This study presents a novel secondary control strategy for a radial microgrid with end-to-end distributed energy resource (DER) interconnections, operating under islanded conditions. The control strategy utilises sparse communication and precludes the presence of a centralised controller. The distributed algorithm has a twofold objective. The first task is to determine the desired power injection at each DER bus for a load change occurring anywhere in the microgrid. The remaining task includes obtaining the bus angle set points at all the DER units such that the actual power injections converge to the desired power injections at each DER bus. The algorithm enables accurate system wide power injection in proportion to the respective DER base ratings. The control strategy is tested on a three-bus, three-DER system with local loads. The controller is shown to work for two different sets of microgrid ratings. The bounds are evaluated for each design parameter specified according to the system nominal ratings to maintain the stability of the distributed algorithm. Proofs are stated to show the convergence of algorithms to the correct power injection solution for all the nodes. Real-time simulation results are presented to corroborate accurate power sharing through the algorithm.