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Abstract A PID‐inspired accelerated distributed optimal control algorithm is proposed for the economic dispatch problem of a multi‐bus DC microgrid, which contains both conventional generators (CGs) and renewable generators (RGs). Firstly, a constrained optimization problem with the aim of minimizing the power generation cost of the DC microgrid is established. To solve the optimization problem, an accelerated distributed optimal control algorithm in the discrete‐time domain is proposed. The convergence speed of the proposed algorithm is significantly improved compared to the existing distributed optimization algorithms without acceleration terms. More importantly, the communication cost is greatly reduced. The proposed algorithm is in a fully distributed manner, which means each controller only relies on the limited information from neighbouring controllers to achieve optimal cooperative control and bus voltage regulation across multiple buses. Finally, the effectiveness of the proposed algorithm is validated through numerical simulations.