Page 112 - Solutions Manual to accompany Electric Machinery Fundamentals

Note: An electronic version of the saturated open circuit characteristic can be found
in file p42_occ.dat, and an electronic version of the air-gap characteristic
can be found in file p42_ag_occ.dat. These files can be used with
MATLAB programs. Column 1 contains field current in amps, and column 2
contains open-circuit terminal voltage in volts. An electronic version of the
short circuit characteristic can be found in file p42_scc.dat. Column 1
contains field current in amps, and column 2 contains short-circuit terminal
current in amps.

4-16. (a) What is the saturated synchronous reactance of this generator at the rated conditions? (b) What is the
unsaturated synchronous reactance of this generator? (c) Plot the saturated synchronous reactance of this
generator as a function of load.
SOLUTION

(a) The rated armature current for this generator is
S 500 kVA
I  A I  L   90.2 A
3 T 3  V 3200 V

The field current required to produce this much short-circuit current may be read from the SCC. It is 0.70
1
2
A . The open circuit voltage at 0.70 A is 2447 V , so the open-circuit phase voltage (= E ) is 2447/ 3
A
= 1313 V. The approximate saturated synchronous reactance X is
S
1413 V
X   15.7 
S
90.2 A
(b) The unsaturated synchronous reactance X is the ratio of the air-gap line to the SCC. This is a
Su
straight line, so we can determine its value by comparing the ratio of the air-gap voltage to the short-
circuit current at any given field current. For example, at I = 1.5 A, the air-gap line voltage is 4470 V,
F
and the SCC is 175 A.

4470 V / 3
X   14.75 
Su
175 A
(c) This task can best be performed with MATLAB. The open-circuit characteristic is available in a file
called p42_occ.dat, and the short-circuit characteristic is available in a file called p42_scc.dat.
Each of these files are organized in two columns, where the first column is field current and the second

1 If you have MATLAB available, you can use the file p42_scc.dat and the interp1 function to look up this
value as shown below. Note that column 1 of p42_scc contains field current, and column 2 contains short-circuit
terminal current.
load p42_scc.dat
if1 = interp1(p42_scc(:,2),p42_scc(:,1),90.2)
if1 =
0.7032

2 If you have MATLAB available, you can use the file p42_occ.dat and the interp1 function to look up this
value as shown below. Note that column 1 of p42_occ contains field current, and column 2 contains open-circuit
terminal voltage.
load p42_occ.dat
vt = interp1(p42_occ(:,1),p42_occ(:,2),0.70)
vt =
2447

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