MicrogridLine

The Line used for the Microgrid found in Pogaku et al.[1] and Bidram et al.[2].

Parameters:

• \(R\) - Resistance

• \(L\) - Inductance

Variables (External):

• \(\omega_{ref}\) - Reference Rotor Angle

• \(v_{D1}\) - Incoming Bus 1 Voltage (D)

• \(v_{Q1}\) - Incoming Bus 1 Voltage (Q)

• \(v_{D2}\) - Incoming Bus 2 Voltage (D)

• \(v_{Q2}\) - Incoming Bus 2 Voltage (Q)

• \(i_{D}\) - Line Current (D)

• \(i_{Q}\) - Line Current (Q)

Contributions to external equations:

• \(0\)    (Reference Rotor Residual)

• \(-i_{D}\)    (Bus 1 residual term)

• \(-i_{Q}\)    (Bus 1 residual term)

• \(i_{D}\)    (Bus 2 residual term)

• \(i_{Q}\)    (Bus 2 residual term)

Internal equations:

• \(\frac{di_{D}}{dt} = -(\frac{R}{L}) i_{D} + \omega_{ref} i_{Q} + \frac{v_{D1} - v_{D2}}{L}\)

• \(\frac{di_{Q}}{dt} = -(\frac{R}{L}) i_{Q} + \omega_{ref} i_{D} + \frac{v_{Q1} - v_{Q2}}{L}\)

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[1]

Pogaku, Nagaraju, Milan Prodanovic, and Timothy C. Green. “Modeling, analysis and testing of autonomous operation of an inverter-based microgrid.” IEEE Transactions on power electronics 22.2 (2007): 613-625.

[2]

Bidram, Ali, Frank L. Lewis, and Ali Davoudi. “Distributed control systems for small-scale power networks: Using multiagent cooperative control theory.” IEEE Control systems magazine 34.6 (2014): 56-77.