Ahmed S. Zamzam

Beyond Relaxation and Newton–Raphson: Solving AC OPF for Multi-Phase Systems With Renewables

This paper focuses on the AC Optimal Power Flow (OPF) problem for multi-phase systems. Particular emphasis is given to systems with high integration of renewables, where adjustments of the real and reactive output powers from renewable sources of energy are necessary in order to enforce voltage regulation. The AC OPF problem is known to be nonconvex (and, in fact, NP-hard). Convex relaxation techniques have been recently explored to solve the OPF task with reduced computational burden; however, sufficient conditions for tightness of these relaxations are only available for restricted classes of system topologies and problem setups. Identifying feasible power-flow solutions remains hard in more general problem formulations, especially in unbalanced multi-phase systems with renewables. To identify feasible and optimal AC OPF solutions in challenging scenarios where existing methods may fail, this paper leverages the Feasible Point Pursuit - Successive Convex Approximation algorithm—a powerful approach for general nonconvex quadratically constrained quadratic programs. The merits of the approach are illustrated using single- and multi-phase distribution networks with renewables, as well as several transmission systems.

Power system state estimation via feasible point pursuit

Accurately monitoring the systems operating point is central to the reliable and economic operation of an autonomous energy grid. Power system state estimation (PSSE) aims to obtain complete voltage magnitude and angle information at each bus given a number of system variables at selected buses and lines. Power flow analysis amounts to solving a set of noise-free power flow equations, and is cast as a special case of PSSE. Physical laws dictate quadratic relationships between available quantities and unknown voltages, rendering general instances of power flow and PSSE nonconvex and NP-hard. Past approaches are largely based on gradient-type iterative procedures or semidefinite relaxation (SDR). Due to nonconvexity, the solution obtained via gradient-type schemes depends on initialization, while SDR methods do not perform as desired in challenging scenarios. This paper puts forth novel feasible point pursuit (FPP)-based solvers for power flow analysis and PSSE, which iteratively seek feasible solutions for a nonconvex quadratically constrained quadratic programming reformulation of the weighted least-squares (WLS). Relative to the prior art, the developed solvers offer superior numerical performance at the cost of higher computational complexity. Furthermore, they converge to a stationary point of the WLS problem. As a baseline for comparing different estimators, the Cramér-Rao lower bound is derived for the fundamental PSSE problem in this paper. Judicious numerical tests on several IEEE benchmark systems showcase markedly improved performance of our FPP-based solvers for both power flow and PSSE tasks over popular WLS-based Gauss–Newton iterations and SDR approaches.

Power system state estimation via feasible point pursuit: Algorithms and Cramér-rao bound

Power system state estimation (PSSE) is a critical task for grid operation efficiency and system stability. Physical laws dictate quadratic relationships between observable quantities and voltage state variables, hence rendering the PSSE problem nonconvex and NP-hard. Existing SE solvers largely rely on iterative optimization methods or semidefinite relaxation (SDR) techniques. Even when based on noiseless measurements, convergence of the former is sensitive to the initialization, while the latter is challenged by small-size measurements especially when voltage magnitudes are not available at all buses. At the price of running time, this paper proposes a novel feasible point pursuit (FPP)-based SE solver, which iteratively seeks feasible solutions for a nonconvex quadratically constrained quadratic programming reformulation of the weighted least-squares (WLS) SE problem. Numerical tests corroborate that the novel FPP-based SE markedly improves upon the Gauss-Newton based WLS and SDR-based SE alternatives, also when noisy measurements are available.

Coupled graph tensor factorization

Factorization of a single matrix or tensor has been used widely to reveal interpretable factors or predict missing data. However, in many cases side information may be available, such as social network activities and user demographic data together with Netflix data. In these situations, coupled matrix tensor factorization (CMTF) can be employed to account for additional sources of information. When the side information comes in the form of item-correlation matrices of certain modes, existing CMTF algorithms do not apply. Instead, a novel approach to model the correlation matrices is proposed here, using symmetric nonnegative matrix factorization. The multiple sources of information are fused by fitting outer-product models for the tensor and the correlation matrices in a coupled manner. The proposed model has the potential to overcome practical challenges, such as missing slabs from the tensor and/or missing rows/columns from the correlation matrices.

Optimal Water-Power Flow Problem: Formulation and Distributed Optimal Solution

This paper formalizes an optimal water–power flow (OWPF) problem to optimize the use of controllable assets across power and water systems while accounting for the couplings between the two infrastructures. Tanks and pumps are optimally managed to satisfy water demand while improving power grid operations; for the power network, an ac optimal power-flow formulation is augmented to accommodate the controllability of water pumps. Unfortunately, the physics governing the operation of the two infrastructures and coupling constraints leads to a nonconvex (and, in fact, NP-hard) problem; however, after reformulating OWPF as a nonconvex, quadratically constrained quadratic problem, a feasible point pursuit-successive convex approximation approach is used to identify feasible and optimal solutions. In addition, a distributed solver based on the alternating direction method of multipliers enables water and power operators to pursue individual objectives while respecting the couplings between the two networks. The merits of the proposed approach are demonstrated for the case of a distribution feeder coupled with a municipal water distribution network.