Active power curtailment is a cost-effective technique for mitigating overvoltage issues as a consequence of distributed generation. However, many solutions treat prosumers at highly sensitive parts of the grid unfairly. The best solution to this problem is to explore the non-linear behavior between active power and voltage to find the fair amount of power that needs to be curtailed to satisfy grid codes. Current state-of-the-art techniques for power curtailment are computationally expensive and case-specific. In this work, a fair value for power curtailment is achieved analytically that is both computationally efficient and generic. The results obtained analytically are validated utilizing an iterative algorithm, which provides a near optimal value for fair power curtailment. The results demonstrate that for single-phase and balanced three-phase networks, analytical and iterative methods have similar control actions and there is a 50% increase in distributed generation infeed at sensitive parts of the grid.