Linear State Estimation with the Pi-Equivalent
To understand the fundamental difference between the measurements used in a traditional state estimator and the measurements used in a linear state estimator it is best to begin with a simple two-port pi-model equivalent of a transmission line. The state of
this simple system will be the voltage magnitude and angle at each end of the transmission line, represented here as a single complex variable. If there is a PMU at each end of the transmission line then it can be assumed that the measurement set for this
system will consists of the voltage phasors at each end of the line and the line flows leaving each end of the line.
Recall that because of the capacitance of transmission lines that the line current on each side of a single line will not be the same.
Consider the pi-equivalent of a transmission line shown below.