This paper analyses the frequency stability of ac grids in the presence of non-dispatchable generation and stochastic loads. Its main goal is to evaluate conditions in which the system is robust to large, persistent active power disturbances without recurring to time-domain simulations. Considering the ongoing energy transition to more renewable sources, defining robustness boundaries is a key topic for power system planning and operation. However, much of the research on long-term studies has not dealt with robust dynamic constraints, while short-term analyses usually depend on time-consuming simulations to evaluate nonlinearities. To bridge this gap, the authors derive an algebraic equation that provides sufficient conditions for robust frequency stability in ac power systems and a relationship among four key quantities: the maximum active power perturbation, the minimum system damping, the steady-state and the transient frequency limits. To achieve this goal, it uses a nonlinear average-model of the ac grid and Lyapunov's direct method extended by perturbation analysis requiring only limited knowledge of the system parameters. The algebraic calculations are validated using time-domain simulations of the IEEE 39-bus test system and results are compared to the traditional Swing Equation model.

中文翻译：

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交流电力系统鲁棒频率稳定的充分条件


本文分析了存在不可调度发电和随机负载的情况下交流电网的频率稳定性。其主要目标是评估系统对大的、持续的有功功率扰动的鲁棒性，而无需重复进行时域仿真。考虑到能源正在向更多可再生能源过渡，定义鲁棒性边界是电力系统规划和运营的一个关键主题。然而，许多长期研究并未涉及稳健的动态约束，而短期分析通常依赖于耗时的模拟来评估非线性。为了弥补这一差距，作者推导了一个代数方程，该方程为交流电力系统的鲁棒频率稳定性提供了充分的条件，并建立了四个关键量之间的关系：最大有功功率扰动、最小系统阻尼、稳态和瞬态频率限制。为了实现这一目标，它使用交流电网的非线性平均模型和通过扰动分析扩展的李亚普诺夫直接方法，仅需要有限的系统参数知识。使用 IEEE 39 总线测试系统的时域仿真验证代数计算，并将结果与​​传统的 Swing 方程模型进行比较。