pith. sign in

arxiv: 2604.21040 · v1 · submitted 2026-04-22 · 📡 eess.SY · cs.SY

Online Long-Term Voltage Stability Margin Estimation for IBR/DER Dominated Power System with Integrated VSM-Aware TSO-DSO Framework

Ahmed Alkhonain , Kiran Kumar Challa , Amarsagar Reddy Ramapuram Matavalam , Alok Kumar Bharati , Venkataramana Ajjarapu This is my paper

Pith reviewed 2026-05-09 23:14 UTC · model grok-4.3

classification 📡 eess.SY cs.SY
keywords voltage stability margininverter-based resourcesTSO-DSO coordinationphysics-informed machine learningpower system optimizationlong-term voltage stabilitydistribution system modeling
0
0 comments X

The pith

A physics-informed machine learning model produces a closed-form voltage stability margin expression that linearizes for real-time TSO optimization in IBR-dominated systems.

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

The paper aims to derive an explicit analytical expression for the long-term voltage stability margin using a physics-informed machine learning model trained on offline co-simulation data of transmission and distribution networks under probabilistic scenarios. This accounts for unbalanced distribution modeling and high penetration of inverter-based and distributed energy resources. The closed-form expression is then linearized and incorporated into the transmission system operator's optimization problem to enforce minimum stability margins in real time while coordinating with distribution operators. A reader would care because increasing renewable integration changes how power systems maintain voltage stability, and this offers a way to monitor and optimize it online without heavy computational burden during operation.

Core claim

An explicit analytical VSM expression is derived from offline T&D co-simulation data using a physics-informed ML-trained model under probabilistic loading and generation mix scenarios, while accounting for unbalanced distribution modeling. The resulting closed-form VSM representation is linearized and embedded into the TSO optimization problem, enabling real-time enforcement of minimum VSM constraints.

What carries the argument

The explicit analytical VSM expression obtained from the physics-informed ML model trained on co-simulation data, which is linearized for embedding into optimization.

If this is right

  • The TSO optimization can enforce minimum VSM constraints in real time.
  • VSM sensitivities allow prioritization of the most influential reactive power resources in both transmission and distribution optimizations.
  • Operational efficiency is enhanced while achieving desired VSM enhancement.
  • High estimation accuracy is maintained as validated through simulations on IEEE test systems.

Where Pith is reading between the lines

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

  • This approach might extend to other stability metrics beyond voltage, such as small-signal stability, by similar ML derivations.
  • If the model generalizes well, utilities could reduce reliance on conservative offline planning margins in favor of dynamic online constraints.
  • Further work could explore how this framework interacts with market operations or uncertainty from renewable forecasting.

Load-bearing premise

The physics-informed ML model trained offline on probabilistic scenarios produces a closed-form VSM expression that stays accurate and generalizes under real-time operating conditions, with linearization not degrading the ability to enforce meaningful constraints.

What would settle it

Running the framework on a real power system and comparing the online VSM estimates against actual stability limits obtained from detailed dynamic simulations under varying IBR output and load conditions; significant mismatches would indicate the expression does not hold.

Figures

Figures reproduced from arXiv: 2604.21040 by Ahmed Alkhonain, Alok Kumar Bharati, Amarsagar Reddy Ramapuram Matavalam, Kiran Kumar Challa, Venkataramana Ajjarapu.

Figure 1
Figure 1. Figure 1: Capability curve for synchronous generator and DERs [PITH_FULL_IMAGE:figures/full_fig_p003_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: Proposed framework The framework combines probabilistic sampling and T&D co-simulation to generate realistic operating scenarios under high IBR/DER penetration. The trained ML models provide (i) an explicit analytical expression for VSM and (ii) sensitivity￾based weights for DER reactive power dispatch. These com￾ponents are then embedded into coordinated TSO–DSO opti￾mization problems [PITH_FULL_IMAGE:fi… view at source ↗
Figure 3
Figure 3. Figure 3: Proposed off-line training framework [PITH_FULL_IMAGE:figures/full_fig_p003_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: Test system In this study, T&D co-simulation is employed to generate PV curves under various load increase directions, capturing the system’s long-term voltage stability behavior. The VSM dataset is driven by projected wind and solar PV generation scenarios from NREL [39], which distinguish between wind￾based IBRs and PV IBR connected at the transmission level due to their different active power profiles. … view at source ↗
Figure 5
Figure 5. Figure 5: illustrates the DER reactive power re-dispatch across multiple nodes under the different coordination strategies. The results highlight clear differences in how reactive power sup￾port is spatially allocated when voltage stability considerations are explicitly incorporated into the optimization framework. In the equally weighted case, reactive power injections are relatively moderate and distributed withou… view at source ↗
read the original abstract

The rapid growth of inverter-based resources (IBRs) and distributed energy resources (DERs) has fundamentally altered the long-term voltage stability characteristics of modern power systems. This article leverages the advantages of machine learning (ML) for the online estimation of long-term voltage stability margin (VSM) and enhancement of VSM through coordinated transmission system operator-distribution system operator (TSO-DSO) optimization. An explicit analytical VSM expression is derived from offline T&D co-simulation data using a physics-informed ML-trained model under probabilistic loading and generation mix scenarios, while accounting for unbalanced distribution modeling. The resulting closed-form VSM representation is linearized and embedded into the TSO optimization problem, enabling real-time enforcement of minimum VSM constraints. We further enhance operational efficiency by incorporating VSM sensitivities into both transmission and distribution optimization, allowing prioritization of the most influential reactive power resources. Simulation studies conducted on the IEEE 30-bus transmission network integrated with multiple IEEE 37-node distribution feeders validate that the proposed framework successfully achieves the desired VSM enhancement while maintaining high estimation accuracy.

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

3 major / 1 minor

Summary. The paper claims to derive an explicit closed-form analytical expression for long-term voltage stability margin (VSM) by training a physics-informed ML model on offline T&D co-simulation data generated under probabilistic loading and generation-mix scenarios (including unbalanced distribution modeling). This expression is linearized and embedded as a constraint in a TSO optimization problem within a VSM-aware TSO-DSO coordination framework, enabling real-time enforcement of minimum VSM while using VSM sensitivities to prioritize reactive-power resources. Validation on the IEEE 30-bus transmission system integrated with multiple IEEE 37-node distribution feeders is reported to achieve the desired VSM enhancement together with high estimation accuracy.

Significance. If the ML-derived closed-form VSM expression generalizes reliably beyond the offline training distribution and its linearization preserves meaningful constraint enforcement, the approach could support practical online VSM monitoring and coordinated control in IBR/DER-heavy grids. The explicit incorporation of unbalanced distribution modeling and the use of sensitivities for resource prioritization are constructive elements that could improve operational relevance over purely transmission-focused methods.

major comments (3)
  1. [Abstract / Simulation studies] Abstract and simulation studies section: the central claim of 'high estimation accuracy' and successful real-time VSM enforcement is not supported by any reported quantitative metrics (e.g., out-of-sample MAE, RMSE, or R² on unseen operating points), training-set size, hyper-parameter details, or linearization-error bounds; without these the generalization and fidelity assumptions remain unverified.
  2. [VSM expression derivation and optimization embedding] The derivation of the closed-form VSM expression via fitting a physics-informed ML model to offline probabilistic co-simulation data, followed by linearization for the TSO problem, creates a potential circularity: enforcement of the VSM constraint largely reproduces the fitted surface rather than an independent physical prediction. A post-optimization comparison of the linearized VSM value against the full nonlinear model (or time-domain simulation) on the IEEE test cases is required to quantify any degradation.
  3. [Validation / IEEE 30-bus + 37-node studies] No sensitivity analysis or additional test cases are provided for operating points outside the probabilistic training scenarios (e.g., extreme IBR/DER configurations or contingency conditions), which directly challenges the weakest assumption that the closed-form expression remains accurate under real-time conditions.
minor comments (1)
  1. [Optimization formulation] Notation for the linearized VSM constraint and the sensitivity coefficients should be introduced with explicit definitions and units to improve readability.

Simulated Author's Rebuttal

3 responses · 0 unresolved

We thank the referee for the constructive and detailed review of our manuscript. We address each major comment point by point below, providing clarifications and indicating revisions that will be incorporated to improve the rigor and completeness of the work.

read point-by-point responses

  1. Referee: [Abstract / Simulation studies] Abstract and simulation studies section: the central claim of 'high estimation accuracy' and successful real-time VSM enforcement is not supported by any reported quantitative metrics (e.g., out-of-sample MAE, RMSE, or R² on unseen operating points), training-set size, hyper-parameter details, or linearization-error bounds; without these the generalization and fidelity assumptions remain unverified.

    Authors: We agree that explicit quantitative metrics strengthen the claims. In the revised manuscript we will update the abstract and expand the simulation studies section to report out-of-sample MAE, RMSE, and R² values for the physics-informed ML VSM estimator evaluated on unseen operating points drawn from the probabilistic T&D co-simulation dataset. We will also include the training-set size, hyper-parameter configuration of the ML model, and explicit bounds on the linearization error. These additions will directly support the reported high estimation accuracy and real-time enforcement performance. revision: yes

  2. Referee: [VSM expression derivation and optimization embedding] The derivation of the closed-form VSM expression via fitting a physics-informed ML model to offline probabilistic co-simulation data, followed by linearization for the TSO problem, creates a potential circularity: enforcement of the VSM constraint largely reproduces the fitted surface rather than an independent physical prediction. A post-optimization comparison of the linearized VSM value against the full nonlinear model (or time-domain simulation) on the IEEE test cases is required to quantify any degradation.

    Authors: The physics-informed ML model is trained directly on data generated by the full nonlinear T&D co-simulations, so the resulting closed-form expression is an explicit approximation of the underlying physics rather than an arbitrary fit. To address the concern about degradation, the revised manuscript will include a dedicated post-optimization validation subsection. For the IEEE 30-bus + 37-node test cases we will evaluate the linearized VSM constraint value at the optimized operating point against the full nonlinear model (and time-domain simulation where feasible) and report the observed deviation, thereby quantifying the fidelity of the embedded constraint. revision: yes

  3. Referee: [Validation / IEEE 30-bus + 37-node studies] No sensitivity analysis or additional test cases are provided for operating points outside the probabilistic training scenarios (e.g., extreme IBR/DER configurations or contingency conditions), which directly challenges the weakest assumption that the closed-form expression remains accurate under real-time conditions.

    Authors: We acknowledge that generalization beyond the training distribution is critical for online applicability. The current probabilistic scenarios already span a broad range of loading, generation-mix, and IBR/DER penetration levels. In the revision we will add a sensitivity analysis subsection together with additional test cases that include extreme IBR/DER configurations and selected N-1 contingencies. For these out-of-distribution points we will report the VSM estimation accuracy of the closed-form expression, thereby providing direct evidence of robustness under conditions closer to real-time operation. revision: yes

Circularity Check

0 steps flagged

No significant circularity; surrogate modeling chain is independent of target result

full rationale

The derivation proceeds from independent offline T&D co-simulations (physics-based) to training a physics-informed ML model, extraction of a closed-form VSM expression, linearization, and embedding as a constraint. This is standard surrogate-based optimization and does not reduce any claimed prediction or enforcement to the fitted inputs by construction. No self-citations, uniqueness theorems, or self-definitional steps are present in the abstract or described chain. Validation on IEEE test cases provides an external check separate from the training data.

Axiom & Free-Parameter Ledger

1 free parameters · 1 axioms · 0 invented entities

The central claim rests on the assumption that offline co-simulation data sufficiently represent real-system behavior and that the ML fit captures the relevant physics without overfitting to the chosen probabilistic scenarios.

free parameters (1)
  • ML model parameters
    Parameters of the physics-informed ML model are fitted to offline T&D co-simulation data to produce the closed-form VSM expression.
axioms (1)
  • domain assumption Detailed T&D co-simulation models accurately capture long-term voltage stability behavior under unbalanced conditions and probabilistic scenarios.
    Invoked when generating the training data used to derive the analytical VSM expression.

pith-pipeline@v0.9.0 · 5524 in / 1444 out tokens · 51134 ms · 2026-05-09T23:14:30.465308+00:00 · methodology

discussion (0)

Sign in with ORCID, Apple, or X to comment. Anyone can read and Pith papers without signing in.

Reference graph

Works this paper leans on

40 extracted references · 40 canonical work pages

  1. [1]

    Annual Energy Outlook 2020,

    EIA, “Annual Energy Outlook 2020,” Jan. 2020. [Online]. Available: https://www.eia.gov/outlooks/aeo/pdf/aeo2020%20full%20report.pdf

    work page 2020

  2. [2]

    Global Market Outlook For Solar Power 2023– 2027,

    SolarPower Europe, “Global Market Outlook For Solar Power 2023– 2027,” Jun. 13, 2023. [Online]. Available: https://www.solarpowereurope. org/insights/outlooks/global-market-outlook-for-solar-power-2023-2027/ detail

    work page 2023

  3. [3]

    Quarterly Energy,

    Australian Energy Market Operator (AEMO), “Quarterly Energy,” Jan. 2024

    work page 2024

  4. [4]

    V oltage and Reactive Control

    NERC, “V oltage and Reactive Control.” [Online]. Available: https://www. nerc.com/pa/Stand/Reliability%20Standards/V AR-001-6.pdf

    work page

  5. [5]

    FERC Order No. 2222 Explainer: Facilitating Participation in Electricity Markets by Distributed Energy Resources,

    FERC, “FERC Order No. 2222 Explainer: Facilitating Participation in Electricity Markets by Distributed Energy Resources,” 2020

    work page 2020

  6. [6]

    IEEE Standard for Interconnection and Interoperability of Dis- tributed,

    IEEE, “IEEE Standard for Interconnection and Interoperability of Dis- tributed,” IEEE Std 1547–2018, 2018

    work page 2018

  7. [7]

    Investigation of Relevant Distribution System Representation With DG for V oltage Stability Margin Assess- ment,

    A. K. Bharati and V . Ajjarapu, “Investigation of Relevant Distribution System Representation With DG for V oltage Stability Margin Assess- ment,”IEEE Transactions on Power Systems, vol. 35, no. 3, pp. 2072– 2081, 2020

    work page 2072

  8. [8]

    Integrated T&D V oltage Stability Assessment Considering Impact of DERs and Distribution Network Topology,

    S. M. H. Rizvi and A. K. Srivastava, “Integrated T&D V oltage Stability Assessment Considering Impact of DERs and Distribution Network Topology,”IEEE Access, vol. 11, pp. 14702–14714, 2023

    work page 2023

  9. [9]

    The continuation power flow: a tool for steady state voltage stability analysis,

    V . Ajjarapu and C. Christy, “The continuation power flow: a tool for steady state voltage stability analysis,”IEEE Transactions on Power Systems, vol. 7, no. 1, pp. 416–423, 1992

    work page 1992

  10. [10]

    Long Term V oltage Stability Assessment of an Integrated Transmission Distribution System,

    A. Singhal and V . Ajjarapu, “Long Term V oltage Stability Assessment of an Integrated Transmission Distribution System,” inProc. 49th North American Power Symposium, Morgantown, WV , 2017

    work page 2017

  11. [11]

    Monitoring Long Term V oltage Instability Due to Distribution and Transmission Interaction Using UnbalancedµPMU and PMU Measurements,

    A. R. R. Matavalam, A. Singhal, and V . Ajjarapu, “Monitoring Long Term V oltage Instability Due to Distribution and Transmission Interaction Using UnbalancedµPMU and PMU Measurements,”IEEE Transactions on Smart Grid, vol. 11, no. 1, pp. 873–883, 2020

    work page 2020

  12. [12]

    Sensitivity Based Thevenin Index With Systematic Inclusion of Reactive Power Limits,

    A. R. R. Matavalam and V . Ajjarapu, “Sensitivity Based Thevenin Index With Systematic Inclusion of Reactive Power Limits,”IEEE Transactions on Power Systems, vol. 33, no. 1, pp. 932–942, 2018

    work page 2018

  13. [13]

    Impact of distributed generator on voltage stability analysis of distribution networks under critical loading conditions,

    T. K. Chattopadhyay, S. Banerjee, and C. K. Chanda, “Impact of distributed generator on voltage stability analysis of distribution networks under critical loading conditions,” inProc. 1st Int. Conf. Non Conven- tional Energy (ICONCE), India, 2014

    work page 2014

  14. [14]

    V oltage stability assessment in power systems using line voltage stability index,

    S. Ratra, R. Tiwari, and K. R. Niazi, “V oltage stability assessment in power systems using line voltage stability index,”Comput. Electr. Eng., vol. 70, pp. 199–211, 2018

    work page 2018

  15. [15]

    Static voltage stability analysis of distribution systems based on network-load admittance ratio,

    Y . Song, D. J. Hill, and T. Liu, “Static voltage stability analysis of distribution systems based on network-load admittance ratio,”IEEE Transactions on Power Systems, vol. 34, no. 3, pp. 2270–2280, 2019

    work page 2019

  16. [16]

    Application of multi-linear regression models and machine learning techniques for online voltage stability margin estimation,

    B. Leonardi, V . Ajjarapu, M. Djukanovic, and P. Zhang, “Application of multi-linear regression models and machine learning techniques for online voltage stability margin estimation,” inProc. 2010 IREP Symp. Bulk Power System Dynamics and Control - VIII (IREP), pp. 1–10, 2010

    work page 2010

  17. [17]

    Adaptive Online Monitoring of V oltage Stability Margin via Local Regression,

    S. Li, V . Ajjarapu, and M. Djukanovic, “Adaptive Online Monitoring of V oltage Stability Margin via Local Regression,”IEEE Transactions on Power Systems, vol. 33, no. 1, pp. 701–713, 2018

    work page 2018

  18. [18]

    PMU-Based V oltage Stability Measurement Under Contingency Using ANN,

    S. Kumar, B. Tyagi, V . Kumar, and S. Chohan, “PMU-Based V oltage Stability Measurement Under Contingency Using ANN,”IEEE Transac- tions on Instrumentation and Measurement, vol. 71, pp. 1–11, 2022

    work page 2022

  19. [19]

    Improving Online V oltage Stability Monitoring in Smart Grids: A Physics-Informed Guided Deep Learning Model,

    H.-Y . Su and C.-C. Lai, “Improving Online V oltage Stability Monitoring in Smart Grids: A Physics-Informed Guided Deep Learning Model,”IEEE Transactions on Industry Applications, vol. 61, no. 2, pp. 1–13, 2025

    work page 2025

  20. [20]

    Online Monitoring of V oltage Stability Margin Using an Artificial Neural Network,

    D. Q. Zhou, U. D. Annakkage, and A. D. Rajapakse, “Online Monitoring of V oltage Stability Margin Using an Artificial Neural Network,”IEEE Transactions on Power Systems, vol. 25, no. 3, pp. 1566–1574, 2010

    work page 2010

  21. [21]

    Phasor Measurement Sensor-Assisted Time- to-Collapse Estimation Under Long-Term V oltage Instability of Smart Grids,

    M. Pandit and R. Sodhi, “Phasor Measurement Sensor-Assisted Time- to-Collapse Estimation Under Long-Term V oltage Instability of Smart Grids,”IEEE Sensors Journal, vol. 24, no. 5, pp. 6523–6531, 2024

    work page 2024

  22. [22]

    A New V oltage Stability-Constrained Optimal Power-Flow Model: Sufficient Condition, SOCP Representation, and Relaxation,

    B. Cui and X. A. Sun, “A New V oltage Stability-Constrained Optimal Power-Flow Model: Sufficient Condition, SOCP Representation, and Relaxation,”IEEE Transactions on Power Systems, vol. 33, no. 5, pp. 5092–5102, Sept. 2018, doi: 10.1109/TPWRS.2018.2801286

    work page doi:10.1109/tpwrs.2018.2801286 2018

  23. [23]

    V oltage Stability Constrained Optimal Power Flow Considering PV–PQ Bus Type Switching: Formulation and Convexification,

    Y . Song, T. Liu, and Y . Hou, “V oltage Stability Constrained Optimal Power Flow Considering PV–PQ Bus Type Switching: Formulation and Convexification,”IEEE Transactions on Power Systems, vol. 39, no. 2, pp. 3336–3348, Mar. 2024, doi: 10.1109/TPWRS.2023.3313656

    work page doi:10.1109/tpwrs.2023.3313656 2024

  24. [24]

    An approach for real time voltage stability margin control via reactive power reserve sensitivities,

    B. Leonardi and V . Ajjarapu, “An approach for real time voltage stability margin control via reactive power reserve sensitivities,”IEEE Transactions on Power Systems, vol. 28, no. 2, pp. 615–625, May 2013

    work page 2013

  25. [25]

    Coordinated Transmission and Distribution AC Optimal Power Flow,

    Z. Li, Q. Guo, H. Sun and J. Wang, “Coordinated Transmission and Distribution AC Optimal Power Flow,”IEEE Transactions on Smart Grid, vol. 9, no. 2, pp. 1228–1240, Mar. 2018

    work page 2018

  26. [26]

    Provision of V oltage Ancillary Services Through Enhanced TSO-DSO Interaction and Aggregated Distributed Energy Resources,

    A. O. Rousis, D. Tzelepis, Y . Pipelzadeh, G. Strbac, C. D. Booth and T. C. Green, “Provision of V oltage Ancillary Services Through Enhanced TSO-DSO Interaction and Aggregated Distributed Energy Resources,” IEEE Transactions on Sustainable Energy, vol. 12, no. 2, pp. 897–908, Apr. 2021

    work page 2021

  27. [27]

    Computing Cost Curves of Active Distribution Grids Aggregated Flexibility for TSO-DSO Coordination

    F. Capitanescu, “Computing Cost Curves of Active Distribution Grids Aggregated Flexibility for TSO-DSO Coordination”, in IEEE Transac- tions on Power Systems, vol. 39, no. 1, pp. 2381-2384, Jan. 2024

    work page 2024

  28. [28]

    Usman, M

    M. Usman, M. I. Alizadeh, F. Capitanescu, I.-I. Avramidis, and A. G. Madureira, ”A novel two-stage TSO–DSO coordination approach for managing congestion and voltages,” International Journal of Electrical Power & Energy Systems, vol. 147, p. 108824, 2023

    work page 2023

  29. [29]

    Improving V oltage Stability by Reactive Power Reserve Management,

    F. Dong, B. H. Chowdhury, M. L. Crow, and L. Acar, “Improving V oltage Stability by Reactive Power Reserve Management,”IEEE Trans- actions on Power Systems, vol. 20, no. 1, 2005

    work page 2005

  30. [30]

    Online voltage stability monitoring using V Ar reserves,

    L. Bao, Z. Huang, and W. Xu, “Online voltage stability monitoring using V Ar reserves,”IEEE Transactions on Power Systems, vol. 18, no. 4, 2003

    work page 2003

  31. [31]

    Investigation of various generator reactive power reserve (GRPR) definitions for online voltage stability/security assessment,

    B. Leonardi and V . Ajjarapu, “Investigation of various generator reactive power reserve (GRPR) definitions for online voltage stability/security assessment,” inProc. IEEE Power and Energy Society General Meeting, Pittsburgh, PA, USA, 2008

    work page 2008

  32. [32]

    ”IEEE Standard for Interconnection and Interoperability of Inverter- Based Resources (IBRs) Interconnecting with Associated Transmission Electric Power Systems,” in IEEE Std 2800-2022 , vol., no., pp.1-180, 22 April 2022

    work page 2022

  33. [33]

    An Approach for Real-Time V oltage Stability Margin Control via Reactive Power Reserve Sensitivities,

    B. Leonardi and V . Ajjarapu, “An Approach for Real-Time V oltage Stability Margin Control via Reactive Power Reserve Sensitivities,”IEEE Transactions on Power Systems, vol. 28, no. 2, 2013

    work page 2013

  34. [34]

    Deriving DERs V AR- Capability Curve at TSO-DSO Interface to Provide Grid Services,

    A. Singhal, A. K. Bharati, and V . Ajjarapu, “Deriving DERs V AR- Capability Curve at TSO-DSO Interface to Provide Grid Services,”IEEE Transactions on Power Systems, vol. 38, no. 2, Mar. 2023

    work page 2023

  35. [35]

    Identification of Repre- sentative Operating Hours for High Renewable Grid Planning,

    K. K. Challa, A. K. Bharati, and V . Ajjarapu, “Identification of Repre- sentative Operating Hours for High Renewable Grid Planning,” inProc. IEEE Kansas Power and Energy Conf. (KPEC), Manhattan, KS, USA, 2025

    work page 2025

  36. [36]

    SMTD Co-Simulation Framework With HELICS for Future-Grid Analysis and Synthetic Measurement-Data Generation,

    A. K. Bharati and V . Ajjarapu, “SMTD Co-Simulation Framework With HELICS for Future-Grid Analysis and Synthetic Measurement-Data Generation,”IEEE Transactions on Industry Applications, vol. 58, no. 1, pp. 131–141, 2022

    work page 2022

  37. [37]

    IEEE 30-Bus Sys- tem

    Illinois Center for a Smarter Electric Grid (ICSEG), “IEEE 30-Bus Sys- tem.” [Online]. Available: https://icseg.iti.illinois.edu/ieee-30-bus-system/

    work page

  38. [38]

    IEEE PES Test Feeder

    IEEE, “IEEE PES Test Feeder.” [Online]. Available: https://cmte.ieee. org/pes-testfeeders/resources/

    work page

  39. [39]

    Renewable Electricity Future Scenario Viewer

    NREL, “Renewable Electricity Future Scenario Viewer.” Available on: https:https://scenarioviewer.nrel.gov/

    work page

  40. [40]

    Sensitivity- Aware Reactive Power Dispatch of DERs to Support Transmission Grid During Emergency,

    A. Alkhonain, A. Singhal, A. K. Bharati, and V . Ajjarapu, “Sensitivity- Aware Reactive Power Dispatch of DERs to Support Transmission Grid During Emergency,” inProc. North American Power Symposium (NAPS), Asheville, NC, USA, 2023

    work page 2023