Chance-constrained optimization for active distribution networks with virtual power lines

Dongwon Lee, Changhee Han, Sungwoo Kang, Gilsoo Jang

Research output: Contribution to journalArticlepeer-review

2 Citations (Scopus)


Active distribution networks (ADNs) experience uncertainties because of the high integration of distributed renewable energy resources (RESs). Stochastic analysis approaches are attracting increasing attention owing to the uncertain nature of RESs and load demands. This study proposes a chance-constrained optimal operation framework for ADNs considering virtual power lines (VPLs) solved via the second- order cone programming (SOCP) optimal power flow (OPF) problem. VPLs comprise virtual lines connected to each network's energy storage systems (ESSs). If one ESS is charged, another ESS is discharged by the same amount. We reformulate the constraints into tractable forms using a simplified Z-bus sensitivity matrix and first-order Taylor expansion to solve via SOCP OPF because the chance constraints on voltage magnitudes are generally non-convex and intractable. The efficacy of the proposed approach was verified through its application to two modified IEEE 33-bus systems, each featuring different consumer units, including commercial, residential, and industrial units. The effectiveness of the proposed methods was demonstrated by comparing three different types of constraints: conventional hard constraints, soft constraints with penalties, and chance constraints. The results showed that although the chance constraints case had a slightly higher voltage violation rate, the network power loss was reduced by 3.4% compared to the conventional hard constraints case. Furthermore, modified 85-bus and 65-bus systems are carried out to verify the algorithm's scalability. The proposed approach achieves a trade-off between voltage regulation and power loss minimization, with a voltage violation rate of 0.88% and a power loss reduction to 1.02%.

Original languageEnglish
Article number109449
JournalElectric Power Systems Research
Publication statusPublished - 2023 Aug

Bibliographical note

Funding Information:
This work was supported by the Korea Institute of Energy Technology Evaluation and Planning (KETEP) grant funded by the Korea government (MOTIE) (No. 20191210301890 ). This work was supported by the Nuclear Safety Research Program through the Korea Foundation Of Nuclear Safety (KoFONS) using the financial resource granted by the Nuclear Safety and Security Commission (NSSC) of the Republic of Korea (No. 2204009 ).

Publisher Copyright:
© 2023 Elsevier B.V.


  • Chance-constrained optimization
  • Distributed generator
  • Second-order cone programming
  • Stochastic analysis
  • Virtual power lines

ASJC Scopus subject areas

  • Energy Engineering and Power Technology
  • Electrical and Electronic Engineering


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