Hello friends, I hope all of you are fine. In today’s tutorial, we are gonna have a look at the** Power and Torque in Synchronous Generator **and their relationship. The synchronous generator is an apparatus that alters mechanical energy into electrical energy. To move its shaft there are many sources like steam turbines, petrol engines or water turbines that provided mechanical energy to the generator. These sources of mechanical power are named as a **prime mover.**

It does not matter which prime mover we are using; the main thing is that it should rotate the rotor at a constant speed irrespective of the variation in the power demand. If the prime mover does not deliver the continuous speed, then the frequency of the power generated by the generator will not be the same. In today’s post, we will have a look at the relation between torque and power of the synchronous generator. so let’s get started with the *power and torque in the synchronous generator.*

## Power and Torque in Synchronous Generator

- The mechanical power provided by the prime mover to the synchronous generator does not transform into electrical power completely.
- The mechanical power that does not convert into electric energy is called loss power.
- The
**power flow diagram of synchronous generators**is described below.

- In the power flow diagram of a synchronous generator, The power provided by the prime mover to the generator is.

P_{in} = T_{app}w_{m}

- Whereas, this input power converted to electricity is given here.

P_{con }= T_{ind}w_{m}

P_{con} = 3E_{A}I_{A}cosγ

- In this equation, the E
_{A}is the internally generated voltage of the generator I_{A}is the armature current, γ is the angle between them. - The power that does not convert into electric energy is wasted in the form of core losses that are eddy current and hysteresis loss, iron loss, windage, and friction losses.

**Power of the Synchronous Generator**

- let find the
**power equation of synchronous generator,** - The out power of the generator that is electrical power can be written as.

P_{out} =√3 V_{T}I_{L }Cosø

- It can be written in phase form.

P_{out} =3 V_{ø}I_{A }Cosø—-(1)

- The reactive power of the generator can be defined as

Q_{out} =√3 V_{T}I_{L }Sinø

- It can also be written in phase form.

Q_{out} =3 VøI_{A }Sinø

- As the Xs>>R
_{A}, so if we neglect the armature resistance (R_{A}) then a very valuable expression can b finds to define the P_{out}of the synchronous generator. - To find this expression we study the given phasor diagram.

- It is the simple phasor diagram of the generator without the armature resistance.
- From a diagram, you can see that the bc portion has the value of E
_{A}sinor X_{s}I_{A}cosø. - so, we have

I_{A}cosø = E_{A}sinδ/X_{s}

- If we put this expression in equation (1) then we have.

P=3 Vø E_{A}sinδ/X_{s}——- (2)

- As there is no resistance in equation (2) so there is no loss in the generator and this equation is for input and the output of the generator.
- From equation (2) we can observe that the output power of the synchronous generator depends on the angle (δ) between the internal generated voltage E
_{A}and the phase (terminal) voltage of the generator. - The angle (δ) is also called the torque angle of the
**synchronous generator.** - The extreme power that can generator produce will be given when the value of torque angle (δ) is ninety degrees.
- When δ =90
^{0}, sin =1, so the power will be.

P_{max} =3V_{ø}E_{A}/X_{s} —- (3)

- The maximum power given in this equation is known as the
**static stability limit**of the generator. - Usually, practically no generator reaches this limit.
- If we observe given below equation again.

P_{out} =3 V_{ø}I_{A }Cosø—-(1)

Q_{out} =3 V_{ø}I_{A }Sinø

P=3 Vø E_{A}sinδ/X_{s}——- (2)

- Let’s suppose that the V
_{ø}in these three equations is constant than the outputs of the active powers are directly proportionate to the I_{A }Cosø and the E_{A }Sinø and the reactive power (Q) is proportionate to the I_{A }Sinø. - These factors are beneficial for the construction of the phasor diagram of the generator when the load varies.

## Torque in Synchronous Generator

- As we know the torque in the synchronous machine is given as.

T_{ind} =KB_{R} x B_{S}

T_{ind} =KB_{R} x B_{net}—-(d)

- The magnitude of the equation (d) can be written as.

T_{ind} =KB_{R}B_{net}sinδ

- In this equation the δ is the angle among the field of the rotor (B
_{R}) and the net field of the generator (B_{net}), it is known as the torque angle. - Another equation for the torque can be calculated by this equation.

P=3 Vø E_{A}sinδ/X_{s}

- As we know that the converted power (P
_{conv}) = T_{ind}w_{m}, so the induced generator torque or synchronous generator is.

T_{ind}= 3 Vø E_{A}sinδ/w_{m}X_{s} ——(f)

- Equation
**‘**f’ gives the value of the torque in the form of electric numbers but the given below equation gives the torque in the form of magnetic terms.

T_{ind} =KB_{R}B_{net}sinδ

You can also read some related topics to synchronous generators that are listed here.

Introduction to Synchronous Generator

Synchronous Generator Equivalent Circuit

Synchronous Generator Phasor Diagram

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

That is the complete article on the power and torque of synchronous generators and **power and torque relation,** if you want to know something more ask in the comments. See you in the next tutorial Synchronous Generator Parameter.

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