On the damping of power systems during inverter-based blackstart
Adolfo Anta, Diego Cifelli
TL;DR
The paper addresses damping challenges during the early stages of grid restoration with inverter-based, grid-forming resources, where backbone energization can suffer from resonances due to low loading. It develops an analytical framework by modeling the backbone line as cascaded $ abla$pi-sections and exploiting the $2$-Toeplitz structure of the state matrix, linking eigenvalues to Chebyshev polynomials to obtain closed-form spectral characterizations. The authors show that voltage-tracking feedback ($k_V$) tends to degrade damping by increasing the imaginary parts of complex eigenvalues, while adding a virtual resistance term ($k_I$) can restore damping; they illustrate these effects with an academic 100 km line and a 9-bus system energization, and discuss extensions to cross-coupled and reactive strategies. The work provides high-level design guidance for grid-forming inverters in black-start, aiding the formulation of specifications and control rules to ensure adequate damping during the critical early restoration phase, thereby improving reliability and speed of recovery.
Abstract
The massive deployment of inverter-based generation poses several challenges to system operators but also offers new opportunities. In the context of grid recovery, inverter-based generation is expected to take over new responsibilities, as conventional generation that are blackstart capable are being decommissioned. Inverter-based facilities, being very flexible and controllable, have the ability to contribute during grid restoration, although it is still unclear how to deal with the limited ratings of batteries, PV, etc. and how to address nonlinear effects such as inrush currents or harmonics. In this direction, the requirements of grid-forming inverters to comply with black start capabilities are still to be defined. During the first steps of a grid restoration process the dynamics of the grid largely vary from the grid behaviour under normal operation. In particular, the grid is nearly unloaded and therefore poorly damped. Indeed, overvoltages and resonances are a common concern during the energization of long transmission lines. In this work we analyse the spectral properties of unloaded transmission lines, and describe the impact of voltage controllers on the damping of the system. As a byproduct, this analysis can be leveraged to propose high level requirements for grid-forming devices, in order to provide adequate damping during the early stages of a grid restoration process.