Active and reactive power and its equations

ACtive reactive and apparent power

1. Active, Reactive, Apparent
power and Power factor

2. Active power or real power or useful
power
The Active power is the power that is dissipated in the resistance of
the load. The REAL Power is the only useful power delivered to the
load.

Reactive power or useless power
The reactive power is the power that is exchanged between
reactive components (inductors and capacitors) i.e it is being
transferred back and forth between the load and the source.
Example: AC Motor loads and other loads require reactive power

4. Utility meters in home measure…………….. And
power company will charge for it.
Residential customers do not pay for………..
and utility meters in homes cannot perform
work.
By using multimeter we can measure current
and voltage and then multiply the readings
together we…………. Power.

5. Ratios of active and reactive power

6. POWER FACTOR
The power factor of a circuit can be defined in one
of the following three ways:
a)Power factor = cosØ= cosine of the angle between
voltage and current.
b)Power factor = R/Z = Resistance/ Impedance
c)Power factor = VIcosØ /VI =
=Active power/Apparent power

7. WHERE DOES THIS REACTIVE POWER COME FROM
Reactive power is mainly present when the voltage and
current are not in phase
1.One Waveform leads the other
2.Phase angle not equal to zero

8. POWER FACTOR
If the circuit is inductive, the current lags
behind the voltage and the power factor is to
as lagging.
However in capacitive circuit , current leads
the voltage and the power factor is said to be
leading.
UNITS
Active power = watts or kW
Reactive Power = VAR or kVAR
Apparent power = VA or kVA

9. Let us illustrate the power relations in an a.c
circuit with an example.
1. Suppose a circuit of 10A at a voltage of 200V
and its p.f is 0.8 lagging. Find Apparent power,
active power and reactive power.

10. Apparent power =2000VA
Active power = 1600W
Reactive power = 1200VAR
The circuit receives an apparent power of 2000VA
and is able to convert only 1600watts into active
power.
The reactive power is 1200VAR and does no useful
work. It merely flows into and out of the circuit
periodically.
In fact, reactive power factor is a liability on the
source because the source has to supply the additional
current(i.e IsinØ).

11. DISADVANTAGES OF LOW POWER FACTOR
Power factor play an important role in AC circuits and
power dissipation depends on this factor. WKT
Power in a Three Phase AC Circuit
P = √3 V x I CosФ
And Current in a Three Phase AC Circuits
i.e I 1 /CosФ….… (1)
∝
Also, Power in a Single Phase AC Circuits
P = V x I CosФ
And Current in a Three phase AC Circuits
I = P / (V x CosФ)
•I 1/CosФ……… (2)
∝

12. It is clear from both equations (1) an (2) that
Current “I” is inversely proportional to CosФ i.e.
Power Factor.

I 1/CosФ
∝
 In other words, When Power Factor increases,
Current Decreases, and when Power Factor
decreases, Current Increases.
Now, in case of Low Power Factor, Current
will be increased, and this high current will
cause to the following disadvantages.

13. 1)LARGE LINE LOSSES (COPPER LOSSES)
We know that Line Losses is directly proportional to the
square of Current “I
2
” .
Power Loss = I
2
xR i.e., the larger the current, the greater
the line losses i.e. I >> Line Losses.
In other words,
Power Loss = I
2
xR = 1/CosФ
2
….. Refer to Equation
“I 1/CosФ”….… (1)
∝
Thus, if Power factor = 0.8, then losses on this power
factor =1/CosФ
2
= 1/ 0.8
2
= 1.56 times will be
greater than losses on Unity power factor.

14. 2) Large kVA rating and Size of Electrical Equipments:
•As we know that almost all Electrical Machinery
(Transformer, Alternator, Switchgears etc) rated in kVA.
But, it is clear from the following formula that Power
factor is inversely proportional to the kVA i.e.
CosФ = kW / kVA
•Therefore, The Lower the Power factor, the larger the kVA
rating of Machines also, the larger the kVA rating of
Machines, The larger the Size of Machines and The Larger
the size of Machines, the Larger the Cost of machines.

15. 3) Greater Conductor Size and Cost
In case of low power factor, current will be
increased, thus, to transmit this high current,
we need the larger size of conductor. Also,
the cost of large size of conductor will be
increased.

16. 4) Poor Voltage Regulation and Large Voltage Drop
Voltage Drop = V = IZ
Now in case of Low Power factor, Current will be increased.
So the Larger the current, the Larger the Voltage Drop.
Also Voltage Regulation
V.R = (V
No Load
– V
Full Load
)/ V
Full Load
In case of Low Power Factor (lagging Power factor) there
would be large voltage drop which cause low voltage
regulation. Therefore, keeping Voltage drop in the
particular limit, we need to install Extra regulation
equipments i.e. Voltage regulators.

17. 5) Low Efficiency
In case of low Power Factor, there would be large
voltage drop and large line losses and this will
cause the system or equipments efficiency too low.
For instant, due to low power factor, there would
be large line losses; therefore, alternator needs high
excitation, thus, generation efficiency would be
low.
 
6) Penalty from Electric Power Supply Company
on Low Power factor
Electrical Power supply Company imposes a penalty of
power factor below 0.95 lagging in Electric power bill. So
you must improve Pf above 0.95.
 

18. CAUSES OF LOW POWER FACTOR
Low power factor is undesirable from economic
point of view. Normally, the power factor of the
whole load on the supply system in lower than
0·8. The following are the causes of low power
factor:
(i)Most of the a.c. motors are of induction type
(1φ and 3φ induction motors)
which have low lagging power factor. These
motors work at a power factor which is
extremely small on light load (0·2 to 0·3) and
rises to 0·8 or 0·9 at full load.

19. (ii) Arc lamps, electric discharge lamps and
industrial heating furnaces operate at low
lagging power factor.
(iii) The load on the power system is varying;
being high during morning and evening and low
at other times. During low load period, supply
voltage is increased which increases the
magnetisation current. This results in the
decreased power factor.

20. A current flowing around an electric circuit
may meet with three different kinds of
opposition or impedance They are caused by
1.Resistance (R),
2. inductance (L), and
3. capacitance (C).

21. Resistance
Of these, resistance is the easiest to
understand, because it has the same effect on
both direct currents and alternating currents.
When the voltage across the two terminals of
a resistance changes, the current changes
immediately. If the voltage rises, the current
rises; and if the voltage falls, the current falls,
and so on. Current and voltage are said to be
in phase.

22. Inductor
Inductors (L) and capacitors (C) behave quite
differently, In "L" circuits a rise in voltage is
accompanied by a rise in current, but this rise is
delayed by a back e.m.f. (see reactance) generated
by the inductor. As the voltage rises and falls, the
current rises and falls, but a fraction of a second
later. So the current flowing through the inductor
is always lagging behind the voltage, and current
and voltage are said to be out of phase.

23. capacitor
In "C" circuits, on the other hand, the current in
the circuit must first flow to the two plates of the
capacitor (round the circuit from plate to plate
and not across the gap between the plates) to
make potential difference across them. As the
current rises, the voltage between the two
plates rises; and as the current falls, the voltage
falls, but the voltage follows the current's lead a
fraction of a second later. Current and voltage
are again out of phase, only in "C" circuits the
current is always leading the voltage.