Optimal transmission switching and grid reconfiguration for transmission systems via convex relaxations

In this paper, we formulate optimization problems to perform optimal transmission switching (OTS) in order to operate power transmission grids most efficiently. In any given electrical network, several of the transmission lines are generally equipped with switches, circuit breakers, and/or reclosers. The conventional practice is to operate the grid using a static or fixed configuration. However, it may be beneficial to dynamically reconfigure the grid through switching actions in order to respond to real-time demand and supply conditions. This has the potential to help reduce costs and improve efficiency. Furthermore, such OTS may be more crucial in future power grids with much higher penetrations of renewable energy sources, which introduce more variability and intermittency in generation. Similarly, OTS can potentially help mitigate the effects of unpredictable demand fluctuations (e.g. due to extreme weather). We explored and compared several different formulations for the OTS problems in terms of computational performance and optimality. I also applied them to small transmission test case networks as a proof of concept to see what the effects of applying OTS are

Improving QC Relaxations of OPF Problems via Voltage Magnitude Difference Constraints and Envelopes for Trilinear Monomials

AC optimal power flow (AC~OPF) is a challenging non-convex optimization problem that plays a crucial role in power system operation and control. Recently developed convex relaxation techniques provide new insights regarding the global optimality of AC~OPF solutions. The quadratic convex (QC) relaxation is one promising approach that constructs convex envelopes around the trigonometric and product terms in the polar representation of the power flow equations. This paper proposes two methods for tightening the QC relaxation. The first method introduces new variables that represent the voltage magnitude differences between connected buses. Using "bound tightening" techniques, the bounds on the voltage magnitude difference variables can be significantly smaller than the bounds on the voltage magnitudes themselves, so constraints based on voltage magnitude differences can tighten the relaxation. Second, rather than a potentially weaker "nested McCormick" formulation, this paper applies "Meyer and Floudas" envelopes that yield the convex hull of the trilinear monomials formed by the product of the voltage magnitudes and trignometric terms in the polar form of the power flow equations. Comparison to a state-of-the-art QC implementation demonstrates the advantages of these improvements via smaller optimality gaps.Comment: 8 pages, 1 figur

New Formulation and Strong MISOCP Relaxations for AC Optimal Transmission Switching Problem

As the modern transmission control and relay technologies evolve, transmission line switching has become an important option in power system operators' toolkits to reduce operational cost and improve system reliability. Most recent research has relied on the DC approximation of the power flow model in the optimal transmission switching problem. However, it is known that DC approximation may lead to inaccurate flow solutions and also overlook stability issues. In this paper, we focus on the optimal transmission switching problem with the full AC power flow model, abbreviated as AC OTS. We propose a new exact formulation for AC OTS and its mixed-integer second-order conic programming (MISOCP) relaxation. We improve this relaxation via several types of strong valid inequalities inspired by the recent development for the closely related AC Optimal Power Flow (AC OPF) problem. We also propose a practical algorithm to obtain high quality feasible solutions for the AC OTS problem. Extensive computational experiments show that the proposed formulation and algorithms efficiently solve IEEE standard and congested instances and lead to significant cost benefits with provably tight bounds

The Value of Distributed Energy Resources (DER) to the Grid: Introductionto the concepts of Marginal Capital Cost and Locational Marginal Value

Distributed Energy Resources (DERs) are argued to be a significant benefit to the electric utility grid. While DERs generate significant benefits to their owners and as well as society, the compensation and operating structure of the distribution system of most utilities is such that DERs result in minimal benefits to the distribution system. As we show, the benefits correctly attributed to the distribution company (the wires company) are a function of what service (real, reactive power) the DER is able to provide, when and where, and at what level of certainty the DER is able to provide the service. We introduce the concepts of Marginal Cost of Capacity (MCC) and Locational Marginal Value (LMV) in the calculation of the value of DERs to the distribution system