Basics: Why is it necessary to perform the precharge resistor calculation?

When a system with DC-link capacitors is turned on, the capacitors are initially uncharged.

For a brief moment, they behave electrically like a short circuit.

Without current limiting, the inrush current can therefore reach extremely high values.

The possible consequences are:

• The main circuit breakers may weld together, stick, and subsequently fail to open.
• The high currents can severely overload the main circuit breakers, semiconductors, and fuses.
• In the worst-case scenario, the hardware may be damaged or destroyed as soon as it is turned on.

Proper calculation and sizing of the precharge resistor limits the inrush current.

This ensures that the capacitors are charged in a controlled manner before the main contactors close.

What formulas do you need to calculate the precharge resistor?

Three key values are required to calculate the precharge resistor:

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

1. Determine the resistance value (R)

The calculation is based on the time constant τ. It describes how quickly a capacitor charges through a resistor.

After 5 * τ, the capacitor has reached approximately 99.3 percent of its final voltage. In electrical engineering, this value is considered to indicate that the capacitor is practically fully charged.

Designing the resistance based on the time constant ensures that the capacitor is fully charged before the main contactors close.

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

2. Check the maximum inrush current (I_max)

The inrush current reaches its peak exactly at (t = 0), that is, at the very moment after power-up. It must not exceed the permissible limits of the contactors and fuses.

• The formula: I_max = U / R

3. Calculate the energy absorption (E)

During the charging process, the resistor converts all of the absorbed energy into heat. This value is often a decisive factor in component selection.

• The formula: E = 0.5 * C * U²

At high DC-link voltages, the energy increases quadratically. This places high demands on the resistor’s pulse withstand capability.

How can you determine the average power dissipation during multiple pre-charges?

If the system turns on repeatedly—for example, three times within 10 seconds—the heat in the resistor accumulates. For an initial estimate, the following applies:

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

If the average power dissipation is too high, the component does not cool down completely between two charging cycles. The temperature rises from cycle to cycle until the resistor becomes thermally overloaded.

What is involved in a complete design?

The calculation alone is not enough. The following specifications must be checked in the resistor’s data sheet:

• the permissible pulse energy as a function of the time constant τ
• the derating behavior, i.e., the reduction in power rating as the ambient temperature rises
• the mounting conditions, including ambient temperature, thermal paste and heat sink

Calculation Example: Precharge Resistor for an 800-Volt System

The following system parameters are used:

• 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, the current limit yields the minimum allowable resistance:

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

The target value is derived from the loading time:

• R_time = t / (5 * C) = 1 s / (5 * 0.001 F) = 200 Ω

The recommended range is therefore between 120 Ω and 200 Ω. A lower value shortens the charging time but increases the inrush current. A higher value reduces wear on the contactors but prolongs the precharge process. Component tolerances must be taken into account during the final selection.

Step 2: Calculate the pulse energy per charging cycle

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

The resistor must convert 320 joules into heat during each precharge cycle. This value forms the basis for the pulse withstand test specified in the data sheet.

In Practice: Why the Choice of Technology Is Crucial

Accurate calculation values are a prerequisite, but no guarantee, for a precharge resistor that will function reliably over the long term. In practice, the physical properties of the component determine whether it can withstand actual operating conditions.

The two most common challenges and their technical solutions:

Challenge 1: High pulse load

Every precharge cycle generates a high amount of energy loss within a few milliseconds. This energy is initially generated inside the resistor. If the material cannot dissipate this localized heat quickly enough, hotspots form that damage the component before the heat even reaches the housing.

Solution: High pulse resistance is crucial. Wire-wound resistors can absorb very high amounts of energy for short periods without sustaining damage. This prevents thermal overload inside the component and enables a compact design combined with high load capacity.

Challenge 2: Heat buildup at high switching frequencies

If the system switches on repeatedly at short intervals, there is little time for cooling between two charging cycles. The residual temperature from the previous cycle adds to the new power dissipation. Over several cycles, the component temperature rises continuously.

Solution: The resistor must be rated for the average power dissipation (P) of the entire operating cycle. Adequate cooling at the installation site is just as important as the component’s rated value itself. 

Do you have specific system parameters and are looking for the right precharge resistor for your application? Or do you have questions about the design?