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 the synchronous generator is described below.
- The power provided by the prime mover to generator is.

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

- Whereas, this input power converted to the 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 and I_{A}is the armature current, γ is the angle between them. - The power that does not convert into the 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**

- 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 write in phase form.

Q_{out} =3 VøI_{A }Sinø

- As the Xs>>R
_{A}, so if we neglected 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 the equation (1) then we have.

P=3 Vø E_{A}sinδ/X_{s}——- (2)

- As there is no resistance in the 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) among 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 produced 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 that 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 torque of the 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.

**Importance of Torque in Synchronous Generators**

Torque basic factor of synchronous generators, since it directly affects the ability to produce power. The magnitude and type of torque produced are important to finding the load capacity of the generator, stability and overall performance.

## Types of Torque in a Synchronous Generator

**1. Starting Torque**

Starting torque is the minimum value of torque needed to start the rotation of a static generator. important for the generator starting process

**2. Pull-out Torque**

Pull-out torque defines the highest torque synchronous generator can handle without the loss of synchronization with the grid

**3. Maximum Torque**

It is the highest rotational force that a generator can bear before getting its mechanical limits

**4. Synchronous Torque**

Synchronous torque is the steady-state torque required to maintain the synchronism of the generator with the grid at a certain load condition

**5. Load Torque**

it is the opposing torque bear by the generator when attached to the load. It finds the generator’s ability to provide power to different loads

**6. Breakdown Torque**

it is the maximum torque a generator can handle without facing mechanical failure.

**7. Pull-in Torque**

Pull-in torque is the torque needed to bring the generator into synchronization if it loses synchronism during work.

# Factors Affecting Torque Production

**1. Magnetic Field Strength**

The strength of the magnetic field in the generator highly affects the torque generation ability.

**2. Rotor Speed**

The rotational speed of the rotor generator affects produced torque value.

**3. Rotor Design and Construction**

The design and manufacturing of the rotor are important to determining the torque features of the generator.

**4. Load Conditions**

The type and magnitude of the attached load affect the torque needs and performance.

**5. Temperature**

Temperature changes can affect the conductivity of the components of the generator, consequently affecting the torque generated

**6. Supply Voltage**

The voltage provided to the generator has an impact on the magnitude of the generated torque.

### Torque Control Methods

**1. Field Current Control**

The adjustment of field current provides accurate control over then the output of the generator torque

**2. Armature Current Control**

Controlling the armature current helps to manage the torque in varying load conditions.

**3. Voltage Control**

Voltage control is the best method to handle torque variations in the generator

**4. Slip Test Method**

The slip test method helps in evaluating the torque characteristics of the generator under different operating conditions.

## Efficiency and Losses in Torque Generation

**1. Copper Losses**

Copper losses cause due to resistance of windings and result in a decrement in torque efficiency

**2. Iron Losses**

Iron losses are produced by the magnetic features of the core materials and can impact torque generation

**3. Mechanical Losses**

Mechanical losses, like friction and windage losses, help to reduce overall torque efficiency.

**4. Stray Load Losses**

Stray load losses are energy losses in different components like bearings and shafts, decreasing the effective torque.

**5. Power Factor and its Impact on Torque Efficiency**

The power factor of the generator can impact the torque efficiency and, in result, overall electrical performance.

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 power and torque of synchronous generator if you want to know something more ask in comments. See you in the next tutorial Synchronous Generator Parameter.

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