Active, Reactive, Apparent and Complex Power
Active Power: (P)
Active Power is the actual power which is really transferred to the load such as transformer, induction motors, generators etc and dissipated in the circuit.
Alternative words used for Real Power (Actual Power, True Power, Watt-full Power, Useful Power, Real Power, and Active Power) and denoted by (P) and measured in units of Watts (W) i.e. The unit of Real or Active power is Watt where 1W = 1V x 1 A. .
Active Power in DC Circuits:
In DC Circuits, power supply to the DC load is simply the product of Voltage across the load and Current flowing through it i.e., P = V I because in DC Circuits, there is no concept of phase angle between current and voltage. In other words, there is no frequency (f) or Power factor in DC Circuits.
Active Power in AC Circuits:
But the situation in Sinusoidal or AC Circuits is more complex because of phase difference (θ) between Current and Voltage. Therefore average value of power (Real Power) is P = VI Cosθ is in fact supplied to the load.
In AC circuits, When circuit is pure resistive, then the same formula used for power as used in DC as P = V I.
You may also read about Power Formulas in DC, AC Single Phase and and AC Three Phase Circuits.
Active Power Formulas:
- P = V x I (In DC circuits)
- P = V x I x Cosθ (in Single phase AC Circuits)
- P = √3 x VLx IL x Cosθ or (in Three Phase AC Circuits)
- P = 3 x VPh x IPhx Cosθ
- P = √ (S2 – Q2)or
- P =√ (VA2 – VAR2) or
Real or True Power or Active Power = √ (Apparent Power2 – Reactive Power2) or
kW = √ (kVA2 – kVAR2)
- P = Power in Watts
- V = Voltages in Volts
- I = Current in Amperes
- Cosθ = Power Factor (Phase angle Difference)
- VL = Line Voltage
- IL = Line Current
- S = Apparent Power in VA (Volt Ampere)
- Q = Reactive Power in VAR (Volt Ampere Reactive)
Reactive Power: (Q)
Also known as (Use-less Power, Watt less Power)
The powers that continuously bounce back and forth between source and load is known as reactive Power (Q)
Power merely absorbed and returned in load due to its reactive properties is referred to as reactive power.
Reactive power is given by Q = V I Sinθ which can be positive (+ve) for inductive loads and negative (-ve) for capacitive load.
The unit of Reactive Power is Volt-Ampere reactive i.e. VAR where 1 VAR = 1V x 1A.
In more simple words, in Inductor or Capacitor, how much magnetic or electric field produced by 1A x 1V is known as the unit of Reactive Power.
- Must read: Is Reactive Power Useful?
Reactive Power Formulas:
- Q = V I Sinθ
- Reactive Power = √ (Apparent Power2– True power2)
- VAR = √ (VA2 – P2)
- kVAR = √ (kVA2 – kW2)
- θ = Phase angle
Apparent Power: (S)
The Product of voltage and current if and only if the phase angle differences between current and voltage are ignored.
Total power in an AC circuit, both dissipated and absorbed/returned is referred to as apparent power
The combination of reactive power and true power is called apparent power
In an AC circuit, the product of the r.m.s voltage and the r.m.s current is called apparent power which is denoted by (S) and measured in units of Volt-amp (VA).
It is the product of Voltage and Current without phase angle.
The unit of Apparent power (S) VA i.e. 1VA = 1V x 1A.
When the circuit is pure resistive, then apparent power is equal to real or true power, but in inductive or capacitive circuit, (when Reactances exist) then apparent power is greater than real or true power.
Apparent Power Formulas:
- S = V I
- S = √ (P + Q2)
- Apparent Power = √ (True power2 + Reactive Power2)
- kVA = √kW2 + kVAR2
Complex Power: (S = P+jQ or S=VI*)
The Complex sum of Real Power (P) and Reactive Power (Q) is known as Complex Power which can be expressed like S = P+jQ and measured in terms of Volt Amps Reactive (generally in kVAR).
It may also be expressed as S=VI* where “I*” is the conjugate of the complex current I. This current “I” flows through a reactive load Z caused by the Voltage.
Complex Power Formulas:
Complex Power in Capacitive Loads
- Z = R – jXC
- I = IP + jIQ
- Cosθ = R / |Z| (leading)
- I* = IP – jIQ
- S = P – jQ
A Capacitive Load provide Leading VARS (i.e. it eliminates VARS and improves the overall power factor of the system). That’s why capacitors are used to correct and improve the power factor.
Complex Power in Inductive Loads
- Z = R + jXL
- I = IP – jIQ
- Cosθ = R / |Z| (lagging)
- I* = IP + jIQ
- S = P + jQ
- Z = Impedance
- R = Resistance
- XL = Inductive Reactance
- XC = Capacitive Reactance
- Cosθ = Power Factor
- P = Active Power
- S = Apparent Power
- Q = Reactive Power
An Inductive Load provide lagging VARS (i.e. it added VARS and decrease the overall power factor.)
Complex power can also be expressed by the following formula.
Resistor absorbs the real power and dissipates in the form of heat and light. Inductor absorbs the reactive power and dissipates in the form of magnetic field Capacitor absorbs the reactive power and dissipates in the form of electric or electrostatic filed
Good to know:
Resistor absorbs the real power and dissipates in the form of heat and light.
Inductor absorbs the reactive power and dissipates in the form of magnetic field
Capacitor absorbs the reactive power and dissipates in the form of electric or electrostatic filed
For easy explanation, all the related quantities can be easily understand by the funny Lays Chips and Beer Analogy for Real or True or Active Power, Reactive Power , Apparent Power and power factor.
- Power Factor
- Causes of low Power Factor
- Advantages of Power factor improvement and Correction
- Disadvantages of Low Power Factor
- Power Factor improvement Methods with Their advantages & Disadvantages
- How to Calculate the Suitable Capacitor Size in Farads & kVAR for Power factor Improvement
- How to Convert Capacitor Farads into kVAR and Vice Versa (For Power factor improvement)
- CAPACITOR BANKS – CHARACTERISTICS AND APPLICATIONS