The Basics: Why do you need the precharge resistor calculation?

The moment you turn on a system with DC-link capacitors, they are discharged. Physically speaking, they act like a short circuit for that split second.

Without a limiting resistor, the inrush current would spike to extremely high levels.

The practical consequences:

• Welded contacts: The main contactors can stick together and can no longer be opened.
• Component stress: Main contactors, semiconductors, and fuses are severely overloaded.
• System failure: In the worst-case scenario, the hardware is destroyed immediately upon power-up.

By correctly calculating and sizing the precharge resistor, we ensure that the capacitor is charged in a controlled manner before the main contactors close.

What formulas are needed for the precharge resistor calculation?

To perform accurate precharge resistor calculation, we use three key values:

• the capacity (C)
• the system voltage (U)
• the desired charging time (t)

1. Determine the resistance value (R)

We use the time constant τ for this purpose. In electrical engineering, a capacitor is considered charged after a time of 5 * τ.

If you perform a precharge resistor calculation based on this, you will ensure that the circuit is fully charged before the main contactors are energized.

• The formula: R = t / (5 * C)
• Example: If a 2,000 µF capacitor is to be charged in 1 s, we calculate: 1 s / (5 * 0.002 F) = 100 Ω

Calculate energy intake (E)

You must also determine this value when performing the precharge resistor calculation, as it is often the deciding factor in component selection.

The resistor must be able to convert all the energy from the charging process into heat without being damaged.

• The formula: E = 0.5 * C * U²
• Especially with high voltages in the DC link, this can quickly result in significant values, which require the resistor to have a high pulse withstand capability.

How do you calculate the average power when the device is repeatedly turned on and off?

If the system preloads regularly (e.g., 3 times in 10 seconds), a rough estimate is:

P_avg =(E_sum)/(t_sum)=3*E /10 s

This average temperature rise determines whether heat “builds up” (keywords: cycling/heat buildup) and causes the component to overheat.

What else is required in practice?

Be sure to check the following in the datasheet:

• Permissible pulse energy as a function of the time constant τ
• Derating (power reduction at elevated temperatures)
• Installation conditions (ambient temperature, thermal paste, heat sink)

A concrete example of a calculation from real-world practice

To illustrate the precharge resistor calculation in practice, let’s consider the following scenario:

• System voltage (U): 800 V
• Intermediate circuit capacitance (C): 1000 µF (0.001 F)
• Desired charging time (t): 1 s
• Maximum current (I_max): 6 A (limited by contactors/fuses)

Step 1: Determine the resistance value

First, we check the minimum allowable resistance based on the current limit:

• R_min = U / I_max = 800 V / 6 A = 120 Ω

We then calculate the value based on the time limit:

• R_zeit = t / (5 * C) = 1 s / (5 * 0,001 F) = 200 Ω

In this case, a resistance of 120 Ω to 200 Ω is ideal. Depending on your priorities (faster charging vs. lower inrush current), you could choose a lower or higher value here. Important: Don’t forget to account for component tolerances!

Step 2: Calculate the energy per precharge cycle

This value is critical for component selection during the precharge resistor calculation:

• E = 0,5 * C * U² = 0,5 * 0,001 F * (800 V)² = 320 J

In Practice: why technology is the key to success

Simply performing the precharge resistor calculation is just theory. In practice, physical details often determine whether a resistor will last.

Here are the two most common challenges and how to solve them using technology:

Challenge 1: Extreme Pulse Loads

During precharging, an enormous amount of energy (E) must be absorbed in a matter of milliseconds. A conventional resistor can be damaged by this localized heat inside the device even before the heat reaches the housing.

✓ The solution: Ensure high pulse resistance. Technologies such as wire-wound resistors can absorb very high amounts of energy in a very short time without sustaining damage. This prevents hotspots and enables reliable operation in a compact design.

Challenge 2: High clock speeds and heat buildup

If the system is turned on and off frequently, the resistor cannot cool down completely between cycles. Heat builds up.

✓ The solution: Choose a resistor with a high average power rating (P) and ensure adequate cooling.