A Two-Step Distribution System State Estimator with Grid Constraints and Mixed Measurements

Abstract

In this paper we consider the problem of State Estimation (SE) in large-scale, 3-phase coupled, unbalanced distribution systems. More specifically, we address the problem of including mixed real-time measurements, synchronized and unsynchronized, from phasor measurement units and smart meters, into existing SE solutions. We propose a computationally efficient two-step method to update a prior solution using the measurements, while taking into account physical constraints caused by zero-injection buses. We test the method on a benchmark test feeder and show the effectiveness of the approach.

Comparison of Bounds for Optimal PMU Placement for State Estimation in Distribution Grids

“…As shown in [8], splitting the problem in two steps yields the same first-order approximation as solving the problem in one step. Moreover, the posterior minimumvariance estimator using the linear update (6), is equal to the maximum-likelihood using a weighted least-squares approach [13]. Therefore, we can conclude that for an SE method that assumes Gaussian noises and performs a maximum likelihood estimation, the posterior covariance will be approximately the one in (7), and thus the method developed here for optimal sensor placement can be also extended for other SE techniques satisfying these conditions.…”

“…As explained in [13], several different sources of information can be available to solve the SE problem: 1) Pseudo-measurements, i.e., load estimations S psd based on predictions and/or known installed load capacity at every bus. Since these pseudo-measurements are estimations rather than actual measurements, we model their uncertainty using a Gaussian noise with a relative large standard deviation (a typical value can be σ psd ≈ 50% [12]).…”

“…Again, we model this uncertainty using a Gaussian noise with a low standard deviation for the magnitude and the angle, σ mag ≈ 1% and σ ang ≈ 0.01 rad respectively. They can be expressed using a linear approximation [13] with magnitude and angle noise due to the measurements and imperfect synchronization. For a number of N meas measurements z meas ∈ C Nmeas we have…”

“…State Estimation Typically, SE consists in finding the voltages that best match the measurements by solving a weighted least-squares problem [1]. As proposed in [13], SE can be decomposed in two parts: First, using the pseudo-measurement estimations or predictions for the loads S psd , we solve the power flow offline to obtain a prior estimate V prior :…”

“…The A-optimal metric represents the sum of the eigenvalues of Σ F,post and thus the sum of the lengths of axes of the confidence ellipsoid [22]. This is the metric typically used for SE methods, since standard SE maximizes the log-likelihood through a weighted least-squares minimization [1], which is equivalent to the minimum-variance estimator using the trace [13]. The D-optimal metric is the natural logarithm of the product of the eigenvalues of Σ F,post and it is related to the logarithm of the volume of the confidence ellipsoid [22].…”