Balanced delta connected load

BALANCED DELTA CONNECTED LOAD

Fig.4.10 shows a balanced delta - connected load of impedance Z in each phase.

Z  = | Z| ∠ϕ

The phasor diagram is also shown in fig.4.10.

Assume the phase sequence to be RYB. Taking ERY as reference

Expression for total power in a 3 phase balanced circuit

Let E ϕ = Voltage per phase

I ϕ = Current per phase

cos ϕ Power factor of the balanced load

Total average power W = 3 E ϕ Iϕ cos ϕ … (i)

Usually, this expression is expressed in terms of line voltage and line current as below:

Case (1): Star connected load:

Substituting these values in equation (i)

Case (2): Delta connected load:

Putting these values in equation (i), we get

E_L and I_L are in volts and amperes respectively.

Then the power W is in watts. Dividing both sides of the equation (iii) by 1000, we get:

W / 1000 =  √3E_L I_L / 1000 cos ϕ

W/1000 is actual power or average power or a real power or true power. (denoted by P) in KW.

√3E_L I_L / 1000 is apparent power (denoted by S) and measured in KV amperes (KVA).

KW = KVA cos ϕ ... (iv)

From equation (iv), we can draw the power triangle which is shown below:

It is right-angled triangle from which we get the relation S = P  + jQ

⇒ S = √ P² + Q² …. (v)

Here P = KVA cos ϕ

= active power

Q = KVA sin ϕ

= reactive power and

S = KVA = apparent power