Transient Forward Harmonic Adjoint Sensitivity Analysis

TL;DR

This paper tackles the efficiency of sensitivity analysis for time-periodic nonlinear circuits in power electronics by introducing transient forward harmonic adjoint sensitivity analysis (TFHA). TFHA couples a transient forward solver with a harmonic balance based adjoint to compute sensitivities dU/dp for many design parameters using a single adjoint solve, after obtaining a transient solution and its periodic Fourier transform. The method uses a harmonic-space Jacobian and a Zienkiewicz-Zhu style error estimator to adapt the number of harmonics, enabling accurate time- and frequency-domain QoI sensitivities with reduced computational effort. Demonstrations on a half-wave rectifier, a boost converter, and an active filter show substantial speedups over direct or HB-only approaches, particularly for time-dependent QoIs and moderately nonlinear systems, highlighting TFHA’s practical impact for rapid design optimization in power electronics.

Abstract

This paper presents a transient forward harmonic adjoint sensitivity analysis (TFHA), which is a combination of a transient forward circuit analysis with a harmonic balance based adjoint sensitivity analysis. TFHA provides sensitivities of quantities of interest from time-periodic problems w.r.t. many design parameters, as used in the design process of power-electronics devices. The TFHA shows advantages in applications where the harmonic balance based adjoint sensitivity analysis or finite difference approaches for sensitivity analysis perform poorly. In contrast to existing methods, the TFHA can be used in combination with arbitrary forward solvers, i.e. general transient solvers.

Figures (10)

• Figure 1: Workflow of the transient adjoint sensitivity method.
• Figure 2: Workflow for the harmonic balance based adjoint sensitivity analysis and the TFHA.
• Figure 3: Schematic of a functional half-wave rectifying circuit.
• Figure 4: Sensitivity of the output voltage w.r.t. the resistance $R$ for the half-wave rectifying circuit in time and frequency domain.
• Figure 5: Boost converter circuit model with parasitics. The elements $L_{1}$, $R_{1}$, $C$ and $M$ model the functional behavior of the boost converter, the elements $R_{2}$, $L_{2}$, $R_{3}$, $L_{3}$, $R_{4}$ and $L_{4}$ are parasitic elements which model the EMC effects on the circuit board.