This letter investigates a new class of optimal power flow problem for distribution systems, where elastic loads respond to real-time nodal prices by adjusting their demands. A fixed point iteration algorithm is suggested to identify an equilibrium. A concise criterion is devised to judge convergence.
The wide integration of gas-fired units and implementation of power-to-gas technologies bring increasing interdependence among the natural gas and electricity infrastructures. This paper studies the equilibrium of the coupled gas and electricity markets, which is driven by the strategic offering behaviors: each producer endeavours to maximize its own profit by taking the market clearing process into consideration. The market equilibrium can be obtained from an equilibrium problem with equilibrium constraints. A special diagonalization algorithm is devised, in which the unilateral equilibrium of the gas or electricity market is found in the inner loop given the rivals' strategies; the interactions of the two markets are tackled in the outer loop. Case studies on two test systems validate the proposed methodology.
This paper proposes a sequential convex optimization method to solve broader classes of optimal power flow (OPF) problems over radial networks. The non-convex branch power flow equation is decomposed as a second-order cone inequality and a non-convex constraint involving the difference of two convex functions. Provided with an initial solution offered by an inexact second-order cone programming relaxation model, this approach solves a sequence of convexified penalization problems, where concave terms are approximated by linear functions and updated in each iteration. It could recover a feasible power flow solution, which usually appears to be very close, if not equal, to the global optimal one. Two variations of the OPF problem, in which non-cost related objectives are optimized subject to power flow constraints and the convex relaxation is generally inexact, are elaborated in detail. One is the maximum loadability problem, which is formulated as a special OPF problem that seeks the maximal distance to the boundary of power flow insolvability. The proposed method is shown to outperform commercial nonlinear solvers in terms of robustness and efficiency. The other is the bi-objective OPF problem. A non-parametric scalarization model is suggested, and is further reformulated as an extended OPF problem by convexifying the objective function. It provides a single trade-off solution without any subjective preference. The proposed computation framework also helps retrieve the Pareto front of the bi-objective OPF via the e-constraint method or the normal boundary intersection method. This paper also discusses extensions for OPF problems over meshed networks based on the semidefinite programming relaxation method.