12 | Electrical Power 

12 | 

Electrical 

Power 

Electrical Power define


Electric power is define as;


The SI unit of power is the watt, one joule per second.  The term wattage is used colloquially to mean "electric power in watts." 

The electric power in watts produced by an electric current I consisting of a charge of Q coulombs every t seconds passing through an electric potential (voltage) difference of V is;

     P  =  work done per unit time    =   W÷t = W÷Q ,  Q ÷ t = V x I   

whereQ is electric charge in coulombst is time in secondsI is electric current in amperesV is electric potential or voltage in volts

What is True Power ?   

Actual or real power consumed amount of power being used by a load equipment.  

Unit is Watts (or ' W' ) and symbol commonly used is 'P'.

Formula: 1

True power formula 

Formula: 2  AC Power formula

What is Apparent Power?


Apparent Power Formula

S  =  V x I      or    S = P ÷ p.f 

What is Reactive Power?  

Reactive power is the resultant power in watts of an AC circuit when the current waveform is out of phase with the waveform of the voltage, usually by 90 degrees if the load is purely reactive, and is the result of either capacitive or inductive loads. Reactive power is used to provide the voltage levels necessary for active power to do useful work.  



Reactive Power Formula

     Q  =  √ S² - P² 

The Power Triangle  


The relationship between real power, reactive power and apparent power can be expressed by representing the quantities as vectors. Real power is represented as a horizontal vector and reactive power is represented as a vertical vector. The apparent power vector is the hypotenuse of a right triangle formed by connecting the real and reactive power vectors. 

This representation is often called the power triangle. Using the Pythagorean Theorem, the relationship among real, reactive and apparent power is:

Real and reactive powers can also be calculated directly from the apparent power, when the current and voltage are both sinusoidal with a known phase angle θ between them:

P = S x cos θ 

Q = S x sin θ 


Real power formula

The ratio of real power to apparent power is called power factor and is a number always between −1 and 1. 

Where the currents and voltages have non-sinusoidal forms, power factor is generalized to include the effects of distortion.

What is Power Factor ?

In electrical engineering, the power factor of an AC power system is defined as the ratio of the real power absorbed by the load to the apparent power flowing in the circuit, and is a dimensionless number in the closed interval of −1 to 1. 

Ideal power factor is  0.85 or greater.

When the angle cos θ  becomes greater, this will draw more current to the connected load. When this happens, the power factor value will drop below 0.84 and this impact overall electrical system. 

If the angle  cos θ  becomes smaller, then this helps improving the power factor value. 

Power factor formula

  p.f = P ÷ S

The effects  of low power factor 

In an electric power system when overall power factor get below 0.85, this may cause series effects onto building or factory electrical system.

Example when electrical loads with a low power factor will draws more current than a load with a high power factor for the same amount of useful power transferred. The higher currents increase the energy lost in the distribution system, and require larger wires and other equipment. Because of the costs of larger equipment and wasted energy, electrical utilities will usually charge a higher cost to industrial or commercial customers where there is a low power factor. 

Common causes is too many inductive loads.

Summary of low power factor:

Solution to low power factor 

It is crucial to raise up the power factor value to achieve at least greater than 0.85 (better if >0.85). This helps to eliminate the problem encounter from effects of lower power factor.  This commonly known as power factor correction (or PFC). 

The only solution to raise up power factor is by using capacitor bank circuit. 

When capacitor bank is install it will increase the power factor of a load, improving efficiency for the distribution system to which it is attached.  Linear loads with low power factor (such as induction motors) can be corrected with a passive network of capacitors or inductors. 

Finding cos θ  angle in degree 

Formula:   cos θ angle = cos-1 pf  =    (°)  

Example calculation

Example:  True  Power   

1)  Voltage is 24 volts, current I = 3A calculate total power, W. 

       Answer:     P = V x I      = 24v  X  3A  =   72 watts


2)  The current is I = 10A and resistance is 65 ohm, calculate total power, W.

       Answer:     P = I^2 x R      =  (6A x 6A)  X  65  =   2340 watts  


3)   Given V = 240 volts, current I = 20A, power factor is 0.88 on load connected, calculate power in single phase.

       Answer:     P = V x I x p.f     = 240v  X  20A x 0.88 =    4224.0 watts


4)   Given V = 415 volts, current I = 30A, power factor is 0.86on load connected, calculate power in three phase. 


       Answer:     P =  √ 3 x V x I x p.f     =   √ 3 X 415v  X  30A x 0.86 =     18,544.5 watts

Example:  Apparent Power 

1)  Given voltage supply is 240 volts and current is 60 ampere, calculate the apparent power, S.

       Answer:      S = V x I         =  240v x 60A  = 14,400 VA   (or 14.4 k VA)


2)  Given power is 24650 watts and power factor is 0.87, calculate the apparent power, S. 

         Answer:    S = P ÷ p.f     = 24,650 W ÷  0.87  =  28,333.33  VA     (or 28.3 k VA)

Example:  Reactive Power 

1)  Given  value of  S = 50 kVA and P = 38 kW, calculate the Q value. 


       Answer:      Q =√S² - P²          =  √50² - 38²  = 32.49 kVAR  

   

     To calculate the current shall apply this, 

             I = kVAR ÷ ( √ 3 X 415v )

     Answer:      I =  32.49 x 1000 VAR  ÷ ( √ 3 X 415v )  = 45.20 ampere


Example:  Angle of cos in degree 

1)  Given  value of  pf = 0.78, calculate the angle of cos θ  in degree. 


       Answer:         cos-1 pf  =    (°)         =  cos-1  0.78  =   38°    (or 38.73)

   

    

Source