Research on intra-day scheduling model of power system with shared energy storage in the provincial electricity spot market based on renewable energy groups combination forecasting

Abstract

This study proposes an intra-day scheduling model for power systems with shared energy storage in provincial electricity spot markets based on renewable energy combination forecasting to mitigate the uncertainty of wind and photovoltaic output. Firstly, an EWM-LSTM-SVM model optimized by EO is proposed to improve prediction accuracy. Then, an intra-day optimal scheduling model with SES is established to minimize system operation cost. The proposed combined model achieves an R² of 0.96, MAE of 14.45, and RMSE of 21.60, significantly outperforming single forecasting models. Case results verify that the method optimizes SES strategies, reduces renewable curtailment and system cost, with total system cost reaching 7,634,351.42 RMB. Finally, policy recommendations are provided for stable market operation and renewable accommodation.

1 Introduction

1.1 Background

With the global energy transition, wind and photovoltaic power have been increasingly integrated into China’s power system. Nevertheless, the inherent intermittency, volatility, and randomness of renewable energy generation lead to large prediction errors, especially under extreme weather, which severely threatens power system security and renewable energy accommodation (Xuejun et al., 2025). Driven by electricity market reform, provincial electricity spot markets have entered full-scale implementation, imposing stricter demands on real-time power balance and resource allocation (Yang, 2026). Inaccurate forecasts further induce large power deviations and economic penalties in intra-day clearing and real-time balancing, weakening scheduling reliability and market participants’ economic benefits. Thus, improving renewable energy forecasting accuracy has become an urgent necessity.

Energy storage is critical for enhancing system flexibility, mitigating renewable fluctuations, and providing peak shaving and frequency regulation services. Compared with the traditional “self-built and self-used” storage mode with high cost and low utilization, shared energy storage (SES), featuring centralized construction and unified operation for multi-entity leasing, significantly improves resource utilization and reduces system costs, representing a key development trend (Zhang et al., 2025). However, the efficient and economic operation of SES highly depends on high-precision intra-day renewable forecasts (Abed et al., 2026). Inaccurate predictions result in unreasonable charge–discharge strategies, limiting SES in smoothing power fluctuations (Rinesh et al., 2024). This dilemma reduces the effective utilization of renewable energy and impairs the revenue of SES in the spot market. Therefore, accurate forecasting is a prerequisite for unleashing the flexible regulation capability of SES and realizing source-grid-storage-load coordinated optimization (Yi et al., 2025).

To tackle the above issues, this study combines renewable energy combination forecasting with SES scheduling and establishes an intra-day scheduling model for provincial spot markets. The model improves forecasting accuracy at the source and provides reliable data for scheduling decisions. This work aims to achieve coordinated optimization of economic efficiency, system security, and renewable energy accommodation, offering theoretical and technical support for addressing prediction uncertainty in the stable operation of provincial electricity spot markets.

1.2 Literature review

Renewable energy output forecasting serves as a crucial prerequisite for achieving optimal scheduling of power systems. Existing forecasting methods can be broadly categorized into three types (Teixeira et al., 2024): physical methods, statistical methods, and artificial intelligence methods. Physical methods are based on numerical weather prediction and physical conversion models of wind and solar resources. Although they possess strong theoretical foundations, they require high-precision meteorological data and face challenges in dynamic adjustment of model parameters. Statistical methods, such as autoregressive integrated moving average (ARIMA) models and Kalman filtering (Yibo et al., 2023), are suitable for stationary time series but struggle to adequately capture the nonlinear and abrupt characteristics of renewable energy output. In recent years, with the rapid advancement of artificial intelligence technologies, forecasting methods represented by machine learning have been widely applied (Guomin et al., 2023) (Mao et al., 2026). Among these, Long Short-Term Memory (LSTM) networks rely their exceptional capability to capture temporal dependencies, demonstrate high accuracy in wind power and photovoltaic power forecasting (Narayanan et al., 2024). However, single models still suffer from insufficient generalization capability when dealing with complex meteorological conditions. Support Vector Machine (SVM), as a machine learning method based on structural risk minimization, exhibits favorable prediction performance under small-sample and nonlinear conditions but struggles to effectively extract long-term temporal features (Gayathry et al., 2025).

To address the limitations of single models, some scholars have begun exploring combination forecasting methods, constructing multi-model fusion mechanisms to achieve complementary advantages among different models (Haupt et al., 2020). Existing combination forecasting approaches predominantly employ equal weighting or simple error inverse weighting methods, which fail to fully account for the dynamic adaptability of different models across varying time periods or meteorological conditions, resulting in overly static weight allocation and insufficient adaptability. The Entropy Weight Method (EWM), as an objective weighting approach, offers the core advantage of dynamically determining weights based on the degree of error variation of each forecasting model across different time series samples. Compared with traditional equal weighting or error inverse weighting methods, the EWM adaptively captures the differences in forecasting performance of LSTM and SVM models under varying meteorological conditions and temporal scales, enabling dynamic optimization of weight allocation. This approach not only avoids the arbitrariness of subjective weighting but also overcomes the lagging issues associated with static weighting in complex meteorological scenarios, thereby significantly enhancing the accuracy and robustness of combination forecasting and providing a more reliable input foundation for the accurate characterization of renewable energy output in subsequent scheduling models.

Scholars both domestically and internationally have conducted extensive research on the operation mechanisms, capacity configuration, and scheduling strategies of SES. Du et al. (Du et al., 2025) proposed an economic scheduling strategy for multi-microgrid load aggregation, considering economic objectives, based on a hybrid game model for electric and thermal energy sharing. Li et al. (Qi et al., 2023) developed a hierarchical optimal scheduling method for multi-energy systems based on Stackelberg game theory, incorporating time-of-use (TOU) hydrogen pricing. Xu et al. (Mengyao et al., 2024) proposed an optimal scheduling method for the collaborative operation of SES across multiple user types, employing the adaptive penalty factor alternating direction method of multipliers (ADMM) algorithm for distributed equilibrium solutions, which enhanced convergence speed while protecting user privacy. Tian et al. (Xin et al., 2023a) introduced a centralized SES operation model based on Stackelberg game theory, enabling dynamic optimization of charging/discharging decisions and energy sharing prices for centralized shared storage. Zheng et al. (Bos et al., 2022) proposed a peer-to-peer energy trading mode embedded with residential SESS units considering benefit conflicts between energy sellers and buyers. The above studies provide valuable references for intra-day optimal scheduling of power systems based on SES. However, most existing studies incorporate SES into the system as an independent flexibility resource, often employing deterministic forecast data for modeling in scheduling models, without fully considering the impact of forecast uncertainty on scheduling results. Therefore, there is an urgent need to construct a two-stage research framework that integrates renewable energy forecasting methods with optimal scheduling.

1.3 Highlights

The remainder of this paper is structured as follows: Section 2 elaborates on the theory and methods of renewable energy combination forecasting. Section 3 constructs an intra-day scheduling model for SES based on combined forecasting. Section 4 presents the overall research framework of the paper. Section 5 validates the effectiveness of the proposed model and framework through case analysis. Finally, Section 6 proposes targeted policy recommendations to provide strong support for the development of provincial electricity spot markets.

2 Renewable energy combined forecasting theory and methods

2.1 EO-LSTM method

2.2 EO-SVM method

SVM was proposed by Vapnik and Cortes in the 1960s–1970s and is commonly used to handle classification and regression problems (Ramayanam et al., 2025). SVM is a binary classification model, and its main idea is to map the feature vectors of instances to points in space, and then draw a line that can effectively separate these points into two categories. Therefore, SVM is suitable for small-scale, nonlinear, high-dimensional binary classification problems. We can represent the data as ,where, denotes the two categories of the data, and represents the number of data samples.

As shown in Figure 1, the hyperplane divides the data into two parts: the lower-left part and the upper-right part. Additionally, one hyperplane parallel to is constructed in each of these two parts, as shown in Equations 2 and 3.

FIGURE 1

SVM obtains the optimal separating hyperplane by maximizing the geometric distance between the planes. The geometric distance between plane and plane is . The SVM algorithm can then be formulated as the following constrained optimal problem, as shown in Equations 4 and 5:

Namely, taking the partial derivatives of Equations 6 and 7 with respect to and respectively, yields:

Substituting the above results into and performing the calculation yields, as shown in Equation 8:

The dual form is obtained as follows in Equations 9–11:

2.3 Entropy weight method

Entropy was first introduced into information theory by Shannon and has since found wide application in fields such as engineering technology, socioeconomics, and beyond (Wu et al., 2025). The EWM is a component of entropy theory, which uses entropy to measure random variables in quantitative information. The principle of the EWM is as follows:

Suppose the dataset contains samples and features, forming a matrix . The matrix X is then normalized to compress the data into the interval [0,1], thereby unifying the dimensions of the data, resulting in the matrix , as shown in Equation 12:

The probability matrix P is then computed as shown in Equation 13:where: is the corresponding evaluation score, is the number of data samples to be assessed, ; denotes the index of the data evaluation criterion, .

The information entropy is then calculated as shown in Equation 14:

The information utility value is then calculated as shown in Equation 15.

3 Intra-day scheduling model construction for SES based on combination forecasting

The renewable energy combination forecasting model described in Section 2 provides deterministic point forecasts of wind and photovoltaic power outputs for each 15-min dispatch interval. These forecasts serve as the input parameters (i.e., and ) for the intra-day scheduling model formulated in this section. While the scheduling model operates on point forecasts, the inherent uncertainty of renewable energy is not ignored. Instead, it is managed through two complementary mechanisms: (i) the reserve capacity constraints (Equation 39) that maintain sufficient upward and downward spinning reserve to accommodate forecast deviations; and (ii) the real-time balancing mechanism of the provincial electricity spot market, which handles residual mismatches through deviation penalty costs included in the objective function (Equation 16). This design explicitly links forecast quality to system operational reliability, as larger prediction errors would require greater reserve capacity and incur higher penalty costs.

The photovoltaic power generation is mainly related to ambient temperature and irradiance intensity. Its cost function is as follows in Equation 24:

The cost function of wind power generation is shown in Equation 27:where, is the cost coefficient of wind power generation, and is the power generated by the wind farm.

4 Framework

FIGURE 2

5 Case study

To verify the accuracy of the proposed model, this case study implements a simulation of renewable energy power combination forecasting and SES optimal scheduling for a provincial electricity spot market using MATLAB. The system includes photovoltaic, wind, energy storage, and thermal power units. Load and environmental data (including solar radiation intensity, ambient temperature, and wind speed) are obtained from a regional power grid in Henan Province, covering the period from 1 July 2023, to 31 July 2023, with a temporal resolution of 15 min. The power generation system in the simulation includes photovoltaic power stations, wind power stations, energy storage power stations, and thermal power units. The load and environmental parameters are adopted from a certain region in Henan Province, the main parameters of conventional energy units are shown in Table 1 (Xin et al., 2023b), and the parameters of the SES are shown in Table 2 (Di et al., 2024). The system simulation runtime is 1440 min, with the minute taken as the scheduling unit and an optimization period of 15 min. All simulations are implemented in MATLAB R2020a, with the scheduling model solved by CPLEX 12.10. The computational platform is equipped with an Intel Core i7-10700 CPU @ 2.90 GHz and 32 GB RAM. In the proposed two-stage framework, the offline training of the combined forecasting model (including EO-based hyperparameter optimization) takes approximately 35 min, while the online intra-day rolling forecasting for all 96 dispatch intervals requires only about 8 s. The intra-day scheduling model, formulated as a mixed-integer linear programming problem, is solved in approximately 12 s per optimization cycle. Therefore, the total runtime for a complete intra-day scheduling cycle is about 20 s, which is well below the typical 15-min dispatch interval in provincial electricity spot markets. Notably, the training phase is completed offline 1 day ahead and does not affect real-time operational efficiency. These results demonstrate that the proposed framework is computationally practical for real-world intra-day rolling dispatch applications.

5.1 Renewable energy combination forecasting results

The proposed model is compared with the single forecasting models including EO-LSTM and EO-SVM on the same test set. Three evaluation indicators are adopted for quantitative assessment, namely, the coefficient of determination (R²), mean absolute error (MAE), and root mean square error (RMSE). The comparison results are listed in Table 3. MAE and RMSE quantify prediction accuracy in the original units (kW), with RMSE being more sensitive to large errors, while R² measures the proportion of variance explained by the model. The sample size for forecasting evaluation consists of 96 dispatch intervals (one full day at 15-min resolution), which is consistent with typical intra-day dispatch horizons. For the scheduling analysis, the same 96-period horizon is used with 1440 min of total simulation runtime.

As shown in Table 3, the proposed combined forecasting model based on the EWM achieves the best predictive performance among all models. It attains an R² of 0.96, an MAE of 14.45, and an RMSE of 21.60, significantly outperforming EO-LSTM and EO-SVM. Compared with the original LSTM and SVM, the proposed model improves R² by 113% and 35%, respectively, while reducing MAE by 81% and 70%. These results demonstrate the effectiveness and superiority of the proposed combined forecasting approach for renewable energy power prediction.

The final prediction results of the model are shown in Figure 3.

FIGURE 3

As shown in Figure 3, all models can capture the general trend of actual power output, but their performances differ considerably in different periods. The EO-LSTM model can effectively track power fluctuations, especially during rapid changes, but shows obvious deviations at local peaks and valleys, with an average prediction error of about 215 kW, mainly due to error accumulation in extreme conditions. In comparison, the EO-SVM model provides a smoother prediction curve with weaker fluctuation tracking ability, but achieves higher stability and a lower average error of about 115 kW.

The proposed combined model integrates the merits of EO-LSTM and EO-SVM, delivering more accurate and stable prediction with an average error of only 75 kW. At critical moments with sharp fluctuations, the proposed model matches the actual values much better than single models.

5.2 Intra-day optimal scheduling results for SES

The overall optimal scheduling results of thermal power units, renewable energy, and SES are shown in Figure 4, while the charging\discharging strategy and state of charge (SOC) of the SES are shown in Figure 5.

FIGURE 4

FIGURE 5

As shown in Figure 4, renewable energy generation exhibits high output during certain periods, characterized by significant intermittency and fluctuation. Thermal power units serve as the base load support, taking on the main power supply responsibility during periods of low renewable output or peak load demand, with relatively stable output, reflecting their regulating and balancing role in the system.

The economic dispatch results are shown in Table 4.

The output of each unit is shown in Figures 6 and 7.

FIGURE 6

FIGURE 7

As shown in Figure 6, the output distribution of the seven units across 96 dispatch intervals exhibits significant temporal differences and inter-unit division of labor characteristics. Overall, the unit output follows the economic dispatch principle of “large units bearing baseload, small units performing peak regulation,” with each unit being optimally committed based on load demand, fuel costs, and start-up/shut-down constraints.

In terms of output levels, Units one and 2, as large-capacity units (with maximum outputs of 230 MW and 130 MW, respectively), undertake the main power generation tasks during the dispatch period. Units three and 4 (with maximum outputs of 85 MW and 80 MW, respectively), as medium-capacity units, are used for load ramping and peak support. Units 5, 6, and 7 (with maximum outputs of 55 MW each), as small-capacity regulating units, are primarily used for fine-grained power matching and reserve support.

Figure 8 illustrates the relationship between the total output of renewable energy and thermal power units and the load.

FIGURE 8

To further investigate the sensitivity of system performance to variations in key parameters and to measure the strength of linear relationships among different variables, the Pearson correlation coefficient method is employed in this paper to perform correlation analysis on five key parameters: load, thermal power output, renewable energy output, storage operation, and total system cost. This analysis serves as a basis for sensitivity discussion, as the correlation coefficients directly reflect the degree to which changes in each parameter influence overall system cost and operational behavior. Specifically, the Pearson correlation coefficient is a statistical measure that quantifies the degree of linear correlation between two variables (Edelmann et al., 2021), with its value ranging between [-1, 1]. indicates a positive correlation between the two variables, while indicates a negative correlation. The closer the absolute value of is to 1, the stronger the linear correlation; conversely, the closer it is to 0, the weaker the linear correlation. The specific calculation formula is shown in Equation 40.where, is the Pearson correlation coefficient between variable and variable . is the sample size. is the value of variable during the -th period. is the value of variable during the -th period. means of all values. means of all values.

The corresponding correlation heatmap matrix is presented in Figure 9.

FIGURE 9

As shown in Figure 9, load and thermal power output are strongly positively correlated (0.79), showing high temporal synergy. Load is significantly positively correlated with total cost (0.76), and thermal power output has the strongest correlation with total cost (0.98), nearly linear, which confirms thermal power as the dominant factor affecting total cost. In contrast, the weak correlation between renewable energy and load (R = 0.09) reveals a temporal mismatch where midday photovoltaic peaks do not align with load demand while renewable output falls short during morning/evening peaks, precisely justifying the necessity of SES to bridge the supply-demand gap over time; the low correlation between renewable energy and total cost (R = −0.15) suggests that implicit costs associated with renewable integration—including backup capacity, ramping services, and curtailment penalties—offset direct cost reduction, implying that market mechanisms require further refinement; and the low correlation between storage and total cost (R = 0.08) indicates that SES’s primary value lies in enhancing system flexibility and renewable accommodation, with its economic benefits manifested indirectly through avoided curtailment and reduced thermal regulation frequency, suggesting that SES economic evaluation should focus on its system-wide flexibility value rather than direct cost contribution alone.

From a sensitivity perspective, the correlation coefficients presented above indicate that total system cost is most sensitive to variations in thermal power output (R = 0.98), implying that any fluctuation in thermal unit commitment or fuel cost would have a near-proportional impact on the overall economic performance. In contrast, the system cost exhibits low sensitivity to renewable energy output (R = −0.15) and storage operation (R = 0.08), suggesting that under the current configuration and market mechanisms, variations in renewable generation and storage dispatch have limited direct impact on total cost—their benefits are primarily indirect, manifested through reduced curtailment and improved flexibility. The weak correlation between renewable energy and load (R = 0.09) further implies that the system’s reliance on thermal power for peak shaving is highly insensitive to changes in renewable output patterns, reinforcing the need for policy interventions to enhance renewable-load coordination.

6 Conclusions and policy recommendations

6.1 Conclusions

This paper proposes a two-stage framework for provincial electricity spot markets that combines renewable energy combination forecasting and SES intra-day optimal scheduling. The EWM-LSTM-SVM model optimized by EO algorithm significantly improves prediction accuracy, with R² = 0.96, MAE = 14.45 and RMSE = 21.60, outperforming single models. The integrated SES scheduling model realizes coordinated optimization of system economy, security and renewable accommodation. Case results verify that SES effectively smooths renewable fluctuations, reduces thermal power costs and curtailment penalties. Forecasting precision directly determines the efficiency of energy storage regulation. Thermal power, renewable energy and SES operate synergistically to enhance system flexibility. The proposed method provides technical support for high-proportion renewable accommodation and stable operation of provincial spot markets.

6.2 Policy recommendations

Establish a unified multi-model fusion forecasting platform, improve data sharing and accuracy incentive mechanisms to support intra-day market clearing.

Incorporate SES into unified grid dispatching, strengthen source-grid-storage-load coordination and ensure operational safety under economic objectives.

Support R&D of advanced forecasting and energy storage technologies, carry out pilot demonstrations and strengthen talent training for market operation.

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