A Linear Outer Approximation of Line Losses for DC-based Optimal Power Flow Problems

Abstract

This paper proposes a novel and simple linear model to capture line losses for use in linearized DC models, such as optimal power flow (DC-OPF) and security-constrained economic dispatch (SCED). The Line Loss Outer Approximation (LLOA) model implements an outer approximation of the line losses lazily and typically terminates in a small number of iterations. Experiments on large-scale power systems demonstrate the accuracy and computational efficiency of LLOA and contrast it with classical line loss approaches. The results seem to indicate that LLOA is a practical and useful model for real-world applications, providing a good tradeoff between accuracy, computational efficiency, and implementation simplicity. In particular, the LLOA method may have significant advantages compared to the traditional loss factor formulation for multi-period, stochastic optimization problems where good reference points may not be available. The paper also provides a comprehensive overview and Line losses on branch (i, j) ∈ E − → p ijPower flow from bus i to bus j on branch (i, j) ∈ E ← − p ijPower flow from bus j to bus i on branch (i, j) ∈ E p iActive power injection at bus i ∈ N θ iVoltage angle at bus i ∈ N v iVoltage magnitude at bus i ∈ N