1) A 50 Hz, 3.75 MVA, 3.18 kV, three-phase synchronous generator with rated curr

Question

1) A 50 Hz, 3.75 MVA, 3.18 kV, three-phase synchronous generator with rated current of In = 682 A has open- and short-circuit characteristic listed in Table 1 and Table 2 respectively. Determine saturated and unsaturated synchronous reactance in per-unit and in Ohms and calulate short circuit ratio. The generator is delivering rated power at 0.95 power factor leading at the rated therminal voltage. Using given open-circuit characteristic approximately determine the field current under rated loading Table 1: Problem 1: short-circuit characteristic Field Current If A 80 Table 2: Problem 1: open-circuit characteristic Field Current I A 20 88100 120 140 160 180 200 220

Explanation / Answer

Unsaturated Synchronous reactance:

When the value of the Field current is lower , then the machine is said to be unsaturated. Thus the corresponding synchronous Reactance value is known as the unsaturated synchronous reactance.

The unsaturated synchronous reactance is given by,

Xs,u = Voc / ISC |(at same If )

we need Voc at If = 80 ( since short circuit characteristics is given at If = 80 only)   

// taken If = 80 ie .we need low value of If

to find the Voc at If = 80, find the slope of the curve

slope = 3440/88 = 39.09

Voc at If = 80 , = 80 * slope = 80 * 39.09

= 3127.273 volts

in per unit ,

= 3127.273 / 3180

= 0.983 per unit.

the short circuit current at If = 80 is 620 A (given in table1)

ISC = 620A

in per unit

ISC / Ir= 620 / 682 = 0.909 per unit.

now the unsaturated synchronous reactance ,

Xs,u = Voc / ISC | (at same If )

= 0.983 / 0.909

= 1.081 per unit.

to find it in ohms lets find zbase,

Zbase = Vbase 2 / Sbase

= (3.18*103)2 / (3.75 * 106 )

= 2.696 ohm

unsaturated synchronous reactance (in ohms) = 1.081 * 2.696 = 2.914 ohms

Saturated Synchronous Reactance:

The saturated synchronous reactance is defined as the reciprocal of the short circuit ratio.

short circuit ratio is defined as the ratio of the amount of field current that results in rated armature voltage divided by the amount of field current that results in rated armature current,

this can be obtained by,

Field current when Voc = 3180 , = 100/3660(slope from table2) * 3180 = 0.0273*3180

= 86.885 A

also we need Field current when Irated = 682 , = 80 / 620 (slope from table1) * 682

= 88 A

therefore short circuit Ratio SCR = 86.885 / 88

= 0.987

now saturated Synchronous Reactance = 1 / SCR = 1 / 0.987

= 1.013 per unit.

= 1.013 * 2.696 = 2.731 ohms

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