PaperlayerView exact revision on arXiv

Source-linked AI summary

Parameter Estimation of Power Electronic Converters with Differentiable Physics Simulation

Pingjunjin Tan, Chunlin Lv, Jinjun Liu, Yang Li

arXiv:2608.30915v1eess.SY

TL;DR

Power-converter condition monitoring needs noninvasive parameter estimation despite limited sensing, nonlinear switching dynamics, and data-distribution challenges. The paper embeds converter time-domain simulation in a differentiable computational graph for gradient-based estimation from sparse measured waveforms, and experimentally shows reliable tracking of critical-parameter variations in a buck converter. Remaining concerns include operating-condition sensitivity, limited parameter identifiability, and uncertainty from measurement noise and synchronization error.

  • Problem

    Condition monitoring requires tracking degrading component parameters from available electrical sensors, while existing methods face auxiliary-sensing burdens, modeling assumptions, data scarcity, and distribution-shift risks.

  • Method

    The method reformulates numerical time-stepping as a differentiable computational graph linking critical converter parameters to measured voltage and current trajectories across topological transitions.

  • Results

    The proposed method reliably tracks relative variations of critical dc–dc buck-converter parameters under practical hardware conditions, while capacitor ESR reaches a maximum relative-change deviation of 18.78% under L1M3C5.

  • Takeaways & Limitations

    Differentiable physics simulation provides a parameter-estimation framework for converter condition indicators and a perspective for physics-informed machine learning in power electronics.

  • Takeaways & Limitations

    Parameter estimates remain sensitive to operating conditions, some parameters have limited identifiability, and measurement noise and synchronization error can affect estimation credibility.

Abstract

from arXiv · show

This article proposes a differentiable physics simulation (DP simulation)-based parameter estimation method for the condition monitoring of power electronic converters. In the proposed method, the time-domain simulation of converter dynamics is embedded into a differentiable computational graph, directly linking device parameters to observed voltage and current trajectories. By formulating differentiable time-stepping operators, the nonlinear dynamics of the converter across different circuit topologies are simulated in a unified, differentiable manner. A dc-dc buck converter is used as a representative case study. Using sparse transient samples from existing sensing channels, the method enables noninvasive parameter estimation without additional sensing hardware. Comprehensive simulation studies are conducted to evaluate the impacts of time-stepping schemes, regularization constraints, and various uncertainty sources on estimation accuracy and robustness. Subsequently, 30 distinct hardware configurations are experimentally tested for validation. The results show that the proposed method can effectively track the relative variations of health-related parameters across the critical components. This DP simulation framework provides a novel perspective for physics-informed machine learning in power electronic applications.

I. INTRODUCTION

Power-converter condition monitoring seeks noninvasive estimation of degrading component parameters from electrical measurements. Existing approaches face hardware, modeling, data, and switching-transition limitations that motivate differentiable physics simulation.

  • Component degradation changes measurable electrical behavior, allowing intrinsic parameters such as MOSFET on-state resistance and capacitor capacitance to serve as health indicators.
  • Parameter-estimation methods span model-based, hybrid, and data-driven categories with different balances of physical constraints, sensing requirements, and computational costs.Fig. 1 organizes these three categories and their subcategories.
  • Auxiliary sensing circuits can directly capture terminal information but introduce potential failure points and complicate integration into mature converter designs.
  • Simplified model-based methods reduce hardware overhead but often assume other circuit parameters are known and constant, despite simultaneous degradation across components.
  • Purely data-driven methods require substantial data and can produce physically inconsistent predictions under training–testing distribution shifts.
  • Existing hybrid time-domain methods use converter dynamics, numerical propagation, or PINNs, but switching-converter Runge–Kutta constraints and neural-network optimization create sampling and convergence difficulties.Existing formulations may require samples aligned with noise-prone switching instants and optimize a highly non-convex parameter space.
  • The proposed DP framework makes numerical integration differentiable, propagates gradients across topological transitions, supports sparse sampling away from switching instants, and estimates critical parameters simultaneously.The framework is presented for a dc–dc buck converter and is described as extensible to other architectures.

II. METHODOLOGY

The buck converter is modeled with switching-dependent dynamics and measured electrical states, then advanced using numerical time-stepping. Runge–Kutta formulations provide the basis for differentiable simulation across converter operating stages.

  • Dynamic Modeling of the Buck Converter in CCM: In continuous-conduction mode, MOSFET switching divides the buck converter into two linear circuit stages represented by distinct equivalent circuits.The stages correspond to MOSFET off-state and on-state operation.
  • Dynamic Modeling of the Buck Converter in CCM: A discrete switching function S ∈ {0, 1} unifies the converter dynamics across semiconductor on/off states under PWM control.
  • Dynamic Modeling of the Buck Converter in CCM: The state variables are inductor current iL and output voltage vo, while the model includes input voltage, diode drop, MOSFET resistance, inductance, capacitance, parasitic resistances, and load resistance.These states directly align the dynamic model with sparsely sampled observational data.
  • Generalized Runge–Kutta Time-stepping Scheme: Numerical time-stepping converts continuous converter dynamics into a discrete representation, iteratively computing the next state from the current state, step size h, and method-specific increment function Φ.
  • Generalized Runge–Kutta Time-stepping Scheme: Runge–Kutta methods evaluate intermediate states and combine them through weighted algebraic sums, with coefficients represented by a Butcher tableau.The tableau contains RK nodes, coefficient-matrix entries, and weights.
  • Generalized Runge–Kutta Time-stepping Scheme: Explicit Runge–Kutta stages are sequential and require exactly ν function evaluations, giving O(ν) time complexity per step.
  • Generalized Runge–Kutta Time-stepping Scheme: Within each switching interval, the buck converter is linear time-invariant, allowing implicit Runge–Kutta stages to be solved as one linear system using Gaussian elimination.

C. Differentiable Physics Simulation for Buck Converter

The framework reformulates buck-converter numerical integration as differentiable operator composition, allowing sparse sampled states to support gradient-based parameter estimation across switching topologies.

  • The converter state evolution is represented as successive differentiable operators parameterized by the target circuit parameters.The parameter vector includes Rdson, vF, L, RL, C, RC, and R.
  • q successive discrete steps advance the initial state u_n to the final state u_n+qh1 over a macroscopic interval.Each operator must provide exact gradients with respect to both the state and target parameters.
  • The buck-converter state vector u_n = [iL(n), vo(n)]T provides the sparsely sampled data used for model training.The framework captures dynamic relationships between sampled states rather than requiring continuous observations.
  • ∆t1 is propagated with q steps and ∆t2 with k steps, switching from the on-state to off-state operator at the intermediate switching node.The micro-step sizes are h1 = ∆t1/q and h2 = ∆t2/k.
  • The objective is the MSE between measured observations and model-derived states, enabling gradient-based identification of physical parameters.The loss compares u^(j+1) with its simulated counterpart ũ^(j+1).

D. Automatic Differentiation and Backpropagation

Automatic differentiation and backpropagation through time provide gradients for the differentiable converter simulation, accounting for both arithmetic dependencies and repeated parameter use across time steps.

  • Automatic differentiation extracts target-parameter gradients by applying the chain rule to arithmetic operations in the dynamic simulation.Reverse-mode AD evaluates the function forward and propagates adjoints backward to the inputs.
  • Reverse-mode AD is efficient for gradients of a scalar objective with respect to many parameters.
  • BPTT unrolls the converter dynamics over time and accumulates step-wise derivatives for the shared parameters θ.This accounts for the cumulative dependence of outputs on past intermediate states.
  • The resulting gradient flow enables gradient-based optimization and efficient computation of higher-order derivatives such as the Hessian matrix.

E. Sampling Strategy and Data Configuration

The sampling strategy prioritizes informative transient behavior while avoiding switching-ring noise, and the framework supports reusing sampled points across intervals and longer simulation horizons.

  • Transient intervals are preferred because their dynamics are more sensitive to parameter variations than steady-state operation.
  • Carrier-synchronized sampling selects predefined carrier valley and peak instants while excluding switching ringing regions.This supports low-frequency acquisition compatible with standard digital control systems.
  • Deterministic controller timing allows sparse samples spanning a switching event to be simulated across topological transitions.
  • Each sampled point can serve as the ending state of one interval and the initial state of the next.The framework can also reuse a single point to infer subsequent sampled points over an extended horizon.
  • The sampling frequency can be reduced from 2fsw to fsw or to one sample over multiple switching cycles.The study first considers one-step prediction before examining extended-horizon and constrained formulations.

III. SIMULATION VERIFICATION AND ROBUSTNESS ANALYSIS

Simulation verification uses MATLAB/Simulink buck-converter data across multiple operating conditions and hardware configurations to assess accuracy and generalization.

  • MATLAB/Simulink generates buck-converter simulation data for multiple operating conditions and hardware parameters.The configurations are listed in Table II and are used to evaluate the method’s generalization capability.

A. Accuracy and Computation Complexity

The method estimates converter parameters from carrier-synchronized transient samples and balances numerical accuracy against computational cost. C, L, and Rload are accurately identifiable, while sampling constraints and shorter transients limit data collection.

  • Data collection: Carrier-synchronized inductor-current and output-voltage samples are collected during converter transients, using data already available in control-loop feedback.Training data can come from startup, shutdown, load switching, and control-mode transitions.
  • Practical boundary: Shorter transient durations at higher switching frequencies make data collection more challenging, although steady-state data may partially alleviate data scarcity.Slow degradation over months or years provides time for collecting the sparse data required by the method.
  • Data collection: Each load-transition dataset contains 30 switching cycles, combining transients caused by R0 → R1, R1 → R2, and R2 → R3.The three transitions form the training dataset for condition monitoring.
  • Accuracy: C, L, and Rload can be accurately identified from the transient observations.These parameters are grouped as θ1 = {C, L, Rload}.
  • Computation complexity: Once Runge–Kutta order is sufficient, increasing integration order or reducing step size yields only marginal identification improvement.The numerical integration error becomes smaller than observation noise and model–plant mismatch.
  • Computation complexity: Increasing integration substeps directly raises computational cost because time-marching simulation and gradient propagation are sequential, whereas GPU-parallel Runge–Kutta orders differ little in runtime.The framework therefore requires balancing estimation accuracy, computational cost, and converter applicability.

B. Regularization Constraint

The regularization strategy addresses ill-posed and coupled parameter estimation by enforcing converter-dynamics consistency in both local and extended time horizons. Longer prediction windows generally improve identifiability, but some coupled resistances remain difficult to separate.

  • Motivation: Small training-loss MSE can coexist with large parameter deviations, indicating that parameter estimation is an ill-posed inverse problem.Weak identifiability means small simulated-waveform mismatches may correspond to substantially different parameter values.
  • Constraint design: The method introduces bidirectional consistency and long-horizon consistency as regularization constraints derived from converter dynamics.These constraints avoid relying solely on narrow prior ranges for parameters that may vary widely during converter lifetime.
  • Bidirectional consistency: Bidirectional consistency requires forward prediction of the next state and backward reconstruction of the current state over a short sampling interval.The constraint uses the converter’s differential-equation dynamics in both time directions.
  • Long-horizon consistency: Long-horizon consistency reduces compensation among coupled parameters by matching measured trajectories across an extended prediction window.RL, Rdson, and vF can produce strongly coupled effects in the observable states iL and vo.
  • Results and boundary: Longer prediction windows generally improve clean-data estimation and make RL and Rdson more distinguishable, but accurate separation remains challenging in Cases V and VI.The limitation is reported for small parasitic resistances and relatively small load variations.
  • Computational trade-off: With Nh = 16, differentiable physical-model training remains within one minute on an NVIDIA GeForce RTX 5060 Ti.Longer windows require more transient samples and increase simulation time approximately linearly with window length.

C. Robustness Analysis

The robustness analysis models both measurement-side randomness and model-side uncertainty. It evaluates how noise, quantization, synchronization, and model–plant mismatch affect parameter estimation under practical operating conditions.

  • Aleatoric uncertainty: Aleatoric uncertainty is imposed through measurement noise, ADC quantization, and synchronization offset among sampled signals.These sources represent randomness in the observation process.
  • Epistemic uncertainty: Epistemic uncertainty is represented by model–plant mismatch caused by incomplete knowledge of the actual converter system.The uncertainty reflects discrepancies between the simplified model and hardware.

MOSFET

The MOSFET-related resistance is evaluated within an equivalent-resistance representation and under stochastic uncertainty. Strongly identifiable parameters remain concentrated, while individual resistance estimates are less accurate than the combined health indicator.

  • Uncertainty setup: The Monte Carlo evaluation applies aleatoric uncertainty from measurement noise, ADC quantization, and synchronization offset, plus epistemic model–plant mismatch.These uncertainty sources are imposed on sampled signals and the converter model.
  • Uncertainty effects: Measurement noise and synchronization offset affect estimation more noticeably than ADC quantization and model–plant mismatch because they directly distort sampled trajectories.The θ1 parameters C, L, and Rload remain accurately estimated under the tested uncertainty combinations.
  • Monte Carlo results: 1000 independent trials under ADC-Sync-1%noise-MPM show tightly concentrated errors for L, C, and Rload, while RC and vF have wider distributions.The result indicates stronger robustness for the strongly identifiable parameter set than for RC and vF.
  • Experimental platform: The experimental buck-converter platform uses replaceable MOSFETs, diodes, inductors, and capacitors for hardware validation.The platform supports component-level configuration changes.
  • Equivalent resistance: Most samples remain within the ±20% band for RD = RL + Rdson under sparse-data uncertainty testing.Each training set contains only 30 switching cycles sampled at twice the switching frequency.

IV. EXPERIMENT VERIFICATION

The buck-converter platform evaluates parameter estimation across replaceable hardware configurations using sparse transient voltage and current measurements. The method tracks dominant parameter trends accurately, while ESR and equivalent resistance estimates show larger deviations and sensitivity to practical uncertainties.

  • Experimental setup: The experimental platform supports replaceable capacitor, inductor, MOSFET, and diode configurations for hardware-validation studies.Capacitor aging is emulated by combining capacitors and series resistors with different values.
  • Data preparation: Each estimation task combines three load-transition transients, with 60 sampled points per record and a 30-cycle recording window.The experimental configuration uses the single-step ERK4 scheme and specified regularization constraints.
  • Evaluation basis: Relative percentage changes are evaluated against the averaged L1M1C1 estimates because offline measurements can differ from effective in-operation parameters.The baseline is the average result of three repeated experiments under the same operating conditions.
  • Primary parameters: Inductance L, capacitance C, and load resistance Rload variations are tracked with high accuracy and narrow distributions across hardware configurations.The results indicate repeatability and stable identification of the converter’s primary parameters.
  • Secondary parameters: Capacitor ESR RC follows the degradation trend, but its maximum relative-change deviation reaches 18.78% under L1M3C5.This deviation is relatively small compared with the reported ESR increase of 161.62%.
  • Secondary parameters: Equivalent resistance RD is less accurate, with approximately 8% variation among L2M2 trials and considerable discrepancies from reference variations.The model treats RL + Rdson as constant although both can vary with temperature and current; nevertheless, RD generally follows the reference trend.

C. Discussion

The discussion positions DP simulation as a differentiable, topology-general framework for converter parameter estimation and broader power-electronics applications. It reports accurate estimation of dominant buck-converter parameters, while identifying operating-condition mismatch and limited identifiability as remaining challenges.

  • Discussion: The framework establishes a differentiable mapping from critical component parameters to externally measured converter waveforms.This mapping may support applications beyond condition monitoring, including converter design optimization and model predictive control.
  • Discussion: DP simulation treats the numerical solver as a differentiable computational graph that can integrate with neural-network-based deep learning.The formulation preserves the physical evolution dynamics while enabling gradient-based optimization.
  • Discussion: The topology-general numerical time-stepping framework is described as extensible to dc–ac inverters and resonant converters.The supplied discussion presents this as potential extension beyond the buck-converter case study.
  • Challenges: Industrial implementation remains constrained by operating-condition sensitivity and limited identifiability caused by weak state sensitivity and strong parameter coupling.The discussion calls for a health-state representation that accounts for mismatch between operating behavior and offline static references.
  • Discussion: Under practical hardware conditions, the method reliably tracks critical buck-converter parameters and provides meaningful condition indicators.The conclusion reports maximum experimental variation deviations within 5% for L, C, and Rload, within 20% for RC and RD.
Loading 2608.30915v1…