Dissipativity Conditions for Maximum Dynamic Loadability

TL;DR

The paper addresses the challenge of achieving high dynamic loadability in grids with fast inverter-based resources by formulating a technology-agnostic energy-dynamics model that captures component interactions via port variables $P$ and the rate of change of instantaneous reactive power $\\dot{Q}$. It derives a sufficient dissipativity condition (Theorem 1) that bounds dynamic loadability based on line energy $E_i^{tl}$, line time constants $\tau^{tl}$, and the rates of change of injections, and it proposes load-side reactive power support as a practical method to increase stability margins. Numerical simulations on a simple network show that weaker transmission lines reduce stable regions on PV curves, while fast, load-side reactive power sources can significantly increase the maximum deliverable power and stabilize the entire load range, with results in good agreement with the theoretical bound. The framework is technology-agnostic and offers a pathway to enhance dynamic grid performance in high-penetration IBR scenarios through fast reactive power control at the load end.

Abstract

In this paper we consider a possibility of stabilizing very fast electromagnetic interactions between Inverter Based Resources (IBRs), known as the Control Induced System Stability problems. We propose that when these oscillatory interactions are controlled the ability of the grid to deliver power to loads at high rates will be greatly increased. We refer to this grid property as the dynamic grid loadability. The approach is to start by modeling the dynamical behavior of all components. Next, to avoid excessive complexity, interactions between components are captured in terms of unified technology-agnostic aggregate variables, instantaneous power and rate of change of instantaneous reactive power. Sufficient dissipativity conditions in terms of rate of change of energy conversion in components themselves and bounds on their rate of change of interactions are derived in support of achieving the maximum system loadability. These physically intuitive conditions are then used to derive methods to increase loadability using high switching frequency reactive power sources. Numerical simulations confirm the theoretical calculations, and shows dynamic load-side reactive power support increases stable dynamic loadability regions.

Figures (6)

• Figure 1: Instantaneous power dynamics through a transmission line connecting two synchronous machines modeled using a Type $IV_1$ model iliczab. The top plot shows the dynamics for two machines with very high inertia, and the bottom plot for those with very low inertia.
• Figure 2: Simple power transfer system comprised of a single generator $G_1$, transmission line $TL_1$ and load $L_1$, with their associated port interactions noted.
• Figure 3: PV curves for the single generator, transmission line load system with three different values for the line inductance. Sections of the PV curve in blue represent regions where the operation was stable, and sections in red represent regions where the operation was unstable.
• Figure 4: Modified generator, transmission line, load system with an additional generator connected on the load side. This generator is configured to only provide reactive power.
• Figure 5: Time response of the RL load following a small disturbance and the dynamics of the generating unit at the load side.