Appendix: Four machines

(1)
Generator
\(S_{B1} = S_{B2} = S_{B3} = S_{B4}\) = 2100 MVA, \(H\) = 3.7 s, \(V_{B}\) = 13.8 kV, \(f\) = 60 Hz, \(R_{S}\) = 2.8544e−3, \(X_{d}\) = 1.305, \(X^{\prime}_{d}\) = 0.296, \(X^{\prime\prime}_{d}\) = 0.252, \(X_{q}\) = 0.474, \(X^{\prime}_{q}\) = 0.243, \(X^{\prime\prime}_{q}\) = 0.18, \(T_{d}\) = 1.01 s, \(T^{\prime}_{d}\) = 1.01 s, \(T^{\prime\prime}_{q0}\) = 0.1 s.
 (2)
Loads
Load1 = 1167 MW + 100 MVAR, Load2 = 3617.5 MW + 100MVAR.
 (3)
Hydraulic turbine and governor
\(K_{a}\) = 3.33, \(T_{a}\) = 0.07, \(G_{\rm{min} }\) = 0.01, \(G_{\rm{max} }\) = 0.97518, \(V_{g {\rm{min}} }\) = − 0.1 pu/s, \(V_{g{\rm {max}} }\) = 0.1 pu/s, \(R_{p}\) = 0.05, \(K_{p}\) = 1.163, \(K_{i}\) = 0.105, \(K_{d}\) = 0, \(T_{d}\) = 0.01 s, \(\beta\) = 0, \(T_{w}\) = 2.67 s.
 (4)
Excitation system
TLP = 0.02 s, \(K_{a}\) = 200, \(T_{a}\) = 0.001 s, \(K_{e}\) = 1, \(T_{e}\) = 0, \(T_{b}\) = 0, \(T_{c}\) = 0, \(K_{f}\) = 0.001, \(T_{f}\) = 0.1 s, \(E_{f{\rm {min}} }\) = 0, \(E_{f{\rm{min}} }\) = 7, \(K_{p}\) = 0.
 (5)
Transformer
\(S_{BT1} = S_{BT2} = S_{BT3} = S_{BT4}\) = 2100 MVA, \(S_{BT3}\) = 4200 MVA, 13.8/500 kV, \(f\) = 60 Hz, \(R_{1} = R_{2}\) = 0.002, \(L_{1}\) = 0, \(L_{2}\) = 0.12, \(D_{1} /Y_{g}\) connection, \(R_{m}\) = 500, \(L_{m}\) = 500.
 (6)
Transmission line
3Ph, 60 Hz,\(L_{1}\) = 50 km, \(L_{2}\) = 20 km, \(L_{3}\) = 220 km, \(R_{1}\) = 0.02546 Ω/km, \(R_{0}\) = 0.3864 Ω/km, \(L_{m}\) = 0.9337e−3 H/km, \(L_{0}\) = 4.1264e−3 H/km, \(C_{1}\) = 12.74e−9 F/km, \(C_{0}\) = 7.751e−9 F/km.
 (7)
SSSC
\(S_{nom}\) = 100 MVA, \(V_{\text{nom}}\) = 500 kV, \(f\) = 60 Hz, \(V_{q{\rm{max}} }\) = 0.2, Max rate of change of \(V_{\text{qref}}\) = 3 pu/s, \(R_{\text{cnv}}\) = 0.00533, \(L_{\text{cnv}}\) = 0.16, \(V_{\text{DC}}\) = 40 kV, \(C_{\text{DC}}\) = 75e−6 F, KP_IVR = 0.00375, KI_IVR = 0.1875, KP_VdcR = 0.1e−3, KP_VdcR = 20e−3.