A method of operating a thyristor-based line-commutated multi-phase power converter on a multi-phase AC voltage connection point, which is supplied by an AC voltage network. Between the AC voltage connection point and an AC voltage connection of the power converter, a series circuit of modules is arranged for each phase. Each of the series circuits has a first electronic switching element, a second electronic switching element, and an electric energy storage device. The voltages of the phases of the AC voltage connection point are measured and, if an undervoltage is detected on a phase of the AC voltage connection point, an additional voltage adding to the voltage of that phase is generated by way of the series circuit of modules allocated to that phase in such a way that the voltage of that phase is increased, at least temporarily.