This paper examines the possibility of providing reactive power support to the grid from wind farms (WFs) as a part of the ancillary service provisions. Detailed analysis of the WF capability curve is carried out considering maximum hourly variation of wind power from the forecasted value. Different cost components are identified, and subsequently, a generalized reactive power cost model is developed for wind turbine generators that can help the independent system operator (ISO) in managing the system and the grid efficiently. Apart from the fixed cost and the cost of loss components, a new method is proposed to calculate the opportunity cost component for a WF considering hourly wind variations. The Cigre 32-bus test system is used to demonstrate a case study showing the implementation of the developed model in short-term system operations. A finding is that higher wind speed prediction errors (a site with high degree of wind fluctuations) may lead to increased payments to the WFs for this service, mainly due to the increased lost opportunity cost (LOC) component. In a demonstrated case, it is found that 2340 $/h is paid to the WF as the LOC payment only, when the wind prediction error is 0.5 per unit (p.u.), whereas 54 $/h is the expected total payment to the WF when the prediction error is 0.2 p.u. for its reactive power service.