In aerospace applications, a ground power unit has to provide balanced and sinusoidal $\text{400}\,\text{Hz}$ phase-to-neutral voltages to unbalanced and nonlinear single-phase loads. Compensation of high-order harmonics is complex, as the ratio between the sampling frequency and compensated harmonics can be very small. Thus, multiple superimposed resonant controllers or proportional-integral (PI) nested controllers in multiple $dq$ frames are not good alternatives. The first approach cannot ensure stability, while the second cannot track the sinusoidal zero-sequence components typically present in unbalanced systems, and unattainably high bandwidth at the inner current control loop is typically required. In this paper, a simple methodology for designing a single-loop, multiple resonant controller for simultaneous mitigation of several high-order harmonics, ensuring stability, is presented. Experimental results, based on a 6 kW four-leg neutral point clamped converter, validate the proposed controller design, showing excellent steady-state and transient performance.