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 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. 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. 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 Dynamic voltage and frequency scaling (DVFS) has been widely used for energy reduction in the modern processors. How to select the optimal frequency that minimizes energy dissipation for the given performance constraint at runtime is a nontrivial problem. The problem becomes more complicated if temperature needs to be constrained (or minimized) simultaneously. The temperature, performance and energy have different nonlinear relationships with frequency voltage scaling ratio and this relationship is closely related to the characteristics of hardware and applications. In this paper, we design a reinforcement learning algorithm to tackle the problem of simultaneous temperature, performance and energy management. The proposed approach allows continuous tradeoff among these three quality measurement of a computer system. It also enables us to set two of the measurements as constraints and optimize the third one. The proposed approach is validated on an Intel Core 2 processor running Linux system.