A Performance and Stability Analysis of Low-inertia Power Grids with Stochastic System Inertia
For power system engineers, this work provides analytical tools to understand and quantify the impact of stochastic inertia on grid performance and stability, which is increasingly relevant with high renewable penetration.
This paper analyzes the performance and stability of low-inertia power grids with stochastic (time-varying) inertia, modeled via a linearized stochastic swing equation with multiplicative noise. It derives closed-form expressions for the H2 norm (performance metric) and a mean-square stability condition, showing how they depend on network topology, system parameters, and disturbance distributions.
Traditional synchronous generators with rotational inertia are being replaced by low-inertia renewable energy resources (RESs) in many power grids and operational scenarios. Due to emerging market mechanisms, inherent variability of RESs, and existing control schemes, the resulting system inertia levels can not only be low but also markedly time-varying. In this paper, we investigate performance and stability of low-inertia power systems with stochastic system inertia. In particular, we consider system dynamics modelled by a linearized stochastic swing equation, where stochastic system inertia is regarded as multiplicative noise. The $\mathcal{H}_2$ norm is used to quantify the performance of the system in the presence of persistent disturbances or transient faults. The performance metric can be computed by solving a generalized Lyapunov equation, which has fundamentally different characteristics from systems with only additive noise. For grids with uniform inertia and damping parameters, we derive closed-form expressions for the $\mathcal{H}_2$ norm of the proposed stochastic swing equation. The analysis gives insights into how the $\mathcal{H}_2$ norm of the stochastic swing equation depends on 1) network topology; 2) system parameters; and 3) distribution parameters of disturbances. A mean-square stability condition is also derived. Numerical results provide additional insights for performance and stability of the stochastic swing equation.