This work presents the characteristics and advantages of using complex controllers applied to space vectors. A mathematical background is presented to show that the harmonic spectrum of a space vector indicates the phase-sequence of each harmonic that composes this vector. As consequence, a reference space vector can be used for applications in which the control system has three-phase reference signals. This approach allows the implementation of complex controllers that present lower order, require less memory elements and have better dynamic response than real controllers. A literature review is made to enable a structural comparison (in terms of computational cost) between several real and complex control schemes based on the internal model principle. Two experimental applications are used to evaluate the performance of complex controllers.
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