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These include:

- Each row of the matrix corresponds to a current phasor measurement in the network
- Each column of the matrix corresponds to an indirectly (via current phasor) or directly observed (via voltage phasor) bus in the system.
- The current phasor measurements and observed busses are enumerated.
- If measurement
**X**(corresponding to row**X**) leaves bus**Y**(corresponding to column**Y**) then the matrix element (**X**,**Y**) will be a 1. - If measurement
**X**(corresponding to row**X**) heads towards bus**Z**(corresponding to column**Z**) then the matrix element (**X**,**Z**) will be a -1. - All remaining entries will be identically zero.

Consider the fictious 5 bus transmission network shown below. The presence of a

current measurement is represented by an arrow above a CT.

The current measurement bus index matrix for this system in a single phase

representation would look like the following:

The

... using SynchrophasorAnalytics.Matrices using SynchrophasorAnalytics.Networks ... Network network = Network.DeserializeFromXml("//pathToNetworkModel"); CurrentMeasurementBusIncidenceMatrix A = new CurrentMeasurementBusIncidenceMatrix(network);

Voltage phasors measurements are actually a direct measurement of the system state and therefore only require a simple identity relationship between the measurement and the state. The voltage measurement-bus incidence matrix is an

This matrix is populated using the following rules.

- Each row of the matrix corresponds to a voltage measurement in the network
- Each column of the matrix corresponds to a bus in the system which has a voltage phasor measurement.
- The voltage phasors and the observed busses are enumerated.
- If measurement
**X**(corresponding to row**X**) is located at bus**Y**(corresponding to column**Y**) then the matrix element (**X**,**Y**) will be a 1. - All remaining entries will be identically 0.

Consider again the small fictitious system shown in the previous section. The location of the voltage measurements are shown by the circles on the busses. For a single phase representation, the

The

... using SynchrophasorAnalytics.Matrices using SynchrophasorAnalytics.Networks ... Network network = Network.DeserializeFromXml("//pathToNetworkModel"); VoltageMeasurementBusIncidenceMatrix II = new VoltageMeasurementBusIncidenceMatrix(network);

It is populated using a single rule:

- For measurement
**X**, the (**X**,**X**) matrix element is the admittance of the branch being measured.

The

... using SynchrophasorAnalytics.Matrices using SynchrophasorAnalytics.Networks ... Network network = Network.DeserializeFromXml("//pathToNetworkModel"); SeriesAdmittance Y = new SeriesAdmittanceMatrix(network);

measurement to the shunt admittance of the line that it is measuring. It is an

where

observed busses in the network.

It is populated using a single rule:

- For measurement
**X**(corresponding to column**X**) leaving bus**Y**(corresponding to row**Y**), the matrix element (**X**,**Y**) is the shunt admittance of the side of the line where measurement was taken.

The

... using SynchrophasorAnalytics.Matrices using SynchrophasorAnalytics.Networks ... Network network = Network.DeserializeFromXml("//pathToNetworkModel"); ShuntSusceptance Ys = new ShuntSusceptanceMatrix(network);

The system matrix is a vertical concatenation of the

Shown below are the matrices for the above example system.

The

... using SynchrophasorAnalytics.Matrices using SynchrophasorAnalytics.Networks ... Network network = Network.DeserializeFromXml("//pathToNetworkModel"); SystemMatrix systemMatrix = new SystemMatrix(network);

Last edited Jul 24, 2013 at 6:41 PM by kevinjones, version 9