Working of Power Triangle

The Power Triangle works by calculating the power factor (cosθ) using the relationship between P, Q, and S. It is basically a right angle triangle that follows the Pythagoras’ theorem .Mathematically we can conclude the two points as follows:

  • Power Factor (cos θ) = P/S
  • S2 =P2+Q2


Power Triangle

Imagine yourself as a kid who wishes to play with a toy car that runs on batteries. You want to play for long and so you want the batteries to last as long as possible. The “Power Triangle” can help you achieve this. The Power Triangle shows what percent of the battery’s power is being used to move the car in the forward direction and what percent of the battery’s power is being used to rotate the motor, or in particular terms the Active Power (P), Reactive Power (Q) and the Real(or Apparent) Power (S). You can use the Power Triangle to reduce the power consumption so that the batteries last longer and you can enjoy much.

In this article we will be going Through What this is the Power triangle, In this, we will go through the Power Factor(Leading as Well as Lagging), then we will go through the Power Triangle of Ac, In this we will go through Active, Reactive and Apparent power in depth. At last, we will conclude our Article with Solved Problems, Its Application with its Advantages and Disadvantages.

Table of Content

  • What is a Power Triangle?
  • Power Factor
  • Effects
  • Working of Power Triangle
  • Properties of Power Triangle
  • Characteristics of Power Triangle
  • Applications of Power Triangle
  • Advantages and Disadvantages of Power Triangle
  • Solved Problems

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What is a Power Triangle?

The power triangle is a right-angle triangle where Hypotenuse is the apparent power or true power (S), the Opposite side is the reactive power (Q) and the leftover Adjacent side is the active power or real power (P). These three parameters of AC circuits follow the Pythagoras’ theorem as S2 =P2+Q2. The angle between P and S gives the Power Factor (or cos θ )....

Power Factor

The angle θ in the Power Triangle given above is called the power factor angle as its cosine that is cos θ gives us Power Factor .Its a dimensionless quantity as its the ratio of average power to the apparent power .In other terms , the power factor is the cosine of the phase difference between voltage and current , its the cosine of the angle of the load impedance....

Leading Power Factor

When the load is largely capacitive, leading power factor arises, resulting in a phase angle (θ) of less than 90 degrees between P and S....

Lagging Power Factor

When the load is largely inductive, lagging power factor happens, resulting in a phase angle (θ) of greater than 90 degrees between P and S....

Power Triangle of AC circuits

In AC Circuits there are three types of power...

Power Factor of AC circuits

Power Factor , cos θ , is an essential component of an AC circuit . It is defined as the ratio of real power (P) to apparent power (S) which is generally a decimal value .It lies in the range 0 to 1 , for example 0.95 or 95%.It also defines the phase angle between V and I...

Evolution of Power Triangle

The Power Triangle is a tool that that gives information about variables P,S,Q and cos θ or Power Factor. The power triangle can be seen as an analogy for evolution. A high power factor is analogous to a well adapted organism that is the circuit is working fruitfully to do useful work and vice versa applies .Evolution is a process of adaptation, similarly the power triangle is a process of optimization and maximizing active power and minimizing reactive power . As evolution of living organisms is a continuous process , new technologies and different ways for power optimization are being developed using the Power Triangle ....

Effects

Effect Low Power Factor High Power Factor Energy Loss Increases Decreases Equipment overheating Increases Decreases Power quality Decreases Increases Voltage drop Increases Decreases...

Working of Power Triangle

The Power Triangle works by calculating the power factor (cosθ) using the relationship between P, Q, and S. It is basically a right angle triangle that follows the Pythagoras’ theorem .Mathematically we can conclude the two points as follows:...

Properties of Power Triangle

The Power Triangle exhibits the following properties:...

Characteristics of Power Triangle

Key characteristics of the Power Triangle include:...

Applications of Power Triangle

The power triangle is used to analyze and improve the efficiency, reliability, and power quality of electrical systems in a variety of real-life applications , to say a few – improving the efficiency of electric motors , improving performance of electronic circuits , reducing electricity bills and many more .Its main application is to cut on cost and get more output in less time ....

Advantages and Disadvantages of Power Triangle

Some of the advantages and disadvantages of Power Triangle are :...

Power Factor Improvement

The process of increasing power factor without altering the voltage or current to the original load is known as power factor correction. Since most loads are inductive , power factor can be improved by installing a capacitor in parallel with the load .The effect of this can be understood with the Power Triangle or the Phasor Diagram .By choosing a suitable size of capacitor , the current can be made to be completely in phase with the voltage , implying unity power factor....

Comparison between Leading & Lagging Power Factor

Characteristic Leading Power Factor Lagging Power Factor Definition Current leads the voltage Current lags the voltage Cause Inductive loads Capacitive loads Effect on power factor Increases power factor Decreases power factor Correction Use capacitors Use inductors...

Solved Problems

Problem 1: A circuit has a real power (P) of 2000 W and an apparent power (S) of 2500 VA. Calculate the power factor ( cos θ )....

Conclusion

Power Factor is the cosine of the phase difference between voltage and current or in other terms its the cosine of the angle of the load impedance or the ratio of real power ( P ) to the apparent power ( S ) . The power factor is lagging if the current lags voltage (inductive load) and the power factor is leading when the current leads voltage ( capacitive load ). The parameters P,Q and S is expressed as P=S cos( θv- θi) , S= VrmsIrms and Q=VrmsIrms sin( θv- θi) where P is calculated in Watts( W ) , Q in VAR and S in VA. The total complex power in a circuit is the sum of the complex powers of all the individual components and the same goes for the total reactive power and total real power, but the apparent power isn’t calculated in the same process. Coming on to the improvement of the power factor , its very important for economic reasons . In short power factor is the game changer of any electrical circuit / device and its very important to consider it while designing . It reduces costs and provides longer shelf life to the electrical devices ....

FAQs on Power Triangle

What is the significance of the power factor in the Power Triangle?...