Reverse harmonic load flow analysis using an evolutionary technique
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Reverse harmonic load flow analysis using an evolutionary technique B. Vedik1 · C. K. Shiva1 · P. Harish2 Received: 31 December 2019 / Accepted: 23 August 2020 © Springer Nature Switzerland AG 2020
Abstract In the present paper, a new approach to estimate the harmonic distortions is proposed by considering the existence of harmonic sources in the power system. The algorithm employs a differential evolution technique by formulating the reverse harmonic load flow problem for each harmonic order and by considering a limited number of phasor measurement units (PMUs) deployed across the power system. The technique utilizes the measured voltage and current harmonics obtained using synchronized PMUs with known transmission network as input data. The proposed technique estimates the harmonic voltage phasors at the unmonitored buses of the power system with reasonable accuracy. The effectiveness and efficiency of the proposed method is validated by applying it to five bus and IEEE 14-bus test systems by considering uncertainty in measurement noise. It is shown that the proposed approach yields optimum solution and provides reliable and accurate harmonic state estimates. Keywords Differential evolution · Reverse harmonic power flow · Harmonic state estimation · Harmonic voltage phasor
1 Introduction With the significant growth of power electronic devices has led to an increase in the harmonic distortion of power supply waveform [1]. Harmonic distortion can be defined as the voltages and currents having frequencies that are integer multiples of the fundamental frequency and further any deviation from the perfect sinusoidal waveform [2]. The penetration of these harmonics into the system not only affects the quality of power supply but also causes a severe problem in various power system components [1]. In order to maintain high-quality power supply, these harmonic sources should be assessed, monitored, and mitigated [3]. Because of this reason, harmonic analysis has become a vital factor in power system analysis and design. Harmonic state estimation (HSE) is a reverse procedure to harmonic load flow analysis. In harmonic power flow analysis, response (harmonic distortion) of the power system is determined by injecting harmonic sources at one or
more locations of the power system network. Whereas in HSE, harmonic sources (harmonic injections) are evaluated for the power system network response given by a set of harmonic measurements [1]. Although the measurement meters are becoming less costly, it is neither efficient nor essential to deploy phasor measurement units (PMUs) at every bus of the power system to perform state estimation. Consequently, various PMU placement methods have been developed to deploy these PMUs optimally across the power system network. In such circumstances, the HSE process is suggested when limited locations are selected for the installation of PMUs [4]. The HSE process utilizes a set of measurements obtained from PMUs along with the system configuration supplied by the topological processor, net
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