Multi-Stage Decision Rules for Power Generation & Storage Investments with Performance Guarantees

TL;DR

This paper introduces multi-stage linear decision rules for power system investment planning under uncertainty, providing guarantees on feasibility, robustness, and performance bounds, and demonstrating their effectiveness on a U.S. power system testbed.

Contribution

It develops a novel chance-constrained optimization framework with performance guarantees for multi-stage investment decisions in power systems using linear decision rules.

Findings

LDRs ensure operational and carbon policy feasibility under uncertainty.

LDRs produce robust, quasi-deterministic investment plans.

Performance bounds guarantee limited sub-optimality of LDRs.

Abstract

We develop multi-stage linear decision rules (LDRs) for dynamic power system generation and energy storage investment planning under uncertainty and propose their chance-constrained optimization with performance guarantees. First, the optimized LDRs guarantee operational and carbon policy feasibility of the resulting dynamic investment plan even when the planning uncertainty distribution is ambiguous. Second, the optimized LDRs internalize the tolerance of the system planner towards the stochasticity (variance) of uncertain investment outcomes. They can eventually produce a quasi-deterministic investment plan, which is insensitive to uncertainty (as in deterministic planning) but robust to its realizations (as in stochastic planning). Last, we certify the performance of the optimized LDRs with the bound on their sub-optimality due to their linear functional form. Using this bound, we guarantee that the preference of LDRs over less restrictive -- yet poorly scalable -- scenario-based optimization does not lead to financial losses exceeding this bound. We use a testbed of the U.S. Southeast power system to reveal the trade-offs between the cost, stochasticity, and feasibility of LDR-based investments. We also conclude that the LDR sub-optimality depends on the amount of uncertainty and the tightness of chance constraints on operational, investment and policy variables.