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A second-order cone model of transmission planning with alternating and direct current lines. (English) Zbl 1430.90168
Summary: We construct a model for transmission planning with both alternating and direct current lines, the latter of which can be interfaced via either line-commutated converters or voltage-source converters. The transmission expansion problem is nonlinear and nonconvex. Thus, nonlinear solvers cannot guarantee their convergence to the global optimum of the problem. We use relaxations and approximations to formulate a mixed-integer second-order cone transmission expansion model, which can be solved to optimality by current industrial solvers. We base our formulation on the branch flow relaxation. We include losses and reactive power placement, and consider direct current lines connected by both line-commutated converters and voltage-sourced converters. We show that our approach lowers the expansion cost on 6-bus and 24-bus system examples. We evaluate the feasibility of our formulation using a semidefinite relaxation of optimal power flow and find that the resulting plan admits feasible or close to feasible power flows.
MSC:
90B10 Deterministic network models in operations research
90B90 Case-oriented studies in operations research
90C11 Mixed integer programming
90C20 Quadratic programming
90C25 Convex programming
Software:
Gurobi; Mosek; MATPOWER; CVXPY
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