相关论文: Examining the rank of Semi-definite Programming fo…
The ground state energy of a many-electron system can be approximated by an variational approach in which the total energy of the system is minimized with respect to one and two-body reduced density matrices (RDM) instead of many-electron…
This paper considers a probabilistic generalization of the $N$-$k$ failure-identification problem in power transmission networks, where the probability of failure of each component in the network is known a priori and the goal of the…
Peak Estimation aims to find the maximum value of a state function achieved by a dynamical system. This problem is non-convex when considering standard Barrier and Density methods for invariant sets, and has been treated heuristically by…
Considering increasing distributed energy resources and responsive loads in smart grid, this paper proposes a stochastic simulation approach for stability analysis of a power system having stochastic loads. The proposed approach solves a…
Today's power generation and distribution networks are quickly moving toward automated control and integration of renewable resources - a complex, integrated system termed the Smart Grid. A key component in planning and managing of Smart…
This paper proposes a sequential convex relaxation method for obtaining feasible and near-globally optimal solutions for unit commitment (UC) with AC transmission constraints. First, we develop a second-order cone programming (SOCP)…
We consider the NP-hard problem of minimizing a convex quadratic function over the integer lattice ${\bf Z}^n$. We present a simple semidefinite programming (SDP) relaxation for obtaining a nontrivial lower bound on the optimal value of the…
A placement problem for multiple Battery Energy Storage System (BESS) units is formulated towards power system transient voltage stability enhancement in this paper. The problem is solved by the Cross-Entropy (CE) optimization method. A…
In this paper an unscented Kalman filter with guaranteed positive semidefinite state covariance is proposed by calculating the nearest symmetric positive definite matrix in Frobenius norm and is applied to power system dynamic state…
This paper studies two fundamental problems in power systems: the economic dispatch problem (EDP) and load shedding. For the EDP, an extension of the problem considering the transmission losses is presented. Because the optimization problem…
Dynamic state estimation (DSE) is becoming increasingly important for monitoring inverter-dominated power systems. Due to their cascading control structures, inverter-based resources (IBRs) exhibit multi-timescale dynamics, leading to stiff…
Despite the numerous uses of semidefinite programming (SDP) and its universal solvability via interior point methods (IPMs), it is rarely applied to practical large-scale problems. This mainly owes to the computational cost of IPMs that…
We propose a framework for integrating optimal power flow (OPF) with state estimation (SE) in the loop for distribution networks. Our approach combines a primal-dual gradient-based OPF solver with a SE feedback loop based on a limited set…
A large number of problems in optimization, machine learning, signal processing can be effectively addressed by suitable semidefinite programming (SDP) relaxations. Unfortunately, generic SDP solvers hardly scale beyond instances with a few…
We consider the problem of designing an optimal quantum detector to minimize the probability of a detection error when distinguishing between a collection of quantum states, represented by a set of density operators. We show that the design…
The problem of effective use of Phasor Measurement Units (PMUs) to enhance power systems awareness and security is a topic of key interest. The central question to solve is how to use this new measurements to reconstruct the state of the…
Recent results in the study of the Hamilton Jacobi Bellman (HJB) equation have led to the discovery of a formulation of the value function as a linear Partial Differential Equation (PDE) for stochastic nonlinear systems with a mild…
The concept of dispatchable region plays a pivotal role in quantifying the capacity of power systems to accommodate renewable generation. In this paper, we extend the previous approximations of the dispatchable regions on direct current…
Given an affine space of matrices $\mathcal{L}$ and a matrix $\Theta\in \mathcal{L}$, consider the problem of computing the closest rank deficient matrix to $\Theta$ on $\mathcal{L}$ with respect to the Frobenius norm. This is a nonconvex…
We propose an estimation method for quantum measurement tomography (QMT) based on semidefinite programming (SDP), and discuss how it may be employed to detect experimental imperfections, such as shot noise and/or faulty preparation of the…