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. The main objective of this paper is to describe a multilevel framework that facilitates seamless integration of existing state estimators (SEs) that are designed to function at different levels of modeling hierarchy in order to accomplish very large-scale monitoring of interconnected power systems. This has been a major challenge for decades as power systems grew pretty much independently in different areas, which had to operate in an interconnected and synchronized fashion. The paper initially provides a brief historical perspective which also explains the existing state estimation paradigm. This is followed by a review of the recent technological and regulatory drivers that are responsible for the new developments in the energy management functions. The paper then shows that a common theoretical framework can be used to implement a hierarchical scheme by which even very large-scale power systems can be efficiently and accurately monitored. This is illustrated for substation level, transmission system level as well as for a level between different transmission system operators in a given power system. Finally, the paper describes the use and benefits of phasor measurements when incorporated at these different levels of the proposed infrastructure. Numerical examples are included to illustrate performance of the proposed multilevel schemes. With the advent of Substation Computer Systems dedicated to protection, control and data logging functions in a Substation, it becomes possible to develop new applications which can utilize the processing power available within the substation. The microcomputer based Symmetrical Component Distance Relay (SCDR) described in the references cited at the end of this paper possesses certain characteristics which facilitate real-time monitoring of positive sequence voltage phasor at the local power system bus. With a regression analysis the frequency and rate-of-change of frequency at the bus can also be determined from the positive sequence voltage phase angle. This paper describes the theoretical basis of these computations and describes results of experiments performed in the AEP power system simulation laboratory. Plans for future field tests on the AEP system are also outlined. Distribution networks are only partially monitored networks, with loads often unbalanced on the phases of the system. Moreover, last generation of distribution networks are facing significant challenges, due to, as an example, the increasing amount of distributed generation (DG), installed in an unplanned manner. Such changing scenario emphasizes issues such as voltage unbalance and imposes new operational requirements, such as distributed voltage control and demand side management. Traditional state estimation techniques are a reliable instrument for monitoring the transmission system, but their application to distribution systems is still under development. In this work, a distribution system state estimator (DSSE) suitable for accurately monitoring unbalanced distribution networks is presented and the impact of the different kind of measurement devices is analyzed and discussed by means of simulations performed on the 13-bus IEEE distribution network. Phasor measurement units (PMUs) are time synchronized sensors primarily used for power system state estimation. Despite their increasing incorporation and the ongoing research on state estimation using measurements from these sensors, estimation with imperfect phase synchronization has not been sufficiently investigated. Inaccurate synchronization is an inevitable problem that large scale deployment of PMUs has to face. In this paper, we introduce a model for power system state estimation using PMUs with phase mismatch. We propose alternating minimization and parallel Kalman filtering for state estimation using static and dynamic models, respectively, under different assumptions. Numerical examples demonstrate the improved accuracy of our algorithms compared with traditional algorithms when imperfect synchronization is present. We conclude that when a sufficient number of PMUs with small delays are employed, the imperfect synchronization can be largely compensated in the estimation stage. 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. 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. 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.