Frequency-Dependent Electric Power Line Modeling for Steady State Harmonic Analysis
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Abstract
The modern electric power system is experiencing an increased level of harmonic frequency components because of the growing use of power electronic devices, such as converters, and nonlinear loads, such as rectifier-end loads. Electric power line models commonly used in system level studies have been historically developed with the assumption that only the fundamental frequency-component (50 or 60 Hz) propagates in the system. These conventional line models, such as the PI and the exact PI models, are therefore sufficiently accurate to represent the line behavior at the fundamental frequency; they are not however as accurate when the propagation of harmonic frequencies is of interest. Frequency-dependent characteristics of electric power lines and subsequent development of frequency-dependent line models have been historically focused on capturing transient behavior, such as resulting from switching and element energizing events, in which the harmonic content is high. Transient analysis is not sufficient to study the harmonic components since the present grid has significant level of steady state harmonic components. Moreover, the models developed for transient analysis are not applicable in frequency domain simulation environments. Although time domain analysis can be performed to study the steady state voltages and currents in large systems, it is unnecessary and computationally burdensome. This research work focuses on the investigation and derivation of a frequency-dependent electric power line model for steady state harmonic studies characterized by a single generic model which can be used for both overhead and underground electric power lines of any length. In order to achieve this goal, first an analytical benchmark model is derived using the analytical equations of the distributed line model expressed in hyperbolic functions and incorporating frequency dependent effects such as the effect of ground return and the skin effect. Two frequency-dependent line modeling approaches are first studied: the multi-segment line model structure and an approximation based line modeling approach. This investigation led to the development of the proposed frequency-dependent electric power line model, which is characterized by a PI structure and represented by a passive circuit realization. The developed frequency-dependent line modeling approaches are evaluated in terms of their effectiveness in system level studies such as harmonic power flow algorithms. Test cases are developed to run harmonic power flow using the different line models. The proposed models are compared with the currently-used models, i.e. the PI and the exact PI models, as well as with the benchmark analytical model. Metrics for comparison are series impedance, shunt admittance and line terminal behavior (harmonic voltage magnitudes and phases). It is observed that the proposed model is easily integrated in the system level analysis tools, such as harmonic power flow, and results in a significantly improved accuracy over the currently-used simple PI or exact PI models.