Inrush current when energising an inductor, linear ODE case study

Antonio Sala, UPV

Difficulty: *** ,       Relevance: ,      Duration: 22:52

Summary:

In this video, the transient overcurrents (inrush current) in an inductor (say, a transformer) are studied as an exasmple of applications of ODE solving to electrical engineering. Only the linear inductor case is studied in this first video, leaving magnetic saturation for forthcoming videos.

First, the circuit model is stated $\frac{di}{dt}=\frac{1}{L}(V-Ri)$, being $V$ the input voltage to a series resistor-inductor circuit.

Then, the ODE is solved for initial condition $i(0)=0$. The result contains an exponential transient which adds to a steady-state solution which is a sinusoidal waveform (steady-state AC current).

Plotting the transient, we discuver that initial current peak is twice the amplitude of the steady-state current.

The initial phases of the response are close to that of a pure inductor. The final fases of the response approach, when $t\to \infty$, i.e., the solution computed with impedances $Z(\omega )=R+L\omega j$, results in $I(\omega )=\frac{1}{Z(\omega )}\cdot V(\omega )$.

The last minutes of the video discuss how to avoid the inrush overcurrent phenomenon: timing the transformer connection so that suitable power electronics equipment connects the unloaded inductor when input voltage has the peak value (approximately). Repeating the plots of the new solution, initial conditions do match the steady-state waveforms so exponential transient and the overcurrent associated to it are elliminated.

Inrush overcurrents are exacerbated if the inductor core undergoes magnetic saturation; these issues are out of the scope of the present video, for brevity and simplicity.

Python version: https://personales.upv.es/asala/DocenciaOnline/Material/Python/linind2.py

*Link to my [ whole collection] of videos in English. Link to larger [ Colección completa] in Spanish.