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JEET, Vol. 11, No. 1, January 2016 
Quick and Accurate Computation of Voltage Stability Margin
Farid Karbalaei 
Area 
A  Electric Power Engineering 
Abstract 
It is well known that the behavior of PV curves is similar to a quadratic function. This is
used in some papers to approximate PV curves and calculate the maximumloading point by minimum
number of power flow runs. This paper also based on quadratic approximation of the PV curves is
aimed at completing previous works so that the computational efforts are reduced and the accuracy
is maintained. To do this, an iterative method based on a quadratic function with two constant
coefficients, instead of the three ones, is used. This simplifies the calculation of the quadratic
function. In each iteration, to prevent the calculations from diverging, the equations are solved on
the assumption that voltage magnitude at a selected load bus is known and the loading factor is
unknown instead. The voltage magnitude except in the first iteration is selected equal to the one at
the nose point of the latest approximated PV curve. A method is presented to put the mentioned
voltage in the first iteration as close as possible to the collapse point voltage. This reduces the number
of iterations needed to determine the maximumloading point. This method is tested on four IEEE
test systems. 
Keyword 
Quadratic approximation,Voltage collapse,Voltage stability margin,Collapse point voltage

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