Resonancia en capacitores sh

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A Practical Harmonic Resonance Guideline for Shunt Capacitor Applications
Zhenyu Huang, Member, IEEE, Wilsun Xu, Senior Member, IEEE, and V. R. Dinavahi, Member, IEEE
Abstract—Shunt capacitors are extensively used in power systems for voltage support and power factor correction. The proliferation ofharmonic-producing loads significantly increases the possibility of system-capacitor resonance. As a result, a practical and easy-to-use procedure to estimate the severity of harmonic resonance is of good interest to industry. The objective of this paper is to present such a method. The paper first proposes a harmonic resonance index. By taking into account the IEEE harmonic limits and the capacitor loadinglimits, a harmonic resonance chart is developed. A detailed harmonic analysis of the system is needed only if the system condition is located in certain regions of the chart. Examples are given to show how the possibility and severity of harmonic resonance can be estimated using the proposed guideline. Index Terms—Capacitors, harmonic resonance, harmonics.

Fig. 1. Equivalent system with capacitor tobe installed.

I. INTRODUCTION PPLICATION of shunt capacitors for voltage support and power factor correction is a common practice in the power industry. With the proliferation of harmonic-producing loads and the increasing awareness of harmonic effects, the possibility of system-capacitor resonance has become a routine concern for shunt capacitor applications [1]–[3]. Whenever a shuntcapacitor is to be added or resized, system planners are interested to know if the proposed capacitor installation would resonate with the system and, if there is a resonance, the severity of the problem. A well-known and commonly practiced method to verify if a capacitor resonates with its supply system is to determine the ratio of the system fault level to the capacitor size [4]. Resonance frequency canbe estimated from this ratio. Our experience shows that this method is too crude to be practically useful. The formula is based on the assumption that the system harmonic reactance is proportional to its fundamental reactance determined from the fault level. There is no guarantee that this assumption is valid for practical interconnected power systems. Furthermore, one cannot determine theseverity of the resonance as not all resonance conditions will cause problems. An alternative to the above method is to conduct harmonic power flow study and/or frequency scan study. The harmonic power flow study is too complicated for this task since the locations of harmonic sources and the source characteristics are typically unknown. The frequency scan study [5]–[7] is more
Manuscript receivedJanuary 8, 2002; revised May 3, 2002. This work was supported by a grant from the Natural Sciences and Engineering Research Council of Canada. The authors are with the Department of Electrical and Computer Engineering, The University of Alberta, Edmonton, AB T6G 2V4 (e-mail: zhuang@;; Digital Object Identifier 10.1109/TPWRD.2003.817726

Auseful. It can reveal the resonance frequencies and the associated magnitudes of the combined system-capacitor impedance. The study is easy to do so the engineers who plan the capacitor installation can perform the study. There is one major difficulty to use the frequency scan method however. If the engineers have obtained the impedance frequency curve, how can they draw a conclusion as to thepotential harmonic impact of the proposed capacitor? The resonance frequency may or may not coincide with a harmonic order. If it does, the existence of harmonic resonance does not necessarily imply that a problem would occur, since the system resistance may provide sufficient damping to the resonance. If it does not coincide with a harmonic frequency, the system damping may still be too small so...
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