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2013-06-01T09:55:45Z

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The '''open-circuit test''', or "no-load test", is one of the methods used in [[electrical engineering]] to determine the [[Electrical impedance|no-load impedance]] in the excitation branch of a [[transformer]].

[[File:Open circuit test.png|right|500px|Circuit diagram for open-circuit test]]

==Method==

The secondary of the transformer is left open-circuited. A [[wattmeter]] is connected to the primary. An [[ammeter]] is connected in series with the primary winding. A [[voltmeter]] is optional since the applied voltage is the same as the voltmeter reading. Rated voltage is applied at primary.

If the applied voltage is normal voltage then normal flux will be set up. Since [[iron loss]] is a function of applied voltage, normal iron loss will occur. Hence the iron loss is maximum at rated voltage. This maximum iron loss is measured using the wattmeter. Since the impedance of the [[Series and parallel circuits|series]] winding of the transformer is very small compared to that of the excitation branch, all of the input voltage is [[voltage drop|dropped]] across the excitation branch. Thus the wattmeter measures only the iron loss. This test only measures the combined iron losses consisting of the [[hysteresis loss]] and the [[eddy current]] loss. Although the hysteresis loss is less than the eddy current loss, it is not negligible. The two losses can be separated by driving the transformer from a variable frequency source since the hysteresis loss varies linearly with supply frequency and the eddy current loss varies with the square.

Since the secondary of the transformer is open, the primary draws only no-load current, which will have some copper loss. This no-load current is very small and because the copper loss in the primary is proportional to the square of this current, it is negligible. There is no copper loss in the secondary because there is no secondary current.

[[Electric current|Current]], [[voltage]] and [[electric power|power]] are measured at the [[primary winding]] to ascertain the [[admittance]] and [[power factor|power-factor angle]].

Another method of determining the series impedance of a real transformer is the [[short circuit test]].

==Calculations==
The current <math>\mathbf{I_0}</math> is very small.

If <math>\mathbf{W}</math> is the wattmeter reading then,

:<math>\mathbf{W} = \mathbf{V_1} \mathbf{I_0} \cos \phi_0 </math>

That equation can be rewritten as,

:<math>\cos \phi_0 = \frac {\mathbf{W}} {\mathbf{V_1} \mathbf{I_0}} </math>

Thus,

:<math>\mathbf{I_m} = \mathbf{I_0} \sin \phi_0 </math>

:<math>\mathbf{I_w} = \mathbf{I_0} \cos \phi_0 </math>

===Impedance===

By using the above equations, <math>\mathbf{X_0}</math> and <math>\mathbf{R_0}</math> can be calculated as,

:<math>\mathbf{X_0} = \frac {\mathbf{V_1}} {\mathbf{I_m}} </math>

:<math>\mathbf{R_0} = \frac {\mathbf{V_1}} {\mathbf{I_w}} </math>

Thus,

:<math>\mathbf{Z_0} = \sqrt {\mathbf{R_0}^2 +\mathbf{X_0}^2} </math>

or

:<math>\mathbf{Z_0} = \mathbf{R_0} + \mathbf{j} \mathbf{X_0} </math>

===Admittance===

The admittance is the inverse of impedance. Therefore,

:<math>\mathbf{Y_0} = \frac {1} {\mathbf{Z_0}} </math>

The conductance <math>\mathbf{G_0}</math> can be calculated as,

:<math>\mathbf{G_0} = \frac {\mathbf{W}} {\mathbf{V_1}^2} </math>

Hence the susceptance,

:<math>\mathbf{B_0} = \sqrt {\mathbf{Y_0}^2 -\mathbf{G_0}^2} </math>

or

:<math>\mathbf{Y_0} = \mathbf{G_0} + \mathbf{j} \mathbf{B_0} </math>

Here, 

<math>\mathbf{W}</math> is the wattmeter reading 

<math>\mathbf{V_1}</math> is the applied rated voltage 

<math>\mathbf{I_0}</math> is the no-load current 

<math>\mathbf{I_m}</math> is the magnetizing component of no-load current 

<math>\mathbf{I_w}</math> is the core loss component of no-load current 

<math>\mathbf{Z_0}</math> is the exciting impedance 

<math>\mathbf{Y_0}</math> is the exciting admittance

==References==
*{{cite book | author=Kosow| title=Electric Machinery and Transformers | publisher=Pearson Education India | year=2007}}
*{{cite book | author=Smarajit Ghosh| title=Fundamentals of Electrical and Electronics Engineering | publisher=PHI Learning Pvt. Ltd. | year=2004}}
*{{cite book | author=Wildi, Wildi Theodore| title=Electrical Machines , Drives And Power Systems, 6th edtn.
| publisher=Pearson | year=2007}}

== See also ==
*[[Short-circuit test]]
*[[Thévenin's theorem]]
*[[Blocked rotor test]]
*[[Circle diagram]]
{{DEFAULTSORT:Open Circuit Test}}
[[Category:Electrical tests]]
[[Category:Transformers (electrical)]]

Semblance analysis - Revision history

103.21.125.55: /* History */