Stabilizing Large-Scale Electric Power Grids with Adaptive Inertia

TL;DR

This work tackles grid stability in low-inertia power systems by introducing a novel adaptive inertia scheme for virtual synchronous generators (VSGs). The inertia at each VSG evolves according to $\dot{m}_i = \alpha_i |\dot{\omega}_i| - \beta_i(m_i - m_{\mathrm{min},i})$, enabling rapid inertia gains during large RoCoF and a return to baseline inertia to suppress long-range oscillations, with stability guaranteed by a deadband-based linearization. Large-scale simulations on the RTS-96 and PanTaGruEl grids show that the adaptive scheme outperforms conventional electromechanical inertia across short- and long-time metrics, and that peripheral or homogeneous VSG distributions yield the best damping of inter-area oscillations. The results support deploying adaptive inertia as a robust, scalable tool to stabilize future decarbonized grids with substantial renewable penetration, including scenarios with widespread inertia reduction. Overall, the paper demonstrates that RoCoF-driven inertia augmentation combined with controlled decay can achieve quasi-optimal disturbance mitigation and improved grid coherency in large-scale networks.

Abstract

The stability of AC power grids relies on ancillary services that mitigate frequency fluctuations. The electromechanical inertia of large synchronous generators is currently the only resource to absorb frequency disturbances on sub-second time scales. Replacing standard thermal power plants with inertialess new renewable sources of energy (NRE) therefore jeopardizes grid stability against e.g. sudden power generation losses. To guarantee system stability and compensate the lack of electromechanical inertia in grids with large penetrations of NREs, virtual synchronous generators, that emulate conventional generators, have been proposed. Here, we propose a novel control scheme for virtual synchronous generators, where the provided inertia is large at short times -- thereby absorbing faults as efficiently as conventional generators -- but decreases over a tunable time scale to prevent coherent frequency oscillations from setting in. We evaluate the performance of this adaptive inertia scheme under sudden power losses in large-scale transmission grids. We find that it systematically outperforms conventional, electromechanical inertia and that it is more stable than previously suggested schemes. Numerical simulations show how a quasi-optimal geographical distribution of adaptive inertia devices not only absorbs local faults efficiently, but also significantly increases the damping of inter-area oscillations. Our results show that the proposed adaptive inertia control scheme is an excellent solution to strengthen grid stability in future low-inertia power grids with large penetrations of NREs.

Figures (16)

• Figure 1: Block diagram of our proposed adaptive inertia scheme. $P_\mathrm{grid}$ is the power flow across the lines connected to the generator. It is given by the sine terms of the power flow equations \ref{['eq:swinggen']}.
• Figure 2: The IEEE RTS-96 network. The red squares are conventional generators, the black triangles are VSGs equipped with the adaptive inertia method, Eq. \ref{['eq:adaptinertia']}, and the blue circles are load nodes. The black arrow indicates the VSG where the power is changed and the red arrow indicates the conventional generator at which a fault is applied. The roman numerals label the different areas and the dashed lines indicate their boundaries.
• Figure 3: Dependence of a) the frequency performance measure, Eq. \ref{['eq:freq']}, b) the RoCoF performance measure, Eq. \ref{['eq:rocof']}, c) the injected inertial energy, Eq. \ref{['eq:energy']}, and d) the resynchronization time, $t_{\rm re}$, on the VSG control parameters $\alpha$ and $\beta$ defined in Eq. \ref{['eq:adaptinertia']}. The fault considered is a change in the power at the generator indicated by the black arrow in Fig. \ref{['fig:rts96']}. Color coded are the ratios of the performance measures with VSGs over those with only conventional generation. Blue colored areas correspond to the adaptive method performing better than conventional generators.
• Figure 4: Frequency performance measure, Eq. \ref{['eq:freq']}, for a fault of size $\Delta P = -0.1\pu$ (left), $\Delta P = -1.0\pu$ (middle), and $\Delta P = -3.0\pu$ (right) on the VSG marked by a black arrow in Fig. \ref{['fig:rts96']}. Color coded are the ratios of the performance measures with VSGs over those with only conventional generation. Blue colored areas correspond to the adaptive method performing better than conventional generators.
• Figure 5: Time evolution of the frequency, $f = \omega/2 \pi$ (top panel), the RoCoF, $\dot{f} = \dot{\omega}/2\pi$ (middle panel), and the inertia (bottom panel) following a change of $\delta P =-1\pu$ at the VSG indicated by the black arrow in Fig. \ref{['fig:rts96']}. The black line corresponds to the default case with only conventional generation. The red line corresponds to the scenario with six generators being equipped with our adaptive method. The blue line corresponds to the adaptive scenario adjusted with an initial inertia of the VSGs set to the value of the default case.