Electrical Machine Design

WEEK 12: SYNCHRONOUS GENERATOR: ARMATURE DESIGN

For polyphase machines, armature windings can be of the following types:

a) concentric-chain, used in slow-speed, large diameter alternators
b) wave winding, used on wound-rotor induction type motors
c) lap winding, used on high speed synchronous machines.

Concentric-chain winding is where conductors are in a single layer, with each contains one coil side. The lap and wave windings are usually two-layered. The spread of the windings, assuming full-pitch winding, with respect to 180 electrical degrees, is calculated by dividing the degrees by the respective number of phase. Likewise the number of slots per pole should also be divisible by the number of phases.

B. CURRENT DENSITY

The current density in the armature conductors ranges from 2,00 to 3,500 amperes per sq. in. in cross section, with the value of k ranging from 700,000 to 1,000,000, and can be calculated using:

C. TOOTH-SLOT PROPORTION

For tooth pitch, l, greater than 2.5 inches is not recommended, but for large turbo-alternators, the tooth pitch may be from 3 to 3.5 inches. Usually, the tooth pitch can be as small as ¾ in, but nominally it is between one to two inches. The depth of the slot should not exceed three times the width. In three-phase machines, the number of slots per pole per phase is usually from one to four, but in turbo-alternators, with large pole pitch, the number of slots maybe greater.

D. LENGTH PER TURN

The length per turn of the winding will depend on the pitch, t, the gross length of the armature, la, voltage, and the slot dimensions. THe actual overhang beyond the end of core, is approximated through ½[ kv + 3 + t/4 ]. The estimated mean length per turn is calculated by using: 2la + 2.5t + 2kv + 6.

E. FULL LOAD DEVELOPED VOLTAGE

Where PEd is the emf component to counteract the resistance drop in armature winding. The voltage generated is dependent on the IR and IX voltage drops. Although the external power factor angle is zero, there is an angle y, called the internal power-factor angle, between the current vector and the vector of the developed emf.

F. REACTIVE VOLTAGE DROP

F. Reactive Voltage Drop.
The calculation of this drop is based on approximation because it is not always easy to separate armature reactance X from armature reaction, the demagnetizing effect of the armature ampere-turns. For single-layer windings, the end flux is:

Fe = knn_sC_sI_cl' maxwells

Where:
k = a correcting factor depending upon the type of machine, the type of winding, and the proximity of masses of iron tending to reduce the reluctance of the flux paths through the coils. Use k = 1.7 for slow- and medium-speed salient-pole generators and k=3.5 for high speed turbo-generators.
n = the number of phases
n_s = the number of slots per pole per phase
C_s = the number of conductors in each slot
I_c = the current carried by the conductor, C_s
l' = equivalent projection of the armature winding beyond the end of the slots. For single-layer type, approximately this value is equal to 1.27 [kv + 3 + (t/4)] centimeters.

overhang

For double-layer windings, the equivalent overhang, l', is equal to b + ½t(a + c). The amount of the end flux will be about 2/p times the amount which links with the single-layer windings.

The emf induced in the end connections, expressed as a percentage of the developed emf, is:

Percentage (IX)ends = 100 F_e/F

Where:
F = the flux per pole which entering the armature core.

If p is the number of poles of the machine, the total number of conductors per phase is pC_sn_s, and the average voltage developed in the end connections by the cutting of the end flux will be 2fF_e(pC_s n_s)X 10^-3. If the flux distribution is sinusoidal, assume form factor to be 1.11, the voltage component developed per phase, or PEd, in a full-pitch winding, by the cutting of the end flux, is:

(IX)ends = (p/Ö2) fF_e(pC_s n_s) X 10^-8

For fractional-pitch windings, take account of the winding factor, d, considering both coil pitch and width of phase belt. Thus the formula must be multiplied by d².

The final formula for end-connection reactance per phase winding for polyphase synchronous machine with double-layer winding therefore becomes

(IX)ends = n Ö2 kd ²f(C_sn_s)pl' X 10^-8 ohms.

For a single-layer winding, the reactance obtained using the above formula must be multiplied by p/2.

G. TOTAL LOSSES FROM ARMATURE CORE

The losses in iron stampings -- teeth and core are calculated using the total losses curve. The radial depth of the armature stampings is calculated by assuming a reasonable flux density in the iron. This is usually between 50,000 and 60,000 lines per sq. in in 60-cycle machines, increasing to 65,000 or even 70,000 in 25-cycle machines.

The permissible density in the teeth rarely exceeds 100,000 lines per sq. in at 60 cycles and 115,000 lines per sq. in at 25 cycles.

Refer to the Notes for the Illustrative Example: Design of Armature (Stator) of A-C Generator, p. 197-207.