# What is the Difference between kW and kVA?

kW is the unit of active power which is consumed by load for doing real work. The real power drawn from the system is also known as active power or average power. kVA is the apparent power drawn from the supply source for the functioning of the electrical equipment. The electrical equipment draws reactive power to meet its magnetizing current requirement.

To understand the concept of apparent power let the concept of reactive power be understood first. The equipment which functions on the magnetic principle always draws reactive power known as kVAr. The kVAr is the power that is not consumed by the equipment but it is stored in the system.

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The reactive elements like inductor, capacitor and non-linear loads like diode,bipolar junction transitor, MOSFET, IGBTS etc. draw reactive current from the supply source. These electrical components consumes reactive power(kVAr) but these do not consume the real power except some minor active power.  Thus the inductor, capacitor and the non linear loads draw reactive power(kVAr) from the supply source.

When an inductor is connected to alternating supply supply source it draws current which lags the voltage by 90 degree.The active power drawn by  inductor is zero, the inductor draws only reactive power (kVAr) except very minor active power in the form of heat loss.

Similar to an inductor, when a capacitor is connected to alternating supply supply source it draws current which leads the voltage by 90 degree.The active power drawn by capacitor is zero, the capacitor draws only reactive power (kVAr) except very minor active power in the form of heat loss.

The reactive components inductor and capacitor do not draw any real power or active power from the system, but these circuit components draw current from the system to meet their reactive power(kVAr) requirement. Thus, the total current drawn from the supply source is the vector sum of the active and reactive current. The concept of all three types of power-active power(kW),reactive power(kVAr) and apparent power(kVA) can be well understood with the power triangle diagram. From above power triangle,

The relationship between kW, kVAr and kVA is as follows.

kVA= kW+ kVAr

kVA2= kW2 + kVAr2

kVA =√(kW2 +kVAr2)

Where,

kVA    – Apparent Power
kW     – Active Power
kVAr   – Reactive Power

If the reactive current drawn is zero, the apparent power is equal to the real or active power. In case of the resistive loads the reactive current is zero and the real power and the apparent power is equal.

In case of the inductive and capacitive loads the apparent power(kVA) is always more than the active power. The apparent power increase with an increase in the reactive power with the same active power. The power factor gets lowered with an increase in the reactive power.

### Relation between KVA and KW

The relation between KVA and KW for single phase and three phase AC circuit is given below.

##### Single Phase Circuit- KVA and KW

The relationship between apparent power and active power is as given below.

kW = kVA CosΦ

Where,

CosΦ is the power factor.

kVA = kW/ CosΦ

The power factor is unity for the resistive loads and thus, the kVA is equal to the kW.

The inductor and capacitor current lags and leads the voltage by 90 degree respectively. For single phase circuit, the active power drawn by the inductor is;

P= kVA CosΦ

Φ = 90

P = kVA x Cos90
P = kVA  x 0     Cos90 =0]

P = 0

Thus the active power drawn by pure inductor is zero. For single phase circuit, the reactive power drawn by inductor is;

Q= kVA SinΦ

Q = kVA x Sin90
Q = kVA  x 1     Sin90 =1]

Q = kVA

Thus, the pure inductor draws reactive power only. The similar case is with capacitor. The capacitor also draws zero active power,it draws only reactive power.

##### Three Phase Circuit- KW and KVA

For three phase circuit the phase voltage is about 58 % of the line voltage.

VLL = √3 VLN

VLN = VLL /√3

The active power(P) in a three phase circuit is;

P = √3 V I CosΦ

Where,

V = Line to line voltage

I   = Line current

The reactive power(Q) in a three phase circuit is;

Q = √3 V I SinΦ

The apparent power(S) in a three phase circuit is;

kVA =√(kW2 + kVAr2)

S= √[(√3 V I cosΦ)2 +(√3 V I SinΦ)2 ]

S = √3 V I

Where,

S is apparent power.

The electrical equipment always draw reactive power for its working and active power for delivering the useful work. Some of the electrical equipment rating is specified in apparent power(kVA)

The manufacturer specify the transformer and alternator rating is kVA because he does not know at what power factor the user will operate the equipment.

#### KW to KVA Calculations

KW to KVA conversion formula is,

KW = KVA X PF

Where,

• KW- Real Power or Active Power
• KVA – Apparent Power
• PF – Power Factor

#### KVA to KW Calculations

KW to KVA conversion formula is,

KVA = KW/ PF

Where,

• KW- Real Power or Active Power
• KVA – Apparent Power
• PF – Power Factor

### Solved problems on kW and KVA

A balanced three phase load draws 100 KW power at power factor 0.90. The system line to line voltage is 440 Volts(RMS). What is the apparent power drawn by the load.

Apparent power
kVA = KW/CosΦ
kVA = 100/0.9
kVA = 111.11

Line current IL
IL= kVA/√3 V
IL= 111.11/(1.732 x 0.440)
IL= 145.79 Amps.

If the power factor of the system is improved to 0.995, what is the kVA and the Line current?

kVA = KW/CosΦ
kVA = 100/0.95
kVA = 105.26

Line current IL
IL= kVA/√3 V
IL= 105.26/(1.732 x 0.440)
IL= 138.12 Amps.
Thus the kVA and line current gets decreased with improvement of power factor.

Thus, the kVA and kW depends on the load power factor.

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