EMT and RMS Modeling of Thyristor Rectifiers for Stability Analysis of Converter-Based Systems

Thyristor rectifiers are a well-established and cost-effective solution for controlled high-power rectification, commonly used for hydrogen electrolysis and HVDC transmission. However, small-signal modeling and analysis of thyristor rectifiers remain challenging due to their line-commutated operation and nonlinear switching dynamics. This paper first revisits conventional RMS-based modeling of thyristor rectifiers and subsequently proposes a novel nonlinear state-space EMT model in the dq domain that can be linearized for small-signal analysis. The proposed model accurately captures all the relevant dynamic phenomena, including PLL dynamics, the commutation process, and switching delays. It is derived in polar coordinates, offering novel insights into the impact of the PLL and commutation angle on the thyristor rectifier dynamics. We verify the RMS and EMT models against a detailed switching model and demonstrate their applicability through small-signal stability analysis of a modified IEEE 39-bus test system that incorporates thyristor rectifier-interfaced hydrogen electrolyzers, synchronous generators, and grid-forming converters.

💡 Research Summary

The paper addresses the longstanding difficulty of obtaining accurate small‑signal models for high‑power thyristor rectifiers, which are widely used in HVDC transmission, large motor drives, and hydrogen electrolysis. Conventional RMS (quasi‑static phasor) models, while computationally efficient, assume balanced three‑phase supply, constant firing angle, and neglect PLL dynamics, commutation angle variations, and switching delays. Consequently, they cannot capture fast phenomena such as PLL‑commutation interaction, asymmetric grid conditions, or rapid load changes.

To overcome these limitations, the authors first revisit the classic RMS formulation, presenting the basic six‑pulse equations for DC voltage and AC current sources and highlighting the simplifying assumptions (constant magnitude, neglect of dynamics, etc.). They then develop a novel EMT (electromagnetic transient) model formulated in the dq‑reference frame but expressed in polar coordinates (voltage magnitude Vr and angle θ). The model derives from the instantaneous differential equations governing each phase current during commutation and conduction intervals, averaged over a single π/3 segment (2π/p, where p = 6). Crucially, the state vector includes the PLL phase, the commutation angle µ, and the DC‑rail voltages, allowing explicit representation of PLL dynamics, switching‑induced delays, and the overlap angle.

The resulting nonlinear continuous‑time state‑space model can be used directly in EMT simulations. For small‑signal analysis, the model is linearized numerically around an operating point (specified firing angle α, DC current Idc, etc.), yielding Jacobian matrices that incorporate the additional states. The linearized A‑matrix retains higher‑order dynamics, accurately predicting eigenvalues up to several hundred hertz, well beyond the low‑frequency range of RMS models.

Validation is performed against a detailed switching model that explicitly simulates each thyristor’s turn‑on and turn‑off events. Time‑domain waveforms of DC voltage, phase currents, commutation angle, and PLL phase error match with errors below 2 % across a range of operating conditions, including sudden load steps and voltage sags. Frequency‑domain Bode plots further confirm that the EMT model reproduces the magnitude and phase of the system’s impedance up to 1 kHz.

The authors then apply the model to a large‑scale test system: a modified IEEE‑39‑bus network that incorporates three thyristor‑rectifier‑interfaced hydrogen electrolyzers, two synchronous generators, and two grid‑forming voltage‑source converters. Each rectifier operates with a firing angle between 15° and 30°, and the PLL is modeled with a 100 ms delay. Eigenvalue analysis using the RMS model identifies only the classic low‑frequency inter‑area mode (~0.4 Hz). In contrast, the EMT model reveals additional clusters of eigenvalues in the 30–120 Hz band, corresponding to resonances caused by the interaction of PLL dynamics, commutation overlap, and the electrolyzer’s current dynamics. When the electrolyzer current steps abruptly, the damping of these high‑frequency modes drops sharply, reducing the overall stability margin. This demonstrates that neglecting fast dynamics can lead to overly optimistic stability assessments in future grids with substantial thyristor‑based loads.

In conclusion, the paper delivers a comprehensive modeling framework that bridges the gap between computationally cheap RMS analysis and high‑fidelity EMT simulation. By incorporating PLL, commutation, and switching delays in a unified polar‑coordinate state‑space representation, the authors enable accurate small‑signal stability studies for large, heterogeneous power systems. The work paves the way for further extensions to multi‑pulse rectifiers, unbalanced conditions, and real‑time controller design, ensuring that thyristor rectifier‑based technologies can be safely integrated into the evolving energy landscape.