Bi-level optimal planning of voltage regulator in distribution system considering maximization of incentive-based photovoltaic energy integration

Xu Xu, Youwei Jia, Chun Sing Lai, Ming Hao Wang, Zhao Xu

Research output: Journal article publicationJournal articleAcademic researchpeer-review


the photovoltaic (PV) energy integration in distribution grids. To describe the amount of dynamic PV energy that can be integrated into the power system, the concept of PV accommodation capability (PVAC) is introduced and modeled with optimization. Our proposed planning model is formulated as a Benders decomposition based bi-level stochastic optimization problem. In the upper-level problem, VR planning decisions and PVAC are determined via the mixed integer linear programming (MILP) before considering uncertainty. Then in the lower-level problem, the feasibility of first-level results is checked by critical network constraints (e.g. voltage magnitude constraints and line capacity constraints) under uncertainties raised by time-varying loads and PV generations. In this paper, these uncertainties are represented in the form of operation scenarios, which are generated by the Gaussian copula theory and reduced by a well-studied backward-reduction algorithm. The modified IEEE 33-node distribution grid is utilized to verify the effectiveness of the proposed model. The results demonstrate that PV energy integration can be significantly enhanced after optimal voltage regulator planning. This paper focuses on optimal voltage regulators (VRs) planning to maximize.

Original languageEnglish
Article number118578439
JournalCSEE Journal of Power and Energy Systems
Issue number99
Publication statusPublished - 2019


  • bi-level stochastic optimization problem
  • critical network constraints
  • photovoltaic energy integration
  • uncertainties
  • Voltage regulator planning

ASJC Scopus subject areas

  • Energy(all)
  • Electrical and Electronic Engineering
  • Electronic, Optical and Magnetic Materials

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