The traction force of a kite can be used to drive a cyclic motion for extracting wind energy from the atmosphere. This paper presents a novel quasi-steady modelling framework for predicting the power generated over a full pumping cycle. The cycle is divided into traction, retraction and transition phases, each described by an individual set of analytic equations. The effect of gravity on the airborne system components is included in the framework. A trade-off is made between modelling accuracy and computation speed such that the model is specifically useful for system optimisation and scaling in economic feasibility studies. Simulation results are compared to experimental measurements of a 20 kW kite power system operated up to a tether length of 720 m. Simulation and experiment agree reasonably well, both for moderate and for strong wind conditions, indicating that the effect of gravity has to be taken into account for a predictive performance simulation. • A modelling framework for predicting the power generated by a kite power system.• Included is a technique to estimate aerodynamic properties of the kite from measurement data.• The characteristic system behaviour of the model is compared to experimental data.• The described model provides a realistic estimation of the power conversion.• Gravitational forces can not be neglected when modelling a complete cycle.