# Star Delta Connection | Complete Overview | It’s 5+ Important Relations

Star Connection and Delta Connection

Image Credit – Pravin MishraMilky Way Galaxy As Seen From Amphulaptsa Base CampCC BY-SA 4.0

## Introduction to Star Connection and Delta Connection

Star and delta connections are the two very well-known methods for establishing a three-phase system. They are an essential and widely used system. This article will discuss the basics of both star and delta connections and relations between phase and link voltage and current within the system. We will also find out the significant differences between star and delta connection.

## Star Connection

Star connection is the method where the similar types of terminals (all three windings) are connected to a single point, known as star point or neutral point. There are also line conductors, which are the free three terminals. The designing of wires at the external circuits makes it a three phase, three wire circuit and makes the star connection. There may be another wire named a neutral wire that makes the system a three phase, four-wire system.

## The relation between Phase Voltage and Link Voltage of Star Connection

The system is considered as a balanced system. For a balanced-systems, an equal amount of current will pass through all 3-phase. That is why, R, Y, B has the same value of current. Now it has consequences. This uniform distribution of current makes the magnitudes of the voltages – ENR, ENY, ENB same and they get displaced by 120 degrees from one another.

In the above images, the arrow represents the direction of currents and voltages (not the actual order though). As we have discussed earlier, due to the uniform current distribution, the three arms’ voltage is equal so that we can write –

ENR = ENY = ENB = Eph.

And we can observe that the voltages in-between two lines is a two-phase voltage.

So, observing the NRYN loop, we can write that,

ENR + ERY – ENY = 0

Or, ERY = ENY – ENR

Now, from vector algebra,

ERY = √ (ENY2 + ENR2 + 2 * ENY * ENR Cos60o)

Or, EL = √ (Eph2 + Eph2 + 2 * Eph * Eph x 0.5)

Or, EL = √ (3Eph2)

Or, El = √3 Eph

In the same way, we can write, EYB = ENB – ENY.

OR, EL = √3 Eph

And,

EBR = ENR – ENB

Or, El = √3 Eph

So, we can say that the relation between the line voltage and phase voltage is:

Line Voltage = √3 x Phase voltage

## Relation Between Phase Current and Line Current in Star Connection

The uniform current flow in phase windings is the similar as the current flow in the line conductor.

We can write –

IR = INR

IY = INY

And IB = INB

Now, the phase current will be –

INR = INY = INB = Iph

And the line current will be – IR = IY = IB = IL

So, we can say that, IR = IY = IB = IL

## Delta connection

Delta connection is another method to establish three phases of an electrical system. The end terminal of the windings is attached to the starting of the other terminals. Three-line conductors are connected from three junctions. The delta connection is set up by tying the ends. For that we combine a2 with b1, b2 with c1 and c2 with a1. Line conductors are the R, Y, B which run from three junctions. The below image depicts a typical delta connection and shows the end-to-end connections.

## The relation between phase voltage and the line voltage of the Delta connection

Let us find out the relation between phase voltage of a delta circuit with the circuit’s line voltage. For that, observe the above image carefully. We can say that the value of the voltage at both the terminal 1 and terminal 2 is the same as the terminal R and terminal Y.

So, we can write – E12 = ERY.

In the same way, we can conclude by observing the circuit, E23 = EYE.

And E31 = EBR

The phase voltages are written as: E12 = E23 = E31 = Eph

The line voltages are written as: ERY = EYB = EBR = EL.

So, we can conclude that, in case of a delta connection, the phase voltage will be equal to the circuit’s line voltage.

## The relation between phase current and line current in delta connection

For a balanced delta connection, the constant voltage value affects the current values. The current values of I12, I23, I31 are equal, but they are displaced by 120 degrees from one another. Observe the below-given phasor diagram.

We can write, I12 = I23 = I31 = Iph

Now, by applying Kirchhoff’s law at junction 1,

We know that the algebraic sum of the current of a node is zero.

So, I31 = IR + I12

The vectoral differences come as IR = I31 – I12

By applying vector algebra,

IR = √ (I312 + I122 + 2 * I31 * I12 * Cos 60o)

Or, IR = √ (Iph2 + Iph2 + 2 * Iph * Iph x 0.5)

As, we have discussed earlier, IR = IL.

Or, IL = √ (3Iph2)

Or, IL = √3 * Iph

In the same way, IY = I12 – I23.

Or, IL = √ 3 * Iph

And, IB = I23 – I31

Or, IL = √ 3 Iph

So, the relation between line current and phase current can be written as:

Line Current = √3 x Phase Current

## Difference between Star and Delta Connection

Star and delta methods are two renowned methods for three phase systems. Depending on various factors, there are some fundamental differences between them. Let us discuss some of them.

## Conversion from Star to Delta and Delta to Star

A star network can be converted into a delta network, and a delta connected network can be converted into a star network if needed. Conversion of circuits is necessary to simplify the complicated course, and thus the calculation becomes more effortless.

### Conversion from Star to Delta

In this conversion, a connected star network is replaced by its equivalent delta connected network. The star and replaced delta figure are given. Observe the equations.

The value of Z1, Z2, Z3 is given in terms of ZA, ZB, ZC.

Z1 = (ZA ZB + ZB ZC + ZC ZA) / ZC = Σ (ZA ZB) / ZC

Z2 = (ZA ZB + ZB ZC + ZC ZA) / ZB = Σ (ZA ZB) / ZB

Z3 = (ZA ZB + ZB ZC + ZC ZA) / ZA = Σ (ZA ZB) / ZA

We can easily convert a connected star network into a delta connected if we know the star-connected network’s value.

### Conversion from Delta to star

In this conversion, a delta connected network is replaced by its equivalent star connected network. The delta and replaced star figure are given. Observe the equations.

The value of ZA, ZB, ZC is given in terms of Z1, Z2, Z3.

ZA = (Z1 Z2) / (Z1 + Z2 + Z3)

ZB = (Z2 Z3) / (Z1 + Z2 + Z3)

ZC = (Z1 Z3) / (Z1 + Z2 + Z3)

We can easily convert a delta connected network into a star connected if we know the value of the delta connected network.

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