Electrical Power in 3-Phase and 1-Phase Systems

Power in an electrical circuit or system is given by:

Where:

I = Current in Amps

V = Voltage in volts

The unit of power is the Watt(W). Power can also be expressed in volt amps (VA) usually in Alternating current systems.

In a D.C system, the current and voltage do not vary over time. Hence the product of voltage and current gives us power in Watt.

In A.C systems, the voltage and current entities are constantly changing in a sinusoidal manner as shown below:

A.C Voltage and Current Waveform

Hence in an A.C system, the product of current and voltage does not give power in Watts but gives power in VA (volt amps).  Power in watt for a single phase A.C system is given by:

Where:

P = power in watts

Iphase = phase current

Vphase = phase voltage

Cos? = power factor

In a three phase electrical system:

Power = 3 x power in single phase:

Delta (Mesh) & Star Connection in 3-phase A.C Systems

Alternating Current (A.C) power is often supplied and consumed in three phase systems that are commonly connected in Delta (Mesh) or Star connections:

Figure 1: Wye and Delta Connections in 3-Phase A.C circuits

The connection in Figure 1a above is known as a delta connection, because the diagram bears a close resemblance to the Greek letter, ?, called delta. The other connection style in figure 1b is known as the star or wye connection. The wye differs from the delta connection in that it has two phases in series. The common point �O� of the three windings is called the neutral because equal voltages exist between this point and any of the three phases. This point is commonly grounded. Typically, transformers, motors and generators can be connected in either Wye or Delta configurations.

Voltage and Current relationships in Delta & Wye connected Systems

(a) Delta connected System

In a Delta connected system(see Fig1a above):

Phase voltage = Line Voltage:

                           

Line current = 1.732 times Phase current i.e

                                

(b) Star or Wye Connected System 

In a Wye connected System (see Figure1b above):

Line current = Phase current

                              

Line voltage = 1.732 times Phase voltage

We have seen that power in a 3-phase system is given by:

 

Substituting the values for phase current and phase voltage for both Delta and Wye connected system into the above formula gives power in watts in a 3-phase A.C circuit connected in either Delta or Wye connection as:

So knowing the line voltage and line current in any 3-phase A.C circuit and the power factor , the power delivered into the system can easily be calculated.