Transients occur on power transmission lines for unpredictable reasons including breakers opening and closing, load variations, and inputs to the grid from renewable energy sources turning on and off. A recursive technique allows a linear function to be fitted to a non-linear grid dynamic of the power line transients. The technique is adaptive and helps to stabilize an impedance injection unit while it injects correcting impedance into a transmission line for the purpose of achieving power flow control. When applied to many injection units the technique may also help to stabilize the overall grid. The stabilization system using the recursive technique provides real-time monitoring of the associated power line and stabilization with respect to power line transients.