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Power Electronics Handbook, 4th Edition by Muhammad H. Rashid

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15.4.3.3 Model Transformation using Decoupling Matrix

Since the system under discussion is a seven-phase one, the complete model can only be elaborated in seven-dimensional space. The first two-dimensional spaces are d-q, the second one is x1-y1, the third one is x2-y2, and the last is zero-sequence component that is absent due to the assumption of isolated neutral. On the basis of the general decoupling transformation matrix for an n-phase system, inverter voltage space vectors in the second two-dimensional subspace (x1-y1) and third two-dimensional subspace (x2-y2) are determined as

v¯x1y1INV=27va+a¯2vb+a¯4vc+a¯6vd+a¯ve+a¯3vf+a¯5vgv¯x2y2INV=27va+a¯3vb+a¯6vc+a¯2vd+a5¯ve+a¯vf+a¯4vg

  (15.134)

Thus, 128 space vectors of phase-to-neutral voltage ...

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