Page 376 - Renewable Energy Devices and System with Simulations in MATLAB and ANSYS

Microgrid for High-Surety Power: Architectures, Controls, Protection, and Demonstration 363

Grid Load

Gas engine

Li-ion battery
PV panel

Fuel cell

H 2
O 2
(a)

λ 1 Grid
AC/DC

λ 2 Gas engine
AC/DC
λ 6
λ 3 Fuel cell Load
DC/DC DC/AC
λ 4 Li-ion battery
DC/DC

λ 5 PV panel
DC/DC
(b)

FIGURE 14.7 Reliability model of bus-centered architecture: (a) Bus-centered architecture and (b) the reli-
ability model.

After expanding Equation 14.12, the expression of MTBF becomes

∞ 
∫
MTBF =  e −(λ 1 +λ 6 t ) +e −(λ 2 +λ 6 t ) +e −(λ 3 +λ 6 t ) +e −(λ 4 +λ 6 t ) +e −(λ 5 +λ 6 )t t − ∑ e −(λλ j + 6 λ t )
i +
ij<6
0   0 <<
λ
+ j λ
i +
+ 5 λ
+ ∑ e −(λλ j +λ k + 6 λ t ) − − ∑ e −(λλ + k + + 6 t )λ λ +e −( 1 λ + 2 λ + 3 λ + 4 λ + )t    dt (14.13)
i
6
l
ij k
ij
0 << <<6 0 << << <6  
kl
Substituting Equation 14.14 into Equation 14.13, the MTBF of the Super UPS can be solved as
Equation 14.15:
∞ 1
∫ e − t = λ (14.14)
λ
0