Pumped hydro storage power plants are a truly renewable solution for large grid-connected energy storage. The evolution toward variable speed operation increases their flexibility and efficiency and ensures their relevance on a changing energy market. Exploiting all possible degrees of freedom in the machine operation as to maximize efficiency of the overall system allows to increase the profitability of the plant. Doing so in real-time on the same hardware-in-the-loop platform used for the validation of the control algorithm saves time and resources. The results presented here are collected from a real-time hardware-in-the-loop platform containing an industrial control platform. This article presents the most energy efficient steady-state and transient operation of an externally excited synchronous machine driven by a matrix modular multilevel converter for a PHSP application. To this end, this work presents a real-time compatible converter loss calculation applicable on the simplified implementation of the converter without the need to model the individual switches.