Day-Ahead Scheduling of IES Containing Solar Thermal Power Generation Based on CNN-MI-BILSTM Considering Source-Load Uncertainty

Abstract

The fluctuating uncertainty of load demand as an influencing factor for day-ahead scheduling of an integrated energy system with photovoltaic (PV) power generation may cause an imbalance between supply and demand, and to solve this problem, this paper proposes a day-ahead optimal scheduling model considering uncertain loads and electric heating appliance (EH)–PV energy storage. The model fuses the multi-interval uncertainty set with the CNN-MI-BILSTM neural network prediction technique, which significantly improves the accuracy and reliability of load prediction and overcomes the limitations of traditional methods in dealing with load volatility. By integrating the EH–photothermal storage module, the model achieves efficient coupled power generation and thermal storage operation, aiming to optimize economic targets while enhancing the grid’s peak-shaving and valley-filling capabilities and utilization of renewable energy. The validity of the proposed model is verified by algorithm prediction simulation and day-ahead scheduling experiments under different configurations.

1. Introduction

Concentrated Solar Power (CSP), as an emerging renewable energy technology, utilizes solar energy resources and converts them into electricity through heat collection and storage devices, which has the advantages of environmental protection, high efficiency, and sustainability. However, the output of photovoltaic power generation is affected by a variety of factors, such as weather and the environment. It is characterized by a certain degree of uncertainty, so optimizing day-ahead scheduling has become the key to ensuring the economical and safe operation of new energy sources, such as photovoltaic power, in the grid [1].

At present, day-ahead scheduling considering new energy has become a research hotspot. In terms of scheduling objects, the research mainly focuses on the coordinated scheduling of traditional energy and new energy, or it focuses on new energy scheduling. Reference [2] proposed a two-phase robust optimal scheduling model for a pumped storage–wind–photovoltaic–thermal co-generation system, which realizes the optimal allocation of a power generation plan through the optimization of multiple energy sources and suppresses power fluctuations in the power grid. Reference [3] developed a model for a wind–photovoltaic–hydroelectric–thermal pumped storage system and established a short-term optimal scheduling model with multiple optimization objectives to improve the economic stability of the system. Reference [4] explored the integration of Concentrated Solar Power (CSP) with other renewable sources to enhance system stability and economic performance.

In terms of scheduling objectives, studies usually cover economic, technical, and low-carbon dimensions, among others. Reference [5] integrated security and economic objectives and proposed a two-stage scheduling framework which realizes the double balance of economic benefits and security synergy. Reference [6] proposed a low-carbon dispatch model for the stochastic nature of renewable energy and a low-carbon modulation mechanism, which enhanced the economic efficiency of the power system under low-carbon-emission conditions. Reference [7] proposed that enhanced sustainability assessment and system flexibility are essential for achieving the efficient and economic operation of integrated energy systems and accurate matching of supply and demand.

In terms of uncertainty, scheduling models can be categorized into two main types: deterministic and uncertain. Reference [8] effectively reflected on the uncertainty of renewable energy by constructing a robust uncertainty set. Reference [9] proposed an optimal scheduling strategy based on a deep reinforcement learning algorithm, which solves the challenge of high-dimensional decision spaces. Reference [10] proposed to construct a two-stage robust optimization model of producers and consumers for the multiple uncertainties of wind power generation and load demand in order to promote the effective use and management of sustainable energy.

Load fluctuation is a key factor to be considered in the day-ahead scheduling of photovoltaic-containing power systems. Reference [11] utilized the WWO algorithm to improve the efficiency of dynamic optimal scheduling in microgrids. Reference [12] proposed a probabilistic power future prediction tool based on time-series clustering, which is used in short-term load forecasting to make forecasts more accurate and intelligent. However, existing studies often ignore the uncertainty of load fluctuations, which may lead to scheduling plan failures. Therefore, the uncertainty of load fluctuation needs to be fully considered in the scheduling of complex integrated energy systems containing photovoltaic power generation [13].

Forecasting technology is an effective means to solve the uncertainty of load fluctuation. Reference [14] investigated the proposed adaptive load forecasting model by customizing AI algorithms and cloud-side collaboration to analyze the accuracy and resource usage, adapting different hardware environments to meet the specific needs of microgrids. Reference [15] proposed a short-term load forecasting model based on EEMD-LN-GRU according to the uncertainty and nonlinear characteristics of electric load. Reference [16] improved the accuracy of capturing short-term changes in electric load through the improved Convolutional Neural Network–Bidirectional Long- and Short-Term Memory (CNN-BILSTM) model. In addition, reference [17] fused mutual information (MI) and BILSTM to dynamically evaluate the importance of features to fit the load fluctuation characteristics. Reference [18] proposed a robust optimization-based scheduling framework to deal with the dual uncertainties of loads and renewable energy sources through interval uncertainty sets. Given this, this paper synthesizes multiple forecasting algorithms in the CNN-MI-BILSTM model, adopts multi-interval uncertainty sets to portray load variability, and improves forecasting accuracy with the help of historical data.

To address the problem that existing studies neglect the impact of load uncertainty on the scheduling of solar thermal storage systems, reference [19] developed a day-ahead co-scheduling method for concentrating solar photovoltaic–wind power that takes into account the uncertainty of source loads, characterizes the uncertainty of intraday source loads with a trapezoidal fuzzy number equivalence model, and carries out the day-ahead optimal dispatch based on the set of day-ahead wind-power output prediction combination scenarios. Reference [20] took into consideration the uncertainty of source loads for electricity–heat conversion and constructed a stochastic optimal dispatch model for a wind–solar complementary fire system with the objective of minimizing the comprehensive operating cost of the combined system. Such models not only optimize the economic objective but also incorporate robustness and stochastic approaches. Reference [21] analyzed the effectiveness of the combined peaking of TPU and CSP power plants with EH and analyzed the principle of a low-carbon power supply for the proposed strategy during peak and off-peak periods. Therefore, it has become necessary to integrate uncertainty-handling methods in the day-ahead scheduling of integrated energy systems containing EH-CSP modules.

To address the challenges posed by uncertain loads in the context of a new energy grid-connected environment, this paper proposes a day-ahead optimal scheduling model that incorporates uncertain loads and EH-CSP (Energy Hub–Concentrated Solar Power) storage. The objective is to achieve supply–demand balance with optimal economic efficiency. This study specifically tackles the limitations of traditional scheduling models in dealing with the volatility of renewable energy sources and the complex coupling between power and heat systems. By accurately simulating load uncertainties, the model closely aligns with real-world operating conditions and provides an in-depth analysis of their impact on the day-ahead scheduling of renewable energy hybrid plants, as well as the operational mechanisms of the EH-CSP system. This improves both the accuracy of scheduling decisions and the overall stability of the system. The main contributions of this paper are as follows:

(1)

An optimal day-ahead scheduling model is developed, considering uncertain loads and EH-CSP storage, with the goal of achieving economic efficiency, grid stability, and operational reliability. Through refined modeling and optimization techniques, the model enhances the overall economic performance of the system and the robustness of grid operations.

(2)

A multi-interval uncertainty set and a CNN-MI-BILSTM model are introduced to improve the accuracy of load forecasting. By overcoming the limitations of traditional models in handling data correlations, the approach significantly enhances prediction reliability and enables rapid, precise forecasting of fluctuating loads.

(3)

A modular modeling approach for EH–photovoltaic power plants is proposed, along with a coupled operation model of power generation and thermal storage modules. This captures the dynamic processes of energy conversion and storage, accounts for environmental impacts on system efficiency, and improves the model’s generality and accuracy in reflecting the operational characteristics of various field stations in a renewable energy co-generation system.

The rest of the article is structured as follows: the second part elaborates the research problem, the third part describes the establishment of the variable-load model for the improved day-ahead scheduling model in the description of the prediction method that constantly improves the data relevance as well as the prediction accuracy, the fourth part proposes a model for the EH–photovoltaic and thermal co-generation system corresponding to the power generation–storage operation relationship, the fifth part presents the solution method of the optimization model, the sixth part provides an analysis through examples, and the seventh part concludes the entire paper with an overview.

2. Problem Formulation

2.1. Day-Ahead Scheduling Model for Integrated Energy Systems

The integrated energy system in this section covers wind, photovoltaic, and solar thermal power generation, and its day-ahead scheduling model aims to minimize the operating cost of the integrated daily plan, which is expressed as follows (Please refer to Appendix A for detailed module-by-module costs)

$$\min :C=C_1+C_2+C_3+C_4$$

(1)

In the formula, $C$ is the daily average cost; $C_1$ represents the daily operating cost; $C_2$ represents the start–stop cost of wind, PV, and solar thermal power generation; $C_3$ represents the equipment maintenance cost; and $C_4$ is the penalty for wind and light abandonment.

The constraints include generation constraints for each unit, creep rate constraints, start- and stop-state constraints, line constraints, and power-balance constraints:

$$0\le P_w(t)\le P_w^N$$

(2)

$$R_w^{down}\le P_w(t)-P_w(t-1)\le R_w^{up}$$

(3)

$$0\le P_{\mathrm{p}}(t)\le P_p^N$$

(4)

$$R_p^{down}\le P_{\mathrm{p}}(t)-P_{\mathrm{p}}(t-1)\le R_p^{up}$$

(5)

$$0\le P_{\mathrm{pb}}(t)\le P_{pb}^{\max }{\mu }_{PB,t}^{su}$$

(6)

$$R_{pb}^{down}\le P_{\mathrm{pb}}(t)-P_{\mathrm{pb}}(t-1)\le R_{pb}^{up}$$

(7)

$$0\le {\mu }_t^{su}+{\mu }_t^{sd}\le 1$$

(8)

$$0\le P_{g,t}\le P_{g,\max }$$

(9)

$$P_w(t)+P_{\mathrm{p}}(t)+P_{pb}(t)-P_{load}\ge 0$$

(10)

In the formulas, $P_w^N$ is the rated capacity of wind turbines; $R_w^{down}$, $R_p^{down}$, $R_{pb}^{down}$, $R_w^{up}$, $R_p^{up}$, and $R_{pb}^{up}$ are the upper and lower limits of the creep rate of the wind, photovoltaic, and solar thermal power generation system; $P_{pb}^{\max }$ is the maximum output power of the solar thermal power generation system; ${\mu }_t^{su}$ and ${\mu }_t^{sd}$ are the start-up and release efficiencies of the solar thermal power generation, respectively; $P_{g,\max }$ is the maximum allowable power of the liaison line; and $P_{load}$ is the power of the load demand. Remark: The current model overlooks load uncertainty, renewable energy consumption efficiency, and CSP storage economics. Ignoring these factors may result in power imbalances due to mismatched generation and demand. Integrating EH-CSP joint optimization into day-ahead scheduling enables coordinated energy utilization, enhances wind and solar absorption, and improves grid reliability through thermal storage’s peak-shaving capability. Thus, incorporating load uncertainty and EH-CSP optimization is essential for secure and economic system operation.

2.2. Day-Ahead Optimal Scheduling Model Considering Uncertain Loads and EH-CSP

Thermal energy storage (TES) can store the excess heat of the concentrating heat collection system when the load demand is low and release energy through thermoelectric conversion when the load demand is high to improve the system’s operation and energy utilization efficiency. Considering the CSP storage, Formula (1) can be improved as follows:

$$C^{\prime }=C_1^{\prime }+C_2^{\prime }+C_3^{\prime }+C_4$$

(11)

$$C_1^{\prime }={\displaystyle \sum _{t=1}^T[c_w{P}_w(t)+c_p{P}_p(t)+c_{pb}{P}_{pb}(t)+c_{tes}{P}_{tes}(t)]}$$

(12)

$$C_2^{\prime }=C_2+{\displaystyle \sum _{t=1}^T[S{U}_{TES}{\mu }_{TES,t}^{su}+S{D}_{TES}{\mu }_{TES,t}^{sd}]}$$

(13)

$$C_3^{\prime }={\displaystyle \sum _{t=1}^T[O{M}_{WT}{P}_w(t)+O{M}_{PV}{P}_p(t)+O{M}_{PB}{P}_{pb}(t)+O{M}_{TES}{H}_{tes}(t)+O{M}_{EH}{E}_{EH}(t)]}$$

(14)

$$P_{tes}(t)=H_{tes}(t){\eta }_2$$

(15)

where $c_{tes}$ represents the unit operating cost of the TES module; $P_{tes}(t)$ is the thermal power for charging/discharging the TES at time $t$; $S{U}_{TES}$ is the start-up cost for thermal-to-electric conversion; $S{D}_{TES}$ is the start-up cost for charging the TES; ${\mu }_{TES,t}^{su}$ = 1 and ${\mu }_{TES,t}^{sd}$ = 1, respectively, indicate the discharge operation and the start-up cost of discharge for the TES module at time $t$; $O{M}_{TES}$ is the maintenance cost coefficient for the TES system; $H_{tes}(t)$ represents the charge/discharge thermal energy of the TES system at time $t$; and ${\eta }_2$ is the thermal-to-electric conversion efficiency of the solar thermal storage system.

The load in Formula (10) is a deterministic expression, while, in essence, the load is a random fluctuation state with substantial uncertainty, and considering the uncertain load is conducive to optimizing the day-ahead scheduling and reducing the day-ahead operating cost. Considering the TES module at the same time, Formula (10) is improved:

$$P_w(t)+P_p(t)+P_{pb}(t)+P_{tes}(t)-P_{load}^{un}(t)>0$$

(16)

where $P_{tes}(t)$ is the conversion power of the TES module at the corresponding time and $P_{load}^{un}(t)$ is the uncertain load power.

The addition of the energy storage constraint to the constraints, as well as the improvement of the supply–demand coordination demand constraints and the EH operation constraints by taking the load uncertainty into account, is written as follows:

$$H_{tes}(t)={\mu }_{tes}^{ch}{H}_{tes}^{ch}(t)+{\mu }_{tes}^{dis}{H}_{tes}^{dis}(t)+E_{EH}(t)$$

(17)

$$0\le H_{tes}^{ch}(t)\le H_{tes}^{ch,\max }{\mu }_{tes}^{ch}$$

(18)

$$0\le H_{tes}^{dis}(t)\le H_{tes}^{dis,\max }{\mu }_{tes}^{dis}$$

(19)

$$0\le {\mu }_{tes}^{ch}+{\mu }_{tes}^{dis}\le 1$$

(20)

$$H_{csp}=H_{tes}^{ch}(t)+H_t^{pb}$$

(21)

$$E_{EH}(t)=P_w(t)+P_p(t)+P_{pb}(t)-P_{load}^{un}(t)$$

(22)

$$0\le E_{EH}(t)\le E_{EH}^{\max }$$

(23)

where $H_{tes}(t)$ is the charging/discharging heat of the TES system at time $t$; $H_{tes}^{ch}(t)$ and $H_{tes}^{dis}(t)$ are the charging and discharging heats of the TES ${\mu }_{tes}^{ch}$ is a binary variable; ${\mu }_{tes}^{ch}=1$ means the heat storage unit for heat storage; ${\mu }_{tes}^{dis}$ is a binary variable; ${\mu }_{tes}^{dis}=1$ represents the heat storage unit for exothermic power; $P_{pb}(t)$ is the output power of the solar thermal power generation at time $t$; $H_{tes}^{ch,\max }$ and $H_{tes}^{dis,\max }$ are the thermal units of the maximum heat storage and exothermic power, respectively; $H_{csp}$ is the total heat absorbed by the concentrating light collector system; and $E_{EH}^{\max }$ is the maximum value of the electric heating device at the time of the conversion.

According to the above-improved model, the optimal scheduling model considering load uncertainty with day-ahead CSP storage is expressed as follows:

$$\min :f(11)$$

(24)

The constraints are as follows:

$$f \left(2\right)–\left(10\right)$$

$$f \left(17\right)–\left(23\right)$$

Remark 1. 

The uncertain load power referred to in Formula (16) of the day-ahead optimal dispatch model concerning the supply–demand balance will be modeled in Section 3.

Remark 2. 

The outputs of the power generation module, $P_{pb}(t)$,  and the heat storage module, $P_{tes}(t)$,  of the photovoltaic power plant are described in Formula (16) in terms of power balance. In this paper, EH is introduced to improve the capacity of wind and solar energy consumption. The energy of the heat storage module in the EH-CSP power plant is not only derived from the concentrating heat and power collection system but also from the energy converted from the abandoned wind and light. Therefore, Section 4 will take the concentrating solar collector system as well as the EH output as the pivot to establish the relationship model of $P_{pb}(t)$ and $P_{tes}(t)$.

3. Load-Power Uncertainty Model Based on CNN-MI-BILSTM

Uncertainty in pure electricity loads affects the balance between supply and demand. If the planned output for each day far exceeds the load demand, there will be an economic loss. If it is not possible to cope with changes in load, the system becomes unstable.

3.1. Uncertainty-Considering Load-Power Model Based on Baseload Prediction

In this section, a multi-interval uncertainty modeling approach is used to construct the load-power uncertainty set.

Multi-interval uncertainty modeling describes the predicted load power by incorporating a probability distribution. Firstly, the predicted power range $\left[P_{load}^{pre}(t)-{\omega }_{\partial ,t}^{-},P_{load}^{pre}(t)+{\omega }_{\partial ,t}^{+}\right]$ is divided into $N_b$ intervals, and the sum of the corresponding times of the $N_b$ intervals is ${\Pi }_{\partial }^{\omega }$, and the corresponding time of each interval, ${\Pi }_{\partial }^{b,\omega }$, depends on the deviation ratio, ${\omega }_{\partial ,t}^{b+}+{\omega }_{\partial ,t}^{b-}/{\omega }_{\partial ,t}^{+}+{\omega }_{\partial ,t}^{-}$, and the probability distribution, ${\rho }_{\partial }^b$; the multi-interval probability distribution is plotted as Figure 1.

$${\displaystyle \sum _{b=1}^{N_b}({\Pi }_{\partial }^{b,\omega }\cdot \frac{{\omega }_{\partial ,t}^{b+}+{\omega }_{\partial ,t}^{b-}}{{\omega }_{\partial ,t}^{+}+{\omega }_{\partial ,t}^{-}}})={\Pi }_{\partial }^{\omega }$$

(25)

$${\displaystyle \frac{{\Pi }_{\partial }^{b,\omega }}{{\Pi }_{\partial }^{b+1,\omega }}}={\displaystyle \frac{{\rho }_{\partial }^b}{{\rho }_{\partial }^{b+1}}}$$

(26)

Formulas (25) and (26) enable the division of a single interval, $\left[P_{load}^{pre}(t)-{\omega }_{\partial ,t}^{-},P_{load}^{pre}(t)+{\omega }_{\partial ,t}^{+}\right]$, into upper and lower error limits and probability distributions. Then, the uncertainty load model is expressed as follows:

$$P_{load}^{un}(t)=P_{load}^{pre}(t)+{\displaystyle \sum _{b=1}^{N_b}({\omega }_{\partial ,t}^{b+}{\epsilon }_{\partial ,t}^{b+}-}{\omega }_{\partial ,t}^{b-}{\epsilon }_{\partial ,t}^{b-})$$

(27)

$$0\le {\displaystyle \sum _{b=1}^{N_b}({\epsilon }_{\partial ,t}^{b+}+}{\epsilon }_{\partial ,t}^{b-})\le 1$$

(28)

$${\displaystyle \sum _{t=1}^{N_t}({\epsilon }_{\partial ,t}^{b+}+}{\epsilon }_{\partial ,t}^{b-})\le {\Pi }_{\partial }^{b,\omega }$$

(29)

$$-{\Lambda }_{\partial }\le {\displaystyle \frac{{\displaystyle {\sum }_{t=1}^{N_t}{\displaystyle {\sum }_{b=1}^{N_b}({\omega }_{\partial ,t}^{b+}{\epsilon }_{\partial ,t}^{b+}}}-{\omega }_{\partial ,t}^{b-}{\epsilon }_{\partial ,t}^{b-})}{{\displaystyle {\sum }_{t=1}^{N_t}{P}_{load}^{pre}(t)}}}\le {\Lambda }_{\partial }$$

(30)

where $P_{load}^{pre}(t)$ is the load prediction value; ${\omega }_{\partial ,t}^{b+}$ and ${\omega }_{\partial ,t}^{b-}$ are the upper and lower error limits corresponding to the period $b$; the introduced variables ${\epsilon }_{\partial ,t}^{b+}$ and ${\epsilon }_{\partial ,t}^{b-}$ limit the uncertain load power within the range $\left[P_{load}^{pre}(t)-{\omega }_{\partial ,t}^{-},P_{load}^{pre}(t)+{\omega }_{\partial ,t}^{+}\right]$; Formula (28) considers that only one deviation will occur at any period from a spatial point of view; Formula (29) ensures that the total uncertainty period for each interval, $N_t$, does not exceed, from a temporal point of view, ${\Pi }_{\partial }^{b,\omega }$; and the constraint (30) controls the range of deviation of the actual output from the predicted value, $\left[-{\Lambda }_{\partial },{\Lambda }_{\partial }\right]$.

The load uncertainty model described above is based on load predictions, $P_{load}^{pre}(t)$. Therefore, the load prediction model is given in Section 3.2, Section 3.3 and Section 3.4

3.2. CNN-LSTM-Based Baseload Prediction Models

Considering the complexity and non-smoothness of the load data, a CNN-LSTM network short-term load prediction method is proposed to accomplish the prediction of the load, $P_{load}^{pre}(t)$.

Figure 2 illustrates the prediction flow of the CNN-LSTM network.

The modeling of each module of the CNN-LSTM network is explained below.

3.2.1. Input Layer

The input layer realizes the transfer of load data to the CNN layer.

3.2.2. CNN Layer

The CNN layer mainly includes the convolutional layer and the pooling layer, which uses the convolutional layer to realize the extraction of static features from the input data through the sliding-window operation of the convolutional kernel and then reduces the dimensionality of the extracted features by using the scale invariance of the key features through the pooling layer, which makes the key features further highlighted and reduces the complexity of the network through parameter sharing. Usually, the key features are extracted from the input data by convolutional and pooling layers, and the dimensionality of the features can be reduced.

The process of the CNN layer is represented as follows:

$$C_1=\mathrm{Re}LU(X\otimes W_1+b_1)$$

(31)

$$P_1=\max (C_1)+b_2$$

(32)

$$C_2=\mathrm{Re}LU(X\otimes W_2+b_3)$$

(33)

$$P_2=\max (C_2)+b_4$$

(34)

$$X_C=Sigmoid(P_2\times W_3+b_5)$$

(35)

where the outputs of convolutional layer 1 and convolutional layer 2 and pooling layer 1 and pooling layer 2 are $C_1$ and $C_2$ and $P_1$ and $P_2$, respectively; $W_1$, $W_2$, and $W_3$ are the weight matrices of the CNN layers, $b_1$, $b_2$, $b_3$, $b_4$, and $b_5$ are the deviation values; $\otimes$ is the convolution operation; and the activation function $Sigmoid$ is chosen for the fully connected layer. The output feature vector of the CNN layer is denoted as $X_C$, and the length of the output of the CNN layer is denoted as $X_C=[x_1\cdots x_{i-1},x_i\cdots ,x_t]$.

3.2.3. LSTM Layer

The basic unit model of the LSTM network is as follows:

$$f_t=\sigma (W_{fx}{x}_t+W_{fh}{h}_{t-1}+b_f)$$

(36)

$$i_t=\sigma (W_{ix}{x}_t+W_{ih}{h}_{t-1}+b_i)$$

(37)

$$g_t=\varphi (W_{gx}{x}_t+W_{gh}{h}_{t-1}+b_g)$$

(38)

$$S_t=g_t\odot i_t+S_{t-1}\odot f_t$$

(39)

$$h_t=\varphi (S_t)\odot o_t$$

(40)

$$o_t=Sigmoid(W_{ox}{x}_t+W_{oh}{h}_{t-1}+b_o)$$

(41)

where $x_t$ is the forgetting gate input; $h_{t-1}$ is the intermediate output; $S_{t-1}$ is a status memory unit; $f_t$, $i_t$, $g_t$, $h_t$, $S_t$, and $o_t$ are the states of the forgetting gate, the input gate, the input node, the intermediate output, and the state unit output gate; $W$ is the matrix weight of the corresponding gate multiplied by the input, $x_t$, and the intermediate output, $h_{t-1}$; $b_f$, $b_i$, $b_g$, and $b_o$ are the offset terms of the corresponding doors; $\odot$ represents the bitwise multiplication of vector elements; and $\varphi$ indicates the change in the tanh function.

3.2.4. Output Layer

Take the output data of the LSTM-layer output gate as the result of the load prediction data:

$$P_{load}^{pre}(t)=o_t$$

(42)

Remark 3. 

The hybrid model short-term load forecasting method based on the CNN-LSTM network can effectively extract the potential relationship between continuous data and discontinuous data in the feature map to form the feature vector and fully mine the internal correlation between time-series data. However, the output feature vector, X_C, of the CNN layer lacks consideration of data correlation, which will cause prediction deviation, so MI is introduced to improve the data correlation.

3.3. MI Reconstruction Method of Input-Layer Data Considering Data Relevance

To solve the problem of prediction deviation, this section introduces eigenvalues to represent the importance value of the input characteristics and constructs an improved load data input correction model.

The characteristic matrix, $X_C^{\prime }$, of the new input LSTM network is obtained by introducing the eigenvalue vector, $M$, as follows:

$$X_C^{\prime }=X_C\cdot M$$

(43)

$$X_C=\left[\begin{array}{ccccc}{x}_{1,1}& \cdots & x_{i,1}& \cdots & x_{t,1}\\ x_{1,2}& \cdots & x_{i,1}& \cdots & x_{t,2}\\ ⋮& & ⋮& & ⋮\\ x_{1,z}& \cdots & x_{i,z}& \cdots & x_{t,z}\end{array}\right]$$

(44)

$$M=\left[\begin{array}{ccccc}M(x_{1,1},o_1)& \cdots & M(x_{i,1},o_i)& \cdots & M(x_{t,1},o_t)\\ M(x_{1,2},o_1)& \cdots & M(x_{i,2},o_i)& \cdots & M(x_{t,2},o_t)\\ ⋮& & ⋮& & ⋮\\ M(x_{1,z},o_1)& \cdots & M(x_{i,z},o_i)& \cdots & M(x_{t,z},o_t)\end{array}\right]$$

(45)

where $X_C$ is the input characteristic matrix corresponding to the CNN output load data set obtained based on (35) and $M$ is the time-varying importance value fluctuation matrix obtained by normalizing the output or input characteristic matrix, $X_C$, of the CNN layer based on MI. It contains important information on input features under different dimensions. The stronger the correlation between the two variables, the greater the $M$ value. When the two variables are independent of each other, the $M$ value is 0. $o_t$ is the output load data obtained at time $t$ based on the input characteristic matrix, $X_C$.

Remark 4. 

The critical value extraction of the CNN-layer output data can accurately predict the data fluctuation, but the training speed of the MI-LSTM method is slow. The load sequence has the characteristics of correlation and strong randomness. The LSTM neural network can only extract and encode the sequence information in one direction. It cannot learn the forward and reverse information rules of the load data. The BI method neural network is proposed to consider the forward and backward sequences at the same time to solve the problem of data dependence.

3.4. Bidirectional BILSTM Improvement Considering Prediction Accuracy

Section 3.2. The LSTM model is used to learn the output characteristic data of the CNN layer. However, the prediction accuracy of this method is not high, and the training speed is slow. Therefore, this section uses the BILSTM with two-way time information to bidirectionally mine the internal relationship between long-time data to improve the training speed and prediction accuracy. The specific structure is shown in Figure 3.

$X_C^{\prime }$ is the input data of the new LSTM network, and $X_C^{\prime }=[x_1^{\prime }\cdots x_{i-1}^{\prime },x_i^{\prime }\cdots ,x_t^{\prime }]$ defines a new network final output power prediction value, $O_t$, as follows:

$$f_t=\sigma (W_{fx}{x}_t^{\prime }+W_{fh}{h}_{t-1}+b_f)$$

(46)

$$i_t=\sigma (W_{ix}{x}_t^{\prime }+W_{ih}{h}_{t-1}+b_i)$$

(47)

$${\tilde{g}}_t=\varphi (W_{gx}{x}_t^{\prime }+W_{gh}{h}_{t-1}+b_g)$$

(48)

$${\tilde{S}}_t={\tilde{g}}_t\odot i_t+S_{t-1}\odot f_t$$

(49)

$$h_t=\varphi ({\tilde{S}}_t)\odot o_t$$

(50)

$$o_t=Sigmoid(W_{ox}{x}_t^{\prime }+W_{oh}{h}_{t-1}+b_o)$$

(51)

$$\overrightarrow{o_t}=\overrightarrow{LSTM}(o_{t-1},x_t^{\prime },c_{t-1})$$

(52)

$$\overleftarrow{o_t}=\overleftarrow{LSTM}(o_{t+1},x_t^{\prime },c_{t+1})$$

(53)

In the formulas, $\overrightarrow{o_t}$ is the forward LSTM output predictive value calculated by inputting the input data, $X_C^{\prime }$, of Formula (43) into the LSTM neural network (46)–(51); $\overleftarrow{o_t}$ is the forward LSTM input predictive value calculated according to the calculation of the $X_C^{\prime }$ reverse input LSTM neural network (45)–(51); $a_t$ and $b_t$ represent the forward and backward output weights, respectively; and $c_t$ is the offset optimization parameter.

The model realizes LSTM training in the forward and reverse directions of $X_C^{\prime }$ and effectively improves the comprehensiveness and integrity of feature selection. The forward LSTM-layer output, $\overrightarrow{o_t}$, is connected to the backward LSTM-layer output, $\overleftarrow{o_t}$, and the final power prediction output value, $o_t$, is obtained through weighted fusion.

The structure of the prediction model of CNN-MI-BILSTM is shown above.

The algorithm of load prediction in Section 3.2, Section 3.3 and Section 3.4 was improved, and the results were input to Section 3.1, which accurately described the uncertain load according to the multi-interval uncertainty set.

4. Consider the Coupling Operation Model of the EH-CSP Combined CSP System

In Section 2.2, considering the mutual coupling between the power operation of the power generation, $P_{pb}(t)$, and the heat storage module, $P_{tes}(t)$, of the CSP power station in the EH-CSP combined system, the excess wind and solar capacity can be effectively transformed into heat energy by integrating EH in the CSP heat exchange platform. Secondly, different from the traditional heat storage–power generation process, this section divides the energy storage and power generation output into two independent modules. The following describes the coupling output of the power generation module, $P_{pb}(t)$, and the heat storage module, $P_{tes}(t)$, of the optical thermal power station assisted by the EH device from the perspective of the internal operation.

4.1. Photothermal Power Generation and TES Coupling Operation Model

This section mainly describes the operation relationship between the CSP power generation module and the energy storage module: the core of this section is to treat the load demand as a connecting bridge and further elaborate the interaction and coupling mechanism between the CSP power generation and the EH energy storage system.

When the load demand is low, the concentrated heat collection system transfers heat to the power generation module and converts it into electric energy for load demand. At the same time, the energy storage module stores heat energy:

$$P_{load}^{un}(t)\le P_w(t)+P_p(t)+P_{pb}(t)$$

(54)

As an electric heat transfer element in a CSP power plant, the EH conversion efficiency can be close to 100%. The amount of abandoned air and light mainly determines the output of EH. The output model is expressed as follows:

$$P_{EH}(t)=P_w(t)+P_p(t)-P_{load}^{un}(t)$$

(55)

$$E_{EH}(t)={\eta }_{EH}{P}_{EH}(t)$$

(56)

where $E_{EH}(t)$ is the heat transferred to the heat storage module, $P_{EH}(t)$ is the wind and solar residual power, and ${\eta }_{EH}$ refers to the electrothermal conversion efficiency when EH works stably.

The energy stored in the energy storage system is expressed as follows:

$$P_{tes}(t)=P_{csp}(t)-P_{pb}(t)+{\eta }_d{E}_{EH}(t)$$

(57)

$$P_{total}(t)={\eta }_d(Q_{pb}(t)-P_{tes}^{ch}(t)/{\eta }_c-E_{EH}(t))$$

(58)

where $P_{csp}(t)$ is the total absorbed power of the CSP concentrator and collector system. When the load demand is low, one part of $P_{csp}(t)$ flows into the PC system to heat the steam to drive the turbine for power generation, $P_{pb}(t)$, and the other part flows into the TES to store heat energy, $P_{tes}(t)$. $P_{tes}^{ch}(t)$ is the charging power of TES; $P_{total}(t)$ represents the total power of the power generation module and the heat storage module; $Q_{pb}(t)$ is the heat transferred to the power generation system by concentrating and collecting heat at time $t$; ${\eta }_d$ is the thermoelectric conversion efficiency; and ${\eta }_c$ is the thermal storage efficiency of the TES (%).

When the load demand is high, the concentrated heat collection system transfers heat to the power generation module, while the energy storage module releases the stored heat energy: the heat released by the energy storage module is used by the power generation module alone.

$$P_{total}(t)={\eta }_d(Q_{pb}(t)+P_{tes}^{dis}(t){\eta }_f+E_{EH}(t))$$

(59)

$$P_{load}^{un}(t)\le P_w(t)+P_p(t)+P_{total}(t)$$

(60)

where $P_{tes}^{dis}(t)$ is the power released by the heat storage system. When the load demand is high, $P_{csp}(t)$ flows into the PC system, heating steam to drive the turbine for power generation, $P_{pb}(t)$, while releasing the heat energy stored in the TES, $P_{tes}(t)$. ${\eta }_f$ is the heat release efficiency of the TES (%).

4.2. Operation Model of the Solar Thermal Power Generation Module Based on Direct Connection and High Efficiency

The thermal storage module and the power generation module of the CSP power generation system are entirely independent; that is, the thermal storage module is specially responsible for storing heat energy and generating power independently, while the output of the power generation module entirely depends on the real-time concentrating and collecting heat system and does not directly use the heat storage, so it is considered that the output of the power generation module is directly connected to the concentrating and collecting heat module, reducing the intermediate steps of energy form conversion.

Because the energy of the CSP power generation and energy storage charging comes from the concentrating heat collection system, the concentrating heat collection system is modeled first. The CSP power station uses the concentrating heat collection system to convert the reflected light energy of the mirror field into heat energy. The thermal power is as follows:

$$Q_{csp}(t)={\eta }_{2}S{D}_t$$

(61)

where $Q_{csp}(t)$ is the thermal power of the concentrating and collecting device, ${\eta }_2$ is the total optical efficiency, $S$ is the mirror field area of the CSP power station, and $D_t$ is the direct irradiation index of light at time $t$.

When the load demand is low, part of $Q_{csp}(t)$ is used for power generation to meet the load demand, and another part is stored through the heat storage system.

$$Q_{csp}(t)=Q_{pb}(t)+Q_{tes}^{ch}(t)$$

(62)

When the load demand is high, $Q_{csp}(t)$ is fully used for power generation to meet the load demand, and the heat storage system releases the stored heat:

$$Q_{csp}(t)=Q_{pb}(t)+Q_{tes}^{dis}(t)$$

(63)

where $Q_{pb}(t)$ is the thermal power transmitted from the concentrating and collecting device to the power generation system, $Q_{tes}^{ch}(t)$ refers to the thermal power transmitted to the heat storage system by the concentrator and collector, and $Q_{tes}^{dis}(t)$ is the thermal power released by the heat storage system.

CSP power generation is defined as the transfer of energy only by the concentrating and collecting system, and the modeling is as follows:

$$P_{pb}(t)={\eta }_d{Q}_{pb}(t)$$

(64)

where $P_{SF}(t)$ is the thermal power directly used by the concentrating and collecting device for power generation and ${\eta }_d$ is the thermoelectric conversion efficiency.

4.3. Operation Model of CSP Storage Module Considering EH-CSP Combination

The independent TES–power generation and direct generation thermoelectric modules enable the power output to be flexibly adjusted according to the actual demand and resource conditions. The heat storage module can store heat energy when the Sun is sufficient for use at night or on cloudy days, while the direct-generation thermal power module adjusts the power generation according to the real-time sunlight conditions, and the combination of the two forms is complementary.

When the load demand is low, from Formula (61), the concentrator and collector will store the heat through the CSP storage system, and the heat energy stored in the energy storage module not only comes from this path but also converts the excess wind and solar output through the electrical heat transfer capacity of the EH, and the heat energy is released when the system needs to operate to drive the steam turbine to generate electricity. This is modeled as follows:

$$P_{tes}^{ch}(t)={\eta }_c(Q_{tes}^{ch}(t)+E_{EH}(t))$$

(65)

When the load demand is high, the heat stored in the CSP storage system is released, which is expressed as follows:

$$P_{tes}^{dis}(t)=(Q_{tes}^{dis}(t)+{\eta }_d{E}_{EH}(t))/{\eta }_f$$

(66)

where $P_{tes}^{ch}(t)$ and $P_{tes}^{dis}(t)$ are the TES storage and release power and ${\eta }_c$ and ${\eta }_f$ are the heat storage and heat release efficiency of the TES (%).

The power output of the TES at time $t$ is expressed as follows:

$$P_{tes}(t)={\eta }_d(-P_{tes}^{ch}(t)/{\eta }_c+P_{tes}^{dis}(t){\eta }_f+E_{EH}(t){)}^{\mathrm{vv}}$$

(67)

where $P_{tes}(t)$ represents the power output of the TES.

5. Solution

The day-ahead optimal scheduling model of shared energy storage considering uncertain loads constructed above can be defined as a mixed-integer nonlinear planning problem. Because it has an NP-hard property, it can be approximated by converting it into a mixed-integer linear programming problem. In this section, Benders + MOPSO is used to solve the optimal scheduling problem.

The decision variables of the day-ahead optimal dispatch model considering uncertain loads and EH solar thermal energy storage include wind power, photovoltaic power, solar thermal output power, and solar thermal energy storage power.

First, rewrite the model (23) in compact mode:

$$\begin{array}{l}\underset{P^{int},P^{tes}}{{\displaystyle \min }}{C}^{int}\left(P^{int}\right)+C^{tes}\left(P^{tes}\right)\\ s.t.A{P}^{int}\le b\\ D{P}^{int}+E{P}^{tes}\le f\end{array}$$

(68)

In Formula (63), the response variable output power of the wind, photovoltaic, and solar thermal power generation modules is expressed as $P^{int}$, and the power change of the solar thermal unit energy storage module is described as $P^{tes}$ in Formulas (A1)–(A3) and (A5). The scheduling response cost, $C^{int}\left(P^{int}\right)$, is a function of $P^{int}$. The cost of CSP storage, $C^{tes}\left(P^{tes}\right)$, is a function of $P^{tes}$, which is composed of the power change of the CSP storage module contained in Formulas (11)–(13). Constraint $A{P}^{int}\le b$ represents the constraint only related to $P^{int}$, i.e., Formulas (2)–(9), and constraint $D{P}^{int}+E{P}^{tes}\le f$ represents $P^{int}$ and $P^{tes}$. The related coupling constraint is expressed in Formulas (16)–(22).

5.1. MOPSO Operational Flow

The Benders decomposition and multi-objective particle swarm optimization (MOPSO) algorithm are combined to optimize the combined output of day-ahead scheduling.

Algorithm 1 describes the process of solving the Pareto-optimal solution by MOPSO using the main decision variable group decomposed by benders as particles. Firstly, the algorithm initializes the particles. At this time, each group of decision variables includes the output power values of the wind, photovoltaic, and solar thermal power generation modules. $P[i]$ is the cost corresponding to each group of decision variables. In Section 2.1, the proposed traditional cost function, C, is the optimal solution, Pbest, of the decision variable; in Section 2.2, the cost function considering the load uncertainty and CSP storage proposed in Section 2.1 is used as the group extremum, Gbest. The inertia weight, velocity, and position of particles are continuously updated, and the Pbest and Gbest corresponding to particles in each scene are solved until the end of the iteration to obtain the global optimal solution in the Pareto solution set.

Algorithm 1: MOPSO algorithm framework

Input: Particle swarm size N (N = 50); dimension, M, of the objective function; maximum number of iterations, MaxIter (MaxIter = 100); acceleration constants, c1 and c2 (usually close to 2); inertia weight, W; initialize particle position, X[N][D]; initialize particle velocity, V[N][D]; initialize personal best position, Pbest[0], and global best position, Gbest[0].

Termination condition: Maximum number of iterations reached.

For t = 1 to MaxIter, do

$Pbest\left[0\right]=\min C_0$ $Gbest[0]=\min C_0^{\prime }$ For i = 1 to N, do $V[i]=\omega *V[i]+c_1*rand()*(\min C_0-P[i])+c_2*rand()*(\min C_0^{\prime }-P[i])$ $P[i]=P[i]+V[i]$ Calculate the current particle fitness, Fi If Fi ($X_i$) > Fi ($\min C_0$), then $\min C=X_i$ Add $\min C$ to Pareto frontier set, p $\min C^{\prime }=selectParetoFront\left(P\right)$ End for $\min C^{\prime }$ End

5.2. Benders+MOPSO Algorithm Solving

In view of the complex correlation between $P^{int}$ and $P^{tes}$, it is not easy to directly solve the model (68). This paper proposes a multi-objective optimization scheme with a decomposition structure based on Benders decomposition and MOPSO, which decomposes the integrated model (68) into a response optimization problem (69) and energy storage optimization problem (70).

$$\begin{array}{l}\underset{P^{int}}{{\displaystyle \min }}{C}^{int}\left(P^{int}\right)\\ s.t.A{P}^{int}\le b\end{array}$$

(69)

$$\begin{array}{l}\underset{P^{int},P^{tes}}{{\displaystyle \min }}{C}^{tes}\left(P^{tes}\right)\\ s.t.D{P}^{int}+E{P}^{tes}\le f\\ P^{int}=P^{int*}\end{array}$$

(70)

In each iteration, Formula (69) optimizes the response quantity and transfers the boundary variable, $P^{int*}$, to Formula (70).

Benders decomposition divides the complex problem into a main problem and sub-problems and approximates the optimal solution through an iterative cutting plane; MOPSO is applied to the main problem for multi-objective optimization and searches for the Pareto-optimal solution set using group intelligence. The combination of the two effectively solves the NP-hard problem.

6. Results and Discussion

This section consists of two parts for the calculation example: one part details the construction of the load uncertainty of the prediction algorithm and the accuracy of the calculation analysis, and the other part addresses the consideration of the EH-CSP thermal storage module on the day before the day scheduling economy and the wind power consumption capacity in the calculation analysis.

6.1. Background

Firstly, the prediction algorithm was evaluated to ensure the feasibility and accuracy of the simulation experiment. This paper selected a specific region of China to choose any day with an interval of 15 min and obtained the maximum load characteristics, the daily load data, and the daily meteorological data.

In this paper, the mean absolute percentage error (MAPE) and root mean square error (RMSE) evaluation indexes were selected to evaluate the prediction algorithm. The calculation formula for each evaluation index is as follows:

$$e_{\mathrm{MAPE}}={\displaystyle \frac{1}{n}}{\displaystyle {\sum }_i^n\left|\frac{y_i-y_r}{y_r}\right|}\ast 100\%$$

(71)

$$e_{\mathrm{RMSE}}=\sqrt{{\displaystyle \frac{1}{n}}{\displaystyle {\sum }_i^n{(y_i-y_r)}^2}}$$

(72)

where $y_r$ denotes the actual value, $y_i$ denotes the predicted value, and $n$ is the sample size; MAPE is used to measure the percentage of the mean absolute error between the predicted value and the actual value, and RMSE is the mean of the squared prediction error squared and then squared, which is more sensitive to the effect of large errors.

Secondly, the results of the day-ahead scheduling example were analyzed. In this paper, 500 MW doubly fed wind farms, 600 MW photovoltaic power plants, and 200 MW tower-type photovoltaic power plants were used to form a wind–heat co-generation system. The power and direct sun index of wind power, PV power, and load predicted by the proposed algorithm are shown in the following figure, and the relevant parameters of the photovoltaic and thermal power plant are shown in

Table 1. Main parameters of 100 MWCSP power station.

Parameter	Value
Maximum output power of CSP plant/MW	100
Photothermal conversion efficiency/%	40
Thermal–electrical conversion efficiency/percent	40
Solar field area/m2	1.3 × 106
Charging (discharging) efficiency of heat storage device/%	98.5
CSP power plant output upper (lower) limit/MW	100
Maximum (small) heat storage capacity of heat storage device/MWh	1500

. The cost coefficient of wind and photovoltaic power generation was $c_w=c_p=90$ CNY/MW, the cost coefficient of maintenance was $O{M}_{WT}=O{M}_{PV}=30$ CNY/MW, the cost of starting and stopping was $S{U}_W=S{D}_W=S{U}_P=S{D}_P=15$ CNY/MW, the cost coefficient of the power generation of the photovoltaic power plant and the power generation cost coefficient of the storage module were $c_{pb}=c_{tes}=60$ CNY/MW and $O{M}_{PB}=O{M}_{TES}=20$ CNY/MW, the cost coefficient of O&M was $O{M}_{PB}=O{M}_{TES}=20$ CNY/MW, the costs of starting and stopping were $S{U}_{PB}=S{D}_{PB}=S{U}_{TES}=S{D}_{TES}==10$ CNY/MW and $O{M}_{PB}=O{M}_{TES}=20$ CNY/MW, the cost coefficient of the O&M was $O{M}_{EH}=10$ CNY/MW of the EH unit, and the maximum wind power (50 MW) and solar abandonment cost factor was $c_{wc}=c_{pc}=108$ CNY/MW.

The predicted power and direct solar insolation (DNI) indices for wind power and photovoltaic power generation are shown in the Figure 4, and the relevant parameters for the photovoltaic power plant are shown in Table 1.

6.2. Model Validation

6.2.1. Validation of the CNN-MI-BILSTM Algorithm in Predicting the Accuracy of Load Data

In this section, to validate the effectiveness and accuracy of the proposed CNN-MI-BILSTM algorithm, the mean absolute percentage error (MAPE), as well as the root mean square error (RMSE), were used as the evaluation metrics, and a certain number of samples were generated based on the city’s past load data, where 70% of the samples were used for the training of the unknown coefficients and 30% were used to check the model’s accuracy and detection rate. The prediction results obtained from the CNN-MI-BILSTM algorithm were compared with those of the BPNN, CNN-GRU, and conventional CNN-LSTM algorithms, as well as the CNN-MI-LSTM algorithm.

In order to compare the uncertain pure electric-load forecasting modeling methods, this experiment first used the control variable method for stepwise model adjustment. Based on the CNN-LSTM network, the importance value of input features was characterized by the MI value between the input features and the load. Completing the processing of correlated data and adding bidirectional moment information, BILSTM was used to mine the intrinsic connection between long-time data bidirectionally. It was compared with the BPNN and CNN-GRU algorithms; firstly, the load data were preprocessed, including operations such as normalization and processing of missing values and outliers, and then the data were fed into the deep learning model.

By applying the sliding-window technique, the original time-series data were sliced. Here, the window width was set to 24 h, which means that the model considered the data from the past full day as input to predict the load value at a point in the future each time. The step size was set to 1, which means that the window slid forward one unit at a time, so that the continuity of the time series could be fully utilized to capture the temporal dynamic features in the data while ensuring that the data utilization was maximized with no omissions.

Figure 5 compares the correlation between the prediction results produced by the adopted CNN-MI-BILSTM algorithm and four other mainstream prediction algorithms with the actual situation. It demonstrates the performance of different algorithms in predicting the daytime power-load variation in Gansu, clearly reflecting that the load fluctuates significantly within a day, especially peaking during the traditional peak period of power consumption, while there is a large drop during the trough period. All the prediction algorithms can fit the trend of the actual load profile well. To accurately quantify the performance,

Table 2. Predictors for different algorithms.

	Norm	${\mathit{e}}_{\mathbf{MAPE}}$	${\mathit{e}}_{\mathbf{RMSE}}$
Model
BPNN		3.22	140.04
CNN-GRU		2.85	127.83
CNN-LSTM		2.67	118.04
CNN-MI-LSTM		2.48	113.27
CNN-MI-BILSTM		2.40	109.83

provides the corresponding MAPE and RMSE metrics for each prediction algorithm.

By inputting 96 data points into different neural networks during the feature day, the final prediction results were compared with the actual data on the second day to obtain $e_{\mathrm{MAPE}}$ and $e_{\mathrm{RMSE}}$ metrics. These are shown in the following table:

Given that the lower of these two metrics represents a higher prediction accuracy, the data in Table 2 directly prove that the CNN-MI-BILSTM algorithm outperforms the compared algorithms in terms of prediction accuracy. First, regarding prediction accuracy, the CNN-MI-BILSTM algorithm can provide more accurate results in predicting the actual data in a particular location in Gansu. A smaller MAPE value means that the model has a low percentage error between the predicted and actual values, reflecting the strong ability of the predicted values to follow the changes in the actual data closely. Second, regarding error magnitude control, a lower RMSE value means that the overall magnitude of the prediction error is small, reducing the risk of uncertainty due to prediction bias. Finally, regarding algorithm effectiveness validation, by comparing it with other mainstream prediction algorithms, the CNN-MI-BILSTM algorithm is confirmed to be more accurate and reliable in dealing with this kind of time-series prediction task.

6.2.2. Validation of the Impact of the Proposed Scheduling Model in Promoting Wind Energy Consumption and Improving Economics

In order to study the impact of the EH-CSP combined solar thermal system integrated into the integrated energy system on the day-ahead optimal scheduling results, this paper set up three models to analyze the scheduling results by comparing the results of the other two scheduling models to verify the effectiveness of the proposed scheduling model in promoting wind energy consumption and reducing the integrated cost of the system. The three comparison models were as follows:

• In the traditional day-ahead dispatching model, only the role of wind power was considered, and the wind–heat co-generation system without CSP was used, in which five 100 MW wind turbines and six 100 MW PV plants were used.
• In conventional power generation, three 100 MW PV plants were replaced by two 100 MW PV plants to form a wind–heat co-generation system.
• Using the Benders + MOPSO solution, in conventional power generation, three 100 MW PV plants were replaced by one 150 MW PV plant, and the EH device was introduced to form the EH–wind–thermal co-generation system.

Figure 6 shows the comparison of the three scheduling models in terms of day-ahead output, and Table 3 reveals the differences in the cost-effectiveness for each scenario: Scenario 1 only considers the role of wind and solar, without considering the impact of the solar thermal factor and EH on day-ahead scheduling, and the corresponding cost of wind and solar abandonment is significantly higher than that of Scenarios 2 and 3. Scenario 2 considers the impact of the solar thermal factor on top of Scenario 1, but does not take into account the effect of EH, and the corresponding cost of dispatching is lower than that of Scenario 1, and the cost of wind and solar abandonment is higher than that in Scenario 3. Scenario 3 takes the impact of combining the EH-CSP with Scenario 2, effectively reducing wind and solar abandonment while further cutting the dispatching cost. Scenario 2 takes into account wind and heat, but not EH, based on Scenario 1, and the corresponding dispatch cost is lower than that of Scenario 1, and the cost of the wind and light abandonment rate is higher than that of Scenario 3. Scenario 3 takes into account the effect of the EH-CSP combination based on Scenario 2, which effectively reduces wind and light abandonment and, at the same time, further cuts down dispatch costs and improves economic efficiency.

The dispatch results of the above three comparative models for a few days previously were as follows:

Figure 6. Scheduling results for each model day.

Figure 6. Scheduling results for each model day.

The total costs of day-ahead scheduling for the three comparison models and the rates of wind and light abandonment were compared.

Table 3. Costs and abandonment rates for each model.

Model	Cost (CNY)	Energy Abandonment Rate
1	1,552,928	11.6%
2	1,357,023	6.15%
3	1,306,027	2.366%

Table 3. Costs and abandonment rates for each model.

Model	Cost (CNY)	Energy Abandonment Rate
1	1,552,928	11.6%
2	1,357,023	6.15%
3	1,306,027	2.366%

Aiming to achieve the goal of the lowest average daily cost, the combined scheduling of wind, photovoltaic (PV), and photothermal power generation was optimized for an integrated energy system. While ensuring that each generation unit operated within its respective constraints, an ideal pre-daily schedule was explored to achieve the best balance between economic efficiency and resource utilization.

6.3. Analysis of Relevant Factors

6.3.1. Analyzing the Effectiveness of the CNN-MI-BILSTM Algorithm with Different Sample Sizes

A certain number of samples were generated based on the load data of the city, where 70% of the samples were used to train the unknown coefficients and 30% were used to test the accuracy and detection rate of the model. The BPNN, CNN-GRU, and regular CNN-LSTM algorithms, the CNN-MI-LSTM algorithm, and the CNN-MI-BILSTM algorithm can make predictions. However, the accuracies of different prediction algorithms corresponding to different sample sizes deviate.

Therefore, Figure 7 shows in detail the accuracy of the CNN-MI-BILSTM algorithm compared with the other four prediction methods under different sample sizes (100, 400, 700, 1000, and 1300). The results clearly show that the CNN-MI-BILSTM algorithm exhibits the highest level of accuracy regardless of the sample size, and the advantage of its prediction accuracy is especially prominent in challenging scenarios with small sample sizes (e.g., 100 samples). As the number of samples grows to 400, 700, and even 1000 and 1300, although the prediction performance of all algorithms generally improves, the CNN-MI-BILSTM algorithm has optimal stability and robustness under different data sizes. Taken together, the proposed CNN-MI-BILSTM algorithm has optimal prediction accuracy under various sample sizes.

6.3.2. Analysis of the Reliability and Economy of the Optimized Configuration of the Combined EH–Wind–Heat System

To study the impact of different capacity configurations on the reliability and economy of the system, this paper verified the reliability of the optimized configuration by analyzing the proportion of the load demand that cannot be met due to insufficient generating resources to the total demand, i.e., the proportion of the critical load loss, under different stochastic configurations, and verified the impact of the various configurations on the economy of the whole system utilizing the cost curves.

Firstly, the reliability of the random configuration was analyzed. Figure 8 and Figure 9 show the analysis of the critical load loss ratio based on the existence of the EH device, a fixed CSP capacity, and the step of wind power according to 20 MW and the PV capacity according to 15 MW, respectively. As shown in the Figure 8, the smaller the generating capacity is than the optimized configuration generating capacity, the larger the corresponding critical load loss ratio, and the critical load loss ratio is zero when the generating capacity is larger than the optimized configuration generating capacity; with a reduction in the wind power and PV unit capacity, the larger the critical load loss ratio; and the generating system with a higher than optimized capacity configuration can achieve zero load loss.

Secondly, to analyze the economics under the random configuration, the cost curve of power generation under the random configuration is given. As shown in the Figure 9, when the power generation capacity is larger than the optimized configuration capacity, the cost gradually increases with the increase in the configuration capacity, and the rate of wind and light abandonment increases. When the generation capacity is smaller than the optimized capacity, the cost gradually decreases as the configuration capacity decreases, and the rate of wind and light abandonment decreases.

The above verifies that the optimized configuration of the EH–wind thermal system can maintain high power supply reliability and economy in the face of the intermittency and uncertainty of renewable energy generation.

7. Conclusions

The paper innovatively proposes a day-ahead optimal scheduling model considering uncertain loads and EH-CSP storage. The model first adopts the multi-interval uncertainty set to portray the uncertainty of loads, and the prediction algorithm is continuously improved to accurately predict the load data using the CNN-MI-BILSTM algorithm. By combining the feature extraction capability of the convolutional neural network, the feature selection advantage of MI, and the powerful capture of time series by BILSTM, the method effectively handles the nonlinear relationships and long- and short-term dependencies in the data, which significantly improves the accuracy and stability of prediction. The accuracy of the proposed algorithm is verified by comparing the prediction results of different prediction algorithms.

In this paper, the CNN-MI-BILSTM algorithm obtains smaller MAPE and RMSE values of 2.40 and 109.83, respectively, compared to other prediction algorithms. The smaller the MAPE value, the smaller the percentage of error between the predicted value and the actual value. The smaller the RMSE value, the smaller the overall magnitude of prediction error, and thus the smaller the risk of uncertainty. The cost of the model, considering the inclusion of EH-CSP and adopting the Benders + MOPSO solution, is CNY 1306027, and the energy abandonment rate is 2.366%, which is significantly lower than that of the model without considering EH-CSP.

The proposed day-ahead optimal dispatch model integrates the output characteristics of new energy power plants, aiming to optimize the balance between the day-ahead dispatch cost and adaptability in the face of uncertain loads, taking into account the flexibility and complementarity of EH and solar thermal storage technologies. Integrating them into the model not only smoothes intraday load fluctuations but also effectively stores and dispatches intermittent wind and solar energy, reducing the scheduling challenges caused by renewable energy uncertainties. A combination of Benders decomposition and MOPSO determines the optimal capacity configuration. Scheduling simulations of the power system in Gansu Province using different unit configurations are conducted, and it is verified that the proposed day-ahead optimal scheduling model considering uncertain loads and EH-CSP storage significantly improves the economic efficiency and environmental sustainability of the scheduling process.