Power flow: the phase angle pushes the active power
Drag the angle and read the power curve
The two bus voltages are held at the same magnitude, and the only thing the handle changes is the angle difference δ. The active power P = (V_s V_r / X) sin δ rises as δ grows, reaches its maximum at 90°, the top of the orange dashed line, and falls if you keep dragging. The dot on the curve is the power flowing right now, and it turns from green to red the moment it crosses that boundary.
The angle difference pushes active power
Picture a line that is almost pure reactance, with one bus at each end. Even when the two voltages have the same magnitude, if one phase leads the other, active power flows from the leading bus to the lagging one. Its size is P = (V_s V_r / X) sin δ, so it grows as the phase difference δ widens. Feed more mechanical input into a generator and its rotor moves slightly ahead, δ opens up, and correspondingly more power goes out into the grid. The handle for active power is the angle, not the voltage.
Reactive power follows the magnitude difference
Between the same two buses, reactive power is driven the other way, by the difference in voltage magnitude. The reactive power at the sending end is Q ≈ (V_s/X)(V_s − V_r cos δ), so for small δ it flows from the bus with the higher magnitude to the one with the lower. That is why a generator handles reactive power by raising its excitation (field current) to lift the voltage magnitude, and active power by raising its mechanical input to advance the phase. Active power goes with angle and reactive power with magnitude, so the two behave almost like two separate handles.
Past 90°, synchronism collapses
P = P_max sin δ reaches its maximum P_max = V_s V_r / X at δ = 90°. Below that point, as load grows and δ widens, the power sent out grows with it and the system can hold on. Past 90° the picture changes: sin δ starts to fall, so widening the angle further delivers less power, the surplus mechanical input accelerates the generator, its phase slips, and synchronism is lost. This is the steady-state stability limit. Transmission lines therefore cut X with series compensation or raise the voltage to enlarge P_max, and they run with δ well below 90°.
Back to the first screen
On the first screen the two voltage magnitudes stayed equal the whole time, yet widening the angle δ set active power flowing and brought it to its peak at 90°. What pushed the power was not how high or low the voltages were but how far one phase led the other. When the curve turned downhill past 90° and the dot went red, it was because the region beyond is unstable: there synchronism is lost and the system collapses. Power-flow analysis comes down to fixing each bus's voltage magnitude and angle, then reading off the active and reactive power flowing in every line.
The power flow so far describes a system whose three phases are balanced. Real faults usually strike only one or two phases and break that balance, and the next unit (PW-D2), on symmetrical components, deals with exactly that. Split the unbalanced phases into three sets of equal-magnitude phasors, the positive sequence with the original phase order, the negative sequence with the order reversed, and the zero sequence with all three phases in step, and the tools for balanced systems can solve unbalanced faults unchanged. The zero sequence you met in A5 as neutral current finds its place here as well.