Electrical Machine Design: Synchronous Generator

WEEK 11: SYNCHRONOUS GENERATOR: GENERAL DESIGN PRINCIPLES

The difference between an AC and a DC Generator is the absence of a commutator in AC. Alternators, or DC Generators, are classified into to two.

a) Machines with Salient Poles. Usually driven at moderate speeds, by belt or direct-couples to reciprocating engines/turbines and whose peripheral speed of the field magnets ranges from 3,000 to 8,000 f.p.m.

b) Machines directly couples to steam turbines. Usually, peripheral speeds reaches the range from 15,000 up to a maximum of 26,000 f.p.m.

B. EMF Developed in Windings

The mean EMF developed is a function of the flux per pole in maxwells, revs per minute and the number of poles.

Ec (mean) = [F x p x N ] / (60 x 10 ⁸)

Where:
F = flux per pole in maxwells
N = revs per minute (rpm)
p = the number of poles.

flux / revolution = F x p
flux / second = F x p ( N / 60)

Effective EMF = Ec x form factor. Where, the form factor is the ratio between the rms value and the mean value or P/(2Ö2), or approximately 1.11.

Distribution Factor (k) Usually equal or less than unity. For a full pitch winding, k is equal to 1.

Where:
n_s = number of slots per pole per phase
b = number of electrical degrees between adjacent slots. Refer to the table below.

Slots per pole	n_s	bo	k
3	1	60	1.000
6	2	30	0.966
9	3	20	0.960
12	4	15	0.958
15	5	12	0.956
18	6	10	0.955

Pitch Factor (k') at fundamental frequency is given by the formula:

Where:
Z = total number of inductors in series per phase
g = coil span in electrical degrees.

If d, winding factor, is equal to k x k' therefore:

E (per phase) = 2.22 d f FZ x 10^-8

C. Power Output

Delta

Wye

E = E_a, I = I_a

E = E_a, I = I_a

At unity power factor, the output:

W = 3E_a x I_a
W = 3E (I / )
W = EI

W = 3E_a x I_a
W = 3 (E/) I
W = EI

Thus, for any power factor:

W = EIcos q

Remember that AC voltages are usually higher than in DC machines. AC can withstand up to 33,000 V but 16,000V is more economical. It could also go up to 16 kV, using step-up transformers, but common applications are pegged at 6.6kV.

D. Pole Properties

At 60 hertz, the pole pitch, t ranges from 6 to 12 inches, with common values used in computations, ranges from 8 to 10 inches. For 25 hertz, the pole pitch, t ranges from 10 to 20 inches. The factor (TI)/p = 12,000 determines the maximum permissible value of the pole pitch, t.

The ratio, r, between the pole arc and the pole pitch, is usually equal to 0.75, more common values ranges from 0.6 to 0.7.

Specific loading, which is dependent on the n, f and voltage, is considered using the following formulas:

Where:
n = number of phases
n_s = number of slots per pole per phase
Cs = number of conductors per slots

Important Note:
1. Small n creates smaller armature diameter but large pole pitch, thus specific loading is smaller. But for large generators, use high values of specific loading to limit the length of the armature and increase critical speed.
2. Low frequency means small iron loss, and more current density.
3. Low emf means less insulation and more room for the copper conductors.
4. When designing an alternator with low voltage, low frequency, and many number of phases, add 20% for the specific loading.

E. Flux Density in Air Gap

The maximum value of air gap is equal to ½pB"g, where B"g is the average density over the pole pitch.

For preliminary calculations, use B"g = 28,000 to 40,000 lines per sq. for 25 hz, and B"g = 24,000 to 25,000 lines per sq. for 60 hz. Remember that the area of pole pitch is defined by the ratio between the flux, F, and the average density over the pole pitch, B"g.

For tooth flux density, use B"t = 115,000 lines per sq. for 25 hz, and B"t = 100,000 lines per sq. for 60 hz. Higher densities are used in some steam-turbine-driven machines, with the view of reducing the size of the motor. Then it is imperative that a good forced ventilation is installed.

The length of the air-gap, d, is dependent on the armature magnetomotive force (mmf), the pole pitch, t, and the specific loading, q. Large air gaps, d, tend to improve regulation, increase magnetic leakage but incurs higher cost due to greater weight of copper conductors. FOr minimum clearance between pole face and armature, d, should approximately equal to 1.25 qt/B"g.

F. Inherent Regulation

Open Circuit Ampere-turn (TI) is equal or less than 1.25 to 1.75 of the Full-Load Ampere-Turn (TI).

The inherent regulation of a generator, at any given load, is defined as the percentage increase in terminal voltage when the load is thrown off, the speed and field excitation remaining constant. This usually lies between 5 and 10 percent at full load on unity power factor, while it may be 20 per cent, or higher, on 85 per cent lagging power factor, with normal full-load current taken from the machines. The regulating qualities of an AC generator depend on both armature reaction and armature reactance, but since these values cannot be made so small, it is rarely aimed to get very good inherent regulation.

Good inherent regulation means that the current on short circuit may be very large. With the exception of high-speed, steam-turbine-driven units, the short circuit current of modern AC generators (with full field excitation) is about three to five times the normal full-load current. Many larger units are purposely designed with large armature reaction and highly inductive windings so that they could withstand momentary short circuits without mechanical injury.