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Publication# State Estimation of Active Distribution Networks: Comparison Between WLS and Iterated Kalman-Filter Algorithm Integrating PMUs

Carlo Alberto Nucci, Mario Paolone, Styliani Sarri

*IEEE Power Engineering Society and Technische Universität Berlin, Germany, *2012

Conference paper

Conference paper

Abstract

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.

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

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.

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.

An increasing number of phasor measurement units (PMUs) are being deployed in power systems in order to enhance the situational awareness and, in the near future, we expect that many networks will be extensively equipped with PMUs. These devices provide accurate and synchronized voltage/current phasors (called synchrophasors) at a reporting rate up to 60 measurements-per-second, which is a significantly different type of information with respect to the commonly-used voltage/current magnitude and power measurements of remote terminal units (RTUs). PMUs are commonly associated with transmission systems, but are gaining consideration also in the context of distribution networks in order to implement fast control schemes due to the presence of highly-volatile distributed generation and for fault location purposes. Power-system state estimation (SE) is a functionality that might largely benefit from the use of synchrophasor measurements. Best current practice consists in estimating the state every few tens of seconds (or even minutes) by using asynchronous measurements of RTUs. A measurement infrastructure exclusively composed of PMUs allows SE to become a linear and not iterative process characterized by a refresh-rate of tens of estimates-per-second and sub-second time-latency. This is what we call real-time SE. Even if SE is a well-established power-system function, it still deserves research in view of the proliferation of PMUs. Improvements in terms of accuracy, computational time and time-latency are required in order to make SE suitable for a wide range of applications, from control to fault management. In this dissertation, we first describe in detail the advantages of using exclusively synchrophasor measurements for the most common SE algorithms, i.e., weighted least squares (WLS), least absolute value (LAV) and Kalman filter (KF). Then, we propose two methods for the on-line estimation of the process-model uncertainties used by the KF, because power-system operating conditions are continuously varying. Our goal is to improve the estimation accuracy by effectively filtering the measurement noise. We designed a heuristic method for quasi-static conditions and a rigorous method that is also able to deal with step changes of the system state. Zero-injections represent equality constraints in the SE problem. We propose a method based on LQ-decomposition for linear WLS-SE that strictly satisfies the equality constraints while reducing the state-vector dimension by the number of constraints. Therefore, the computational time is significantly reduced and the problem becomes less ill-conditioned. An important contribution of this dissertation consists in the validation of the theoretical findings via real-scale experiments. We deployed PMUs at every bus in two real power-systems located in Switzerland. First, we demonstrate the practical feasibility of running SE at high refresh-rate (50 estimates-per-second) and low time-latency (below 70 ms). Second, we compare and discuss the results of WLS, LAV and KF by using real synchrophasor measurements. Finally, we intend to prove that PMU-based real-time SE exhibits unique accuracy, refresh rate and time-latency, which satisfy the requirements of fault location and, potentially, protective relaying. We propose a fault detection and faulted-line identification method based on WLS-SE, which works for any network and fault type as well as in presence of large amount of distributed generation.