Tractable Probabilistic Models for Investment Planning

Abstract

Investment planning in power utilities, such as generation and transmission expansion, requires decade-long forecasts under profound uncertainty. Forecasting of energy mix and energy use decades ahead is nontrivial. Classical approaches focus on generating a finite number of scenarios (modeled as a mixture of Diracs in statistical theory terms), which limits insight into scenario-specific volatility and hinders robust decision-making. We propose an alternative using tractable probabilistic models (TPMs), particularly sum-product networks (SPNs). These models enable exact, scalable inference of key quantities such as scenario likelihoods, marginals, and conditional probabilities, supporting robust scenario expansion and risk assessment. This framework enables direct embedding of chance-constrained optimization into investment planning, enforcing safety or reliability with prescribed confidence levels. TPMs allow both scenario analysis and volatility quantification by compactly representing high-dimensional uncertainties. We demonstrate the effectiveness of the approach through a representative power system planning case study, illustrating its computational and reliability advantages over traditional scenario-based models.