The novel MPGD-based photon detectors of COMPASS RICH-1 consist of large-size hybrid MPGDs with multilayer architecture including two layers of Thick-GEMs and a bulk resistive MicroMegas. The top surface of the first THGEM is coated with a CsI film which also acts as photo-cathode. These detectors have been successfully in operation at COMPASS since 2016. Concerning bias-voltage supply, the Thick-GEMs are segmented in order to reduce the energy released in case of occasional discharges, while the MicroMegas anode is segmented into pads individually biased with positive voltage while the micromesh is grounded. In total, there are about ten different electrode types and more than 20000 electrodes supplied by more than 100 HV channels, where appropriate correlations among the applied voltages are required for the correct operation of the detectors. Therefore, a robust control system is mandatory, implemented by a custom designed software package, while commercial power supply units are used. This sophisticated control system allows to protect the detectors against errors by the operator, to monitor and log voltages and currents at 1 Hz rate, and automatically react to detector misbehaviour. In addition, a voltage compensation system has been developed to automatically adjust the biasing voltage according to environmental pressure and temperature variations, to achieve constant gain over time. This development answers to a more general need. In fact, voltage compensation is always a requirement for the stability of gaseous detectors and its need is enhanced in multi-layer ones.In this paper, the HV system and its performance are described in details, as well as the stability of the novel MPGD-based photon detectors during the physics data taking at COMPASS.