Tractable Probabilistic Models for Investment Planning

TL;DR

This paper introduces a novel approach for power utility investment planning under uncertainty using sum--product networks, enabling efficient probabilistic analysis and reliability assessment without large scenario enumeration.

Contribution

It presents a new method employing sum--product networks for tractable probabilistic modeling in power investment planning, improving computational efficiency and probabilistic resolution.

Findings

Efficient probabilistic queries with sum--product networks.

Enhanced reliability assessment without large scenario trees.

Competitive computational performance in case study.

Abstract

Investment planning in power utilities, such as generation and transmission expansion, requires decisions under substantial uncertainty over decade--long horizons for policies, demand, renewable availability, and outages, while maintaining reliability and computational tractability. Conventional approaches approximate uncertainty using finite scenario sets (modeled as a mixture of Diracs in statistical theory terms), which can become computationally intensive as scenario detail increases and provide limited probabilistic resolution for reliability assessment. We propose an alternative based on tractable probabilistic models, using sum--product networks (SPNs) to represent high--dimensional uncertainty in a compact, analytically tractable form that supports exact probabilistic queries (e.g., likelihoods, marginals, and conditionals). This framework enables the direct embedding of chance constraints into mixed--integer linear programming (MILP) models for investment planning to evaluate reliability events and enforce probabilistic feasibility requirements without enumerating large scenario trees. We demonstrate the approach on a representative planning case study and report reliability--cost trade--offs and computational behavior relative to standard scenario--based formulations.