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.
Under perfectly balanced three-phase operating conditions, the zero and negative sequences are absent, hence the state-estimation and signal analysis in this case are carried out using only the positive-sequence model @cite_13 @cite_41 . When system imbalance occurs, the zero and negative sequences are nonzero, and the PMU’s output exhibits nonstationary frequency deviations @cite_12 , @cite_29 . In addition, the positive-sequence measurements become non-circular as described in @cite_10 , @cite_17 . In the pioneering works of @cite_10 and @cite_17 , new methods were derived for frequency-estimation based on non-circular models and the Clarke’s transformation. These methods use the positive and negative sequences and analyze the measurements in the time domain. The mismatch estimation error caused by using the balanced state estimation under imbalance is studied in @cite_13 and the influence of imperfect synchronization on the state estimation is described in @cite_16 . In @cite_6 a distribution system state estimator suitable for monitoring unbalanced distribution networks is presented. A practical procedure to decrease the state estimation error introduced by load imbalances is developed in @cite_37 .
@cite_13 @cite_37 @cite_41 @cite_29 @cite_6 @cite_16 @cite_10 @cite_12 @cite_17
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This paper investigates the errors introduced in the positive sequence state estimation due to the usual assumptions of having fully balanced bus loads generations and continuously transposed transmission lines. A three-phase state estimator is first developed in order to verify the actual error free solution in the phase coordinates. Then, several tests are conducted using different assumptions regarding the availability of single and multi-phase measurements. It is demonstrated that incomplete metering of three-phase system quantities may lead to significant errors in the positive sequence state estimates for certain cases. Such cases may also lead to incorrect bad data detection and elimination, further deteriorating the quality of the state estimate. IEEE 30 bus test system is used to illustrate these cases. Most energy management system applications are based on the positive sequence network model. Since most systems do not operate under fully-balanced operating conditions, methods to minimize the impact of the balanced operation assumption on the network applications must be developed. This paper studies the impact of load imbalances on state estimation results by comparing state estimates using different measurement assumptions. In particular, the use of PMUs and systematic tuning of measurement weights are studied as practical ways of addressing this issue. Several scenarios are simulated using IEEE test systems with different measurement configurations and performance improvement of the state estimator in response to the proposed changes is illustrated by simulations. A novel technique for online estimation of the fundamental frequency of unbalanced three-phase power systems is proposed. Based on Clarke's transformation and widely linear complex domain modeling, the proposed method makes use of the full second-order information within three-phase signals, thus promising enhanced and robust frequency estimation. The structure, mathematical formulation, and theoretical stability and statistical performance analysis of the proposed technique illustrate that, in contrast to conventional linear adaptive estimators, the proposed method is well matched to unbalanced system conditions and also provides unbiased frequency estimation. The proposed method is also less sensitive to the variations of the three-phase voltage amplitudes over time and in the presence of higher order harmonics. Simulations on both synthetic and real-world unbalanced power systems support the analysis. Accurate estimation of system frequency in real time is a prerequisite for the future smart grid, where the generation, loading, and topology will all be dynamically updated. In this article, we introduce a unified framework for the estimation of instantaneous frequency in both balanced and unbalanced conditions in a three-phase system, thus consolidating the existing approaches and providing next-generation solutions capable of joint adaptive frequency estimation and system fault identification. This is achieved by employing recent developments in the statistics of complex variables (augmented statistics) and the associated widely linear models, allowing us to benefit from a rigorous account of varying degrees of noncircularity corresponding to different sources of frequency variations. The advantages of such an approach are illustrated for both balanced and unbalanced conditions, including voltage sags, harmonics and supply-demand mismatch, all major obstacles for accurate frequency estimation in the smart grid.