Stochastic Transmission Planning: Latent Factor Approximation of AC Costs With DC Subproblems

Transmission planning requires solving an optimal power flow problem for each considered investment plan for multiple operating conditions. AC power flow formulations are more accurate, but for transmission planning on large systems may be computationally intractable and can converge to local optima. Regional transmission studies usually rely on linearized DC power flow formulations, which reduce computation time but sometimes produce solutions that are inferior when the AC flows are resolved. We propose an approach to regional-scale transmission planning that approximates the AC power flow results using the faster DC formulation. An initial sample of investment plans is simulated with both AC and DC power flows, and then the singular value decomposition is applied to characterize the error between the two formulations and form a projection that estimates the AC costs from the DC costs. The estimation is used in a DC formulation of the transmission investment problem. We show that the proposed approach accurately estimates the AC operation costs and returns expansion plans that are consistently reliable with AC power flows. We also demonstrate that traditional DC formulations can produce low-cost, AC-feasible investment plans if enough representative hours are selected and weighted effectively.