EE313 - The transformer

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Title: The transformer

Aim: To perform the open-circuit test, short-circuit test and load test in order to;

1. Determine its equivalent circuit parameters

2. Predict its performance characteristics on load

3. Compare predicted results with actual performance results

Apparatus: See your laboratory manual for the apparatus.

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THEORY:

 Open Circuit and Short Circuit Tests on Single Phase Transformer

       The efficiency and regulation of a transformer on any load condition and at any power factor condition can be predetermined by indirect loading method. In this method, the actual load is not used on transformer. But the equivalent circuit parameters of a transformer are determined by conducting two tests on a transformer which are,

1. Open circuit test (O.C Test)
2. Short circuit test (S.C.Test)

      

The parameters calculated from these test results are effective in determining the regulation and efficiency of a transformer at any load and power factor condition, without actually loading the transformer. The advantage of this method is that without much power loss the tests can be performed and results can be obtained. Let us discuss in detail how to perform these tests and how to use the results to calculate equivalent circuit parameters.

1. Open Circuit Test (O.C. Test)

       The experimental circuit to conduct O.C test is shown in the Fig. 1.

Fig 1. Experimental circuit for O.C. test

       The transformer primary is connected to a.c. supply through ammeter, wattmeter and variac. The secondary of transformer is kept open. Usually low voltage side is used as primary and high voltage side as secondary to conduct O.C test.

       The primary is excited by rated voltage, which is adjusted precisely with the help of a variac. The wattmeter measures input power. The ammeter measures input current. The voltemeter gives the value of rated primary voltage applied at rated frequency.

       Sometimes a voltmeter may be connected across secondary to measure secondary voltage which is V₂ = E₂ when primary is supplied with rated voltage. As voltmeter resistance is very high, though voltmeter is connected, secondary is treated to be open circuit as voltmeter current is always negligibly small.

      When the primary voltage is adjusted to its rated value with the help of variac, readings of ammeter and wattmeter are to be recorded.

The observation table is as follows

          V_o = Rated voltage
          W_o = Input power
           I_o = Input current = no load current

       As transformer secondary is open, it is on no load. So current drawn by the primary is no load current I_o. The two components of this no load current are,

           I_m = I_o sin Φ_o
           I_c = I_o cos Φ_o
where  cos Φ_o = No load power factor
And hence power input can be written as,
           W_o = V_o I_o cos Φ_o
       The phasor diagram is shown in the Fig. 2.

Fig. 2

       As secondary is open, I₂ = 0. Thus its reflected current on primary is also zero. So we have primary current I₁ =I_o. The transformer no load current is always very small, hardly 2 to 4 % of its full load value. As I₂ = 0, secondary copper losses are zero. And I₁ = I_o is very low hence copper losses on primary are also very very low. Thus the total copper losses in O.C. test are negligibly small. As against this the input voltage is rated at rated frequency hence flux density in the core is at its maximum value. Hence iron losses are at rated voltage. As output power is zero and copper losses are very low, the total input power is used to supply iron losses. This power is measured by the wattmeter i.e. W_o. Hence the wattmeter in O.C. test gives iron losses which remain constant for all the loads.

.^..          W_o = P_i  = Iron losses
       Calculations : We know that,
             W_o = V_o I_o cos Φ
             cos Φ_o = W_o /(V_o I_o ) = no load power factor
Once cos Φ_o is known we can obtain,
              I_c  = I_o cos Φ_o
 and        I_m = I_o sin Φ_o
       Once I_c  and I_m are known we can determine exciting circuit parameters as,
              R_o = V_o /I_c   Ω
and        X_o = V_o /I_m   Ω

Key Point : The no load power factor cos Φ_o is very low hence wattmeter used must be low power factor type otherwise there might be error in the results. If the meters are connected on secondary and primary is kept open then from O.C. test we get R_o' and X_o' with which we can obtain R_o and X_o knowing the transformation ratio K.

2. Short Circuit Test (S.C. Test)

       In this test, primary is connected to a.c. supply through variac, ammeter and voltmeter as shown in the Fig. 3.

Fig. 3 Fig 1. Experimental circuit for O.C. test

       The secondary is short circuited with the help of thick copper wire or solid link. As high voltage side is always low current side, it is convenient to connect high voltage side to supply and shorting the low voltage side.

       As secondary is shorted, its resistance is very very small and on rated voltage it may draw very large current. Such large current can cause overheating and burning of the transformer. To limit this short circuit current, primary is supplied with low voltage which is just enough to cause rated current to flow through primary which can be observed on an ammeter. The low voltage can be adjusted with the help of variac. Hence this test is also called low voltage test or reduced voltage test. The wattmeter reading as well as voltmeter, ammeter readings are recorded. The observation table is as follows,

       Now the current flowing through the windings are rated current hence the total copper loss is full load copper loss. Now the voltage supplied is low which is a small fraction of the rated voltage. The iron losses are function of applied voltage. So the iron losses in reduced voltage test are very small. Hence the wattmeter reading is the power loss which is equal to full load copper losses as iron losses are very low.

.^..           W_sc = (P_cu) F.L. = Full load copper loss
      Calculations : From S.C. test readings we can write,
              W_sc = V_sc I_sc cos Φ_sc
.^..            cos Φsc = V_sc I_sc /W_sc = short circuit power factor
               W_sc = I_sc² R_1e = copper loss
.^..             R_1e =W_sc /I_sc²
while        Z_1e =V_sc /I_sc = √(R_1e² + X_1e²)
.^..             X_1e = √(Z_1e² - R_1e²)

       Thus we get the equivalent circuit parameters R_1e, X_1e and Z_1e. Knowing the transformation ratio K, the equivalent circuit parameters referred to secondary also can be obtained.

Important Note : If the transformer is step up transformer, its primary is L.V. while secondary is H.V. winding. In S.C. test, supply is given to H.V. winding and L.V is shorted. In such case we connect meters on H.V. side which is transformer secondary through for S.C. test purpose H.V side acts as primary. In such case the parameters calculated from S.C. test readings are referred to secondary which are R_2e, Z_2e and X_2e. So before doing calculations it is necessary to find out where the readings are recorded on transformer primary or secondary and accordingly the parameters are to be determined. In step down transformer, primary is high voltage itself to which supply is given in S.C. test. So in such case test results give us parameters referred to primary i.e. R_1e, Z_1e and X_1e.

Key point : In short, if meters are connected to primary of transformer in S.C. test, calculations give us R_1e and Z_1e if meters are connected to secondary of transformer in S.C. test calculations give us R_2e and Z_2e.

3. Calculation of Efficiency from O.C. and S.C. Tests

      We know that,
       From O.C. test, W_o =  P_i
       From S.C. test,  W_sc = (P_cu) F.L.

Thus for any p.f. cos Φ₂ the efficiency can be predetermined. Similarly at any load which is fraction of full load then also efficiency can be predetermined as,

where       n = fraction of full load

where       I₂= n (I₂) F.L.

4 Calculation of Regulation

       From S.C. test we get the equivalent circuit parameters referred to primary or secondary.

       The rated voltages V₁, V₂ and rated currents (I₁) F.L. and (I₂) F.L. are known for the given transformer. Hence the regulation can be determined as,

       where I₁, I₂ are rated currents for full load regulation.
       For any other load the currents I₁, I₂ must be changed by fraction n.
.^..    I₁, I₂ at any other load = n (I₁) F.L., n (I₂) F.L.

Key Point : Thus regulation at any load and any power factor can be predetermined, without actually loading the transformer.

For Procedure and Circuit Diagram, See your Electrical Laboratory Manual on page 3. 

 Fill Up Tables in Your Manual and Continue To….

PRECAUTIONS:

For Precautions, See General Electrical Lab Precautions

Answers to Questions:

No Questions in this experiment.

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About Stephen Djes

Stephen Djes is a passionate Graduate of Engineering from the University of Benin, and he is geared towards helping fellow engineering students in the great institution of UNIBEN to do better at academics.