In a multi-terminal HVDC power transmission network (10) comprising at least three HVDC converter stations (1 to 6) interconnected by at least two transmission lines (12, 14, 16, 18, 20), where at least one of the transmission lines is a long line, an active voltage source device (30) is series connected to one of the transmission lines (20), which maintains the DC voltage of the transmission lines of the network to be within a predefined voltage range by injecting an additional DC voltage in series with the one transmission line (20).