Prediction Model-Assisted Optimization Scheduling Strategy for Renewable Energy in the Microgrid

Abstract

As the global reliance on renewable energy sources grows, wind and photovoltaic power, as pivotal components, pose significant challenges to power system dispatch due to their volatility and uncertainty. To effectively address this challenge, this paper proposes a renewable energy optimization dispatch strategy based on a prediction model. First, this paper constructs a prediction model combining functional data analysis and recurrent neural networks (RNNs) to achieve an accurate prediction of renewable energy output. On this basis, considering the economic and environmental benefits of system operation, an optimal multi-objective dispatch model for renewable energy is established, and the multi-objective optimization problem is transformed into a single-objective optimization problem using weighting methods to reduce the complexity of the solution. Finally, a typical microgrid test system is used to verify the effectiveness and feasibility of the proposed method. The results of the numerical example show that the proposed model can achieve an accurate prediction of renewable energy sources, reduce the conservatism of traditional dispatch decisions, and balance economic and environmental benefits.

1. Introduction

The implementation of the national strategy of “peak carbon dioxide emissions” and “carbon neutrality” has promoted the rapid development of the renewable energy industry. The local development of renewable energy can reduce the use of traditional thermal power generation and mitigate environmental pollution. However, renewable energy generation is significantly influenced by natural conditions and exhibits considerable volatility and randomness [1,2]. Therefore, accurately forecasting renewable energy and load while maintaining the stability of the power system and ensuring users’ electricity demand holds significant research importance. Traditional load forecasting often employs classical mathematical models, leading to various classic prediction algorithms such as regression analysis and time series analysis [3,4]. With the rise of artificial intelligence algorithms, more and more studies have adopted such algorithms in the field of load forecasting [5,6]. However, as the construction and development of digital power grids progress, higher requirements for the accuracy of load forecasting are also being put forward [7].

The deviation in renewable energy forecasting does not possess mathematical statistical characteristics. To address the volatility and uncertainty on the generation side as well as the randomness on the demand side of renewable energy power systems, researchers have proposed the concept of elastic energy control (also known as flexible energy control or adaptive energy control), whose core lies in achieving an elastic balance between energy supply and demand by combining the generation side of renewable energy and energy storage devices, thus promoting the improvement of renewable energy utilization rates [8,9]. Elastic regulation on the generation side involves the elastic adjustment of power output from thermal power, hydropower, wind power, photovoltaic power, and other sources. The regulation of energy storage devices, on the other hand, provides dynamic balance to the power supply and demand by utilizing the energy storage and release characteristics of energy storage equipment, thereby enhancing the power system’s adaptability to the volatility and randomness of renewable energy, increasing renewable energy utilization efficiency, and further ensuring the safety and stable operation of the power grid. Taking into account the possibility of significant variations in electricity selling prices due to environmental conditions, under known operating conditions, reference [10] analyzes the different operating costs of thermal power units during different peak shaving stages, while reference [11] establishes a detailed energy consumption cost model for thermal power unit peak shaving, focusing on the analysis of the relationship between the economic efficiency of the system dispatch scheme and the depth of peak shaving for thermal power units.

In the realm of renewable energy generation, the precise modeling of weather conditions forms the bedrock for forecasting endeavors. Nonetheless, numerous atmospheric processes remain incompletely investigated, and the modeling of weather processes at the spatial scale pertinent to renewable energy stations is still in its nascent stages, primarily hinging on empirical and hypothetical mathematical formulations [12]. Furthermore, the evolution of weather systems needs to be described using high-dimensional, nonlinear, time-varying partial differential equations. Due to their inherent chaotic effects, the accuracy of extrapolation predictions will rapidly decrease as the forecast horizon increases. Studying wind power forecasting methods and reducing prediction errors can directly reduce wind power reserve arrangements, making it an effective approach for the rational arrangement of power generation plans [13]. Currently, the thinking behind wind farm output forecasting can be divided into two main categories: one is to first predict wind speed and then calculate the generation power using comprehensive information such as the turbine’s output characteristics and its spatial layout in the wind farm; the other is to directly predict the output of the wind farm. Specific algorithms can be divided into three types: statistical algorithms, physical methods, and combinations of the two [14,15,16]. Among them, for wind power forecasting serving short-term dispatch, previous research recommends using statistical algorithms. After decades of development, artificial neural network algorithms have matured, and relevant research studies have shown that they have good forecasting performance for wind speed or wind power forecasting, becoming one of the widely adopted research methods in wind power forecasting [17]. Optimizing generation plans and dispatch schemes is a primary means to improve wind power consumption capacity [18]. Reference [19] studied the optimal power flow of power systems with wind farms. To describe the impact of wind power randomness, it used a stochastic model to represent wind power output and established an optimal power flow model based on stochastic chance-constrained programming. The solution was obtained through a combination of stochastic simulation and genetic algorithms. However, this method is a static optimization that does not consider the limits of generator output ramp rates, which may render the calculation results infeasible in practice. Reference [20] studied the dynamic optimization dispatch problem of power systems with wind farms. Based on the error coefficient of wind power forecasting, it considered positive and negative spinning reserves for wind power to establish a dynamic economic dispatch model. However, the determination of the prediction error coefficient relies solely on experience, which may lead to unreasonable reserve arrangements in practical applications. Reference [21] modeled the dynamic economic dispatch problem based on stochastic chance-constrained programming, which considers the random distribution of wind power forecasting errors and provides new ideas for scheduling issues involving wind farms. Reference [22] employed a fuzzy decision-making model to perform fuzzy modeling and solution for wind power forecasting errors and wind power output separately. In addition, some researchers have also achieved good results by adopting a hybrid machine learning method [23] and a novel artificial intelligence method [24], effectively promoting the construction of the electricity market and the level of renewable energy consumption.

In terms of optimal power flow scheduling methods for power grids, reference [25] proposes an optimal power flow method for wind power scheduling that considers reserve costs and wind curtailment costs related to wind power uncertainty. Reference [26] introduces a reactive power optimization model for distribution networks that simultaneously considers static voltage stability margin and system network losses, handling the uncertainty of wind power output through a scenario-based approach. Reference [27] puts forward a reactive power dispatch method for distribution networks that takes into account the uncertainty of wind power and load, which handles the uncertainty of wind power and load through a cumulative probability power flow method. Reference [28] proposes a reactive power optimization method for distribution networks to optimize system network losses and voltage distribution, considering the impact of wind power prediction errors on the reactive power regulation capability of doubly fed wind turbines. Reference [29] presents a stochastic reactive power optimization method for distribution networks with wind power and photovoltaic power generation based on chance-constrained programming. This model aims to minimize the expected network losses while requiring that node voltage constraints are satisfied with a certain probability level. Reference [30] proposes a CVaR risk-based photovoltaic inverter dispatch model for the operation of low-voltage distribution networks with photovoltaic power generation, which provides auxiliary service supply to the distribution network. This model has good scalability and can be used for minute-level, hour-level, and day-ahead distribution network operation optimization. However, research in this field is still relatively scarce, and the following issues currently exist:

(1)

There is still a need to optimize the prediction accuracy of renewable energy power in real-world scenarios. Although neural network models based on data mining have achieved certain results, their ability to mine the time series characteristics of historical moments still has room for improvement.

(2)

The uncertainty of renewable energy power prediction can lead to operational instability and economic decline in the power system. However, the current economic dispatch of power systems has limited capabilities to respond to wind power prediction uncertainty, making it difficult to effectively cope with fluctuations in renewable energy output.

For comparison, the key innovations of this paper are summarized as follows:

(1)

This paper introduces an innovative prediction model that integrates FDA with RNN for the precise forecasting of the output of renewable energy sources such as wind power and photovoltaics. This fusion approach leverages the strengths of FDA in handling continuously varying data, enabling the effective capture and prediction of the volatility and uncertainty in renewable energy output.

(2)

Based on this prediction model, this paper further proposes an optimal multi-objective scheduling model for renewable energy, which comprehensively considers both the economic and environmental efficiency of system operation. By employing the weighting method, it transforms the complex multi-objective optimization problem into a single-objective optimization problem, thereby reducing the complexity of the solution while ensuring the feasibility and effectiveness of the scheduling strategy in practical applications.

2. Construction of Accurate Prediction Models for Renewable Energy

2.1. Functional Data Analysis Strategy

Taking wind power as an example, wind energy, as an environmentally friendly renewable energy source, has been widely applied. However, it is characterized by randomness and volatility, necessitating an accurate prediction of wind turbine output for rational scheduling. Currently, most research on wind power output prediction employs machine learning and intelligent algorithms to construct prediction models. Wind farms typically have multiple wind turbines, but the data used for general wind power output prediction are often aggregated from all turbines in a single farm or multiple farms, ignoring the independence of individual turbine outputs. This approach enhances the randomness of the training data and affects prediction accuracy. On the other hand, training and predicting the output of each turbine separately would require significant computational power and time, and the results of individual turbine predictions also contain high levels of uncertainty. For instance, if a turbine is shut down for a period of time, the overall prediction accuracy will be negatively impacted. Therefore, to balance the output of individual turbines and the overall output of the wind farm, this paper proposes a prediction model combining functional data analysis (FDA) and recurrent neural networks (RNNs).

FDA is a generic method for studying functional data with infinite dimensions over time. It treats functional data as a whole, encompassing techniques such as functional linear models, functional principal component analysis, and functional factor analysis. For multi-dimensional time series, FDA linearizes the discrete time series and then performs principal component analysis on the linearized functional family. The specific steps are described below:

• Functional Linear Model

Firstly, the basis function method is adopted, where discrete data are fitted into smooth functions through linear combinations of a sufficient number of known functions. Commonly used basis functions include Fourier basis functions and spline basis functions. Among them, spline basis functions are functions defined by multiple polynomial segments, often used for handling non-periodic functions. Due to the randomness of wind turbine output, this paper employs the B-spline basis function system. The B-spline basis function is a polynomial function defined within an interval divided into (i + 1) sub-intervals by nodes, where each sub-interval is a polynomial of a specified order m. Its recursive definition within the interval is as follows:

$$N_{i,0}(u)=\left\{\begin{array}{c}1, u_i\le u\le u_{i+1}\hfill \\ 0, otherwise\hfill \end{array}\right.$$

(1)

$$N_{i,p}(u)={\displaystyle \frac{u-u_i}{u_{i+p}-u_i}}{N}_{i,p-1}(u)+{\displaystyle \frac{u_{i+p+1}-u}{u_{i+p+1}-u_{i+1}}}{N}_{i+1,p-1}(u)$$

(2)

where u_i represents the interval nodes, and p is the degree of the basis function. $N_{i,p}(u)$ is defined as the p-th degree B-spline for the i-th segment.

2.

Functional Principal Component Analysis

Functional principal component analysis reduces the dimensionality of large amounts of information into a few representative components, minimizing the interference caused by information overlap and facilitating the analysis of multidimensional data.

Assuming a dataset has N dimensions, the original data are denoted as $x_i(t),t\in T,i=1,2,\cdots ,N$. The mean and variance of the original data are then defined as:

$$\overline{x}(t)={\displaystyle \frac{{\displaystyle \sum _{i=1}^N{x}_i(t)}}{N}}$$

(3)

$$Va{r}_i(t)={\displaystyle \frac{{\displaystyle \sum _{i=1}^N{[x_i(t)-\overline{x}(t)]}^2}}{N-1}}$$

(4)

The total variance of the original data’s p-dimensional random variable is:

$$tr(V)={\displaystyle \sum _{i=1}^{N}Va{r}_i(t)}$$

(5)

The ratio of the variance of the k-th principal component to the total variance is called the contribution rate of the k-th principal component. If the cumulative contribution rate of the current k principal components reaches more than 85%, it indicates that the first k principal components can already represent the information of the original data relatively comprehensively. In traditional principal component analysis, coefficient vectors are used to represent the weights of different components on the original data, while in functional data, the coefficient vectors become weight functions $\xi (s)$. The principal component scores are denoted as:

$$z_i={\displaystyle \int \xi (t)}{x}_i(t)dt$$

(6)

The solution for functional principal components involves finding a set of orthogonal weight functions $\xi (s)$, where the covariance between functional data $x_i(t)$ and $x_i(s)$ is defined as:

$$v(s,t)={\displaystyle \frac{{\displaystyle \sum _{i=1}^N{x}_i(t)x_i(s)}}{N}}$$

(7)

The weight function ξ(s) can be solved through the following characteristic equation, where λ represents the non-negative eigenvalue:

$${\displaystyle \int \xi (t)}v(s,t)dt=\lambda \xi (s)$$

(8)

The commonly adopted method to solve this characteristic equation is the basis function expansion method. Given that the original data are represented by a system of K basis functions:

$$x_i(t)={\displaystyle \sum _{k=1}^K{c}_{ik}{\varphi }_k(t)}$$

(9)

Matrix representation is $X=C\varphi$, and the matrix representation of covariance is:

$$v(s,t)={\displaystyle \frac{\varphi (s)\text{'}C\text{'}C\varphi (t)}{N}}$$

(10)

Assuming the matrix representation of the basis function expansion for the weight function is $\xi (t)=\varphi (t)\text{'}b$ and b represents the expansion coefficients of the weight function, the characteristic equation can be transformed into:

$${\displaystyle \int \frac{\varphi (s)\text{'}C\text{'}C\varphi (t)\varphi (t)\text{'}b}{N}}dt=\lambda \varphi (s)\text{'}b$$

(11)

By first finding the expansion coefficients of the weight function, we can then obtain the weight function itself.

2.2. Recurrent Neural Network Prediction Algorithm

Power prediction serves as an important basis for grid dispatch, and thus it is necessary to forecast the renewable energy power at the dispatch time before energy dispatch is conducted. The accuracy of short-term prediction is related to the algorithm used for forecasting. Therefore, to improve the prediction accuracy, this paper proposes a forecasting algorithm based on time series and Seq2Seq network.

Seq2Seq is a special kind of RNN. In traditional neural networks, different elements are independent of each other, and signals are transmitted between the input layer, hidden layer, and output layer through fully connected ways, with no signal transmission among nodes within the same layer. However, when dealing with time series issues, data at different time nodes are interrelated, making traditional neural networks no longer applicable. In such scenarios, recurrent neural networks, as shown in Figure 1, are typically employed.

As can be seen from Figure 1, an RNN also includes an input layer x, a hidden layer h, and an output layer y, and different hidden layers are interconnected. For the state of the hidden layer h_t at time t, there is:

$$h_t=f(U{x}_t+W{s}_{t-1})$$

(12)

The output y_t at time t is:

$$y_t=g(V{h}_t)$$

(13)

where U, W, and V are the shared parameters used for signal transmission in the network, and f and g are the activation functions for the hidden layer and output layer, respectively. As can be seen from Figure 1, in the classic RNN structure, the sequence dimensions of the input and output are the same, which does not align with the application scenario of this paper. Therefore, the paper introduces the Seq2Seq network, whose basic structure is shown in Figure 2.

Seq2Seq consists of an Encoder and a Decoder. At time t, Seq2Seq sequentially inputs the input sequence X = {x₁, x₂, …, x_m} into the input end of the Encoder. Through the pre-set nonlinear transformation units in the Encoder, an intermediate vector is obtained and stored. Then, the Decoder utilizes the stored information and the output values from the previous N time steps, t − 1, t − 2, …, t − N, to obtain the output y_t. The mathematical expression of the Seq2Seq model is as follows:

$$\left\{\begin{array}{c}c=f(x_1,x_2,\cdots ,x_m)\\ y_t=g(c,y_1,y_2,\cdots ,y_{t-1})\end{array}\right.$$

(14)

As can be seen from Equation (14), the introduction of the Encoder–Decoder allows for variable input and output sequences, thus ensuring the usability of the RNN network in power prediction scenarios. The nonlinear transformation function of the Encoder can be selected based on the application scenario of the RNN network. In this paper, the GRU (gate recurrent unit) function is used. GRU consists of three gates: the update gate r, the output gate h, and the reset gate z. The flow of signals in GRU is as follows:

$$\left\{\begin{array}{c}{r}_t=\sigma (W_r{x}_t+U_r{h}_{t-1}+b_r)\\ z_t=\sigma (W_z{x}_t+U_z{h}_{t-1}+b_z)\\ h_t^1=\tanh (W_h{x}_t+U_h(r_t{h}_{t-1})+b_h)\\ h_t=(1-z_t)h_{t-1}+z_t{h}_t^1\end{array}\right.$$

(15)

3. Microgrid Dispatch Model

The typical microgrid structure with multiple types of renewable energy sources is shown in Figure 3, which includes renewable energy generation equipment such as photovoltaic and wind power, diesel generators, and battery energy storage systems. The microgrid can achieve off-grid/grid-connected operation through the grid-connected circuit breaker.

3.1. Objective Function

For the operation of a microgrid, its main objective is to minimize the total operating cost. In addition, with the development of low-carbon power systems, power system operators are gradually paying attention to environmental benefits. Therefore, this paper establishes the objective function from both economic and environmental perspectives.

(1)

Economic Optimization Objective Function.

This objective aims to minimize the operating cost of a microgrid with multiple types of renewable energy sources. Specifically, it is expressed as:

$$\min f_{EC}=C_E+C_F+C_{om}$$

(16)

where C_E represents the cost of purchasing electricity from the distribution network; C_F represents the fuel cost; and C_om represents the maintenance cost.

The detailed calculation formulas for each part are shown in Equations (17)–(19) as follows.

$$C_E={\displaystyle \sum _{t=1}^T{c}_e^t{P}_e^t\Delta t}$$

(17)

where $c_e^t$ represents the electricity price of the distribution network during time period t; $P_e^t$ represents the input power from the upper-level grid during time period t; and $\Delta t$ represents the optimization time interval, which is usually taken as 1 h.

$$C_F={\displaystyle \sum _{t=1}^T{c}_{fuel}}{\displaystyle \frac{P_{mt}^t}{H{\eta }_{mt}}}\Delta t$$

(18)

where $c_{fuel}$ represents the unit fuel cost; ${\eta }_{mt}$ is the power generation efficiency of the diesel generator; $P_{mt}^t$ is the output power of the diesel generator during time period t; and H is the calorific value of unit fuel combustion.

$$C_{om}={\displaystyle \sum _{t=1}^T[{\lambda }_{mt}{P}_{mt}^t+{\lambda }_{pv}{P}_{pv}^t+{\lambda }_{wt}{P}_{wt}^t+{\lambda }_{bess}(P_{ch}^t+P_{dis}^t)]}$$

(19)

where λ_mt, λ_pv, λ_wt, and λ_bess represent the maintenance cost per unit of output power for the diesel generator, photovoltaic, wind turbine, and battery energy storage system, respectively; $P_{pv}^t$ and $P_{wt}^t$ represent the photovoltaic and wind turbine power generation during time period t; and $P_{ch}^t$ and $P_{dis}^t$ represent the charging and discharging power of the battery energy storage system during time period t.

(2)

Environmental Optimization Objective Function.

The objective is to minimize the pollutant emissions from the microgrid, which mainly originate from the diesel generator and the power generation of the upper-level grid. The relevant mathematical model can be expressed as:

$$\min f_{EN}={\displaystyle \sum _{k=1}^M(a_k{P}_{mt}^t+B_k{P}_e^t)\Delta t}$$

(20)

where $a_k$ represents the emission coefficient of the k-th pollutant per unit of electricity generated by the diesel generator; $B_k$ represents the average emission coefficient of the k-th pollutant per unit of electricity transmitted by the distribution network; and M represents the number of pollutant types.

3.2. Constraints

When a microgrid is operating, it needs to satisfy the power balance constraint, as shown in Equation (21).

$$\left\{\begin{array}{c}{u}_{ch}^t{P}_{ch}^{\min }\le P_{ch}^t\le u_{ch}^t{P}_{ch}^{\max }\\ (1-u_{ch}^t)P_{dis}^{\min }\le P_{dis}^t\le (1-u_{ch}^t)P_{dis}^{\max }\\ S_{ES}^t=S_{ES}^{t-1}+(P_{ch}^t{\eta }_{ch}+P_{dis}^t/{\eta }_{dis})\Delta t\\ S_{ES}^{\min }\le P_{ch}^t\le S_{ES}^{\max }\end{array}\right.$$

(21)

where $u_{ch}^t$ is a 0–1 binary variable representing the charging status of the battery energy storage system, with a value of 1 during charging and 0 in other states. $P_{ch}^{\min }$ and $P_{ch}^{\max }$ represent the minimum and maximum charging power of the battery energy storage system, respectively. $P_{dis}^{\min }$ and $P_{dis}^{\max }$ represent the minimum and maximum discharging power of the battery energy storage system, respectively. $S_{ES}^t$ and $S_{ES}^{t-1}$ represent the energy stored in the battery at time t and t − 1, respectively. ${\eta }_{ch}$ and ${\eta }_{dis}$ represent the charging and discharging efficiency of the bidirectional converter of the energy storage system at time t.

The equipment in the microgrid also needs to satisfy certain operational constraints. The specific expressions are as follows:

$$\left\{\begin{array}{c}{P}_{pv}^{\min }\le P_{pv}^t\le P_{pv}^{\max }\\ P_{wt}^{\min }\le P_{wt}^t\le P_{wt}^{\max }\\ P_{mt}^{\min }\le P_{mt}^t\le P_{mt}^{\max }\end{array}\right.$$

(22)

where $P_{pv}^{\max }$ and $P_{pv}^{\min }$ represent the upper and lower limits of the photovoltaic output power; $P_{wt}^{\max }$ and $P_{wt}^{\min }$ represent the upper and lower limits of the wind turbine output power; and $P_{mt}^{\max }$ and $P_{mt}^{\min }$ represent the upper and lower limits of the diesel generator output power.

For the above multi-objective scheduling model with multiple types of renewable energy systems, its economic and environmental objectives are processed using the weighting method, as shown in Equation (23). Then, the mixed-integer programming model is further solved using the commercial software CPLEX 12.1.0.

$$\min f_{total}={\omega }_{EC}{f}_{EC}+{\omega }_{EN}{f}_{EN}$$

(23)

4. Case Study

To demonstrate the effectiveness and accuracy of the proposed method in this paper, a simulation analysis was conducted using an operational dataset of a microgrid. The structure of the microgrid is shown in Figure 3. The operation and maintenance costs of the photovoltaic, wind turbine, diesel generator, and battery energy storage system are 0.65, 0.8, 0.7, and 0.75 USD/kW, respectively. The types of pollutants emitted by the upper-level grid and diesel generator mainly include NO_X, CO₂, SO₂, and CO. For these four types of emissions, the emission coefficients of the upper-level grid are 2.85 g/kWh, 585 g/kWh, 4.25 g/kWh, and 6.2 g/kWh, while the emission coefficients of the diesel generator are 3.8 g/kWh, 650 g/kWh, 4.8 g/kWh, and 7.4 g/kWh.

4.1. Short-Term Renewable Energy Forecasting Accuracy Validation

To verify the effectiveness and accuracy of the proposed forecasting model combining functional data analysis and RNN, this paper compares it with other conventional methods, specifically M1 (method proposed in reference [17]), M2 (method proposed in reference [19]), and M3 (method proposed in reference [27]). Prediction analyses were conducted for four typical scenarios of wind power and photovoltaic output, and the relevant results are shown in Figure 4 and Figure 5 below.

It should be noted that the data in Figure 4 and Figure 5 are sampled at different time steps because the training samples of the photovoltaic and wind power datasets used are collected at different time scales. Therefore, the time compensation for the data output from the training prediction is also different and needs to be consistent with the training samples. In Figure 4, due to the dense sampling points (i.e., the time step is too short), there appears to be no significant difference. As shown in Figure 5, there is a significant difference in prediction accuracy among different methods. There are several main reasons for this phenomenon. Different prediction models are based on various mathematical principles and algorithms, such as statistical models, physical models, and artificial intelligence models. These models exhibit different levels of adaptability and effectiveness when dealing with wind power prediction problems, which can lead to variations in prediction accuracy. Model complexity is one of the crucial factors affecting prediction accuracy. Overly simplistic models may not fully capture the complex and variable characteristics of wind power, while excessively complex models may suffer from overfitting, resulting in decreased prediction performance on new data. Additionally, the generalization ability of the model is also a significant factor determining prediction accuracy. Furthermore, it is important to note that the time scale of the prediction model directly impacts prediction accuracy. Generally, shorter prediction time scales often yield higher prediction accuracy because wind power variations are relatively more stable and predictable in the short term. However, different application scenarios have different requirements for prediction time scales, so it is necessary to select an appropriate prediction time scale based on actual circumstances. Similarly, the sampling time resolution of the dataset is also a crucial factor affecting prediction accuracy. High-resolution data can more accurately reflect the instantaneous variation characteristics of wind power, thereby improving prediction accuracy. However, high-resolution data also imply a larger data processing volume and higher computational costs. Data quality directly affects the training effectiveness and prediction accuracy of the prediction model. If the dataset contains issues such as noise, missing values, and outliers, it will lead to a decrease in the performance of the prediction model. To more intuitively demonstrate the accuracy differences among various methods,

Table 1. Average forecasting accuracy using different methods.

Different Methods	Average Accuracy of Wind Power Forecasting/%	Average Accuracy of Photovoltaic Power Forecasting/%
The proposed method	95.4	96.6
M1	92.3	95.2
M2	93.5	94.6
M3	93.7	94.9

provides the specific accuracy under different scenarios.

The data in Table 1 are averaged from 100 datasets. For wind power scenarios, the maximum and minimum prediction accuracies of the proposed method are 98.4% and 92.6%, respectively; for photovoltaic power scenarios, the maximum and minimum prediction accuracies of the proposed method are 97.9% and 93.5%, respectively. As seen in Table 1, in the field of wind power and photovoltaic forecasting, the prediction model combining FDA and RNN outperforms general reinforcement learning or machine learning models in terms of accuracy, primarily due to its strong capability in handling time series data. RNN is a neural network model specifically designed for processing time series data, capturing temporal dependencies and dynamic changes in the data through its internal recurrent structure. This characteristic makes RNN particularly effective in time series forecasting tasks such as wind power and photovoltaic forecasting. In contrast, general machine learning models (such as linear regression and decision trees) may not fully capture the dynamics and long-term dependencies in the data when processing time series data, thereby affecting prediction accuracy.

Meanwhile, FDA also holds significant advantages. FDA is a powerful data analysis method, especially suitable for handling functional data with continuity and smoothness. In wind power and photovoltaic forecasting, FDA can more accurately capture the continuous processes of wind speed, light intensity, and other variables, extracting features closely related to the prediction target. When FDA is combined with RNN, the functional features extracted by FDA can enhance the input representation of RNN, further improving the model’s predictive ability.

Moreover, RNN models possess strong learning capabilities. With complex network structures and robust learning abilities, RNN can handle complex nonlinear relationships and high-dimensional data. This enables RNN to more accurately fit the complex patterns in wind power and photovoltaic data. In contrast, general reinforcement learning models may be limited by their simple model structures and learning abilities, unable to fully adapt to the complexity and dynamics of wind power and photovoltaic data. Through its internal recurrent structure, RNN can process input sequences of different lengths and adapt to varying data distributions. This grants RNN strong adaptability and generalization capabilities in wind power and photovoltaic forecasting. General machine learning models may perform poorly when dealing with input sequences of varying lengths or data with different distributions, thus limiting their effectiveness in practical applications.

4.2. Optimality Verification of the Scheduling Model

This article employs a multi-objective optimization approach and utilizes the weighting method to transform the multi-objective optimization problem into a single-objective optimization problem. This approach reduces the complexity of the solution while balancing economic and environmental considerations.

Table 2. Comparison of optimization objectives of different models.

Model	Operating Cost/USD	Pollutant Emissions/kg
Economic Optimality	1785	1958
Environmental Optimality	2332	1325
Algorithm Proposed in This Article	1856	1437

provides a comparison of different optimization objective functions.

As observed in Table 2, compared to the single-objective dispatch strategy optimized for economic efficiency, the proposed multi-objective dispatch strategy in this article increases the operating cost by 3.83% but reduces pollutant emissions by 36.3%. On the other hand, when compared to the single-objective dispatch strategy optimized for environmental friendliness, although the pollutant emissions increase by 7.8%, the operating cost decreases by 25.6%. This demonstrates that the proposed multi-objective dispatch strategy can effectively reduce the operating cost of the microgrid while also minimizing pollutant emissions. For larger-scale test systems, the constraints to be considered are largely the same. Taking a regional distribution network system as an example, only the power balance constraint needs to be replaced with a generalized AC power flow constraint. The proposed method can still ensure the existence of a feasible solution under the premise of a rapid solution, which demonstrates its good robustness and applicability.

5. Conclusions

This study addresses the challenges posed by the volatility and uncertainty of wind power to power system dispatch by proposing an optimized renewable energy dispatch strategy based on an accurate wind power forecasting model. By constructing a predictive model combining functional data analysis (FDA) and recurrent neural networks (RNNs), the model successfully achieves the forecasting of renewable energy output, providing a reliable basis for power system dispatch. Furthermore, considering the economic and environmental requirements of system operation, this article establishes an optimal multi-objective dispatch model for renewable energy, effectively balancing the economic and environmental benefits of the power system.

Verified in a typical microgrid test system, the proposed method has proven its effectiveness and feasibility. Experimental results show that the wind power forecasting model presented in this article not only improves forecasting accuracy and reduces forecasting errors, but also significantly reduces the conservatism of traditional dispatch decisions, providing a more flexible and efficient solution for power system dispatch. Through analysis, the prediction accuracy of the proposed method can be maintained above 95%. Compared with conventional methods, the prediction accuracy can be improved by up to 3.1%. Based on this, compared with a single scheduling model, the operating cost and carbon emissions of the proposed scheduling model are reduced by 25.6% and 36.3%, respectively. Meanwhile, the optimal multi-objective dispatch model for renewable energy maximizes economic benefits while fully considering environmental factors, providing strong support for the sustainable development of power systems. In the future, we will further research and explore more advanced wind power forecasting technologies and optimized dispatch methods to cope with the changing needs and challenges of power systems.