Below is a 2-bus system with two transmission lines.
For the above diagram we will assume the values of 1.2 and 0.8 p.u. for
the reactances of the transmission lines, 1 p.u. for the value of the
generator bus |V1|, and a unity power factor at the load bus
(i.e. ß = 0). The combined reactance for this two
transmission line system is X = 0.48 p.u. For purposes of this DEMO
and simplicity of all forthcoming plots we have rounded this to X = 0.5
p.u. Below is the representative PV plot for this two transmission line
system with X = 0.5 p.u.
Just as above, the PV curves that follow are based on the assumption of
a two transmission line system operating with different line reactances.
Should something occur to cause a loss of a transmission line, the PV
plot would change to look like one of the plots below.
The top plot shows
the PV curve that would result if the transmission line that failed had
a high reactance and the remaining operable line had a low reactance (X
= 0.8 p.u.).
The lower plot shows the PV curve that would result if the
transmission line that failed had a low reactance and the remaining operable
line had a high reactance (X = 1.2 p.u.). The plot shows that the operating point A
move to the second position nearly approaches the condition of "voltage collapse".
On both plots Pt. A now lies on the smaller PV curve. This places the
system below normal operating parameters and the large voltage drop creates
a breach of voltage security.
The loss of a transmission line can be corrected with the addition of
shunt capacitance by adjusting ß in the below PV equation.
|V2|2 = |V1|2/2
- ßPDX ± [|V1|4/4 -
PDX (PDX + ß|V1|2)]1/2
