# Inrush current

Resistance curve of an incandescent lamp at different voltages; the cold resistance is only about 7% of that at operating temperature, the inrush current consequently almost 15 times the nominal value.
Inrush current curve of an incandescent lamp 230 V ~ / 250 W.

As inrush current refers to the electric current which flows immediately after switching an electrical load. It differs from the nominal current and must be taken into account when designing electrical equipment such as switches , fuses , relays , etc., as it can be a multiple of the nominal current flowing later. However, the increased inrush current can also be limited or avoided entirely with suitable (additional) circuits ( inrush current limiter , also called soft starter switch or "soft starter").

Transformers , switched-mode power supplies , electric motors , incandescent lamps and filaments (e.g. the heating wires of electron tubes ) typically have a high inrush current; this can be more than 10 times the operating current. The duration of the increased inrush current can be between a few milliseconds and several seconds, depending on the type of electrical consumer .

Electrical fuses and circuit breakers must be dimensioned in such a way that, on the one hand, they trip in the event of permanent overcurrents and, on the other hand, they tolerate excessive inrush currents. The reaction to short current surges is referred to as the tripping characteristic and must be matched to the inrush current of the connected devices. For example, the fuse wire of a slow fuse has a sufficiently high thermal capacity that prevents its temperature from reaching the critical value during the inrush current. The measured variable for triggering the fuse is the value, the integral of the current square over time ( melting integral ). This value represents the energy that is consumed by the fuse when it is switched on. Miniature circuit breakers are also specified with regard to the response threshold of their magnetic release (short-circuit release); To avoid unintentional tripping, the maximum inrush current must not exceed this value. ${\ displaystyle I ^ {2} t}$

## Causes of excessive inrush current

### Inductive components

Inrush current I L through a coil as a function of time. The time axis is normalized to the time constant τ.
Inrush current curve on a 230 V / 60 W mains transformer: the asymmetrical current pulses (direct current component) only dissipate over several mains voltage periods.

If an inductive component such as a coil is connected to a DC voltage source, the inrush current initially increases slowly because the induced counter-voltage counteracts the applied voltage according to Lenz's rule . With large inductances, it can take seconds to reach the rated current . DC solenoids and relays therefore always have inrush currents that are lower than the operating current.

With AC voltage, however, an increased current can flow shortly after switching on; With ideal coils, this can be a maximum of twice the nominal current. If the coil contains an iron core, however, much higher inrush currents are possible:

• The core of a transformer can become magnetically saturated a short time after being switched on , especially if it is premagnetized ( remanence ). In the saturation, the reactance of the coil is low and a multiple of the nominal current can flow. The cause and countermeasures are explained in more detail in Switching on the transformer .
• Contactors and pull magnets that are operated with AC voltage cause high inrush currents because there is a large air gap at the moment of pick-up and therefore the inductance and reactance are small.

### engine

Electric motors (both DC and AC motors) have a high inrush current, because more power and thus more current is required to accelerate the rotating centrifugal mass to the nominal speed than to maintain the speed. This portion of the inrush current is called the starting current. An increased current flows until the stationary speed is reached; Depending on the size of the motor, the flywheel mass and the load, this time can be between fractions of a second and many seconds.

Disregarding the inductance, the starting current of a DC motor corresponds to the current when the motor is stopped. This can be calculated from the applied voltage and the resistance of the windings according to Ohm's law : ${\ displaystyle U}$${\ displaystyle R}$

${\ displaystyle I _ {\ mathrm {A}} = {\ frac {U} {R}}}$.

When the motor is running, on the other hand, a voltage is induced which is proportional to the speed and opposes the applied terminal voltage; the current is then the quotient of the difference between the two voltages and the resistance: ${\ displaystyle U _ {\ mathrm {ind}}}$${\ displaystyle I}$

${\ displaystyle I = {\ frac {U-U _ {\ mathrm {ind}}} {R}}}$.

The high starting current results in an increased torque that accelerates the motor. The current decreases with increasing speed until the steady-state speed is reached.

With asynchronous motors , the inductive resistance of the winding is greatly reduced when the motor is at a standstill, because the rotor ( squirrel-cage rotor ) acts like a short-circuited secondary winding of a transformer . The inductive resistance only increases when the rotor reaches the driving speed, i.e. H. when the speed of the rotor has almost reached that of the rotating field. The squirrel cage rotor of asynchronous motors can be designed so that the starting current is lower, but then their already low starting torque (the breakaway torque that can be generated by the motor) decreases even further and the losses increase.

In addition, most electric motors for alternating voltage (e.g. asynchronous motors ) have an inrush current caused by the iron core (possible magnetic saturation, see section " Inductive components "). In contrast to the inrush current, this portion of the inrush current is only of short duration (a few mains periods). A typical asynchronous motor has a magnetically induced inrush current increase of 4–12 times and a starting current of approx. 4–8 times its rated current, depending on the type.

### capacitor

Inrush current I C through a series connection of resistance and capacitance as a function of time

Capacitors are normally not charged when they are switched on and - with DC voltage - act briefly like a short circuit . With AC voltage, the inrush current depends on the instantaneous voltage at the point in time at which the switch is closed. A zero-crossing switch is optimal when the capacitor is discharged , because the inrush current of the capacitor is then minimal.

Examples are capacitors for reactive current compensation , etc. a. with fluorescent lamps . In the case of charging capacitors after the rectifier of primarily switched- mode power supplies and frequency converters, switching on the zero voltage is generally not sufficient to avoid a high inrush current. Soft start devices are suitable here, which gradually charge the not yet loaded charging capacitor, the smoothing capacitor, to the peak voltage of the power grid.

Soft starters, electronic inrush current limiting circuits or NTC thermistors are used for capacitive switch-on processes .

### Consumers with PTC behavior

Inrush current of a car light bulb

Incandescent lamps and heating coils (e.g. radiant heaters, cathode heating of electron tubes ) are metallic PTC thermistors , they conduct particularly well when they are cold. If they warm up due to the current flowing through them, their ohmic resistance increases, which means that the current only then falls to the nominal value. The higher the working temperature and the purity of the metals in the filament, the higher the inrush current; therefore the inrush current is particularly high for halogen lamps and projection lamps and can exceed 15 times the rated current.

The inrush current of incandescent lamps and heating coils can hardly be reduced by switching them on at the minimum voltage of the alternating voltage, since the process of heating includes several periods of the alternating voltage (see picture above).

Radiators and electric stoves, on the other hand, do not have any increased inrush currents, since their heating elements are made of alloys such as constantan , the resistance of which is only slightly dependent on the temperature, and the working temperatures are lower than with incandescent lamps.

## Countermeasures

There are special devices for limiting the inrush current for electric motors and transformers; they are mentioned in the article soft start . With single-phase AC motors and three-phase motors, phase control provides a remedy (soft start), with three-phase motors also a frequency converter . The classic star-delta starting circuit is also used to limit the starting current for asynchronous squirrel cage three-phase motors .

For smaller transformers and capacitor loads (switched-mode power supplies), an inrush current limiter with NTC thermistor is often connected upstream. Thermistors (URDOX resistance) were also connected upstream of the heating coils of the electron tubes of older tube devices with series heating in order to limit the inrush current - but there they prevented the heating coils from burning through. Transformers can also use a transformer relays are switched without any inrush current. Switching power supplies can with a special design of the transformer relays are switched without inrush current.

Powerful incandescent lamps, which have to be switched on very frequently for stage lighting or lighting organs, for example, are often operated preheated, i.e. only dimmed to such an extent that they just barely shine visibly ( pre-heat ). This measure significantly reduces the inrush current, which not only avoids power surges on the network, but also increases the service life of the incandescent lamps. The Pre Heat reduces the high inrush current from up to 15 times the rated current to around 1.5 to 4 times and reduces the time that elapses when dimming up until full light output.