Interval forecasting of electric load based on an IBKA-Optimized MSTCN–BiLSTM–QR Model: an empirical study on the U.S. residential load data

Abstract

Considering the critical role of short-term power load forecasting in ensuring safe and stable power system operation, this study proposes an interval forecasting model based on an Improved Black-winged Kite Algorithm (IBKA)-optimized MSTCN–BiLSTM–QR framework. Multivariate time series inputs are first constructed, then a Multi-Scale Temporal Convolutional Network (MSTCN) extracts multi-scale temporal features, while BiLSTM captures bidirectional dependencies, enhancing representation of nonlinear load characteristics. Quantile Regression (QR) converts point forecasting into interval forecasting, enabling effective uncertainty characterization, and IBKA optimizes key hyperparameters to improve convergence and accuracy. Empirical analysis uses residential load data from four U.S. regions (U1–U4) and compares the model with CNN-LSTM, CNN-BiLSTM, TCN-LSTM, Transformer–TCN–GRU, TCN-Informer-BiGRU, and TCN-QRNN. Benchmark tests on six functions (F1–F6) show IBKA achieves optimal or near-optimal Best, Mean, and Std values, outperforming GWO and BKA, and demonstrating superior global search and convergence stability. For point forecasting, IBKA-MSTCN-BiLSTM-QR attains an average R² of 0.9929, outperforming TCN-Informer-BiGRU (0.9921) and Transformer–TCN–GRU (0.9904). MAPE decreases to 1.943%, ~26.8% lower than CNN-LSTM, and RMSE reaches 0.0372 kW, ~30.6% lower. Interval forecasting at 80% confidence yields PICP 0.798–0.818 and MPICD 0.063–0.075 kW; at 95% confidence, PICP 0.946–0.958 and MPICD 0.095–0.112 kW, indicating balanced coverage and interval width. Additional dataset validation confirms strong cross-dataset generalization. Ablation studies show full model performance (PICP = 0.844, MPICD = 0.0425 kW) declines when removing IBKA, MSTCN, or BiLSTM, highlighting the contribution of each component and the synergy of MSTCN and BiLSTM. Overall, the proposed model achieves high accuracy, robustness, and reliability in complex load scenarios, providing effective support for power system dispatch optimization and risk-aware decision-making.