One of critical concerns in the operation of grid-connected dispersed generating units is the occurrence of islanding. It is known that the islanding may pose hazards to utility personnel and complicate the orderly reconnection of grid. Hence, in this paper, a new algorithm based on the monitoring of the change in partial derivativef/partial derivativeP(L) to detect the islanding is proposed. By the proposed method, a detection index can be evaluated that serves as a useful reference to activate the protective relays. This approach has been applied to investigate different scenarios, including the loss of grid and the parallel operation. Effects of load change and power-quality disturbances to the detection performance are also examined. From these test results, they help solidity the feasibility and effectiveness of the approach for the applications considered.