Stochastic Optimization of DG Planning in Unbalanced Distribution Networks Under Time-of-Use Pricing
Received: 2 April 2026 | Revised: 27 April 2026 and 6 May 2026 | Accepted: 10 May 2026 | Online: 6 June 2026
Corresponding author: Trieu Ngoc Ton
Abstract
The increasing penetration of Distributed Generation (DG) and demand variability necessitate planning models that explicitly account for uncertainty in Distribution Networks (DNs). This paper proposes a stochastic optimization framework for DG planning in unbalanced networks under time-of-use pricing. The problem is formulated as a bilevel model, where the upper level represents the distribution system operator, and the lower level captures the demand-response behavior. Uncertainty in load and generation is modeled using a scenario-based approach. The original bi-level formulation is reformulated into a single-level problem using Karush-Kuhn-Tucker (KKT) conditions and solved via a metaheuristic optimization method to handle nonlinear and non-convex characteristics. Simulation results on the IEEE 33-bus and 69-bus systems demonstrate consistent improvements in power loss reduction, voltage profile, and operational cost. The findings indicate that these improvements are primarily driven by the integrated modeling framework, which jointly accounts for uncertainty, demand response, and network imbalance, rather than the optimization algorithm itself. The proposed approach provides a robust and practical solution for distribution system planning under uncertainty.
Keywords:
stochastic optimization, distributed generation, bi-level optimization, demand response, time-of-use pricing, unbalanced distribution networksReferences
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Copyright (c) 2026 Trieu Ngoc Ton, Loc Huu Pham, Tuyen Ngoc Hoang, Loi Van Pham, Hai Hoang Lai, Tan Minh Le
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