Optimal Allocation and Sizing of Capacitors for Distribution Systems Reinforcement Based on Minimum Life Cycle Cost and Considering Uncertainties

V. V. Thang*, N. D. Minh
Thainguyen University of Technology (TNUT), Thainguyen, Vietnam

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© 2017 Thang and Minh.

open-access license: This is an open access article distributed under the terms of the Creative Commons Attribution 4.0 International Public License (CC-BY 4.0), a copy of which is available at: This license permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.

* Address correspondence to this author at the Thainguyen University of Technology - Electric Power System Thainguyen, Viet Nam Electric Power System Vietnam, Tel: 0084-915176569; E-mail:



The power and voltage losses have been greatly concerned in the distribution system planning and operation because low normal voltage, high impedance and load density of the system lead to increases in losses and decreases in bus voltages.


Therefore, an optimization model for the distribution system reinforcement improving efficiency of distribution systems by integrating capacitors is proposed. The optimal allocation and sizing of capacitors are determined concurrently with optimal upgrading sizing and timeframe of feeders and substations. The objective function of model is to minimize life cycle cost over reinforcement scheme including investment and operation costs of equipment in distribution systems (including feeders, substations and capacitors) and costs for purchasing energy from the electric market.


The typical load curves for each day and season with uncertainties modeled by a Probability Distribution Function (PDF) and Time of Use (TOU) price applied to enhance accuracy of calculation results and suitability for real operation conditions. General Algebraic Modeling System (GAMS) is applied to undertake calculations in a test system.

Keyword: Distribution System, Optimization, Capacitor, Life cycle cost, GAMS, Uncertainties.