The modular multilevel converter is composed of many equal submodules connected in series, each having to ideally withstand the same voltage and current stresses. The resulting configuration when each SM capacitor feeds its own auxiliary power supply is unstable during at least part of the converter precharge process. SM capacitor voltages can diverge until a protection trips in. The system can be stabilized by adding a balancing resistor in parallel to each SM capacitor. In this work, models for the dc-side precharge of the modular multilevel converter are proposed and its dynamics are analyzed in depth. The worst case parameter combination is found by running the models for all possible combinations within certain discrete ranges. A conservative estimation of the balancing resistor value is proposed by analysis of the results.