Page 190 - Hybrid-Renewable Energy Systems in Microgrids

Sensitivity and transient stability analysis of fixed speed wind generator 171

R and R are stator and rotor resistance, Ψ and Ψ are stator and rotor flux, T is the
s
r
r
e
s
electromagnetic torque, w , w , w are the synchronous angular frequency, rotor angu-
2
s
r
lar frequency, and rotor slip frequency (all in pu), and w is the base angular frequency
b
(377 rad/s].
2.2.2 Capacitor bank modeling
A capacitor bank is connected at terminal of IG to maintain unity power factor opera-
tion at rated condition, which can be expressed in terms of capacitor voltage by the
state equation:
dV  1 L 
C sd =− ψ + m I + I + Cω V sq  ω (9.20) CdVsddt=−1Lsψsd+LmLsIrd
dt   L s sd L s rd dt s  b CdVsqdt=−1Lsψsq+LmLsIrq+Iqt−CwsVsdwb
+Idt+CwsVsqwb

dV  1 L 
C sq =− ψ + m I + I − Cω V sd  ω (9.21)

dt  L s sq L s rq qt s  b
where C is the capacitance bank, I and I are the d-axis and q-axis transmission line
dt
qt
current in pu, respectively.
2.2.3 Transmission line modeling

For the equivalent transmission line, the d-q axis current equations are obtained by the
state equation:

dI
(
L dt =−V − R I + L ω I + V ω ) (9.22) LtdIdtdt=−Vsd−RiIdt+LtwsI
t sd idt t sqt gd b
dt qt+Vgdwb
dI
(
L qt =−V − R I − L ω I + V ω ) (9.23) LtdIqtdt=−Vsq−RiIqt−LtwsI
t sq iqt t sdt gq b
dt dt+Vgqwb
where R and L are the equivalent resistance and inductance of the transmission line,
t
t
respectively, I and I are the d-axis and q-axis pu line current, respectively, V and
sd
qt
dt
V are the d-axis and q-axis pu stator voltages, respectively. V and V are the d-axis
gd
sq
qd
and q-axis pu grid voltages, respectively, all in pu.
2.2.4 SDBR modeling
A small series dynamic braking resistor (SDBR) can be inserted in the studied system
immediately after IG during network disturbance. With the use of power electronics
switches, SDBR contributes directly to the balance of active power during fault. SDBR
modeling is accomplished by the insertion of a resistor in the fixed speed WTGS as
shown in Fig. 9.5 It increases the voltage at the terminal of IG and eventually improves
wind farm stability during a grid fault [22,23]. In normal operation mode, the resistor