Development and Applicability of Online Passivity Enforced Wide-Band Multi-Port Equivalents For Hybrid Transient Simulation

Abilash Thakallapelli; Sudipta Ghosh; Sukumar Kamalasadan

arxiv: 1907.09524 · v1 · pith:PYGGZ5PWnew · submitted 2019-07-17 · 📡 eess.SP · cs.SY· eess.SY

Development and Applicability of Online Passivity Enforced Wide-Band Multi-Port Equivalents For Hybrid Transient Simulation

Abilash Thakallapelli , Sudipta Ghosh , Sukumar Kamalasadan This is my paper

Pith reviewed 2026-05-24 20:29 UTC · model grok-4.3

classification 📡 eess.SP cs.SYeess.SY

keywords frequency dependent network equivalentpassivity enforcementrecursive least squareshybrid transient simulationmulti-port equivalentsz-domain admittance matrixpower system modeling

0 comments

The pith

An online recursive least squares algorithm with passivity enforcement identifies multi-port frequency dependent network equivalents directly from data.

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

This paper develops a method for building single and multi-port frequency dependent network equivalents by applying a passivity-enforced online recursive least squares algorithm that identifies the input admittance matrix in the z-domain. The resulting architecture supports real-time hybrid models of reduced power systems that combine transient stability analysis with the identified equivalents. It works even when network parameters are unknown within the frequency range of interest and produces models that can be implemented directly in discrete time while satisfying accuracy, stability, and passivity requirements. The approach is demonstrated on two-area, IEEE 39-bus, and 68-bus test systems.

Core claim

The proposed architecture identifies the FDNE even with unknown network parameters in the frequency range of interest, and yet can be implemented directly due to discrete formulation while maintaining desired accuracy, stability, and passivity conditions.

What carries the argument

Passivity-enforced online recursive least squares identification algorithm that extracts the input admittance matrix in z-domain

If this is right

The identified FDNEs integrate directly into real-time hybrid models that combine transient stability analysis with electromagnetic transient detail.
Single-port and multi-port equivalents are produced by the same discrete-time identification process.
The method applies to standard test cases including two-area, IEEE 39-bus, and IEEE 68-bus power system models while preserving accuracy and stability.

Where Pith is reading between the lines

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

Online identification could support adaptive FDNE updates when network topology or loading changes during operation.
The z-domain discrete formulation may reduce interface overhead when coupling with existing digital real-time simulators.
Extending the passivity enforcement step to include measurement noise bounds could widen the range of practical field data that can be used.

Load-bearing premise

An online recursive least squares identification algorithm, once passivity is enforced, will produce an admittance matrix whose accuracy and stability hold for the full frequency range of interest without requiring prior knowledge of network parameters.

What would settle it

A simulation in which the identified FDNE is driven at a frequency or operating point outside the identification window and exhibits instability or loss of passivity.

Figures

Figures reproduced from arXiv: 1907.09524 by Abilash Thakallapelli, Sudipta Ghosh, Sukumar Kamalasadan.

**Figure 2.** Figure 2: TSA Calculation GND5 [PITH_FULL_IMAGE:figures/full_fig_p004_2.png] view at source ↗

**Figure 3.** Figure 3: Proposed dynamic equivalent of two area system [PITH_FULL_IMAGE:figures/full_fig_p004_3.png] view at source ↗

**Figure 4.** Figure 4: The relative speed of Gen.2 w.r.t Gen.1 0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 time(s) 600 800 1000 1200 1400 1600 1800 Active Power (MW) EMT+TSA Based Model (AGG) EMT+TSA Based Model EMT Based Model 1 1.02 1.04 1.06 1.08 1.1 1.12 600 800 1000 1200 1400 High Frequency Oscillations [PITH_FULL_IMAGE:figures/full_fig_p005_4.png] view at source ↗

**Figure 7.** Figure 7: Admittance vs frequency of external area (two area system) [PITH_FULL_IMAGE:figures/full_fig_p006_7.png] view at source ↗

**Figure 8.** Figure 8: The eigenvalue of real-part of admittance matrix (1-port) [PITH_FULL_IMAGE:figures/full_fig_p007_8.png] view at source ↗

**Figure 9.** Figure 9: Boundary bus current calculation for FDNE only [PITH_FULL_IMAGE:figures/full_fig_p007_9.png] view at source ↗

**Figure 10.** Figure 10: Relative speed of Gen.2 w.r.t Gen.1 0 1 2 3 4 5 time(s) 600 800 1000 1200 1400 1600 Active Power (MW) EMT+FDNE Based Model (Proposed) EMT+FDNE Based Model (VF) EMT Based Model 1 1.02 1.04 1.06 1.08 1.1 1.12 600 800 1000 1200 1400 High Frequency Oscillations [PITH_FULL_IMAGE:figures/full_fig_p008_10.png] view at source ↗

**Figure 18.** Figure 18: Bus 17 Voltage 0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 time(s) -2 -1 0 1 2 3 Relative Speed (rad/s) EMT+FDNE+TSA Based Model (AGG) EMT+FDNE+TSA Based Model EMT Based Model [PITH_FULL_IMAGE:figures/full_fig_p009_18.png] view at source ↗

**Figure 19.** Figure 19: Relative speed of generator gen.1 w.r.t gen.2 [PITH_FULL_IMAGE:figures/full_fig_p009_19.png] view at source ↗

**Figure 15.** Figure 15: Admittance vs frequency of external area (39 Bus System) [PITH_FULL_IMAGE:figures/full_fig_p009_15.png] view at source ↗

**Figure 16.** Figure 16: The corrected eigenvalue of real-part of admittance matrix (3-port) [PITH_FULL_IMAGE:figures/full_fig_p009_16.png] view at source ↗

**Figure 17.** Figure 17: Bus 26 Active Power original model [PITH_FULL_IMAGE:figures/full_fig_p009_17.png] view at source ↗

**Figure 20.** Figure 20: Admittance vs frequency of external area (68 Bus System) [PITH_FULL_IMAGE:figures/full_fig_p010_20.png] view at source ↗

**Figure 21.** Figure 21: Bus 60 Voltage 0.8 1 1.2 1.4 1.6 1.8 2 2.2 2.4 time (s) -0.05 0 0.05 0.1 Relative Speed (rad/s) EMT+FDNE+TSA Based Model (AGG) EMT+FDNE+TSA Based Model EMT Based Model 1 1.05 1.1 1.15 -0.05 0 0.05 0.1 [PITH_FULL_IMAGE:figures/full_fig_p010_21.png] view at source ↗

**Figure 22.** Figure 22: Relative speed of generator 10 w.r.t generator 16 [PITH_FULL_IMAGE:figures/full_fig_p010_22.png] view at source ↗

read the original abstract

This paper presents a method for developing single and multi-port frequency dependent network equivalent (FDNE) based on a passivity enforced online recursive least squares identification algorithm, which identifies the input admittance matrix in z-domain. Furthermore, with the proposed architecture, a real-time hybrid model of the reduced power system is developed that integrate transient stability analysis and FDNE. Main advantages of the proposed architecture are, it identifies the FDNE even with unknown network parameters in the frequency range of interest, and yet can be implemented directly due to discrete formulation while maintaining desired accuracy, stability, and passivity conditions. The accuracy and characteristics of the proposed method are verified by implementing on two-area, IEEE 39 and 68 bus power system models.

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.

Desk Editor's Note private letter to a colleague

The paper gives a practical online RLS pipeline for passivity-enforced multi-port FDNEs in z-domain for hybrid power-system simulation, but supplies almost no quantitative fit metrics or excitation checks.

read the letter

The main takeaway is that the authors combine online recursive least squares with an explicit passivity step to identify the z-domain admittance matrix of single- and multi-port FDNEs, then embed the result directly in a hybrid EMT-TSA simulator. The discrete formulation avoids continuous-to-discrete conversion headaches and the method is claimed to work without prior knowledge of the network parameters inside the frequency band of interest. That combination is a modest but legitimate extension of existing identification tools already used in the field. The verification is performed on the two-area system plus the IEEE 39- and 68-bus models, which is the right class of test cases for this community. The architecture description is clear enough that someone working on real-time equivalents could reproduce the basic flow. The soft spots are straightforward. The abstract (and the information available) contains no numerical error measures, no baseline comparisons against offline least-squares or vector-fitting methods, and no discussion of how the passivity projection changes the fit quality or the location of poles. RLS convergence still depends on persistent excitation; typical power-system transients supply limited spectral content, so high-frequency inter-port coupling can remain poorly determined. The stress-test note on that point is therefore worth checking in the full manuscript. If the paper only shows time-domain waveforms on the standard test cases without frequency-response error plots or excitation-sensitivity results, the central accuracy claim stays hard to evaluate. This work is aimed squarely at power engineers who build hybrid simulators and need online equivalents. It is not aimed at readers outside that subfield. The thinking is coherent on its own terms and the authors engage the relevant prior literature on FDNEs and passivity. It deserves a serious referee to examine the implementation details, any additional figures that may exist beyond the abstract, and whether the passivity step preserves accuracy across the full band.

Referee Report

2 major / 1 minor

Summary. The manuscript presents a method for developing single- and multi-port frequency-dependent network equivalents (FDNE) via a passivity-enforced online recursive least-squares identification algorithm that identifies the input admittance matrix directly in the z-domain. It further describes a real-time hybrid model integrating transient stability analysis with the FDNE for reduced-order power-system representations. The central claims are that the approach identifies the FDNE even when network parameters are unknown within the frequency range of interest, can be implemented directly due to its discrete formulation, and maintains accuracy, stability, and passivity; verification is stated on two-area, IEEE 39-bus, and 68-bus models.

Significance. If substantiated, the work would offer a practical route to online FDNE construction for hybrid EMT-TSA simulators without requiring full network parameter knowledge, leveraging the discrete z-domain form for direct embedding. The emphasis on passivity enforcement and real-time applicability addresses a recognized need in large-scale power-system transient studies. However, the significance is limited by the absence of quantitative error metrics or excitation analysis, which are necessary to confirm that the fitted models remain accurate and passive over the full band of interest.

major comments (2)

[Abstract] Abstract: the verification on IEEE 39- and 68-bus models is asserted without any quantitative error metrics, baseline comparisons against existing FDNE methods, or discussion of how the passivity-enforcement step modifies the underlying RLS fit; this information is load-bearing for the accuracy and stability claims.
[Method] Method (RLS identification and passivity step): the claim that the z-domain RLS fit followed by passivity projection yields an admittance matrix whose accuracy and stability hold across the entire frequency range of interest, even with unknown parameters, lacks supporting analysis of persistent excitation or extrapolation error; power-system transients supply limited spectral content, so high-frequency poles and inter-port couplings may remain under-determined.

minor comments (1)

[Abstract] Abstract: grammatical error in 'a real-time hybrid model ... is developed that integrate transient stability analysis' (should be 'integrates').

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the constructive feedback. We respond to each major comment below and indicate the revisions that will be incorporated.

read point-by-point responses

Referee: [Abstract] Abstract: the verification on IEEE 39- and 68-bus models is asserted without any quantitative error metrics, baseline comparisons against existing FDNE methods, or discussion of how the passivity-enforcement step modifies the underlying RLS fit; this information is load-bearing for the accuracy and stability claims.

Authors: We agree that the abstract would benefit from quantitative support. In the revised manuscript we will update the abstract to report specific error metrics (maximum relative error in admittance magnitude and phase over the frequency band) for the IEEE 39-bus and 68-bus cases, add a concise baseline comparison statement, and include a brief clause noting that passivity enforcement is performed via a minimal projection that preserves the accuracy of the underlying RLS fit. revision: yes
Referee: [Method] Method (RLS identification and passivity step): the claim that the z-domain RLS fit followed by passivity projection yields an admittance matrix whose accuracy and stability hold across the entire frequency range of interest, even with unknown parameters, lacks supporting analysis of persistent excitation or extrapolation error; power-system transients supply limited spectral content, so high-frequency poles and inter-port couplings may remain under-determined.

Authors: The manuscript currently supports the claims through time-domain verification on the cited benchmark systems. We acknowledge that an explicit discussion of persistent excitation and extrapolation behavior would strengthen the presentation. In the revision we will expand the method section with an analysis of the spectral content present in the transients used for identification and will demonstrate, via additional results from the test cases, that the online RLS-plus-projection procedure maintains accuracy and passivity across the band of interest. We maintain that the empirical evidence already indicates the approach is robust even when network parameters are unknown, but agree to add the requested supporting discussion. revision: partial

Circularity Check

0 steps flagged

No significant circularity; method is explicit data-driven identification with external verification

full rationale

The paper proposes an algorithmic procedure for constructing FDNEs via online RLS identification of the z-domain admittance matrix followed by passivity enforcement, then verifies performance on standard IEEE test systems (two-area, 39-bus, 68-bus). No derivation chain asserts first-principles predictions or uniqueness results that reduce to fitted parameters or self-citations by construction. Accuracy and stability claims rest on simulation outcomes against known network models rather than internal redefinition of inputs as outputs.

Axiom & Free-Parameter Ledger

0 free parameters · 0 axioms · 0 invented entities

Only the abstract is available; no explicit free parameters, axioms, or invented entities are stated. The method implicitly relies on standard RLS assumptions (persistent excitation, appropriate model order) and the domain assumption that passivity enforcement preserves accuracy, none of which are quantified here.

pith-pipeline@v0.9.0 · 5670 in / 1189 out tokens · 24519 ms · 2026-05-24T20:29:52.110466+00:00 · methodology

discussion (0)

Reference graph

Works this paper leans on

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Implicitly coupled elec- tromechanical and electromagnetic transient analysis using a frequency- dependent network equivalent,

X. Zhang, A. J. Flueck, and S. Abhyankar, “Implicitly coupled elec- tromechanical and electromagnetic transient analysis using a frequency- dependent network equivalent,” IEEE Trans. on Power Del. , vol. 32, no. 3, pp. 1262–1269, Jun 2017

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Inertial and slow coherency aggre- gation algorithms for power system dynamic model reduction,

J. Chow, P. Accari, and W. Price, “Inertial and slow coherency aggre- gation algorithms for power system dynamic model reduction,” IEEE Trans. on Power Syst. , vol. 10, no. 2, pp. 680–685, May 1995

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A. Thakallapelli, S. J. Hossain, and S. Kamalasadan, “Coherency based online wide area control of renewable energy integrated power grid,” in Proc. PEDES, IEEE , Dec 2016, pp. 1–6

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