Hello friends, I hope all of you are fine. In today’s tutorial, we are gonna have a look at** Synchronous Generator Capability Curves. **This curve of the synchronous generator tells about the limits in which a generator can continue its operation without any damage. It also recognized as the functioning chart of the synchronous generator. The restrictions that are defined by this curve are described here. The load associated with the generator should according to the rating of the generator. The load of the generator also follows the rated values of the generator’s mechanical power source (prime mover).

The value of the I_{F }should be in the bearable value of the generator, so it cannot damage the windings. The angle of the load must be less than ninety degrees. In today’s post, we will have a look at how these limits are practically works and their effects. So let’s get started with the *Synchronous Generator Capability Curves.*

#### Synchronous Generator Capability Curves

- The heats limits of the stator and the rotor of the generator, and some other exterior restrictions can be defined by the
**generator capability curve.** - A capability curve can be made from the complex apparent power of the generator S=P +Qj.
- It is found from the phasor diagram of the generator, by supposing that the V
_{ø}has constant value at the rated voltage of the generator.

- In a given diagram, you can see the phasor diagram of the generator when it is connected with the inductive load and its rated voltage.

- An orthogonal set of axes is constructed on the diagram with its initial point at the tip of Vø and represents in V.
- In the diagram that is denoted as A, the perpendicular part AB has the length of X
_{s}I_{A}cosø and the length of the horizontal part (OA) is X_{s}I_{A}sinø. - The active power of the generator is given as.

P=3V_{ø}I_{A}cosø

- The reactive power Q of the synchronous generator is given as.

Q= 3V_{ø}I_{A}sinø

- The apparent power S is given as.

S =V_{ø}I_{A}

- So the vertical (AB) and the horizontal (OA) components of this curve can be written in active and reactive power. Its drawn in above figure and denoted as B.
- The alteration factor required to change the gage of the axes from volts to voltampere’s (power units) is 3V
_{ø}/X_{s}

P=3V_{ø}I_{A}cosø= 3Vø/ X_{s} (X_{s}I_{A}cosø)

Q= 3V_{ø}I_{A}sinø=3Vø/ X_{s} (X_{s}I_{A}Sinø)

- At the axis of the voltage, the vertex of the phasor diagram is at the negative of the V
_{ø}on the horizontal axis. - The vertex of the power diagram is.

Q= 3V_{ø}/Xs (-Vø)

= -(3V^{2}ø)/(X_{s})

- The field current of the generator is directly proportionate to the flux of the generator and the flux is directly proportionate to the internal generated voltage E
_{A}=Kwø - The length equivalent to internal generated voltage E
_{A }on the power diagram is written as.

D_{E} = -(3E_{A}Vø)/(X_{s})

- The armature current is directly proportional to the X
_{s}I_{A}and the length equivalent to X_{s}I_{A}on the power diagram is 3V_{ø}I_{A}.

- The concluding of the synchronous generator capability is shown in a given figure.

- It is the graphical representation between the active power and the reactive power, active power is shown on the x-axis and Q on the y-axis.
- Lines of constant I
_{F}match to lines of constant internal generated voltage, that are revealed as circles of magnitude 3E_{A}V_{ø}/X_{s}positioned on the point.

Q = -3V^{2}_{ø}/X_{s}

- The I
_{A }boundary looks like the circle equivalent to the rated I_{A}or rated KVA’s, and the I_{F}boundary looks like a circle equivalent to the rated field current or internal generated voltage. - The points that exist in both circles are a safe functioning point for the generator.
- We can also represent the other limitations on the figure, like extreme power of the prime mover and the stationary stability boundary. It is shown in a given diagram.

**Short-Time Operation and Service Factor of Synchronous Generator**

- The most significant restriction for normal working of the generator is the heating of its both windings, armature and the field windings.
- These heating restrictions normally apply at a point below the extreme power that the generator can provide mechanically or magnetically.
- The normal synchronous generator has ability to provide three hundred percent power of its rated power till that points it both windings armature and field burn out.
- This capability of the generator to provide higher power than its rated power is used to deliver temporary power surges for starting of the motor and analogous load transients.
- There is a possibility to run generator power larger than the rated power for a long time, as long as the windings do not have time to heat-up beforehand the extra load is detached.

- For instance, a generator that can provide power to the one-megawatt load indefinitely can has ability to provide power to the 1.5-megawatt load for some minutes without serious damage, and for a gradually larger time at less power.
- Though the load should finally be detached, or the windings will damage.
- As the power will increases over the rated value the generator will bear it only for a couple of minutes or can damage.
- The given diagram shows this factor.

- You can see from the picture that the for overloading the required time is in s for heating of the generator.
- ln this generator, a twenty % overloading can endure for thousand seconds, a hundred % overloading can be bear for thirty seconds, and a two hundred% overloading can endured for ten sec before harming the generator.
- The extreme value of the temperature that any electrical machine can bear depends on the winding’s insulation class.
- There are 4 main classes of the winding’s insulation A, B, F, H.
- Whereas there is some changing intolerable temperature that relies on the design of the machine and temperature calculation technique.
- these classes usually resemble temperature increases of sixty, eighty, one hundred five, and one hundred twenty-five Celsius, correspondingly, over ambient temperature.
- The larger the insulation class of an electrical machine, then a large the amount of power can get out from the machine without any damage to the machine.
- Heating and damaging the windings in any electrical machine is a very common issue.

- It is a general rule that for every ten Celsius increment in the temperature of the windings that is mention on the machine’s nameplate, the average life-time of a machine will remain half. Can see in figure.

- Nowadays the insulation materials are less vulnerable to break-down than before, but temperature increment still severely decreases their lifetime.
- Due to these reasons never connect the load beyond the limit of the synchronous machine.

**How well is the power requirement of a machine known?**

- Before connection, there are only an estimated approximations of load, due to this, general machines normally have a service factor.
- The service factor is the ratio of the extreme power of the machine to the power mentioned on the nameplate of the machine.
- The generator that has a service factor of 1.15 can be functioned at one hundred percent % of the rated-load without any damage.
- The service factor on a generator offers a boundary of fault in case the loads were inappropriately assessed.

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

Introduction to Synchronous Generator

Synchronous Generator Equivalent Circuit

Synchronous Generator Phasor Diagram

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 Transients

That’s all about Synchronous Generator Capability Curves I have mentioned each and everything related to Synchronous Generator Capability Curves. If you have any query ask in comments. See you in next tutorial.

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