Optimization is ubiquitous in power system engineering. Drawing on powerful, modern tools from convex optimization, this rigorous exposition introduces essential techniques for formulating linear, second-order cone, and semidefinite programming approximations to the canonical optimal power flow problem, which lies at the heart of many different power system optimizations. Convex models in each optimization class are then developed in parallel for a variety of practical applications like unit commitment, generation and transmission planning, and nodal pricing. Presenting classical approximations and modern convex relaxations side-by-side, and a selection of problems and worked examples, this is an invaluable resource for students and researchers from industry and academia in power systems, optimization, and control.

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Convex Optimization of Power Systems

Optimal allocation of capacitors in radial/mesh distribution systems using mixed integer nonlinear programming approach

Under the smart grid paradigm, distribution systems with large penetrations of photovoltaic-based power generation are called to optimize their operational resources to achieve a more efficient and reliable performance. In this context, this paper proposes a multiperiod mixed integer second order cone formulation to optimize distribution feeders operation. The model takes into account the feeder physical behavior; discrete control equipment (tap changers and capacitors banks) with a maximum allowable daily switching operation number; photovoltaic inverters operation; and the uncertain nature of solar energy and loads. A two–stage robust optimization framework is used to include the uncertainty into the model, where discrete and continuous control actions are assumed to be part of the first and second stage of this model, respectively. The conservativeness level of the robust model is controlled by an polyhedral uncertainty set whose vertexes are adaptively adjusted in a data–driven fashion in order to better capture complex spatiotemporal dependencies among uncertain parameters. Extensive computational experiments are performed utilizing modified versions of various IEEE test feeders. The performance of the proposed data–driven model is contrasted against traditional deterministic and robust budget–constrained models, using a rolling horizon out–of–sample evaluation methodology. When compared to the deterministic model, the data–driven approach yields a reduction in power losses of approximately 15% and a reduction up to 98% in hourly voltage violations. Results also suggests that the proposed approach exhibits better performance in terms of both average and conditional–value–at–risk metrics in comparison to budget–constrained models.

Power Management in Active Distribution Systems Penetrated by Photovoltaic Inverters: A Data-Driven Robust Approach

Improving the energy efficiency of an islanded distribution network using classical and innovative computation methods

A control optimization model for CVaR risk of distribution systems with PVs/DSs/EVs using Q-learning powered adaptive differential evolution algorithm

This paper introduces a mixed-integer conic programming approach to solve the optimal capacitor placement problem in radial distribution networks. The problem is formulated to allow optimally placing fixed and switched-type capacitors; its objective is to minimize the peak power losses, the energy losses, and the costs associated with the required capacitor banks while satisfying the physical and technical constraints on the network. The proposed solution is based on the conic quadratic format of the power flow equations. As a result of using the conic format, the relaxation becomes convex and therefore a global solution to the capacitor planning problem can be obtained using a branch-and-cut algorithm. The method is tested on two radial test systems with 34 and 83 nodes having up to 12 load levels and is validated by comparison with previously published solution results.

S. A. Abou Jawdeh

Papers

Mixed integer conic programming approach for optimal capacitor placement in radial distribution networks