Optimal Scheduling of the Active Distribution Network with Microgrids Considering Multi-Timescale Source-Load Forecasting

Abstract

Integrating distributed generations (DGs) into distribution networks poses a challenge for active distribution networks (ADNs) when managing distributed resources for optimal scheduling. To address this issue, this paper proposes a day-ahead and intra-day scheduling approach based on a multi-microgrid system. It starts with a CNN-LSTM-based generation and load forecasting model to address the impact of generation and load uncertainties on the power grid scheduling. Then, an optimal day-ahead and intra-day scheduling framework for ADN and microgrids is introduced using predicted generation and load information. The day-ahead scheduling is responsible for optimizing the power interactions between ADN and the connected microgrids, while intra-day scheduling focuses on minimizing the operational costs of microgrids. The effectiveness of the proposed scheduling strategy is verified via case studies performed on a modified IEEE 33-node ADN. The results show that the network loss of ADN and the operation costs of microgrids are reduced by 17.31% and 32.81% after the microgrid is integrated into the ADN. The peak-valley difference in microgrids decreased by 13.12%. The simulation shows a significant reduction in operational costs and load fluctuations after implementing the proposed day-ahead and intra-day scheduling strategy. The seamless coordination between the day-ahead scheduling and intra-day scheduling allows for the precise adjustment of transfer power, alleviating peak load demand and minimizing network losses in the ADN system.

1. Introduction

From the end of the 20th century, the bud of the new energy technology revolution began to grow and develop. The development and utilization of clean energy and other renewable energy resources have sparked the wave of the global energy revolution [1,2,3]. Responding to the national initiative to promote renewable energy, distributed power generation units have been integrated into the distribution grid, boosting the “grid resilience” of the ADN [4]. However, the integration of large-scale DGs changes both the configuration and efficiency of the ADN. The variable power output from DGs can modify the power flow direction, leading to significant voltage fluctuations. If the power supply is not controlled and managed, its stability will continue to deteriorate. The optimal scheduling of ADN actively plays its attributes of active control and active regulation to achieve a safe, reliable, high-quality, and economic power supply. Currently, optimal scheduling research on ADN theory has approached perfection. In Ref. [5], a mixed-integer linear programming model improves the load coefficient of the power grid by batch-scheduling residential, commercial, and industrial loads under various operational constraints. Ref. [6] integrates incentive-based demand response planning with reconfiguration methods into day-ahead scheduling of microgrids, greatly reducing operating costs and network losses. Ref. [7] establishes a three-level bidding scheduling framework. The first two levels optimize the cost for load aggregators, while the second level optimizes scheduling based on load priority. Ref. [8] combines customer-oriented and public utility demand-side management strategies to solve energy management issues in microgrids, utilizing a Black Widow optimization algorithm for resolution. Ref. [9] investigates the optimal operation and economic scheduling of a multi-microgrid active distribution system. The author analyzed the power exchange between microgrids and the charging/discharging behavior of energy storage systems to achieve overall system economy and reliability. The research results are of great significance for guiding the operation and management of actual microgrids. Ref. [10] introduces a distributed Agent architecture aimed at suggesting an optimal scheduling approach for ADN. This method is based on multi-agents working together to enhance the efficiency of ADN. Ref. [11] transforms multi-objective optimization into a single-objective problem from the aspects of power quality, power regulation, peak shaving, and valley filling of ADN. However, this paper does not consider the influence of a multi-time scale solution on the voltage deviation of ADN.

Renewable energy generation often exhibits variability. Load demand also varies. This situation necessitates that distribution networks adopt more flexible scheduling strategies. Such strategies assist these networks in adapting to uncertainties. They guarantee both reliability and cost-effectiveness in power supply. Ref. [12] proposes an optimal scheduling strategy for a virtual power plant based on Conditional Value at Risk (CvaR) distribution-robust optimization. This strategy aims to maximize the revenue of the Virtual Power Plant by aggregating distributed energy storage and photovoltaic (PV) systems on the demand side while considering the uncertainty of renewable energy sources and loads. Ref. [13] considers renewable energy and load uncertainty and conducts distributed optimal operation research on the PV-energy storage-load microgrid. By employing probability theory and stochastic optimization methods, the authors propose a new optimization algorithm to achieve the optimal operation of microgrids in uncertain environments. The research findings contribute to enhancing the flexibility and adaptability of microgrids. Ref. [14] addresses the multiple uncertainty problem of DG by using a comprehensive norm made up of the 1-norm and infinity-norm as the distribution information set for uncertain probabilities. It simulates the DG scenario based on the generated adversarial network of Wasserstein distance and gradient penalty. Ref. [15] proposes a distributed robust optimization algorithm based on Wasserstein distance. This approach resolves the optimization problem related to the uncertainty of generation, load, and storage, and it can utilize dynamic electricity pricing to tackle energy scheduling between the distribution network and microgrid. Ref. [16] develops a source-load uncertainty analysis framework based on a time series joint scheduling strategy, adopting the sample weighted average. Currently, research on generation and load uncertainty exhibits notable deficiencies. These include limitations in accuracy arising from simplified model assumptions, a restricted capacity to address complex issues, and insufficient verification of practical applications. Such factors undermine the validity and applicability of research findings in real-world contexts.

Despite the significant achievements in the optimization scheduling of ADNs, there are still some research gaps and shortcomings. Firstly, existing research mostly focuses on the optimization scheduling problems of a single or a few microgrids, with less research on ADNs with large-scale and complex network structures. Secondly, the development and utilization of demand response resources still need to be strengthened, especially in the context of emerging technologies such as electric vehicles and energy storage. In addition, the impact of renewable energy and load uncertainties on the optimization scheduling of ADNs cannot be ignored, requiring further research on robust optimization, stochastic planning, and other methods to address these uncertainties. Since microgrids are more adaptable and flexible compared to conventional ADNs, they have a broader range for development [17,18,19,20]. There has been extensive research on the optimal placement of microgrids in China, with an increasing number of projects being carried out to confirm the viability and efficiency of this placement [21]. In 2011, the State Grid introduced China’s microgrid technology system for the first time. By 2021, renewable energy production in the country accounted for 29.7% of the total electricity generation. The advancement of microgrid technology plays a vital role in accommodating the rapid growth of DGs [22]. For example, a microgrid with PVs and energy storage systems was developed to ensure a stable power supply to Wuyuan Ba in Xiamen, China. This system integrates various technologies to enhance automation and information technology comprehensively. The successful implementation of this trial project has significantly improved power supply reliability and quality in the area, offering vital support for both primary and secondary electricity demands [23].

Microgrids can meet the diverse needs of users for electrical energy quality and can separate from the ADN system in the face of natural disasters, providing users with safe, reliable, and stable electrical energy. However, the uncertainty of the output of large-scale distributed power sources leads to an increase in short-circuit currents in the system, making it unable to provide stable and reliable electrical energy to the distribution grid. This paper combines multi-time scale concepts and establishes a day-ahead and intra-day scheduling model for ADNs and microgrids. According to the coordination optimization scheduling of day-ahead scheduling and intra-day scheduling and the use of optimization algorithms, the simulation results of the model are achieved, verifying its feasibility and effectiveness.

Based on the above background, this paper proposes a generation and load forecasting model based on multi-time and space scales to restrain the influence of generation and load uncertainty on ADNs. Taking node balance as the spatial scale and regulation time window as the time scale, the CNN-LSTM algorithm predicts future load changes. At the same time, this action can help to find the optimal scheduling strategy. This paper examines the generation and load characteristics of ADN as the foundational analysis and develops the day-ahead and intra-day scheduling model for ADN and microgrids. The day-ahead scheduling aims to optimize the interactive power between the main network and the microgrid. The intra-day scheduling aims to optimize the operating economic cost of the microgrid. At the same time, the corresponding constraint conditions are put forward. The GA-PSO algorithm is utilized to solve the model. The control parameters are adjusted adaptively to quickly find the global optimal scheme. In summary, the innovations of this paper are listed as follows:

(1)

This paper proposes a generation and load forecasting model based on the CNN-LSTM model. The generation and load operation data are selected for spatial reconstruction. The Convolutional Neural Network (CNN) model extracts the input variables. The Long Short-Term Memory (LSTM) network can obtain the advantages of internal relations between data. The goal is to forecast the data for generation and load operations in the ADN;

(2)

To solve the problem of grid connection between microgrid and ADN, a day-ahead and intra-day scheduling strategy of ADNs under multiple time scales is proposed. Day-ahead scheduling strategy optimizes the transferring power between ADN and the microgrid, while the intra-day scheduling focuses on optimizing the microgrid’s operating economic cost.

The rest of the paper is organized as follows: Section 2 introduces a multi-timescale scheduling framework for ADNs with microgrids connected. Section 3 includes the establishment of a generation and load forecasting model based on CNN-LSTM. Section 4 constructs a day-ahead and intra-day scheduling model for ADNs with microgrids, which can operate efficiently under multiple time scales. The day-ahead scheduling optimizes the transferring power between the ADNs and the connected microgrids, while the intra-day scheduling optimizes the microgrid’s operating economic cost in a rolling-horizon manner. Section 5 presents a simulation case based on the improved IEEE 33-node network. Finally, Section 6 concludes this paper.

2. The Multi-Timescale Scheduling Strategy for ADNs with Microgrids

To maximize the integration of DGs while considering the source-load uncertainties, this paper proposes a multi-timescale scheduling strategy for ADNs with microgrids. It starts with a CNN-LSTM model that is capable of predicting the source-load power curves at multi-timescales. Then, it introduces a day-ahead and intra-day scheduling model for ADN and microgrids that utilizes predicted generation and load values. The day-ahead scheduling focuses on optimizing the transfer of power between ADN and the connected microgrids, while intra-day scheduling aims to optimize the economic operating cost of the microgrid in a rolling-horizon manner. Therefore, by integrating research findings on optimization and scheduling methods within the generation and load region, it is feasible to implement “intra-zone optimization” followed by “inter-zone coordination” to maximize the use of traditional power sources.

However, while operating at the intraday timescale, wind and solar energy systems must exhibit a high level of responsiveness to optimize generation and load across a wide area. The previous strategy of coordinating and optimizing generation may only partially meet the real-time optimization demands for intra-day scheduling, reducing the efficiency of intra-day optimization scheduling. Therefore, intra-day scheduling mitigates the impact of variability in generation and load output on fault recovery in ADNs through rolling optimization. During the intra-day phase, the anticipated generation and load output for the next hour is forecasted, and the initial 15-min optimization strategy is applied for scheduling. This process then repeats in the subsequent phase to refine the intra-day plan. As each region optimizes its decisions independently within the power grid, there is also an exchange of active regulation plans among regions to achieve coordinated and optimized scheduling. This method enhances the scheduling of power generation and load balance, accommodating rapid fluctuations in generation and load power, thus improving overall grid efficiency.

(1)

On the day-ahead planning horizon, the objective of scheduling is to reduce the network losses within the ADN. The control variables include flexible loads, DGs, and energy storage systems integrated within the ADN. When microgrids are connected to the ADN, the operational capacities of all flexible resources, along with the power exchanges between the ADN and the microgrids, are considered decision-making parameters. Utilizing forecasts for generation, demand, and PV output, a comprehensive scheduling strategy is formulated every 24 h.

(2)

The scheduling objective of the intra-day optimization model is to minimize the economic operation cost. It focuses on optimizing the scheduling scheme of the microgrid. This utilizes the results of day-ahead scheduling to determine the minimum economic cost of the microgrid in grid-connected mode and establishes the intra-day generation and load scheduling model for each microgrid. Based on this, the generation and load real-time partition coordination optimization scheduling model for ADN is proposed. Considering the randomness and real-time performance of intra-day controllable loads, rolling optimization is employed for intra-day optimization control.

After considering all aspects, this paper proposes a more specific framework for optimizing and coordinating generation and load scheduling. The framework, illustrated in Figure 1, consists of two parts for coordinated optimization and scheduling. This paper demonstrates that the proposed model will effectively address the inherent variability and uncertainty of power output from DGs, thus significantly enhancing the efficiency of power scheduling schemes. Furthermore, by incorporating predicted generation and load values, the suggested day-ahead and intra-day scheduling model for ADN and microgrids is proven to demonstrate optimal performance.

3. A Multi-Timescale Source-Load Prediction Model and Its Validation

The electricity produced by DGs, such as wind turbines and solar panels, can be affected by various factors, including the climate, environment, and geographical location. This uncertainty can make it difficult to control and operate. In that case, it may become necessary to disconnect DGs from the power grid. The purpose is to prevent any further damage or destruction to the system. The withdrawal of the system will result in a decrease in voltage due to changes in the system’s power. This change will have a significant impact on the distributed network.

In this chapter, this paper focuses on optimizing the scheduling of DGs in a microgrid through proper integration [24]. By considering the characteristics of wind power generation, PV power generation, battery storage, and flexible loads, we have developed a daily scheduling model for the microgrid. This model coordinates the output of DGs to maintain power balance within the microgrid and achieve optimal operational efficiency. This research provides a theoretical foundation for the subsequent chapter on the day-ahead and intra-day scheduling of ADNs at multiple time scales [25].

3.1. Characteristic Analysis of Microgrid

Generally speaking, the microgrid is a micro-network composed of small distributed power generation units scattered in a specific area. The general structure of a microgrid is shown in Figure 2. Microgrids and ADNs are connected to exchange electric energy, prioritizing providing electric energy to internal loads and meeting the electric energy demand of internal loads in the system. When the micro-source is short of power supply, the microgrid provides additional electric energy. On the contrary, when the power is surplus, it can provide power to the ADN. The microgrid promotes the peak shaving and valley filling of the power grid through the flexible interaction between power supply and load. It maximizes the benefits between the microgrid and the ADN.

3.2. A CNN-LSTM-Based Multi-Timescale Source-Load Prediction Method

This section utilizes MATLAB programming to analyze the correlation between grid operation state, PV power output, wind turbine output, and load. The traditional time series prediction method needs to extract their deep characteristics promptly. The model proposed in this paper is a day-ahead scheduling model, which can be applied to different time scales. This paper will take the historical data of PV, wind turbine output, and load for spatial reconstruction, and the CNN model will extract the input variables. The LSTM network can obtain the advantages of internal relations.

3.2.1. CNN Model

CNN model includes convolution computation and has a depth structure. The CNN model also has a convolution layer and pooling layer structure, unlike other neural networks. The convolution layer is responsible for extracting the local features of the data. The convolutional layer is characterized by a weight-sharing structure, where the same feature map utilizes identical convolutional kernels during feature extraction. It efficiently obtains effective representations from the original data by alternately using convolutional and pooling layers, thereby automatically extracting local features of the data and constructing a complete feature vector [26].

3.2.2. LSTM Model

Traditional recurrent neural networks (RNN) do not easily extract long sequence data, leading to gradient instability. The LSTM network is improved based on RNN. It introduces a new internal state and logic gate control mechanism. The former controls the data transmission path through linear circulation, which can extract the internal distribution characteristics of longer time series data. The forget gate integrates input $x_t$ with the state memory unit $c_{t-1}$ and the intermediate output $h_{t-1}$ to determine the portion of the state memory unit to forget, which helps in retaining useful information while preventing the propagation of unnecessary information from the previous time step. The roles of the input gate and output gate are to read the data and transmit the processed data to the next time step, with the calculation formula as follows:

$$\{\begin{array}{l}{i}_t=\sigma (W_{xi}{x}_t+W_{hi}{h}_{t-1}+b_i)\\ f_t=\sigma (W_{xf}{x}_t+W_{hf}{h}_{t-1}+b_f)\\ o_t=\sigma (W_{xo}{x}_t+W_{ho}{h}_{t-1}+b_o)\\ {\overline{c}}_t=\tanh (W_{xc}{x}_t+W_{hc}{h}_{t-1}+b_c)\\ c_t=f_t\odot c_{t-1}+i_t\odot {\overline{c}}_t\\ h_t=o_t\odot \tanh (c_t)\end{array}$$

(1)

where $f_t$, $i_t$, ${\overline{c}}_t$, $o_t$, $h_t$ and $c_t$ represent the states of the forget gate, input gate, input node, output gate, intermediate output, and state unit at time t, respectively; $W_{xi}$, $W_{xf}$, $W_{xo}$, and $W_{xc}$ are the weights of input gate, forgetting gate, output gate, and cell state, respectively; $W_{hi}$, $W_{hf}$, $W_{ho}$, and $W_{hc}$ are the weights of input gate, forgetting gate, output gate, and cell state, respectively; $b_i$, $b_f$, $b_o$, and $b_c$ are the offset vectors of each part; and ⊙ means that the elements between vectors are multiplied according to the position of the response. $\sigma (·)$ represents the sigmoid activation function and $\tanh (·)$ represents a hyperbolic tangent activation function.

CNN-LSTM combines the advantages of both CNN and LSTM networks, taking multi-dimensional time series composed of multiple features and sub-sequences decomposed by mode as input data. Each row T represents a specific time, each column M represents a specific feature value within time step T, and each column N represents the mode decomposition index. Then, after convolution and pooling operations, spatial features are obtained. LSTM takes the obtained one-dimensional sequence as input, connects it with fully connected layers, and finally performs regression prediction on actual power data by combining the predicted values of spatial features.

3.2.3. Establishment of the CNN-LSTM-Based Source-Load Prediction Model

This paper takes the CNN-LSTM combined model to predict the power of wind turbines, PVs, and loads connected to the power grid. Compared with CNN and LSTM models, the proposed model has an outstanding ability to extract data features and an excellent ability to process time series. In the combined model, the CNN network is first used to process the historical data of DGs. After being extracted by CNN into time series, the feature quantities are fed into LSTM for generation and load forecasting.

Firstly, the original dataset is obtained, and the correlation coefficient matrix between the target power grid and the DG output is calculated by using the microgrid operation state data and the DG output data. Figure 3 shows the overall prediction model established using the CNN-LSTM algorithm framework.

The input time matrix is expressed as $X=[X_i,X_{i,f},X_{i,tl},X_{i,th}]$, where $X_i$ is the historical input variable of the target power grid and $X_{i,tl}$ and $X_{i,th}$ are the historical output variables of the wind turbines and PVs connected to the power grid, respectively. The goal is to predict the charging power demand of microgrids in the future by rolling.

Variables are input into the prediction model. Firstly, the spatial feature information of the reconstructed space is extracted by CNN and $X=[X_i,X_{i,f},X_{i,tl},X_{i,th}]$ is input into the CNN layer. The convolution layer is composed of multiple filters. By convolving the input data layer by layer, the short-term features in the time dimension and the local dependence between variables are extracted, and the convolved data are transmitted into the LSTM network as a whole for long-sequence prediction. The formula for the convolution operation of the k-th filter on the input matrix x is shown in the following formula:

$$h^k=\mathrm{RELU}(W^k\ast X+b^k)$$

(2)

where $h^k$ is the eigenvector output by the k-th convolution kernel; $\ast$ represents convolution operation; activation function $RELU(x)=\max (0,x)$; $W^k$ is the weight matrix of the k-th convolution kernel; and is the bias vector of the k-th convolution kernel.

On this basis, the LSTM network takes advantage of its ability to better capture the long-term information in the sequence, effectively processing the sequence data. Simultaneously, the LSTM network employs Formula (1) for time series prediction and outputs the prediction values from the LSTM layer.

This paper applies a piecewise linear decay learning rate and K-fold cross-validation to tackle underfitting and overfitting issues in the CNN-LSTM model. The piecewise linear decay approach permits a higher learning rate during the initial training stage, accelerating model convergence and reducing underfitting risks. As training advances, the learning rate decreases, which allows for more accurate weight adjustments and diminishes the chances of overfitting. Furthermore, K-fold cross-validation evaluates the generalization capability of both training and test sets, leading to a more precise detection of underfitting or overfitting and enabling effective model performance optimization.

$$\mathrm{lr}(t)={\mathrm{lr}}_{\mathrm{st}}+({\mathrm{lr}}_{\mathrm{ed}}-{\mathrm{lr}}_{\mathrm{st}})\times {\displaystyle \frac{t}{T}}$$

(3)

where t represents the current epoch number (starting from 0); T is the total number of epochs; ${\mathrm{lr}}_{\mathrm{st}}$ is the initial learning rate; ${\mathrm{lr}}_{\mathrm{ed}}$ is the final learning rate; and lr(t) is the learning rate for the t-th epoch.

3.2.4. Case Studies

To evaluate the accuracy and effectiveness of the proposed CNN-LSTM prediction model, the historical aggregate power consumption of a low-voltage feeder with PVs and wind turbines connected and is applied as the model training and validation data. Considering the integer characteristics of the operation data of the low voltage ADN, it is necessary to round the prediction results. To reduce the gap before and after rounding as much as possible, the rounding function is selected: mean absolute percentage error (MAPE) $I_{\mathrm{MAPE}}$, mean absolute error (MAE) $I_{\mathrm{MAE}}$, and root mean square error (RMSE) $I_{\mathrm{RMSE}}$. Each index can be expressed as

$$I_{\mathrm{MAPE}}={\displaystyle \frac{1}{t}}{\displaystyle \sum _{i=1}^t\left|\frac{{\widehat{e}}_i-e_i}{e_t}\right|}\times 100\%$$

(4)

$$I_{\mathrm{MAE}}={\displaystyle \frac{1}{t}}{\displaystyle \sum _{i=1}^t|{\widehat{e}}_i-e_i|}$$

(5)

$$I_{\mathrm{RMSE}}=\sqrt{{\displaystyle \frac{1}{t}}{\displaystyle \sum _{i=1}^t{({\widehat{e}}_i-e_i)}^2}}$$

(6)

where t is t periods of the test set and $e_i$ and ${\widehat{e}}_i$ are the real value and predicted value of the power in the i-th period, respectively.

This paper employs a scheduling cycle of 24 h with a scheduling unit of 1 h. It utilizes the six-day load data from the low voltage ADN as the training sample, with a sampling frequency of 15 min. The entire load data for the next 15 min are predicted. Figure 4 displays the historical load variations in the specific low voltage ADN over six days.

In this paper, the six-day load data of the low-voltage ADN is used as the training sample. The sampling rate is 15 min. The load power of the next 15 min is predicted. According to the selected historical data on loads, fans, and PVs, the first 75% is assigned as the training dataset while the remaining 25% serves as the verification dataset. These datasets are put into the CNN-LSTM prediction model for power forecasting. Figure 5 and Figure 6 display power prediction profiles for both the training and verification sets. The blue line represents the actual power data values, while the red line depicts the predicted values generated by the model. The analysis of the two images demonstrates a significant correlation between the actual power values of the training and test datasets and the power value curves predicted by the CNN-LSTM model. This consistency suggests that the model effectively captures the trend variations in generation and load power within the ADN and can deliver reliable power forecasting results in real-world applications.

The proposed method is compared with other methods to verify its effectiveness. Four algorithms, the Gated Recurrent Unit (GRU) [27], LSTM [28], Stacked Autoencoders (SAE) [29], and Deep Belief Network (DBN) [30], are used to predict generation and load power. The prediction errors of different algorithms are shown in Figure 7. The algorithm proposed in this paper has the highest prediction accuracy, and the prediction effect is better than other prediction algorithms.

4. A Day-Ahead and Intra-Day Scheduling Strategy for Microgrids

The day-ahead scheduling of ADN can be modeled as a complex nonlinear programming problem, which is non-convex. It is challenging to obtain the global optimal solution through traditional methods. In this paper, the GA-PSO swarm intelligence algorithm is used as the solving algorithm of the day-ahead scheduling model.

Step 1: Gather historical generation and load power data from ADN and microgrids and input these data into a CNN-LSTM model for dynamic prediction of generation and load power curves.

Step 2: The day-ahead scheduling model aims to minimize the network loss of the ADN system as the objective function while reducing operational costs. Based on the predicted generation and load power curves for 24 h, create a scheduling plan every 24 h, producing real-time controllable generation and load power curves for the ADN and optimal Point of Common Coupling (PCC) real-time power curves from the day-ahead scheduling.

Step 3: The intra-day scheduling model targets minimizing the total operating cost of the microgrids, employing a rolling optimization approach. Prepare a one-hour control plan 15 min in advance, providing the user only with the control results for the first 15 min, finally outputting real-time controllable generation and load power curves for the microgrids and PCC planned power curves from the intra-day scheduling.

Step 4: The day-ahead scheduling model computes the PCC power, which serves as the scheduling instruction for trading between the lower microgrid and ADN. The intra-day scheduling model performs optimization calculations under the condition of fixed PCC power. If a solution exists, the optimization concludes with the final scheduling result; otherwise, the optimization result serves as feedback to the day-ahead scheduling model, which adjusts the constraints on PCC power limits and recalculates, updating the real-time power curves for the optimal PCC point until a convergent feasible solution is reached.

Step 5: Output optimal scheduling scheme.

The flow chart of the day-ahead and intra-day scheduling model is shown in Figure 8.

After incorporation into ADN, the microgrid transforms the system from a simple active network into a complex AC/DC active network. The ADN and microgrid function act autonomously while also being interdependent. The integration of a microgrid not only alters the distribution of power flow within ADN but also raises the scheduling complexity of ADN. The day-ahead and intra-day scheduling framework of ADN is shown in Figure 9.

4.1. The Optimal Scheduling Model of the Day-Ahead Scheduling

The object of the day-ahead scheduling model is the ADN after integrating the microgrid. This model seeks to minimize the total network loss of the ADN, which is reflected in the performance of the ADN. It optimizes the transfer of power between the microgrids and the main grid. Upon connection, the ADN sets the power and output of each DG as constraints, while setting the PCC power as the decision variable.

4.1.1. Objective Function of the Day-Ahead Scheduling Model

$$f_{\mathrm{loss}}=\min \sum _{t=1}^T\sum _{i=1}^N{P}_{\mathrm{loss},i,t}$$

(7)

$$P_{\mathrm{loss},i,t}=P_{\mathrm{g},i,t}-P_{\mathrm{load},i,t}$$

(8)

$$C_{\mathrm{g},i}={\displaystyle \sum _{i-1}^N{a}_i{P}_{\mathrm{g},i,t}^2+b_i{P}_{\mathrm{g},i,t}+c_i}$$

(9)

where f_loss is the 24-h network loss of the ADN; N is the scheduling time; L is the number of ADN system nodes; and P_loss,I,t is the power loss of line i at time t. $P_{\mathrm{g},i,t}$ represents the output power of the generator at node i during time period t; $P_{\mathrm{load},i,t}$ indicates the active power load at node i during time period t. $C_{\mathrm{g},i}$ denotes the generation cost of the generator at node i in the ADN system; $a_i$, $b_i$, and $c_i$ are the consumption characteristic parameters of the generator at node i.

4.1.2. Constraints of the Day-Ahead Scheduling Model

The hierarchical dispatching of ADN must consider the operational constraints of the power grid. This paper also considers the operational constraints of DGs to guarantee the safe and efficient operation of the power grid.

(1)

Flow constraints

$$\{\begin{array}{l}{P}_{i,t}=U_{i,t}\sum _{j=1}^N{U}_{j,t}\left(G_{ij}\cos {\theta }_{ij,t}+B_{ij}\sin {\theta }_{ij,t}\right)\\ Q_{i,t}=U_{i,t}\sum _{j=1}^N{U}_{j,t}\left(G_{ij}\sin {\theta }_{ij}\left(t\right)+B_{ij}\cos {\theta }_{ij,t}\right)\end{array}$$

(10)

where $P_i\left(t\right)$ and $Q_i\left(t\right)$ are the active and reactive power injected by node i at time t; $U_{i,t}$ and $U_{j,t}$ are, respectively, the voltage amplitudes of node i and node j; $G_{ij}$ and $B_{ij}$ are, respectively, the conductance and susceptance of nodes i and j; abd ${\theta }_{ij,t}$ is the phase Angle difference at time t.

(2)

Security constraint

The node voltage and node power ADN branch power should be within the permissible range to ensure the safety of ADN stability during ADN operation. In addition, the voltage of the balancing node and voltage-controlled node should be kept stable [31].

$$\{\begin{array}{c}{U}_{\min }\le U_{j,t}\le U_{\max },j\in N^{\mathrm{PQ}}\\ U_{j,t}=U_{j,\mathrm{con}},j\notin N^{\mathrm{PQ}}\\ \sqrt{{(P_{j,t})}^2+{(Q_{j,t})}^2}\le S_{j,\max }\\ \sqrt{{(P_{ij,t})}^2+{(Q_{ij,t})}^2}\le S_{ij,\max }\end{array}$$

(11)

where $N^{\mathrm{PQ}}$ is the set of PQ nodes. $U_{\min }$ and $U_{\max }$ are, respectively, the maximum and minimum allowable values of node voltage; $U_{j,\mathrm{con}}$ is the voltage rating of a balanced or voltage-controlled node; and $S_{j,\max }$ and $S_{ij,\max }$ are, respectively, the maximum allowable capacity of node j and line ij.

(3)

Output constraints of DGs

$$\{\begin{array}{l}{P}_{n,\min }^{\mathrm{DG}}\le P_{n,t}^{\mathrm{DG}}\le P_{n,\max }^{\mathrm{DG}}\\ Q_{n,\min }^{\mathrm{DG}}\le Q_{n,t}^{\mathrm{DG}}\le Q_{n,\max }^{\mathrm{DG}}\\ -{\mathsf{\Delta }}_{\mathrm{down},n}^{\mathrm{DG}}⩽P_{n,t}^{\mathrm{DG}}-P_{n,t-1}^{\mathrm{DG}}⩽{\mathsf{\Delta }}_{\mathrm{up},n}^{\mathrm{DG}}\end{array}$$

(12)

where $P_{n,t}^{\mathrm{DG}}$ and $Q_{n,t}^{\mathrm{DG}}$ represent the active and reactive power outputs scheduled for the n-th DG during the time period t; $P_{n,\min }^{\mathrm{DG}}$ and $P_{n,\max }^{\mathrm{DG}}$ denote the minimum and maximum limits of active power output for the n-th DG; $Q_{n,\min }^{\mathrm{DG}}$ and $Q_{n,\max }^{\mathrm{DG}}$ indicate the minimum and maximum limits of reactive power output for the n-th DG; and ${\mathsf{\Delta }}_{\mathrm{down},n}^{\mathrm{DG}}$ and ${\mathsf{\Delta }}_{\mathrm{up},n}^{\mathrm{DG}}$ are the maximum ramp-down and ramp-up rates for the n-th DG.

(4)

PCC power constraint

$$P_{\mathrm{pcc},m,\min }\le P_{\mathrm{pcc},,t,m}\le P_{\mathrm{pcc},m,,\max }$$

(13)

where $P_{\mathrm{pcc},m,,\max }$ and $P_{\mathrm{pcc},m,\min }$ are, respectively, the maximum and minimum values of the transferring power in the m-th microgrid and $P_{\mathrm{pcc},,t,m}$ is the transferring power between the ADN and the m-th microgrid at time t.

4.2. The Optimal Scheduling Model of the Intra-Day Scheduling

The intra-day scheduling focuses on the microgrid system, ensuring its economic advantages by coordinating energy storage, flexible load, and distributed energy. Given the limited scale of DG in microgrids, the adoption rate of wind and PV energy is 100%. The optimization objective is to minimize the operating costs of the microgrid, establishing a dynamic scheduling model for controllable power sources within the grid-connected microgrid. Generation costs include the costs of controllable power sources within microgrids, depreciation costs of energy storage batteries, and interconnection costs with the grid.

4.2.1. Objective Function of the Intra-Day Scheduling Model

$$C_{\mathrm{lower}}=\min {\displaystyle \sum _{t=1}^T(C_{\mathrm{MG},t}+C_{\mathrm{DE},t}+C_{\mathrm{EX},t})}$$

(14)

where $C_{\mathrm{lower}}$ represents the total economic operation cost of microgrids in the all-day dispatching process. T stands for the scheduling period (set as 24 h); $C_{\mathrm{MG},t}$ represents the operational costs of all controllable power sources included in the microgrids during time period t. $C_{\mathrm{DE},t}$ is the depreciation cost generated during the charge/discharge process of batteries incorporated within all microgrids during time period t. $C_{\mathrm{EX},t}$ refers to the costs of transactions between the microgrids and the ADN at time t.

(1)

Controllable power sources costs within microgrids

The operation and maintenance expenses associated with a microgrid refer to the costs required to ensure the proper functioning of the equipment. Its operation and maintenance cost $C_{\mathrm{MG},t}$ is shown in Formula (15), as follows:

$$C_{\mathrm{MG},t}={\displaystyle \sum _{m=1}^M{\displaystyle \sum _{l=1}^L(C_{\mathrm{op},l,t,m}+C_{\mathrm{fu},l,t,m}+C_{\mathrm{st},l,t,m})}}$$

(15)

where $C_{\mathrm{MG},t}$ signifies the total operational cost of microgrids at time t; $C_{\mathrm{op},l,t,m}$, $C_{\mathrm{fu},l,t,m}$, and $C_{\mathrm{st},l,t,m}$ represent the operation and maintenance costs, fuel costs, and unit startup costs of controllable power sources l within the m-th microgrid during time period t, respectively; M denotes the number of microgrids and L indicates the number of controllable power sources.

$$\{\begin{array}{l}{C}_{\mathrm{op},l,t,m}=D_{l,t}{K}_{\mathrm{op},l}{P}_{l,t}\\ C_{\mathrm{fu},l,t,m}=D_{l,t}{K}_{\mathrm{fu},l}\cdot V_{\mathrm{fu},l}(P_{l,t})\\ C_{\mathrm{st},l,t,m}=D_{\mathrm{st},l,t}{K}_{\mathrm{st},l}\end{array}$$

(16)

where $P_{l,t}$ indicates the output power of controllable power source l within the microgrid during time period t; $D_{l,t}$ signifies the working status of controllable power source l during time period t (if $D_{l,t}$ equals 1, it means active; if 0, it stops); $D_{\mathrm{st},l,t}$ represents the activation status of controllable power source l during time period t ($D_{\mathrm{st},l,t}$ equals 1 means the controllable power source is initiated); $K_{\mathrm{op},l}$, $K_{\mathrm{fu},l}$, and $K_{\mathrm{st},l}$ are the cost coefficients for operation and maintenance, fuel price, and startup costs of controllable power source l, respectively; and $V_{\mathrm{fu},l}(P_{l,t})$ is the fuel consumption of controllable power source l during time period t.

(2)

Depreciation costs of energy storage batteries

$$C_{\mathrm{DE},t}={\displaystyle \sum _{m=1}^M{P}_{\mathrm{sb},t,m}\cdot \lambda (P_{\mathrm{sb},t,m})}$$

(17)

where $P_{\mathrm{sb},t,m}$ is the charge/discharge power of the energy storage battery in the m-th microgrid during time period t; $\lambda (P_{\mathrm{sb},t,m})$ is the depreciation coefficient for the charge/discharge of energy storage batteries during time period t.

(3)

Interconnection costs with the grid

The interconnection costs with the grid only exist under the grid-connected mode, influenced by the difference between the real-time required PCC interaction power and the optimal PCC interaction power from the day-ahead scheduling control, as well as the real-time electricity price of the microgrid system [32]. The formula for calculating $C_{\mathrm{EX},t}$ is as follows:

$$C_{\mathrm{EX},t}=={\displaystyle \sum _{m=1}^M{\rho }_{t,m}(P_{\mathrm{pcc},t,m}^{MG}-P_{\mathrm{pcc},m,t}^{\mathrm{ADN}})}$$

(18)

where $P_{\mathrm{pcc},m,t}^{\mathrm{ADN}}$ is the optimal PCC interaction power between ADN and the m-th microgrid obtained from the day-ahead scheduling model at time t and $P_{\mathrm{pcc},t,m}^{MG}$ is the PCC interaction power needed by the m-th microgrid at time t. ${\rho }_{t,m}$ is the real-time electricity price for the interaction between the m-th microgrid and ADN at time t.

4.2.2. Constraints of the Intra-Day Scheduling Model

When establishing the intra-day scheduling model, this paper also considers power balance constraint, power constraint of DGs, energy storage constraint, and flexible load constraint.

(1)

Power balance constraint

$${\displaystyle \sum _l^L{P}_{l,t}}+P_{\mathrm{PV},t}+P_{\mathrm{WT},t}+P_{\mathrm{sb},t}+P_{\mathrm{pcc},,t,m}=P_{\mathrm{DL},t}-P_{\mathrm{DR},t}$$

(19)

where $P_{l,t}$ is the output of controllable power source l during time period t; $P_{\mathrm{PV},t}$ is the power of PV power generation device at time t; $P_{\mathrm{WT},t}$ is the power of wind power generation unit at time t;$P_{\mathrm{sb},t}$ is the charge/discharge power of energy storage at time t; $P_{\mathrm{pcc},,t,m}$ is the power of the connection line between the m-th microgrid and ADN at time t;$P_{\mathrm{DL},t}$ is the power of electrical load at time t; and $P_{\mathrm{DR},t}$ is the power of flexible load at time t.

(2)

Power constraint of DGs

$$P_{l,\min }\le P_{l,t}\le P_{l,\max }$$

(20)

where $P_{l,\max }$ and $P_{l,\min }$ indicate the maximum and minimum active power produced by controllable power source l, with values set at 0.2 and 0.9, respectively.

(3)

Energy storage constraint

$$SOC\min \le SO{C}_t\le SOC\max$$

(21)

$$\{\begin{array}{c}-\min \left\{P_{\mathrm{ch},\max },P_{\mathrm{ch},\sup ,t}\right\}\le P_{\mathrm{ch},t}\le 0\\ \begin{array}{l}0\le P_{\mathrm{dis},t}\le \min \left\{P_{\mathrm{dis},\max },P_{\mathrm{dis},\sup ,t}\right\}\\ P_{\mathrm{ch},\sup ,t}=E_{\mathrm{sb}}(SO{C}_{\max }-SO{C}_t)/\mathsf{\Delta }t\\ P_{\mathrm{dis},\sup ,t}=E_{\mathrm{sb}}(SO{C}_t-SO{C}_{\min })/\mathsf{\Delta }t\end{array}\end{array}$$

(22)

where SOC_min is the minimum SOC value of the battery; SOC_max is the maximum state of charge of the battery; $P_{\mathrm{ch},\max }$ and $P_{\mathrm{dis},\max }$ refer to the maximum charging and discharging power of the energy storage battery, both taken as $0.2E_{\mathrm{sb}}/h$; and $P_{\mathrm{ch},\sup ,t}$ and $P_{\mathrm{dis},\sup ,t}$ represent the maximum charging and discharging power at the end of time period t, where $E_{\mathrm{sb}}$ denotes the total installed capacity of the energy storage battery. For more detailed information, please refer to reference [33].

(4)

Flexible load constraint

The amount of reducible load in the microgrid should be within a certain range, which is determined by the maximum amount or proportion of load abatement, and the power factor of the reducible load is assumed to be constant.

$$\{\begin{array}{c}0⩽P_{tr,m,t}⩽P_{tr,m,\max }\\ 0⩽P_{rl,m,t}⩽P_{rl,m,\max }\end{array}$$

(23)

where $P_{tr,m,t}$ stands for the transfer load power of the m-th microgrid during time period t; $P_{rl,m,t}$ denotes the interrupted load power of the m-th microgrid during the same period; $P_{tr,m,\max }$ represents the maximum transfer load power of the m-th microgrid; and $P_{rl,m,\max }$ refers to the maximum interruptible load power of the m-th microgrid.

4.3. Model Solving Based on the GA-PSO Algorithm

This paper aims to develop a scheduling model for a micro power grid that optimizes the ADN with day-ahead and intra-day scheduling. This complex and multi-dimensional optimization process has several variables and non-linear functions. The traditional classical intelligent algorithms are not enough to meet the requirements of global searching and fast convergence.

However, with the combination of Genetic Algorithm (GA) and Particle Swarm Optimization (PSO), GA-PSO has a robust global search ability and fast convergence speed. Therefore, taking GA-PSO can effectively solve this complex problem. The flow chart of the GA-PSO algorithm is shown in Figure 10. Figure 11 displays the performance comparison of various optimization algorithms used to solve the model. This includes five algorithms, GA-PSO, PSO, GA, Whale Optimization Algorithm (WOA) [34], and Grey Wolf Optimizer (GWO) [35]. Considering the overall trend of the curve, the GA-PSO algorithm demonstrates high convergence speed and accuracy. Furthermore, GA-PSO consistently maintains stable and efficient optimization capability throughout the entire iteration process. In contrast, while other algorithms exhibit certain performances at different stages, they do not achieve the overall high efficiency and stability exhibited by GA-PSO.

5. Case Studies

To verify the accuracy and effectiveness of the day-ahead and intra-day scheduling model of ADN based on the GA-PSO algorithm, this paper analyzes the ADN and microgrid by selecting the IEEE 33-node network and making an improvement based on it, which includes two microgrids, MG1 and MG2. Figure 12 shows the structure of the optimal scheduling system of ADN. It is worth noting that if the microgrid’s capacity is insufficient, it cannot provide sufficient support to the ADN. As a result, there are specific requirements for the capacity of the microgrid in the intra-day scheduling model. The microgrid’s power supply must reach 20% of the ADN load. To validate the efficacy of the proposed approach, the test environment detailed in this study comprises a 2.20 GHz Intel Core i7 processor, 16 GB of RAM, MATLAB 2020a.

The voltage of the node network is 12.66 kV and the reference power is 10 MW. MG1 and MG2 correspond to node 14 and node 30 of IEEE33 in the microgrid, respectively. The MG1 and MG2 mainly comprise wind turbines, PV generators, micro gas turbines, and energy storage devices. Each parameter setting can be found in the

Table 1. The parameter setting of 33-node network.

Parameter	Value
the voltage of the node network	12.66 kV
the reference power of the node network	10 MW
the upper limit of the predicted load value of MG1	180 kW
the upper limit of the predicted load value of MG2	130 kW
the upper limit of the predicted load value of the wind turbines	39 kW
the upper limit of the predicted output value of the PV	42 kw

. The energy storage device’s charging and discharge efficiency are 95%. The initial SOC value of the energy storage device is 50%, the upper limit is 90%, and the lower limit is 20%. The unit cost of natural gas is 2.08 (CNY/m³). This paper assumes that the absorption rate of wind power and PV is 100%.

The day-ahead scheduling of the simulation example takes the ADN as the object to optimize the scheduling. Firstly, the wind power output, PV output, and charging power are predicted within a 24-h day. Taking a 24-h day as a scheduling period, the predicted load value is the load of each 33-bus system. The microgrid takes a 15-min scheduling level, with predicted values for the next 96 scheduling moments based on charging power and load forecasting data for wind power, PV, and power demand. The parameter setting of GA-PSO can be found in

Table 2. The parameter setting of GA-PSO.

Parameter	Value
the crossover probability pc	0.7
the mutation probability mp	0.3
the inertia weight ω	[0.4, 0.9]
the learning factor c1	[0.5, 2.5]
the learning factor c2	[0.5, 2.5]
the maximum particle velocity	300
the maximum number of iterations	800
the particle population size	1000
$\lambda 1$	0.3
$\lambda 2$	0.7
the excitation coefficient $\partial$	0.45

.

The ADN load forecasting curve is shown in Figure 13. Private electric vehicles can be charged upon arrival at the company in the morning on working days. The peak time for charging is in the evening after work, and the frequency of charging in the evening is higher than in the morning. From 0:00–5:00, the system is in a low power consumption state, and from 8:00 to 14:00, the power consumption is at its peak.

The predicted load of micro-grid PV, wind turbines, MG1, and MG2 in the day-ahead scheduling model are shown in Figure 11 below. As can be seen from the figure, the overall load demand of MG1 and MG2 is from 7:00 to 16:00, and the load demand of MG1 is relatively high, while the overall load fluctuation in MG2 is relatively stable. The electricity demand includes both the flexible daily load. The maximum predicted load of MG1 is 188 kW, and the maximum predicted load of MG2 is 136 kW. The maximum predicted power output for the microgrid is 37 kW for wind turbines and 38 kW for PV panels. Energy storage is regulated according to load demand.

Based on the GA-PSO algorithm, the power, network loss, and voltage values in the ADN system and microgrid are solved, respectively. The transferring power of MG1 and MG2 connected to the microgrid is shown in Figure 14.

It can be seen from Figure 15 that at 0:00–7:00, the transferring power is positive. The microgrid will now deliver electricity to the ADN online to match the demand and also draw power from the ADN. From 8:00–23:00, the transferring power is negative. It is obvious that the microgrid acts as a power supply to sell power to the ADN and provide power to the ADN. It can be seen that the microgrid only sells electricity to the ADN in the morning and evening during peak load consumption periods. The maximum transferring power of line 1 is 199 kW. The maximum transferring power of line 2 is 200 kW. It should be pointed out that the transferring power of the ADN is precisely opposite to the scheduling result of the microgrid.

Network loss is essential to safe, reliable, and economical ADN operation. In ADNs and microgrids, the rational distribution of active and reactive power is determined by the power flow calculation, and the network loss is closely related to the power flow calculation. Figure 16, above, reflects the network loss before and after the incorporation of the microgrid into the ADN. The comparison figure is shown in Figure 16. It can be seen that from 0:00 to 23:00, the network loss of the microgrid before the grid connection is 3.2796 MW, and the network loss after the grid connection is 2.712 MW, which is 17.31% less than that before the connection. It can be found that the network loss of the microgrid shows an apparent downward trend after it is integrated into the ADN. It shows that the network loss is effectively reduced after the microgrid is connected to the grid. As can be seen from the figure, at this moment, the microgrid sells power to the ADN. It provides power to the ADN so that the ADN can reduce the output of other distributed power sources and finally effectively reduce the network loss.

In the day-ahead optimal scheduling process of the microgrid, the TOU price was selected in this paper to adjust the demand side response of load, as shown in Figure 17.

The scheduling results of the microgrid connected with 15 and 30 nodes in the ADN are shown in Figure 18 and Figure 19. The electrical load comprised the daily load, with the transferable load expressed separately. The cable power of MG1 and MG2 is positive when 0:00–7:00 and negative when 8:00–23:00.

Based on the scheduling results in Figure 18 and Figure 19, representative time intervals for detailed analysis should be selected.

(a)

Low Load Period (0:00–7:00)

Period 1 (0:00–3:00): During this timeframe, electricity demand remains minimal, leading to lower time-of-use electricity prices. The electricity generated by the wind turbines fulfills the microgrid’s demand. Concurrently, microgrids MG1 and MG2 effectively distribute power at competitive rates. The day-ahead and intra-day scheduling system prioritizes the intelligent management of renewable energy outputs, such as wind, maximizing low-cost periods for energy storage or distribution, thereby preparing for imminent peak demand.

Period 2 (3:00–4:00): The battery initiates charging by drawing power from the ADN. This critical function of the intra-day scheduling system activates charging during low time-of-use electricity price periods, allowing for discharge during high price periods. This strategy reduces overall costs and enhances the system’s economic efficiency.

Period 3 (4:00–7:00): As load demand incrementally rises, transmission power escalates until it peaks. The intra-day scheduling system maintains power supply stability and continuity by adjusting tie line output to facilitate the microgrid’s transition into peak demand scenarios.

(b)

Peak Hours (8:00–23:00)

Period 1 (8:00): Entering the peak electricity consumption period, prices rise. The microgrid begins supplying power to the ADN to meet heightened load demands. The day-ahead and intra-day scheduling system primarily coordinate output from various power sources, particularly micro-gas turbines and renewable resources, ensuring a stable electricity supply.

Period 2 (10:00): Wind turbine output reaches its peak. The day-ahead and intra-day scheduling system optimizes renewable energy utilization by intelligently regulating wind power generation while dynamically adjusting micro-gas turbine output to align with actual demand and ensure a balanced power supply.

Period 3 (12:00): PV output begins to peak. The intra-day scheduling system continues to synchronize multiple power sources, including wind, PV, and micro-gas turbines, ensuring that the power supply aligns with load requirements.

Period 4 (13:00–19:00): Load demand surges significantly. During this phase, the micro-gas turbine serves as the primary power output, supplying electrical energy to fulfill load demands. The intra-day scheduling system guarantees power supply continuity and reliability through dynamic adjustments of micro-gas turbine output while intelligently allocating wind and PV energy production.

Period 5 (13:00–23:00): This period represents load flattening, with the micro-gas turbine sustaining its primary output role. The intra-day scheduling system ensures a stable and economical power supply by consistently monitoring load fluctuations, promptly adjusting micro-gas turbine output, and intelligently scheduling alternative energy sources.

As can be seen from Figure 20, when the time is 0:00–3:00, it is the electricity consumption trough period, and the time-of-use electricity price in this period is the lowest. Time 8:00 is the peak of electricity consumption, and the price in this period is the highest. Under the effect of optimal scheduling of the micro-grid and reasonable response of demand side, peak cutting and valley filling of the micro-grid load are realized.

Table 3. The comparison of optimal scheduling network loss and economic cost results for microgrid interconnection.

Operational Modes of ADN	Network Loss (MW)	Microgrid Operation Costs (CNY)	Peak-Valley Difference in Microgrid (KW)
ADN with microgrids connected	2.712	1720	106
ADN without microgrids connected	3.2796	2560	122

shows that the microgrid has a network loss of 3.2796 MW, an operation cost of CNY 2560, and a daily peak-valley difference of 122 KW when it prioritizes economic cost. When the ADN participated in optimizing micro-grid scheduling, the system’s network loss was reduced to 2.712 MW, the operating cost was cut down to CNY 1720, and the day-ahead peak-valley difference was 106 KW. The results show that the network loss of the main grid and the operation costs of microgrids are reduced by 17.31% and 32.81% after the microgrid is integrated into the ADN. And peak-valley difference in the microgrid decreased by 13.12%. It can be intuitively seen that after integrating the microgrid into ADN, the network loss, operation cost, and peak-valley difference in the system all have an apparent downward trend.

The optimization outcomes indicate that the day-ahead and intra-day scheduling framework can considerably lower the aggregate operating expenses of the entire system while markedly diminishing the network losses within the ADN system. When the microgrid is integrated with the primary grid, it not only supplies additional energy resources but also responds promptly to real-time load variations, thereby aiding in the reduction in the system’s peak load and enhancing energy utilization efficiency. During load fluctuations, the model is capable of swiftly adjusting the power of the connecting line, ensuring the stable functioning of the entire system. Specifically, by optimizing the power of the link line, excess energy can be transferred from the microgrid to the main grid during peak load times to alleviate the main grid’s burden. Conversely, during periods of low load, the operation can be reversed, allowing power to flow from the main grid to the microgrid to maximize the utilization of the microgrid’s energy sources.

6. Conclusions

This paper mainly carried out the following work.

In the generation and load characteristic analysis, multiple models were proposed to describe the characteristics of critical elements in the ADN. The wind power generation and PV generation models were used to describe the characteristics of distributed wind and PV generation. The micro gas turbine model was used to model the power generation characteristics of micro gas turbines. The energy storage device model considered energy storage devices’ charging and discharging characteristics and efficiency. The flexible load model describes the characteristics of adjustable loads.

In the scheduling framework for ADNs and microgrids, this paper proposes separate scheduling models for both day-ahead scheduling and intra-day scheduling. The day-ahead scheduling model formulates optimization objectives and constraints pertinent to the entire ADN, orchestrates resource allocation across the network, and achieves enhanced economic efficiency and reliability through optimal scheduling techniques. Moreover, the intra-day scheduling model addresses operational costs, load variances, and peak-to-valley differentials, concentrating on energy management and load scheduling within the microgrid. This model allows for agile adjustments to power generation and consumption based on real-time demand, thereby decreasing reliance on the external grid and optimizing self-sufficiency and economic advantages. This optimization model significantly bolsters the system’s stability and security, equipping it to manage effectively various emergencies, including supply–demand imbalances triggered by extreme weather events, which are vital for maintaining continuous and high-quality power supply and supporting the uninterrupted functioning of socio-economic activities.

This paper analyzes the output characteristics of various energy sources such as wind power, PV, gas turbine, energy storage units, electric vehicles, and flexible load in ADN’s “source” side. Based on this analysis, a day-ahead and intra-day scheduling model of ADN and micro-grid is established and solved using the GA-PSO algorithm to obtain the optimal scheduling method. The simulation node’s 24-h ADN system load data are predicted along with the microgrid’s wind turbines and PVs. The model was simulated, verified, and analyzed by combining the load forecast data with wind turbines and PV forecast data. The results show that the network loss of the main grid and the operation costs of microgrids are reduced by 17.31% and 32.81% after the microgrid is integrated into the ADN. And peak-valley difference in the microgrid decreased by 13.12%. Compared with ADN without microgrids, there are very significant changes in economic and technical indicators.

In this paper, a day-ahead and intra-day scheduling strategy for ADN under multi-time scales is proposed, which lays a certain theoretical foundation for subsequent research. However, there are still many shortcomings: the research is not thorough o comprehensive enough and it needs to be improved in the following aspects:

(1)

In this paper, considering the optimal scheduling of ADNs, it is essential to address the challenges posed by the intermittent and uncertain nature of wind and PV power generation, which is significantly influenced by environmental conditions. Future research should incorporate methodologies such as scenario analysis to conduct a comprehensive and nuanced examination of these uncertain factors;

(2)

The placement and capacity of control systems such as SOP, significantly influence economic scheduling outcomes. Future considerations will focus on optimizing the configuration of these control systems.