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Center for Nonlinear Studies |
We explore optimization methods for both planning the placement and sizing and the operation of Flexible Alternating Current Transmission System (FACTS) devices for relieving power transmission grid congestion created by load growth or fluctuations of intermittent renewable resources. We limit our selection of FACTS devices to those that can be approximated as changing transmission line inductance. The problem is stated as a non-convex optimization over the vector of line inductance modifications with the cost represented by the l1-norm of the vector. The optimization is subject to constraints that require that no transmission lines are overloaded for any of a set of generator and load configurations (contingencies) which otherwise would be overloaded without the FACTS inductance corrections. We develop off-line heuristics that reduce this non-convex optimization to a sequence of Linear Programs (LP) by iteratively linearizing the constraints analytically around the current vector of inductances. The algorithm is accelerated further with a cutting plane method which greatly reduces the number of active constraints during the optimization, while checking feasibility of the non-active constraints post-factum. Our hybrid algorithm solves a typical single-contingency problem over the MathPower Polish Grid model (3299 lines and 2746 nodes) in 40 seconds per iteration on a standard quad-core computer—a speed up that allows the sizing and placement of a family of FACTS devices to correct a large set of anticipated contingencies. By testing multiple interesting examples we show that our algorithms finds feasible solutions that are always sparse, i.e., FACTS devices are placed on only a few lines. We also observe that FACTS are not always placed on or near the subset of originally congested transmission lines. This is a joint work with S. Backhaus and M. Chertkov.
Host: Michael Chertkov