RLC Parameter Identification from Voltage & Current Waveforms

Terminal waveforms contain enough information to fit a useful equivalent only when the assumed topology leaves a distinct signature in the data. Identification is therefore not "solve a formula for $R,L,C$"; it is a joint problem of topology, excitation, estimation, and validation.

Start from a forward model #

Examples include

$$v(t)=Ri(t)+L\frac{di}{dt}$$

for a series $R$-$L$ model, or

$$i(t)=\frac{v(t)}{R}+C\frac{dv}{dt}$$

for a parallel $R$-$C$ model. With sampled data, arrange the equation as a regression in parameters and fit all samples together rather than dividing point by point near zeros.

For the instantaneous-power projection used by Mishchenko:

$$R=\frac{U^2}{P},\qquad i_r(t)=i(t)-\frac{P}{U^2}u(t).$$

That identifies the dissipative projection exactly over the selected interval. Assigning the residual to $L$ or $C$ is a separate topology assumption.

Data requirements #

• Voltage and current channels must share a clock and calibrated phase response.
• Excitation must vary enough to separate resistive and storage effects.
• The sampling rate and antialias filtering must preserve the modeled bandwidth.
• Initial conditions and operating mode must be known or estimated.
• Derivatives need smoothing, integral formulations, or state-space estimation because direct finite differences amplify measurement noise.

Fit, constrain, validate #

Estimate parameters on one dataset while enforcing physical bounds where appropriate. Then predict another interval, amplitude, frequency, or load condition without refitting. Report waveform residuals, power residuals, and whether errors are correlated with current, phase, temperature, or operating mode.

Diagnose model mismatch #

Strongly time-varying parameters, negative storage values, structured harmonic residuals, or sensitivity to the derivative filter are evidence that the topology or state description is inadequate. Adding parameters can reduce training error while making identifiability worse; prefer the smallest model that passes out-of-sample tests.

In real data, direct numerical differentiation is usually the weakest step. Prefer an integral formulation, filtered derivative, or state-space estimator, then report how the parameter estimate changes with the filtering choice.