Relation Between kVA and kW 

1.0Introduction

In physics and electrical engineering, two important quantities used to measure power are kVA (kilovolt-ampere) and kW (kilowatt). Although both are used in power systems, they represent different aspects of power.

• kVA represents apparent power.
• kW represents real (or active) power.

Understanding the relation between kVA and kW is essential when studying power systems, alternating current (AC) circuits, and the role of the power factor.

2.0What is kVA?

• Definition: kVA (kilovolt-ampere) is the unit of apparent power in an electrical system.
• Apparent power is the combination of real power (kW) and reactive power (kVAR).

Formula for Apparent Power:

$S=V\times I$

Where:

• S = Apparent Power (VA or kVA)
• V = Voltage (volts)
• I = Current (amperes)

1 kVA = 1000 VA

3.0What is kW?

• Definition: kW (kilowatt) is the unit of real power or active power.
• It represents the useful power that performs actual work such as running motors, lighting, heating, etc.

Formula for Real Power:

$P=V\times I\times cos\varphi \varphi$

Where:

• P = Real Power (Watts or kW)
• cos⁡ϕ = Power factor (ratio of useful power to total power)
• 1 kW = 1000 W

4.0What is the relationship between kVA and kW?

The relationship between kVA (kilovolt-ampere) and kW (kilowatt) is defined by the power factor. In simple terms, kW represents the real power—the power that does useful work—while kVA represents the apparent power—the total power delivered to a circuit. The two are equal only in purely resistive circuits where the power factor is 1. In most AC circuits, the presence of reactive components (inductors and capacitors) causes a phase difference between voltage and current, making kVA greater than kW. The fundamental relation is given by:

5.0Power Triangle: Active, Reactive, and Apparent Power

To understand the relation between kVA and kW, we must learn the power triangle.

• Active Power (P, in kW): Does useful work.
• Reactive Power (Q, in kVAR): Power wasted due to phase difference between current and voltage.
• Apparent Power (S, in kVA): Total supplied power.

This shows the vector relationship among the three powers.

$S^2=P^2+Q^2$

6.0Mathematical Relation Between kVA and kW

The key relation comes from the role of the power factor (cos φ):

kW=kVA×cos⁡ϕ

Where:

• kW = Real Power
• kVA = Apparent Power
• cos φ = Power Factor

7.0Formula for Conversion Between kVA and kW

1. From kVA to kW: $kW=kVA\times \text{Power factor}$
2. From kW to kVA: $kVA=\frac{kW}{\text{Power Factor}}$

Understanding Power Factor

• Definition: Power factor is the ratio of real power (kW) to apparent power (kVA).
• $\text{Power Factor}=\frac{kW}{kVA}$
• Range: 0 to 1
• High power factor: Efficient use of electrical power.
• Low power factor: More energy wasted, higher apparent power requirement.

8.0Units of kVA and kW

• kVA (Apparent Power):
• • Unit: Kilovolt-ampere (kVA)
  • Dimension: $[M{L}^2{T}^{-3}{I}^{-1}]$
• kW (Real Power):
• • Unit: Kilowatt (kW)
  • Dimension: $[M{L}^2{T}^{-3}]$

9.0Real-Life Examples of kVA and kW

1. Household Appliances: A 1.5-ton air conditioner rated at 2 kVA may only deliver ~1.6 kW of real power if power factor = 0.8.
2. Power Plants: Generators are rated in kVA because they must handle both real and reactive power.
3. Industrial Use: Motors and transformers are rated in kVA, but electricity bills are calculated in kW (kWh) since that’s actual usable power.

10.0Applications of kVA and kW in Physics and Engineering

• In AC Circuits: Understanding reactive, active, and apparent power helps in designing efficient systems.
• In Power Distribution: Transformers are rated in kVA, but consumer meters record energy in kWh (kilowatt-hour).
• In Electrical Machines: Performance is analyzed using both kW (useful output) and kVA (capacity).

11.0Difference Between kVA and kW