*From worst case simulations to a full statistical approach*

*The question of de-rating necessities when IGBT modules are connected in parallel is as old as the device technology. When trying to answer this question, usually the engineer quickly finds himself in a dilemma.*

*By M. Buschkühle, C. Messelke, Infineon Technologies AG*

In the past, several approaches to the subject have been presented including some statistical considerations but up to now nobody answers the crucial question to which probability degree device limits are overrun when less de-rating is done than suggested by the worst-case approach. Infineon’s Monte-Carlo simulation tool can give this information.

### Former approaches (Worst case analyses)

Parameter fluctuations of paralleled switched IGBT-modules cause current imbalances and consequently different module temperatures. Question is to what extent modules may be used when paralleled as compared to a single operation.

Former approaches like “worst case” assumptions derived from data-sheet maximum values end up in de-rating factors which suggest that paralleling is not a good idea at all.

The following example shows a DC-current imbalance calculation of five FF200R12KT3 modules in parallel at a given total current of 700A as can be seen in Figure 1. The environmental Parameters per module are : U_{DC}= 600V, I_{RMS}= 140A, f_{Motor}= 50 HZ, f_{sw}= 6500Hz, and cos φ = 0,9.

If all modules provide exactly typical static and dynamic parameters given in the datasheet the temperature under operation calculates to T_{J}=114°C.

With a saturation voltage all modules at the maximum spec limit the junction temperature increases by 8°C to 122°C.

Next we perform a so called “worst case” approach.

One module (sort 1) has the typical saturation voltage the other four modules (sort 2) are at the maximum spec limit as can be seen in Figure 2.

The module (sort 2) with the typical saturation voltage carries a current of 197A. The maximum junction temperature under switching conditions is exceeded by 10°C to 135°C. The modules at the maximum spec limit take a current of 126A at a junction temperature of 119°C. This matter of fact shows, paralleling under the worst case assumptions is only under excessive de-rating possible. But is this really necessary? How big is the probability? These questions can now be answered as follow.

### Monte-Carlo method

The Monte-Carlo method offers the possibility to observe effects, which come from variations of devices over a large range of samples. The fundaments of this method are random numbers. It is possible to create this numbers via a roulette wheel.

Infineon’s Monte-Carlo simulation tool (Figure 3) generates a set of parameters for each of n paralleled modules.

The following sentences describe the elementary process of the Monte-Carlo simulation step by step.

The first step contains the calculation of the current sharing from the randomly chosen on-state voltages. In the following step of simulation the program adds switching losses at calculated current for each module. Subsequently the calculation of the junction temperature is made by multiplication the further calculated losses with the module’s R_{th}.

The last step is an adjustment between on state and switching losses to the calculated junction temperature.

The Monte-Carlo simulation tool repeats these four steps until the junction temperatures converge for each module. The flow chart in Figure 4 shows the procedure of the losses calculation for a random module configuration.

This displayed process is used for each generated module configuration and via this iterative method a temperature dependencies of all parameters are included.

### Parameter variation

Several parameters and their distribution must be considered to get a simulation close to the reality.

For the current imbalance V_{CEsat} values are appropriate input parameters. Variations of V_{CEsat} are well known from 100% final test data. A typical histogram of the saturation voltage of a 1200V IGBT³ chip is given in Figure 2.

Further reasons for the temperature difference between the paralleled modules are unbalances in the switching behaviour.

There are two main reasons for these asymmetries, first the Chip parameter variations (e.g. variations of the input capacitance, V_{GEth} variations) and on the other side the system parameter variations (e.g. variations in the gate driver stage).

From lab-characterizations the standard deviation of statistical turn-on and turn-off losses is characterized as 5-7% of the typical value.

Besides of the statistical variations of the turn-off losses there is a systematic trade-off relation between E_{off }and the V_{CEsat}. The less the saturation voltage, the more is the turn-off loss of the IGBT chip and vice versa. The trade-off function is also implemented in the Monte-Carlo simulation tool.

As mentioned before, system parameter variations can also influence the turn-on losses. Variations in the gate driver stage have to be taken in the account when they dominate the chip parameter variations. This may be fluctuations of delay or transit times of optocouplers or fluctuations of the gate driver input impedance.

In many cases, the systematic imbalances within a setup dominate over the statistic fluctuations. These imbalances may be asymmetric resistances in the current paths or asymmetric parasites, especially stray inductances.

For exact results of the Monte-Carlo simulation it is very important to get all information about systematic imbalances within the real set-up. The more set up parameter available or known the more exactly are the ppm statements afterwards.

### Simulation Results

As a result the distribution functions of the device currents and the junction temperatures are generated. The following histograms show the results of the Monte-Carlo simulation for the example of five paralleled FF200R12KT3 modules after 40000 simulation runs. The first histogram (Figure 5) shows maximum temperatures within the set of 5 modules. Figure 6 shows a box plot of all five modules and additionally the maximum temperature distribution.

### PPM statements

The results of the simulation allow answering questions like: What is the ppm rate of configuration in which the maximum specified junction temperature will be exceeded? This statement can be very helpful for the customer and helps to choose the adequate module for the application. The distribution of the maximum junction temperatures of the exemplary calculation is equivalent to a logarithmic normal distribution (see next diagram).

With this function and the corresponding standard deviation it is possible to specify a ppm-rate of module configurations which exceed a specified junction temperature.

Based on the calculation at the beginning it is possible to forecast a ppm-rate of paralleled IGBT-modules which exceed the maximum junction temperature (in this case TJ=125°C) of 0.56 ppm. The worst case calculation gives just the maximum value of 135°C.

**Conclusion**

With the method of Monte-Carlo simulation of paralleled IGBT-modules it is possible to calculate current imbalances, switching losses and junction temperatures based on random module parameters and systematic imbalances within a set up.

Based on this results it is possible to calculate expected ppm rates exceeding the maximum junction temperature.

In this given example, the 'worst case' analyses says that it is possible to get 135°C. The Monte Carlo analyses give much more information. Just 0.56 modules per million will exceed the temperature limit of the IGBT. These statements support the developer of converters to find the applicable kind of module for the converter.