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Transients in hydropower plants can result in serious disturbances in a plant operation and damage of mechanical and civil components. The best way to prevent such adverse outcomes is to conduct a transient-state analysis using a mathematical model of the hydropower plant system. Based on the collected data on 270 hydropower plants with cross-flow turbines, regression equations were derived that relate a cross-flow turbine specific speed, rated speed, runner diameter and runner width to the rated turbine head and discharge. The obtained equations were used to estimate the turbine performance characteristics using available unit hill charts of three different cross-flow turbines. Finally, the estimated performance characteristics were used to form the boundary condition ‘cross-flow turbine’ within the unsteady 1D mathematical model. The model was validated through case studies by comparing calculated and measured changes in the turbine speed and inlet pressure, induced by sudden load rejection. The difference between the calculated and measured peak pressures was up to 5% during the most critical period, that is, from the moment of load rejection up to the guide vanes closure. In the case of turbine speed, the difference between the peak values was less than 10% in the same period. © The Author(s) 2022.