Collaborative planning model of digital economy and renewable energy microgrid based on double-layer optimization

Abstract

With the growing importance of renewable energy integration and digital energy management, optimizing the coordination between microgrids and the digital economy has become a critical challenge. This study proposes a collaborative planning model based on a double-layer optimization (DLO) framework that combines Non-dominated Sorting Genetic Algorithm II (NSGA-II) with elite strategy in the upper layer and Gurobi solver in the lower layer. The model is designed to jointly optimize investment cost, carbon emissions, and renewable energy utilization. Experimental evaluations using public datasets showed that the proposed model achieved an average accuracy of 0.92 and a root mean square error of 0.28 under low-load conditions. The system maintained high performance under different data volumes, with carbon emissions reduced to 15 kgCO²/h, optimization time of 4.2 seconds, and energy conversion efficiency reaching 90%. These results demonstrate that the DLO framework improves both computational efficiency and environmental sustainability, providing a practical tool for intelligent microgrid planning and carbon-conscious decision-making.

Keywords

double-layer optimization microgrid collaborative planning Gurobi NSGA-II

Introduction

With the intensification of the global energy crisis and the increasingly severe environmental pollution problems, how to efficiently utilize renewable energy (RE) and improve the sustainability of the energy system has become a vital research topic in the present energy field. As a new type of energy management system, microgrids can effectively integrate and utilize distributed generation resources, energy storage systems, and smart grid technology to achieve efficient use and management of energy.^1,2 The core advantage of microgrids lies in their ability to optimize power distribution and management, as well as their strong flexibility and autonomy. They can operate independently of the main grid, ensuring the reliability and stability of energy. Especially in the context of the increasingly widespread application of RE, microgrids have become an important means to promote the transition to green energy. However, there are many challenges in the operation of microgrids, especially in achieving optimal planning and scheduling under dynamic environmental conditions and balancing the contradiction between the volatility of RE and electricity demand.^3,4 Traditional energy management methods often rely on manual experience or a single optimization algorithm, making it difficult to achieve optimal scheduling in multi-objective and multi-constraint environments. Moreover, when faced with complex big data and ever-changing operating environments, the computational efficiency is low and it is easy to fall into local optimal solutions. Zhang et al. proposed a multi-objective optimization (MOO) design of a track ring resonant cavity sensor based on the Back Propagation Non-dominated Sorting Genetic Algorithm II (BP-NSGA-II) to improve the performance of optical resonators in anemia detection and overcome the constraints of sensitivity and quality factor. This method achieved dual optimization of sensitivity and quality factor, with advantages such as small error and short learning time, providing a novel optimization method for designing track ring resonators.⁵ Despite these advances, current models typically run in a single-layer architecture, either optimizing investment plans or short-term operations, but rarely run simultaneously in a unified structure. Moreover, few works address the integration of elite-preserving evolutionary strategies with high-efficiency solvers such as Gurobi. This study addresses these gaps by proposing a double-layer optimization (DLO) model that hierarchically decouples strategic and operational decisions, improves convergence via elite retention, and enables robust optimization under data variability. This integrated architecture offers both interpretability and scalability, making it a practical alternative to existing microgrid planning solutions. This paper provides a novel optimization planning approach for microgrid systems by introducing a DLO framework. Unlike conventional NSGA-II-based methods that typically rely on a single-layer structure to handle multi-objective trade-offs, the proposed DLO model explicitly decouples long-term strategic planning from short-term operational decision-making. This hierarchical separation enables more targeted optimization in each layer, improves computational tractability, and ensures better solution generalization under dynamic data environments. In addition, the integration of Gurobi as the bottom-level exact solver and NSGA-II, which retains elites at the upper level, ensures diversity and convergence speed, solving common problems such as premature convergence and local optimality in traditional metaheuristic methods.

Collaborative planning model for microgrid

Modeling of intelligent microgrid system

The intelligent microgrid system consists of multiple components such as a distributed generation system, energy storage system, operation and maintenance management system, and power transmission system. Distributed generation systems mainly utilize RE such as solar and wind power to achieve on-site energy production and reduce traditional energy consumption. Energy storage systems are used to balance the fluctuations between power supply and demand, especially in the uncertain situation of RE power generation, and can store excess electricity and release it when demand is high.^6–8 The operation and maintenance management system adopts intelligent technology to monitor, detect, and predict the operation status of the power grid in real-time, thereby ensuring the reliability of the system. The power transmission system is responsible for transporting electrical energy from the power generation end to the power consumption end, usually combined with smart grid technology, to achieve precise scheduling and distribution of electricity. This study selects data center microgrids as the research object and establishes a planning collaborative model. The microgrid framework of the data center is displayed in Figure 1.

Figure 1.

Microgrid structure of data center.

In Figure 1, the data center microgrid consists of an RE system, energy storage system, power distribution unit, server cluster, cooling system, and other components. Firstly, RE systems such as solar and wind energy generate electricity through different channels, which are then transmitted to energy storage systems to regulate and store energy. Energy storage systems can not only store energy, but also release electricity into the grid according to demand.^9,10 The power distribution unit system, as a power distribution unit, distributes energy to different parts of the data center to ensure the required power supply for each part. In addition, the server cluster is connected to the cooling system, which controls the temperature of the servers to prevent equipment damage caused by overheating. The control signal and request queue section is responsible for managing and coordinating the operation of the entire microgrid system. They receive instructions from the energy management system in the data center and process user task requests and operation instructions. The energy flow, data flow, and information flow of the system are closely connected to modules through different paths, thereby achieving dynamic regulation and efficient management of energy use. Figure 2 shows the power consumption structure of the data center.

Figure 2.

Power consumption structure of data center.

In Figure 2, the power consumption of the data center mainly comes from three parts, namely, servers, cooling equipment, and internal power distribution systems. The server is the core component of the data center and is responsible for executing various computing tasks and data processing work, therefore its power consumption is relatively high. With the increasing demand for data processing, the number of servers and power requirements are also constantly growing.¹¹ Cooling equipment is used to maintain the temperature of internal equipment in data centers and prevent equipment from overheating and causing malfunctions. The internal power distribution system is responsible for distributing power from external sources to various devices within the data center, ensuring the stable operation of each part. The peak power of a single server in a data center is shown in equation (1).

p_{t}^{server} = \frac{(p^{peak} - p^{idle}) λ_{t}}{μ} + p^{idle} s_{t}; \forall t

(1)

In equation (1), $p_{t}^{server}$ is the power of the server. $p^{peak}$ and $p^{idle}$ are the power of the server at maximum load and idle. $λ_{t}$ is the workload. $μ$ is the service speed. The power consumption of refrigeration equipment is shown in equation (2).

p_{t}^{cool} = \frac{p_{t}^{servers}}{0.0068 {(T_{t}^{\sup})}^{2} + 0.0008 T_{t}^{\sup} + 0.458}

(2)

In equation (2), $p_{t}^{cool}$ is the power of the server cooling equipment. $T_{t}^{\sup}$ is the supply air temperature of the cooling equipment, expressed as equation (3).

T_{i}^{m} = T_{i}^{\sup} + \frac{1}{ρ f κ} (\frac{p_{t}^{servers}}{S_{i}} - \frac{1}{q - 1}) \leq T^{red}

(3)

In equation (3), $T_{i}^{m}$ is the inlet temperature of the server. $ρ$ is the air density. $f$ is the air flow rate during equipment operation. $κ$ is the specific heat capacity of air. The data center requires a large infrastructure to allocate stable power, so the power of the internal distribution system is shown in equation (4).

p_{t}^{PDU} = p_{t}^{PDU . idle} + ν^{PDU} {(p_{t}^{server})}^{2}

(4)

In equation (4), $p_{t}^{PDU}$ and $p_{t}^{PDU . idle}$ are the power and idle power of the internal distribution system. $ν^{PDU}$ is the energy consumption coefficient.

Collaborative planning model of microgrid based on DLO

After completing the modeling of the smart microgrid system, it is necessary to optimize many parameters to achieve collaborative planning of microgrids. This study uses a DLO strategy and NSGA-II and Gurobi to handle the issue. NSGA is an evolutionary algorithm for handling MOO problems. Its core is to sort individuals in the population, determine the superiority relationship of each individual on multiple objectives, and select the optimal solution based on these relationships. In NSGA, individuals are classified based on their dominance relationships in the target space. In MOO, if a solution is not inferior to another solution in all objectives and is at least better in one objective, then that solution is considered to dominate the other solution.¹² NSGA divides the population into multiple levels through Non-Dominated Sorting (NDS), with the first level being the optimal solution set, meaning that these solutions are not dominated by other solutions. The second level refers to the solutions that are dominated by the solutions in the first level but not by other levels, etc. Through this approach, NSGA can balance multiple objectives and select a set of non-dominated solutions. However, NSGA also has some limitations, such as a lack of understanding of spatial diversity and high computational costs when the population becomes large. To overcome these issues, NSGA-II is later proposed, which optimizes NSGA, particularly in terms of computational efficiency and maintaining diversity in solution space. The important innovation of NSGA-II is the introduction of elite strategies, ensuring that the best individuals from each generation can be passed on to the next generation. The introduction of an elite strategy ensures that the optima is not lost due to crossover or mutation operations, which helps to improve the quality of the solution and accelerate convergence speed. Its structure is shown in Figure 3.

Figure 3.

Schematic diagram of elite strategy.

In Figure 3, the current generation parent population divides individuals in the parent population into different dominant sets through NDS. These dominating sets represent different Pareto frontiers. The purpose of NDS is to divide the population according to dominance relationships and prioritize the selection of non-dominated individuals. Next, individuals in each frontier are further sorted by crowding degree ranking. Individuals that are relatively sparse in the target space are selected to keep the diversity of solutions. Then, suitable individuals are selected from the parent population and subjected to crossover and mutation operations to generate novel offspring populations. Through the elite strategy, it ensures that the best individual of each generation can be directly passed on to the next generation, avoiding the loss of the optimal solution. The elimination step refers to selecting the better individuals from the new population formed by merging the parent and child generations to form a new parent generation. This step selects through NDS and crowding distance to ensure the quality and diversity of the population. The basic process of NSGA-II is exhibited in Figure 4.

Figure 4.

NSGA-II algorithm flow.

In Figure 4, step 1 is to initialize the population and generate the first-generation population of individuals. The next step is to determine whether to generate a new generation population. If not, it is needed to perform NDS and select crossover and mutation operations to generate new individuals. If a new generation population is generated, it will enter the iterative step and gradually optimize. After generating new individuals, it is necessary to merge the parent and child individuals and perform fast NDS. After sorting, suitable individuals are selected for crossover and mutation operations based on their fitness.^13–15 The next step is to determine whether to continue generating new individuals until the maximum number of generations is reached or the stopping condition is met. If the number of generated new individuals is less than the maximum number of generations, iteration will continue until the condition is met. The fitness function is shown in equation (5).

f (x) = \sum_{i = 1}^{n} w_{i} \cdot x_{i}

(5)

In equation (5), $f (x)$ is the fitness function. $x_{i}$ is the $i$ -th attribute of an individual. $w_{i}$ is the weight of this attribute. $n$ is the total number of attributes. In this study, weights are assigned using a hybrid approach: for the upper-layer evolutionary algorithm, initial weights are set based on expert knowledge, with cost minimization, carbon emission reduction, and RE utilization prioritized in a 4:3:3 ratio. The selection of these weights is to reflect the balance between economic and environmental goals, and to maintain a fixed convergence consistency across generations. By continuously iterating and updating the population, and using operations such as selection, crossover, and mutation, the quality of the solution is improved, ultimately achieving the search for the global optimal solution.^16–18 Gurobi is an efficient mathematical optimization solver widely used to solve various optimization problems, including linear programming, integer linear programming, mixed integer programming, quadratic programming, quadratic constrained programming, and more. The Gurobi optimizer uses various advanced algorithms to solve large-scale and complex optimization problems. A hybrid approach combining NSGA-II and Gurobi is adopted in this study to fully exploit the complementary strengths of evolutionary algorithms and mathematical programming. Although NSGA-II performs well in handling MOO problems and exploring a wide range of solution spaces, it often struggles to execute complex system constraints or ensure feasible solutions in discrete real-time environments. On the other hand, Gurobi is a powerful deterministic solver that can effectively solve Mixed-Integer Linear Programming (MILP) problems with strict operational constraints. However, Gurobi is not very suitable for non-convex, multi-objective formulas, or capturing global Pareto boundaries. The proposed framework utilizes global search capability and local accuracy by delegating strategic high-level decisions to the NSGA-II layer and delegating lower-level operational sub-problems to Gurobi. This hybrid design ensures that macro-level planning (e.g., sizing of renewable resources) is optimized across multiple objectives, while micro-level dispatch decisions (e.g., battery scheduling, grid interaction) remain feasible, constraint-compliant, and cost-efficient. The combination offers superior scalability, realism, and convergence performance compared to using either method in isolation. The microgrid collaborative planning model based on DLO is shown in Figure 5.

Figure 5.

Collaborative planning model for microgrid based on DLO.

The upper layer (NSGA-II) handles strategic planning variables such as wind/solar capacity and battery sizing, while the lower layer (Gurobi) solves real-time operational variables such as load dispatch and charging strategies. Arrows represent the data flow between layers, while legends distinguish between planning inputs and optimization outputs. In Figure 5, the top layer consists of planning variables, including wind turbine power generation, photovoltaic power generation, battery capacity, etc. The goal is to maximize annual investment returns and minimize carbon emissions.^19,20 Next, the NSGA-II is utilized for optimization. On the basis of this algorithm, the objective function is continuously iterated and updated to optimize the planning variables to achieve the optima. In this framework, the operational strategy is the core, which involves dynamic adjustment of the power output and proportion of wind and photovoltaic power generation, and batteries. These variables are influenced by factors such as actual operating conditions, historical data, and scenario inputs. The model needs to develop the optimal operating strategy based on these variables to achieve the goals of minimizing annual investment costs and carbon emissions. The operational strategy of the middle layer provides a detailed list of input and output variables related to power generation, such as current load capacity, battery charging and discharging efficiency, and power demand. Scene input includes multiple aspects of input data, such as historical load, lighting intensity, wind speed, etc., and is further optimized for model decision-making through data processing methods such as classification, clustering, and calculating scene probabilities.^21,22 Ultimately, through mixed variable linear programming and operational objective optimization strategies, the framework can help achieve specific operational goals of the power system, reduce the burden on the system in practical operations, and improve operational efficiency. To further clarify the internal mechanics of the DLO framework, it is essential to distinguish the roles of the upper and lower layers and describe their interaction. The upper layer is implemented through the NSGA-II algorithm, focusing on long-term strategic planning by generating candidate solutions for macro-level planning variables such as RE capacity, battery storage size, and initial scheduling strategy. These candidate solutions, represented as chromosomes in the evolutionary algorithm, are then passed to the lower layer, which is responsible for executing detailed operational optimization through the Gurobi solver. The lower layer interprets each upper-layer candidate as a set of constraints and inputs and then solves a deterministic optimization problem subject to real-time load profiles, renewable fluctuations, and operational constraints. It returns objective function values such as investment cost, carbon emissions, and system losses back to the upper layer. These values are used to evaluate the fitness of each solution in the NSGA-II population, guiding the selection, crossover, and mutation steps in the next generation. This bidirectional flow (decision variables top-down, performance feedback bottom-up) ensures that the model can capture both global planning efficiency and local operational feasibility.

To ensure tractable optimization, the proposed DLO model makes several key assumptions: Energy demand profiles are assumed to be known in advance and follow historical load distributions derived from public datasets. These profiles do not account for extreme fluctuations due to sudden failures or emergency events. RE generation is modeled based on typical diurnal patterns of solar and wind energy, using statistical distributions derived from historical meteorological data. The stochastic variability of generation is simplified by selecting representative scenarios through clustering. System constraints include battery storage capacity, charging/discharging limits, maximum load-carrying capacity, and minimum operational thresholds. These are kept fixed for each simulation period. Grid interaction is assumed to be possible at all times with no curtailment or outages, and grid electricity prices remain stable during the optimization period.

Performance of collaborative planning model for microgrid

Performance analysis of intelligent microgrid system model

This study chose to use a computer equipped with Windows 10 system and 8 GB memory, and equipped with Intel Core i5-6300 CPU to fully meet the computational needs of the experiment. In the implementation of the upper-layer NSGA-II algorithm, the following hyperparameters were applied based on a combination of standard practices in the literature and preliminary tuning experiments. The population size was set to 100, which provided a good balance between maintaining diversity and ensuring convergence stability. The crossover probability was configured at 0.9 using a Simulated Binary Crossover (SBX) operator, which was commonly adopted in real-coded genetic algorithms for its ability to explore new regions in the solution space. By conducting grid searches on [0.01, 0.1, 0.25], the mutation probability was set to 0.1, where lower values led to premature convergence and higher values led to excessive randomness. This setting was also consistent with the results of the elite strategy ablation experiment. The total number of generations was set to 100, ensuring sufficient evolutionary iterations without excessive computational burden. Tournament selection with a size of 2 was used as the parent selection strategy, and polynomial mutation was adopted to introduce localized variations. Elitism was enabled to ensure that the best individuals in each generation were preserved. In this study, two publicly available datasets were adopted to support model training and performance evaluation: the UCI Data Center Energy Consumption Dataset and the Kaggle Open Power System Data. The UCI dataset contained fine-grained measurements from server rooms and cooling systems, including features such as CPU utilization, workload intensity, ambient temperature, cooling equipment power, and real-time energy usage. The Kaggle dataset included hourly RE generation profiles, grid-side load demand, and system voltage data across several European microgrids. The pretreatment steps were as follows: first, all numeric features were normalized to the [0,1] range using min-max scaling to maintain consistency across different measurement units. Missing values in the time series, particularly those due to sensor dropout or logging anomalies, were addressed using linear interpolation and forward-filling techniques. Redundant or low-variance features were removed through Pearson correlation analysis and variance thresholding to improve model efficiency and generalizability. To simulate the variability of RE generation, historical daily profiles of solar and wind output were clustered into 10 representative scenarios using the K-means algorithm, which were then used as stochastic inputs in the upper-level planning layer of the DLO model. The selection of these datasets was based on their high granularity, public availability, and relevance to the simulation of hybrid microgrid systems. Their comprehensive coverage of both energy consumption and renewable generation made them ideal benchmarks for validating the performance and generalization of the proposed planning model.

To assess the robustness and stability of the proposed DLO framework, a sensitivity analysis was conducted on key parameters of the NSGA-II algorithm and the Gurobi solver. For the population size, values ranging from 20 to 120 were tested with increments of 20. It was observed that a smaller population (20 or 40) led to faster convergence but significantly reduced diversity in Pareto frontiers, resulting in suboptimal trade-offs between objectives. In contrast, population sizes of 80 and above consistently yielded higher accuracy (ACC > 0.90) and lower RMSE (<0.30), despite longer runtime. For mutation probability, settings from 0.01 to 0.3 were examined. When the mutation rate was below 0.05, premature convergence was frequently observed, while excessively high mutation rates (>0.25) increased randomness and degraded solution quality. An intermediate value of 0.1–0.15 was found to provide the best balance between exploration and exploitation, leading to stable convergence and superior performance. The Gurobi solver’s tolerance for optimality gap (MIPGap) varied from 0.01 to 0.1. Stricter tolerance values (0.01) resulted in slightly better optimization ACC but at the expense of significantly longer computation time. A relaxed tolerance of 0.05 achieved a good trade-off, maintaining high solution quality while ensuring efficient convergence. The parameter analysis is shown in Table 1.

Table 1.

Parameter analysis.

Parameter setting	ACC	RMSE	Optimization time (s)
PopSize = 20	0.84	0.38	2.1
PopSize = 60	0.89	0.32	3.5
PopSize = 100	0.92	0.28	4.2
MutRate = 0.01	0.85	0.36	2.8
MutRate = 0.10	0.91	0.29	4.1
MutRate = 0.25	0.87	0.34	4.3
MIPGap = 0.01	0.91	0.27	6.2
MIPGap = 0.05	0.9	0.29	4.5
MIPGap = 0.10	0.89	0.31	3.9

According to Table 1, the sensitivity analysis indicated that the DLO model was relatively robust within a practical range of parameter settings. Optimal performance was observed when the NSGA-II population size was set to 100, mutation probability to 0.1, and Gurobi optimality gap tolerance to 0.05. These settings were adopted for all subsequent experiments in this study to ensure consistency and performance reliability. This study selected ACC and root mean square error (RMSE) as evaluation metrics, as shown in Figure 6.

Figure 6.

Comparison of ACC and RMSE under different experimental conditions. (a) ACC, (b) RMSE.

In Figure 6(a), the ACC of each experiment gradually increases over time, indicating that as time goes on, the model gradually improves and the ACC is improved. The ACC of the three experiments shows a significant increasing trend, with the second and third experiments generally having higher ACC than the first experiment. The third experiment achieves a maximum ACC of over 0.9 at 9 hours, while the first experiment has a maximum ACC of only around 0.7. In Figure 6(b), as time goes on, the RMSE value gradually decreases, indicating that over time, the model’s error gradually decreases and the prediction becomes more accurate. In the three experiments, the RMSE value of the third experiment is the lowest at the last time point, about 0.22, while the RMSE value of the first experiment remains at around 0.28 at 10 hours. The experiment shows that the research models can all exhibit excellent performance. Table 2 presents the results of analyzing the comprehensive performance of each model.

Table 2.

Comprehensive performance analysis table.

Working condition	ACC	RMSE	MAE	MSE
High load	0.79	0.45	0.42	0.31
Medium load	0.88	0.35	0.31	0.25
Low load	0.92	0.28	0.25	0.21
Working condition	AUC	F1	Time/s	/
High load	0.70	0.65	121	/
Medium load	0.80	0.75	104	/
Low load	0.85	0.85	84	/

In Table 2, as the operating load decreases, the performance of the model gradually improves. Under high load conditions, the ACC of the model is 0.79, RMSE is 0.45, MAE is 0.42, and MSE is 0.31, validating that the prediction ACC is relatively low, the error is large, and the performance of the model under high load is limited. Under medium load conditions, ACC increases to 0.88, and RMSE, MAE, and MSE also significantly decrease to 0.35, 0.31, and 0.25, respectively, indicating that the model’s adaptability to medium load conditions has been enhanced and the prediction performance is good. Under low-load conditions, the ACC of the model reaches its highest value of 0.92, the RMSE drops to 0.28, the MAE is 0.25, and the MSE is 0.21, showing the best performance. This indicates that under low load conditions, the model has the best prediction ACC and the smallest error. The Area Under the Curve (AUC) and F1 values also show similar trends with changes in operating conditions. This indicates that the proposed model can adapt to most situations.

Performance analysis of collaborative planning model for microgrid based on DLO

To further validate the performance of the model, NSGA-II and Gurobi are selected as comparison models in this study, as shown in Figure 7.

Figure 7.

Comparison of ACC and RMSE of various models. (a) ACC, (b) RMSE.

In Figure 7(a), with increasing iterations, the ACC of all three algorithms tends to improve. Notably, the DLO algorithm demonstrates significant advantages in the early stages, with ACC rising sharply from 0.5 to nearly 1.0, indicating robust optimization capabilities. In contrast, the ACC improvement for the NSGA-II and Gurobi algorithms is more gradual, particularly for the Gurobi algorithm, which exhibits only a modest increase. Figure 7(b) shows that the RMSE gradually decreases with continued iterations, suggesting that the error is effectively mitigated through iterative optimization. The DLO algorithm achieves the most rapid error reduction in the initial iterations, while the other two algorithms display a comparatively slower rate of decrease. After approximately 80 iterations, the RMSE of the DLO algorithm is significantly lower than that of the others, implying that it more effectively approximates the optimal solution. These results collectively demonstrate that the proposed model exhibits superior performance across both ACC and error minimization metrics. The performance of each model is analyzed under various data volumes, as shown in Figure 8.

Figure 8.

ACC and optimization time analysis under different data volumes. (a) Accuracy analysis under different data volumes, (b) optimization time analysis under different data volumes.

In Figure 8(a), as the data volume rises, the ACC of the three algorithms generally improves, and the DLO algorithm performs the best, maintaining high ACC at all data volumes. Specifically, when the data volume is 200, the ACC of DLO is about 0.91, while the ACC of NSGA-II and Gurobi is relatively low, at 0.88 and 0.81, respectively. As the data volume grows, the ACC gradually improves, especially when the data volume reaches 1,000, the gap between the three significantly narrows. DLO performs well in stability under large data volumes and can better handle large-scale datasets. The ACC improvement of NSGA-II and Gurobi is relatively small. In Figure 8(b), with the increase of data volume, the optimization time significantly increases, especially for the Gurobi algorithm, which shows a more obvious increasing trend in optimization time with the increase of data volume. The optimization time of NSGA-II is relatively stable, maintained between 5 and 6 seconds. The optimization time of the DLO shows good control ability, with a small increase in optimization time and always maintained at a low level, about 3 to 4 seconds. The DLO algorithm has greater model performance. To verify the role of the elite strategy in the NSGA-II process, ablation experiments are performed by disabling the elite preservation mechanism and comparing the model performance with the complete DLO configuration. The results are shown in Table 3.

Table 3.

Analysis of ablation experiment results.

Experimental condition	ACC	RMSE	Time/s	Calculate resource utilization rate/%	Iterations	Carbon emissions/(kgCO₂/h)	Utilization of RE/%	System reliability/%	Energy conversion efficiency/%
DLO model	0.92	0.28	4.2	85	30	15	82	98	90
Single layer optimization	0.85	0.35	3.8	78	25	18	75	95	85
Gurobi	0.88	0.32	5.1	80	40	17	78	96	88
NSGA-II	0.84	0.37	4.5	75	35	20	72	94	83
Remove elite strategy	0.90	0.3	4.8	82	38	16	79	97	87

In Table 3, the complete DLO model achieves the best performance across all metrics. Specifically, its classification ACC reaches 0.92, the RMSE is minimized at 0.28, and the optimization time is 4.2 seconds. The calculated resource utilization rate is 85%, the number of iterations is 30, the carbon emissions are 15 kgCO₂/h, the RE utilization rate is 82%, the system reliability is 98%, and the energy conversion efficiency reaches 90%. By comparison, the single-layer optimization model exhibits a reduced ACC of 0.85 and an increased RMSE of 0.35. Although the optimization time is slightly shorter at 3.8 seconds, the remaining metrics deteriorate. When NSGA-II is excluded from the model, the ACC drops to 0.88, the RMSE rises to 0.32, and the optimization time increases to 5.1 seconds. The resource utilization decreases to 80%, the iteration count increases to 40, the carbon emissions are 17 kgCO₂/h, the RE utilization rate drops to 78%, the system reliability to increases 96%, and the energy conversion efficiency increases to 88%. Upon removal of the Gurobi solver, performance further declines: ACC falls to 0.84, RMSE climbs to 0.37, optimization time becomes 4.5 seconds, resource utilization drops to 75%, iterations increase to 35, carbon emissions rise to 20 kgCO₂/h, RE utilization reduces to 72%, system reliability decreases to 94%, and energy conversion efficiency falls to 83%. These results confirm that the complete DLO model consistently outperforms other configurations across all evaluation metrics, validating its design effectiveness and superiority. To further evaluate the effectiveness and generality of the proposed DLO framework, two additional state-of-the-art MOO algorithms are incorporated into the experimental comparisons: Multi-Objective Particle Swarm Optimization (MOPSO) and Multi-Objective Differential Evolution (MODE). These algorithms are widely used in energy scheduling, resource allocation, and load scheduling problems, representing alternative evolutionary paradigms for solving complex optimization tasks. All methods are implemented under consistent parameter settings and evaluated using identical datasets and optimization targets, including minimizing carbon emissions, maximizing RE utilization, and reducing investment cost.

From Table 4, the proposed DLO model consistently outperforms the other algorithms in terms of solution ACC and error reduction. Although MOPSO and MODE provide fairly good approximations, their convergence speed is slower and residuals are higher compared to the hybrid structure of NSGA-II and Gurobi. Moreover, the DLO demonstrates a more favorable balance between ACC and optimization time, indicating its superior efficiency in processing large-scale and multi-constraint microgrid optimization tasks. These results confirm that the DLO framework not only integrates the strengths of both population-based and exact solvers but also provides a competitive alternative to other heuristic methods in MOO scenarios.

Table 4.

Comparative performance of optimization algorithms.

Algorithm	ACC	RMSE	Optimization time (s)
DLO	0.92	0.28	4.2
NSGA-II	0.84	0.37	4.5
Gurobi	0.88	0.32	5.1
MOPSO	0.86	0.34	4.8
MODE	0.87	0.33	5

Conclusion

This study proposed a DLO-based microgrid collaborative planning model for RE and microgrid systems, and combined NSGA-II algorithm with Gurobi solver to solve the model. Through verification, the model has shown excellent performance in ACC, RMSE, optimization time, carbon emissions, and RE utilization. Under high load conditions, the ACC of the model was 0.79 and the RMSE was 0.45. Under medium load conditions, ACC increased to 0.88 and RMSE decreased to 0.35. Under low load conditions, the ACC of the model reached its highest value of 0.92, and the RMSE further decreased to 0.28. In addition, in the ablation experiment, the complete DLO model performed better than the single layer optimization model in terms of computational resource utilization, convergence speed, and system reliability. The increase of ACC from 0.84 to 0.92 indicated a significant reduction in scheduling bias, which means that the load forecasting and energy allocation plans generated by the DLO model are more in line with the actual system requirements. This enhanced operational stability and reduced the risk of overloading or under-supplying critical loads. Similarly, the reduction in RMSE indicated improved precision in energy dispatch decisions, leading to tighter control of battery charging cycles and better alignment between generation and demand, thereby extending equipment lifespan. Research has shown that DLO models can effectively improve the economy and sustainability of microgrid systems. However, the model has several limitations. First, its performance heavily depends on the ACC and resolution of the input datasets, especially regarding energy demand forecasts and RE generation profiles. Inaccurate or coarse-grained input may lead to suboptimal or non-generalizable solutions. Second, although the DLO framework is modular, its scalability for national scale or multi-microgrid configurations has not been validated and requires additional adjustments to adapt to the interdependence and regulatory constraints of the power grid. Third, although the NSGA-II and Gurobi combination improves performance, it increases the computational complexity, which may pose challenges for real-time applications or edge deployments with limited resources. In future work, the deployment of the DLO model in real-time microgrid environments will be further explored. Key challenges include reducing computational latency for real-time response, ensuring interoperability with existing control platforms, and handling uncertainties in input data streams. Addressing these practical aspects will be essential for transitioning the proposed optimization framework from research to real-world microgrid operation. Although current experiments utilize the open source datasets of UCI and Kaggle to provide valuable insights into system behavior under standard conditions, they may not fully capture real-world complexities. However, these datasets may not fully capture the random variability and dynamic disturbances found in actual microgrid deployments. The future work plan is to use real-world on-site data to validate the proposed model, such as peak values caused by weather, irregular battery degradation patterns, or load distribution of grid supply price fluctuations for utility companies. Possible data sources include industrial smart microgrid pilot zones, university energy management systems, and urban demonstration projects. Incorporating such datasets will allow for stress-testing the DLO framework under more realistic, noisy, and uncertain environments, thereby enhancing the robustness and generalization of the optimization strategy for practical deployment scenarios.

In terms of sustainability, the DLO model contributes to carbon emission reductions through multiple integrated mechanisms. Firstly, by optimizing the temporal dispatch of RE, the model prioritizes clean generation over grid imports, effectively reducing the reliance on fossil-fuel-based electricity. Secondly, the model dynamically adjusts energy storage usage to absorb surplus renewable generation and shift load demand, reducing peak-time grid dependency. This strategy minimizes the carbon intensity of each unit of energy consumed. Furthermore, the improved precision in scheduling leads to a decrease in standby losses and unnecessary battery cycling, thereby reducing indirect energy waste. However, these environmental benefits may be accompanied by certain trade-offs. For instance, maximizing renewable penetration often requires oversizing storage systems or accepting less economically optimal dispatch strategies to maintain carbon goals. In some scenarios, the model must choose between lower investment costs and lower emissions, depending on objective weight settings. This reflects a broader policy challenge in balancing sustainability and financial feasibility. By adjusting objective function weights and scenario preferences, the DLO model allows decision-makers to fine-tune this balance according to environmental regulations or carbon pricing signals.

Footnotes

ORCID iD

Jiachen Zhang

Funding

The authors received no financial support for the research, authorship, and/or publication of this article.

Declaration of conflicting interests

The authors declared no potential conflicts of interest with respect to the research, authorship, and/or publication of this article.

References

Liu

, et al. Improved PSO algorithm Application research for new energy consumption in Microgrid combination Optimisation model. Int J Power Energy Syst 2024; 44(10): 1–11, Li C, Kang Z, Yu H, et al. Research on Energy Optimization Method of Multi-microgrid System Based on the Cooperative Game Theory. Journal of Electrical Engineering & Technology, 2024, 19(5):2953-2962.

Zhou

Zhao

Zeng

, et al. A method for generating and reconstructing power grid substation topology based on Lstm Lasso model. Int J Power Energy Syst 2025; 45(203): 0560.

Jokar

Niknam

Dehghani

, et al. Efficient microgrid management with meerkat optimization for energy storage, renewables, hydrogen storage, demand response, and EV charging. Energies 2024; 17(1): 26–44.

Bao

Liu

. Short-term electricity price forecasting based on empirical mode decomposition and deep neural network. Int J Artif Intell Tool 2022; 31(6): 21–32.

Zhang

Liu

JZX

. Design and optimization of a runway resonator sensor based on BP-NSGA II for anaemic disease. Opt Rev 2024; 31(1): 54–64.

Yao

Teo

. Optimal power dispatch for a chlorine factory with fuel cells participating in incentive-based demand response. IEEE Trans Ind Inf 2024; 20(3): 4517–4526.

Lautert

Cambambi

CAC

Ortiz

MDS

, et al. Optimal power dispatch in microgrids using mixed-integer linear programming. Automatisierungstechnik 2024; 72(11): 1030–1040.

Liu

Etenovi

. An optimized multi-objective reactive power dispatch strategy based on improved genetic algorithm for wind power integrated systems. Int J Electr Power Energy Syst 2022; 136(5): 107764.1–107764.11.

Sharma

Sabitha

Prabhakaran

, et al. A hybrid swarm intelligence approach for resolving reactive power dispatch issues in power system: optimal placement and sizing of UPFC. Adv Eng Software 2022; 170(21): 414–421.

10.

Paul

Roy

Mukherjee

. Study of wind-solar based combined heat and power economic dispatch problem using quasi-oppositional-based whale optimization technique. Optim Control Appl Methods 2023; 44(2): 480–507.

11.

Mehmood

Khan

Ali

. Renewable generation intermittence and economic dispatch control of autonomous microgrid with distributed sliding mode. Int J Electr Power Energy Syst 2021; 130(10): 1069–1077.

12.

Velasquez

Quijano

Cadena

, et al. Distributed stochastic economic dispatch via model predictive control and data-driven scenario generation. Int J Electr Power Energy Syst 2021; 129(7): 1067–1081.

13.

Zhu

Liu

. Distributed dual gradient tracking for economic dispatch in power systems with noisy information. Elec Power Syst Res 2022; 211(10): 1–8.

14.

Wang

Zou

, et al. Distributed algorithm for economic dispatch with transmission losses under digraph. Int J Electr Power Energy Syst 2023; 149(41): 1090–1102.

15.

Mokayed

Quan

Alkhaled

, et al. Real-time human detection and counting system using deep learning computer vision techniques. Artif Intell Appl 2023; 1(4): 221–229.

16.

Song

Tae

Lim

, et al. Reactive power dispatch algorithm for a reduction in power losses in offshore wind farms. Energies 2023; 16(21): 1–16.

17.

Arasteh

Sanjari

Abdollahi

, et al. A new fuzzy model for investigating the effects of lightning on the risk-based self-scheduling strategy in a smart grid. Int J Electr Power Energy Syst 2021; 129(7): 106–117.

18.

Rajasingam

Rasi

Deepa

. Retraction Note: optimized deep learning neural network model for doubly fed induction generator in wind energy conversion systems. Soft Comput 2024; 28(1): 235.

19.

Liu

Chen

, et al. Short-term load forecasting based on LSTNet in power system. Int Trans Electr Energ Syst 2021; 31(12): 1–14.

20.

Ciechulski

Osowski

. High precision LSTM model for short-time load forecasting in power systems. Energies 2021; 14(11): 1–15.

21.

Adegoke

Sun

Wang

, et al. A mini review on optimal reactive power dispatch incorporating renewable energy sources and flexible alternating current transmission system. Electr Eng 2024; 106(4): 3961–3982.

22.

Zamzam

Shaban

Massoud

. Optimal reactive power dispatch in ADNs using DRL and the impact of its various settings and environmental changes. Sensors 2023; 23(16): 133–149.