Page 197 - Hybrid-Renewable Energy Systems in Microgrids

Sensitivity and transient stability analysis of fixed speed wind generator 177

Figure 9.7 Variation of real and imaginary part of mechanical mode with respect to
shaft stiffness with SDBR (V dgrid = 0.5 pu).

Generator Inertia: The sensitivity of mechanical modes with respect to the genera-
tor inertia is given in the following:

∂ λ 9 ∂ λ 9 ∂a 3,2 ∂ λ 9 ∂a 3,1 ∂ λ 9 ∂a 3,3
9
9
∂H = ∂a . ∂H + ∂a . ∂H + ∂a . ∂H (9.33) ∂ λ ∂ H r = ∂ λ ∂ a 3,2. ∂
r 3,2 r 3,1 r 3,3 r a 3,2 ∂ H r + ∂ λ ∂ a 3,1. ∂ -
9
a 3,2 , a 3,1 and a 3,3 are computed from the state matrix A and listed in the appendix. a3,1∂Hr+∂λ ∂a3,3.∂a3,3∂Hr
9
From Fig. 9.8, it is clear that as the generator inertia is increasing, the natural fre-
quency of the system is decreasing for the mechanical mode. Incorporation of SDBR
slightly increases the natural frequency as it does not have significant contribution to
this mode. However, if we change the operating condition (V dgrid = 0.5 pu), SDBR pre-
vents the system from being highly nonlinear and the eigenvalues stay within stability
margin while the system without SDBR loses its stability and all eigenvalues moves
to the unstable region.
Varying the generator inertia, while keeping all other parameters constant, does not
have significant impact on the variation of the electrical mode with or without SDBR
as the generator inertia is a mechanical parameter and does not have an effect on the
electrical mode.
Turbine Inertia: The sensitivity of the mechanical modes with respect to the turbine
inertia is given in the following:

∂ λ 9 = ∂ λ 9 . ∂a 1,2 + ∂ λ 9 . ∂a 1,1 + ∂ λ 9 . ∂a 1,3 (9.34)
∂H ∂a ∂H ∂a ∂H ∂a ∂H ∂ λ 9 ∂ H t = ∂ λ 9 ∂ a 1,2. ∂
t 1,2 r 1,1 r 1,3 r a 1,2 ∂ H r + ∂ λ 9 ∂ a 1,1. ∂ -
a , a and a are computed from the state matrix A and listed in the appendix. a1,1∂Hr+∂λ 9 ∂a1,3.∂a1,3∂Hr
1,2
1,3
1,1
From Fig. 9.9, it is evident that as the turbine inertia increases, the natural fre-
quency of the system decreases for the mechanical mode. As this is a mechanical
mode parameter, the system response is similar to the shaft stiffness and turbine iner-
tia. At worst operating condition (V dgrid = 0.5 pu), system without SDBR losses stabil-
ity while SDBR dynamics maintains stability.