Physically Constrained Temporal State Estimation of Voltage and Current Phasors in Distribution Grids
Author
Maack, Christian Dausel
Term
4. semester
Education
Publication year
2026
Submitted on
2026-08-03
Abstract
This thesis investigates whether temporal state tracking can improve the reconstruction of voltage and line-current phasors in a distribution feeder where only a subset of nodes and lines are directly measured. The work is based on a physically motivated grid model in which the network equations (including Kirchhoff’s laws) are represented in a reduced-dimensional coordinate system that enforces known physical constraints. In this reduced space, a pointwise maximum-likelihood estimator, which reconstructs the grid state at each time instant independently, is compared with a temporal estimator formulated as a linear Gaussian state-space model whose parameters are learned using expectation–maximization and whose trajectories are refined by Rauch–Tung–Striebel smoothing. Both estimators are first evaluated on synthetic data under varying observation layouts, noise levels, and temporal persistence, and then on a reference trajectory for the Landau feeder derived from Observability Grid Monitoring (OGM). The results show that temporal estimation can reduce the reconstruction error for hidden voltage states in both simulated and measured scenarios, whereas the benefit for hidden current states is more mixed and the pointwise estimator remains competitive. The measured-data study further reveals that a homogeneous current-balance model is insufficient to capture the OGM-derived trajectories, and that known node and shunt current contributions must be explicitly incorporated into the physical constraint model. Overall, the thesis provides a systematic framework for physically consistent temporal state estimation in distribution grids and discusses the performance, robustness, and limitations of the proposed approach, as well as directions for future research.
Denne afhandling undersøger, om tidslig tilstandssporing kan forbedre rekonstruktionen af spændings- og linjestrømsfaser i en distributionsledning, hvor kun en del af noder og linjer er målt. Udgangspunktet er et fysisk begrundet netværksmodel, hvor de elektriske ligninger (bl.a. baseret på Kirchhoffs love) omskrives til et lavdimensionelt koordinatsystem, der respekterer kendte fysiske begrænsninger. I dette rum sammenlignes en punktvis maksimum-likelihood estimator, der rekonstruerer tilstanden tidspunkt for tidspunkt, med en tidslig estimator baseret på et lineært Gaussisk tilstandsrum, hvor parametrene estimeres med expectation–maximization og efterfølgende glattes med Rauch–Tung–Striebel-smoothing. Begge metoder evalueres først på syntetiske data under forskellige observationsscenarier, støjniveauer og tidslige afhængigheder og derefter på en referencetidsrække for Landau-føderen, genereret af Observability Grid Monitoring (OGM). Resultaterne viser, at den tidslige metode kan reducere rekonstruktionsfejlen for skjulte spændingstilstande i både simulerede og målte data, mens gevinsten for skjulte strømtilstande er mere begrænset, og den punktvise estimator fortsat er konkurrencedygtig. Analysen af de målte data demonstrerer desuden, at en homogen strømbalancemodel ikke er tilstrækkelig til at beskrive OGM-baserede tilstande, og at kendte node- og shuntstrømsbidrag derfor må indarbejdes eksplicit i den fysiske begrænsningsmodel. Afhandlingen bidrager dermed med en systematisk ramme til fysisk konsistent, tidslig tilstandsskatning i distributionsnet og diskuterer både præstation, robusthed og modellens begrænsninger samt mulige retninger for videre arbejde.
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