  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.
