Factors Affecting Alternator Size

Efficiency increases as power increases

1 KW \(\Rightarrow \eta = 50\%\) whereas 10 MW \(\Rightarrow \eta = 90\%\)

1000 MW and above \(\Rightarrow \eta = 99\%\)

power output per kilogram increases as power increases

1 KW weighs 20 Kg (i.e. 50 W/Kg), then, 10 MW weighing 20,000 Kg yield 500 W/Kg

Conclusion: Larger alternator weigh relatively less than smaller ones and are consequently cheaper

As size increases cooling problem (high power loss per unit surface area)

Effective cooling system (cost increases, sets upper limit)

50 MW (cold air), 50-300 MW (Hydrogen cooling), 1000 MW (hollow water-cooled conductors)

Low speed alternator are bigger than high speed alternators of the same power

\(\checkmark\) Like dc gen, as , also varies, due to the following :

voltage drop/phase \(I_aR_a\) in phase with \(I_a\)

practically negligible

\(\Phi\) setup by \(I_a\) do not cross the air-gap but take different paths, known as

\(\Phi_L\) independent of saturation but dependent on \(I_a\)

\(\Phi_L\) sets up reactance emf which is ahead of \(I\) by \(90^{\circ}\)

of the load has a considerable effect on the armature reaction

Combined MMF wave is sinusoidal which

moves synchronously, fixed relative to the poles,

amplitude \(\propto\) load current,

position depends on p.f. of the load

, less emf

field excitation need to be increased to compensate the weakening

, more emf

field excitation need to be reduced

partly distortional and partly demagnetising

\[X_s = X_L+X_a^{\ast}\] \(^\ast\) The ohmic value of \(X_a\) varies with the p.f. the load because armature reaction depends on load p.f.

\[Z_s=R_a+jX_s\]

For different loading: