Stochastic Dynamics and Stability Analysis in Power Systems
Summary
Modern power systems increasingly integrate variable renewable sources and power‐electronic interfaces, introducing significant random fluctuations into generation and load. Stochastic dynamics provides a framework for modelling these uncertainties through random processes and stochastic differential equations, enabling the explicit characterisation of system behaviour under variable disturbances. Stability analysis in this context encompasses probabilistic and stochastic forms of small‐disturbance, transient and voltage stability, reflecting the likelihood of maintaining synchronism, acceptable voltage levels and secure operation following random excitations. Key mathematical tools include Lyapunov functions adapted for stochastic systems, Fokker–Planck–Kolmogorov equations for probability density evolution, and stochastic averaging methods to reduce high‐dimensional models to tractable forms. Numerical techniques such as Milstein–Euler discretisation and Monte Carlo simulation support practical assessment, while analytical approaches yield explicit criteria for stability bounds and reliability measures. Applications range from single‐machine infinite‐bus models and two‐area networks with correlated wind speeds to grid‐connected doubly fed induction generators subject to random blade stresses. The global significance lies in ensuring secure, efficient and resilient operation of future low‐carbon power grids under inherent uncertainties.
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Stochastic Dynamics and Stability Analysis in Power Systems publication trend
The graph below shows the total number of articles in stochastic dynamics and stability analysis in power systems across all publications each year (not limited to Nature Index journals).
Technical terms
Stochastic differential equation: An equation describing the evolution of system states under both deterministic dynamics and random perturbations, typically involving Wiener or Gaussian noise terms.
Small-signal stability: The ability of a power system to maintain synchronism under infinitesimal disturbances, analysed by linearising the dynamic equations around an operating point.
Fokker–Planck–Kolmogorov equation: A partial differential equation governing the time evolution of the probability density function of a stochastic process, linking drift and diffusion terms to probability flows.
Stochastic averaging method: A reduction technique that transforms a high-dimensional stochastic system into a lower-order averaged model, facilitating analytical derivation of stability and reliability measures.
References
- Classification Study of New Power System Stability Considering Stochastic Disturbance Factors. Sustainability (2023).
- Linearization threshold condition and stability analysis of a stochastic dynamic model of one-machine infinite-bus (OMIB) power systems. Protection and Control of Modern Power Systems (2021).
- Stochastic aggregated dynamic model of wind generation with correlated wind speeds. Electric Power Systems Research (2022).
- Stochastic stability analysis method for doubly fed generator sets considering random blade stress. Energy Science & Engineering (2024).
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