Hello friends, I hope all of you are fine. In today’s tutorial, we are gonna have a look at the Phasor Diagrams of a Synchronous Generator and how they describe the different parameters of synchronous generator. The phasor diagram is a very significant factor of the power system analysis. As the output of the synchronous generator is alternating current, so it can easily be explained by the phasor diagrams. If we draw the output voltage and current in such a geometrically way that they show some relation among them, the resultant diagram called a phasor diagram.
In the last tutorial, we discussed the synchronous generator equivalent circuit. If first, you read it then it will be easy to understand the phasor diagrams of the synchronous generator. In today’s post, we will have look at different parameters related to phasor diagram, will learn how to make these diagrams. So, let’s get started with the phasor diagram of the synchronous generator.
Phasor Diagram of a Synchronous Generator
 In the electrical power system, there are three main types of load first one is resistive, the second one is capacitive and the third one is inductive.
 We will connect all these three loads with the synchronous generator and will see their effect and will draw their phasor diagram.
Phasor Diagram of a Synchronous Generator at Unity P.F
 The given diagram shows the relation among the parameter like phase voltage (Vø), internal generated voltage (E_{A}), armature current (I_{A}), synchronous reactance (X_{S}) and some other factors by phasor diagram when the generator is working with the resistive load and have unity power factor.
V_{ø}= E_{A} – jX_{s}I_{A}– R_{A}I_{A}
 We can observe from the abovegiven equation that internal generated voltage (E_{A}) are will be equal to the phase or terminal voltage of the generator if we deduct the voltage loss due to armature resistance and the synchronous reactance from it.
 All these parameters and their facts are shown in an abovegiven diagram.
Phasor Diagram of a Synchronous Generator at lagging and leading P.F
 In a given diagram, we have construed the phasor diagram of the synchronous generator when it relates to the inductive load, in this case, the power factor will be lagging.
 There is also a phasor diagram of the synchronous generator when it connected with the capacitive load, in this case, the power factor will be leading.
 If we compare the lagging and leading load phasor diagrams of the synchronous generator we can conclude that to get a specific value of the phase or terminal voltage and armature current we will require larger amount of internal generated voltage E_{A} for the inductive load (lagging) than the capacitive load (leading).
 So, we will have to provide a larger field current at the rotor in case of inductive load (lagging load) than the leading load to generates the same amount of the terminal voltage (Vø).
 As we know.
E_{A} = Køw

 In this equation, E_{A} is internally generated voltage.
 ‘K’ is constant.
 ‘∅’ is flux.
 ‘w’ is speed of rotation of the rotor.
 In this equation, ‘w’ should be nonvariant to keep the frequency constant.
 For the given amount of the field current at rotor and current consumed by load, the magnitude of the phase voltage (Vø) will be less for inductive load and high for the capacitive load.
 In all synchronous machines, whether it is a motor or a generator, the value of the synchronous reactance (Xs) is high than the armature windings resistance (R_{A}), so sometimes R_{A} is ignored for quality observation of the voltage changing.
 But in case of different mathematical problems, R_{A} should be considered.
 In real synchronous machines, the synchronous reactance is normally much larger than the winding resistance R_{A}, so R_{A} is often neglected in the qualitative study of voltage variations. For accurate numerical results, R_{A }must be considered.
Power Factor and Power Control
 The power factor of a synchronous generator is measured by the angle between the voltage and current phasors in the phasor diagram. The value of the power factor can be lagging, leading, or unity
 A lagging power factor exists when the current phasor lags the voltage phasor. It means that current passing through the generator when voltage is decreasing, means in total negative reactive power output from the generator
 The leading power factor causes when the current phasor leads to the voltage phasor. it means that current is passing through the generator when the voltage is increasing that causing positive reactive power output
 Unity power factor occurs when the current phasor is in phase with the voltage phasor. it means that current is passing through the generator when voltage is at its peak, which causes total zero reactive power output from the generator
The power control of a synchronous generator can be done by varying the field current. The field current is the current that passes through the field winding of the generator and finds the strength of the field in the generator. The strong magnetic field causes the high output voltage of the generator. By adjusting the field current power factor of the generator can be controlled. For instance, if the field current is increased voltage will also increase and the power factor will go to unity. If field current reduces the voltage will decreases and the power factor will lag.
The phasor diagram of a synchronous generator can be used to visualize the power factor of the generator. The angle between voltage and current phasors is power factor angle. The power factor angle can be used to measure the power factor of the generator
This formula is used for measuring the power factor of a synchronous generator:
power factor= cos(power factor angle)
For example, if the power factor angle is 30 degrees, then the power factor value will be 0.866.
The power control can be used to increase the power factor of the generator. This can be good for the power system as a whole, as it can help to decrease losses and improve the efficiency of the system.
FAQs
A synchronous generator is an electrical machine that transforms mechanical energy into electrical energy. It is done by rotating a magnetic field in a coil of wire, which induces an electric current in the coil. The frequency of the output voltage from a synchronous generator is measured by the speed of rotation of the magnetic field.
 What is a phasor diagram?
A phasor diagram is a graphical denotation of the relationship between different electrical parameters. The quantities are denoted by vectors, which are arrows that have a magnitude and a direction. The direction of the vector shows the phase angle of the quantity.
 What are the important phasors in a synchronous generator phasor diagram?
The important phasors in a synchronous generator phasor diagram are:
 The generated voltage (Eg)
 The armature current (Ia)
 The terminal voltage (Vt)
 The load impedance (Z)
A synchronous generator and a synchronous motor are the same machines, but they operate with different principles. A synchronous generator is used to produce electricity, while a synchronous motor uses electricity. The main difference between them is the direction of the armature current. In a synchronous generator, the armature current passes in the same direction as the generated voltage, while in a synchronous motor, the armature current flows in the reverse direction of the produced voltage.
 What is the significance of the angle between the generated voltage and the armature current in a synchronous generator phasor diagram?
The angle between the produced voltage and the armature current is known as the power factor angle. The power factor angle measures the power factor of the synchronous generator. The power factor is calculates how efficiently the synchronous generator is transforming mechanical energy into electrical energy.
 What is the difference between a lagging power factor and a leading power factor?
A lagging power factor is a power factor where the armature current lags the generated voltage. A leading power factor is a power factor where the armature current leads the produced voltage. A lagging power factor is more common than a leading power factor.
 What is the effect of increasing the load on a synchronous generator?
When the load on a synchronous generator rises, the armature current also rises. This results in the power factor angle to reduce. If the load is increased very much, the power factor angle can reach 90 degrees, at which point the synchronous generator will become unstable.
 What is the effect of increasing the field current on a synchronous generator?
When the field current on a synchronous generator is increased, the generated voltage also increases. This causes the power factor angle to rise. If the field current is increased very larger, the power factor angle can become 90 degrees, at which point the synchronous generator will become unstable.
 How can the power factor of a synchronous generator be improved?
The power factor of a synchronous generator can be increased by increasing the field current or by connecting a capacitor across the terminals of the generator. Increasing the field current rises the generated voltage, which causes the power factor angle to rise. Connecting a capacitor across the terminals of the generator makes a leading power factor, which enhances the overall power factor of the system.
 What are the applications of synchronous generators?
Synchronous generators common applications are
 Power generation
 Motor control
 Clock synchronization
 Telecommunications
 Industrial applications
You can also read some related topics to synchronous generators that are listed here.
Introduction to Synchronous Generator
Synchronous Generator Equivalent Circuit
Synchronous Generator Power and Torque
Synchronous Generator Parameters
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
This is the complete tutorial about phasor diagram of the synchronous generator if you have any queries ask in comments. See you in the next tutorial Power and Torque in Synchronous Generator. Have a good day.
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