The synchronous reactance of a cylindrical-rotor machine is 1.2 per unit (p.u.). The machine is connected to an infinite bus whose voltage is 1 p.u. through an equivalent reactance of 0.3 p.u. For a power output of 0.7 p.u., the power angle is found to be 30 deg. (a) Find the excitation voltage, Ef

Question

The synchronous reactance of a cylindrical-rotor machine is 1.2 per unit (p.u.). The machine is connected to an infinite bus whose voltage is 1 p.u. through an equivalent reactance of 0.3 p.u. For a power output of 0.7 p.u., the power angle is found to be 30 deg.

(a) Find the excitation voltage, [latex]E_{f}[/latex] , and the pull-out power.

(b) For the same power output, the power angle is to be reduced to 25 deg. Find the value of the reduced equivalent reactance connecting the machine to the bus to achieve this. What would be the new pull-out power?

Accepted Answer

(a) We are given

[latex]\begin{array}{l}{{X_{t}=1.5~{\mathrm{p.u.}}}}\ {{P=P_{\mathrm{max}}\sin\delta}}\ {{0.7=P_{\mathrm{max}}\sin30 \mathrm{deg}}}\end{array}[/latex]

Hence

[latex]P_{\mathrm{max}}=1.4 \mathrm{p.u.}[/latex]

Thus we calculate

[latex]1.4={\frac{E_{f}(1)}{1.5}} \ E_{f}=2.1[/latex]

(b) We use the power relation

[latex]0.7=P_{\mathrm{max}}\sin25\,\mathrm{deg} \ P_{\mathrm{max}}=1.66 \ 1.66={\frac{E_{f}V}{X_{n e w}}}={\frac{2.1(1)}{X_{n e w}}} \ X_{n e w}={\frac{2.1}{1.66}}=1.27{\mathrm{~p.u.}} \ x_{e}=1.27-1.2=0.07{\mathrm{~p.u}}.[/latex]

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