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Digital Twin of Distribution Power Transformer for Real-Time Monitoring of Medium Voltage from Low Voltage Measurements

Panayiotis Moutis, Omid Alizadeh-Mousavi

arXiv:2012.02286v1eess.SYcs.SY

TL;DR

Direct MV monitoring can be costly, risky, and disruptive, despite the need to observe distribution-system behavior in real time. The paper estimates MV transformer waveforms from LV measurements using a transformer model, reporting instrument-transformer-comparable accuracy and successful field validation.

Abstract

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Real-time monitoring of distribution systems has be-come necessary, due to the deregulation of electricity markets and the wide deployment of distributed energy resources. To monitor voltage and current at sub-cycle detail, requires, typically, major investment undertaking and disruptions to the operation of the grid. In this work, measurements of the low voltage (LV) side of distribution transformers (T/F) are used to calculate in real time the waveforms of their medium voltage (MV) sides, based on a mathematical model of said T/F. This model is, essentially, the dig-ital twin of the MV side of the T/F. The method calculates T/F MV waveforms of voltage and current, and active and reactive power as accurately as an instrument T/F, captures all harmonics con-tent, is unaffected by asymmetrical loading and identifies most sys-tem faults on the MV side of the T/F. The digital twin method en-ables monitoring of distribution T/F that avoids MV instrumenta-tion, does not suffer in accuracy and may be readily deployable. Field data from an actual MV-LV T/F, agree with simulation re-sults showcasing the efficacy of the digital twin method.

A. Variables and Parameters

The section introduces real-time distribution-system monitoring as a response to DER-related concerns, while noting that direct MV measurement can be costly, risky, and disruptive. It also outlines transformer-monitoring research and defines notation used in the paper.

A. Variables and Parameters

  • R, L, u, i, t, n, N, and f denote resistance, inductance, voltage, current, time, discretized time steps, total sampled steps, and frequency.Source: A. Variables and Parameters · p. 1

B. Scripts and indices

  • The scripts use S and M for series and shunt branches, 1 and 2 for windings, s for sampling, k for scenarios, d and r for twin and real waveforms, and A, B, C for phases.Source: B. Scripts and indices · p. 1

I. INTRODUCTION

  • DER deployment raises technical concerns, and online monitoring is presented as supporting system awareness, flexibility services, fault localization, infrastructure planning, and power quality.Source: §I · p. 1

A. Distribution System and Transformer Monitoring Review

  • Distribution monitoring research includes state estimation, PMUs, SCADA, and smart meters, while direct MV transformer measurement can bring costs, risks, and grid disruptions.Transformer studies address losses, fault and in-rush currents, harmonics, insulation, equipment faults, ageing, and instrument-transformer accuracy; Fig. 1 depicts circuit models at varying detail.Source: A. Distribution System and Transformer… · pp. 1–2, Figure 1 · p. 2

B. Innovation of the Power Transformer Digital Twin

The paper proposes monitoring distribution-transformer MV waveforms in real time from LV measurements rather than directly measuring the MV side. It presents this approach as a lower-cost, less disruptive route to accurate monitoring and fault diagnosis.

B. Innovation of the Power Transformer Digital Twin

II. METHODOLOGY AND REQUIRED ASSUMPTIONS

The method uses low-voltage waveform measurements and a single-phase transformer model to estimate medium-voltage voltage and current waveforms. Its preferred equivalent circuit and operating assumptions define the digital twin’s calculation.

II. METHODOLOGY AND REQUIRED ASSUMPTIONS

  • Low-voltage voltage and current measurements feed a single-phase transformer model that estimates the corresponding medium-voltage waveforms.The model also calculates medium-voltage harmonic content when it is present in the low-voltage measurements.Source: A. Digital Twin of a Single-Phase… · pp. 2–3
  • Circuit model (b), with series resistance and reactance lumped on one side, is the preferred digital-twin model; the setup assumes the transformer avoids core saturation.The authors note that a piece-wise formulation may complement the setup if saturation occurs.Source: A. Digital Twin of a Single-Phase… · p. 3
  • The discretized calculation uses the current and previous samples, and high sampling rates are needed to avoid missing harmonic content.The previous sample is required because the formulation includes derivative and integral terms.Source: A. Digital Twin of a Single-Phase… · p. 3

B. Digital Twin of a Three-Phase Power Transformer

The three-phase method combines three single-phase digital twins and maps their outputs according to transformer vector group. Its testing framework compares calculated medium-voltage quantities with a full transformer model across varied scenarios and repeated simulations.

B. Digital Twin of a Three-Phase Power Transformer

  • Three phase-specific low-voltage inputs feed separate single-phase twins, whose outputs are combined by vector group; tests consider changing loads, harmonics, imbalance, faults, and sampling rate.For Dy connections, the method cannot calculate medium-voltage current harmonics at orders that are multiples of three.Source: B. Digital Twin of a Three-Phase Power… · p. 3, §III · p. 4

III. TESTING FRAMEWORK AND ASSESSMENT METRICS

  • MATLAB tests compare the twin’s calculated medium-voltage waveforms and power with a full-model transformer, using sampled low-voltage waveforms and an assumed GridEye measurement device.The simulated topology uses a voltage source, MV-LV transformer, and load impedance; the setup is described as representative of typical distribution-transformer connections.Source: §III · p. 4

A. Statistical Testing of Digital Twin Methodology

  • 24 scenarios vary load, harmonic presence, and sampling rate; about 17,000 simulations per scenario target a 99% confidence interval at ±1% error.The load cases include constant, increasing, and decreasing load, while sampling rates include 5, 10, 30, and 52 kHz.Source: A. Statistical Testing of Digital Twin… · p. 4

B. Testing of Digital Twin Methodology under System Faults, Unbalanced Loading and Tap-Changing Operations

The tests examine whether faults, unbalanced conditions, tap changes, and transformer-model filtering affect the digital twin. Normal-operation accuracy is assessed against actual MV waveforms using normalized average and maximum point errors.

B. Testing of Digital Twin Methodology under System Faults, Unbalanced Loading and Tap-Changing Operations

  • 72 scenarios compare simulated twin and actual MV waveforms under near-rated loading, with harmonics present as a worst-case monitoring condition.Fault, unbalance, grounding, tap-change, and fault-location conditions are among the factors assessed.Source: B. Testing of Digital Twin Methodology… · p. 4

C. Filtering Effect of the Digital Twin on Harmonics

  • Tests assess whether the transformer model captures all voltage and current components by comparing digital-twin and actual MV-side waveform Fourier transforms during changing load with harmonics, plus model and circuit Bode diagrams under high and low loading.Source: C. Filtering Effect of the Digital… · p. 4

D. Assessment Metrics

  • Average and maximum point errors are normalized by the actual waveform RMS; voltage, current, active and reactive power, and frequency are compared.Frequency is estimated from zero crossings across ten consecutive periods.Source: D. Assessment Metrics · p. 5
  • For load changes at 0.2 s, errors are evaluated over 0.16–0.24 s, and scenario statistics include metric averages, maxima, and minima across simulations.The interval spans two electric cycles before and after the change.Source: D. Assessment Metrics · p. 5

IV. RESULTS AND DISCUSSION

The results section is organized into scenario-based results followed by a discussion of the methodology’s efficacy.

  • Results are grouped by scenario characteristics, then discussed in relation to the proposed methodology’s efficacy.Source: §IV · p. 5

A. Results

Normal-operation results report waveform and derived-quantity errors, while fault tests identify conditions that affect phase-voltage estimates. Asymmetrical loading and tap changes are also evaluated.

A. Results

  • Tables III–IV report average, maximum, and minimum error statistics with harmonics; voltage average errors are greater than without harmonics, while other values have similar statistics.The comparison is for the same load-change type and sampling rate.Source: 1) Statistical Testing under Normal… · p. 5

1) Statistical Testing under Normal Operation:

  • 7.6% was the maximum average active-power error (Δx̃_t) at fs=10kHz for increasing load without harmonics.Separately, the average maximum current error (Δx_t,M) was 6.2% at fs=30kHz for constant load with harmonics; the source expresses it with respect to actual active-power RMS.Source: 1) Statistical Testing under Normal… · p. 6

2) System Faults, Unbalanced Loading and Tap-Changing Operations:

  • With an ungrounded upstream voltage source, the tested MV-side LG-fault phase voltages compare successfully; other successful fault cases depend on fault type and grounding topology.Reported successful cases include LL faults regardless of topology, LG/LLG faults with an ungrounded substation LV side, and LG/LLG faults on a Yy transformer grounded on both sides.Source: 2) System Faults, Unbalanced Loading… · p. 7
  • For MV-side faults, line-to-line voltages, line currents, and active and reactive powers are calculated correctly regardless of transformer and distribution-system grounding topologies.MV phase voltages can be miscalculated for LG or LLG faults under specified grounding and transformer-topology conditions, and for faults on the LV side.Source: 2) System Faults, Unbalanced Loading… · pp. 6–7
  • The digital twin calculates all MV-side voltage and current waveforms correctly in the tested asymmetrical-source-voltage and asymmetrical-load cases; tap-changing does not affect its accuracy.The authors attribute the tap-change result to changes in model parameters without changes to its mathematical behavior.Source: 2) System Faults, Unbalanced Loading… · p. 7

3) Filtering Effect of T/F and Digital Twin on Harmonics:

The harmonic analysis compares the digital-twin and actual-transformer circuit responses and waveform spectra. It reports substantially different suppression of higher harmonics beyond the 20th harmonic.

3) Filtering Effect of T/F and Digital Twin on Harmonics:

B. Discussion

Under normal operation, the digital twin’s error behavior depends on sampling rate and harmonic content, while its error intervals and low-load cases qualify how the reported metrics should be interpreted. Voltage waveforms are preferred for frequency estimation.

B. Discussion

  • The expected error interval uses average maximum-error metrics around average-error metrics, which the authors describe as more realistic than a standard-deviation interval.For constant load, Fig. 10 shows the interval with and without harmonics; analogous increasing- and decreasing-load graphs are omitted.Source: 1) Statistical Testing under Normal… · p. 8, Figure 10 · p. 8

1) Statistical Testing under Normal Operation:

  • At fs ≥ 30 kHz without harmonics, average maximum errors fall within the 0.1–3% voltage-RMS accuracy interval for instrument voltage transformers [17]; with harmonics, comparable performance is reported only for the average metric at fs ≥ 10 kHz.Errors decrease as fs increases; at 30 kHz, the analyzed voltage energy contents are nearly identical for the actual and digital-twin models at the most affected frequencies.Source: 1) Statistical Testing under Normal… · p. 8
  • High maximum active- and reactive-power errors occur only below 5% transformer loading; nameplate-power normalization would make them less than 4%.The reported metrics are normalized by the RMS of each waveform.Source: 1) Statistical Testing under Normal… · p. 8
  • Voltage waveforms should be preferred over current waveforms for estimating system frequency because their maximum errors are lower.Average frequency errors are about the same for voltage- and current-based estimates, with a slight preference for voltage.Source: 1) Statistical Testing under Normal… · pp. 8–9
  • Harmonics affect voltage-waveform accuracy more than current, power, or frequency; sufficiently high sampling rates preserve accurate MV waveform calculations despite harmonics.The discussion attributes the difference to voltage drops across series impedances and greater damping of higher-frequency voltage components in the digital-twin model.Source: 1) Statistical Testing under Normal… · p. 9

2) System Faults, Unbalanced Loading and Tap-Changing Operations:

Fault behavior depends on whether the event is visible in LV measurements, while field measurements from a Swiss transformer broadly corroborate the simulation results. The field comparison also identifies a current-error exception associated with low loading and RMS normalization.

2) System Faults, Unbalanced Loading and Tap-Changing Operations:

  • For some MV-side LG or LLG faults, zero-sequence voltage and current do not propagate to the LV side, so the method cannot calculate phase voltages correctly.This boundary is described for grounded MV systems and YGy or Yyg transformers.Source: 2) System Faults, Unbalanced Loading… · p. 9
  • For LV-side faults, LV voltage measurements see toward the fault and can cause incorrect MV calculations, but the method captures the LV fault that operators prioritize.The passage attributes the calculation issue to the typically smaller fault impedance and near-zero voltage on affected phases.Source: 2) System Faults, Unbalanced Loading… · p. 9

V. FIELD TEST VALIDATION OF DIGITAL TWIN OF DISTRIBUTION POWER TRANSFORMER METHODOLOGY

  • The field test used synchronized LV- and MV-side measurements from a Swiss MV-LV transformer, with four waveform datasets of about 10 minutes each.GridEye devices logged both sides; the LV waveforms were input to the digital twin and its calculated MV waveforms were compared with measured MV waveforms.Source: §V · p. 9
  • Field waveforms corroborate accurate MV-side calculations from LV inputs; voltage and power metrics fall within simulation intervals, while current metrics exceed their maxima.Fig. 12 compares digital-twin and measured MV current, phase voltage, active power, and reactive power; the four field datasets were sampled at 13.2 kHz.Source: Figure 12 · p. 10, §V · p. 10
  • All four field datasets had transformer loading below 5% of the 630 kVA nameplate; normalizing current errors by nominal current would make them no more than 4%.The authors attribute the higher-than-simulation current metrics to normalization by the respective waveform RMS.Source: §V · p. 10

VI. CONCLUSION

The paper presents an LV-measurement-driven digital twin for monitoring MV-side transformer waveforms and reports that its accuracy improves with input sampling rate. It identifies a specific compensated-ground-fault phase-voltage boundary and proposes further field assessment and extensions.

VI. CONCLUSION

  • The digital twin calculates MV-side transformer waveforms from LV measurements, captures most system faults and harmonics, and has accuracy comparable to an instrument transformer.Its accuracy increases as the sampling rate of the input LV waveforms increases.Source: §VI · p. 10
  • The next assessment step is deployment on a distribution-system monitoring device to evaluate field performance, installation costs, and disruption.The paper also identifies applying the method to MV-to-high-voltage transformers as a possible extension.Source: §VI · p. 10
  • The proposed method’s phase-voltage calculation needs improvement for compensated MV ground faults when both transformer windings are not grounded.The conclusion says MV current flows and line-to-line voltages can be calculated accurately under all MV fault conditions, while phase voltages fail in the specified cases.Source: §VI · p. 10

VII. APPENDIX

The appendix lists the simulation transformer and load parameters, then gives transformer and GridEye measurement specifications for the Swiss field-data tests.

A. Simulation Testing on MATLAB

  • The three-phase MV-LV transformer is rated 50 kVA at 400 V/20 kV, with 0.0075 pu winding resistances, 0.02 pu leakage inductances, and 500 pu magnetizing resistance and inductance; varying LV loads are 0.75–5.25 Ω and 1.5–17 mH.Source: A. Simulation Testing on MATLAB · p. 10

B. Digital Twin Tests with Field Data from T/F in Switzerland

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