1 Abstract--This paper presents the main aspects observed in analyzing Complex Voltage Unbalance Factor (CVUF) behavior resulting from the variation of voltage magnitudes and angles. The goal is to identify possible incoherencies regarding the use of the CVUF, and also to investigate whether this factor is more sensitive to variations in magnitude or angles under various voltage unbalance conditions. This study also evaluates the efficiency of the use of the CVUF angle and its association with positive component magnitudes. The results indicate that the CVUF should not be used as a single and sufficient parameter for the quantification of voltage unbalances, which highlights the need to develop a new indicator which may establish a more clear and simple association between this disturbance and its effects on electrical equipment. Index Terms--Voltage Unbalance, Complex Voltage Unbalance Factor, Complex Voltage Unbalance Factor Behavior, Variations in Voltage Magnitudes and Angles. I. NOMENCLATURE C B A V V V , , – line-to-neutral voltage phasors of phases A, B and C; 2 1 0 , , V V V – voltage phasors of the components of the zero, positive and negative sequences; a – Fortescue operator, having unitary magnitude and angle equal to 120º; VUF – voltage unbalance factor (symmetrical components method); CVUF – complex voltage unbalance factor (symmetrical components method). II. INTRODUCTION EVERAL attempts have been made to identify the effects of voltage unbalances on electrical installation loads [1]- [3]. Voltage unbalances provoke, among other problems, excessive losses, overheating, insulation degradation, and a reduction in the lifespan of motors and transformers. Equipment protection systems are also affected, which result in interruptions in production processes. Therefore, any solution aimed at maximizing the lifespan and the working efficiency of motors and transformers in the event of electrical system disturbances should be supported by adequate knowledge and quantification of the parameters involved. In this regard, the following aspects should be considered: • Current methodologies neither are adequate nor present clear justifications regarding their choices and applications. Therefore, voltage unbalance quantification should be based on methods which assume a strong correlation with possible effects on electrical system equipment; • The wide range of models and characteristics of modern equipment, which produce different sensitivity levels when submitted to voltage unbalances; • The absence of performance or immunity standards for equipment submitted to different voltage unbalance conditions; and • The high costs which may be involved with this phenomenon. In this context, this study aimed: 1) to present the main results obtained from the analyses of the effects of voltage magnitude variations on CVUF behavior; 2) to identify the possible incoherencies regarding its use; 3) to investigate whether unbalances are more sensitive to variations in voltage magnitudes than to variations in angles under different unbalance conditions; and 4) to evaluate the efficiency of 2 methods suggested by [1] and [2], namely the use of the CVUF angle, and the association of the positive component magnitude with the CVUF. Presented below are the equations of the unbalance quantification method used in this study and the structure used to perform the simulations involving the CVUF. III. THE COMPLEX VOLTAGE UNBALANCE FACTOR In this study, the symmetrical component method will be used. It is allegedly the most reliable method of voltage unbalance quantification [4], due to the simultaneous utilization of voltage magnitudes and angles. Let us consider V a , V b , and V c as the set of line-to-neutral voltage phasors. The components of the zero, positive and negative sequences, respectively V 0 , V 1 , and V 2 , may be obtained from the following transformation (equation 1): () 1 1 1 1 1 1 3 1 2 2 2 1 0 ⎥ ⎥ ⎥ ⎦ ⎤ ⎢ ⎢ ⎢ ⎣ ⎡ ⎥ ⎥ ⎥ ⎦ ⎤ ⎢ ⎢ ⎢ ⎣ ⎡ = ⎥ ⎥ ⎥ ⎦ ⎤ ⎢ ⎢ ⎢ ⎣ ⎡ c b a V V V a a a a V V V Analysis of the Complex Voltage Unbalance Factor Behavior Resulting from the Variation of Voltage Magnitudes and Angles Ferreira Filho, A. L, Cormane, J. A. A., D. C. Garcia, M. V. C. Costa, M. A. G. Oliveira, F. A. do Nascimento S ▀▀ ▀▀ 978-1-4244-7245-1/10/$26.00 ©2010 IEEE