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Direct Torque Control with Space Vector Modulation (DTC-SVM) of ...

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Sensorless Speed <strong>Direct</strong> <strong>Torque</strong> <strong>Control</strong> <strong>with</strong> <strong>Space</strong> <strong>Vector</strong> <strong>Modulation</strong> (<strong>DTC</strong>-<strong>SVM</strong>)<br />

I<br />

=∆ I sin 2γ<br />

(6.4)<br />

sβ<br />

s m<br />

where I<br />

s<br />

is DC component in Is<br />

α<br />

and<br />

∆ Is<br />

amplitude <strong>of</strong> fluctuated component.<br />

The current components in α,<br />

β can be modeled as an average value <strong>of</strong> I<br />

s<br />

plus some<br />

<strong>of</strong>fset value<br />

∆<br />

Is<br />

, as a function <strong>of</strong> the mechanical position γ m<br />

. Fig. 6.4 shows the<br />

current components given in Eq. (6.1-2), which are function <strong>of</strong> the phase angle 2γ m<br />

.<br />

Solving those Eqs. (6.1 and 6.2) in respect to mechanical rotor position, two domains <strong>of</strong><br />

mechanical rotor position can be obtained as:<br />

Isβ<br />

γ<br />

m1<br />

=<br />

(6.5)<br />

2( I − I )<br />

sα<br />

s<br />

= Isβ<br />

γ<br />

m2<br />

2( I − I )<br />

+ π (6.6)<br />

sα<br />

s<br />

The estimated rotor positions for other combination <strong>of</strong> sign( I s<br />

)<br />

summarized in Table 6.7.<br />

+ and sign( I s<br />

)<br />

− are<br />

15π<br />

π<br />

−<br />

8 8<br />

7π<br />

9π<br />

−<br />

8 8<br />

π 3π<br />

−<br />

8 8<br />

9π<br />

11π<br />

−<br />

8 8<br />

3π<br />

5π<br />

−<br />

8 8<br />

11π<br />

13π<br />

−<br />

8 8<br />

5π<br />

7π<br />

−<br />

8 8<br />

13π<br />

15π<br />

−<br />

8 8<br />

I sα − I s + I sβ<br />

+ +<br />

+ −<br />

−<br />

−<br />

−<br />

I sα<br />

− I s − I sβ<br />

γ m<br />

+<br />

I sβ<br />

2(<br />

I sα<br />

− I s )<br />

I sβ<br />

+ π<br />

2(<br />

I sα<br />

− I s )<br />

I sα<br />

+ I s π<br />

− +<br />

2I<br />

sβ<br />

4<br />

I sα<br />

+ I s 5π<br />

− +<br />

2I<br />

sβ<br />

4<br />

I sβ<br />

π<br />

+<br />

2( I s α − I s ) 2<br />

I sβ<br />

3π<br />

+<br />

2( I s α − I s ) 2<br />

I sα<br />

+ I s 3π<br />

− +<br />

2I<br />

sβ<br />

4<br />

I sα<br />

+ I s 7π<br />

− +<br />

2I<br />

sβ<br />

4<br />

Table 6.7. Mechanical rotor position calculations.<br />

Long pulsewise voltage test<br />

This test help us to choose the proper estimated value <strong>of</strong> mechanical rotor position from<br />

two values calculated during the short pulse wise voltage test.<br />

126

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