant P_{i}^{{dis}}\left( t \right) \leqslant P_{i}^{{\hbox{max} }}} \end{array}} \right.$$

(5)

In Eq. (5), $P_{i}^{{\hbox{max} }}$ refers to the maximum charging and discharging power that can pass through the energy storage unit. $P_{i}^{{ch}}\left( t \right)$ stands for the charging power of the energy storage device at t, and $P_{i}^{{dis}}\left( t \right)$ is the discharge power at t. The interaction power constraint between microgrid clusters can be obtained from the above equation, as shown in Eq. (6).

$$P_{{\hbox{min} }}^{{mg}} \leqslant P_{i}^{{mg}}\left( t \right) \leqslant P_{{\hbox{max} }}^{{mg}}$$

(6)

In Eq. (6), $P_{{\hbox{min} }}^{{mg}}$ refers to the minimum interaction power between microgrid clusters. $P_{{\hbox{max} }}^{{mg}}$ is the maximum interaction power between microgrid clusters. $P_{i}^{{mg}}\left( t \right)$ is the total value of interaction power between microgrid clusters. The interaction power constraint between microgrids and distribution networks is shown in Eq. (7).

$$P_{{\hbox{min} }}^{{gird}} \leqslant P_{i}^{{gird}}\left( t \right) \leqslant P_{{\hbox{max} }}^{{gird}}$$

(7)

In Eq. (7), $P_{{\hbox{min} }}^{{gird}}$ signifies the minimum value of power consumption interaction. $P_{{\hbox{max} }}^{{gird}}$ signifies the maximum value of power consumption interaction. The scheduling model should consider the power generation and output of each energy source and the energy scheduling of islanding and grid connected operation modes [24]. The economic optimization scheduling methods for microgrids based on these two modes are shown in Fig. 3.

Fig. 3

Optimization scheduling method for microgrid cluster

In the islanding operation mode, the complexity of internal scheduling and energy storage management of microgrids has increased. It is necessary to reduce the high cost of local power generation and maintenance while balancing supply and demand. In grid connected operation mode, microgrids improve the flexibility of energy dispatch by exchanging electricity with the distribution network, and optimize operating and environmental costs through electricity market transactions.

Optimization scheduling model for microgrid cluster based on improved moth flame algorithm

The optimization scheduling method for microgrid clusters is key to achieving efficient, stable, and sustainable power supply. However, with the increasing demand for new energy system inputs and multi-objective optimization, traditional optimization methods have gradually shown shortcomings in dealing with complex and multi-constrained optimization problems. Based on this, an IMFO on the basis of chaotic mapping and Gaussian mutation is designed to optimize the microgrid cluster scheduling model. The IMFO algorithm is inspired by moths flying around flames [6]. There are two types of individuals in IMOF, moths and flames. Moths choose to fly and search around the flame in a spiral pattern. After searching, the moth will move its position to maintain the flame as the optimal position in the moth and flame cluster, which is the optimal solution [25, 26]. The bio-mimetic of IMFO is displayed in Fig. 4.

Fig. 4

Biomimetic schematic diagram of IMFO

In IMOF, the individual positions of the moth population are initialized firstly, as expressed in Eq. (8).

$$M=\left\{ {\begin{array}{*{20}{l}} {{m_{1,1}}}&{{m_{1,2}}}& \cdots &{{m_{1,d}}} \\ {{m_{2,1}}}&{{m_{2,2}}}& \cdots &{{m_{2,d}}} \\ \cdots & \cdots &{}& \cdots \\ {{m_{n,1}}}&{{m_{n,2}}}& \cdots &{{m_{n,d}}} \end{array}} \right.,{O_M}=\left\{ {\begin{array}{*{20}{l}} {{O_{M1}}} \\ \hline {{O_{M2}}} \\ \cdots \\ {{O_{Mn}}} \end{array}} \right.$$

(8)

In Eq. (8), d is the variable dimension. M is the initial population of moths. ${O_M}$ signifies the fitness matrix of M. m signifies the spatial coordinate of the population. The initialization expression for flame position is shown in Eq. (9).

$$F=\left\{ {\begin{array}{*{20}{l}} {{f_{1,1}}}&{{f_{1,2}}}& \cdots &{{f_{1,d}}} \\ {{f_{2,1}}}&{{f_{2,2}}}& \cdots &{{f_{2,d}}} \\ \cdots & \cdots &{}& \cdots \\ {{f_{n,1}}}&{{f_{n,2}}}& \cdots &{{f_{n,d}}} \end{array}} \right.,{O_F}=\left\{ {\begin{array}{*{20}{l}} {{O_{F1}}} \\ \hline {{O_{F2}}} \\ \cdots \\ {{O_{Fn}}} \end{array}} \right.$$

(9)

In Eq. (9), F is the initial flame position. ${O_F}$ signifies the fitness matrix of F. The repositioning of moths in IMOF is achieved using the logarithmic spiral method, as shown in Eq. (10).

$${M_i}={D_i}{e^{bt}}\cos \left( {2\pi t} \right)+{F_j}$$

(10)

In Eq. (10), ${D_i}$ is the path length. b is a constant. t signifies a random in [1, –1]. When t is 1, the moth is near the flame and the distance is short. When t is -1, the moth’s spatial position is far away from the flame and the distance is relatively long. The ${D_i}$ is shown in Eq. (11).

$${D_i}=\left| {{F_j} - {M_i}} \right|$$

(11)

In Eq. (11), ${M_i}$ represents the updated coordinates of the moth’s position. ${F_j}$ is the coordinate before updating the flame position. During the algorithm iteration process, the position of the flame is constantly updated and reduced. When only the last flame is left, it is the optimal flame required by the algorithm. The updated expression for the flame position is shown in Eq. (11).

$${N_F}={f_{round}}\left( {n - l\frac{{n - 1}}{T}} \right)$$

(12)

In Eq. (12), l is the current iteration count. n signifies the initial population size. T signifies the total iterations for the population to find the optimal result. ${f_{round}}$ is the total iterations when the moth updates to the optimal position. Due to the tendency of the MFO to fall into local optima in the later stages of population iteration, chaos mapping is introduced to optimize the MFO algorithm in order to solve this problem. Sine chaotic mapping has a simple mathematical form, which can make the population more evenly distributed in the search space and help improve the MFO’s ability to escape from local optima [27]. The Sine chaotic mapping is shown in Eq. (13).

$${z_{k+1}}=\frac{a}{4}\sin \left( {\pi {z_k}} \right)$$

(13)

In Eq. (13), ${z_k}$ is the variable value at the k-th iteration, and ${z_{k+1}}$ refers to the variable value at the $k+1$. The values of some variables in ${z_{k+1}}$ are shown in Eq. (14).

$$a \in \left( {0,4} \right],z \in \left( {0,1} \right),a=4,{z_0}=0.152$$

(14)

In Eq. (14), a is a random number from 0 to 4. z is a variable value ranging from 0 to 1. When a is 4, the variable value of ${z_0}$ at the 0th time is 0.152. In addition, introducing Gaussian mutation can more accurately explore the local solution space and find better solutions [28], as shown in Eq. (15).

$$X\left( x \right)=x\left( {1+G\left( {0,1} \right)} \right)$$

(15)

In Eq. (15), x refers to the parameter value of the initial population. $G\left( {0,1} \right)$ is a numerical value with a mean and variance of 0 and 1, respectively. $X\left( x \right)$ is the parameter value that has undergone Gaussian mutation processing and iteration. The steps of the IMFO algorithm obtained through the above optimization are shown in Fig. 5.

Fig. 5

IMFO algorithm step diagram

IMFO first initializes the parameters, which uses the Sine chaotic mapping in formula (14) to initialize the moth population and solution space, to increase the diversity of the search space. Then, they are sorted according to the size of the best fitness value. After obtaining the optimal fitness value for sorting, the path length between the two can be calculated using formula (15). After obtaining the distance value, whether it meets the termination criteria is determined. If it does not meet the criteria, the process return to calculate the fitness value for recalculation. If it meets the criteria, the loop process ends and outputs the optimal solution.

Results

This section first verifies the effectiveness of the optimization scheduling scheme for microgrid cluster operation. Then the effectiveness of the IMFO-based microgrid cluster optimization scheduling model is tested under different grid operation modes.

Validity verification of optimization scheduling scheme for microgrid cluster operation

To verify the proposed optimization scheduling scheme for microgrid cluster operation, three interconnected microgrids are selected, consisting of gas turbines, wind power, photovoltaics, and energy storage devices. The time of use electricity price for one day is displayed in Table 2.

Table 2 Time of use electricity price for microgrids

The study tests the operating cost of microgrid cluster optimization scheduling under different iterations, as displayed in Fig. 6. Figure 6 (a) displays the operating cost of the microgrid cluster in islanding mode. Before optimizing, the operating cost was 4286.21 yuan after 160 iterations. After optimizing, the operating cost was 3912.3 yuan after 160 iterations, with a decrease of 8.7% compared with before optimization. Before scheduling optimization, there is a situation where the operating cost increases during the iteration process. This is because the load of microgrids and the supply of renewable energy are dynamically changing. These dynamic changes will affect the effectiveness of scheduling optimization, leading to an increase in operational costs during the iteration process. Figure 6 (b) displays the operating cost in grid connected mode, which decreased from 4632 yuan to 4067.2 yuan before optimization. After optimizing the scheduling, the operating cost decreased from 4326 to 3975 yuan. At 160 iterations, it decreased by 351 yuan compared with before optimization. The experimental results indicate that the economic optimization scheduling of microgrid clusters has high economic benefits.

Fig. 6

Operating costs of microgrid clusters under islanding and grid connected modes

Figure 7 shows the wind power generation and total energy consumption before and after optimization. Among them, Fig. 7 (a) displays the wind power generation before and after optimization. The total wind power generation before optimization was about 449.5 kWh. After optimization, the total wind power generation was about 510 kWh, wit an increase of 11.86% compared with the total power generation before optimization. Optimizing the scheduling scheme significantly improves the efficiency of wind power generation. Figure 7 (b) displays the total energy consumption before and after optimization scheduling. The total energy consumption before optimization was about 841 kWh, while the total energy consumption after microgrid cluster optimization scheduling was about 659 kWh, wit a reduction of 21.64%. This indicates that optimizing the scheduling scheme can effectively reduce the total energy consumption by coordinating energy storage systems and improving power generation processes.

Fig. 7

Wind power generation and total energy consumption before and after optimization of microgrid cluster scheduling

Table 3 compares the scheduling results of load demand, distributed generation, and energy storage status for microgrid clusters. During the high load period at 9:00 and 12:00, the optimized economic benefits increased by 22 yuan and 19 yuan respectively, indicating that the optimal dispatching of the microgrid cluster realized higher economic benefits by making full use of the distributed generation and energy storage system at high load. During the peak load periods of 3pm and 6pm, the optimized scheduling increased economic benefits by 22 yuan and 14 yuan respectively, proving that it can effectively cope with peak load periods. In summary, the optimization scheduling method for microgrid clusters can effectively improve economic benefits in all time periods.

Table 3 Microgrid Cluster’s load demand, distributed generation, energy storage status, and optimized scheduling results

Performance evaluation of optimization scheduling model for microgrid cluster based on IMFO

To verify the performance of the IMFO constructed in the study, the experimental testing environment uses Intel^® Core™ i7-9700 K, 32GB RAM, SSD hard drive type, 1 TB capacity. The Nvidia GeForce RTX 2080Ti graphics card is used to support the operation of algorithms. Genetic Algorithm (GA) [29], Lion Swarm Optimization (LSO) [30], and MFO [31] are compared. The parameter settings for energy sources like wind turbines, fuel cells, photovoltaic arrays, and gas turbines are shown in Table 4.

Table 4 Parameter settings for energy sources like wind turbines, fuel cells, photovoltaic arrays, and gas turbines

The loss and operational efficiency comparison of IMFO are displayed in Fig. 8. In Fig. 8 (a), The average loss value of IMFO stabilized at 20% after 10–50 iterations. The average loss value of IMFO decreased by 8% when comparing GA and LSO. IMFO has a significant advantage in finding the minimum loss value, and can more effectively reduce the loss in microgrid scheduling, thus improving the overall economic benefit and resource utilization. In Fig. 8 (b), IMFO has the highest operational efficiency, reaching 97.19%. The running efficiency of GA and LSO are 96.30% and 96.94%, respectively. In contrast, IMDO increased by 0.89% and 0.25%, respectively. While these differences are small, these gains can accumulate into significant performance gains in large-scale microgrid cluster scheduling. The results demonstrate that IMFO has high effectiveness and reliability in optimal scheduling microgrid cluster.

Fig. 8

Wind power generation and total energy consumption before and after optimization of microgrid cluster scheduling

Figure 9 (a) displays the power output of wind, photovoltaic, and fuel cells in the islanding operation mode of microgrid cluster scheduling optimization. From 12am to 6am and from 12pm to 8pm, the output of solar, wind, and other power generation equipment was low and did not meet the load requirements. At this time, fuel cells need to be used to provide electricity. Figure 9 (b) shows the operating cost of microgrid cluster optimization scheduling at different iterations. After 100 iterations, the IMFO algorithm tended to be stable, and the operating cost converged to 1023.3 yuan, which was significantly better than MFO, LSO, GA and other algorithms in terms of optimization performance. The IMFO algorithm has better performance and convergence speed in optimizing scheduling strategies, which can effectively reduce cost and improve the operational efficiency and stability of microgrid systems.

Fig. 9

The output and operating costs of various energy sources in islanding operation mode

Figure 10 (a) shows the power output of wind, photovoltaic, and fuel cells in the grid connected operation mode of microgrid cluster scheduling optimization. From 00:00 to 07:00, the microgrid cluster purchased electricity from the distribution network to meet the load demand due to the low output of photovoltaic and wind turbines. From 08:00 to 12:00, if the power supply of the microgrid cluster met the needs of users and there was surplus electricity, it sells electricity to the distribution network to obtain profits and reduce cost. Figure 10 (b) shows the operating cost of microgrid cluster optimization scheduling at different iteration periods. After 110 iterations, the cost convergence of IMFO algorithm was 946.5 yuan, which was lower than other methods. The improved microgrid cluster optimization scheduling model can enable the microgrid cluster to adopt the optimal economic operation mode at different time periods, maximize the utilization, and further optimize economic benefits by purchasing or selling electricity to the distribution network. In addition, the IMFO can find or approach the global optimal solution in fewer iterations, demonstrating its effectiveness in handling complex microgrid cluster optimization scheduling problems.

Fig. 10

The output and operating costs of each energy source in parallel operation mode

Discussion and conclusion

In order to improve the energy scheduling performance of microgrid clusters and reduce the operating costs during the energy scheduling process, a microgrid cluster optimization scheduling model based on IMFO algorithm is proposed. In order to evaluate its effectiveness and rationality, relevant experiments were conducted. Basu et al. considered the day ahead dispatching of the microgrid and chose quasi opposite learning and fast convergence evolutionary planning technology, which reduced the cost by 0.52%~0.78% [32]. In contrast, the proposed IMFO algorithm reduces operating costs by 8.7% in islanding mode. This indicates that the IMFO algorithm can effectively reduce operating costs and improve economic benefits. The IMFO algorithm can optimize the efficiency and economic benefits of energy utilization, effectively coordinate the various subsystems in the microgrid cluster, achieve rational allocation and utilization of energy, thereby reducing operating costs and environmental pollution.

And Jain and other scholars reduced algorithm constraints by combining MFO and mayfly hybrid optimization algorithms to solve emission scheduling and economic load. The results indicate that this algorithm has lower operating costs and better convergence [33]. Meanwhile, the proposed IMFO algorithm stabilizes with fewer iterations, demonstrating faster convergence speed and stability. Specifically, the average loss value of the proposed IMFO algorithm stabilizes at 20% after 10 to 50 iterations, with a running efficiency of up to 97.19%. IMFO can converge quickly with fewer iterations, ensuring the efficiency and reliability of scheduling results.

In summary, the algorithm proposed in this study has shown excellent performance in reducing operating costs, improving operational efficiency, and economic benefits. Its efficiency, reliability, and superior optimization capabilities enable it to further enhance the overall performance of microgrid clusters, providing strong support for the development of distributed energy systems. The limitation of the study is that if there are multiple microgrids in the distribution network cluster, it can lead to voltage quality issues. In the future, voltage quality issues will be taken as the objective function and improved based on microgrid cluster scheduling optimization.