Condition for Zero and Maximum Voltage Regulation

Voltage regulation is given by this approximation

V.R. =  IR Cosφ± IR X Sinφ ] / VR

  • For Zero voltage regulation : Zero voltage regulation means, Sending end voltage and Receiving end voltage become equal. This case is also known as ideal voltage regulation.

When V.R. = 0

IR CosφR + IR X SinφR = 0

R Cosφ= – X SinφR

tan φR = – ( R/X )

φR = – tan-1( R/X )

φR = cot-1( X/R )

cot-1( X/R ) + tan-1( X/R ) = Π / 2

cot-1( X/R ) = Π / 2 –  tan-1( X/R )

φ= Π / 2 –  tan-1( X/R )

tan-1( X/R ) ∈ (-Π/2 , +Π/2 )

NOTE : Here Reference phasor is IR

φR ∈ ( -Π , 0 ) ,  angle between Iand VR is negative, means leading power factor ( Iis leading the voltage VR

  • For maximum voltage regulation :

Condition for maximum V.R.  ≫  ∂(V.R.) ∕ ∂φR = 0

∂(V.R.) ∕ ∂φR = [-R Sinφ+ X CosφR] = 0

tan φR = X / R

φR =tan-1( X / R )

φR ∈ ( 0, Π/2 )  [Because Both X and R are Positive]

φR > 0 [ Lagging power factor ≫ Current is lagging to Voltage ]

voltage-regulation5

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