In state-of-the-art energy systems modelling, reservoir hydropower is represented as any other thermal power plant: energy production is constrained by the plant's installed capacity and a capacity factor calibrated on the energy produced in previous years. Natural water resource variability across different temporal scales and the subsequent filtering effect of water storage mass balances are not accounted for, leading to biased optimal power dispatch strategies. In this work, we aim at introducing a novelty in the field by advancing the representation of reservoir hydropower generation in energy systems modelling by explicitly including the most relevant hydrological constraints, such as time-dependent water availability, hydraulic head, evaporation losses, and cascade releases. This advanced characterization is implemented in an open-source energy modelling framework. The improved model is then demonstrated on the Zambezi River Basin in the South Africa Power Pool. The basin has an estimated hydropower potential of 20,000 megawatts (MW) of which about 5,000 MW has been already developed. Results show a better alignment of electricity production with observed data, with a reduction of estimated hydropower production up to 35% with respect to the baseline Calliope implementation. These improvements are useful to support hydropower management and planning capacity expansion in countries richly endowed with water resource or that are already strongly relying on hydropower for electricity production.