1. A Comparative Reliability Analysis of the Power Conditioning System
for Grid Connected Photovoltaic (PV) Applications
Md Arifujjaman, Jitendra Morankar
RES Americas, Broomfield, CO 80021, USA
Abstract — A comparative reliability analysis of a 2- and 3-
level inverter based Power Conditioning System (PCS) is
presented for a grid connected Photovoltaic (PV) applications.
The PCSs examined are: an intermediate boost converter
integrated with a 2- and 3-level inverter connected to a PV
module. The reliability analysis reveals that the MTBF of the 3-
level system is 10 years, while the 2-level system is 6 years.
Afterwards, the reliability is compared for one year and over time
for both systems. It has been found that a 3-level system remains
more reliable than the 2-level system and over time it exhibits the
same higher nature of reliability in contrast to the 2-level system.
The investigation is further enhanced to identify the least reliable
component of the system and it is shown that the boost converter
has the dominant effect on the system reliability as compared to
inverter. This research indicates that a 3-level power conditioning
system is an optimum choice for grid connected PV applications.
Index Terms — Conduction loss, inverter, photovoltaic,
reliability, switching loss.
I. INTRODUCTION
The most imperative feature for connecting a Photovoltaics
(PV) with the electric grid is to integrate an optimum Power
Conditioning System (PCS) that allows power injection to the
grid, reduces mechanical stress on balance of plant
components, and increases reliability. The PCS may have a
different Mean Time Between Failures (MTBF) due to the
contribution of the same stress in diverse proportion on their
power electronic components. This is owing to the fact that the
reliability of the power electronic components is influenced by
the component temperature and its variations [1].
Recent research intermittently endeavors to determine the
reliability and advancement of the inverter rather than the
power conditioning system itself. As far as the inverter is
concerned which is an essential part of the PCS, reliability of
such grid connected inverters is ambiguous although several
key aspects to increase the reliability of such inverters have
been identified by previous researchers [1]-[3]. The dominant
factor that contributes to low technical reliability is the heat
generation caused by the power losses when the current flows
through the semiconductor devices [3-5]. A reduction in heat
generation can significantly increase the reliability. In
addition, fans inside the inverter have a limited lifetime and
deserve special attention [3]. Nevertheless, there are other
aspects (e.g. humidity, modularity, and packaging) that also
require special attention beyond the technical improvement
and are not a part of this present study.
Most of the reliability calculations are based on the accessible
data provided by the military handbook for the reliability
prediction of electronic equipment which is criticized for
being obsolete and pessimistic [6]. A comparative reliability
analysis of different PCS has been carried out based on the
military handbook by Aten, et al [6]; however, the absence of
environmental and current stress factors can pose grim
constraints on the calculated reliability value. Rohouma, et al
[7] provided a reliability calculation for an entire PV unit
which can be considered as more worthwhile, however, the
approach lacks a valid justification as the data provided by the
author is considered from the manufacturers’ published data
which is somewhat questionable. This is due to the fact that
the reliability calculations using purely statistical methods,
manufacturers data, or military handbook data [7]-[9] neglect
the operating point of a component. Moreover, the total
number of components could vary for two systems (which
have the same objective) in order to meet a certain criterion of
the overall system. Although higher components in the power
conditioning system will exhibit less reliability and vice versa,
the effects of the covariates could be different and
consequently could lead to a variation in the reliability [10].
Furthermore, a reliability evaluation for the power
conditioning system of a grid connected PV system is essential
in order to optimize the system performances as well as system
cost. Another important point to mention is that reliability
analysis based on the covariate factor is strongly influenced by
the standard reliability data book also. The variation in
covariate factor varies the reliability of an integrated system
which is composed of numerous semiconductor devices.
Moreover, it is well understood that an error in reliability
prediction for a system could prove to be fatal for the high
penetration of PV power.
In addition, the PCSs are composed of semiconductor
devices and indeed, power losses occur during operation.
Moreover, as the PCSs are connected to a PV; the power
losses will vary with the array voltage and current. As a result,
while calculating the power losses of a PCS, one should also
consider the variation of the losses for each operating point to
clarify the effectiveness of a specific system for the entire V-I
characteristic regime. A calculation of power losses of PCS for
a given operating condition is performed in [11]-[14] in terms
of the total semiconductor device power losses. However,
calculating individual semiconductor devices power loss
model lacks a considerable valid justification. This is because,
firstly, a non-linear loss model approach is unable to reflect

2. the switching losses of the semiconductor devices, which
could be a dominant factor during the high switching state [11,
12]. Secondly, power loss model based on the data provided
by the manufacturers is ambiguous and pessimistic [13, 14].
Thirdly, physics-based simulation models of semiconductor
devices power losses requires implicit integration methods,
leading to an increased simulation time. Furthermore, it
requires detail knowledge of the dimensions of the devices
[15, 16]. There have been very limited efforts found on
modeling of the PCS power losses used in PV applications. In
[16] presented the concept of maximum device rating power
loss model of the PCS, however, switching losses is often
ignored
Based on the above discussions, it can be asserted that most
of the attempts for the power loss and reliability calculation
have been developed based on several assumptions and often
neglected a fraction of the entire PCS power losses that affects
the reliability the most. Furthermore, a comparison of
reliability calculation in the PV domain is almost null. This
discrepancy could affect the preference of an efficient grid-
connected PV that is in a great need for high penetration of the
renewable power. As a consequence, this research aims at
advancing the use of grid-connected PV by modeling the
power losses of the semiconductor devices for a 2- and 3-level
PWM inverter based PCS for a fixed operating point of the
PV. Based on the power generation and loss with a pre-
determined operating point, a global power loss is calculated
for each system. Afterwards, reliability is calculated where
temperature is used as a stress factor which is a common
practice during calculation of the power electronics
components reliability [1]. The MTBF for both systems is
presented and in addition, the least reliable component of the
2- and 3-level inverter based system is identified through
quantitative analysis. Throughout this paper, a 2-level inverter
based PCS and 3-level inverter based PCS will be written as a
2-level system and 3-level system respectively.
This paper is organized as follows: Followed by a detail
literature review in the first section, the selected PV systems
are presented in the second section. The third section describes
the modelling approach to obtain the power loss in the
semiconductor devices for a predetermined operating
condition is described. The fourth section narrates the
reliability calculation by using the semiconductor devices
power loss model, while the simulation results and discussions
are presented and discussed in the fifth section and finally, the
findings of the investigations are highlighted in the conclusion.
II. PCS FOR GRID CONNECTED SYSTEMS
The PCS for grid connected PV applications typically
requires a DC-DC converter followed by a grid connected
inverter. The inverter is available with a variety of
configuration. A 2-level inverter could be an industry choice
due to the availability and ease of control, nevertheless, a 3-
level inverter could also achieve the same objective with lower
harmonics and cheaper switches. Fig. 1a shows a 2-level
system employs a Boost Converter (BC) and a grid-connected
2-level Pulse Width Modulated (PWM) inverter and Fig. 2a
shows a 3-level system employs a boost converter and a grid-
connected 3-level PWM inverter that has been examined in
this investigation.
Fig. 1 Typical power conditioning system a) 2-level PCS
system, b) 3-level PCS
III. POWER LOSS MODEL
A mathematical model of the power losses in the
semiconductor devices (diodes/IGBTs) is required in order to
compare the efficiency of the PCS. The losses for the
semiconductor devices are strongly dependent on the voltage
and current waveforms. Simplified analytical derivation of
voltage and current equations associated with the individual
semiconductor devices are derived to determine the power
losses as generated during the conduction and switching states
of the semiconductor devices.
A. 2-level Inverter Based System
The conduction and switching loss of the boost converter is
calculated by assuming an ideal inductor (LD
2-lvl
) at the input.
For a boost converter, the IGBT is turned on for a duration d,
while the diode conducts for the duration (1- d). The on-state
current of the IGBT is the input current, Idc1
2-lvl
, while the 2-
level inverter input current, Idc2
2-lvl
is given by [17]
 2 2
2 1 1lvl lvl
dc dcI I d 
  (1)
The conduction loss for the diode, Pc,d-B
BC
and IGBT, Pc,i-
B
BC
can be obtained by multiplying their on-state voltage and
current with the respective duty cycle and is given by [17]
   2 2
, 1 0 1 . 1BC lvl lvl
c d B dc f d dcP I V r I d 
    (2)
 2 2
, 1 0 1 .BC lvl lvl
c i B dc ce ce dcP I V r I d 
   (3)
The actual commutation voltage and current for the boost
converter are the DC link voltage, Vdc2
2-lvl
and input current to

3. the 2-level inverter, Idc1
2-lvl
. The switching loss of the diode,
Ps,d-B
BC
and IGBT, Ps,i-B
BC
in the boost converter are given by
2 2
2 1
,
, ,
. .
lvl lvl
BC dc dc
s d B sw SR
r d r d
V I
P f E
V I
 
  (4)
 
2 2
2 1
,
, ,
. .
lvl lvl
BC dc dc
s i B sw ON OFF
r i r i
V I
P f E E
V I
 
   (5)
The sum of (2) to (5) gives the total losses, Pt,(d+i)-B
BC
,( ) , , , ,
BC BC BC BC BC
t d i B c d B c i B s d B s i BP P P P P         (6)
With the exclusion of snubber circuit, the 2-level inverter
consists of 6 IGBTs and 6 anti-parallel diodes. The conduction
losses of a diode, Pc1,d-I
2-lvl-INV
and IGBT, Pc1,i-I
2-lvl-INV
for the
inverter can be expressed as [18],
 
22 2 2
1, 0
1 1 1 1
8 3 2 8
lvl INV lvl lvl
c d I d om f omP r I V I
 
   

   
      
   
(7)
 
22 2 2
1, 0
1 1 1 1
8 3 2 8
lvl INV lvl lvl
c i I ce om ce omP r I V I
 
   

   
      
   
(8)
where Iom
2-lvl
is the maximum value of the sinusoidal output
current, iom
2-lvl
.
For the 2-level inverter, the commutation voltage and
current are the DC link voltage and output current. An
approximated solution for the switching loss of a diode, Ps1,d-I
2-
lvl-INV
and IGBT, Ps1,i-I
2-lvl-INV
is given by [18]
2 2
2 2
1,
, ,
1 lvl lvl
lvl INV dc om
s d I sw SR
r d r d
V I
P f E
V I
 
 
  (9)
 
2 2
2 2
1,
, ,
1 lvl lvl
lvl INV dc om
s i I sw ON OFF
r i r i
V I
P f E E
V I
 
 
   (10)
The loss, Pt,(d+i)-I
2-lvl-INV
of the inverter is obtained as the sum
of (7) to (10) and expressed by (11), while the total loss, Pt
2-lvl
for the intermediate boost converter based 2-level inverter is
expressed by (12).
 
2 2
1, 1,2
, 2 2
1, 1,
6
lvl INV lvl INV
c d I c i Ilvl INV
t d i I lvl INV lvl INV
s d I s i I
P P
P
P P
   
  
     
 
 
 
   
(11)
 
2 2 2
, ,( ) ,
lvl PCS BC lvl INV lvl INV
t t d R t d i B t d i I
P P P P     
    
   (12)
A. 3-level Inverter Based System
The conduction losses Pc are comprised of losses in the
IGBTs and diodes. The conduction losses for each switch can
be calculated by (13)
2
0c avg f rmsP U I r i  (13)
where U0 is the forward voltage drop with zero current, rf is
the forward resistance, Iavg is the average current and irms is the
root-means-square of the current.
The currents for IGBTs T1 and T4 of the 3-level inverter
are [18]
 
3
3
sin cos
4
lvl
lvl INV om
avg
MI
I    


 
     (14)
 
3
2 3
2 4 1
1 cos cos 2
4 3 3
lvl INV
lvl
om
rms
MI
I  

 

 
   
 
(15)
where Iom
3-lvl
is the peak current of the output voltage; φ is
the phase difference between output voltage and current; M is
the modulation index .
The currents for T2 and T3 of the 3-level inverter are
3
3 3
sin cos
4
lvl INV
lvl lvl
om om
avg
I MI
I   
 
 
 
      (16)
 
2 3 2 3
2 3 4 1
1 cos cos 2
4 4 3 3
lvl lvl
lvl om om
rms
I MI
I  

 
  
    
 
(17)
In principle the diodes from D1 to D4 don’t carry any
current, because the current of T1 commutes to D5, the current
of T4 commutes to D6 and the current of T2 commutes to T3.
As a result, the conduction loss of the diode D5/D6 can be
calculated as
3 2 3
3 0
, 5 6
3 2 3
0
4
2
cos
3
lvl lvl
lvl INV d om d om
c d d
lvl lvl
d om d om
U I r I
P
U I r I
M


 
 
 
 
 
  
 
 
  
 
(18)
By considering the current through T1 and T4 of the
inverter, the conduction loss becomes
 3
3 2 3
, 1 4 0 , 1 4 , 1 42
lvl INV
lvl INV lvl
c T T i avg T T if rms T TP U I r i
 
  
   (19)
In a similar manner the conduction losses of T2 and T3 of
the inverter is
 3 3 2 3
, 2 3 0 , 2 3 , 2 32lvl INV lvl lvl
c T T i avg T T if rms T TP U I r i   
   (20)
Using (18), (19) and (20), the total conduction losses can be
determined by
 3
, 5 6 , 1 4 , 2 33lvl PCS
c c d d c T T c T TP P P P 
   (21)
The switching losses Psw are comprised of losses in the
IGBTs and diodes of the 3-level inverter. The switching losses
for each switch can be calculated as
3 3
3 2 2
. .
lvl lvl
lvl INV dc dc
sw SW R
ref ref
V I
P f E
V I
 
 
 (22)
where fsw is the switching frequency of the inverter; ER is the
recovery energy of the switch.
The switching losses of the diode and IGBT can be found by
(23) and (24) respectively
3 3
3 2 2
, 5 6
, ,
2
. .
lvl lvl
lvl INV SW SR dc dc
sw d d
ref d ref d
f E V I
P
V I
 
 
 (23)
  3 3
3 2 2
, 1 4
, ,
2
. .
lvl lvl
SW ON OFFlvl INV dc dc
sw T T
ref i ref i
f E E V I
P
V I
 
  
 (24)
The total switching losses can be calculated as
 3 3 3
, 5 6 , 1 43lvl INV lvl INV lvl INV
sw sw d d sw T TP P P     
  (25)
So the total power losses of the of a boost converter based
3-level inverter can be determined by using (21) and (25) as
3 3 3
,
lvl BC lvl INV lvl INV
t t d R c swP P P P    
   (26)

4. IV. RELIABILITY CALCULATION
Reliability is the probability that a component that will
satisfactorily perform its intended function under given
operating conditions. The average time of satisfactory
operation of a system is the MTBF and the MTBF calculated
in this investigation is carried out at the component level and
is based on the life time relationship where the failure rate is
constant over time in a bathtub curve. In addition, the system
is considered repairable. It is assumed that the system
components are connected in series from the reliability
standpoint. The lifetime of a power semiconductor is
calculated by considering junction temperature as a covariate
for the expected reliability model. The junction temperature
for a semiconductor device can be calculated as
lossJ A JAT T P R  (27)
where RjA is the thermal resistance between the junction and
ambient; TA and TJ is the ambient and junction temperature
respectively; Ploss is the power loss (switching and conduction
loss) generated within a semiconductor device.
The life time, L(TJ) of a semiconductor is then described as
  0 expJ
J
B
L T L
T
 
  
 
(28)
where L0 is the quantitative normal life measurement (hours)
assumed to be 1×106
; B=(EA/K), K is Boltzman's constant
which has a value of 8.6×10-5
eV/K, EA is the activation
energy, which is assumed to be 0.2 eV, a typical value for
semiconductors, ΔTJ is the variation of junction temperature
and can be expressed as
1/ 1/ 1/A JT T T   (29)
The failure rate is described by
 
1
JL T
  (30)
The system level failure rate, λsystem is then obtained as the
summation of the component level failure rates, λi as:
system
1
N
i
i
 

  (31)
The Mean Time Between Failures, MTBFsystem and
reliability, Rsystem of the system are given respectively by
system systemMTBF 1/  (32)
system
systemR
t
e

 (33)
V. RESULTS AND DISCUSSIONS
The analytical calculations illustrated in the above sections
were carried out to determine the total power losses and
reliability for both configurations under a predetermined
operating condition. It is assumed that the 4 PV Modules are
connected in parallel and supply 52V and 120Amps. The
boost converter and inverter switching frequency is considered
as 3 kHz and to investigate the worst-case scenario of the
power loss in this numerical simulation study, the modulation
index is assumed unity and load current is assumed in phase
with the output voltage. In addition, the variation of duty cycle
of the boost converter for both configurations is considered as
a maximum value. This is due to the fact that the
semiconductor devices will transmit the maximum indirect
power, i.e., maximum stress on the devices thus resembles the
worst case scenario. The thermal model of the converters is
neglected provided that the heat sink is adequate enough to
maintain the semiconductors proper working. Power wasted in
the power supplies for the control of the converters is also
ignored (It may be between 10-20W). The analytical
calculation is based on the SEMIKRON IGBT module
SKiM300MLI12E4 [18] for both system to make a fair
comparison.
The power losses for the boost converter and inverter for the
2-level inverter based PCS is presented in Fig. 2a. It shows
that the total conduction and switching losses of the boost
converter is 1613W and 1103W respectively, while the total
conduction and switching losses of the inverter is 102W and
232W respectively. It is noted that the total conduction and
switching losses of the boost converter is high compared to the
inverter. This is due to the fact that the SOFC generates high
current and low voltage at the predetermined operating
condition and consequently, the conduction and switching
losses are high. On the other hand, inverter operates with a low
current and connected to the high voltage grid for the same
power as boost converter, making the conduction and
switching losses less.
The corresponding power losses for the boost converter and
inverter for the 3-level inverter based PCS are given in Fig.
2b. The total conduction and switching losses of the boost
converter is the same as 2-level based PCS. This is because
both 2- and 3- level inverter based PCS are adopting the same
boost converter configuration. However, the 3-level inverter
conduction and switching losses are 48 W and 33W
respectively. A lower power loss compared to a 2-level
inverter is expected as lower stress on the switches.
The calculation of the failure rate of the PCS for the 2-level
system is 2.01×10-5
and the MTBF is 4.97×104
hours (6
years). The corresponding records for the 3-level system are
1.22×10-6
and 8.13×104
hours (10 years). As shown, the need
to replace the PCS for the 2-level system is 6 years of
operation. This leads to a more vulnerable system as compared
to the lifespan of the PV application, which is usually 25 to 30
years of operation. Also from the financial standpoint,
replacement of such a complex PCS is expansive and needs a
highly skilled repair professional. In contrast to the 2-level
system, the 3-level system exhibits longer lifetime of 10 years
of operation and remain in a good agreement with the lifespan
of the PV application.
Fig. 3 shows the reliability of the PCS (BC and inverter as
well as total) for a period of one year (8760 hours) for the 2-
and 3-level system. The result reveals that the reliability of the
PCS for the 2-level system drops to 90% after one year, while

5. Fig. 2 Power loss of the systems a) 2-level power conditioning
system, b) 3-level power conditioning system
Fig. 3 Reliability of the 2- and 3-level power conditioning
system during a year
Fig. 4 Reliability of the 2- and 3-level power conditioning
system over time
Fig. 5 Effect of reliability variation on the 2-level system
Fig. 6 Effect of reliability variation on the 3-level system

6. the reliability of the PCS for the 3-level system remains
above 92% in the same time frame. The reliability of the
systems with time is presented in Fig. 4. It is easily noted that
the reliability of the 2-level reaches less than 50% at 50000
hours (5.7 years). In contrast, the reliability of the 3-level
system remains more than 50% within the same time frame,
which certainly could save cost of repair for the system. In
both scenarios, the 3-level system illustrates higher reliability
than 2-level system.
Following the calculation of the reliability of the systems,
an attempt is made to identify the subsystems in the PCS that
are the least reliable. To achieve this objective, the MTBF of
the BC is decreased by 50% while the MTBF of the inverter is
unaltered. In the same way, the effect of changes in the MTBF
for each of the boost converter and inverter on the system
reliability has been calculated and is presented in Fig. 5 and
Fig. 6 for a 2-level and a 3-level system respectively. It is
evident that the BC has the most dominant influence on the
system reliability, while the inverter has less significant effect.
This study confirms the results through quantitative analysis.
VI. CONCLUSION
A comparative reliability analysis of the PCS for grid
connected PV applications is presented. Temperature is used
as a stress factor and it is found that the 2-level system suffers
from low reliability as compared to the 3-level. The least
reliable component of the PCS is identified as the boost
converter for both 2- and 3-level and verified by analysis. It is
shown that the 3-level power conditioning system could be an
optimum choice for PV system applications.
DISCLAIMER
The authors have investigated an in-depth analysis with the
best of his knowledge; however, the authors do not take any
responsibilities, under any circumstances, if this research does
not meet the performance expectations as exercised by any
individuals, any research groups, or any industries. In addition,
the research presented in this article is the authors’ own, and
does not represent any company’s positions, strategies, or
opinions.
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