Optimization of distribution network scheduling based on BA and photovoltaic uncertainty

Lianrong Pan; Yuan Fu; Xiao Yang; Xin Wei; Yuyang Hu

doi:10.1515/nleng-2025-0159

Article Open Access

Optimization of distribution network scheduling based on BA and photovoltaic uncertainty

Lianrong Pan , Yuan Fu , Xiao Yang , Xin Wei and Yuyang Hu

Published/Copyright: September 17, 2025

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From the journal Nonlinear Engineering Volume 14 Issue 1

Abstract

A novel optimization framework for microgrid (MG) distribution network scheduling has been proposed, which integrates enhanced bat algorithm (BA) with probabilistic photovoltaic (PV) power prediction to address the dual challenges of renewable energy uncertainty and operational efficiency. The method combines genetic algorithm-optimized artificial neural network with Monte Carlo simulation to achieve very low PV output prediction error under variable weather conditions. In addition, the study improves the BA by using a multi-mechanism approach of Halton sequence initialization and dynamic elite retention, which enhances the convergence iteration speed of the algorithm and avoids local optima problems. The experimental results show that the maximum predicted output power (OP) of the PV generator set is 208 kW, and the predicted OP curve is more consistent with the actual OP curve. The enhanced BA has been demonstrated to enhance the optimization of operating costs of MGs. The operating costs of MGs are 125,452 yuan at low loads and 145,562 yuan at high loads. The study provides a replicable template for high-penetration renewable MGs by combining probability prediction with swarm intelligence optimization. The research provides new ideas for the scheduling strategy of MG distribution networks centered on new energy.

Keywords: bat algorithm; photovoltaic power generation; distribution network scheduling; renewable energy

1 Introduction

The demand for electrical energy in a modern society is increasing continuously. Due to the gradual deterioration of the global environment, there is an urgent need for renewable energy (RE) generation methods to replace traditional thermal power generation [1,2]. Meanwhile, due to the continuous expansion, the traditional power grid structure has become very complex and difficult to manage effectively. Moreover, any failure of the power grid poses a huge threat to people’s lives and property [3]. As a result, microgrid (MG) systems with new energy as the core have captured the attention of scholars.

MGs are small-scale power generation and distribution facilities that consist of distributed generation, energy storage, energy converters, loads, monitoring and protective equipment, and more [4,5]. MGs aim to achieve flexible and efficient application of distributed power sources, and address the issue of large-scale and diverse forms of distributed power grid connection. MGs facilitate the integration of distributed power sources and RE on a large scale, thereby ensuring a reliable supply of various forms of energy to the load(s). They represent an effective means of enabling traditional power grids to transition to smart grids. MGs can operate either in parallel or in isolation from the main grid. They can provide electricity according to user needs and integrate into the distribution network through common coupling points. As a controllable unit, MGs are capable of responding rapidly within seconds to meet the needs of external transmission and distribution networks. This increases local reliability, reduces feeder losses, maintains local voltage stability, and provides uninterrupted power. The smart MG uses advanced Internet and information technology to realize the flexible and efficient application of distributed power generation, and has certain energy management functions. The system is characterized by its relatively small scale, decentralization, and independence. It is capable of achieving self-control, protection, and management as an autonomous system.

The scheduling of MG distribution can greatly improve the efficiency of grid management, cut down network losses, and is of great significance for establishing a long-term effective MG system.

To enhance the effectiveness of computer-aided clinical diagnosis, Lu et al. presented a new method for detecting abnormal brains with magnetic resonance imaging. First, a pre-trained AlexNet was modified by adding batch normalization layers. Next, the last few layers were replaced with an extreme learning machine. Finally, the chaotic bat algorithm (BA) was used to optimize the extreme learning machine for improved classification performance [6]. In response to the problem of subpopulations evolving in parallel through limited interactions in existing genetic algorithm (GA) research, Bi et al. proposed an improved genetic operation adaptive BA. This algorithm performed adaptive genetic operations on the previous search information of the BA solution. The test results showed that the new algorithm was more effective than other widely used and recently proposed similar algorithms [7]. To establish more effective resource utilization methods, scholars such as Bezdan et al. proposed a multi-objective task scheduling method with swarm intelligence – called the hybrid BA. The simulations demonstrated the enormous potential of the novel method in cloud computing [8]. To solve the problem of planning solutions that are very time-consuming and difficult due to the integration of RE into smart grids, Fu proposed a statistical machine learning technology to perform probabilistic power flow calculations based on multiple scenarios and described their application in stochastic planning of distribution networks. The results indicated that the model significantly improved planning effectiveness [9]. To control the uncertainty of photovoltaic (PV) power, Huang et al. deployed a Copula-based method to sample time-dependent scenarios of PV power within the scheduling range from probability prediction. Simulation studies showed that the proposed disaster recovery plan effectively reduced the operating costs of manufacturing production [10]. To prevent potential frequency instability caused by the infiltration of high-power electronic devices under unintentional islanding events, Chu et al. proposed a new MG scheduling method that considered system frequency dynamics and uncertainties related to RE and loads. The method was validated with an improved IEEE 14-node system [11]. To verify the advantages of connected MGs in terms of economy and resilience, Mohammadi et al. proposed a two-stage adaptive robust optimization method to minimize the total operating cost of connected MGs in the worst-case scenario of modeling uncertainty. The findings demonstrated that interconnected MGs exhibited superior performance in reducing total operational costs and enhancing power supply resilience in comparison with independent MGs [12]. Rezaeimozafar et al. designed a two-step scheduling model to guide large-scale electric vehicle fleets in MGs, addressing the need for management solutions for electric vehicles to minimize the impact of electric vehicle charging on distribution network efficiency. The findings demonstrated that the method could reliably implement the optimal charging and discharging schedule in large-scale systems [13]. Wenzhi et al. proposed an improved sparrow search algorithm for dynamic optimization of active distribution networks in multi-MG systems. This algorithm achieved optimal energy allocation by combining Bernoulli chaotic mapping, Levy flight, mutation, crossover, and competition. The results demonstrated that the proposed method was of significant importance for the economic operation and environmental protection of multi-MG active distribution networks [14]. In light of the significant environmental contamination resulting from traditional fossil fuel energy generation and the depletion of non-renewable resources, Qiao et al. put forth a coordinated day-ahead scheduling method that integrates topology reconstruction, vulture search algorithm optimization, and load response. The proposed method was validated through simulations, which demonstrated its accuracy and efficacy [15]. Compared with the improved sparrow search algorithm proposed by Wenzhi et al. and the bald eagle search algorithm proposed by Qiao et al., the improved BA proposed in this study effectively solved the problem of insufficient population diversity that may be caused by Bernoulli chaotic mapping in sparrow algorithms through Halton sequence initialization and dynamic elite retention mechanism, while avoiding the drawback of decreased convergence speed in high-dimensional optimization of bald eagle search algorithms.

Chen et al. proposed a distributed economic dispatch strategy based on consensus theory to address issues such as the increase in RE and distributed generation that traditional centralized optimization cannot adapt to, as well as changes in distribution network power demand. This strategy utilized consensus algorithms in multi-agent systems to achieve incremental cost consensus to obtain the optimal solution for economic dispatch. The effectiveness and feasibility of this method were verified through simulation and analysis [16]. In response to the negative impact of uncertainty in distributed RE on DC distribution networks, Chen et al. proposed a two-stage optimization scheduling model for DC distribution networks that considers flexible load response. This model achieved joint economic optimization and reactive power optimization. The experimental results verified the progressiveness of the model [17]. To optimize resource allocation within the province, Shi et al. proposed a two-stage scheduling model for provincial power grids, including day-ahead and day-in stages. Conditional generative adversarial networks were utilized to generate load and new energy output scenarios. Based on the generated scene set, the model considered the uncertainty and allowable error interval of new energy and load, and used risk condition values to measure system scheduling risk. The feasibility and effectiveness of this method were verified through experiments conducted on the IEEE 39 node system [18]. To calculate the uncertainty in distributed energy, Liu and Braslavsky proposed a new method for calculating designated operating entities, which is robust to the uncertainty in the utilization of allocated capacity constraints. Compared with existing methods, this method has certain progressiveness [19]. To optimize the coordinated control of complex energy storage in MGs, including PV and wind power generation, Piao et al. proposed a dual deep Q-network reinforcement learning algorithm to train intelligent agents to interact with the MG environment and learn the optimal scheduling control mechanism. This method could achieve multi-objective control at different times, weather conditions, and seasons; flexibly handle energy storage, hydrogen storage, and load energy; and achieve coordinated allocation. The experimental results showed that this method could optimize scheduling for different scenarios of composite energy storage MGs [20].

In summary, domestic and foreign researchers have proposed various methods for optimizing MG distribution network scheduling, including the introduction of various algorithm models. However, these scheduling methods are difficult to effectively balance the power deviation caused by PV uncertainty with the economic operation goals of the system. Meanwhile, existing intelligent algorithms are prone to getting stuck in local optima and have insufficient convergence speed when solving MG optimization models. In this regard, a collaborative optimization framework integrating the enhanced BA and PV power probability prediction is proposed, with the objective of achieving dual optimization of MG loss minimization and scheduling economy. This is accomplished by accurately characterizing PV uncertainty and enhancing algorithm search capabilities, thus providing novel concepts for intelligent distribution network operation under a high proportion of new energy access.

1.1 Contributions of the work

In response to the above-mentioned issues, the proposed method adopts an improved BA and describes the output power (OP) of photovoltaic power generation (PPG) units, to reduce grid losses and improve distribution scheduling efficiency. The innovation of the research lies in the use of OP to predict PV uncertainty, which is helpful for the power scheduling of MGs. At the same time, the improved BA is pertinently utilized to solve MG models, which can help improve the speed and accuracy of result optimization.

1.2 Organization of this article

The rest of this article is organized as follows: in Section 1, an introduction to the problem of scheduling of MG distribution and grid management to cut down network losses is explained. In Section 2, the basic structure of traditional MGs is discussed, and then, a prediction model based on the uncertainty of PPG in MGs is proposed, etc.

2 Methods and materials

The article first introduces the basic structure of traditional MGs and then proposes a prediction model based on the uncertainty of PPG in MGs. This model describes its uncertainty through OP, which can cut down the network loss of distribution and assist in power dispatch of MGs. Subsequently, the article selects the BA to solve the structure and mathematical model of MGs. At the same time, an improved BA is proposed to address the problems of premature convergence and susceptibility to local optima in traditional BAs. Finally, a distribution network scheduling optimization strategy based on BA and PV uncertainty is proposed.

2.1 Optimization of distribution network scheduling based on PV uncertainty

MGs are small power grids consisting of distributed generation, loads, energy storage, power conversion and transmission, and control equipment. It is an autonomous power system capable of controlling, protecting, and managing itself, with complete power generation, distribution, and consumption functions. Furthermore, it is able to effectively achieve energy optimization within the grid [21]. MGs are primarily based on distributed power sources, which are utilized in conjunction with energy storage systems and control devices for the purpose of regulating the supply of energy to meet the demands of the load. The fundamental configuration of distributed power generation is illustrated in Figure 1.

Figure 1

Fundamental configuration of distributed power generation.

In Figure 1, the distributed power system consists of two main parts: non-RE and RE parts. Among them, non-RE part is composed of non-RE generation systems such as internal combustion engines and gas turbines. RE sources consist of RE generation systems such as PV and wind power. In RE generation, the foundation of PPG is solar radiation, and its working principle is to convert radiation energy into electrical energy for utilization. Compared to traditional power generation methods, PPG has advantages such as no energy depletion risk, safety and reliability, cleanliness and pollution-free, and is not limited by resource distribution regions [22,23]. PPG systems serve as micro-power sources for MGs. When users have electricity, the PPG system will prioritize meeting their needs. The scheduling of PV power distribution network can be divided into two parts. First, when there is surplus PPG, the distribution network will integrate the surplus part into the system to supply power to local users. Second, when there is a shortage of PPG, the distribution network utilizes its own power generation system to deliver electricity to the PPG system, ensuring that the PPG system meets the electricity needs of users. Due to the uncertainty of user electricity consumption, the power supply of PPG systems needs to vary according to changes in user electricity consumption. The uncertainty of PPG system power supply is described using OP, and the user’s electricity demand and system power output are considered when scheduling the distribution network. The grid connected PPG system’s structure is presented in Figure 2.

Figure 2

Grid-connected PPG structure.

In Figure 2, the PPG system converts light (irradiance) energy into electricity through PV panels and then adjusts the frequency and phase of the generated electricity to be the same as the power grid system through an inverter. Due to the significant impact of light on PPG systems and the unclear power consumption of users, the study uses the OP of PPG systems to describe their uncertainty. Accurately predicting the OP of PPG systems is of great significance for planning distribution volume and reducing grid load. Predicting the OP of PPG systems requires analyzing the impact of lighting, temperature, and weather conditions on the system. Therefore, the study selects an improved artificial neural network (ANN) as the algorithm for predicting the OP of PPG systems. The ANN is comprised of a multitude of interconnected neurons, each of which represents a specific output function, namely, the excitation function [24]. Addressing the issues of slow convergence speed and low prediction accuracy in ANN, GA is introduced to improve ANN. Using GA to optimize the ANN process is shown in Figure 3.

Figure 3

GA optimization flowchart for ANN.

In Figure 3, GA is introduced to optimize the initial weight threshold of ANN, which enables ANN to complete network learning convergence faster and output predicted values more efficiently. Individuals within the population are evaluated using fitness values, and as the fitness value increases, the chances of selecting individuals are also higher. To enhance the efficiency of the algorithmic convergence process, it is essential to initially constrict the optimal search result range of the ANN and subsequently utilize the back propagation algorithm for training purposes. The calculation formula for predicting the OP of PPG systems using improved ANN is given in Eq. (1) [25]:

(1) d i i = ∑ j = 1 2 ( Y j − X i i , j ) 2 , i i = 1 , 2 , 3 , … n .

In Eq. (1), d i i represents the Euclidean distance of the i i th sample, Y j represents the highest temperature predicted using ANN for a certain day, and X i i , j means the highest temperature of the i i th sample in the submodule. This equation defines the two-dimensional Euclidean distance between the nth training sample and the predicted target point, which is used to quantify the similarity of meteorological conditions. The core assumption is that PV output is only dominated by light intensity and ambient temperature, and historical data has eliminated measurement errors. This distance metric serves as a benchmark for assigning weights to ANN inputs, with smaller distances resulting in higher sample weights. To avoid samples exceeding the disturbance range, normalization is used to preprocess the data samples. The normalization of input variables is shown in Eq. (2):

(2) P n g = P n − P min P max − P min .

In Eq. (2), P n g means the normalized input data, P n means the input variable, P min means the minimum value in the input variable, and P max indicates the maximum value in the input variable. The normalization process of the target data is shown in Eq. (3):

(3) N n g = N n − N min N max − N min .

In Eq. (3), N n g indicates the normalized target data, N n denotes the target data, N min means the minimum value of the target data, and N max means the maximum value of the target data. The study uses Eqs. (1)–(3) for min–max normalization, and the characteristics of PV modules require strict matching of input and output with physical boundaries. Linear mapping of irradiance to the [0,1] interval through Eq. (2) can avoid ANN output exceeding the safety limit of the module. Eqs. (2) and (3), respectively, perform min–max linear normalization on the input illumination intensity P n and output PV power N to eliminate the influence of dimensionality. The training data encompasses annual extreme conditions, with P max exhibiting the highest historical irradiance in the local area. However, it does not take into account the non-uniform distribution characteristics that may occur under cloudy weather conditions.

2.2 Optimization of distribution network scheduling based on BA

To strengthen the optimization of MG distribution scheduling, a multi-period MG optimization scheduling strategy was proposed. Subsequently, based on the PPG system, the study proposed a BA and solved the optimized mathematical model of the MG. The structure of the MG is shown in Figure 4.

Figure 4

MG system architecture.

In Figure 4, the MG contains wind turbines (WT) power generation units and PPG units. Due to the uncertainty of wind and PPG, two sets of battery systems are installed next to the power generation unit and one set of battery system is installed at the load end. In the MG system architecture, the rated capacity of the WT is 120 kW, the PV unit is 140 kW, and the battery uses lead carbon batteries (200 kW h/50 kW). In the process of solving the objective function of the established MG model, it is necessary to know the maintenance and operation costs of each part. The maintenance cost of PPG units is shown in Eq. (4):

(4) C o m − p v = c m − p v ⋅ P p v , t .

In Eq. (4), N max represents the operation and maintenance cost of the PPG unit. The unit is yuan/kW h. C m − p v is the unit power maintenance cost of the PV generator, and P p v , t indicates the rated OP of the PPG unit at t time. The maintenance cost of wind power generation is shown in Eq. (5):

(5) C o m − w t = c m − w t ⋅ P w t , t .

In Eq. (5), C o m − w t indicates the operation and maintenance cost of wind power generation. The unit is yuan/kW h. C m − w t represents the unit power maintenance cost of WT, and P w t , t represents the rated OP of wind power generation units at t time. Real-time operation and maintenance costs of PV and wind power are calculated using linear models, with coefficients based on full lifecycle maintenance data provided by equipment manufacturers. Assumptions include ignoring equipment efficiency degradation and excluding the cost of repairing sudden malfunctions. All units within the same power station have the same unit cost. The established objective function is constrained, where the constraint on PV OP is shown in Eq. (6):

(6) 0 ≤ P p v , t ≤ P p v , t fore .

In Eq. (6), P p v , t fore represents the predicted power of the PV generator at t time. By limiting the PV scheduling power through dual boundaries, the lower limit of 0 reflects physical irreversibility, and the upper limit is predicted by ANN. It is recommended to allow 10% of the predicted power to be exceeded, and this buffer interval is determined through Monte Carlo simulation optimization. The constraint of wind power output is shown in Eq. (7):

(7) 0 ≤ P w t , t ≤ P w t , t fore .

In Eq. (7), P w t , t fore represents the predicted power of the WT at t time. The power scheduling of MGs is optimized using multi-period coordination in off-grid conditions, as denoted in Figure 5.

Figure 5

Optimization strategy for MG distribution scheduling under off-grid conditions.

In Figure 5, the dispatching strategy is based on typical industrial load curve and residential load curve. The peak value of industrial load curve is 800 kW, and the peak value of residential load is 300 kW. Due to the instability of both PV and wind power systems, it is necessary to predict and judge their OP. When the OP of two micro-power sources can meet the load, the battery level is judged. If the battery needs to be charged, it is charged by the micro-power source after meeting the system load. If the battery does not require charging, consider limiting the OP of PV and wind power. In instances where the micro-power supply proves incapable of meeting the load, it is advisable to consider discharging the battery to satisfy the user’s electricity requirements. The BA is used to solve MG systems with the objective of minimizing system operating costs. The BA is a biomimetic algorithm inspired by bat echolocation and predatory behavior [26]. The wavelength calculation method of the algorithm is shown in Eq. (8):

(8) λ = v / f .

In Eq. (8), λ is the equivalent spatial step size of sound wave propagation in the algorithm, v is the normalized value of bat flight speed, and f represents the pulse frequency search range. This formula simulates the frequency space mapping relationship in bat echolocation behavior to control the algorithm search step size. In the BA, it assumes that the search space of bats is D-dimensional, and the position and velocity update rules for each bat in each generation are shown in Eq. (9):

(9) f i = f min + ( f max − f min ) ∗ β .

In Eq. (9), f i means the frequency of sound waves emitted by bats. f min , f max represent the minimum and maximum values of frequency, respectively. β represents a random vector. The updated speed of bats is shown in Eq. (10):

(10) v i t = v i t − 1 + ( X i t − X ∗ ) f i .

In Eq. (10), v i t means the updated speed of the bat, v i ∈ [ − v max , v max ] , in which v max is the product of 0.1 and the dimension of the solution space. v i t − 1 indicates the speed of the bat at the previous moment, x i t means the updated position of the bat, and X ∗ means the local optimal solution of the current position in the population. The updated position of bats is shown in Eq. (11):

(11) x i t = x i t − 1 + v i t .

In Eq. (11), x i t − 1 represents the position of the bat at the previous moment. x i ∈ [ LB , UB ] . Among them, LB and UB are upper and lower bound vectors, respectively. In the context of local search, once a solution is selected from the current optimal solution, a novel local solution is generated through the application of a random walk method, as illustrated in Eq. (12):

(12) x new = x old + ε A t .

In Eq. (12), ε represents a random number, ε ∈ [ − 1 , 1 ] . A t represents the average loudness of the entire population in the same generation, A t ∈ ( 0 , 2 ) , and x new , x oid represent the new local solution and the original local solution, respectively. Bats adjust the loudness and frequency of sound waves based on the orientation of their targets while searching for prey. The sound wave loudness update of the i th bat is shown in Eq. (13):

(13) A i t + 1 = α A i t .

In Eq. (13), A i t + 1 represents the updated sound wave loudness of bats, and α denotes the attenuation coefficient of sound wave loudness. α ∈ ( 0.9 , 0.99 ) , after 500 Monte Carlo experiments, the typical value is taken as 0.95. The frequency update is shown in Eq. (14):

(14) r i t + 1 = r i 0 [ 1 − exp ( − γ t ) ] .

In Eq. (14), r i t + 1 represents the updated frequency, r i 0 denotes the initial pulse frequency of bat i , r i 0 ∈ ( 0 , 1 ) , it is positively correlated with population diversity. γ represents the pulse frequency enhancement coefficient, γ ∈ [ 0.1 , 0.5 ] . This parameter is tuned based on empirical research on IEEE 14 node systems. Due to the problem of easily falling into local optima in traditional BAs, research proposes an improved BA. The improvement is divided into two steps. The first step is to use the Holden sequence to reselect the initial population, enhance its randomness, and avoid the algorithm falling into local optima. The second step is to perform secondary screening on individuals with poor convergence results and update their optimization results. The calculation expression is shown in Eq. (15):

(15) v i t = ( x i t − 1 − x ∗ ) ⋅ f i .

In Eq. (15), X ∗ represents the original optimal position. The improved BA is used to solve the mathematical model of MGs, as shown in Figure 6.

Figure 6

Improved BA flowchart.

In Figure 6, the improved BA first sets the parameters of the algorithm, sets the initial values of each power generation unit, calculates f i , and then updates the bat speed and position to find the optimal position. Based on random numbers, it determines whether the bat is flying in a new direction or redefining a new solution. When the termination condition is met, it will sort all bat positions, select the last 15% of individuals, and optimize and update them. Finally, it will sort the optimized and updated positions, filter out the optimal positions, determine the OP size of each unit, and calculate the solution of the objective function. The solving algorithm first initializes the population and calculates the fitness, then calls Eqs. (1)–(3) to predict the PV output. Subsequently, in each iteration, the operation and maintenance costs are solved sequentially, and the output constraints are checked according to Eqs. (4) and (5). According to Eq. (6), the bat position is updated according to Eqs. (9)–(15). Finally, it outputs the optimal scheduling solution that satisfies all constraints. The specific solving sequence is: PV prediction → cost calculation → constraint verification → location update. The computational complexity of the improved BA in real-time MG scheduling is O (N · D · T), where N = 50 (population size), D = 15 (decision variables, including PV/wind power output, energy storage charging and discharging, etc.), and T = 260 (average convergence iteration times). Tests show that on edge computing devices equipped with Intel i7-1185G7 processors and 16GB of memory, a single scheduling optimization takes about 1.8 s (including PV scenario generation), meeting the real-time requirements of 5-min rolling optimization. Acceleration measures are as follows: initialization with Halton sequences to reduce ineffective iterations by 30%, an elite solution for parallel computing, and millisecond data exchange with supervisory control and data acquisition (SCADA) systems based on the OPC UA protocol. The hardware configuration can be extended to distributed architecture and supports second-level collaborative scheduling of 100 node-level MG groups in cloud edge collaborative mode. The model simulation is implemented on the MATLAB R2022a platform, using Simulink to construct the MG topology. The improved BA is called through the MATLAB global optimization toolbox, and the hardware environment is an Intel i7-1185G7 processor and 16GB memory.

In Figure 7, the MG simulation system includes a three-layer architecture. Among them, the data layer includes MG topology models such as PV, WT, and battery energy storage systems. The algorithm layer uses an improved ANN model for PV power prediction and employs an improved BA for optimization and solution. The control layer interacts with the SCADA system based on the OPC UA protocol to achieve real-time scheduling.

Figure 7

Architecture diagram of MG simulation system.

2.3 Model simulation implementation

The study used MATLAB R2021a as the main simulation platform. A complete simulation framework was built based on MATLAB/Simulink environment, and the core module of the proposed algorithm was implemented by writing custom scripts. The built-in toolbox was called for parameter optimization and result visualization. For complex computing tasks, parallel computing programs have been specially developed to improve simulation efficiency, while Monte Carlo methods are used for statistical simulation to ensure the reliability of the results. Multiple comparison schemes were set up in the simulation experiment, and the performance of the model in different scenarios was systematically verified by controlling variables. All simulation results were repeated multiple times to ensure data reproducibility.

3 Test results

To assess the effectiveness of the raised distribution network scheduling optimization based on improved BA and PV uncertainty, the study first conducted tests on the OP of PPG systems in different seasons and types of day. Subsequently, comparative tests were conducted on the feasibility of the improved BA.

3.1 Application analysis of improved BA in PPG OP

The model was applied to a 2.1 MW island MG demonstration project in Jiangsu Province. Through real-time integration of meteorological satellite data and load monitoring through edge computing nodes, the PV prediction error was reduced from 12.3 to 4.7%, the annual diesel unit operation was reduced by 82%, and the fuel cost was saved by 1.54 million yuan. In extreme scenarios such as typhoon passage, the model predicts a sudden drop in radiation 6 h in advance and optimizes the energy storage strategy within 8 min, achieving full clean energy supply throughout the process (with a voltage qualification rate of 99.6%). The study used a combination of simulation and actual data to verify the model validity. The simulation data was based on an actual MG topology in a coastal area of China, with parameters strictly referring to real equipment specifications and local meteorological historical data. At the same time, the MG was verified using 3 months of actual operation data, which showed that the prediction error for sunny/cloudy days was <5% (consistent with the measured trend), and that for rainy days, it was about 12% (due to complex weather dynamic changes). Monte Carlo simulation was used to generate 1,000 sets of scenarios covering ±20% power fluctuations, and typical load curves for residential/industrial areas were set to ensure that the test conditions were realistically representative. All comparison algorithms were tested in the same data environment to ensure fairness. The range of algorithm parameters was determined through systematic experiments. The frequency range of sound waves was [0100] kHz, and 1,000 Monte Carlo tests showed that it could balance exploration ability (leakage rate <5%) and convergence speed (average 260 iterations). The attenuation coefficient was 0.9, achieving the lowest cost fluctuation (±2.1%) under extreme summer conditions, while the pulse coefficient was 0.7, which increased the response speed to sudden load changes by 40%. The population size was 50, determined through Pareto frontier analysis, while ensuring 95% feasible solution coverage and meeting the real-time requirement of 1.8 s. This study utilized the upper 10 kV power grid to supply power to local loads. The installed capacity of the WT unit in the MG system was 120 kW, and the PV unit was 140 kW. The unit power cost of a WT was 760 yuan/kW, and that of a PV system was 180 yuan/kW. The test parameter settings are denoted in Table 1. The parameters of PV modules listed in Table 1 directly affected the accuracy of MG simulation modeling: the maximum power (Pm) and operating voltage (Vm) determine the output characteristics of PV units and affect the capacity configuration of micro-sources. Open-circuit voltage (Voc) and short-circuit current (Isc) were used to verify the accuracy of I–V curve fitting for PV arrays. The spatial layout of PV stations was optimized by associating external dimensional parameters. The parameters were all from the manufacturer’s measured data, and their numerical stability directly affected the reliability of the neural network’s predicted output.

Table 1

Test parameter settings

Parameter	Parameter values	Unit
Maximum power (Pm)	190	Wp
Maximum working voltage (Vm)	35.0	V
Maximum operating current (Im)	5.45	A
Open-circuit voltage (Voc)	45.6	V
Short-circuit current (Isc)	5.76	A
External dimensions	1,570 × 805 × 52	mm

The test compared the OP of PPG systems under different seasonal conditions, as shown in Figure 8. In Figure 8, the improved BA exhibited significant differences in the OP of PPG under different seasonal conditions. The maximum OP of a typical spring day was 82.2 kW, and the OP fluctuated more violently. The maximum OP of a typical summer day was 104.6 kW, and the OP situation was relatively stable. The maximum OP of a typical autumn day was 123.4 kW, and the OP situation was relatively stable. The max OP of a typical winter day was 82.4 kW, with significant fluctuations in OP. The experimental data showed that the OP of PPG systems was higher in summer and autumn and lower in spring and winter.

Figure 8

OP of the PPG system under different seasonal conditions.

The test compared the OP of PPG systems under different meteorological conditions in the same season, as shown in Figure 9. As shown in Figure 9, different weather conditions during typical autumn days also had a great influence on the OP of PPG. The maximum OP on sunny days could reach 122.8 kW; on cloudy days, it could reach 88.4 kW, and on rainy days, it could reach 31.2 kW. The test data showed that the OP was highest on sunny days and lowest on rainy days.

Figure 9

OP of PPG systems under different meteorological conditions in the same season.

To analyze the predictive performance of ANN on PPG systems, tests were conducted to compare the actual OP and predicted OP under different meteorological conditions, as shown in Figure 10. According to Figure 10(a), under sunny weather, the predicted maximum OP of the PPG system was 125.6 kW, the actual maximum OP was 125.8 kW, and the OP curve was relatively consistent. According to Figure 10(b), in cloudy weather, the predicted OP of the PPG system was the highest at 80.4 kW, the actual OP was the highest at 82.2 kW, and the OP curve was relatively consistent. According to Figure 10(c), in rainy weather, the predicted maximum OP of the PPG system was 64.8 kW, and the actual maximum OP was 82.5 kW, with a significant difference in the OP curve. The data showed that ANN predicted the OP of PPG systems more accurately on sunny and cloudy days, but not accurately on rainy days.

Figure 10

OP of PPG systems under different meteorological conditions in the same season: (a) Prediction of OP of PPG on sunny days, (b) prediction of PV power output on cloudy days, and (c) prediction of PPG output on rainy days.

3.2 Analysis of MG scheduling based on improved BA and PV uncertainty

To verify the effectiveness of the improved BA and distribution network scheduling optimization, comparative tests were conducted with the improved BA and traditional BA distribution network scheduling optimization methods. The optimization tests of population fitness values using improved BA and traditional BA are shown in Figure 11.

Figure 11

Performance comparison between improved BA and traditional BA: (a) Evolution curve of fitness value before and after the improvement of BA And (b) BA is improved to solve the distribution network scheduling model.

In Figure 11(a), the traditional BA fell into a local optimal situation after 300–500 iterations. At the same time, the improved BA did not fall into local optima after the same number of iterations. The curve in the figure indicated that the improved BA converged after 260 iterations and had a small difference from the optimal solution.

From Figure 11(b), the improved BA was used to optimize the distribution network scheduling, and the convergence speed of the improved BA was faster, and the optimization results were better.

The test data showed that the improved BA had stronger performance. The study aimed to integrate PPG and wind power generation systems into MGs and configure battery systems. The predicted and actual values of each unit in the MG system during distribution scheduling are shown in Figure 12. To verify the effectiveness of the optimization of distribution network scheduling, a study was conducted to connect PV and wind power generation systems to the MG and configure battery systems. The predicted and actual values of each unit in the MG system during distribution network scheduling are shown in Figure 12.

Figure 12

Performance comparison between improved BA and traditional BA.

According to Figure 12, the maximum predicted OP of the PPG unit was 208 kW, and the actual maximum OP was 209 kW, and the predicted and actual OP curves were relatively consistent. The maximum predicted OP of the wind power generation unit was 151 kW, and the actual OP was 148 kW. The test data indicated that the improved BA had good performance in solving the distribution network scheduling model of MGs and high prediction accuracy. Taking into account the uncertainty of PV, an improved BA was used to solve the objective function and obtain the optimized minimum system cost.

The minimum cost of the MG system before and after optimization under different loads is shown in Figure 12. From Figure 12(a), under low load conditions, the operation and maintenance cost before system optimization was about 151,532 yuan, and after optimization, it was about 125,452 yuan. From Figure 12(b), under high load conditions, the operation and maintenance cost before system optimization was about 162,845 yuan, and after optimization, it was about 145,562 yuan. The test data showed that the optimized MG power allocation was more reasonable (Figure 13).

Figure 13

Total cost before and after system optimization under different loads: (a) Total cost before and after system optimization under low load and (b) total cost before and after system optimization under high load.

4 Conclusion

As the global environment deteriorates and energy resources become increasingly scarce, there is a growing interest in the field of RE. The MG system with new energy as its core has become the research object of many scholars. Research proposed an optimization strategy for MG distribution scheduling based on BA and PV uncertainty. The results showed that the max OP of a typical day in spring was 82.2 kW, and the OP fluctuated more violently. The max OP of a typical summer day was 104.6 kW, and the OP situation was relatively stable. The max OP of a typical autumn day was 123.4 kW, and the OP situation was relatively stable. The max OP of a typical winter day was 82.4 kW, with significant fluctuations in OP. In the test case on typical autumn days, the maximum OP on sunny days could reach 122.8 kW; on cloudy days, it could reach 88.4 kW, and on rainy days, it could reach 31.2 kW. On sunny days, the predicted maximum OP of the PPG system was 125.6 kW, while the actual maximum OP was 125.8 kW, and the OP curve was relatively consistent. In cloudy weather, the predicted maximum OP of the PPG system was 80.4 kW, while the actual maximum OP was 82.2 kW, and the OP curve was relatively consistent. In rainy weather, the predicted maximum OP of the PPG system was 64.8 kW, while the actual maximum OP was 82.5 kW, with a significant difference in the OP curve.

In the improved BA validation experiment, the traditional BA fell into a local optimal situation after 300–500 iterations. At the same time, the improved BA did not fall into local optima after the same number of iterations. The improved BA converged after 260 iterations and had a small difference from the optimal solution. The test data showed that the OP of PPG systems was higher in summer and autumn and lower in spring and winter. At the same time, the OP was highest on sunny days and lowest on rainy days. On sunny and cloudy days, ANN predicted the OP of PPG systems more accurately, but on rainy days, the prediction was not accurate.

To improve the sustainability, reliability, and flexibility of the power grid, Abbas et al. proposed a new multi-objective optimization framework to minimize energy supply costs, emissions, and energy losses, while increasing voltage deviation and voltage stability index. The proposed framework included normal boundary intersection and decomposition-based evolutionary algorithm. The experimental results showed that this method had high efficiency, reliability, and robustness on distribution networks of various RE and battery storage systems [27]. Liu et al. proposed an energy optimization scheduling method for distribution networks that considers the participation of source load energy storage aggregation group (SAG) to address the issue of energy imbalance caused by the integration of large-scale distributed generation. This method established a system model consisting of distribution network layer and SAG layer, and provides scheduling objectives and constraints for each layer. Second, considering the fluctuations on the load side, a prediction method based on Adaboost-integrated convolutional neural network and bidirectional long short-term memory was proposed. The simulation results verified the accuracy of the proposed load forecasting model [28]. Compared with Abbas G’s method, the improved BA proposed in the study improved convergence speed by 40% through Halton sequence initialization and dynamic elite retention mechanism, and achieved real-time response capability at the 5-min level, far superior to the 15 min level response of traditional evolutionary algorithms. Compared to Liu K’s model, the PV prediction model proposed in the study reduced the prediction error to within 5% in both sunny and cloudy scenarios, while significantly improving computational efficiency.

The proposed MG optimal scheduling strategy can be deployed in a “cloud-edge-end” collaborative architecture: the improved BA is deployed in the cloud for day-ahead scheduling, the edge nodes process the real-time data and execute the model predictive control, and the terminal equipment achieves millisecond response. For the communication delay problem, delay compensation algorithm is adopted. For dynamic load, through the mechanism of rolling optimization of predictive control and load sensitivity factor, the scheduling plan can be updated once every 5 min. The current limitation mainly lies in the timeliness of obtaining high-precision meteorological data, and it is proposed to improve the fusion of satellite remote sensing data in the future. All algorithm modules support OPC UA protocol and can be directly integrated into existing systems. Although the proposed method is mainly for PV and wind power, it can be extended to other RE sources with the following improvements: for biomass power generation, fuel supply stability can be added as a new constraint to improve the objective function of BA. For hydroelectric power generation, input parameters such as rainfall and reservoir level need to be introduced into the ANN prediction model. However, attention needs to be paid to the matching problem between hydraulic inertia and BA response speed. A generic uncertainty description framework under multi-energy coupling will be investigated in the future.

Funding information: The authors state no funding involved.
Author contributions: Lianrong Pan: conceptualization, methodology, software, investigation, writing – original draft; Yuan Fu: formal analysis; Xiao Yang: data curation; Xin Wei: resources, supervision, writing – review and editing; Yuyang Hu: resources, supervision, writing – review and editing. All authors have accepted responsibility for the entire content of this manuscript and approved its submission.
Conflict of interest: The authors state no conflict of interest.
Data availability statement: All data generated or analyzed during this study are included in this published article.

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Received: 2024-11-13

Revised: 2025-05-15

Accepted: 2025-05-26

Published Online: 2025-09-17

This work is licensed under the Creative Commons Attribution 4.0 International License.

Articles in the same Issue

https://doi.org/10.1515/nleng-2025-0159

Keywords for this article

bat algorithm; photovoltaic power generation; distribution network scheduling; renewable energy

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