Measurements: The measurements utilized in this approach are all available measurements in the substation mainly from SCADA, Relays, IEDs, fault disturbance recorders and PMUs. The measurements are categorized into GPS-synchronized and non-synchronized ones. Mathematically these two categories are treated differently.
The GPS-synchronized phasor measurement set consists of voltage and current measurements, both magnitude and phase in all three phases. Voltage measurements are direct state measurements. Current measurements can be expressed in terms of linear measurement equations with respect to the system state, provided that a rectangular coordinate formulation is used. Non-synchronized measurements consist of SCADA measurements of voltage and, possibly, current magnitude, active and reactive power flows at each side of the substation transformer and on the substation end of the lines. Such measurements are typically obtained via analog measurement devices and are in general related to the system state via a set of non-linear equations. In our formulation such measurement equations are of degree at most quadratic. In addition to the actual measurements the approach is facilitated by a number of pseudo-measurements. These are defined below.
Pseudo-measurements of the voltages at the other end of the lines (neighboring substations): These pseudo measurements are illustrated in Figure 5. Given measurements of (all three phases) and (all three phases) of a line i at a substation k and a 3-phase model of the line allows the calculation of the voltage pseudo-measurement at the other end of the line (neighboring substation). Other pseudo-measurements are available and utilized.