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arxiv: 1907.03138 · v1 · pith:VFNABQ4Fnew · submitted 2019-07-06 · 📡 eess.SY · cs.SY

Decentralized Dynamic State Estimation in Microgrids

Bang L. H. Nguyen , Tuyen V. Vu , Tuan A. Ngo This is my paper

Pith reviewed 2026-05-25 01:41 UTC · model grok-4.3

classification 📡 eess.SY cs.SY
keywords decentralized state estimationdynamic state estimationmicrogridsKalman filterdq0 reference framephasor synchronizationcomputational complexity
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0 comments X

The pith

Phasor synchronization in the dq0 frame decouples microgrid voltage and current measurements from states and inputs, simplifying the Kalman filter.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper proposes a decentralized dynamic state estimation scheme for microgrids that applies a Kalman filter to voltage and current measurements. Phasor synchronization transforms these measurements into the dq0 reference frame, which removes orthogonal functions from the relationship formulas. This removal permits the measurements to be decoupled directly into separate state and input vectors. The resulting structure lowers the computational complexity of the filter while adjusting process noise covariances according to the covariance of the measured inputs. Theoretical analysis and simulation results are used to validate the approach.

Core claim

By placing voltage and current measurements in the dq0 reference frame through phasor synchronization, orthogonal functions are excluded from their relationship formulas. This exclusion allows the measurements to be decoupled into state and input vectors, which in turn reduces the computational complexity of the Kalman filter applied to dynamic state estimation in microgrids. The filter incorporates process noise covariances modified with respect to the covariance of the measured input values.

What carries the argument

Decoupling of measurement values to state and input vectors, enabled by excluding orthogonal functions via phasor synchronization in the dq0 frame.

If this is right

  • The Kalman filter operates with reduced computational complexity because measurements are decoupled into independent state and input vectors.
  • Process noise covariances are modified in proportion to the covariance of the measured input values.
  • The scheme enables decentralized state estimation across microgrid components without requiring full centralized measurement coupling.
  • Theoretical analysis combined with simulation results confirms the validity of the decoupled estimation.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • The same decoupling step could be tested on larger distribution networks if phasor synchronization hardware is available at each node.
  • Lower filter complexity may support higher sampling rates or longer prediction horizons in real-time microgrid control.
  • Any mismatch between assumed and actual phasor synchronization accuracy would directly increase estimation error, providing a clear diagnostic metric.

Load-bearing premise

Voltage and current measurements in the dq0 reference frame through phasor synchronization can exclude orthogonal functions from their relationship formulas, allowing valid decoupling to state and input vectors.

What would settle it

Run the decoupled Kalman filter on microgrid data where the dq0 measurements retain orthogonal functions after synchronization; if the state estimates diverge from those of the standard coupled filter or from ground-truth values, the decoupling premise fails.

Figures

Figures reproduced from arXiv: 1907.03138 by Bang L. H. Nguyen, Tuan A. Ngo, Tuyen V. Vu.

Figure 1
Figure 1. Figure 1: Proposed decentralized dynamic state estimation scheme. or in three-phase. However, the orthogonal functions that caused nonlinearity still presented in the formulas. Thanks to the development of intelligence electronics devices (IED) and micro-phasor measurement units (µPMU) for distribution grids, the monitoring points associated with protection can be increased with less expensive cost [7]. Besides, dis… view at source ↗
Figure 2
Figure 2. Figure 2: Electrical diagram of a three-DGU three-bus microgrid system. , , ,   1 i abc ti abc oi abc ti d v i i dt C  . (2) By applying the abc/dq0 Park transformation in the same rotating frame of ωt, the below equations are achieved: , , , , ,   , ti 1 ti dq ti dq ti dq ti dq i dq ti ti dq d R i j i i v v dt L L       , (3) , , , ,   1 i dq i dq ti dq oi dq i t d v j v i i dt C     . (4) In the … view at source ↗
Figure 5
Figure 5. Figure 5: Comparison of estimated, noisy and true value of id1 [PITH_FULL_IMAGE:figures/full_fig_p005_5.png] view at source ↗
Figure 3
Figure 3. Figure 3: Comparison of estimated, noisy and true value of vd1 [PITH_FULL_IMAGE:figures/full_fig_p005_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: Comparison of estimated, noisy and true value of vq1 [PITH_FULL_IMAGE:figures/full_fig_p005_4.png] view at source ↗
Figure 8
Figure 8. Figure 8: Zoomed comparison of estimated, noisy and true value of iq1 [PITH_FULL_IMAGE:figures/full_fig_p006_8.png] view at source ↗
Figure 9
Figure 9. Figure 9: Comparison of estimated, noisy and true value of id12 [PITH_FULL_IMAGE:figures/full_fig_p006_9.png] view at source ↗
Figure 10
Figure 10. Figure 10: Comparison of estimated, noisy and true value of iq12 V. CONCLUSION A simple decentralized dynamic state estimation scheme based on the same dq0-rotating reference frame in microgrids is proposed and analyzed. The advantage of this scheme over the previous research in the same category is linear formulation with dynamic state-space models. In addition, by revising the process noised, the noisy inputs do n… view at source ↗
read the original abstract

This paper proposes a decentralized dynamic state estimation scheme for microgrids. The approach employs the voltage and current measurements in the dq0 reference frame through phasor synchronization to be able to exclude orthogonal functions from their relationship formulas. Based on that premise, we utilize a Kalman filter to dynamically estimate states of microgrids. The decoupling of measurement values to state and input vectors reduces the computational complexity. The Kalman filter considers the process noise covariances, which are modified with respect to the covariance of measured input values. Theoretical analysis and simulation results are provided for validation.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

2 major / 1 minor

Summary. The paper proposes a decentralized dynamic state estimation scheme for microgrids that transforms voltage and current measurements into the dq0 reference frame via phasor synchronization. This is claimed to exclude orthogonal functions from the measurement-to-state/input relationships, enabling a decoupled Kalman filter structure that reduces computational complexity. Process noise covariances are modified according to the covariances of the measured inputs. Theoretical analysis and simulation results are provided to support the approach.

Significance. If the decoupling premise holds under realistic microgrid conditions, the method could provide a lower-complexity alternative for real-time state estimation in distributed power systems, which is relevant for stability monitoring and control. The explicit modification of process noise based on input measurements is a concrete implementation choice that could be reproducible if the equations are fully specified. However, the abstract supplies no equations, error metrics, or quantitative complexity comparisons, limiting assessment of whether the claimed reduction is achieved without accuracy loss.

major comments (2)
  1. [Abstract] Abstract: The central premise that phasor synchronization in the dq0 frame excludes orthogonal functions (e.g., time-varying sin/cos terms) from the measurement equations is stated without derivation or explicit measurement model. This is load-bearing for the decoupling claim and complexity reduction; the manuscript must show the pre- and post-transformation equations and address residual frequency deviation effects.
  2. [Abstract] Abstract (and any theoretical section): No indication is given of how the process-noise covariance modification remains valid once the orthogonal terms are removed, nor are any error metrics, covariance values, or complexity counts (e.g., floating-point operations before/after decoupling) supplied. Without these, the simulation validation cannot be evaluated against the complexity-reduction claim.
minor comments (1)
  1. [Abstract] The abstract refers to 'theoretical analysis and simulation results' but provides neither equations nor quantitative outcomes; adding at least one key equation and a table of estimation errors or runtime metrics would improve clarity.

Simulated Author's Rebuttal

2 responses · 0 unresolved

Thank you for the opportunity to respond to the referee's comments. We address each major comment below and will revise the manuscript to provide the requested derivations, explanations, and quantitative details.

read point-by-point responses

  1. Referee: [Abstract] Abstract: The central premise that phasor synchronization in the dq0 frame excludes orthogonal functions (e.g., time-varying sin/cos terms) from the measurement equations is stated without derivation or explicit measurement model. This is load-bearing for the decoupling claim and complexity reduction; the manuscript must show the pre- and post-transformation equations and address residual frequency deviation effects.

    Authors: We agree the abstract is too concise on this point. The full manuscript derives the measurement model in Section II, showing how the Park transformation with phasor synchronization removes the time-varying sin/cos terms from the voltage/current-to-state relationships under nominal frequency. We will revise by adding the explicit pre- and post-transformation equations to the abstract or a new introductory paragraph and include a short discussion of residual frequency deviation effects, noting the small-deviation assumption used in our analysis. revision: yes

  2. Referee: [Abstract] Abstract (and any theoretical section): No indication is given of how the process-noise covariance modification remains valid once the orthogonal terms are removed, nor are any error metrics, covariance values, or complexity counts (e.g., floating-point operations before/after decoupling) supplied. Without these, the simulation validation cannot be evaluated against the complexity-reduction claim.

    Authors: The process-noise covariance is updated directly from the measured inputs after the dq0 transformation; because the decoupling removes the orthogonal coupling, the noise statistics remain independent and the modification stays valid. We will expand the theoretical section with this explicit justification. We will also add simulation error metrics (e.g., RMSE), the specific covariance values employed, and a quantitative complexity comparison (FLOPs or operation counts before vs. after decoupling) to the results section. revision: yes

Circularity Check

0 steps flagged

No significant circularity in the derivation chain

full rationale

The paper presents the exclusion of orthogonal functions via dq0 phasor synchronization as an enabling premise for decoupling measurements to state and input vectors, then applies a Kalman filter with modified process noise covariances. This premise is not derived from the filter outputs or results; the covariance adjustment is described as an adaptation rather than a redefinition. No equations or steps reduce by construction to inputs, no self-citations are load-bearing for the central claim, and no uniqueness theorems or ansatzes are smuggled in. The derivation chain remains self-contained with the stated assumptions about the reference frame.

Axiom & Free-Parameter Ledger

0 free parameters · 2 axioms · 0 invented entities

The central claim rests on the unverified premise that phasor synchronization in dq0 excludes orthogonal functions and on standard Kalman filter assumptions; no free parameters or new entities are explicitly introduced in the abstract.

axioms (2)
  • domain assumption Standard Kalman filter assumptions (linear or locally linear dynamics, Gaussian noise) apply to the microgrid system.
    The method directly employs a Kalman filter, which requires these background conditions.
  • domain assumption Phasor synchronization allows exclusion of orthogonal functions from the voltage/current relationship formulas in the dq0 frame.
    This is the explicit premise stated in the abstract that enables the subsequent decoupling.

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Reference graph

Works this paper leans on

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