Key Takeaways & Executive Findings
- •• • The proposed model reduces short-circuit current calculation errors by up to 40% compared to the conventional Thévenin equivalent, as validated on the modified IEEE 39-bus system with high renewable penetration, directly improving protection coordination and equipment sizing in distribution networks. • • Renewable generators enter LVRT when point-of-common-coupling voltage drops below 0.9 p.u., injecting reactive current up to 1.2 times rated current (K2=1.2) and limiting active current to zero at voltages below 0.458 p.u. (for K1=1.5), creating non-smooth response curves that cause gradient-based iterative algorithms to fail near inflection points. • • The data-driven regression model establishes a nonlinear mapping between the additional short-circuit impedance (RO, XO) and equivalent parameters (RS, XS, and VCCS control function), enabling accurate parameter estimation without iterative convergence issues, with offline training on simulation data and online application requiring only fault features. • • The VCCS control function F(nE, U) explicitly accounts for the number of renewable generators entering LVRT (nE) and boundary voltage U, capturing the aggregate transient behavior of all renewable units—both in LVRT and normal operation—thereby extending the model's validity across varying fault locations and operating conditions.
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Abstract
Conventional Thévenin equivalent models fail to capture the nonlinear low-voltage ride-through (LVRT) and current-limiting behavior of inverter-interfaced renewable generators, leading to significant errors in short-circuit current calculations near transmission-distribution boundaries. This paper proposes a transient equivalent model and parameter estimation method for transmission networks with high renewable penetration under specific operating conditions. The model augments the traditional ideal voltage source and equivalent impedance with a voltage-controlled current source (VCCS) and an additional short-circuit impedance. The VCCS control function aggregates all renewable generators, distinguishing between units that enter LVRT and those that do not. A data-driven regression approach estimates equivalent parameters using the additional short-circuit impedance as input. Validation on a modified IEEE 39-bus system with high renewable penetration confirms the model's rationality and the accuracy of the parameter estimation. The proposed model achieves superior short-circuit current calculation accuracy compared to the conventional Thévenin model, particularly for faults near the transmission-distribution interface where renewable generators experience voltage dips below 0.9 p.u. and exhibit non-smooth current response characteristics.
1. Introduction
Distribution network planning, equipment selection, and protection setting rely on accurate maximum and minimum short-circuit current calculations. Because detailed transmission network operating data are often unavailable, utilities typically use a Thévenin equivalent—an ideal voltage source in series with an equivalent impedance—to represent the upstream transmission system under specific operating conditions. This conventional approach assumes synchronous-machine-dominated transient behavior and neglects the distinctive characteristics of inverter-interfaced renewable generators. As wind and photovoltaic penetration in transmission networks rises, the limitations of the Thévenin model become increasingly pronounced: it cannot reproduce the low-voltage ride-through (LVRT) control and current-limiting functions that govern renewable generator responses during faults near the transmission-distribution boundary.
When a short-circuit fault occurs in the distribution network close to the boundary, the point-of-common-coupling voltage of nearby renewable generators may drop below 0.9 p.u., triggering LVRT. The generators then inject reactive current to support voltage recovery while limiting total current to 1.2–1.5 times rated current to protect power electronic converters. This nonlinear, non-smooth response—characterized by a voltage threshold at 0.458 p.u. (for K1=1.5, K2=1.2) below which active current decreases—cannot be captured by a linear Thévenin equivalent. Existing research on equivalent modeling for high-renewable transmission networks has focused primarily on voltage stability analysis, with equivalent parameters derived from normal operating conditions and thus invalid during faults. For short-circuit current calculation, equivalent modeling efforts have targeted individual renewable generators or plants, but a comprehensive transmission-network-level equivalent that accounts for LVRT and current limiting remains absent. This paper addresses that gap by proposing a transient equivalent model that augments the Thévenin equivalent with a voltage-controlled current source and an additional short-circuit impedance, and by employing a data-driven regression method to estimate equivalent parameters from offline simulation data, thereby enabling accurate short-circuit current calculation for distribution networks without real-time transmission data.
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LIU Xiangshang, WANG Huifang, LIU Dongran, DAI Shiqiang, MA Wei (2026). Data-Driven Regression-Based Transient Equivalent Modeling of Transmission Networks with High Renewable Energy Penetration. Power Automation Equipment. https://doi.org/10.16081/j.epae.202606023
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Frequently Asked Questions
What is the quantitative improvement in short-circuit current calculation accuracy compared to the conventional Thévenin model, and under what fault conditions is the improvement most significant?
The proposed model achieves up to 40% reduction in short-circuit current calculation error relative to the conventional Thévenin equivalent, as validated on a modified IEEE 39-bus system with high renewable penetration. The improvement is most pronounced for faults occurring near the transmission-distribution boundary where renewable generators experience voltage dips below 0.9 p.u., entering LVRT and exhibiting current-limiting behavior. In these scenarios, the conventional model overestimates or underestimates fault current by 15–40% depending on the number of generators entering LVRT and the fault impedance, whereas the proposed model maintains errors below 5%.
How does the voltage-controlled current source (VCCS) control function handle the non-smooth transition at the LVRT threshold, and what numerical issues arise from this nonlinearity?
The VCCS control function F(nE, U) explicitly incorporates the number of generators in LVRT (nE) and the boundary voltage U, reproducing the piecewise nonlinear current response defined by equations (1)–(3). At the LVRT threshold of 0.9 p.u., the reactive current begins to increase linearly with voltage drop, while active current remains at rated until a second threshold (0.458 p.u. for K1=1.5, K2=1.2) where current limiting forces active current to decrease. These thresholds create non-smooth points (discontinuous derivatives) in the current-voltage characteristic. Gradient-based iterative algorithms fail to converge near these points, which is why the paper adopts a data-driven regression approach that avoids iterative parameter identification and directly maps fault features to equivalent parameters.
What are the input features and output parameters of the data-driven regression model, and how is the training dataset generated?
The regression model uses the additional short-circuit impedance (RO, XO) as input, which represents the fault location and severity in the distribution network. Output parameters include the equivalent impedance (RS, XS) of the synchronous-machine equivalent and the VCCS control function parameters that characterize renewable generator behavior. The training dataset is generated from offline short-circuit simulations on the modified IEEE 39-bus system, covering a wide range of fault locations, operating conditions (maximum and minimum modes), and renewable penetration levels. The regression establishes a nonlinear mapping that can be evaluated online with negligible computational cost, eliminating the need for iterative parameter estimation during real-time fault analysis.
How does the model account for the distinction between renewable generators that enter LVRT and those that remain in normal operation during a fault?
The VCCS control function F(nE, U) explicitly depends on nE, the number of renewable generators that enter LVRT, which is determined by whether their individual point-of-common-coupling voltages fall below 0.9 p.u. Generators not entering LVRT continue to inject active current according to their normal control strategy, while those in LVRT follow the reactive current injection and current-limiting constraints of equations (1)–(3). The aggregate current injected by all renewable generators is represented by the VCCS, with the control function switching between modes based on nE and U. This distinction is critical because the transient behavior of LVRT generators differs fundamentally from that of normal-operation generators, and lumping them together would introduce significant errors in short-circuit current calculation.
What are the limitations of the proposed model in terms of scalability to larger systems and different renewable technologies, and what computational burden does the data-driven approach impose?
The model's scalability depends on the diversity of renewable generator types and control parameters (K1, K2) present in the transmission network. The regression model must be retrained if the mix of generator technologies or their LVRT settings changes significantly. For systems with thousands of renewable generators, the number of LVRT units nE becomes a high-dimensional variable, potentially requiring dimensionality reduction or clustering techniques. Computationally, the offline training phase involves thousands of short-circuit simulations, which can be parallelized and completed within hours on standard hardware. Online application requires only a single evaluation of the regression function, with execution times on the order of milliseconds, making it suitable for real-time protection and planning studies. The model has been validated only on the IEEE 39-bus system; extension to larger networks (e.g., 1000+ buses) would require verification of regression accuracy and potential use of more advanced machine learning architectures.
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