On the Duality Between Quantized Time and States in Dynamic Simulation

TL;DR

The paper addresses the computational burden of time-domain power-system simulations by formalizing a duality between time discretization and state quantization via quantized-state system (QSS) methods. It develops a second-order QSS-AB2 scheme and a dual-time formulation where time evolves as $t'(x)=\phi(t)$ with $\phi=1/|f|$, enabling time-step control inspired by classical integrators. An adaptive quantum-size strategy via a PI controller, $\Delta q_{k+1}=\left( {tol/|\sigma_k|}\right)^{\alpha}\left({|\sigma_{k-1}|}/{|\sigma_k|}\right)^{\beta}\Delta q_k$, balances efficiency and accuracy and is compatible with standard implicit solvers. Case studies on a large-scale power-system model demonstrate notable speedups with controlled accuracy, suggesting a new family of numerical methods that blend time discretization and state quantization for dynamic simulations.

Abstract

This letter introduces a formal duality between discrete-time and quantized-state numerical methods. We interpret quantized state system (QSS) methods as integration schemes applied to a dual form of the system model, where time is seen as a state-dependent variable. This perspective enables the definition of novel QSS-based schemes inspired by classical time-integration techniques. As a proof of concept, we illustrate the idea by introducing a QSS Adams-Bashforth method applied to a test equation. We then move to demonstrate how the proposed approach can achieve notable performance improvements in realistic power system simulations.

Figures (4)

• Figure 1: Test equation $x'=-0.6 x$: QSS1 solution.
• Figure 2: Test equation $x'=-0.6 x$: Event quantization timing errors.
• Figure 3: Three-phase fault: Rotor speed of machine at bus 1237.
• Figure 4: Three-phase fault: Variations of $\Delta q$ and $\Delta t$, QSS-AB2-Ad.