Calculate the final values of field-winding current, load angle, stator d-axis flux linkage, and initialfield-winding current for a torque step from zero to 0.9 per unit at a reduced stator flux-linkage modulus of 0.3 pu using the reference machine parameters from Table 8.1.

Question

Calculate the final values of field-winding current, load angle, stator d-axis flux linkage, and initial field-winding current for a torque step from zero to 0.9 per unit at a reduced stator flux-linkage modulus of 0.3 pu using the reference machine parameters from Table 8.1.

Accepted Answer

According to Equation (8.227), the field-winding current should be

[latex] i_{fref}= \frac{Ψ^{2}_{s ref} +L_{d}L_{sq}\frac{T^{2}_{eref} }{Ψ^{2}_{s ref} } }{L_{md}\sqrt{[Ψ^{2}_{sref}+L^{2}_{q}\frac{T ^{2}_{eref} }{Ψ^{2}_{sref} } ]} } =\frac{0.3^{2}+1.17\cdot 0.57\cdot \frac{0.9^{2} }{0.3^{2} } }{1.05\sqrt{[0.3^{2}+0.57^{2}\cdot \frac{0.9^{2} }{0.3^{2} } ]} } =3.35 [/latex]

The load angle will be as follows.

[latex] \delta _{s1} =atan (\frac{T_{eref}L_{q} }{Ψ^{2}_{sref} } ) = atan (\frac{0.9\cdot 0.57}{0.3^{2} } ) =80 [/latex]

The d-axis stator flux-linkage final component can be solved according to the load angle and the stator flux-linkage modulus.

[latex] Ψ_{d1} = \cos \delta _{s1} \cdot Ψ_{sref} =\cos 80° \cdot 0.3 = 0.052 [/latex]

Finally, the d-axis current components can be solved from Equation(8.226) and Equation(8.227).

[latex] i_{d1} =\frac{Ψ_{d1}- L_{md}i_{f1} }{L_{d} } = \frac{0.052- 1.05\cdot 3.35}{1.17} =- 2.96 [/latex]

[latex] i_{f0} = \frac{L_{d}(i_{f1}+i_{d1} )-Ψ_{d0} }{L_{d}- L_{md} } = \frac{1.17\cdot (3.35-2.96)-0.3}{1.17-1.05} = 1.3 [/latex]

Question 8.2: Calculate the final values of field-winding current, load an...

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