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Plane Wave Dynamic Model of Electric Power Networks with High Shares of Inverter-Based Resources

Amirhossein Sajadi, Bri-Mathias Hodge

TL;DR

This work introduces a plane wave dynamic model for electric power networks that incorporates electromagnetic momentum stored around transmission lines, a factor neglected by traditional swing-equation-based analyses. By deriving plane-wave dynamics from Maxwell's equations and validating against EMT simulations and real-world PMU data, the authors show that line-bound momentum can be a significant, time-varying portion of system inertia, especially as inverter-based resources rise. The study demonstrates that two-dimensional, frequency-volt dynamics capture stability and transients more accurately in high-IBR grids, with implications for grid strength, forced oscillations, and planning toward 100% renewables. The findings suggest potential practical benefits from leveraging electromagnetic momentum and transitioning toward voltage/factor-based control paradigms to enhance robustness in future all-renewable power networks.

Abstract

Contemporary theories and models for electric power system stability are predicated on a widely held assumption that the mechanical inertia of the rotating mass of synchronous generators provides the sole contribution to stable and synchronized operation of this class of complex networks on subsecond timescales. Here we formulate the electromagnetic momentum of the field around the transmission lines that transports energy and present evidence from a real-world bulk power network that demonstrates its physical significance. We show the classical stability model for power networks that overlooks this property, known as the "swing equation", may become inadequate to analyze systems with high shares of inverter-based resources, commonly known as "low-inertia power systems". Subsequently, we introduce a plane wave dynamic model, consistent with the structural properties of emerging power systems with up to 100% inverter-based resources, which identifies the concept of inertia in power grids as a time-varying component. We leverage our theory to discuss a number of open questions in the electric power industry. Most notably, we postulate that the changing nature of power networks with a preponderance of variable renewable energy power plants could strengthen power network stability in the future; a vision which is irreconcilable with the conventional theories.

Plane Wave Dynamic Model of Electric Power Networks with High Shares of Inverter-Based Resources

TL;DR

This work introduces a plane wave dynamic model for electric power networks that incorporates electromagnetic momentum stored around transmission lines, a factor neglected by traditional swing-equation-based analyses. By deriving plane-wave dynamics from Maxwell's equations and validating against EMT simulations and real-world PMU data, the authors show that line-bound momentum can be a significant, time-varying portion of system inertia, especially as inverter-based resources rise. The study demonstrates that two-dimensional, frequency-volt dynamics capture stability and transients more accurately in high-IBR grids, with implications for grid strength, forced oscillations, and planning toward 100% renewables. The findings suggest potential practical benefits from leveraging electromagnetic momentum and transitioning toward voltage/factor-based control paradigms to enhance robustness in future all-renewable power networks.

Abstract

Contemporary theories and models for electric power system stability are predicated on a widely held assumption that the mechanical inertia of the rotating mass of synchronous generators provides the sole contribution to stable and synchronized operation of this class of complex networks on subsecond timescales. Here we formulate the electromagnetic momentum of the field around the transmission lines that transports energy and present evidence from a real-world bulk power network that demonstrates its physical significance. We show the classical stability model for power networks that overlooks this property, known as the "swing equation", may become inadequate to analyze systems with high shares of inverter-based resources, commonly known as "low-inertia power systems". Subsequently, we introduce a plane wave dynamic model, consistent with the structural properties of emerging power systems with up to 100% inverter-based resources, which identifies the concept of inertia in power grids as a time-varying component. We leverage our theory to discuss a number of open questions in the electric power industry. Most notably, we postulate that the changing nature of power networks with a preponderance of variable renewable energy power plants could strengthen power network stability in the future; a vision which is irreconcilable with the conventional theories.
Paper Structure (7 sections, 7 equations, 5 figures)

This paper contains 7 sections, 7 equations, 5 figures.

Table of Contents

  1. Introduction
  2. Results
  3. Discussion
  4. Outlook and Closing Remarks
  5. Author Contributions Statement
  6. Funding
  7. Competing Interests Statement

Figures (5)

  • Figure 1: Assessment of power system dynamics with and without electromagnetic momentum. The results here signify the importance of the electromagnetic momentum of power lines in power system dynamics, especially during operating conditions with a preponderance of IBRs, where the momentum from generators is low (low-inertia systems - highlighted by the red zone).
  • Figure 2: Observation of electromagnetic momentum in real-world high voltage power lines. The PMU data analysis indicates the existence of a considerable electromagnetic momentum in the longer lines and the significant impact this momentum could have on power system dynamics. The left column shows the time-domain trace, and the right column shows the migration of eigenvalues in complex plane.
  • Figure 3: Dynamic stability in power network using the plane wave model. The results indicate an increase in the frequency deviations as the number of GFMs in the system increases whilst the SGs are present, but the transients could be damped faster. Nonetheless, the fast responding capability of GFM helps with the prevention of undesired activation of the under-frequency load shedding (UFLS) frequency relay - the UFLS threshold shown here is the continent-wide requirement for the North American power grid, according to the PRC-NPCC-02 standard NERC_UFLS_standard.
  • Figure 4: Parametric sensitivity of plane wave to small-signal stability; controller malfunction and forced oscillations. $D_\omega$ and $D_v$ represent corrupt frequency and voltage controllers, respectively, that induce oscillations in electric angle and magnetic flux linkage, respectively. The results indicate the frequency oscillations can propagate into voltage oscillations, evident in (\ref{['fig:fig2_case_low_Dw']}), but the voltage oscillations may not infect the frequency dynamics, thus the voltage oscillations remain locally bounded, evident in (\ref{['fig:fig2_case_low_Dv']}).
  • Figure 5: Parametric sensitivity to large-signal plane wave stability; grid strength. The results indicate the significance of three contributing factors to the grid stability: (i) the ability of generators to supply sufficient power during transient operation - (\ref{['fig:fig2_case_low_Pg']}) and (\ref{['fig:fig2_case_low_Qf']}), (ii) the generator's dynamic characteristics - (\ref{['fig:fig2_case_low_Mw']}) and (\ref{['fig:fig2_case_low_Mv']}), (iii) the transmission network's characteristics - (\ref{['fig:fig2_case_high_X']}) and (\ref{['fig:fig2_case_high_XR']}).