The problem of imbalance detection in a three-phase power system using a phasor measurement unit (PMU) is considered. A general model for the zero, positive, and negative sequences from a PMU measurement at off-nominal frequencies is presented and a hypothesis testing framework is formulated. The new formulation takes into account the fact that minor degree of imbalance in the system is acceptable and does not indicate subsequent interruptions, failures, or degradation of physical components. A generalized likelihood ratio test (GLRT) is developed and shown to be a function of the negative-sequence phasor estimator and the acceptable level of imbalances for nominal system operations. As a by-product to the proposed detection method, a constrained estimation of the positive and negative phasors and the frequency deviation is obtained for both balanced and unbalanced situations. The theoretical and numerical performance analyses show improved performance over benchmark techniques and robustness to the presence of additional harmonics.
In the literature, various definitions are given for imbalance in a power system, where the fundamental performance measures are the voltage unbalance factor (VUF) @cite_12 , @cite_19 , @cite_21 and the percent voltage unbalance (PVU) @cite_4 . The VUF is the ratio of the magnitudes of negative- and positive-sequence voltages and the PUV is equal to the ratio of the maximum voltage magnitude deviation of the zero, positive, and negative sequences from the average of the three-phase voltage magnitudes @cite_26 . The phase angle imbalance, which is not reflected in either the VUF or PVU measures, can be described by the phase voltage unbalance factor (PVUF) @cite_28 and the complex VUF (CVUF) @cite_15 , @cite_1 . The limitations of these commonly-used methods can be found, for example, in @cite_39 . An online identification method of the level, location, and effects of voltage imbalance in a distribution network is derived in @cite_36 based on distribution system state estimation. However, the existing non-parametric methods for detection of imbalance are insufficient (e.g., @cite_39 @cite_15 @cite_1 @cite_20 ). Derivation of parametric detection methods is expected to improve the detection performance.
@cite_26 @cite_4 @cite_28 @cite_36 @cite_21 @cite_1 @cite_39 @cite_19 @cite_15 @cite_20 @cite_12
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This paper uses a real load test to investigate the effects of an unbalanced voltage supply on an induction motor's performance. Based upon various experiments, including: (1) cases with the same unbalance voltage factor but different unbalanced voltages; (2) cases with only one unbalanced voltage but different degrees of unbalance; and (3) cases with the same positive-sequence voltage but different negative-sequence voltages, the importance of the positive-sequence voltage in the motor's apparent performance and of the negative-sequence voltage in the hidden damage are pointed out. Finally, it is strongly suggested that the related regulations, and a motor's derating factor and temperature rise curves should be based on not only a voltage unbalance factor, but also the magnitude of the positive-sequence voltage. In this paper an analysis of five different definitions of voltage unbalance developed by various power communities (CIGRE, NEMA, IEEE, and IEC) is presented, in order to understand their performance and difference among them. The purpose of this work is to analyze and quantify the voltage unbalance, so that these results may become useful to minimize the harmful effects of voltage unbalance. To quantify the voltage unbalance, five existing voltage unbalance definitions are calculated and their numerical values are used in analyzing the behavior of these definitions for the unit change in their magnitude and angle of voltage phasors. Most of the loads in industrial power distribution systems are balanced and connected to three power systems. However, voltage unbalance is generated at the user's 3-phase 4-wire distribution systems with single & three phase. Voltage unbalance is mainly affected by load system rather than power system. Unbalanced voltage will draws a highly unbalanced current and results in the temperature rise and the low output characteristics at the machine. It is necessary to analyze correct voltage unbalance factor for reduction of side effects in the industrial sites. Voltage unbalance is usually defined by the maximum percent deviation of voltages from their average value, by the method of symmetrical components or by the expression in a more user-friendly form which requires only the three line voltage readings. If the neutral point is moved at the 3-phase -4-wire system by the unbalanced load, by the conventional analytical method, line and phase voltage unbalance leads to different results due to zero-sequence component. This paper presents a new analytical method for phase and line voltage unbalance factor in 4-wire systems. Two methods indicate exact results Voltage unbalance is a costly and potentially damaging phenomenon. It affects both distribution network operators (DNOs) and customers. As part of a move toward greater network visibility, DNOs are increasingly motivated to monitor their networks in finer detail using an increasingly diverse range of monitoring devices. If the information from monitoring devices can be collated intelligently, the impact of unbalance and other power-quality issues can be accurately estimated throughout the network. In this paper, a new methodology is presented which utilizes distribution system state estimation (DSSE) to estimate the level, location, and impact of voltage unbalance on a real distribution network. The developed methodology is novel, pulling together and advancing existing research on DSSE and unbalance. The methodology is validated using data from a real U.K. distribution network with significant unbalance. The methodology is shown to be capable of statistically estimating the level, location, and effects of unbalance within the network, even when some areas of the network are unobservable. The negative effects of a particular unbalanced voltage on the performance of an induction motor are studied in this paper. The paper suggests that the available definitions of unbalanced voltages are not comprehensive and complete. Therefore, the results of these analyses on motor performance are not very reliable. To prove this claim, a three-phase 25-hp squirrel-cage induction motor is analyzed under different unbalanced conditions. It is shown that it is necessary to define a more precise unbalanced factor for more accurate results. Experimental results verify the theoretical analysis. 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. This paper examines the proper application of induction machines when supplied by unbalanced voltages in the presence of over- and undervoltages. Differences in the definition of voltage unbalance are also examined. The approach adopted is to use NEMA derating for unbalanced voltages as a basis to include the effects of undervoltages and overvoltages, through motor loss calculations. Performance analysis of three-phase induction motors under supply voltage unbalance conditions is normally carried out using the well-known symmetrical components analysis. In this analysis, the voltage unbalance level at the terminals of machine is assessed by means of the NEMA or IEC definitions. Both definitions lead to a relatively large error in predicting the performance of a machine. A method has recently been proposed in which, in addition to voltage unbalance factor (VUF), the phase angle has been accounted. This means that the voltage unbalance factor is regarded as a complex value. This paper shows that although the use of the complex VUF reduces the computational error considerably, it is still high. This is proven by evaluating the derating factor of a three-phase induction motor. A method is introduced to determine the derating factor precisely using the complex unbalance factor for an induction motor operating under any unbalanced supply condition. A practical case for derating of a typical three-phase squirrel-cage induction motor supplied by an unbalanced voltage is studied in the paper. This paper endeavors to present a comprehensive summary of the causes and effects of voltage unbalance and to discuss related standards, definitions, and mitigation techniques. Several causes of voltage unbalance on the power system and in industrial facilities are presented as well as the resulting adverse effects on the system and on equipment such as induction motors and power electronic converters and drives. Standards addressing voltage unbalance are discussed and clarified, and several mitigation techniques are suggested to correct voltage unbalance problems. This paper makes apparent the importance of identifying potential unbalance problems for the benefit of both the utility and customer.