Using the PowerWorld Simulator case from Problem 6.59, if the rating on the line between buses 1 and 3 is \(65 \mathrm{MW}\), the current flow is \(59 \mathrm{MW}\) (from one to three), and the current bus one generation is \(160 \mathrm{MW}\), analytically determine the amount this generation can increase until this line reaches \(100 \%\) flow. Assume any change in the bus 1 generation is absorbed at the system slack.

Data From Problem 6.59:-

Open PowerWorld Simulator case Problem, which models a seven bus system using the dc power flow approximation. Bus 7 is the system slack. The real power generation/load at each bus is as shown, while the per unit reactance of each of the lines (on a 100 MVA base) is as shown in yellow on the one-line. (a) Determine the six by six \(\mathbf{B}\) matrix for this system and the \(\mathbf{P}\) vector. (b) Use a matrix package such as Matlab to verify the angles as shown on the one-line.