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Publication# Static and recursive PMU-based state estimation processes for transmission and distribution power grids

Jean-Yves Le Boudec, Mario Paolone, Styliani Sarri, Lorenzo Zanni

*The Institution of Engineering and Technology - IET, *2015

Book chapter

Book chapter

Abstract

In the operation of power systems, the knowledge of the system state is required by several fundamental functions, such as security assessment, voltage control and stability analysis. By making reference to the static state of the system represented by the voltage phasors at all the network buses, it is possible to infer the system operating conditions. Until the late 1970s, conventional load flow calculations provided the system state by directly using the raw measurements of voltage magnitudes and power injections. The loss of one measurement made the calculation impossible and the presence of measurement errors affected dramatically the computed state.To overcome these limitations, load flowtheory has been combined with statistical estimation constituting the so-called state estimation (SE). The latter consists in the solution of an optimization problem that processes the measurements together with the network model to determine the optimal estimate of the system state. The outputs of load flow and SE are composed of the same quantities, typically the voltage magnitude and phase at all the network buses, but SE uses all the types of measurements (e.g., voltage and current magnitudes, nodal power injections and flows, synchrophasors) and evaluates their consistency using the network model. The measurement redundancy is key to tolerate measurement losses, identify measurement and network parameter errors, and filter out the measurement noise. The foregoing properties of SE allow the system operator to obtain an accurate and reliable estimate of the system state that consequently improves the performance of the functions relying on it. Traditionally, SE has been performed at a relatively low refresh rate of a few minutes, dictated by the time requirements of the related functions together with the low measurement acquisition rate of remote terminal units (RTUs). Nowadays, the emerging availability of phasor measurement units (PMUs) allows to acquire accurate and time-aligned phasors, called synchrophasors, with typical streaming rates in the order of some tens of measurements per second. This technology is experiencing a fast evolution, which is triggered by an increasing number of power system applications that can benefit from the use of synchrophasors. SE processes can exploit the availability of synchrophasor measurements to achieve better accuracy performance and higher refresh rate (sub-second). PMUs already compose the backbone of wide area monitoring systems in the context of transmission networks to which several real-time functionalities are connected, such as inter-area oscillations, relaying, fault location and real-time SE. However, PMUs might represent fundamental monitoring tools even in the context of distribution networks for applications such as: SE [5, 6], loss of main [7], fault event monitoring, synchronous islanded operation [9] and power quality monitoring. The recent literature has discussed the use of PMUs for SE in distribution networks both from the methodological point of view and also via dedicated real-scale experimental setups. Since the pioneering works of Schweppe on power system SE in 1970, most of the research on the subject has investigated static SE methods based on weighted least squares (WLS). Static SE computes the system state performing a “best fit” of the measurements belonging only to the current time-step. Another category of state estimators are the recursive methods, such as the Kalman filter (KF). In addition to the use of the measurements and their statistical properties, they also predict the system state by modelling its time evolution. In general, recursive estimators are characterized by higher complexity and the prediction introduces an additional source of uncertainty that, if not properly quantified, might worsen the accuracy of the estimated state. Besides, their ability to filter out measurement noise could not be exploited due to the low SE refresh rate: even in quasi-steady state conditions, the measurement noise was smaller than the state variations between two consecutive time-steps. However, the effectiveness of power system SE based on KF has been recently reconsidered thanks to the possibility to largely increase the SE refresh rate by using synchrophasor measurements. The chapter starts by providing the measurement and process model of WLS and KF SE algorithms and continues with the analytical formulation of the two families of state estimators, including their linear and non-linear versions as a function of the type of available measurements. Finally, two case studies targeting IEEE transmission and distribution reference networks are given.

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Carlo Alberto Nucci, Mario Paolone, Styliani Sarri

One of the challenging tasks related to the realtime control of Active Distribution Networks (ADNs) is represented by the development of fast (i.e. sub-second) state estimation (SE) processes. As known, the problem of SE of power networks links the measurements performed in the network with a set of non-linear equations representing the links between the network node voltage phasors (i.e. the system states) and measured quantities. The calculation of these voltages is accomplished by the solution of a minimization problem by using, for instance, Weighted Least Squares (WLS) or Kalman filter (KF) methods. The availability of phasor measurement units (PMUs), characterized by high accuracy and able to directly measure node voltage phasors, allows, in principle, a simplification of the SE problem. Within this framework, the paper has two aims. The first is to propose a procedure based on the use of the Iterated KF (IKF) aiming at making achievable, in a straightforward manner, the SE of ADNs integrating PMU measurements. The second goal is to present a sensitivity analysis of the performances of WLS vs IKF methods as a function of the measurements and process covariance matrices.

Mario Paolone, Marco Pignati, Styliani Sarri, Lorenzo Zanni

The accuracy of state estimators using the Kalman Filter (KF) is largely influenced by the measurement and the process noise covariance matrices. The former can be directly inferred from the available measurement devices whilst the latter needs to be assessed, as a function of the process model, in order to maximize the KF performances. In this paper we present different approaches that allow assessing the optimal values of the elements composing the process noise covariance matrix within the context of the State Estimation (SE) of Active Distribution Networks (ADNs). In particular, the paper considers a linear SE process based on the availability of synchrophasors measurements. The assessment of the process noise covariance matrix, related to a process model represented by the ARIMA [0,1,0] one, is based either on the knowledge of the probabilistic behavior of nodal network injections/absorptions or on the a-posteriori knowledge of the estimated states and their accuracies. Numerical simulations demonstrating the improvements of the KF-SE accuracy achieved by using the calculated matrix Q are included in the paper. A comparison with the Weighted Least Squares (WLS) method is also given for validation purposes.

The evolution from passive to Active Distribution Networks (ADNs) is producing large changes in the operation of these electrical systems. In particular, violations of grid operational constraints, higher dynamics and limited amount of controllable resources represent main limiting factors in the optimal operation of ADNs in presence of massive stochastic distributed generation. In order to deal with these issues, the emergence of ADNs requires the definition of suitable Energy Management Systems to achieve specific operation objectives (i.e., optimal voltage/congestion controls, updated protection schemes etc.). These functions are significantly improved if the system state is known with high accuracy, high refresh rates and low time latencies. Unfortunately, typical refresh rates of traditional State Estimation (SE) processes designed for transmission networks are in the order of few minutes, whereas the time frames of the above functionalities are between few milliseconds to few seconds. Hence, it becomes necessary to define, develop and validate the three-phase Real-Time State Estimation (RTSE) processes characterised by high refresh rates (i.e., in the range of several tens of estimation per second), small latencies (i.e., in the range of few tens of ms) and high accuracy. In this direction, the ADNs SE is facilitated by the emerging technology of Phasor Measurement Units (PMUs) which allow acquiring accurate, time-aligned phasors with typical streaming rates in the order of some tens of f.p.s. Additionally, PMUs measurements of synchrophasors allow formulating the SE problem in a linear way. PMU measurements can be acquired and stored in a real-time (RT) database, provided by Phasor Data Concentrators (PDCs) suitably coupled with the RTSE. This enables, in theory, the performance assessment of the whole RTSE chain. However, the assessment of the RTSE accuracy with real PMUs in a real grid is impossible since the true state is hidden. It is, yet, possible to overcome this limitation by using a Real Time Simulator (RTS) and design a RT setup that allows knowing the true state. This RT setup should be GPS-synchronized, to enable the RTSE accuracy and time latencies assessment. Within the above context, this thesis focuses on the definition of SE methods together with their formal and numerical performance assessment. In particular, the first part of the thesis discusses the formulation of static (e.g., weighted least squares - WLS) and recursive (e.g., Kalman Filter - KF) algorithms fed by synchronized phasors and/or other traditional measurements provided by remote terminal units. Then, the thesis discusses the formal comparison of the accuracy of KF vs. WLS and proves that the former behaves better if its process model is correct. For the case of linear SE, the thesis discusses the method for the verification of the exactness of the so-called measurement noise covariance matrix. The subsequent part of the thesis provides the numerical validation and performance assessment of the RTSE process via offline simulations. This analysis is conducted by using IEEE benchmark distribution and transmission networks as well as real distribution feeders. The last part of the thesis focuses on the experimental validation of the RTSE chain via an experimental RT setup. In this last part, the thesis describes the structure and the individual components simulated in the RT experimental setup as well as the whole validation procedure.