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This paper investigates the problem of how to effectively smooth the short-term tie-line power fluctuations for grid-connected industrial microgrids (IMGs) from demand side. A wide-area closed-loop control architecture is proposed by directly and continuously modulating load power consumption, e.g., the aluminum electrolysis load. To optimally design the load smoothing controllers, an output regulation approach combined with LQ optimal control is developed. In particular, dominant frequencies of wind power fluctuations are analyzed and incorporated into the exogenous system that models time-varying disturbances. Simulations are conducted for a real industrial microgrid in the Inner Mongolia, China, to validate the practical feasibility and effectiveness of the proposed smoothing control strategy. It is demonstrated that the demand side control based on output regulation is able to achieve not only zero steady error in rejecting the time-varying wind power disturbance but also guarantee the satisfactory dynamic performance of modulated loads for the grid-connected IMG. [ABSTRACT FROM AUTHOR]