1. Introduction

2. Literature Review

3. Methodology and Procedures

3.1. Load Forecasting

The integration of deep learning techniques into the energy sector has significantly advanced the ability to address various critical issues related to electricity demand forecasting, smart grid scheduling, and fair energy distribution. Load forecasting utilizes deep learning models such as LSTM to predict future electricity demand based on historical usage patterns, enabling more accurate and efficient grid management. In the realm of smart grid scheduling and optimization, deep reinforcement learning algorithms optimize the allocation of energy resources in real time, ensuring both system reliability and equity in energy distribution. Moreover, fair energy distribution ensures that energy resources are allocated in a manner that prevents disproportionate access, particularly for vulnerable populations, while also addressing social equity in power market analysis by analyzing pricing, access, and market behavior through fairness-driven models. The prediction of energy poverty is another critical area, where machine learning models predict households or regions at risk of energy deprivation, providing insights for targeted interventions. Lastly, fairness-constrained deep optimization introduces fairness constraints into energy optimization models, ensuring that policies and operational decisions are not only economically efficient but also equitable, particularly for underserved and low-income communities. These interdisciplinary approaches collectively pave the way for a more sustainable, efficient, and equitable energy system.

Here is the approach to solving the electricity demand forecasting problem using Long Short-Term Memory (LSTM), in English. The process involves data preprocessing, model construction, training, and evaluation, with the relevant mathematical formulas and pseudocode provided.

1. Data Preparation and Preprocessing

Collect Data: Gather historical electricity demand data, weather data (temperature, humidity, etc.), and other relevant features like holidays and events.

Data Preprocessing:

Normalization: Normalize or standardize the input data to ensure faster convergence during training.

Create Time Windows: Divide the data into fixed-length time windows. For example, use the past 24 hours of data to forecast the next hour's electricity demand.

Mathematical Formula: Normalization: Given the data point x, normalize it as:

$$x^{\prime }={\displaystyle \frac{x-\mu }{\sigma }}$$

Time Window: Split the data into input-output pairs:

$$\left\{x_t,y_t\right\},t=1,2,\dots ,T$$

where xt is the input at time step t (e.g., the previous 24 hours of demand data), and yt is the target value (the next hour's demand).

2. Building the LSTM Model

LSTM networks consist of multiple components:

Forget Gate: Determines how much of the past information to forget.

Input Gate: Determines how much new information to store.

Output Gate: Determines the current output of the LSTM.

The operation of LSTM is described as follows:

Forget Gate: Determines how much past information to retain.

$$f_t=\sigma \left(W_f\cdot \left[h_{t-1},x_t\right]+b_f\right)$$

Input Gate: Decides how much current information to store.

$$\begin{array}{c}{i}_t=\sigma \left(W_i\cdot \left[h_{t-1},x_t\right]+b_i\right)\\ {\tilde{C}}_t=\tanh \left(W_C\cdot \left[h_{t-1},x_t\right]+b_C\right)\end{array}$$

Update Memory Cell:

$$C_t=f_t\cdot C_{t-1}+i_t\cdot {\tilde{C}}_t$$

Output Gate: Determines the current output of the LSTM.

$$\begin{array}{c}{o}_t=\sigma \left(W_o\cdot \left[h_{t-1},x_t\right]+b_o\right)\\ h_t=o_t\cdot \tanh \left(C_t\right)\end{array}$$

These components work together to capture long-term dependencies in the input data.

3. Model Training

Loss Function: Typically, the Mean Squared Error (MSE) is used to measure the prediction error.

$$\mathcal{L}={\displaystyle \frac{1}{N}}\sum _{t=1}^N {\left(y_t-{\hat{y}}_t\right)}^2$$

where is the true demand value and is the predicted demand value.

Optimization Algorithm: Common optimization algorithms include Adam, SGD, etc., which minimize the loss function through backpropagation.

4. Model Evaluation and Validation

Cross-validation: Split the data into training, validation, and test sets to ensure the model's generalization ability.

Evaluation Metrics: Common evaluation metrics include RMSE (Root Mean Squared Error) and MAE (Mean Absolute Error).

$$\begin{array}{rr}\mathrm{R}\mathrm{M}\mathrm{S}\mathrm{E}& =\sqrt{{\displaystyle \frac{1}{N}}{\displaystyle \sum _{t=1}^N} {\left(y_t-{\hat{y}}_t\right)}^2}\\ \mathrm{M}\mathrm{A}\mathrm{E}& ={\displaystyle \frac{1}{N}}{\displaystyle \sum _{t=1}^N} \left|y_t-{\hat{y}}_t\right|\end{array}$$

5. Model Deployment and Prediction

Forecasting: Once the model is trained, it can be used to forecast future electricity demand based on new input data.

Real-time Updates: As new data becomes available, the model can be updated periodically to improve its predictions.

6. Pseudocode Implementation

Below is the pseudocode for implementing the LSTM-based electricity demand forecasting model:

Figure 1. LSTM-based electricity demand forecasting model.

Figure 1. LSTM-based electricity demand forecasting model.

7. Explanation of Pseudocode

Load Data: We load the historical electricity demand data, typically stored in a CSV or database format.

Normalize Data: The data is normalized to ensure that all features have a similar range, which helps the model converge faster.

Create Time Windows: We use the past window size hours of data as input to predict the next hour’s demand.

Split Data: The dataset is split into training and test sets (80% for training and 20% for testing).

Initialize LSTM Model: The LSTM model is initialized with 50 units (neurons) and a single output layer for regression.

Compile Model: The model is compiled with the Adam optimizer and MSE as the loss function.

Train Model: The model is trained for 10 epochs with a batch size of 32.

Make Predictions: After training, the model is used to make predictions on the test set.

Evaluate Model: RMSE and MAE are calculated to evaluate the performance of the model.

Real-time Forecasting: Once the model is trained, it can be used to forecast future electricity demand based on new incoming data.

Figure 2. Power Plant Protection System using Long Short-Term Memory.

Figure 2. Power Plant Protection System using Long Short-Term Memory.

Smart Grid Scheduling and Optimization refers to the process of efficiently managing the generation, storage, and distribution of electricity across a smart grid, while ensuring system reliability, cost-effectiveness, and equity in energy access. The goal is to optimize the operation of various components of the grid, such as power plants, renewable energy sources, energy storage systems, and consumers, while minimizing operational costs and maximizing grid stability. This process can be achieved using techniques such as optimization algorithms, machine learning, and deep learning models.

3.3. Fair Energy Distribution

Fair energy distribution refers to the equitable allocation of energy resources among various users or regions, ensuring that no group is disproportionately disadvantaged, particularly in the context of energy poverty or vulnerable populations. The goal is to design energy allocation mechanisms that prioritize fairness alongside efficiency, ensuring that every consumer has access to affordable and sufficient energy. This can be achieved using various approaches, such as optimization algorithms, game theory, and market mechanisms that integrate fairness constraints into the allocation process.

1. Problem Formulation

The problem of fair energy distribution involves balancing the equity and efficiency in the allocation of energy resources. The objective is to minimize disparities in energy access while considering system constraints like energy availability, demand satisfaction, and economic costs.

Objective Function

The general objective function in a fair energy distribution problem aims to minimize the total cost while also promoting fairness in energy access. It can be formulated as:

$$\mathrm{Minimize}{C}_{\mathrm{total}}={\displaystyle \sum }_{i=1}^N\left[C_{\mathrm{gen}}\left(i\right)+C_{\mathrm{trans}}\left(i\right)\right]$$

Where:

$C_{\mathrm{total}}$ is the total operational cost of energy generation and transmission.

$C_{\mathrm{gen}}\left(i\right)$ is the cost of generating energy for user i.

$C_{\mathrm{trans}}\left(i\right)$ is the cost of transmitting energy to user i.

The objective function can be modified to incorporate fairness by introducing fairness penalties or equality measures. Fairness Constraints The energy distribution must meet certain fairness criteria. Common fairness metrics include equity-based fairness (ensuring an equal share of energy for all users) and proportional fairness (ensuring that the energy allocation reflects individual needs or contributions).

Equity-Based Fairness: One way to enforce equity is by minimizing the disparity in energy access. A fairness constraint can be formulated as:

$$\max \left(P_{max}\left(i\right)-P_{min}\left(i\right)\right)\le ϵ$$

Where:

$P_{max}$ is the maximum energy allocated to user i.

$P_{min}$ is the minimum energy allocated to user i.

$ϵ$ is a small tolerance value that ensures fairness by limiting the disparity in energy access across users.

Proportional Fairness: In proportional fairness, the allocation should be proportional to individual needs, usage, or contributions. This can be achieved using a utility-based approach:

$$\mathrm{Maximize}{U}_{\mathrm{fair}}={\displaystyle \sum }_{i=1}^{N}1\log \left(P_i\right)$$

Where:

$U_{\mathrm{fair}}$ is the utility function that measures fairness, with the logarithmic form promoting proportional fairness.

$P_i$ is the energy allocated to user I This approach ensures that each user's utility increases proportionally to their allocated energy, which is beneficial for users with higher needs (e.g., low-income households).

Shapley Value (Cooperative Game Theory Approach): The Shapley value is a fairness measure derived from cooperative game theory that allocates resources based on the contribution of each participant. For energy allocation, the Shapley value for each user

i can be computed as:

$${\varphi }_i={\displaystyle \frac{1}{N!}}{\displaystyle \sum }_{S\subseteq N\setminus i}1\left(\mathrm{Marginal} \mathrm{Contribution} \mathrm{of}i\right)$$

Where:

${\varphi }_i$ is the Shapley value for user iii, representing the fair share of energy resources.

S represents the subset of users excluding iii.

N is the total set of users.

Figure 3. Fairness in local energy systems.

Figure 3. Fairness in local energy systems.

4. Target specific communities or individuals for energy assistance programs.

Table 1. Performance Metrics Summary Table.

Figure 4. Energy balance after power optimization.

Figure 4. Energy balance after power optimization.

5. Conclusion

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