This study presents a comparative study on dynamic behaviour of two different types of wind turbines (WTs) that are widely used in power systems. Mathematical modelling of two types of WTs in the multi-machine power system is presented, and a suitable framework for the study is provided. To compare the cost of provision of stability service by each of two different WTs, a technical–economical two-objective optimisation problem considering damping indices and generation cost will be formulated and solved by multi-objective gravitational search algorithm method. The presented strategy is carried out for each WT and Pareto-optimal curves are extracted. It is shown that in a system with poor dynamic situation, expensive production units are used that this phenomenon will increase generation cost. Generation costs are analysed by considering two WTs, doubly fed asynchronous generator and permanent magnet synchronous generator and dynamic condition for each type are evaluated. Two scenarios are assumed for evaluation; the first one without retuning of stabilisers and the second one with stabilisers retuned due to system generation situation. The proposed scheme is tested on modified 16-machine 5-area network and simulation results are compared.