Machine learning and time–frequency feature framework for optimal DER planning in radial networks

The rapid integration of photovoltaic and wind-based distributed energy resources (DERs) into radial distribution networks has introduced operational challenges such as voltage instability, increased losses, and unpredictable system behaviour under renewable variability. These issues require optimization frameworks that are both computationally efficient and capable of modelling uncertainty. This paper presents a Machine Learning-Enhanced Cheetah Optimizer (ML-EChOA) that integrates time–frequency voltage analysis with surrogate-assisted metaheuristic search to achieve fast and accurate techno-economic DER allocation. Voltage time series are transformed into spectrograms and scalograms, from which Local Binary Pattern features are extracted to capture transient behaviour. A Gradient Boosting surrogate is trained on these features to approximate power-flow outcomes, enabling the optimizer to evaluate candidate solutions with minimal computational overhead. Deterministic and probabilistic scenarios — generated through LSTM-based forecasting of solar, wind, and load profiles — ensure that the optimization remains robust under uncertainty. The proposed approach produces substantially improved voltage quality, reduced losses, and enhanced economic performance while converging faster than conventional metaheuristics. These results illustrate the potential of ML-EChOA as a scalable, intelligent, and uncertainty-aware optimization tool for renewable integration and future smart distribution networks.