Optimal planning of shared energy storage for wind-solar-thermal distributed energy system clusters based on improved renewable energy forecasting

Abstract

Aiming at wind-solar intermittency and low coupling between renewable energy forecasting and shared energy storage (SES) planning in wind-solar-thermal distributed energy clusters, this paper proposes a two-stage framework combining high-precision power forecasting and multi-objective SES planning. A VMD-EO-SVM model improves prediction accuracy. A multi-objective planning model minimizes operating costs and maximizes renewable energy accommodation. Case results verify its effectiveness for low-carbon cluster operation.

1 Introduction

1.1 Background

With the advancement of carbon peaking and neutrality targets, wind and solar power have experienced rapid development, accelerating the low-carbon, distributed and flexible transformation of power grids (Li Mengjia et al., 2024). Wind-solar-thermal distributed energy system clusters are widely concerned for boosting local renewable energy consumption and easing grid regulation pressure (Wang et al., 2025). Nevertheless, the inherent volatility and intermittency of wind-solar power degrade system operational efficiency and stability under large-scale integration (Xuejun et al., 2025). Shared energy storage (SES) serves as an effective countermeasure by realizing shared energy regulation, smoothing power fluctuations and curtailment (Li Jinmeng et al., 2024).

Compared with storage systems configured independently for individual distributed energy systems, SES allows multiple generation and consumption entities to use a common storage facility. Differences in renewable generation and load profiles among these entities create partially complementary charging and discharging requirements. Aggregating these requirements through SES can reduce redundant storage capacity and improve the utilization of storage resources. In a wind-solar-thermal distributed energy system cluster, SES can also absorb surplus renewable power from different subsystems and release the stored energy when additional system flexibility is required. The value of SES therefore lies not only in energy shifting, but also in the coordinated use of storage resources among multiple entities.

From the investment perspective, the shared configuration also allows the capital cost of storage construction to be distributed among participating entities rather than being borne independently by each user. Participants can access the required storage service without constructing a complete storage system for their own use, while the corresponding operating or service costs can be allocated according to the adopted sharing arrangement. This mechanism reduces the financial burden associated with independent storage investment and increases the utilization of installed storage capacity by serving multiple users with heterogeneous demand profiles.

Precise wind-solar power forecasting provides core data for SES planning and operation (Liu and Song, 2025; Jia et al., 2025). In a forecasting-driven planning framework, the predicted renewable power profiles determine the estimated timing and magnitude of power surplus and shortage, which directly affect the required charging and discharging power and the duration of energy shifting. Forecasting errors may therefore propagate to the planning stage and lead to deviations in the estimated power and capacity requirements of SES. Improving forecasting accuracy before storage planning can reduce this source of uncertainty and provide more reliable input for storage configuration. Accordingly, this study integrates renewable power forecasting with SES planning to improve power balance, renewable energy utilization, and the economic operation of wind-solar-thermal distributed energy system clusters.

1.2 Literature review

Renewable power generation suffers strong intermittency, and forecasting methods are categorized into physical, statistical and intelligent types. Physical models rely on meteorological data and NWP (Zhao et al., 2026); statistical approaches adopt ARIMA (Huang, 2026; Yuan et al., 2026; Zhang Yagang et al., 2024), STL (Liu and Zhang, 2024; Zhu et al., 2024; Tong et al., 2026) and regression analysis (Yang et al., 2025); intelligent methods include SVM (Patel et al., 2025; Oruç et al., 2026; Chen et al., 2024), Extreme Learning Machines (ELMs) (Herwan Sulaiman et al., 2025; Bala Duranay, 2023; Zhang Yuhao et al., 2024), LSTM (Dokur et al., 2025), Convolutional Neural Networks (CNNs) (Wen and Xie, 2026) and hybrid models integrating VMD (Peng et al., 2024) and EO (Lin et al., 2025) for better feature extraction.

SES planning is vital for renewable energy consumption in wind-solar-thermal clusters, with existing studies adopting bi-level optimization (Hou et al., 2025), robust optimization (Li et al., 2026), bi-level optimization (Wang et al., 2026), two-stage robust optimization (Kang et al., 2025), cooperative game (Li Cuiping et al., 2024), digital intelligence-driven synergy (Zhou et al., 2025) and other frameworks while considering practical constraints (He and Zhang, 2025). However, renewable power forecasting and storage planning are still commonly treated as separate problems. Forecasting studies mainly focus on reducing prediction errors, whereas SES planning studies generally use predetermined renewable power profiles as model inputs. As a result, the influence of forecasting accuracy on storage configuration has received limited attention. In addition, existing hybrid forecasting methods often focus on either signal decomposition or parameter optimization, while the combined effects of multi-scale decomposition and parameter optimization have not been sufficiently examined. To address these limitations, this study develops a two-stage forecasting and planning framework. VMD is used to extract the multi-scale characteristics of renewable power series, EO is applied to optimize the key parameters of SVM, and the resulting power forecasts are introduced directly into the multi-objective SES planning model. This framework establishes a direct connection between renewable power forecasting and storage configuration and provides a more reliable basis for SES planning under variable renewable generation.

1.3 Highlights

The rest of this paper is organized as follows. Section 2 introduces VMD, EO and SVM fundamentals. Section 3 develops the multi-objective SES planning model with objectives and constraints. Section 4 presents the two-stage forecasting-planning coupled framework. Section 5 conducts case validation using measured data. Section 6 draws conclusions.

2 Renewable energy prediction theory and methods

2.1 Multiscale decomposition of volatility–VMD method

Wind power generation is highly random and non-stationary. As an adaptive method for nonlinear non-stationary time series, VMD decomposes historical wind power data into frequency-specific stationary subsequences to reduce complexity, nonlinearity and non-stationarity, with its bandwidth-constrained variational problem mathematically formulated as:

In the formula, is the Dirac function, that is, the unit impulse function, is the k-th modal component, representing each sub-signal obtained by decomposition; is the center frequency of the k-th power modal component; is the imaginary unit; and is the original signal to be decomposed. To eliminate the limitations of the above factors, a quadratic penalty operator and a Lagrange multiplier are usually added to transform the minimization problem involved in Equation 2 into an unconstrained optimization problem of Equation 3.

In this equation, serves as the quadratic penalty operator. Lambda represents the Lagrange multiplier, and indicates the convolution operator.

Subsequently, calculate the value of in the frequency domain.

In the formula, i and n can take arbitrary values, and is used to mark the transformation of the signal from the time domain to the frequency domain. , , and are the Fourier transformed , and .

Finally, Equations 4, 5 are used to update the relationship between and , that is

In the formula, is the step size parameter for updating the Lagrange multiplier, which will have an impact on the convergence speed and stability of the iteration.

The iteration process is based on the preset noise discrimination accuracy . When this accuracy is reached, the iteration is stopped and the operation results are output.

In the equation, represents the convergence progress.

Ultimately, the original power sequence will be decomposed into k narrow-band intrinsic mode functions (IMFs). Each IMF has a different center frequency in the frequency domain, representing different characteristics of the original signal.

2.2 Equilibrium state measurement of volume–EO method

2.3 Power output prediction–SVM method

In SVM modeling, each input sample in a low-dimensional space is first mapped into a higher-dimensional feature space through a nonlinear mapping function . Subsequently, a linear regression function is constructed in this high-dimensional space, which can be expressed as:

To transform the regression problem into a tractable optimization task, the structural risk minimization principle is adopted. Specifically, a tolerance parameter is introduced to define an insensitive loss zone, within which errors are not penalized. To account for samples outside this zone, two slack variables and are added to relax the constraints. The resulting optimization problem is formulated as

Subject to the following constraints:

To solve this constrained optimization problem, the Lagrange multiplier method is employed. By constructing the Lagrangian function and applying the duality theorem, the original problem is transformed into a dual optimization problem involving the maximization of the following objective function:where , are the Lagrange multipliers associated with each constraint, and denotes the kernel function used to compute the inner product in the high-dimensional space without explicitly performing the nonlinear mapping. Based on the solution of the dual problem, the final regression function can be ex pressed as

Among various kernel functions, the radial basis function (RBF) is often considered ideal for its wide convergence region and high resolution. Therefore, the RBF is selected as the kernel function in this study, defined aswhere controls the width of the RBF kernel.

Based on the above methods, the proposed forecasting procedure connects VMD, EO, and SVM in sequence. The original renewable power series is first decomposed by VMD into several frequency-specific components. EO then searches for suitable values of C and γ for the SVM prediction model. The optimized SVM is applied to each decomposed component, and the resulting component-level forecasts are reconstructed to obtain the final wind or solar power forecast. This procedure allows signal decomposition and parameter optimization to be incorporated into the same forecasting process.

3 Multi-objective planning model of SES in wind-solar-thermal distributed energy system clusters

The SES planning stage uses the wind and solar power profiles obtained from the forecasting stage as time-varying inputs. These profiles describe the expected timing and magnitude of renewable power surplus and shortage and are therefore directly related to power balance, renewable curtailment, and storage operation. Higher forecasting accuracy can reduce the difference between the renewable power assumed during planning and the expected operating conditions. This provides a more reliable basis for determining the rated power, energy capacity, and charging and discharging requirements of SES.

The planning model considers two objectives: minimizing the total system cost and maximizing renewable energy utilization. The main planning variables are the rated power and energy capacity of SES, while the operational variables include charging and discharging power, thermal-unit output, and renewable energy curtailment over the scheduling horizon. For each storage configuration, system operation must satisfy the power balance constraint, renewable curtailment limits, SOC and charging and discharging constraints, and the operating constraints of thermal units. Increasing the size of SES can provide greater flexibility for absorbing renewable power and supporting the system during periods of power shortage. However, a larger storage system also increases investment and operation costs. The planning model therefore determines a storage configuration that balances economic performance and renewable energy utilization under the specified system conditions.

3.1 Objective function

3.2 Constraint

• Power Balance Constraint

  Ensures the supply-demand balance at each time step:

• Curtailment Constraints

  Wind and solar curtailment is less than the predicted power:

• Energy Storage Constraints

  These constraints describe the operational characteristics of the energy storage system.

• Operational Constraints of Thermal Power Units

4 Framework

The overall research framework consists of two consecutive stages: renewable power forecasting and multi-objective SES planning for wind-solar-thermal distributed energy system clusters. The complete research procedure is illustrated in Figure 1.

FIGURE 1

5 Case study

5.1 Data description

This study adopts 15-min-interval measured wind-solar power data from Belgium (2020–2021) with high temporal resolution to capture short-term generation fluctuations. Missing values are imputed and outliers eliminated in preprocessing to guarantee data quality. Given the diurnal characteristic of photovoltaic power (negligible output outside 8:45–16:30), only data within this window are used for modeling to avoid redundancy and improve efficiency. Processed wind-solar time series are shown in Figures 2 and 3.

FIGURE 2

FIGURE 3

The main operational parameters of the thermal power units in the distributed energy system are listed in Table 1, while the energy storage system is treated as a configuration object, and its main parameters are given in Table 2.

The unit power and capacity costs in Table 2 represent the initial capital investment parameters of SES. These parameters are converted to equivalent daily investment costs according to the service life of the storage system when calculating the objective function.

The load data used in this study corresponds to a typical daily load profile measured in a region of Belgium, with a time resolution of 15 min, covering the electricity demand variations over a 24-h period, as shown in Figure 4. This dataset is used to represent the load characteristics under typical operating conditions.

FIGURE 4

To improve the reproducibility of the forecasting experiments, the main parameter settings of VMD, EO, LSTM, and CNN are provided in Table 3. For VMD, the original renewable power series is decomposed into five IMFs using a quadratic penalty factor of 500 and a convergence tolerance of 1 × 10⁻⁷. For EO, the population sizes are set to 20 for EO-SVM and 15 for VMD-EO-SVM, while the corresponding maximum numbers of iterations are 30 and 20. The search ranges of C and γ are set to [1, 800] and [0.005, 50], respectively, for both models. The benchmark LSTM and CNN models use the same input tensor shape of (48, 1) and are trained using the Adam optimizer, an initial learning rate of 0.001, and the MSE loss function. Detailed parameter settings are summarized in Table 3.

5.2 Prediction results analysis

5.2.1 VMD decomposition results

To characterize the multi-scale features of wind and photovoltaic power series, the VMD method is employed to decompose the original time series into a set of IMFs with limited bandwidth. The decomposition results are presented in Figures 5 and 6, respectively.

FIGURE 5

FIGURE 6

As illustrated in Figures 5 and 6, wind and solar power series are decomposed into frequency-stratified modal components: high-frequency parts capture short-term fluctuations, whereas medium-/low-frequency counterparts reflect the overall smooth temporal trends with favorable multi-timescale separability.

5.2.2 Prediction performance analysis

To quantify wind-solar power forecasting performance, RMSE, MAE and R² are used as metrics (Table 4). The proposed VMD-EO-SVM outperforms all counterparts: for solar power, it attains RMSE = 42.60, MAE = 34.40 and R² = 0.9776, greatly lowering prediction errors and enhancing fitting consistency relative to basic SVM, EO-SVM and VMD-SVM; for wind power, it achieves RMSE = 71.83, MAE = 54.55 and R² = 0.9217, outperforming SVM and CNN with reduced errors and improved goodness-of-fit. Overall, deep learning models (LSTM, CNN) perform poorly in error indices, while conventional SVM suffers from limited overall accuracy despite partial stability.

The results of SVM, VMD-SVM, EO-SVM, and VMD-EO-SVM also provide a component-level comparison of the proposed forecasting framework. For solar power, the RMSE decreases from 195.21 for SVM to 56.08 for EO-SVM, indicating that parameter optimization substantially improves the prediction performance of SVM. When VMD is further combined with EO-SVM, the RMSE decreases to 42.60, which represents a reduction of 24.04% relative to EO-SVM. A similar pattern is observed for wind power. The RMSE decreases from 91.30 for SVM to 84.84 for EO-SVM and further to 71.83 for VMD-EO-SVM, corresponding to an additional reduction of 15.33% relative to EO-SVM.

The results also show that the contribution of VMD depends on its integration with the forecasting model. For wind power, VMD-SVM does not outperform the original SVM in terms of RMSE, which indicates that signal decomposition alone does not necessarily improve prediction accuracy. In contrast, VMD-EO-SVM achieves the lowest RMSE and MAE and the highest R² for both wind and solar power. This result suggests that VMD and EO perform complementary functions. VMD reduces the complexity of the original power series by separating variations at different frequency scales, while EO improves the parameter configuration of SVM. Their combined use provides more stable forecasting performance than either component used separately.

To provide a more direct comparison with the benchmark models, Table 4 also reports the percentage reduction in RMSE achieved by VMD-EO-SVM relative to each comparison model. For solar power, the RMSE is reduced by 38.79%, 55.09%, 78.18%, 68.34%, and 24.04% relative to LSTM, CNN, SVM, VMD-SVM, and EO-SVM, respectively. For wind power, the corresponding reductions are 37.95%, 50.68%, 21.32%, 24.61%, and 15.33%. These results provide a more direct quantitative comparison of the forecasting improvement achieved by VMD-EO-SVM.

As shown in Figure 7, wind power forecasting curves demonstrate that the proposed VMD-EO-SVM closely tracks actual power values across the whole period, especially under strong fluctuations, whereas other models show obvious deviations.

FIGURE 7

LSTM and CNN underestimate peaks and smooth sharp variations, losing local details; conventional SVM and VMD-SVM track trends poorly at abrupt transitions. By contrast, VMD-EO-SVM maintains superior amplitude-trend consistency, especially at peaks and valleys. Consistent with solar forecasting results in Figure 8, its prediction closely matches actual output throughout daylight hours and better approximates peak generation, while other models suffer from lag or overestimation.

FIGURE 8

Moreover, parity plots further verify model fitting performance (Figure 9). Wind power predictions of VMD-EO-SVM cluster closely around the diagonal with R² = 0.9217, while solar power points are more tightly distributed along the diagonal and achieve R² = 0.9776, demonstrating superior fitting accuracy.

FIGURE 9

5.3 Configuration results analysis

5.3.1 SES configuration and operational characteristics

Table 5 summarizes the main results of the multi-objective SES planning model. Under the system conditions considered in this study, the optimized rated power and energy capacity of SES are 947 MW and 5,615 MWh, respectively. The corresponding energy-to-power ratio is approximately 5.93 h. This duration indicates that SES is required not only to smooth short-term power fluctuations but also to shift energy across several hours. The rated power determines the ability of the storage system to respond to relatively large short-term differences between renewable generation and system demand, while the energy capacity determines the amount of renewable energy that can be transferred from surplus periods to periods of insufficient generation or high load.

The optimized configuration also reflects the trade-off between renewable energy utilization and storage cost. Increasing the rated power and energy capacity can improve the ability of the system to absorb surplus renewable generation and reduce the regulation requirements of thermal units. However, an excessively large storage system would increase investment and operation costs. With the optimized configuration of 947 MW and 5,615 MWh, the renewable energy accommodation rate reaches 90.3%, while the total system cost is 66,956,684 CNY. The operating results in Figure 10 further support the rationality of this configuration. SES mainly charges during periods of renewable power surplus and discharges when renewable generation is insufficient or load demand is relatively high, while SOC remains within the specified operating range. These results indicate that the storage configuration is determined by both the magnitude and temporal distribution of the imbalance between renewable generation and system demand.

FIGURE 10

Figure 10 shows SES operational features: it follows low-charge and high-discharge operation with charge-discharge mutual exclusion, and its SOC remains within the safe 0.1–0.9 range without overcharge or overdischarge. SES charges to absorb excess wind-PV power during high-output periods to reduce curtailment, and discharges heavily at peak loads to supplement power supply and ease thermal power peaking pressure.

5.3.2 System power balance analysis

Figure 11 shows the 96-period power distribution of the wind-solar-thermal system with SES, confirming real-time power balance at each time step.

FIGURE 11

Wind and solar power exhibit obvious temporal complementarity, providing stable renewable supply with daytime solar generation and nighttime wind output. Thermal power acts as the base source to dynamically regulate power for system reliability, while SES optimizes power balance by storing excess renewable power in low-load periods and releasing it at peak loads to ease thermal peaking pressure. Such multi-source coordination mitigates renewable intermittency and realizes efficient power balance throughout the scheduling cycle.

5.3.3 Thermal power unit output characteristics

Figures 12 and 13 depict the operation of seven thermal power units. Units 1–2 operate stably as base-load units, whereas Units 3–7 act as peaking units with dynamic output regulation. Peaking units are shut down during high renewable generation to cut coal use, leading to low startup-shutdown costs (41,720 CNY). All units satisfy ramp-rate and minimum on/off-time constraints for stable power adjustment.

FIGURE 12

FIGURE 13

6 Conclusion

This study develops a VMD-EO-SVM-based high-precision wind-solar power forecasting approach and a multi-objective SES planning model for wind-solar-thermal distributed energy clusters. Combining variational mode decomposition with equilibrium optimizer tuning, VMD-EO-SVM well captures non-stationary and nonlinear characteristics of wind-solar series, outperforming SVM, LSTM, CNN and other benchmarks with solar metrics (RMSE = 42.60, MAE = 34.40, R² = 0.9776) and wind metrics (RMSE = 71.83, MAE = 54.55, R² = 0.9217).

The SES planning model minimizes operational costs and maximizes renewable accommodation, jointly optimizing SES sizing and operation strategies. Case studies yield an SES rated power of 947 MW and capacity of 5,615 MWh, with total system cost of 66,956,684 CNY and a 90.3% renewable accommodation rate, supporting real-time power balance and hierarchical thermal unit dispatch.

From the perspective of resource sharing, SES provides a common source of operational flexibility for the distributed energy system cluster. Different wind, solar, load, and thermal regulation requirements can be coordinated through the same storage facility. This shared use can improve the utilization of storage resources and reduce redundant storage capacity that may result from independent configuration for individual subsystems. The planning results therefore reflect not only the energy-shifting function of storage but also the value of coordinated storage use among multiple entities. The shared configuration also provides a practical basis for distributing storage investment among multiple participants, thereby reducing the capital burden on individual users while improving the utilization of the common storage resource.

The results also provide practical implications for the planning of renewable-energy-based distributed energy system clusters. Renewable power forecasting and storage configuration should be considered within a coordinated planning process because forecasting errors can affect the estimated storage requirements. Improving the quality of renewable power forecasts can therefore support more reliable SES configuration. For the practical application of SES, clear mechanisms are also required for capacity allocation, charging and discharging priority, cost sharing, and benefit distribution among participating entities. These arrangements can improve the utilization of shared storage resources and reduce unnecessary duplication of independently configured storage. Future demonstration projects may further evaluate forecasting accuracy, renewable energy accommodation, storage utilization, and system cost within a common assessment framework to support integrated planning and operation.

A limitation of the present study is that the forecasting model mainly uses historical power data and does not explicitly include meteorological variables. Historical wind and photovoltaic power series reflect the effects of the weather conditions that occurred during the observation period and therefore contain part of the corresponding meteorological information. However, this indirect representation may be insufficient when future weather conditions differ substantially from historical patterns, particularly during rapidly changing or extreme weather events. Future research will incorporate explicit meteorological variables and numerical weather prediction information, including wind speed, solar irradiance, and temperature, into the forecasting framework. The effects of extreme weather conditions on renewable power forecasting and the resulting SES planning decisions will also be examined.

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