In this study, a new non-local active compensation method is developed for a multi-microgrid (MMG) system. The current industry practice is to utilise local harmonic current and reactive power compensation methods, however, local compensation methods are not practical for large MMG system with widely dispersed non-linear loads, because each non-linear load would require its own compensator. To overcome this problem, a novel compensating technology called a series-shunt network device (SSND) is installed between a pair of microgrids in the proposed MMG system. The SSND reduces the number of local compensators required while also performing additional functions in comparison with conventional devices. For effective control of the SSND, an improved model predictive control (MPC) algorithm, which gives better tracking accuracy and faster setpoint change than that of a conventional proportional-integral controller, is also presented. Analysis and simulations verify the capability of SSND in performing both local and non-local active compensation of harmonic current and reactive power in the proposed MMG system under various test scenarios. Simulation results show that the MPC-controlled SSND can achieve effective compensation, thereby resulting in a very low current total harmonic distortion value of 2.4% and a unity power factor at the distribution grid side.