- The paper introduces an error index to quantify Type-2 interface errors by measuring voltage magnitude differences between full EMT and hybrid simulations.
- It demonstrates through balanced, unbalanced, and oscillatory case studies that expanding the EMT region and adjusting the error index can reliably assess interface accuracy.
- The study proposes a novel three-sequence interface that recovers accurate unbalanced event behavior with negligible extra computational cost.
Quantifying and Improving Accuracy in EMT-TS Hybrid Simulation
Motivation for Hybrid EMT-TS Simulation
The increasing deployment of inverter-based resources (IBR) in power grids introduces non-negligible fast electromagnetic dynamics such as sub-/super-synchronous oscillations, which are not adequately captured by traditional positive-sequence transient stability (TS) simulation methods. Full electromagnetic transient (EMT) simulation can capture these dynamics but is computationally prohibitive for large-scale systems due to fine time discretization and high model detail. Consequently, hybrid EMT-TS simulation—partitioning the grid to simulate critical regions with EMT and the remainder with TS—offers a pragmatic accuracy–efficiency trade-off and has already seen industrial adoption. However, the accuracy of quantities at the EMT-TS interface, especially under non-ideal (e.g., unbalanced, harmonic-rich, or oscillatory) conditions, is a persistent and minimally understood problem.
The paper rigorously separates hybrid simulation errors into two classes:
- Type-1 (Modeling Error): Due to fundamental model discrepancies in TS representation for regions not captured by EMT.
- Type-2 (Interface Error): Directly attributable to loss and/or distortion of fast or non-positive-sequence signals exchanged at the EMT-TS interface.
The work focuses exclusively on Type-2 errors. The true interface error is defined via the L2-norm of the difference in per-unit voltage magnitude at the interface, comparing the (reference) full EMT simulation with the hybrid results over a defined post-disturbance window. While this is ideal for benchmarking, full EMT results are prohibitive for routine utility studies.
To facilitate practical error monitoring, the paper introduces an error index computable solely from hybrid simulation signals. This index is constructed as the integral of the L2-norm of the difference between the three-phase instantaneous voltages reconstructed from TS-side phasors and those directly measured in EMT, normalized for comparability with the true error definition. A modified version of the index is presented to suppress spurious inflation of error under low-voltage boundary conditions, utilizing a Heaviside step function to mask intervals where TS phasors become unreliable.
Systematic Evaluation via Case Studies
Balanced Faults
Simulation on a canonical 4-bus system shows that, for balanced three-phase disturbance cases, the hybrid interface is robust: both true error and the proposed index remain consistently low, irrespective of boundary location or network short-circuit characteristics. Occasionally, large error index values can arise during low boundary voltage intervals, but the modified index distinguishes between genuine EMT-region accuracy loss and TS-side artifacts.
Unbalanced Faults
For unbalanced faults, significant interface errors are observed when the EMT region is small, i.e., the boundary is close to the fault location. The error index—unlike prior metrics requiring full EMT data—reliably identifies such scenarios. Expansion of the EMT region consistently mitigates both the true and indexed error, supporting the practical use of the index as a boundary placement tool. Notably, for unbalanced faults, the modified index brings no benefit, as the phasor magnitude remains sufficiently above the low-voltage threshold.
Oscillatory Conditions
By injecting both modulated (MFOs) and superimposed forced oscillations (SFOs) at various frequencies, the analysis exposes the interface’s limitations for dynamic phenomena which span the TS/EMT boundary. For MFOs, phase misalignment across the boundary is reflected in the error index, with potential to disrupt phasor-based modal analysis. For SFOs, frequency components injected within the EMT region are shown to be completely blocked by the interface, which has critical implications for dynamic studies involving distributed oscillatory resources. The presented error index can quantify such distortions, but cannot resolve the physical participation of grid elements in blocked modes.
Three-Sequence Interface Solution
The failure of conventional (positive-sequence-only) interfaces under unbalanced conditions prompts the development of a three-sequence (3-seq) interface. By communicating all sequence components (positive, negative, zero) across the boundary, and by carefully sending current instead of power from EMT to TS, the 3-seq interface is able to recover accurate behavior for unbalanced events, as demonstrated in dedicated PSCAD emulation tests. The additional computational burden is negligible relative to the dominating EMT region, making the 3-seq interface immediately practical for adoption in future commercial hybrid simulation packages.
Implications and Future Directions
The work delivers essential methodology for real-time, simulation-only quantification of hybrid interface errors, removing prior dependence on full EMT ground truth. The index is robust across key classes of disturbances and directly supports systematic, empirical determination of EMT region boundaries in operational simulations—a long-standing practitioner pain point. The introduction of the 3-seq interface model opens the door for accurate hybrid analysis of unbalanced grid phenomena without large-scale EMT region expansion.
However, the analysis identifies clear limitations for hybrid simulation in oscillatory scenarios. Oscillatory energy transfer and modal participation can be fundamentally distorted or blocked at the interface, implying that for studies where such dynamics are critical, the entire participating region must be simulated in EMT, or hybrid interface models must be fundamentally redesigned.
Future research will focus on:
- Establishing standardized thresholds for the error index across various fault and disturbance types to support automated boundary selection.
- Validating index-driven boundary selection protocols on realistic, large-scale grid models.
- Developing advanced interface methods (potentially leveraging network equivalencing and reduced delay strategies) to further close the accuracy gap exposed in oscillatory and unbalanced conditions.
Conclusion
This paper presents a practical error index for EMT-TS hybrid simulation interface accuracy assessment, rigorously validated against full EMT references, and directly applicable in operational hybrid simulation workflows. The adoption of the 3-sequence interface model is demonstrated to substantially improve unbalanced event simulation fidelity. The findings underscore the necessity of boundary and interface model selection as a function of event type, and provide a practical platform for further advancement in hybrid simulation accuracy and industrial applicability (2604.14523).