Abstract
We explore optimization methods for planning the placement, sizing and operations of flexible alternating current transmission system (FACTS) devices installed to relieve transmission grid congestion. We limit our selection of FACTS devices to series compensation (SC) devices that can be represented by modification of the inductance of transmission lines. Our master optimization problem minimizes the l1 norm of the inductance modification subject to the usual line thermal-limit constraints. We develop heuristics that reduce this non-convex optimization to a succession of linear programs (LP) that are accelerated further using cutting plane methods. The algorithm solves an instance of the MatPower Polish Grid model (3299 lines and 2746 nodes) in 40 seconds per iteration on a standard laptop—a speed that allows the sizing and placement of a family of SC devices to correct a large set of anticipated congestions. We observe that our algorithm finds feasible solutions that are always sparse, i.e., SC devices are placed on only a few lines. In a companion manuscript, we demonstrate our approach on realistically sized networks that suffer congestion from a range of causes, including generator retirement. In this manuscript, we focus on the development of our approach, investigate its structure on a small test system subject to congestion from uniform load growth, and demonstrate computational efficiency on a realistically sized network.
Highlights
Power grids are undergoing significant evolution that often results in increased stress from sources including fluctuating renewable generation, generation retirement, and the continual growth and evolution of electrical loads
Our model considers the effect of a Flexible Alternating Current Transmission System (FACTS) device[20] as a continuous modification of the inductance of a transmission line—a model that is directly applicable to ThyristorControlled Series Compensation (TCSC) devices that use a continuously controllable reactor in parallel with a bank of switchable capacitors[9]
We developed an approach to the placement and sizing of SC devices to relieve congestions in transmission networks
Summary
Power grids are undergoing significant evolution that often results in increased stress from sources including fluctuating renewable generation, generation retirement, and the continual growth and evolution of electrical loads. To fully extract the benefit of FACTS devices, one ought to build in the operations and control of FACTS devices into algorithms for optimal placement and sizing that consider the entire network, not just a small section of the network. A second challenge to the optimal placement and sizing of FACTS devices is the non-local nature of power flows over transmission networks and the need to consider system-wide impacts of FACTS placement. By combining the methods discussed above, we seek to formulate and solve a comprehensive FACTS placement and sizing problem that considers the transmission system as a whole while combining aspects of planning and operations. We apply our method to realistically-sized networks with sources of network stress such as generator retirement In this manuscript, we focus on the development of the approach, and we use uniform load growth as a exemplary case.
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