Line and Grid Impedance Impact on the Performances of a Parallel Connected Modular Inverter System

International Journal of Power Electronics and Drive System (IJPEDS)
Vol. 6, No. 1, March 2015, pp. 100~108
ISSN: 2088-8694  100
Journal homepage: http://iaesjournal.com/online/index.php/IJPEDS
Line and Grid Impedance Impact on the Performances of a
Parallel Connected Modular Inverter System
Tahar Zebbadji, Seddik Hadji and Rachid Ibtiouen
Laboratoire de Recherche en Electrotechnique, LRE, Ecole Nationale Polytechnique d’Alger, ENP, Algeria
Article Info ABSTRACT
Article history:
Received Dec 8, 2014
Revised Jan 22, 2015
Accepted Feb 4, 2015
With the rising fuel cost, increasing demand of power and the concerns for
global climate change, the use of clean energy make the connection of power
electronics building bloc in the heart of the current research. The high output
current applications make the parallel connection of modular inverters to be a
solution for the use of low power building block inverters where the output
power cannot be handled by a single inverter configuration. In this context,
average-modeling using average phase–leg technique allows the n-parallel
connected inverters to be analyzed accurately and rapidly without requiring
the complexity of the full switched inverter topology. The obtained analytical
solution along with the equivalent circuit model makes easier the design of
the control loop. The analytical solution of the n-parallel connected inverters
shows the impact of the line and grid impedance on the performance of the
overall system. The impact of this coupling has to be investigated such that
the main feature of paralleling inverters is guaranteed and that the inverter
mode of operation will not be compromised. The main advantage of
paralleling inverters can be lost for a certain coupling impedance
considerations.
Keyword:
Average phase-leg technique
Coupling Impedance Impact
Modular inverter
Parallel connection
Performances
Copyright © 2015 Institute of Advanced Engineering and Science.
All rights reserved.
Corresponding Author:
Tahar Zebbadji,
Laboratoire de Recherche en Electrotechnique, L.R.E,
Ecole Nationale Polytechnique d’Alger,
10, Avenue Hacene Badi, BP 182, El-Harrach, 16200, Algiers, Algeria.
Email: tahar.zebbadji@g.enp.edu.dz
1. INTRODUCTION
In the recent years,a rapid growth in the production of electrical energy from renewable energy
sources has been made. This has led to a great development in the power electronics area. Indeed, the output
of each renewable energy source should be connected to a specific converter or inverter such that the
converted energy will be available at the consumer level [1], [2].
In order to meet the growth of power demand of the industry, research in power electronics still
needs to find solutions to the energy conversion at high power levels [3], [4]. Knowing that the conversion of
electrical energy uses power electronics components,inverters based on these switches show better
performances if they are used at high switching frequencies [5], with low stresses. However, the switches can
withstand only limited values of current and voltage. Although, the power ratings of power semiconductor
devices have increased considerably since the introduction of the first commercial switch, the maximum
power ratings may be limited by technical or economical considerations. Therefore, for a higher power
transfer, a degradation of efficiency with the increase of the switching frequency occurs. Unfortunately, to
achieve an acceptable efficiency while increasing switching frequency, the trends enhance active research on
various types of connected inverter modules such that just a fraction of the output power of the system is
handled by each module. So at high level, complete power converters are developed around the power
modules with either parallel or series connection.

IJPEDS ISSN: 2088-8694 
Line and Grid Impedance Impact on the Performances of a Parallel Connected Modular… (Tahar Zebbadji)
101
If the system is operating in parallel, the total output power can be partitioned in a way that the
overall efficiency can be kept as high as possible, then it has to be clarified at which point the number n of
parallel inverters has to be increased in order to achieve maximum efficiency [6]. In this study, n identical
inverters are connected in parallel both at the input and output, so that the output current and power meet
higher requirements applications. This connection is made by mean of the different line impedances to the
grid trough a grid impedance. This coupling along with the number n of inverters to be connected in parallel
influence greatly on the performances of the overall circuit.
The study focuses on the development of the parallel connection of inverters which is often used to
achieve power levels beyond the capacity of the high power available from a single conventional structure:
such a system constitutes a special connection of building blocks to provide a highly reliable system [7], [8].
The obtained structure is capable of delivering high output current. Therefore, parallel connection of inverters
has become a desirable solution, particularly in areas where a high demand for energy is required with high
output current. Paralleling is used to achieve the following characteristics: redundancy, flexibility,
standardization of low power components ratings, reliability, size reduction, low cost of maintenance, etc.
Although the modular multilevel converters[9] offers some major advantages as to reduce the amplitude of
harmonics injected into the load, the ability to work at low frenqueny with acceptable efficiency etc. but the
standartisation and flexibility may be compromised.
Therefore, a comprehensive study of the global behavior of the circuit is considered. Modeling is
more than necessary for a quick and methodical study of the steady and dynamic states. Several modeling
techniques can then be used. The technique used in this work is theaverage phase-leg technique [11], which
describes a simple averaging model to be accurately and rapidly simulated without the need for the full
switched models.
Beside these advantages, parallel connection of inverters presents undesirable constraints that can be
stated as current unbalance, instability due to the interaction of the different modules, circulating current
between modules [10] (deterioration of the efficiency and form factor of the output currents ),synchronization
problem of the output currents, etc.
In this first paper,we present a modular inverter architecture in which an n parallel-connected
inverters system is tied to an infinite grid via line and grid impedances. Because of the time varying aspect of
the system, transformation in d-qframe is required to solve for the general solution independently of the
circuit parameters. Then, a simplified average equivalent model is derived where analytical solution of
different transfer functions can be analyzed whatever the number nof inverters is. The open loop stability for
the n-parallel-connected inverters is analyzed with respect to the different parameters of the
circuit.Finally,analytical results are given to show the effects of the coupling impedance and the number n of
inverters to be connected in parallel on the performances of the system. Then a criterion is stated to first
respect the mode of operation of the overall circuit and second to guarantee the main purpose of paralleling
inverter modules.
2. PHASE-LEG ANALYSIS OF THE N PARALLEL MODULAR CONNECTED INVERTER
The average phase-leg technique is one of the essential techniques used in the analysis of switched
mode power conversion [11]-[12]. It allows the switched system to be described by a simple averaging
circuit model, which then enables its precise and rapid simulation without the need for full switched inverter
models. Then, the inverter switches can be replaced by a function representing their average value.
The structure is composed of n identical parallel connected inverters at boththe input and output
sides. It supplies a special load, i.e. a three phase infinite grid characterized by a grid inductance (
cbag LLLL  ) and a grid resistance ( cbag RRRR  ) and a maximum line to neutral voltage amplitude
equal to E. Such a load is considered to show that, evenwith a particular case (infinite grid); the model used
gives satisfactory results.The n-parallel inverter shares the same DC link, which can be connected to the
output of a photovoltaic or wind energy system.
Each inverter is connected to the infinite grid by the means of the line impedance which is
characterized by a passive first order filter ( kjL , , kjR , ), where “j” designs the phase line (a, b or c) and “k”
designs the inverter number. Figure 1 shows thesystem structure of the n-parallel connected inverters
considered in this study.
In the current-bidirectional switch based inverters, the average model of the phase leg has a voltage
source in one side and a current source in the other side and where id is defined as the duty cycle of the top
switch. The most widely applied PWM technique for the three phase voltage source inverter is the sine pulse
modulation [13]. The averaging for the three-phase inverter is based on the phase-to-phase averaging in
which the common mode components are intentionally neglected.

 ISSN: 2088-8694
IJPEDS Vol. 6, No. 1, March 2015 : 100 – 108
102
Figure 1. Circuit structure for the n-parallel connected inverters
Using the phase-leg technique, the electrical equations of the different phases during one switching
period are given by Equation (1):



































 
 
 
  
 

 

 

  

n
k
accici
n
k
akckg
akck
g
kk
ai
ai
ci
ci
n
k
cbbibi
n
k
ckbkg
ckbk
g
kk
ci
ci
bi
bi
n
k
baaiai
n
k
bkakg
bkak
g
kk
bi
bi
ai
ai
n
k
n
k
n
k
ckkbkkakkin
g
in
in
eeiRiiR
dt
d
dt
di
L
Vdd
dt
di
L
dt
di
L
eeiRiiR
dt
di
dt
di
L
Vdd
dt
di
L
dt
di
L
eeiRiiR
dt
di
dt
di
L
Vdd
dt
di
L
dt
di
L
idididi
dt
dV
C
Vv
dt
di
L
1 1
233
1 1
313
1 1
1323
1 1 1
31323
)()(
)(
)()(
)(
)()(
)(
(1)
Where:
-Lin and iak are respectively the input inductance and the phase line a current of the kth
inverter.
- C is the DC side capacitance.
-ea , eb and ec represent the three phase line to neutral voltagesof the infinite grid.
-d3k-2, d3k-1, d3k represent respectively the duty cycles of the phase a, b and cof the kth
inverter.
With sinusoidal PWM, the duty cycles are varied sinusoidally in synchronism with the ac line. The
system is assumed to be perfectly balanced. The set of the above equations can be written in the state space
form [14], [15] of 3n+2 order.
This will lead to a set of a complex nonlinear time varying averaged state space system of equations
that describes the overall circuit behavior. It is necessary to make a change of coordinates to convert ac
sinusoidal quantities to dc quantities prior to the average process. The reference frame in which the averaged
state space exhibits a time invariant system of equations is chosen such as a multi-phase system appears as a
stationary one in a coordinate rotating at the same instantaneous velocity [16]. This is done using the Park

103
transform. For the sake of simplicity, the n inverters along with the line and grid impedances are considered
identical such that:











gcba
lcibiai
gcba
lcibiai
LLLL
LLLL
RRRR
RRRR
(2)
Doing so, the transformed set of the previous equations in the rotating dq coordinates can be written
as follow:
dqdqdqdq BXAX 

(3)
Where the matrices dqA , dqB and dqX have the following representation:















































L
R
L
d
L
R
L
d
L
R
L
d
L
R
L
d
C
d
C
d
C
d
C
d
C
L
A
qn
dn
q
d
qndnqd
in
dq










00
00
0
00
00
0
1
00000
1
0
1
1
11
(4)









L
e
L
e
L
e
L
e
L
v
B
qdqd
in
gt
dq 0 (5)
 qndnqdin
t
dq iiiiViX 11 (6)
Where:

















g
l
g
l
i
m
qi
i
m
di
L
n
L
L
R
n
R
R
d
d
d
d
i
i


sin
2
3
cos
2
3
(7)
Where i is the phase angle between the output voltage of every single inverter and the infinite grid voltage,
imd is the modulation index of the duty cyclesand, de and qe are respectively the forward and backward
components of the three phase infinite grid line-to-line voltage.
Referring to the matrices given in Equation (4) and (6), one can rewrite the electrical equations in
the d-qframe. From these equations, the average circuit model of the n-parallel connected inverters with
different parameterscanbe derived. Therefore one can obtain the average circuit model which will have the
same general representation as the one derived using the average connection coefficient reflected to the DC
or AC side [17]-[19]. If all the inverters are identical and have the same ddi dd  and qqi dd  , the average

 ISSN: 2088-8694
104
equivalent circuit model of Figure 3 can either be reflected to the DC side or the utility dq side. The fictive
transformer [20] shown in Figure 3 models only the primary current and voltage from the DC to the utility
side with a turn ratio of 3
dd for the direct component and 3
qd
for the indirect component. The steady state
response can be obtained in the d-qframe. The inverse transform can be applied to obtain the time response of
any desired state.
Figure 3. A simplified average equivalent circuit model
From the above circuit, one can analyze the input impedance, the different transfer functions, the
output impedance seen from the DC side, etc., and then the stability analysis of the open loop circuit can be
performed. From the equivalent circuit model, one can derive any transfer function that needs to be
investigated.The analytical expression of the characteristic equation nD given by:
 )((2 2222342
LRCLLLRsCLsLCLD inininn
)(2)8/32()8/3 222222
LRsdLLRsLdL minmin  (8)
The location of the zeros of nD (whatever the number n of parallel-connected inverter is); which are
functions of the parameters of the circuit, determines the stability of the overall structure.
The transfer function of the input current with respect to the input voltage and output voltage is
given by:
n
d
m
gmm
in
D
sELRsL
d
svRdsLRCLdCLRssCL
si
)()sin()cos()cos((
22
)()
8
3
))(
8
3
(2[(
)(
222222232
 

(9)
Note also that the position of the zeros and poles of the given transfer function depends on the parameters of
the inverters which are LdCRL min ,,,, . If all the zeros of the characteristic equation are located in the left half
s-plane, the steady state input current inI and the phase output current aI in the grid can be given by the
following expressions:
2
2
)cos(238/3
Z
ZdERvd
I
mgm
in
 

(10)






 )
6
cos()
6
cos(
2
1




 tVtv
d
Z
I mg
m
a (11)

105
Where Z and θ are respectively the magnitude and the argument of the equivalent coupling impedance
defined as being equal to jLR  .
From Equation (10) and (11), the coupling impedance plays an important role in both the transient
and steady state variables of the overall circuit. This coupling impedance depends directly on the grid
impedance and just a fraction of the line impedance. The above analytical equations describe the steady state
input current of the n inverters connected in parallel whatever the value of the number n is. The performances
of the overall circuit can then be analyzed with respect to all the transfer function parameters by means of
any mathematical tool.
3. RESULTS AND INTERPRETATIONS
For a given value of gmin vdL ,,,  and C , the characteristic equation shows clearly that the location
of zeros depends on the value of n,Rand L. For a null coupling resistance, the four zeros are located on the
imaginary axis. This contributes to an unstable system. To justify what is stated above, one can solve a
numerical example as given in Table 1.
For a two-parallel connected inverters and null coupling resistance, the characteristic equation has
four zeros located on the imaginary axis of the s domain: this makes the system unstable (s12 = ± j154,
03) and(s34 = ± j407, 92).Therefore, for a stable open loop system, a coupling resistance has to be inserted in
the circuit. The move of these zeros from the imaginary axis is more relevant for the case of the variation of
the grid resistance rather than that of the line resistance.
Figure 4 shows the step response of the average input current for the case where the grid impedance
is considered to be null. The base current is taken to be equal to the input current for an individual inverter
with a null grid impedance: this gives a base average input current equal to 35A.
This last figure shows that an increase in the line resistance for the case of two parallel-connected
inverter will induce a decrease of the steady state input current. This decrease might change completely the
mode of operation of the hall structure. In this case, if the line resistance is greater than0.223Ω, the overall
system works in the rectifier mode rather than the inverter mode.
Table 1. Parameters For The Analyzed Example
Input Voltage
Input filter
Inverter
specifications
2,6.0,
6
 ndm


Line
parameters  1.0,340 ll RHL 
The infinite
grid
parameters
kHzfHLVE g 50,170,2220  

 05.0gR
For a larger line or grid resistance, the step response of the input current shows better performances.
This ensures a stable system with acceptable performances but at the detrimental of the overall circuit
efficiency. The steady state input current decreases as the line or grid resistance increases (Figure 4).
The increase of the numbern of the inverters to be connected in parallel (from 1 to 3) lets the system
(see figure 5) reaches an average input current greater than the base current but at a rate which does not
comply with the paralleling principle. This is mainely due to the presence of the grid impedance.
Figure 6 illustrates the effects of both the line resistance while keeping the grid resistance constant
and the grid resistance while keeping the line resistance constant. First, the mode of operation of the overall
circuit can be either in the inverter mode or in the rectifier mode depending on the value of the line or grid
resistance. For the case (a), the inverter modeis obtained for a grid resistance smaller than 0.0617Ω while for
the case (b), this same mode is obtained for a line resistance smaller than 0.1224Ω. Second, for the inverter
mode, the rate of variation of the input current is greater for the case (a) rather than the case (b).
Figure 7 shows that for the inverter mode of operation, the value of the grid inductance for the case
(a) has to be greater than 0.000135H meanewhile for the case (b) the line inductance has to be greater than
Vvg 400
mFCmHLin 5;5 

 ISSN: 2088-8694
106
0.00027H. The rate of variation of the input current is greater for the case of the grid inductance variation
rather than the line inductance variation.
Figure 4. Step response of the average input current
(p.u) for two parallel-connected inverters with null
grid resistance and different values of line resistance:
 5.0a ,  2.0b ,  1.0c ,  05.0d
Figure 5. Step response of the input current (p.u) for
a given number of parallel-connected inverters: n =1;
b- n=2 and c- n=3
Figure 6. Line and grid resistance effects on the
steady state input current (p.u): a) variation of gR , b)
variation of lR
Figure 7. Line and grid inductance effects on the gR
steady state input current (p.u): a) variation of gL , b)
variation of lL
.
Figure 8 illustrates how the system can lose the main advantage of paralleling inverters: an arbitrary
value of the grid impedance lets a limited increase in the input current. If the grid impedance is taken to be
equal to zero, the input current with respect to the number n of inverters to be connected in parallel increases
in a linear manner. Otherwise, this increase is nonlinear and tends to be limited as n increases. This is
because of the reflected impedance seen fromthe DC side which increases nonlinearly with the number nof
inverters to be connected in parallel. However, for the case (d), the increase of the reflected impedance is
linear. Thus, for a maximum power transfer from the DC side to the grid, the grid impedance should be as
small as possible.
For a five parallel-connected inverters, the curve (d) shows a 500%increase in the input current
while the curve (a) shows only a 142% increase in it. In the case (a), the grid impedance has dramatically
decreased the input power such that the five parallel-connected inverter structure is not even equivalent to a
two parallel-connected inverters with null grid impedance.
This makes the choice of the coupling impedance a priority in an n parallel-connected inverters. Therefore,
the connection port of a parallel modular structure is a key point in the design considerations.
0 0.05 0.1 0.15
-10
-5
0
5
10
15
20
25
Time (sec)
Averageinputcurrent(p.u)
dcba
0 0.02 0.04 0.06 0.08 0.1
-2
0
2
4
6
8
Time (sec)
b ca
0 0.2 0.4 0.6 0.8 1
-3
-2
-1
0
1
2
3
Resistance ( Ohm)
a
b
0 0.002 0.004 0.006 0.008 0.01
-2
-1
0
1
2
3
4
5
Inductance ( Henry )
a b

107
Figure 8. Average input current(p.u) with respect to thenumber n of parallel connected inverters with
differentgrid impedance ),( gg LR :a- 05.0 , mH17.0 ;b- 02.0 , mH068.0 ; c- 01.0 , mH034.0 d-0  ,
0mH
4. CONCLUSION
The phase leg technique applied to the n-parallel connected inverters gives, on one hand, a closed
form solution for the 3n+2 order system whatever the number n of the inverters to be connected in parallel is.
On the other hand, the obtained simplified average equivalent circuit model can be used to derive the
different transfer functions of the overall circuit. This allows the analysisof the open loop system
performances of the circuit with a precise determination of the poles and zeros location ofany transfer
function of the system. Their position is closely linked to the value of the coupling impedance, the number
nof inverters connected in parallel and the different parameters of the circuit. The value of the line and grid
resistance plays an important role for the performances at the detrimental of the system efficiency.
Furthermore, the variation of the coupling impedance that can be either affected by the line or grid
impedance may completely change the mode of operation of the global circuit and then the purpose of such a
circuit can be compromised.
The increase of the number n of the inverters to be connected in parallel may not always allow a
linear increase of the average input current: this is mainly due to the equivalent coupling impedance seen by
the n parallel inverters connected to the special load (infinite grid). However, if the grid impedance is too
small compared to the line impedance, then the increase of the number of inverters to be connected in parallel
tends to be close to a linear increase of the input current. This important result imposes that for a parallel-
connected inverter, the connection point of the different modules should be as close as possible to the grid.
This will guarantee the main advantage of paralleling inverters that is the linear increase of power as the
number of inverters connected in parallel is increased; otherwise, this principle will be compromised.
REFERENCES
[1] TG Wilson. The Evolution of Power electronics. IEEE Transactions on Power electronics. 2000; 15(3): 439-446.
[2] Xiong Fei Wang, Josep M Guerrero, Frede Blaabjerg, and Zhe Chen. A Review of Power Electronics Based
Microgrids. Journal of Power Electronics. 2012; 12(1): 181-192.
[3] V Zomgiebel, E Spahn, G Buderer, A Welleman, W Fleishmann.Compact High Voltage IGBT Switch for Pulsed
Power Applications. IEEE Transactions on Magnetics. 2009; 45(1): 531-535.
[4] S Luo, Z Ye, R Lin, F Lee. A Classiﬁcation and Evaluation of Paralleling Methods for Power Supply Modules.
30th
IEEE Power Electronics Specialists Conference.1999; 2: 901-908.
[5] P Lunieski, U Jansen. Benefits of system-Oriented IGBT Module Design for High Power Inverters. European
Conference on Power Electronics and Applications. 2007; 1-10.
[6] JW Kolar, F Krismer, Y Lobsiger, J Muhlethaler, T Nussbaumer, J Minibok. Extreme Efficiency Power Electronics.
7th
International Conference on Integrated Power Electronics Systems. Nuremberg, Germany. 2012; 1-22.
[7] Harish K Krishnamurthy, Raja Ayyanar. Building Block Converter Module for Universal (AC-DC, DC-AC, DC-DC)
Fully Modular Power Conversion Architecture. Power Electronics Specialists Conference. 2007; 483-489.
[8] F Wang, S Rosado, T Thacker, D Boroyevich. Power Electronics Building Blocks for Utility Power System
Applications. Power Electronics and Motion Control Conference. 2004; 1: 354-359.
[9] Sreedhar Madichetty, Abhijit Dasgupta. Modular Multilevel Converter PartI: A Review on Topologies, Modulation,
Modeling and Control Schemes. International Journal of Power Electronics and Drive System (IJPEDS). 2014;
4(1): 36-50.
[10] TP Chen. Circulating Zero-Sequence Current Control of Parallel Three-Phase inverters. IEE Electrical Power
Applications. 2006; 153(2): 282-288.
1 2 3 4 5
0
1
2
3
4
5
Number of inverters connected in parallel
a
b
c
d

 ISSN: 2088-8694
108
[11] Zhihong Ye, Dushan Boroyerich, Fred Lee. Modeling and Control of Zero-Sequence Current in Parallel Multi-
phase Converters. Power Electronics Specialists Conference. 2000; 2: 680-685.
[12] I Etxeberri-Otadui, JM Azurmendi, J San- Sebastien, T Nieva, U Larranaga. Design of Power electronics Building
Blocks (PEBB) for Multi-MW Modular Traction Converters. Energy Conversion Congress and Exposition (ECCE).
2010: 4217- 4222.
[13] Zulkifilie Bin Ibrahim, Md Liton Hossain, Imadi Bin Bugis, Nik Munaji Nik Mahadi, Ahmed Shukri Abu Hasim.
Simulation Investigation of SPWM, THPWM and SVPWM Techniques for Three Phase Voltage Source Inverter.
International Journal of Power Electronics and Drives System (IJPEDS). 2014; 4(2): 223-232.
[14] Chien Liang Chen, Jih Sheng Lai, Martin D, Yuang Shung Lee. State Space modeling, and implementation of
paralleled inverters for microgrid applications. Applied Power Electronics Conference. 2010: 619-626.
[15] J Mahdari, A Emadi, MD Bellar, M Ehsani. Analysis of Power Electronics Converters Using the Generalized State
Space Averaging Approach. IEEE Transactions on Circuit and Systems I. 1997; 44(8): 767-770.
[16] Juan C Vasquez, Josep M Guerrero, Mehdi Savaghebi, Joaquim Eloy Garcia, Remus Teoderescu. Modeling,
Analysis and Design of Stationary Reference Frame Droop Controlled Parallel Three Phase Voltage Source
Inverters. IEEE Transactions on Industrial Electronics. 2012; 60(1): 1271-1280.
[17] Iftikhar A Khan, Robert W Erickson. Synthesis and Analysis of Harmonic-Free Three phase Inverters .IEEE
Transactions on Power Electronics. 1994; 9(6): 567-579.
[18] T Zebbadji. Voltage Sharing via Feedback for DC Series Connection of Switched-Mode Converters. Master thesis,
University of Colorado, Boulder, 1987.
[19] T Zebbadji, S Hadji, R Ibtiouen. A simple average model and analysis of an n parallel connected inverters. 15th
workshop on Control and Modeling of Power Electronics (COMPEL 2014), Santander, Spain, 2014.
[20] RW Erickson, D Maksimovic. Fondamentals of Power Electronics. Kluwer Academic Publisher, 2nd
Edition. 2001.
BIOGRAPHIES OF AUTHORS
Tahar Zebbadji received his Engineer Diploma from the Ecole Nationale Polytechnique
d’Alger in 1984 and then obtained the Master degree from the University of Colorado, Boulder,
USA in 1987.He is currently a senior lecturer in the department of electrical enegineering at the
Ecole Nationale Polytechnique, ENP, Algiers. He is a member of the reseach team of the
Laboratoire de Recherche en Electrotechnique, ENP, Algiers.His area of interet is the
modelling and control of power electronics converters.
Seddik Hadji received the degree of Ingénieur in Electrical Engineering in 1979 from the Ecole
Nationale Polytechnique of Algiers (ENP-Alger), the M.Sc. (Eng) in Electronic and Electrical
Engineering in 1986 from the University of Birmigham, UK (within the Power Electronics and
Transportation Systems – PETS Group (1983–1986) and the Ph.D. degree in the same field in
2007 from ENP-Alger. He worked as a Lecturer and as a Senior Lecturer (1987–2009) at the
University of Béjaïa where he carried out research work (1991–2009) with the Laboratoire de
Recherche en Technologie Industrielle et de l’Information-LTII (2000–2009). He is currently a
Professor with the Ecole Préparatoire en Sciences et Techniques of Algiers (EPST-Alger) and
an Associate Director of research with ENP-Alger. His research interests include electric
traction, power factor correction, active filters, PWM converters and PWM multilevel
converters, and PV and Wind energy conversion systems.
Rachid Ibtiouen received the PHD degree in electrical engineering from Ecole Nationale
Polytechnique (ENP), Algiers, Algeria, and Institut National Polytechnique de Lorraine, Nancy,
France, in 1993. He integrated the Groupe de Recherche en Electrotechnique et Electronique de
Nancy, Nancy, from 1988 to 1993. From 2005 to 2013, he was the Director of the Laboratoire
de Recherche en Electrotechnique at ENP. He is the Head of the Department of Electrical
Engineering at ENP. He is currently a Professor and the Associated Director of Research with
ENP. His current research interests include modeling electric systems and drives.

Line and Grid Impedance Impact on the Performances of a Parallel Connected Modular Inverter System

More Related Content

What's hot (20)

Similar to Line and Grid Impedance Impact on the Performances of a Parallel Connected Modular Inverter System (20)

More from IAES-IJPEDS (20)

Recently uploaded (20)

Line and Grid Impedance Impact on the Performances of a Parallel Connected Modular Inverter System