Using the PowerWorld Simulator case from Problem 6.59, if the rating on the line between buses 1 and 2 is \(150 \mathrm{MW}\), the current flow is \(101 \mathrm{MW}\) (from bus 1 to bus 3 ), and the bus 1 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.

Problem 6.59

Open PowerWorld Simulator case Problem 6_59, which models a seven-bus system using the de 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 oneline.

(a) Determine the six-by-six 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 oneline.