When many power conditioning systems (PCS) of distributed generation are connected to the distribution line, the problem of islanding operation may arise. A grid-connected PCS should detect islanding operation for personnel and equipment safety. However, the islanding detection function might interfere with each other. To cope with this problem, the reactive-power-injection frequency shift islanding detection method (RPIFS-IDM) was developed. Japanese grid-interconnection code claims that RPIFS has enough capability for the detection with less interference. However, the suppression of interference between PCSs using this method has not been explained theoretically. In this paper, the frequency shift by RPIFS is modelled by a recurrence formula, using the amount of active and reactive power imbalance between loads and PCSs as parameters. This model enables to predict the frequency shift of the islanding system. Therefore, it gives the basis of discussions on the interference under the situation where PCSs employing RPIFS are connected intensively.