When starting a transformer, have you ever been puzzled by its buzzing sound or baffled by blown fuses and tripped circuit breakers? If you’ve encountered these issues, it’s likely that inrush current within the transformer is to blame. Transformer inrush current refers to the sudden surge of current that occurs when the circuit is first energized, and this surge can be several times higher than the normal operating current. The main cause of this phenomenon is the inductive nature of the transformer: the current in an inductor cannot change instantaneously. Therefore, when the transformer is initially powered on, its inductive impedance and magnetic field are not yet fully established, preventing it from effectively limiting the current flow as it would during normal operation. In that brief moment, the transformer behaves similarly to a short circuit, resulting in inrush current and leading to these unexpected circuit behaviors.
Manage Transformer Inrush Current
Although inrush current in transformers is a common phenomenon, if not properly managed, it can lead to several negative effects. Inrush current can cause the insulation materials of the transformer to degrade, thereby shortening the device’s lifespan; it can lead to temporary voltage drops in the power grid, which may affect the normal operation of other equipment; and it can also reduce the transformer’s operating efficiency, increasing energy consumption. These effects indicate that improper management of transformer inrush current can potentially cause damage to both the transformer itself and the surrounding equipment.
As shown in the figure below, when the AC waveform crosses zero, the current flowing through can be very high, causing the inrush current absorbed by the transformer to exceed the saturation current. In such cases, effective management of transformer inrush current is crucial; otherwise, it could severely impact the magnetic performance of the core.
So, how should we address this issue when we encounter it?
The simplest solution is to incorporate an NTC thermistor into the circuit. As shown in the figure below, we connect the NTC thermistor in series with the input line to limit the inrush current in the transformer.
Transformer Inrush Current Calculation
Now that we understand how to manage inrush current for transformers, a new question arises: What is right NTC thermistor for your circuit? We will complete the calculation through the following 7 simple steps.
- Define Transformer Parameters
When calculating for your own circuit, use the actual parameters. Here, we use a 40VA transformer with the following parameters:
- Rated Power of Transformer: 40VA
- Input Voltage: 110VAC
- Define Inrush Current Assumptions
In the calculation, we will base our assumptions on the following criteria. Depending on the shape of the transformer core, you need to choose “10” or “30” in the first assumption:
- Inrush Current = 30 x Steady-State Current (SSI)
- Maximum Tolerable Inrush Current = 1/5 of Inrush Current
- Frequency = 50Hz
Notes:
- Use the formula 10 x SSI for rectangular cores.
- Use the formula 30 x SSI for toroidal cores.
- The above values are typical values derived from oscilloscope trace analysis.
- The maximum tolerable inrush current can reduce the inrush current by 80%.
- Calculate Steady-State Current
Using the data provided in Step 1, we calculate the transformer’s steady-state current in normal operation.
SSI = KVA of Transformer / Input Voltage = 40VA / 110VAC = 0.364A
- Calculate Inrush Current
Next, we calculate the inrush current generated when the transformer is first powered on, as detailed in Step 2.
Inrush Current = 30 x 0.364 = 10.91A
- Calculate Inductive Impedance
Inductive impedance indicates the degree of opposition to current from the coil and core. Let’s calculate it.
Inductive Impedance (XL) = Peak Voltage / Inrush Current
Inductance = Inductive Impedance / 2π (Frequency)
XL = 110 x 1.414V / 10.91 = 14.25 ohms
L = 14.25 ohms / 2 (3.14160) (50) = 45.4 millihenries
- Calculate Energy Requirement
Next, we calculate the energy required to prevent the thermistor from self-destruction.
Energy = 1/2 x (Inductance) x (Inrush Current)² = 1/2 x 45.4 / 1000 H x (10.91)² = 2.70 Joules
- Calculate Minimum Cold Resistance
Finally, we calculate the minimum cold resistance of the thermistor.
Peak Voltage = 1.14 x Input Voltage
Minimum Cold Resistance of Thermistor = Peak Voltage / Max Tolerable Inrush Current = 110 x 1.414 / (1/5 x 10.91) = 71.30 ohms
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