In a low voltage microgrid， because the impedances of transmission lines and inverters mainly consist of resistances， the output active and reactive powers of a grid-connected inverter can be regulated by respectively adjusting the voltage amplitude and phase. This control strategy has a certain anti-islanding capability. The expressions of phase and amplitude for a parallel RLC load are derived. The reactive power expression of a grid-connected inverter in the islanding mode is given. Based on these expressions， the mathematical model of variable frequency of grid-connected inverter in the islanding mode is developed， and the non-detection zone（NDZ）is obtained. In order to reduce the NDZ， a method with positive frequency feedback is proposed， and the selection principle for coefficient of positive frequency feedback is discussed. Simulation results show the feasibility of the proposed detection method.