Ac circuit analysisabout power

In summary: Reactive_sync = sqrt(500^2 - (1600*tan (acos 0.9))^2)Now you can find the power factor of synchronous motors based on this reactive power and the given real power of 500 kVA.In summary, to find the power factor of synchronous motors in this system, we use the total reactive power and real power of the system to calculate the reactive power of the synchronous motors. From there, we can use the reactive power and real power of the synchronous motors to find their power factor. This can be done using Pythagoras theorem or by using the relationship between real and reactive power in a power triangle.
  • #1
herbgriffin
17
0

Homework Statement


An induction motor load of 2000 kVA has power factor 0.80 lagging. Synchronous motors totaling 500 kVA are added an operated at a leading power factor. If the overall power factor is then 0.90 lagging, what is the power factor of the synchronous motors?


Homework Equations


i use power triangle to solve the values of powers in induction motor..


The Attempt at a Solution


i have solve the reactive power = 1200 kvar ; p=1600 kw..
i am confuse how to use the total power factor... in need to find the real power in the synchronous motors... in order to find the power factor of the synchronous motors...
 
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  • #2
It's vectors and algebraic problem. Write down all all real and reactive powers and solve for unknowns.

We add real powers together and reactive power together.

Say, induction motor has pf of 'x'.

Your total system real power will be 1200+500*x
Your total system reactive power will be1600 + ...
Relation between total real and reactive power is given by pf of 0.9
 
  • #3
hello sir i am the one who ask the question about ac circuit analysis power...i am confuse on what other equations i will make since there reactive power are different other one is lagging and other one is leading. i am really confused sir and i am afraid if the same procedure of problem will come out on our exam ... thank you sir and sorry for the disturbance

Yes the reactive powers are different: one is positive other is negative. Let's say reactive power of synchronous is Reactive_sync

Then the total system reactive power will be be 1600 - Reactive_sync

Now, we have x and y components of the total system.

y/x = tan (acos pf_total_system)...
 
  • #4
rootX said:
Yes the reactive powers are different: one is positive other is negative. Let's say reactive power of synchronous is Reactive_sync

Then the total system reactive power will be be 1600 - Reactive_sync

Now, we have x and y components of the total system.

y/x = tan (acos pf_total_system)...

how can i find the reactive power of the synchronous motors when there is no given phase angle...will i use arccosine of x to find x?...
 
  • #5
herbgriffin said:
how can i find the reactive power of the synchronous motors when there is no given phase angle...will i use arccosine of x to find x?...

Yes that's right. Or you can use Pythagoras theorem .
 
  • #6
rootX said:
Yes that's right. Or you can use Pythagoras theorem .

is this equation correct (1600-arcos x...)/(P1+P2) = tan (arcos 0.90)
how will i find x when there is arcos...please help... i am really confuse...thank you for your time sir...
 
  • #7
It wouldn't be as ugly if you use Pythagoras theorem.
 

Related to Ac circuit analysisabout power

What is AC circuit analysis?

AC circuit analysis is the study and evaluation of electrical circuits that have alternating current (AC) as their source of power. This includes understanding the behavior of different circuit components, such as resistors, capacitors, and inductors, and how they interact with each other in an AC circuit.

What is the difference between AC and DC circuits?

The main difference between AC (alternating current) and DC (direct current) circuits is the direction of the current flow. In AC circuits, the direction of the current constantly changes, while in DC circuits, the current flows in only one direction. Additionally, AC circuits often have components such as capacitors and inductors that affect the behavior of the circuit, while DC circuits typically only have resistors.

What is power in an AC circuit?

Power in an AC circuit is the rate at which energy is transferred or consumed. It is measured in watts and is a combination of both the voltage and current in the circuit. In an ideal AC circuit, power is calculated by multiplying the voltage by the current, but in real circuits, factors such as resistance, reactance, and impedance can affect the power calculation.

How do you analyze power in an AC circuit?

To analyze power in an AC circuit, you need to understand the different components and their effects on power. This includes calculating the power factor, which measures the efficiency of power transfer in the circuit, and using techniques such as phasor diagrams and complex numbers to solve for power values. It is also important to consider the effects of reactive power and harmonics in an AC circuit analysis.

Why is AC circuit analysis important?

AC circuit analysis is important because AC power is the most commonly used form of electricity in our daily lives. It is used in household appliances, lighting, electronic devices, and in power grids that transmit electricity over long distances. Understanding AC circuit analysis allows us to design and troubleshoot electrical systems, ensuring efficient and safe use of power.

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