Key Takeaways & Executive Findings
- •• • For a 96-turbine DC-collector offshore wind farm, the proposed hierarchical hybrid decoupling achieves an 11.99x speedup over the detailed model (simulation time reduced from 2.04×10^5 s to 1.7×10^4 s), whereas series-only and parallel-only decoupling yield only 8.77x and 6.22x speedups, respectively. This 36.7% improvement over series-only decoupling directly translates to reduced computational cost for real-time hardware-in-the-loop testing. • • The method maintains high accuracy: MAE for a-phase voltage Va is 0.1011 p.u., and RMSE is 0.6318 p.u.; for output active power Pout, MAE is 0.0616 p.u. and RMSE is 0.0877 p.u. These errors are within acceptable bounds for control and protection system validation, ensuring that decoupling does not compromise simulation fidelity. • • Scalability is demonstrated across wind farm sizes: speedup increases monotonically with turbine count—2.76x for 4 turbines, 4.65x for 12, 8.96x for 40, and 11.99x for 96—indicating that the hierarchical hybrid method becomes increasingly advantageous for large-scale farms, where detailed simulation becomes computationally prohibitive (2.04×10^5 s for 96 turbines). • • The hybrid method outperforms single-strategy decoupling: at 96 turbines, it achieves 11.99x speedup versus 8.77x (series-only) and 6.22x (parallel-only), a 36.7% and 92.8% relative improvement, respectively. This validates the layered integration of MATE and its dual as a superior approach for complex series-parallel topologies, reducing matrix size and enabling synchronous partition solving.
China Clean Energy & Battery Radar
Get verified English translations, SEM micrographs & open-access PDF alerts from China's leading state key laboratories delivered to your inbox every Monday at 08:00 EST.
Abstract
Real-time electromagnetic transient (EMT) simulation of DC-collector offshore wind farms is constrained by microsecond time steps, high model order from cascaded power electronic converters, and the inability of conventional decoupling methods to handle complex series-parallel topologies without introducing artificial delays. Existing non-delay decoupling methods, such as multi-area Thevenin equivalence (MATE) and compensation method, rely on branch tearing and are ill-suited for systems with numerous common-bus partitions, leading to excessive link variables and singular admittance matrices. This paper proposes a hierarchical hybrid non-delay decoupling parallel method that integrates MATE and its dual (node-tearing) approach through a layered architecture. The method constructs a mixed equivalent model tailored to DC-collector offshore wind farms, enabling flexible selection between unified and hierarchical solution modes for link variables based on operating conditions. A complete non-delay decoupling simulation workflow is established and validated on a DC series-parallel grid-connected offshore wind farm test case implemented in MATLAB. Results demonstrate that the proposed method reduces solution matrix dimensions and achieves significant speedup without compromising accuracy. For a 96-turbine wind farm, the hybrid decoupling model achieves an 11.99x speedup over the detailed model, compared to 8.77x for series-only decoupling and 6.22x for parallel-only decoupling. Mean absolute errors (MAE) for key variables remain below 0.1011, and root mean square errors (RMSE) below 0.6318, confirming high fidelity. The method enhances parallel simulation performance and offers a generalizable solution for real-time EMT simulation of large-scale offshore wind farms.
1. Introduction
Offshore wind farms employing DC collection systems face significant challenges for electromagnetic transient (EMT) simulation due to their complex topologies, high penetration of power electronic converters, and the need for microsecond-scale time steps. Traditional decoupling methods, such as transmission line natural delay or artificial delay via explicit integration, are inadequate because offshore farms lack sufficient line lengths and delay-based approaches introduce numerical instability and dynamic response lag. Non-delay methods like MATE and compensation method are limited to branch tearing, which becomes inefficient when partitions share common buses, leading to excessive link variables and singular admittance matrices. These limitations hinder real-time simulation required for control and protection system validation during the planning stage.
This paper addresses these bottlenecks by proposing a hierarchical hybrid non-delay decoupling parallel method that integrates MATE (branch tearing) and its dual (node tearing) within a layered architecture. The method constructs a mixed equivalent model tailored to DC-collector offshore wind farms, allowing flexible selection between unified and hierarchical solution modes for link variables. A complete simulation workflow is implemented and validated on a DC series-parallel grid-connected offshore wind farm. Experimental results show that for a 96-turbine farm, the hybrid model achieves an 11.99x speedup over the detailed model, with MAE and RMSE for key variables remaining below 0.1011 and 0.6318, respectively. This demonstrates that the proposed method significantly enhances simulation efficiency without compromising accuracy, offering a scalable solution for real-time EMT simulation of large offshore wind farms.
Loading authentic research manuscript (Pages 1–5)...
WANG Bofeng, XU Jin, WU Pan, QI Chen, MIAO Fenglin, WANG Keyou (2026). Hierarchical Hybrid Non-Delay Decoupling Parallel Method for Electromagnetic Transient Simulation of DC-Collector Offshore Wind Farms. Power Automation Equipment. https://doi.org/10.16081/j.epae.202606005
Research & Educational Purpose Only: The translations, structured abstracts, analytical annotations, and data reports provided by SinoGreenTechare intended exclusively for academic research, internal corporate R&D, and educational benchmarking. They do not constitute formal engineering, chemical safety, legal, or professional advice.
Copyright & Intellectual Property Notice: Original copyright of the underlying source articles and experimental data remains with the respective authors, institutions, and original publishing journals. SinoGreenTech claims intellectual property only over its proprietary translations, analytical syntheses, and AEO structured enhancements in accordance with international fair use and academic citation principles.
Frequently Asked Questions
What is the computational bottleneck in EMT simulation of DC-collector offshore wind farms, and how does the proposed method address it?
The bottleneck arises from the high model order due to numerous power electronic converters, microsecond time steps, and complex series-parallel topologies. Traditional decoupling methods either require long transmission lines (unavailable offshore) or introduce artificial delays that compromise stability. The proposed hierarchical hybrid method integrates MATE and its dual to handle both branch and node tearing, reducing matrix size and enabling parallel solution. For a 96-turbine farm, it reduces simulation time from 2.04×10^5 s to 1.7×10^4 s, achieving an 11.99x speedup while maintaining MAE below 0.1011 p.u.
How does the accuracy of the hybrid decoupling method compare to the detailed model, and what are the error metrics?
The hybrid method maintains high fidelity: for a-phase voltage Va, MAE is 0.1011 p.u. and RMSE is 0.6318 p.u.; for output active power Pout, MAE is 0.0616 p.u. and RMSE is 0.0877 p.u. These errors are within acceptable limits for control and protection studies, confirming that decoupling does not introduce significant deviations. The method ensures precision loss is minimal, as validated against the detailed model.
What are the scalability limits of the proposed method, and how does speedup vary with wind farm size?
Scalability is demonstrated from 4 to 96 turbines: speedup increases from 2.76x (4 turbines) to 11.99x (96 turbines). The hybrid method consistently outperforms single-strategy decoupling—at 96 turbines, it achieves 11.99x versus 8.77x (series-only) and 6.22x (parallel-only). This trend indicates that the hierarchical approach becomes more advantageous for larger farms, where detailed simulation is impractical (2.04×10^5 s for 96 turbines). The method is thus suitable for real-time simulation of large-scale offshore wind farms.
What are the key implementation challenges when deploying this method in real-time hardware-in-the-loop (HIL) simulation?
Implementation challenges include managing the layered decoupling architecture to ensure synchronous partition solving and avoiding singular admittance matrices. The method requires careful selection of unified versus hierarchical solution modes based on operating conditions. However, the matrix decoupling特性 enables parallel computation, and the use of MATLAB for validation demonstrates feasibility. For HIL, the reduced matrix size (e.g., 11.99x speedup) lowers computational load, but real-time constraints demand optimized communication between partitions. The method's flexibility in handling switch events without re-decoupling is a key advantage for HIL applications.
How does the proposed method compare economically to traditional decoupling approaches in terms of computational resource savings?
The hybrid method reduces simulation time by up to 91.7% (from 2.04×10^5 s to 1.7×10^4 s for 96 turbines), directly lowering computational resource requirements. Compared to series-only decoupling (8.77x speedup) and parallel-only (6.22x), the hybrid achieves 11.99x, a 36.7% and 92.8% relative improvement, respectively. This translates to fewer hardware resources or faster simulation cycles, reducing costs for real-time simulation and enabling more extensive design iterations. The method's ability to avoid re-decoupling during switch events further saves engineering effort and computational overhead.
Related Chinese Research & Cross-Citations
Impedance Modeling and Parameter Optimization Method for Wind Farms Considering Station-Level Control
Large-scale wind farms integrated into weak grids are susceptible to broadband oscillations, a problem that existing impedance models and control parameter optimization methods fail to address systematically because they neglect station-level control and frequency coupling effects. This paper proposes a station-level control strategy based on available power allocation and an adaptive compass search (ACS) algorithm for optimizing station control parameters. A sequence impedance method incorporating frequency coupling effects establishes the aggregated wind farm impedance, and the grid-connected multiple-input multiple-output (MIMO) system is decoupled into positive- and negative-sequence single-input single-output (SISO) impedance models. A high-precision wind farm impedance model that accounts for station-level control is constructed, and the Nyquist criterion evaluates the suppression effect of station control on broadband oscillations. The ACS algorithm optimizes station control parameters to enhance the adaptability of wind farm impedance to external grid impedance, thereby reducing oscillation risk. RT-LAB platform simulations validate the impedance modeling method and control parameter optimization. Results demonstrate that considering station-level control yields a high-precision wind farm impedance model. Compared with genetic algorithm (GA), particle swarm optimization (PSO), grey wolf optimizer (GWO), and sparrow search algorithm (SSA), ACS is more suitable for optimizing wind farm control parameters. Under specific weak-grid conditions, ACS-optimized station control parameters effectively improve grid-connected stability of the wind farm.
Active and Reactive Power Coordinated Voltage Support Control Method for High-Inertia Energy-Storage Synchronous Condenser
The high-inertia energy-storage synchronous condenser (SC-HI-ES) can provide reactive power support by adjusting excitation current and active power support by actively varying rotor speed. However, the absence of a prime mover makes its control capability difficult to quantify, preventing coordinated active and reactive power support for grid voltage. This paper analyzes the factors influencing SC-HI-ES power control capability, derives rotor current equations considering stator and rotor circuit constraints, and establishes the power controllable range (PCR) under rotor current constraints and speed variations. The relationship between the PCR and voltage support power demand is parsed, and a coordinated active-reactive power voltage support control method is proposed. Case studies validate the method's effectiveness. Results show that the proposed method enhances voltage support and avoids rotor current over-limit. Compared with methods ignoring speed variation or controlling only reactive power, the proposed method dynamically calculates PCR-based power demand under current speed, and through coordinated active and reactive power control, maximally satisfies the point of common coupling voltage target while ensuring rotor current does not exceed allowable values. This provides effective technical support for SC-HI-ES application in new-type power systems. Frequency control capability characterization and frequency-coordinated control are identified as future research directions.
Hardware-in-the-Loop Test Platform for Photovoltaic High-Frequency Controllers Based on UREP + FPGA
Real-time constraints prevent CPU-based electromagnetic transient simulators from accurately sampling high-frequency PWM signals at microsecond step sizes, leading to insufficient HIL test precision and even instability of the closed-loop system. This paper introduces a PWM averaging technique to construct a novel UREP (electromagnetic transient real-time simulator) + FPGA hardware-in-the-loop test platform. To achieve accurate PWM acquisition, the FPGA's nanosecond-level clock resolution increases the number of sampling points within a single switching period from a few points under microsecond simulation steps to several thousand points. The FPGA implements fixed-step PWM averaging, converting discrete switching states into continuous duty cycles that serve as control signals for the UREP-side inverter average model. This technique avoids frequent topology updates and state matrix reconstructions triggered by switching events, reduces high real-time computational resource consumption, improves numerical stability of the in-loop system, and enhances HIL test accuracy under large-step real-time constraints. Simulation cases and industrial-grade controller HIL tests verify the platform's feasibility and accuracy. The platform provides an efficient, reproducible verification scheme for photovoltaic controller control strategies and offers a feasible technical path for domestic electromagnetic transient real-time simulation platforms to conduct high-frequency controller HIL tests.
Design and Implementation of a Distributed Simulation Architecture for Modern Power Systems Based on Data Distribution Service
The integration of high-penetration renewable energy and power electronic converters has intensified the dynamic complexity of modern power systems, imposing stringent demands on simulation accuracy and computational efficiency. This paper proposes a distributed simulation architecture based on Data Distribution Service (DDS) that leverages dispersed computing resources to enhance scalability and efficiency while preserving numerical fidelity. The power system model is mathematically decoupled into multiple independently solvable basic subsystems, and a generic data transmission interface is designed using DDS. A time-consumption balancing scheme groups and distributes these subsystems across multiple devices, and a two-layer synchronization strategy enables efficient parallel simulation. The architecture is validated on a two-area four-machine system, the IEEE New England 10-machine 39-bus system, and the WECC 29-machine 179-bus system. Compared with centralized simulation, the average error on the two-area four-machine system remains below 1.05%. Simulation efficiency improvement reaches approximately 10% on the 10-machine 39-bus system and about 48% on the 29-machine 179-bus system. The results confirm high accuracy across different system scales and demonstrate that efficiency gains become more pronounced as system size increases, validating the architecture's scalability and compatibility. The proposed framework offers a promising pathway for large-scale power system simulation and supports future integration with edge computing and cross-platform deployment.
Heterogeneous Weighted Graph Partitioning and Decoupling Optimization Strategy for Electromagnetic Transient Parallel Simulation of AC/DC Distribution Networks
The increasing penetration of power electronic devices in AC/DC distribution networks imposes stringent computational demands on electromagnetic transient (EMT) parallel simulation. Conventional transmission-line delay decoupling methods are ill-suited to the strong electrical coupling characteristic of such networks. This paper proposes a non-delay decoupling parallel simulation acceleration framework based on heterogeneous weighted graph partitioning. An empirical computational cost evaluation model for each parallel decoupling stage is established, and a heterogeneous weighted graph model is constructed to precisely characterize the simulation computational complexity of AC/DC distribution network components, mapping matrix dimensions of device mathematical models to graph node weights. A multi-objective graph partitioning scheme is formulated that simultaneously balances partition computational overhead and minimizes the number of tie-line variables, complemented by an optimal partition number screening strategy. Simulation validation is conducted on three large-scale AC/DC distribution network composite test cases: IEEE 34-node, IEEE 123-node, and European Low Voltage (European LV) systems, all retrofitted with DC sections. Results demonstrate that the proposed empirical computational cost model achieves a simulation time fitting goodness-of-fit R² > 0.97, indicating high predictive accuracy. Under optimal partition configuration, the proposed method attains parallel speedup ratios of 12.11–15.77, significantly outperforming conventional natural partitioning schemes and effectively enhancing the EMT parallel simulation efficiency of AC/DC distribution networks.
Eigenvalue Computation Techniques for Small-Signal Stability Analysis of Large-Scale New-Type Power Systems: A Review and Outlook
The escalating 'double-high' penetration of power electronics in new-type power systems has rendered conventional electromechanical transient small-signal stability analysis inadequate, necessitating electromagnetic transient (EMT) small-signal stability assessment. Eigenvalue analysis, grounded in rigorous theoretical foundations, is widely applied but faces two critical bottlenecks when scaled to large systems: the construction of EMT linearized state-space equations and the solution of high-order state-matrix eigenvalues. This review examines the urgent demand for EMT model eigenvalue analysis in large-scale new-type power systems. It systematically surveys research status and challenges across three domains: equilibrium-point modeling of EMT models, linearized state-space modeling, and efficient computation of critical eigenvalues. For equilibrium-point modeling, the paper evaluates Park transformation, double Park transformation, shifted frequency analysis (SFA), time-scale transformation, and Floquet-theory-based trajectory linearization. For linearized state-space modeling, it assesses component-level and network-level linearization strategies. For eigenvalue computation, it reviews partial eigenvalue algorithms, sparse matrix techniques, and model-order reduction methods. Key challenges include the inability of Park transformation to handle asymmetric or single-phase systems, the computational burden of Floquet transition matrix eigendecomposition, and the poor scalability of dense eigenvalue solvers for systems exceeding thousands of states. The paper concludes by identifying future research directions, including structure-preserving linearization, GPU-accelerated sparse eigenvalue algorithms, and data-driven model reduction, to enable practical EMT small-signal stability analysis for systems with 18.4 billion kW of installed renewable capacity by 2030.