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

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Modeling and control modes <strong>of</strong> PM synchronous motor drives<br />

M l<br />

U sd<br />

+<br />

−<br />

pbΩmΨsd<br />

∫<br />

Ψ sd<br />

Ψ PM<br />

−<br />

1<br />

L d<br />

I sd<br />

Ψ<br />

sq<br />

I<br />

sd<br />

p b<br />

R s<br />

−<br />

3<br />

p<br />

2 b<br />

M e<br />

−<br />

1<br />

J<br />

∫<br />

Ω m<br />

R s<br />

U sq<br />

−<br />

−<br />

∫<br />

Ψ sq<br />

1<br />

L q<br />

I sq<br />

Ψ<br />

sd<br />

I<br />

sq<br />

pbΩmΨsq<br />

p b<br />

Figure 2.9. Block scheme <strong>of</strong> PM synchronous machine in rotating dq , frame.<br />

Based on equations (2.64-2.67) we can also draw the vector diagram <strong>of</strong> PM<br />

synchronous motor (Fig. 2.10). From this vector representation it can see the positions<br />

<strong>of</strong> the vectors (currents, voltages and fluxes). Especially, power angle φ (angle between<br />

voltage and current vectors) and torque angle defined in two manners: as an angle<br />

between current and rotor flux vectors -δ I<br />

, or as angle between stator flux and rotor<br />

flux vectors -δ Ψ<br />

.<br />

q−axis<br />

β<br />

U s<br />

RI<br />

s<br />

s<br />

I s<br />

Ψ sq<br />

I sq<br />

LI<br />

d sd<br />

ΩΨ<br />

s<br />

s<br />

φ<br />

Ψ s<br />

LqI<br />

sq<br />

I sd<br />

δ I<br />

δ Ψ<br />

θ r<br />

Ψ sd<br />

θ Ψs<br />

Ψ PM<br />

d −axis<br />

rotor<br />

α ( A)<br />

stator<br />

Figure 2.10. <strong>Vector</strong> diagram <strong>of</strong> PM synchronous motor in rotor reference frame dq. ,<br />

24

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