Hello friends, I hope all of you are fine. In today’s tutorial, we are gonna have a look at Open Circuit Test and Short Circuit Test of Synchronous generator and their relationship. There are many factors of electrical power network rely on the usage of the generator models for the estimation of the power system behavior, the correctness of these estimations relies on the correctness of the parameters of the generator using in the system. Some of these parameters are not easy to find so producers of the generators mentioned these parameters on the datasheet.
In today’s post, we will have a look at different parameters of a synchronous generator that should be examined before installation of the generator. To easy understating of the parameter of a generator, you must have knowledge of the synchronous generator resultant circuit. So, let’s get started with the Open Circuit Test and Short Circuit Test of Synchronous generator.
Open Circuit Test and Short Circuit Test of Synchronous generator
 During the measurement of the resultant circuit of the synchronous generator, we find the three parameters, that are very important to study the complete performance of the real world synchronous generator.
 These three parameters are described here.

 The armature resistance.
 The relation between field current and internal generated voltage E_{A}
 Synchronous reactance X_{s}
 To find these three parameters we will perform some tests on the synchronous generator that are described here with the detailed
Open Circuit Test of the Synchronous Generator
 To accomplish this test the generator should move at its rated speed, noload should be at its terminals, and the value of the field winding current should be 0.
 After following these steps, we will vary the field current step by step and calculate the terminal voltage at each step.
 As there is no load at the output terminals of the generator, so there will be zero armature current.
 Hence the internal generated voltage E_{A} will equal to the phase voltage V_{ø}.
 By using this data, we can construct the curve among the internally generated voltage that equals the terminal voltage and the field current.
 This graph between E_{A} and the field current is known as the opencircuit characteristic (OCC) of the synchronous generator.
 By this graphical representation, we can find the value of internal generated voltage E_{A} any value of the field current.
 The graph of the opencircuit characteristic is shown in a given diagram,
 You can observe from the graph that at the start the curve is a straight line then it is not straight line it due to saturation.
 The reluctance offered by the unsaturated region is lesser than the reluctance of the air gap, at the start when iron is not saturated the field current and the terminal voltage are in direct relation with each other.
 When iron gets saturates, the reluctance offered by the iron becomes larger than the increment in the flux is not directly proportional to the field current, so the curve is not straight line after some interval.
 The linear part of the opencircuit characteristics known as the air gap line.
Short circuit test of Synchronous Generator
 To do a short circuit test first of set the value of field current at 0 and connect the output terminals of the generator by the ammeter.
 After that find the value of the armature current (I_{A}) by changing the field current.
 This graph among the field current and the armature current known as the shortcircuit characteristic (SCC).
 You can see that it is a linear graph.
 To understand this straightline behavior let’s have a look at the equivalent circuit of the synchronous generator when it is shortcircuited this circuit is shown below.
 From this circuit, you can find the value of the armature current (I_{A}) that is given here.
I_{A} =E_{A}/(R_{A}+jX_{s})
 The magnitude of the armature current is given here,
I_{A} =E_{A}/√(R^{2}_{A}+X^{2}_{s})
 The phasor diagrams of the short circuit test of the synchronous generator are shown below.
 The fields during the short circuit test are physically shown in a given diagram.
 As the stator field B_{s} crosses the effect of the rotor magnetic field (B_{R}) so the total field B_{net} has low value.
 As the value of the B_{net} is lesser so the generator is unsaturated short circuit characteristic curve is linear.
 To recognize what data these two features have output, note from a given figure that the V_{ø} is 0.
 From this figure, the interior impedance of the generator is given here.
Z_{s} = √(R^{2}_{A}+X^{2}_{s})
= E_{A}/I_{A}
 As we know that synchronous reactance Xs is greater than the armature resistance R_{A} so this equation becomes.
Xs= E_{A}/I_{A}
= V_{ø,oc}/I_{A}
 If the value of the internally generated voltage (E_{A}) and armature current (I_{A}) is known, we can compute the value of the synchronous reactance.
 Measure the internal generated voltage E_{A} from the opencircuit characteristic (OCC) at the specified value of the field current.
 Measure the shortcircuited current I_{A} at the field current from the opencircuit characteristic (OCC)
 Put the values of the internal generated voltage E_{A} and the I_{A} in given below equation and find the value of the synchronous reactance.
Xs= E_{A}/I_{A}
 There is some issue for this technique to the measurement of the synchronous reactance.
 As the internal generated voltage E_{A} is measured from the OCC at that point where the generator is partly saturated for a higher value of the field current and the armature current (I_{A}) taken from the SCC where the generator is unsaturated for all values of the field current.
 So, at the larger field current, the internal generated voltage calculated from the OCC at a specified value of the I_{F} is not similar to the internal generated voltage measured from the SCC at the same value of the field current I_{F}.
 This difference affects the value of the synchronous reactance X
 So, the result by this method can be applied to the saturation point, the unsaturated X_{S} can be measured by this equation at any value of the I_{F} in the straightline part of the opencircuit characteristic (OCC).
Xs= E_{A}/I_{A}
 The estimated value of X_{S} fluctuates with the gradation of saturation of the opencircuit characteristic curve, therefore the value of the X_{S} to be used in a specified problem must be measured at the estimated load on the generator.
 A graph of estimated (approximated) Xs as a function of I_{F} is in a given figure.
 It is significant to identify a resistance of winding as well as its Xs, resistance can be measured by the by providing dc voltage to the windings when the generator is not working
 During the dc application, the value of the reactance of the winding will be 0.
 This method does not give proper results because the alternating current resistance is somewhat higher than the value of the direct current resistance.
ShortCircuit Ratio Synchronous Generator
 It is the ratio of the field current needed for the rated voltage at opencircuited conditions to the field current needed to produce rated armature current at shortcircuited conditions.
 Though the shortcircuit ratio tells nothing new that is not we know about synchronous generator reactance. But in industries, this fact is used so we should have knowledge of it.
You can also read some related topics to a synchronous generator that is listed here.
Introduction to Synchronous Generator
Synchronous Generator Equivalent Circuit
Synchronous Generator Phasor Diagram
Synchronous Generator Power and Torque
Synchronous Generator Operating Alone
Synchronous Generator Parallel Operation
Synchronous Generator parallel with Large Power system
Synchronous Generator Parallel with same Size Generator
Synchronous Generator Capability Curves
Synchronous Generator Transients
That is the detailed article on the Synchronous Generator Parameter we did different tests for finding different parameters if you have any query ask in comments. See you in the next tutorial Synchronous Generator Operating Alone.
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