DC MACHINES PROBLEM SET
SEPARATELY-EXCITED GENERATORS
1. The armature of a separately excited dc generator has a resistance of 0.16 ohm.
When run at its rated speed, it yields 132 V on open circuit and 126 V on full
load. How much power is delivered to the external circuit?
DC SERIES GENERATORS
2. A series generator delivers a current of 90 A at 240 V. Its armature and series
field resistances are 0.10 Ω and 0.05 Ω respectively. Find the generated voltage.
DC SHUNT GENERATORS
3. A dc shunt generator is supplying a load of 1.8 kW at 200 V. Its armature and
field resistances are 0.4 Ω and 200 Ω respectively. What is the generated emf?
DC COMPOUND GENERATORS
SHORT-SHUNT COMPOUND GENERATOR
LONG-SHUNT COMPOUND GENERATOR
4. A long shunt compound generator has full load output of 100 kW at 250 V.
Armature resistance 0.05 Ω. Series field resistance 0.03 Ω. Shunt field resistance
55 Ω. Determine the emf generated.
5. A short shunt compound generator supplies a current of 80 A at 110 V. If the
resistance of the armature, shunt field and series field are respectively 0.025 Ω,
40 Ω and 0.02 Ω, Calculate the induced emf.
DC GENERATOR WITH THE DIVERTER RESISTANCE
6. In a compound generator connected short shunt, the terminal voltage is 230 V,
when the generator delivers 150 A. The shunt field current is 2.5 A, armature
resistance 0.032 Ω, series field resistance 0.015 Ω, the diverter resistance 0.030
Ω. Determine power generated in the armature.
PARALLEL OPERATION OF GENERATORS
Case 1: Given internal parameters of the generators like armature resistance, field
resistance, voltage generated, etc
𝐼1 + 𝐼2 = 𝐼𝑡
𝐼𝑎1 = 𝐼1 + 𝐼𝑠ℎ1
𝐼1 = 𝐼𝑎1 − 𝐼𝑠ℎ1
𝐼2 = 𝐼𝑎2 − 𝐼𝑠ℎ2
𝐼𝑎1 + 𝐼𝑎2 = 𝐼𝑡 + 𝐼𝑠ℎ1 + 𝐼𝑠ℎ2
𝐸1 − 𝑉𝐿 𝐸2 − 𝑉𝐿 𝑃𝐿
𝑉𝐿
𝑉𝐿
+
= +
+
𝑅𝑎1
𝑅𝑎2
𝑉𝐿 𝑅𝑠ℎ1 𝑅𝑠ℎ2
𝑃𝑜𝑤𝑒𝑟 𝑠ℎ𝑎𝑟𝑒𝑑 𝑏𝑦 𝐺𝑒𝑛 1 = 𝑉𝐿 𝐼1
𝑃𝑜𝑤𝑒𝑟 𝑠ℎ𝑎𝑟𝑒𝑑 𝑏𝑦 𝐺𝑒𝑛 2 = 𝑉𝐿 𝐼2
7. Two dc shunt generators each having an armature resistance of 0.02 Ω and a
field resistance of 250 Ω operated in parallel to supply a common load of 5000 A.
Determine the common terminal voltage if the induced emf in the two machines
are 500 and 510 volts, respectively.
Case 2: Given external parameters of the generators like voltage regulations, voltage at
no-load, voltage at rated load, rated power, etc
Using similar triangles
Using similar triangles
𝑉𝑁𝐿 −𝑉𝐹𝐿
𝑉𝐿 −𝑉𝐹𝐿
𝑉𝑁𝐿 −𝑉𝐹𝐿
𝐼𝐹𝐿 −𝐼𝐿
𝐼𝐹𝐿
𝐼𝐹𝐿
=
=
𝑉𝑁𝐿 −𝑉𝐿
𝐼𝐿
𝐼𝐿 = 𝐼𝐹𝐿 −
𝐼𝐹𝐿 (𝑉𝐿 −𝑉𝐹𝐿 )
𝑉𝑁𝐿 −𝑉𝐹𝐿
𝐼𝐹𝐿𝐴 (𝑉𝐿 −𝑉𝐹𝐿𝐴 )
𝐼𝐿𝐴 = 𝐼𝐹𝐿𝐴 −
𝑉𝑁𝐿𝐴 −𝑉𝐹𝐿𝐴
𝐼𝐿𝐵 = 𝐼𝐹𝐿𝐵 −
𝐼𝐹𝐿𝐵 (𝑉𝐿 −𝑉𝐹𝐿𝐵 )
𝑉𝑁𝐿𝐵 −𝑉𝐹𝐿𝐵
If %VR is given
𝑉𝑅 =
𝑉𝑁𝐿 −𝑉𝐹𝐿
𝑉
𝑁𝐿
𝐹𝐿
𝑉𝑁𝐿𝐴 −𝑉𝐿
𝐼𝐿𝐴 = (𝐼𝐹𝐿𝐴 )
𝑉𝑁𝐿𝐴 −𝑉𝐹𝐿𝐴
𝑉𝑁𝐿𝐵 −𝑉𝐿
𝐼𝐿𝐵 = (𝐼𝐹𝐿𝐵 ) 𝑉
𝑁𝐿𝐵 −𝑉𝐹𝐿𝐵
If %VR is given
𝑉𝑅 =
𝑉𝐹𝐿
−𝑉
𝐼𝐿 = (𝐼𝐹𝐿 ) 𝑉 𝑁𝐿−𝑉 𝐿
𝑉𝑁𝐿 −𝑉𝐹𝐿
𝑉𝐹𝐿
𝑉𝑁𝐿 − 𝑉𝐹𝐿 = 𝑉𝑅(𝑉𝐹𝐿 )
𝑉𝑁𝐿 − 𝑉𝐹𝐿 = 𝑉𝑅(𝑉𝐹𝐿 )
𝑉𝑅(𝑉𝐹𝐿 )
𝑉𝐿 −𝑉𝐹𝐿
𝑉𝑅(𝑉𝐹𝐿 )
𝐼𝐹𝐿 −𝐼𝐿
𝐼𝐹𝐿
𝐼𝐹𝐿
=
𝐼𝐿 = 𝐼𝐹𝐿 −
𝐼𝐹𝐿 (𝑉𝐿 −𝑉𝐹𝐿 )
𝑉𝑅(𝑉𝐹𝐿 )
𝐼𝐿𝐴 = 𝐼𝐹𝐿𝐴 −
𝐼𝐿𝐵 = 𝐼𝐹𝐿𝐵 −
𝐼𝐹𝐿𝐴 (𝑉𝐿 −𝑉𝐹𝐿𝐴 )
𝑉𝑅𝐴 (𝑉𝐹𝐿𝐴 )
𝐼𝐹𝐿𝐵 (𝑉𝐿 −𝑉𝐹𝐿𝐵 )
𝑉𝑅𝐵 (𝑉𝐹𝐿𝐵 )
𝐼𝐿𝐴 +𝐼𝐿𝐵 = 𝐼𝑡
=
𝑉𝑁𝐿 −𝑉𝐿
𝐼𝐿
𝑉
−𝑉𝐿
𝑁𝐿
𝐼𝐿 = (𝐼𝐹𝐿 ) 𝑉𝑅(𝑉
𝐹𝐿 )
𝑉
−𝑉𝐿
𝐼𝐿𝐴 = (𝐼𝐹𝐿𝐴 ) 𝑉𝑅𝑁𝐿𝐴
(𝑉
𝐴
𝑉
𝐹𝐿𝐴 )
−𝑉𝐿
𝐼𝐿𝐵 = (𝐼𝐹𝐿𝐵 ) 𝑉𝑅𝑁𝐿𝐵
(𝑉
𝐵
𝐹𝐿𝐵 )
𝐼𝐿𝐴 +𝐼𝐿𝐵 = 𝐼𝑡
PW shared by Gen A = 𝐼𝐿𝐴 𝑉𝐿
PW shared by Gen B = 𝐼𝐿𝐵 𝑉𝐿
8. Two shunt generators operate in parallel. Generator A has a terminal voltage of
260 V on no load and 220 V when supplying 30 A. Generator B has a voltage of
270 V on no load and 220 V when supplying 45 A. Calculate the kW shared by
generator A when the total current shared is 65 A.
9. Two generators are operating in parallel to deliver a total current of 240 A. The
rating of the generators are as follows:
Gen 1
Gen 2
Regulation
6%
4%
Rated kW
50
100
Rated V
500
500
Assume a linear characteristic on both machines. Find the current delivered by
each machine.