This paper focuses on electricity demand forecasting and its uncertainty representation using a hybrid machine learning (ML) model in the eastern control area of southeastern Mexico. In this case, different sources of uncertainty are integrated by applying the Bootstrap method, which adds the characteristics of stochastic noise, resulting in a hybrid probabilistic and ML model in the form of a time series. The proposed methodology addresses a function density probability, which is the generalized of extreme values obtained from the errors of the ML model; however, it is adaptable and independent and simulates the variability that may arise due to unforeseen events. Results indicate that for a five-day forecast using only demand data, the proposed model achieves a Mean Absolute Percentage Error (MAPE) of 4.358%; however, incorporating temperature increases the MAPE to 5.123% due to growing uncertainty. In contrast, a day-ahead forecast, including temperature, improves accuracy, reducing MAPE to 1.644%. The stochastic noise component enhances probabilistic modeling, yielding a MAPE of 3.042% with and 2.073% without temperature in five-day forecasts. Therefore, the proposed model proves useful for regions with high demand variability, such as southeastern Mexico, while maintaining accuracy over longer time horizons.

This paper evaluates the impact of congestion on transmission lines when the operation cost is minimized using economic dispatch (ED), comparing the results obtained with the Nash–Cournot Equilibrium (NCE). A methodology is developed for the optimal power flow solution through the NCE, considering the network topology (upper and lower generation limits, upper and lower limits of the transmission lines, and power balance) for a nine-node system without and considering two bilateral power transactions. The results show that the operation cost is higher when the NCE is implemented than ED. However, the problem of congestion in the transmission lines is reduced due to the equilibrium obtained in the power dispatch against minimizing the operation cost in the dispatch; the transmission lines with the most significant participation tend to become congested when additional bilateral transactions occur. Finally, the above is verified by obtaining the mean and median of the transmission line percentages used in the two simulations.

Since intercepted sensor data can reveal user activities, lightweight cryptography is essential for protecting information in resource-constrained devices. Although ARX-based lightweight schemes offer high computational efficiency, their lack of inherent non-linear substitution and permutation layers motivates their integration into secure cryptographic designs. This paper proposes LSEPI (Lightweight Sensor Encryption Using PI), a lightweight stream cipher for protecting electrical sensor data. LSEPI employs a single-round substitution-permutation design that combines the AES substitution box with a key-dependent dynamic permutation and a dynamically selected XOR mask derived from the secret key and the digits of the number $\pi$. To mitigate the computational cost of pseudorandom sequence generation, the first 20 KB of the decimal expansion of $\pi$ are stored on both the ESP32 and Android device. Encryption is performed on the ESP32 during the simultaneous acquisition and computation of voltage, current, power, and energy, while decryption is performed on an Android application for user-selected time intervals. Statistical evaluation shows that LSEPI achieves an entropy of 7.9971 with a single encryption round, comparable to Speck-CTR with 32 rounds (7.9970) and Ascon (7.9969), and higher than the approximately 7.18 reported for recent lightweight proposals. The encrypted data also satisfies the chi-square goodness-of-fit criterion, exhibits correlation coefficients close to zero, and achieves average avalanche effects of 50.005% for one-bit plaintext changes and 50.08% for one-bit key changes. GLCM-based texture metrics are comparable to those of Speck-CTR and Ascon. The known-plaintext analysis indicates that recovering the key-dependent masking sequence requires determining or inverting the key-dependent permutation; thus, despite the use of XOR operations, the attack does not directly succeed. From a computational perspective, LSEPI requires 135 μs per sensor record after initialization, adding only 0.04% overhead to the computation of the electrical variables on the ESP32.