The Theory of Automatic Regulators. 
279 
t' 
> 
(13) 
Example. — A 500 kilowatt generator for 550 volts, 910 amperes, at 100 
revolutions per minute, with a shunt resistance of 58"3 ohms, is to be 
regulated by means of a sluggish automatic regulator. We are asked to 
determine the times T and t\ 
The following further data are given : 
Table. 
Load. 
Exciting current. 
a 
L in Henrys.* 
0 R 
0 
8-20 
0-87 
202 
3-45 
1 
4 
8-39 
0-892 
198 
3-39 
1 
2 
8-60 
0-912 
193 
3-29 
f 
8-97 
0-967 
185 
3-17 
1 
1 
9-42 
1-0 
176 
3-02 
* L = J ^ ^ These values depend somewhat on the temperature. 
Suppose now the relay acts when the voltage ife h per cent, above 
or below the normal, or 2S = 1 per cent, and 8 = 0-005, and that the 
maximum load rushes are from 125 to 500 kilowatts. 
We have- 
T ^ 1 ^ /«' 
8 
X 3-23/ 
1 - 0-892 
^0-005 
1 
^ 34 seconds. (For ^ take mean value.) 
This is the time required for the whole range of regulation, i. e. from 
a = 0 to a = 1. Suppose the regulator is so constructed that, when on 
its first contact, the exciting current is 60 per cent, of the maximum value 
(a = 0-6), then the minimum time in which the regulator should be 
allowed to move from the first to the last contact must not be less than 
(1 — 0-6) X 34 = 13-6 seconds. 
The minimum time to be taken by the regulator by passing from a 
contact corresponding to a,„, or J load, and normal voltage, to a contact 
which corresponds to a„ = 1, or full load, is (1 — 0-892) 
seconds. Within this time no load changes must take place. 
The same result is obtained from 
X 34 = 3-7 
to 
^ 2 
> 8 
= {1 - 0-892)3 - 0-0052 
0-005 
3-7 seconds. 
20 
3-23 
9 
