Page 375 - Renewable Energy Devices and System with Simulations in MATLAB and ANSYS

362 Renewable Energy Devices and Systems with Simulations in MATLAB and ANSYS ®
®

By combining Equations 14.1 and 14.3, the system efficiency can be calculated in the following,
assuming grid is source 1:

 M 1
 ∏ η j1 , when grid is normal

 = j 1
η =  n  M i  (14.5)
 ∑ = i 2 i W ∏ = j 1 η ij  

 n , iif grid fails
 ∑ i W
 = i 2
The system reliability is related to the available energy transfer path to the load. More redundant
power conversion paths mean higher reliability. According to the reliability theory, the reliability R(t)
and mean time between failure (MTBF) for the series and parallel system can be calculated as follows:
n
R series () = ∏ e −λ t i (14.6)
t
i=1
∞ ∞ n
()
MTBF series = ∫ R series t dt = ∫∏ e −λ t i dt, (14.7)
0 0 i=1
n
−λ
R parallel () =− ∏ − ( 1 e ) (14.8)
t
1
t i
i=1
∞ ∞  n 
∫ ∏
()
−λ
MTBF parallel = ∫ R parallel t dt = 1 − − ( 1 e )  ddt (14.9)
t i
0 0   i=1  
where λ is the failure rate of component i in the Super UPS system, and reliability model can be
i
built based on topologies of power conversion paths. Only the reliability of converters is considered.
Then MTBF can be calculated through the reliability model. For instance, the reliability model
of star architecture II is shown in Figure 14.7. In the reliability model, the failure rate of grid, gas
engine, fuel cell, battery, and PV are λ , λ , λ , λ , and λ , respectively. Five modules including util-
1
3
4
5
2
ity, gas engine, fuel cell, battery, and PV are paralleled first as a whole. Then it has a series connec-
tion with the load inverter whose failure rate is λ . According to Equation 14.8, the reliability of the
6
five paralleling units R is expressed as follows:
p
t 3 λ
λ
−λ
t 5 λ
−λ
Rt () =−( 1 − e )( 1 − e )( 1 − e )( 1 − e )( 1 − e ) (14.10)
1
t 2
t 4
t 1
P
According to Equation 14.6, the system reliability R is the product of R and R as given in the
p
s
inv
following equation:
p ()

λ
t 5 λ
−λ
−λ
p ⋅
Rt () = RR inv = Rt e −λ t 6 = 1 −( 1 − e )( 1 − e )( 1 − e ) 1 ( − e )( 1 − e )  e −λ t 6 (14.11)
t
λ 4 t
t 3
t 2
t 1
s  
According to Equation 14.7, the MTBF of Super UPS is expressed as
∞ ∞
− (
∫
−λ λ 5 t
−
−
−
−
MTBF = Rdt = ∫   1 −( 1 e − 1 tλ )( 1 e − 2 tλ )( 1 e − 3 tλ )( 1 e − 4 tλ ) 1 e )   e − λ 6 t dt (14.12)
S
0 0