Multi-objective optimal power flow considering voltage stability index and emergency demand response program
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ORIGINAL PAPER
Multi‑objective optimal power flow considering voltage stability index and emergency demand response program Ebrahim Kiani1 · Hasan Doagou‑Mojarrad1 · Hadi Razmi1 Received: 6 July 2019 / Accepted: 17 June 2020 © Springer-Verlag GmbH Germany, part of Springer Nature 2020
Abstract In this paper, optimal power flow problem has been implemented and evaluated simultaneously with the emergency demand response program (EDRP), considering the economic and environmental aspects, as well as the voltage stability enhancement of power system. Moreover, employing DRPs is a way to control customers’ electric energy consumption and to improve network reliability. The EDRP is one of the various demand response programs that provides incentives for participants in the program to reduce their consumption during peak hours or shift to off-peak hours. In order to solve the multi-objective function and achieve optimal compromise, the multi-objective Non-Dominated Sorting Genetic Algorithm II was used in this study. The proposed model was implemented on a 30-bus IEEE system. The results show that the proposed model is very effective in reducing fuel costs, emission and improving voltage stability. Keywords Optimal power flow (OPF) · Voltage stability · Emergency demand response List of symbols x The vector of state variables u The vector of control variables g(x, u) Equality constraints h(x, u) Inequality constraints PG,i The active power generation of i th generator VG,i The voltage magnitude of i th generator inci The incentive coefficient at the i th responsive load NG The number of generations NDR The number of responsive loads NL The number of loads NT The number of transmission lines Nobj The number of objective functions NB The number of buses Nnd The number of non-dominated solutions * Hasan Doagou‑Mojarrad [email protected] Ebrahim Kiani [email protected] Hadi Razmi [email protected] 1
Department of Electrical Engineering, East Tehran Branch, Islamic Azad University, Tehran, Iran
VL,i The voltage magnitude of i th PQ bus QG,i The reactive power generation of i th generator ST,i The loading of the i th transmission line ai , bi and ci The fuel cost coefficients of the i th generating unit ( ) E t, t′ Demand elasticity d0,i (t) and di (t) The amount of load at i th response bus before and after the implementing EDRP at the time t , respectively 𝜌0 (t) and 𝜌(t) The electricity prices before and after the implementing EDRP during the period t , respectively inc(t) Incentive coefficient at the time t pen(t) Penalty factor at the time t 𝛼i , 𝛽i and 𝛾i The emission coefficients of the i th generating unit 𝜆 Loading capability 𝜆c Critical loading capability P0L,i (t) and Q0L,i (t) The original load at i th bus active and reactive, respectively P0G,i (t) The active generation at i th bus active in base case tp The time of peak-load 𝜹 and V The vector of bus voltages angles and magnitudes, respectively
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RUi and RDi Up and down ra
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