--- title: "Transformer inrush current, doubling effect" subject: "Electrical Machines" chapter: 2 key: "semester_4/electrical_machines:inrush-current-doubling-effect" source: https://www.bctengineer.com/q/semester_4/electrical_machines/inrush-current-doubling-effect site: BCT Engineering --- # Transformer inrush current, doubling effect Electrical Machines · Chapter 2: Transformer - Asked in: 2071 Magh (old course), 2+6 marks - Video: [MAGNETIZING INRUSH CURRENT IN TRANSFORMER OR DOUBLING EFFECT IN TRANSFORMER](https://www.youtube.com/watch?v=Eb2j6TOGE6E) — Electrical understood - Answer checked by Claude Opus 5.5 (high effort) on 2026-10-14 - Page: https://www.bctengineer.com/q/semester_4/electrical_machines/inrush-current-doubling-effect - Whole chapter: https://www.bctengineer.com/md/semester_4/electrical_machines/chapter-2 ## Question What is meant by transformer inrush current? Discuss the term "doubling effect" in transformer in detail. ## Short answer Inrush current is the large transient magnetizing current at energization (5–10 times full-load) due to core saturation. The doubling effect occurs when switching at voltage zero: flux must start from residual flux and can peak at about 2φm + φr, driving the core deep into saturation and demanding high current. ## Answer **Inrush current** is the large transient magnetising current drawn by a transformer when it is first connected to the supply. Its peak can reach 5 to 10 times the full-load current (even more in small transformers), and it dies away over a few cycles to a few seconds (longer in large units). #### Doubling effect If the supply voltage is $v = V_m\sin(\omega t + \theta)$, the flux needed in steady state is $\phi = -\phi_m\cos(\omega t + \theta)$, because flux lags voltage by 90°. At the instant of switching the flux cannot change suddenly, so it starts from the residual flux $\phi_r$, and a decaying transient flux is added to the steady-state value. **Case: switching on at the instant when the supply voltage is zero** ($\omega t = 0$). - In steady state, the flux at this instant would be at its negative maximum ($-\phi_m$). - But the core flux just before switching is the residual flux $\phi_r$ (often small), and it cannot change suddenly. - So the flux starts from $\phi_r$ and follows $$ \phi = \phi_r + \phi_m(1 - \cos\omega t) $$ - Half a cycle later ($\omega t = \pi$), the flux reaches $$ \phi_{max} = 2\phi_m + \phi_r $$ The peak flux is therefore about **twice the normal peak**, and more if residual flux is present in the same direction. This is the **doubling effect**. ```text flux 2phi_m | .-. | / \ phi_m | / steady-state | / .-"-. 0 -+-/-"------"-------> t voltage zero when switched ``` #### Consequence - A normal transformer is designed to work at a flux density near the knee of the $B$–$H$ curve (about 1.5 to 1.7 T). Twice the flux drives the core deep into saturation, where the permeability falls sharply. - A very large magnetising current is then needed to produce this flux, and this is the inrush current. It has a high harmonic content (mainly second harmonic) and decays as the transient flux is damped by the winding resistance. **Case: switching on at voltage maximum** gives no transient: the flux starts at zero, which is already its steady-state value at that instant, so the inrush is minimal. **Effects and remedies:** inrush can trip overcurrent relays and stress the windings. It is reduced by switching through a series (pre-insertion) resistor and by point-on-wave closing, and relay maloperation is avoided by harmonic restraint in differential relays. ## Check yourself The answer's key points as multiple-choice questions, with the correct option and why. 1. Inrush current is: A. A steady short-circuit current B. The no-load current in steady state C. The current in the secondary at no load D. A large transient magnetising current when first energised, 5 to 10 times full load or more Answer: D. It dies away over a few cycles to a few seconds. (Key point: Inrush) 2. Which switching instant gives the largest inrush? A. When the supply voltage is zero B. When the supply voltage is maximum C. At full load D. When residual flux is exactly opposite Answer: A. Steady-state flux would be at -phi_m but flux starts near phi_r, so a transient flux is added. (Key point: Worst switching instant) 3. Half a cycle later the flux peak is about: A. phi_m B. 2 phi_m + phi_r C. phi_m/2 D. phi_m - phi_r Answer: B. phi = phi_r + phi_m(1 - cos wt) reaches 2 phi_m + phi_r at wt = pi. (Key point: Doubling) 4. Why does twice the flux produce a very large current? A. Winding resistance falls to zero B. Voltage doubles C. The core saturates, permeability falls sharply, so much more magnetising current is needed D. Turns ratio changes Answer: C. Normal flux is near the knee of the B-H curve. (Key point: Why large current) 5. Switching at voltage maximum gives: A. Maximum inrush B. Double inrush C. Short circuit D. Minimal inrush, as flux starts at its steady-state value Answer: D. No transient flux is needed. 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