978-1-4799-3561-1/14/$31.00 ©2014 IEEE PMAPS 2014 Probabilistic Assessment of the Process-Noise Covariance Matrix of Discrete Kalman Filter State Estimation of Active Distribution Networks L. Zanni, S. Sarri, M. Pignati, R. Cherkaoui and M. Paolone École Polytechnique Fédérale de Lausanne (EPFL) Lausanne, Switzerland lorenzo.zanni@epfl.ch Abstract—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. Keywords—Active distribution networks; Kalman filter; probabilistic assessment; process noise covariance matrix; real-time state estimation; phasor measurement unit I. INTRODUCTION One of the main challenging tasks related to the operation of Active Distribution Networks (ADNs) is the development of accurate and fast (i.e. sub-second) State Estimation (SE) processes (e.g., [1], [2]). In what follows we make reference to a SE process that uses time-tagged measurements available with high refresh rate (typically those streamed by Phasor Measurement Units – PMUs – with rates of tens of frames per second [3], [4]). Indeed, all the functionalities associated to the Real-Time (RT) operation of ADNs like: (i) optimal voltage control, (ii) feeders congestion management, (iii) losses minimization, (iv) fault detection and location, (v) post-fault management, and (vi) increase of the system reliability [5]-[8], might be largely improved if the knowledge of the network state is available with high accuracy and refresh rate (e.g., [9], [10]). A well-known approach used for the estimation of power networks state relies on the use of the Kalman Filter (KF) (e.g. [11]-[17]). As known, compared to traditional Weighted Least Square (WLS) method (e.g., [18]), it accounts the available measurements and the time-varying nature of the process to be identified by means of a suitable-defined process model that predicts the system state in advance. As a consequence, the KF is a two-stage algorithm. The first ‘prediction part’ projects the previous time step state forward in time by means of a pre- defined process model. The second ‘estimation part’ corrects the predicted state by accounting the available measurements and the accuracies of both process model and measurements. In this respect, one of the key factors that largely influence the KF accuracy is the knowledge of two error covariance matrices: (i) the so-called process noise covariance matrix, and (ii) the measurement noise covariance matrix. As discussed in [19], if both noise covariance matrices are not properly defined, the robustness of the KF algorithm is not necessarily satisfied. Additionally, in [17] the relative influence of these two uncertainties has been discussed with reference to the SE of ADNs performed by using the Iterative KF (IKF) process. Concerning the measurement noise covariances, they represent the accuracies of the measurement devices and can be easily inferred. On the other hand, the process noise covariances represent the uncertainties introduced by the process model to predict the next system state. It is worth observing that, in general, in the literature dealing with power systems SE using the KF, the values of the process noise covariance matrix are arbitrarily selected although, in principle, they need to be computed if the process is known (e.g., [20], [21]). Therefore, an appropriate assessment of this matrix is of fundamental importance for the maximization of the KF-SE accuracy and represents the objective of this paper. Within this framework, the Authors of [22] have summarized and discussed some of the novel methods proposed in the last decade for the estimation of the noise covariance matrix for non-linear state estimators. In [23], the Authors have analyzed the tuning of the process and noise covariance matrices in order to optimize the performance of a fault detection process based on the Extended KF (EKF). More recently, in [13] it has been presented a two-stage KF for power systems SE: in the first stage an adaptive KF algorithm identifies and corrects the impact of incorrect system modeling and/or bad PMU measurements; in the second stage the estimated bus voltages are fed into an EKF to obtain the dynamic states. The research leading to the results presented in this paper has received funding from the NanoTera Swiss National Science Foundation project S 3 - Grids and from the European Community's FP7-ICT-2011-8 under the grant agreement n° 318708 (C-DAX).