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Strategy for power or voltage, with proportion-integral (PI) controllers. as shown in Figure 5. In VCC, the d–q decoupling control strategy is realized through four PI controllers. The outputs of the VCC are the dynamic phasors of the fundamental frequency components. Therefore, a fourth-order model can be formulated in order to illustrate the dynamics of PI controllers. d x 1 d t = i dref − i sd d x 2 d t = i qref − i sq d x 3 d t = P ref − P or d x 3 d t = U dcref − U dc d x 4 d t = Q ref − Q or d x 4 d t = U acref − U ac (11) where P ref , Q ref U dcref and U acref are the reference values of active power P, reactive power Q, DC voltage U dc , and AC voltage U ac , respectively. The reference currents i dref and i qref are given below. i dref = k pl P ref − P + k i 1 x 3 or k pl U dcref − U dc + k i 1 x 3 i qref = k p 2 Q ref − Q + k i 2 x 4 or k p 2 U acref − U ac + k i 2 x 4 (12) where k p j and k i j are the proportional constant and integral constant of the jth PI controller, repectively.The outputs of the MMC control system denoted by U cd and U cq are the dynamic phasors of the fundamental frequency components in the d–q frame, as follows u cd = u d − ω L i q − k p 3 i dref − i d − k i 3 x 1 u cq = u q + ω L i d − k p 4 i qref − i q − k i 4 x 2 (13) PLL consists of two PI controllers. The dynamic of the PLL can be described as d x 5 d t