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Shunt FACTS devices, such as, a Static Var Compensator (SVC), are capable of providing local reactive power compensation. They are widely used in the network to reduce the real power loss and improve the voltage profile. This paper proposes a planning model based on mixed integer conic programming (MICP) to optimally allocate SVCs in the transmission network considering load uncertainty. The load uncertainties are represented by a number of scenarios. Reformulation and linearization techniques are utilized to transform the original non-convex model into a convex second order cone programming (SOCP) model. Numerical case studies based on the IEEE 30-bus system demonstrate the effectiveness of the proposed planning model.
We present a two-level branch-and-bound (BB) algorithm to compute the optimal gripper pose that maximizes a grasp metric in a restricted search space. Our method can take the grippers kinematics feasibility into consideration to ensure that a given g
We study the problem of learning a linear model to set the reserve price in an auction, given contextual information, in order to maximize expected revenue from the seller side. First, we show that it is not possible to solve this problem in polynomi
We study robust convex quadratic programs where the uncertain problem parameters can contain both continuous and integer components. Under the natural boundedness assumption on the uncertainty set, we show that the generic problems are amenable to ex
We introduce and study conic geometric programs (CGPs), which are convex optimization problems that unify geometric programs (GPs) and conic optimization problems such as semidefinite programs (SDPs). A CGP consists of a linear objective function tha
The most important ingredient for solving mixed-integer nonlinear programs (MINLPs) to global epsilon-optimality with spatial branch and bound is a tight, computationally tractable relaxation. Due to both theoretical and practical considerations, rel