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distributed Stochastic Reserve Scheduling in AC Power Systems With Uncertain Generation

IEEE TRANSACTIONS ON POWER SYSTEMS 2019年第2期34卷 1005-1020页

作者： Rostampour, Vahab ter Haar, Ole Keviczky, Tamas Delft Univ Technol Delft Ctr Syst & Control NL-2628 CD Delft Netherlands

This paper presents a framework to carry out multi-area stochastic reserve scheduling (RS) based on an ac optimal power flow (OPF) model with high penetration of wind power using distributed consensus and the alternating direction method of multipliers (ADMM). We first formulate the OPF-RS problem using semidefinite programming (SDP) in infinite-dimensional spaces that is in general computationally intractable. Using a novel affine policy, we develop an approximation of the infinite-dimensional SDP as a tractable finite dimensional SDP, and explicitly quantify the performance of the approximation. To this end, we adopt the recent developments in randomized optimization that allow a priori probabilistic feasibility guarantees to optimally schedule power generating units while simultaneously determining the geographical allocation of the required reserve. We then use the geographical pattern of the power system to decompose the large-scale system into a multi-area power network, and provide a consensus ADMM algorithm to find a feasible solution for both local and overall multi-area network. Using our distributed stochastic framework, each area can use its own wind information to achieve local feasibility certificates, while ensuring overall feasibility of the multi-area power network under mild conditions. We provide numerical comparisons with a new benchmark formulation, the so-called converted dc (CDC) power flow model, using Monte Carlo simulations for two different IEEE case studies.

关键词： AC power systems distributed stochastic consensus ADMM distributed scenario program distributed stochastic reserve allocations multi-area AC power systems stochastic reserve scheduling

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distributed Computational Framework for Large-Scale Stochastic Convex Optimization

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ENERGIES 2021年第1期14卷 23-23页

作者： Rostampour, Vahab Keviczky, Tamas Univ Groningen Engn & Technol Inst Groningen ENTEG Nijenborgh 4 NL-9747 AG Groningen Netherlands Delft Univ Technol Delft Ctr Syst & Control NL-2628 CD Delft Netherlands

This paper presents a distributed computational framework for stochastic convex optimization problems using the so-called scenario approach. Such a problem arises, for example, in a large-scale network of interconnected linear systems with local and common uncertainties. Due to the large number of required scenarios to approximate the stochasticity of these problems, the stochastic optimization involves formulating a large-scale scenario program, which is in general computationally demanding. We present two novel ideas in this paper to address this issue. We first develop a technique to decompose the large-scale scenario program into distributed scenario programs that exchange a certain number of scenarios with each other to compute local decisions using the alternating direction method of multipliers (ADMM). We show the exactness of the decomposition with a-priori probabilistic guarantees for the desired level of constraint fulfillment for both local and common uncertainty sources. As our second contribution, we develop a so-called soft communication scheme based on a set parametrization technique together with the notion of probabilistically reliable sets to reduce the required communication between the subproblems. We show how to incorporate the probabilistic reliability notion into existing results and provide new guarantees for the desired level of constraint violations. Two different simulation studies of two types of interconnected network, namely dynamically coupled and coupling constraints, are presented to illustrate advantages of the proposed distributed framework.

关键词： stochastic optimization scenario convex program distributed computation distributed stochastic systems distributed scenario program decentralized scenario program plug-and-play framework

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