A Framework for Constrained Static State Estimation in Unbalanced Distribution Networks

Abstract

State estimation plays a key role in the transition from the passive to the active operation of distribution systems, as it allows to monitor these networks and, successively, to perform control actions. However, designing state estimators for distribution systems carries a significant amount of challenges. This is due to the physical complexity of the networks, e.g., phase unbalance, and limited measurements. Furthermore, the features of the distribution system present significant local variations, e.g., voltage level and number and type of customers, which makes it hard to design a "one-size-fits-all" state estimator. The present paper introduces a unifying framework that allows to easily implement and compare diverse unbalanced static state estimation models. This is achieved by formulating state estimation as a general constrained optimization problem. The advantages of this approach are described and supported by numerical illustration on a large set of distribution feeders. The framework is also implemented and made available open-source.

Exact Modeling of Non-Gaussian Measurement Uncertainty in Distribution System State Estimation

“…To the best of the authors' knowledge, and as per recent SE review papers [25], [26], the remainder of the DSSE literature resorts to zero-mean Gaussian assumptions or approximations, and this is the first work on MLE-based SE with unbalanced power flow equations, which are required for a realistic representation of DS [27]. This work further differentiates itself from transmission MLE papers [17], [18] by formulating DSSE as a constrained non-convex problem, based on a generic "optimization-first" DSSE set-up like that in [4]. From a MLE-SE standpoint, this allows to use any continuous pdf to describe (pseudo-)measurements, as well as having a combined objective to separately consider Gaussian and non-Gaussian quantities, exploiting the computational advantages of Gaussian assumptions when possible.…”

“…These add correlations between power generation variables, which is also a variation on standard DSSE, in which all random variables are usually assumed to be independently distributed [6]. The MLE-SE is based on the DSSE concepts described in [4], and is available open-source 1 . It is possible and relatively easy for the readers/users to further extend the code to tackle additional MLE-SE cases.…”

“…and to a weighted least absolute value [4] minimization if x j is Laplacian. In (11), µ j indicates the (pseudo)-measurement value, and 1/σ 2 j its weight, which is the inverse of the distribution variance and depends on the measurement accuracy.…”

“…From a computational standpoint, it is more convenient to use the simplified notation in (11) rather than (10). The same holds if the distribution is assumed Laplacian, in which case the residuals can be formulated as linear inequality constraint, as illustrated in [4], with no computational burden. Assuming that SM errors are Gaussian distributed, while pseudomeasurements are not, (2) becomes:…”

“…In this light, state estimation (SE) gives the potential to better understand the distribution system (DS) and serves as a basis to successively perform optimization and control actions [2]. While SE is industrial practice in the transmission system, the same SE techniques cannot be directly applied to the DS, as this inherently presents different features and additional implementation challenges, which have been discussed in numerous papers, e.g., [2]- [4]. One of the challenges towards the design and implementation of reliable Distribution System SE (DSSE) is the paucity of available measurement devices, which results in the need for forecasts of non-metered loads and generators to obtain full system observability.…”