An S \(\ell _1\) LP-active set approach for feasibility restoration in power systems

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• 作者：Taedong Kim ; Stephen J. Wright
• 刊名：Optimization and Engineering
• 出版年：2016
• 出版时间：June 2016
• 年：2016
• 卷：17
• 期：2
• 页码：385-419
• 全文大小：1,449 KB
• 刊物类别：Mathematics and Statistics
• 刊物主题：Mathematics
  Optimization
  Engineering, general
  Systems Theory and Control
  Environmental Management
  Agriculture
  Operation Research and Decision Theory
  
• 出版者：Springer Netherlands
• ISSN：1573-2924
• 卷排序：17

文摘

We consider power networks in which it is not possible to satisfy all loads at the demand nodes, due to some attack or disturbance to the network. We formulate a model, based on AC power flow equations, to restore the network to feasibility by adjusting load at demand nodes or power production at generators, but doing so in a way that minimizes a weighted measure of the total power adjustment, and affects as few nodes as possible. Besides suggesting an optimal response to a given attack, our approach can be used to quantify disruption, thereby enabling “stress testing” to be performed and vulnerabilities to be identified. Optimization techniques including nonsmooth penalty functions, sequential linear programming, and active-set heuristics are used to solve this model. We describe an algorithmic framework and present convergence results, including a quadratic convergence result for the case in which the solution is fully determined by its constraints, a situation that arises frequently in the power systems application.KeywordsAC power flow equationsComposite nonsmooth optimizationSequential linear programmingActive-set methods