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ELECTRICAL MACHINES 1
CIA-II ANSWER KEY
Part B
15 a i)
Determination of Efficiency
The efficiency of DC machine like any other machine is determined by the ratio of output power
to that of the input power.
There are three methods of determining the efficiency of a machine.
1.
2.
3.
Direct method
Indirect method
Regenerative method
The 1st equation is giving an idea about the direct estimation of the efficiency. In this method
the machine is fully loaded and the output is directly measured. This method of measurement is
only applied for the small machines. The 2nd and 3rd equations are giving an idea about the
indirect estimation of the efficiency. Indirect method is helpful of determining the efficiency of
shunt wound generator and compound wound generators. In this method it is required to
determine to determine the losses only. So, power supply is required to supply the losses only
without loading the machine. For the regenerative method of determining efficiency, it is
required to have two identical machines. One machine is used as motor and drives the other and
the other is used as generator and feedback the power into the supply. Two machines are
mechanically coupled. Therefore the losses can be determined because the internal power drawn
is only to supply losses of the two machines. Except these testes, the insulation test and the test
for making the commutation satisfactory is done while building up the machine.
ii) Losses of a DC machines
Copper Losses or Electrical Losses in DC Machine or Winding Loss
The copper losses are the winding losses taking place during the current flowing through the
winding. These losses occur due to the resistance in the winding. In DC machine, there are only
two winding, armature and field winding. Thus copper losses categories in three parts; armature
loss, field winding loss, and brush contact resistance loss. The copper losses are proportional to
square of the current flowing through the winding.
Armature Copper Loss in DC Machine
Armature copper loss = Ia2Ra Where, Ia is armature current and Ra is armature resistance. These
losses are about 30% of the total full load losses.
Field Winding Copper Loss in DC Machine
Field winding copper loss = If2Rf Where, If is field current and Rf is field resistance. These
losses are about 25% theoretically, but practically it is constant.

15) b)
Hopkinsons Test
Hopkinson's Test is another useful method of testing the efficiency of a DC machine. It is a
full load test and it requires two identical machines which are coupled to each other. One of these
two machines is operated as a generator to supply the mechanical power to the motor and the
other is operated as a motor to drive the generator. For this process of back to back driving the
motor and the generator, Hopkinson's test is also called back-to-back test or regenerative test.If
there are no losses in the machine, then no external power supply would have needed. But due to
the drop in the generator output voltage we need an extra voltage source to supply the proper
input voltage to the motor. Hence, the power drawn from the external supply is therefore used to
overcome the internal losses of the motor-generator set. Hopkinson’s test is also called
regenerative test or back to back test or heat run test.
Connection Diagram of Hopkinson's Test
Here is a circuit connection for the Hopkinson's test shown in figure below. A motor and a
generator, both identical, are coupled together. When the machine is started it is started as motor.
The shunt field resistance of the machine is adjusted so that the motor can run at its rated speed.
The generator voltage is now made equal to the supply voltage by adjusting the shunt field
resistance connected across the generator. This equality of these two voltages of generator and
supply is indicated by the voltmeter as it gives a zero reading at this point connected across the
switch. The machine can run at rated speed and at desired load by varying the field currents of
the motor and the generator.

Calculation of Efficiency by Hopkinson's Test
Let, V = supply voltage of the machines
Then, Motor input = V(I1 + I2) I1 = The current from the generator I2 = The current from the
external source And, Generator output = VI1..................(1) Let, both machines are operating at
the same efficiency 'η'. Then, Output of motor = η x input = η x V(I1 + I2) Input to generator =
Output of the motor = η X V(I1 + I2) Output of generator = η x input = η x [η x V(I1 + I2)] = η2
V(I1 + I2)..................(2) From equation 1 an 2 we get, VI1 = η2 V(I1 + I2) or I1 = η2 (I1 + I2)
Now, in case of motor, armature copper loss in the motor = (I1 + I2 I4) Ra. Ra is the armature resistance of both motor and generator. I4 is the shunt field current of
the motor. Shunt field copper loss in the motor will be = VI4
2
Next, in case of generator armature copper loss in generator = (I1 + I3)2Ra I3 is the shunt field
current of the generator. Shunt field copper loss in the generator = VI3 Now, Power drawn from
the external supply = VI2 Therefore, the stray losses in both machines will be W = VI2 - (I1 + I2 I4)2 Ra + VI4 + (I1 + I3)2 Ra + VI3 Let us assume that the stray losses will be same for both the
machines. Then, Stray loss / machine = W/2
Efficiency of Generator
Total losses in the generator, WG = (I1 + I3)2 Ra + VI3 + W/2 Generator output = VI1 Then,
efficiency of the generator,
Efficiency of Motor
Total losses in the motor, WM = (I1 + I2 - I4)2 Ra + VI4 + W/2 Motor input = V(I1 + I2) Then,
efficiency of the motor,
Advantages of Hopkinson's Test
The merits of this test are…
1.
This test requires very small power compared to full-load power of the motor-generator
coupled system. That is why it is economical. Large machines can be tested at rated load
without much power consumption.
2.
Temperature rise and commutation can be observed and maintained in the limit because
this test is done under full load condition.
3.
Change in iron loss due to flux distortion can be taken into account due to the advantage
of its full load condition.
4.
Efficiency at different loads can be determined.
Disadvantages of Hopkinson's Test
The demerits of this test are
1.
2.
3.
It is difficult to find two identical machines needed for Hopkinson's test.
Both machines cannot be loaded equally all the time.
It is not possible to get separate iron losses for the two machines though they are different
because of their excitations.

4.
It is difficult to operate the machines at rated speed because field currents vary widely.
16) a)
These two tests are performed on a transformer to determine
1.
2.
3.
equivalent circuit of transformer
voltage regulation of transformer
efficiency of transformer. The power required for these open circuit test and short
circuit test on transformer is equal to the power loss occurring in the transformer.
Open Circuit Test on Transformer
The connection diagram for open circuit test on transformer is shown in the figure. A
voltmeter, wattmeter, and an ammeter are connected in LV side of the transformer as shown. The
voltage at rated frequency is applied to that LV side with the help of a variac of variable ratio
auto transformer.
The HV side of the transformer is kept open. Now with the help of variac, applied voltage gets
slowly increased until the voltmeter gives reading equal to the rated voltage of the LV side. After
reaching at rated LV side voltage, all three instruments reading (Voltmeter, Ammeter and
Wattmeter readings) are recorded.
The ammeter reading gives the no load current Ie. As no load current Ie is quite small compared
to rated current of the transformer, the voltage drops due to this current that can be taken as
negligible. Since, voltmeter reading V1 can be considered equal to secondary induced voltage of
the transformer, the input power during test is indicated by watt-meter reading. As the
transformer is open circuited, there is no output, hence the input power here consists of core
losses in transformer and copper loss in transformer during no load condition. But as said earlier,
the no load current in the transformer is quite small compared to full load current, so copper loss
due to the small no load current can be neglected. Hence, the wattmeter reading can be taken as
equal to core losses in transformer. Let us consider wattmeter reading is Po.
Where Rm
is shunt branch resistance of transformer. If, Zm is shunt branch impedance of transformer.
Therefore,
if
shunt
branch
reactance
of
transformer
is
Xm,
These values are referred to the LV side of
transformer as because the test is conduced on LV side of transformer. These values could easily
be referred to HV side by multiplying these values with square of transformation ratio.

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