Smart planning of PV and battery systems under uncertain demand and generation: A data-driven robust optimization approach

This paper presents a novel adaptive, data-driven robust optimization framework for the optimal sizing and operation of photovoltaic (PV) and battery energy storage systems. The framework explicitly models uncertainty in the decision-making parameters—PV generation and electricity demand—using advanced machine learning techniques to improve accuracy and realism. Unlike traditional fixed interval–based approaches for modeling uncertainty, the proposed method constructs flexible, data-driven uncertainty sets by combining three advanced techniques: Density-Based Spatial Clustering of Applications with Noise, Gaussian Mixture Models, and Principal Component Analysis. Specifically, the clustering method filters noise and removes outliers from historical data, the Gaussian mixture approach identifies hidden probabilistic structures through clustering, and principal component analysis reduces the dimensionality of the data while preserving the main patterns of variation. These refined uncertainty sets are embedded in an adjustable robust optimization model formulated in two stages: the master problem determines “here-and-now” sizing decisions, while subproblems optimize “wait-and-see” operational responses under uncertainty. The main contributions of this study can be summarized as: (i) Modeling PV-Battery System Sizing and Operation under Uncertainty in a Time-of-Use Pricing Scenario, (ii) Using Machine Learning–Driven Uncertainty Modeling, Considering Both the Hourly and Seasonality Trends over Parameters, and (iii) Comprehensive Evaluation through Simulation and Sensitivity Analysis under 120 scenarios—including demand-generation fluctuations and temporal shifts—using 500 Monte Carlo simulations per scenario. The proposed framework is applied to real-world household energy profiles and benchmarked against interval-based robust optimization models. Results indicate that traditional approaches, owing to their conservative uncertainty assumptions, tend to recommend smaller and less efficient system sizes, resulting in higher long-term costs. In contrast, the proposed data-driven framework consistently achieves lower net present costs over a 20-year planning horizon across various simulation scenarios.