**6.1**

Space vectors of three-phase variables, such as the voltage, current, or flux, are very convenient for the analysis and control of induction motors. Voltage space vectors of the voltage source inverter have already been formally introduced in Section 4.5. Here, the physical background of the concept of space vectors is illustrated.

**FIGURE 6.1 Space vector of stator MMF.**

which explains the abc—>dq transformation described by Eq. (4.11). For the stator MMFs,

and

Transformation equations (6.5) and (6.6) apply to all three-phase variables of the induction motor (generally, of any three-phase system), which add up to zero.

Stator MMFs are true (physical) vectors, because their direction and polarity in the real space of the motor can easily be ascertained. Because an MMF is a product of the current in a coil and the number of turns of the coil, the stator current vector, is, can be obtained by dividing «5f by the number of turns in a phase of the stator winding. This is tantamount to applying the abc—»dq transformation to currents, /as, ihs, and ics in individual phase windings of the stator. The stator voltage vector, vs, is obtained using the same transformation to stator phase voltages, vas, vbs, and vcs. It can be argued to which extent is and vs are true vectors, but from the viewpoint of analysis and control of induction motors this issue is irrelevant.

**FIGURE 6.2 Stator currents and voltages: (a) wye-connected stator, (b) delta-connected stator.**

# SPACE VECTORS OF MOTOR VARIABLES (Induction Motor)

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