A new approach to predict the additional costs of reactive power system services delivered by large hydrogenerators is proposed in this letter. It is based on the application of the accumulated average efficiency (AAE), which has recently been proposed. An optimal operational path within the capability diagram with minimal losses is derived. This path can be used to calculate additional losses from operational regimes deviating from the optimal one for each active power level. Finally, the additional losses are accumulated in a similar manner as the AAE to estimate the extra cost of the operational regime, with ideal operation as the reference. In addition, the accuracy of a data clustering approach is explored to speed up the computation of the AAE and the accumulation of additional costs.