DistributedGenerator

Source: GridKit/Model/PowerElectronics/DistributedGenerator/README.md

The Distributed Generator Component found in references 1 and 2.

Parameters:

  • \(\omega_b\) - Reference Rotating Frame

  • \(\omega_c\) - Cutoff Frequency

  • \(m_p\) - Drop Gain, Frequency Range

  • \(V_n\) - Nominal Set Point of D-Axis Output Voltage

  • \(n_q\) - Voltage Range

  • \(F\) - PI Controller Parameter in 1 & 2

  • \(K_{pv}\) - PI Controller Parameter in 1 & 2

  • \(K_{iv}\) - PI Controller Parameter in 1 & 2

  • \(K_{pc}\) - PI Controller Parameter in 1 & 2

  • \(C_f\) - Shunt??

  • \(r_{Lf}\) - Resistance of line f

  • \(L_{f}\) - Inductance of line f

  • \(r_{Lc}\) - Resistance of line c

  • \(L_{c}\) - Inductance of line c

Variables (External):

  • \(\omega_{ref}\) - Network reference \(\omega\)

  • \(V_{a}\) - Incoming Bus Voltage (a)

  • \(V_{b}\) - Incoming Bus Voltage (b)

Variables (Internal):

  • \(\delta\) - Rotor difference from reference

  • \(\omega\) - Frequency

  • \(P\) - Real Power

  • \(Q\) - Reactive Power

  • \(\phi_{d}\) - Output Voltage Control PI Variable

  • \(\phi_{q}\) - Output Voltage Control PI Variable

  • \(\gamma_{d}\) - Output Current Control PI Variable

  • \(\gamma_{q}\) - Output Current Control PI Variable

  • \(i_{ld}\) - Current of Line l (dq-space)

  • \(i_{lq}\) - Current of Line l (dq-space)

  • \(v_{od}\) - Voltage of Bus o (dq-space)

  • \(v_{oq}\) - Voltage of Bus o (dq-space)

  • \(i_{od}\) - Current of Line o (dq-space)

  • \(i_{oq}\) - Current of Line o (dq-space)

Equations (External, Residuals):

  • \(\omega_{com} - \omega\)    (If this generator is considered the reference one, otherwise 0)

  • \(\cos(\delta) i_{od} - \sin(\delta) i_{oq}\)

  • \(\sin(\delta) i_{od} + \cos(\delta) i_{oq}\)

Equations (Internal):

  • \(\omega_{com} = \omega_{b} - m_{p} P\)

  • \(\frac{d\delta}{dt} = \omega_{com} - \omega\)

  • \(\frac{dP}{dt} = \omega_c ( v_{od} i_{od} + v_{oq} i_{oq} - P)\)

  • \(\frac{dQ}{dt} = \omega_c ( v_{od} i_{oq} + v_{oq} i_{od} - Q)\)

  • \(v_{od}^* = V_{n} - n_q Q\)

  • \(v_{oq}^* = 0\)

  • \(\frac{d\phi_{d}}{dt} = v_{od}^* - v_{od}\)

  • \(\frac{d\phi_{q}}{dt} = v_{oq}^* - v_{oq}\)

  • \(i_{ld}^* = F i_{od} - \omega_{b} C_{f} v_{oq} + K_{pv} (v_{od}^* - v_{od}) + K_{iv} \phi_{d}\)

  • \(i_{lq}^* = F i_{oq} - \omega_{b} C_{f} v_{od} + K_{pv} (v_{oq}^* - v_{oq}) + K_{iv} \phi_{q}\)

  • \(\frac{d\gamma_{d}}{dt} = i_{ld}^* - i_{ld}\)

  • \(\frac{d\gamma_{q}}{dt} = i_{lq}^* - i_{lq}\)

  • \(v_{id}^* = -\omega_{b} L_{f} i_{lq} + K_{pc} ( i_{ld}^* - i_{ld}) + K_{ic} \gamma_{d}\)

  • \(v_{iq}^* = -\omega_{b} L_{f} i_{ld} + K_{pc} ( i_{lq}^* - i_{lq}) + K_{ic} \gamma_{q}\)

  • \(\frac{di_{ld}}{dt} = -(\frac{r_{Lf}}{L_{f}}) i_{ld} + \omega_{com} i_{lq} + \frac{v_{id}^* - v_{id}}{L_f}\)

  • \(\frac{di_{lq}}{dt} = -(\frac{r_{Lf}}{L_{f}}) i_{lq} + \omega_{com} i_{ld} + \frac{v_{iq}^* - v_{iq}}{L_f}\)

  • \(\frac{dv_{od}}{dt} = \omega_{com} v_{oq} + \frac{i_{ld} - i_{od}}{C_f}\)

  • \(\frac{dv_{oq}}{dt} = -\omega_{com} v_{od} + \frac{i_{lq} - i_{oq}}{C_f}\)

  • \(V_{bd,in} = \cos(\delta) V_{a} - \sin(\delta) V_{b}\)

  • \(V_{bq,in} = -\sin(\delta) V_{a} + \cos(\delta) V_{b}\)

  • \(\frac{di_{od}}{dt} = -(\frac{r_{Lc}}{L_{c}}) i_{od} + \omega_{com} i_{oq} + \frac{v_{od} - V_{bd,in}}{L_f}\)

  • \(\frac{di_{oq}}{dt} = -(\frac{r_{Lc}}{L_{c}}) i_{oq} + \omega_{com} i_{ld} + \frac{v_{oq} - V_{bq,in}}{L_f}\)

Note all internal direct equalities are simplified into the differential equations.

  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.