Key Takeaways & Executive Findings
- •• • Algorithm modification via mathematical format innovation expands absolute performance boundaries but suffers from multi-dimensional performance conflicts that weaken net performance gains; fixed algorithmic structures cannot respond to time-varying simulation demands, creating a fundamental rigidity that limits industrial deployment in scenarios requiring adaptive transient analysis across multi-timescale coupling. • • Algorithm adaptation achieves optimal computational resource allocation within given performance boundaries through real-time scheduling and combination, yet existing strategies exhibit singular adjustment objectives and state-sensing dimensions, with parameters and switching logic heavily dependent on manual experience—severely constraining robustness and creating operational bottlenecks for large-scale renewable integration. • • The three solution stages—numerical integration, nonlinear algebraic equation solution, and linear algebraic equation solution—exhibit coupling relationships that demand coordinated consideration within an integrated framework; isolated optimization of any single stage yields suboptimal overall performance, necessitating holistic algorithm design for high-proportion power electronic device scenarios. • • Future integration of algorithm modification and algorithm adaptation can expand performance adjustment ranges and enhance responsiveness to time-varying demands; artificial intelligence fusion with traditional numerical methods offers a pathway to replace empirical parameter design and achieve precise algorithm regulation, potentially resolving the accuracy-convergence-efficiency trilemma in large-scale new-type power system simulation.
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Abstract
The large-scale integration of renewable energy sources has imposed strong nonlinearities and multi-timescale coupling on modern power systems, rendering conventional time-domain simulation solution algorithms inadequate for offline transient analysis of large-scale new-type power systems with high proportions of power electronic devices. This review systematically addresses the performance optimization problem of time-domain simulation algorithms. First, new requirements are identified across three solution stages: numerical integration, nonlinear algebraic equation solution, and linear algebraic equation solution. Second, existing research progress is consolidated under two core optimization paradigms—algorithm modification and algorithm adaptation—with their respective advantages and challenges analyzed. Algorithm modification pursues mathematical format innovation to expand absolute performance boundaries, while algorithm adaptation achieves optimal resource allocation within given boundaries through real-time scheduling and combination. The review concludes that the core challenge lies in coordinating multi-dimensional performance conflicts and responding to time-varying simulation demands. Persistent deficiencies include: in algorithm modification, multi-dimensional performance conflicts hinder reform efforts, diminish performance gains, and fixed algorithmic structures cannot respond to time-varying requirements; in algorithm adaptation, adjustment objectives and state-sensing dimensions remain singular, with parameters and switching logic heavily reliant on manual experience, severely constraining robustness. Future directions advocate integrating both paradigms to expand performance adjustment ranges and enhance responsiveness to time-varying demands, while exploring artificial intelligence fusion with traditional numerical methods to replace empirical parameter design and achieve precise algorithm regulation.
1. Introduction
Conventional phasor-based offline time-domain simulation has served as the primary analytical tool for transient stability assessment in power systems, yet its foundational numerical algorithms were architected for synchronous-machine-dominated grids with smooth, continuous dynamics and moderate equation dimensionality. The large-scale integration of wind and photovoltaic generation, together with high-proportion power electronic device interconnection, has fundamentally altered system characteristics and stability mechanisms. Detailed models now incorporate phase-locked loops, current inner loops, and other small-timescale control loops whose equation structures have grown increasingly complex, intensifying system stiffness. Simultaneously, multi-region grid interconnection and expanding renewable capacity have caused equation dimensions to surge, inflating computational burdens beyond the capacity of traditional solution algorithms to deliver acceptable accuracy, convergence, and efficiency simultaneously.
Existing performance optimization approaches encompass hardware acceleration via high-performance processors and computing units, parallelization of simulation algorithms through task decomposition and communication reorganization, and solution algorithm optimization targeting numerical integration, nonlinear equation solution, and linear equation solution formats or parameter configurations. Hardware and parallelization gains ultimately depend on the underlying solution algorithms, and since solution algorithms constitute the mathematical foundation translating system models into simulation results, their optimization represents the fundamental pathway to breaking through phasor simulation performance bottlenecks. This review systematically deconstructs the solution process into three stages, analyzes key contradictions and core problems facing each stage under high-proportion power electronic device integration, consolidates existing optimization techniques with their advantages and challenges, and projects future research directions to provide systematic reference for high-performance time-domain simulation solution algorithm development.
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HUANG Litao, XIAO Xianghui, ZHANG Junbo, SUN Daorang, LIN Ziming, DENG Jianyong, LIU Yang (2026). Research Progress and Challenges in Phasor-Based Time-Domain Simulation Solution Algorithms for New-Type Power Systems. Power Automation Equipment. https://doi.org/10.16081/j.epae.202606009
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Frequently Asked Questions
What specific failure mechanisms in conventional numerical integration algorithms prevent accurate simulation of high-proportion power electronic systems, and what operational thresholds define the boundary of applicability?
Conventional numerical integration algorithms—implicit trapezoidal, improved Euler, and Runge-Kutta methods—are designed for continuous, smooth system dynamics. High-proportion power electronic devices introduce logic switching and controller limiting non-smooth links that create structural mathematical contradictions with phasor-based continuous dynamics. Accurate simulation requires hybrid system models capable of co-processing continuous state evolution and discrete event mutations. Traditional algorithms cannot simultaneously guarantee device-level transient response precision and system-level full-process simulation efficiency, with the accuracy-stability-efficiency trilemma intensifying as multi-scale coupling degree increases. The boundary of applicability is defined by the point at which non-smooth link density and multi-timescale coupling cause conventional algorithms to fail convergence or produce unacceptable numerical damping.
Why does algorithm adaptation currently fail to deliver robust performance in industrial-scale new-type power system simulation, and what specific deficiencies in state-sensing and decision logic constrain its deployment?
Algorithm adaptation strategies exhibit singular adjustment objectives and state-sensing dimensions, meaning they monitor limited system state variables and optimize for narrow performance metrics. Parameters and switching logic are predominantly set through manual experience rather than systematic derivation, creating severe robustness constraints. When simulation conditions deviate from empirically-tuned scenarios—such as during unforeseen fault transients or atypical renewable generation fluctuations—the adaptation logic fails to respond appropriately. This empirical dependency also prevents systematic verification and validation, creating regulatory and operational risks for utilities deploying these methods in critical grid planning studies.
What is the coupling relationship between the three solution stages, and why does isolated optimization of any single stage yield suboptimal overall performance?
The three stages—numerical integration, nonlinear algebraic equation solution, and linear algebraic equation solution—exhibit coupling relationships where algorithm selection in one stage constrains or enables performance in others. Numerical integration format determines the structure and stiffness of the resulting nonlinear algebraic equations; nonlinear solution iteration methods determine the frequency and conditioning of linear equation solves; linear solver performance directly impacts nonlinear iteration convergence speed. Isolated optimization of any single stage ignores these dependencies, yielding suboptimal overall performance. For example, optimizing linear solver efficiency without considering nonlinear iteration structure may reduce per-iteration cost but increase total iteration count, producing no net gain. Coordinated consideration within an integrated framework is mandatory for meaningful performance improvement.
How can artificial intelligence fusion with traditional numerical methods replace empirical parameter design, and what concrete performance improvements does this integration promise?
Artificial intelligence integration targets the replacement of experience-based parameter design through learned representations of optimal algorithm configurations conditioned on real-time system state. Rather than relying on manually-tuned switching thresholds and iteration parameters, AI models can map high-dimensional state observations to optimal algorithm selections and parameter values, achieving precise regulation across varying simulation conditions. This approach addresses the robustness deficiency of current adaptation strategies by eliminating manual experience dependency and enabling systematic generalization to unseen operating scenarios. The promised improvements include expanded performance adjustment ranges, enhanced responsiveness to time-varying demands, and resolution of the accuracy-convergence-efficiency trilemma that currently limits large-scale new-type power system simulation.
What are the scalability bottlenecks when applying these solution algorithm optimizations to multi-region interconnected grids with renewable capacity exceeding hundreds of gigawatts?
Scalability bottlenecks emerge from equation dimension explosion as multi-region grid interconnection and renewable device integration expand. System model equation dimensions surge with each added region and device, causing computational volume to inflate beyond linear scaling. Algorithm modification approaches face fixed algorithmic structures that cannot adapt to changing problem scales, while algorithm adaptation strategies with singular state-sensing dimensions cannot capture the full complexity of multi-region interactions. Communication overhead in parallelization further compounds scalability limits. The fundamental bottleneck is that current optimization paradigms address either absolute performance boundaries or resource allocation within boundaries, but neither simultaneously expands boundaries while adapting to scale-dependent performance requirements—a gap that integrated modification-adaptation frameworks and AI-fused numerical methods aim to close.
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