J. Energy Power Sources
Vol. 2, No. 6, 2015, pp. 230-238
Received: May 20, 2015, Published: June 30, 2015
Journal of Energy
and Power Sources
www.ethanpublishing.com
Power Loss Investigation for 13-level Cascaded
H-Bridge Multilevel Inverter
Basem Alamri and Mohamed Darwish
CEDPS, Brunel University, London, UK
Corresponding author: Basem Alamri (Basem.Alamri@brunel.ac.uk)
Abstract: In recent years, voltage source multilevel inverters are being applied extensively in industry as they have many advantages
compared to conventional two level inverters. Some of these advantages such as higher output voltage at low switching frequency, low
voltage stress (dv/dt), lower Total Harmonic Distortion (THD), less Electro-Magnetic Interference (EMI), smaller output filter and
higher fundamental output. However, the evaluation of multilevel inverter losses is much more complicated compared to two level
inverters and required more computations burdens. This study presents an on-line model for precise evaluation of conduction and
switching losses in cascaded H-bridge multilevel inverter. The model is simple and efficient and gives clear and easy to implement
procedure of loss calculation. A single-phase 13-level cascaded H-bridge with IGBT’s as switching devices has been considered as a
case study of the proposed model. The inverter has been controlled by applying SHE in which the switching angles were determined
using the Genetic Algorithm (GA). The modelling and simulation has been conducted using MATLAB-SIMULINK software.
Keywords: Cascaded H-bridge multilevel inverter (CHB-MLI), conduction losses, switching losses, selective harmonic elimination
(SHE).
1. Introduction
Nowadays, the use of multilevel inverters has been
grown significantly in many industrial power
applications. The multilevel inverters are considered
very attractive as they generate low harmonic
component at low switching frequency. Also, they
operate at lower losses, lower blocking voltage of
switching devices, and low Electro-Magnetic
Interference (EMI) [1]. Basically, there are three main
commercial topologies of multilevel voltage-source
inverters well established in industry which are:
Cascaded H-bridge (CHB-MLI), Neutral-Point
Clamped (NPC-MLI) and Flying Capacitor (FC-MLI).
Among these topologies, the CHB-MLI is very widely
applied in industry for high power applications. It is
used in high voltage and high power levels and it
requires small number of devices, consequently, it has
a reliable modular structure compared to the NPC-MLI
and FC-MLI.
At the stage of power system planning and
multilevel inverter design, precise calculation of
inverter power loss is significantly important to
evaluate system efficiency, reliability and system
economical operation. Practically, loss evaluation in
multilevel inverter is not an easy task and much more
challenging compared to basic two level inverters.
This is due to the fact that the current differ in each
power switch in the inverter. This paper presents a
precise modelling of switching and conduction losses
in CHB-MLI. Different methods have been suggested
in literatures to calculate the power loss in multilevel
inverters. Some of these methods are based on online
model calculation from the simulated circuit and some
are done based on deep mathematical analysis and
calculations. In [2], each IGBT was modelled by
characteristic curves applying curve fitting exponential
equations as a function of load current. In [3], a
general procedure for calculating switching and
Power Loss Investigation for 13-level Cascaded H-Bridge Multilevel Inverter
conduction losses of power semiconductors in
numerical circuits has been presented. The model is
based on online circuit simulation. Switching
functions have been implemented in [4] to model the
inverter losses for three phase nine level cascaded
H-bridge inverter in which the load was assumed to be
mixed RL load at a modulation index of 0.85. All the
previous
papers
applied
online
modelling
for
calculating the losses by applying curve fitting to
characterize the IGBT based on the actual device
datasheet. On the other hand, in [5-7], the losses of
multilevel
inverter
were
calculated
using
mathematical model in which the voltage across the
switch is modelled by a threshold voltage and a series
resistance.
This paper presents a model for detailed calculation
of conduction and switching losses in CHB-MLI based
on the method applied in [3] with some modification to
be applied for multilevel inverters. The proposed
model is based on online simulation in which the
inverter losses are evaluated precisely with much less
computational burdens. Generally, there are four types
of losses in multilevel inverters which are: (1)
Conduction loss; (2) Switching loss; (3) OFF-state loss
and (4) Gate loss. In practice, the OFF-state and Gate
losses are found to be very small and normally
neglected. Hence, in this study, only conduction and
switching losses are considered throughout the
analysis.
As it is most widely applied for medium voltage,
high power applications, the CHB-MLI has been
selected for this analysis with IGBT’s as power
switching devices. In order to control the inverter,
Selective Harmonic Elimination (SHE) technique is
applied. In this control strategy, the switching angles
are to be determined in which the total harmonic
distortion is minimized ate the inverter output. Genetic
Algorithm (GA) optimization method is applied for
solving the system of transcendental equations of SHE.
Then, simulation is performed to evaluate the
conduction and switching losses based on the proposed
231
model. Curve fitting tool is used to generate the
equations implemented in the model based on the
power switch datasheet.
2. Cascaded H-Bridge Multilevel Inverter
(CHB-MLI)
Diode-Clamped (DC-MLI) and Flying Capacitor
(FC-MLI) are widely used for industrial medium
voltage- high power applications when just low
number of levels (typically three) is required. On the
other hand, Cascaded H-Bridge inverter (CHB-MLI) is
preferred for high voltage-high power, HVDC utility
applications. This is mainly due its modular structure
which can be extended for higher number of levels with
no much complexity. In addition to that, with
CHB-MLI, higher power and voltage capability can be
reached by using the lowest number of required devices
compared to DC-MLI and FC-MLI. At CHB-MLI, a
series connection of single phase H-bridge inverters
with separate dc sources is implemented. The main
concept is that each H-bridge cell will generate three
different voltages and the output waveform can be
synthesized by the sum of the voltages generated by
each cell. In practice, the separate dc sources might be
solar panel PV cells or fuel cells [1].
An m-level CHB-MLI circuit layout is
demonstrated in Fig. 1. The number of levels is equal
to m=2×S+1, where m, is number of output levels,
S, is the number of cascaded H-bridges. In this paper,
the inverter is required to be connected with 11 kV line
to line grid voltage at 13-level CHB-MLI. The
switching devices have been selected to be of IGBT
type FZ400R33KL2C_B5, which has a blocking
voltage capability of 3.3 kV, and a maximum forward
current of 400 A and its shown in Fig. 2. Datasheet for
this type IGBT is given in [8]. Each cell is connected to
a dc link supply of 1.7 kV. Modulation index of (0.9)
was used throughout the analysis. The inverter has
been modelled in MALTAL-SIMULINK with main
objective of precisely calculating the conduction and
switching losses of the inverter.
232
Power Loss Investigation for 13-level Cascaded H-Bridge Multilevel Inverter
Fig. 3
Output stepped-voltage waveform for n-level
inverter.
Fig. 1 Single-phase m-level cascaded H-bridge inverter
circuit layout.
5
3
2
4
1
Fig. 2 IGBT module FZ400R33KL2C_B5 circuit diagram [8].
3. Selective Harmonic Elimination (SHE)
Different modulation techniques have been applied,
to control the output of voltage waveform in multilevel
inverters. These control techniques can be classified
basically based on the switching frequency fs , into low
or high switching frequency techniques. Space Vector
Control (SVC) and Selective Harmonic Elimination
(SHE) are considered low switching techniques in
which the power switch is commutated only one or two
times during one cycle. On the other hand, various
PWM techniques are used as high switching frequency
techniques in which the power switch is being switched
many times within a cycle [1]. In this paper, SHE has
been implemented to control the inverter as the
application of SHE results in lower switching losses
and less EMI due to its low switching [4]. Furthermore,
it can eliminate some of the dominant low order
harmonics and hence minimize the size of the required
filter at the inverter output.
SHE control applies pre-defined switching angles to
compose the desired multilevel fundamental voltage
and eliminate some of the predominant low order
harmonics. The use of SHE results in minimizing the
Total Harmonic Distortion (THD) at the inverter output.
The switching angles are pre-determined off-line and
hence the SHE is considered an open loop control
technique. Fig. 3 shows the stepped-voltage waveform
for n-level CHB-MLI.
Applying Fourier’s expansion, the stepped voltage
wave form can be written as a sum of sine and cosine
periodic signals and a constant. Such signal consists of
odd and even harmonics. As a result of the quarter
symmetry of the waveform, the even harmonics and the
dc constant are cancelled. Hence, only odd harmonics
are remaining. Assuming a balanced three phase
system, all triplen harmonics are zero. Generally, the
output voltage waveform can be written as:
∞
van wt =
4Vdc
cos k∝1 +cos k∝2 …+cos k∝s sin kwt (1)
kπ
k=1,3,5,…
233
Power Loss Investigation for 13-level Cascaded H-Bridge Multilevel Inverter
where S is the number of H-bride cells of the
inverter.
It is clear from Fig. 3 that all switching angles are in
ascending order and less than 90º.
θ1 < θ2 <⋯< θS < 90º
(2)
And it is possible to eliminate the (S - 1) harmonic
by solving the following system of non-linear set of
equations.
cos θ1 + cos θ2 + ⋯ + cos θS = S × Mi
cos 5θ1 +cos 5θ2 +⋯ +cos 5θS =0
cos 7θ1 + cos 7θ2 + ⋯ + cos 7θS = 0
(3)
⋮
⋮
⋮
⋮
⋮
⋮
cos hθ1 + cos hθ2 + ⋯ + cos hθS = 0
where
Mi is the modulation index;
h=3S-k, is the highest harmonic order which can
be eliminated. K takes the value of 1 for even number
of S, and takes the value of 2 for odd number of S [9].
This system of equations is a highly non-linear
system and also called transcendental equations or
SHE equations. The number of equations is equal the
number of H-bride cells of the inverter. To solve such
system, different techniques have been applied.
Iterative and Evolutionary Algorithms (EA) are the
most commonly used in literatures. Newton-Raphson
(NR) has been applied extensively for this problem as
an iterative technique. The key disadvantage is that
when the inverter level gets higher, the algorithm is
getting more difficult to converge into a solution. In
addition to that, iterative techniques do need good
initial guessed switching angles to help the algorithm
converge into a feasible solution. On the other hand,
Evolutionary Algorithms (EA) was found to be very
powerful and can solve the problem applying
intelligent approaches. The main idea is to transform
the problem of SHE into an optimization problem, in
which the set of transcendental equations will be the
constraints for the optimizer. In this paper, the problem
of SHE for 13-level CHB-MLI is solved using Genetic
Algorithm (GA) as it shows better results compared to
Newton Raphson (NR) and Particle Swarm Optimization
(PSO) [10]. In the next section, a detailed explanation
of how to apply GA for solving SHE is presented.
4. Genetic Algorithm (GA) for SHE
Genetic Algorithm (GA) is a heuristic global
evolutionary
optimization
algorithm
based
on
mechanics of natural selection and genetics. By
Comparing GA to other optimization techniques, the
main difference is that GA search by population not by
individual points. GA has been implemented widely for
solving both constrained and unconstrained optimization
problems. GA is considered a simple and easy to
implement technique, hence, it can be easily
implemented to solve for the switching angles in the
problem of SHE. The main structure of any GA
optimization consists of five steps which are: (1)
Initialization of the population; (2) Evaluation of
fitness function; (3) Selection; (4) Apply genetic
operators, and (5) Stopping Criterion [10-11].
STEP 1: Initialization
The algorithm is initialized in this step. First, All the
parameters of the optimization problem are coded. The
coding can be in a binary or floating-point string. Then,
based on the coded parameters, a set of solutions is
randomly.
STEP 2: Evaluation of Fitness Function
In order to test the goodness of a generated solution
in Step 1, a fitness function is to be applied as a
measure tool. In this study, an objective function was
defined as a Fitness Value (FV). Defining the fitness
function is a crucial step and should be done very
carefully as it has a great effect on the quality of the
optimized solution. The objective function should
satisfy the fundamental voltage required, eliminate the
possible low order harmonics and minimize the THD
of the output waveform as well [10].
ObjF = |V1 - SMi |4 +|V5 |2
+ |V7 |2 + ⋯ + |Vz |2 + THD
(4)
where V1 , V5 and V7 , are the amplitudes of
fundamental, 5th and 7th harmonics respectively. Vz ,
is the highest odd harmonic that can be eliminated. S
234
Power Loss Investigation for 13-level Cascaded H-Bridge Multilevel Inverter
is the number of cascaded H-bridges. For 13-level
inverter, 17 is the highest harmonic order that can be
eliminated when applying SHE.
STEP 3: Selection
At selection step, parents are selected based on
selection rules to produce offspring chromosomes. The
chosen parents are the main contributors to form the
next generation. In this the fittest individual are likely
to survive and the less fit are eliminated.
STEP 4: Crossover and mutation
In the crossover, a number of bits are swapped
between different parents. Here, some genes are
exchanged to form a new improved combination.
Another very important operator to be applied is called
Mutation, in which the genes are alerted.
STEP 5: Stopping Criterion
This step tells the algorithm when to stop and
terminate and is a very important step. Therefore, it
decides the optimum solution as an output.
5. Power Loss Evaluation
There are mainly four types of power losses occur
during the operation of power electronics switching
devices. These are [3]: (1) Conduction losses; (2)
Switching losses; (3) OFF-state losses, and (4) Gate
losses. In practice, the Off-state and Gate losses are
very small and normally neglected. Because of this,
only conduction and switching losses have been
investigated in this paper. Loss estimation of multilevel
inverters is considered a complicated task compared to
two level conventional inverters. This is because that in
multilevel inverters, each semiconductor devise has
different current compared to other devices which
implies different losses behavior for each one. The
current differ in the switches due to having different
on-state ratio of each switch for one leg during a period
of output phase voltage. Furthermore, at high number
of levels, the switching frequency of each switch will
not be identical for all switches which increase the
complexity to power loss calculations.
This paper investigates the power loss problem in
multilevel inverter. A simplified model is proposed for
calculating the conduction and switching losses of
CHB-MLI precisely. The proposed model uses the
method applied in [12] which based on online
calculations. The operating temperature of the
switching devices was assumed to be maximum at 150º.
The model is based on on-line calculation in which
MATLAB-SIMULINK software has been used for the
modelling. Mixed load of R = 60 Ω and L = 20 mH,
has been considered for this study. The simulated
results were compared to the case where the load is
changing from purely resistive load gradually to purely
inductive load. The objective is to provide a
comprehensive study of the inverter losses behavior at
different load conditions.
5.1 Conduction Losses
Conduction losses, for a semiconductor device, can
be defined as the losses which occur while the power
device is on the on-state and conducting current. As
the number of cascaded cells in CHB-MLI gets higher,
the conduction loss increases proportionally. At
conduction stage, the power dissipation can be
calculated by multiplying the on-state saturation
voltage by on-state current [3, 12].
pConduction = |ic | · von
(5)
Here, the absolute value for the current as the
conducting current is always positive for the power
switch. Thorough research literatures, Most of the
papers usually are modelling the on-state voltage by
inserting a voltage Vo, representing the voltage drop
of the device called threshold voltage, connected to a
resistor ron, in series, representing the current
dependency which is added in series with the ideal
switch. The main drawbacks of this modelling
methodology are [3]:
(1) Additional parameters to be added in series
with the ideal switches, which require rebuilding the
circuit partially;
(2) As the model is not based on actual curves of
the device datasheet, the model might not be accurate
Power Loss Investigation for 13-level Cascaded H-Bridge Multilevel Inverter
in calculating the loss.
However, the proposed model, computes the
conduction losses in much easier and more efficient
way. In this model, the on-state voltage is represented
by a quadratic equation in terms of the on-state current.
The quadratic equation can be obtained by applying
curve fitting tool based on the actual curves in the
device datasheet. For each power switch device, there
will be two quadratic equations, one represents the
main IGBT switch and one representing the
antiparallel diode. In the MATLAB-SIMULINK
model, it is required to separate the pure switch
current and pure diode current. Once, separated, the
conduction losses can be obtained simply by applying
as shown in Fig. 4.
which results in a turn-on loss of less than 1%
compared to the turn-off loss in modern diodes [3,
12].
Practically, there are five main factors which could
affect the behavior of switching loss. These factors are:
(1) the current being switched, (2) the blocking
voltage, (3) the junction temperature, (4) the gate
resistor and (5) the wiring stray inductance [3].
Usually, the switching loss is considered a major
drawback in multilevel inverters which cause high rise
in the operating cost and reduce inverter efficiency in
HVDC applications.
In this paper, an on-line model for switching loss
estimation is presented which is based on the actual data
sheet of the switching devices. First, energy factor (K)
5.2 Switching Losses
By definition, the switching loss is the power
dissipated during the turn-on and the turn-off
switching of the power semiconductor device. This
loss occurs on both the switch and the antiparallel
diode. The switching loss is very highly proportional
to the switching frequency fs , and hence it contributes
significantly to the inverter total loss especially for
inverters applying SPWM. Considering the power
switch, there are the turn-on loss (Eon) and the
turn-off loss (Eoff). However, for the antiparallel
diode, only the turn-off (Erec) loss is considered as the
turn-on loss is normally neglected. This is due to fast
conducting of the diode when it get forward biased
235
Fig. 4 Conduction losses calculation block [12].
Fig. 5 Switching losses calculation block [12].
Fig. 6 Basic flow model of proposed methodology for losses calculation in CHB-MLI [12].
236
Table 1
Power Loss Investigation for 13-level Cascaded H-Bridge Multilevel Inverter
Best: 0.0867083 Mean: 0.0870983
IGBT curve fitted equations based on datasheet.
2.5
vce = -2 × 10-6 I2c + 0.0073Ic + 1.173
vD = -3 × 10-6 I2D + 0.0061ID + 0.7479
KIGBT-on = 8 × 10-6 I2c - 0.0064Ic + 4.2836
KIGBT-off = 3 × 10-6 I2c - 0.0031Ic + 2.2269
curves are to be obtained by dividing the energy by
switching current. Then, curve fitting tool is applied to
approximate the energy factor curves by second order
polynomials. After that, the energy factor curve
equation is multiplied by the switching current which
should give the energy loss. This energy loss is further
multiplied by the switching frequency in order to get
the power loss [3, 12]. A normalization factor is
applied as adjustment in the loss calculation in case
the blocking voltage is different. Fig. 5 presents the
block implemented for the switching loss calculation.
The complete block for the proposed modelling of
losses calculation in CHB-MLI is shown in Fig. 6.
Table 1 summarizes the modeling equations of the
selected IGBT switch (FZ400R33KL2C_B5) obtained
by curve fitting.
Mean fitness
2
Fitness value
KDiode-rec = 8 × 10-6 I2D - 0.0098ID + 3.8363
Best fitness
1.5
1
0.5
0
0
Fig. 7
10
20
30
40
50
60
Generation
70
80
90
100
GA performance in solving SHE problem.
Total Inverter Losses = 3.765 kW
Switching
11%
Conduction
89%
6. Simulation Results and Discussion
The proposed online model for loss evaluation has
been built in Simulink based on the block diagram
shown in Fig. 6. In this section, the simulation results
obtained will be presented. The simulated inverter has
the following parameters:
• VL - L = 11 kV , at the output voltage of the
inverter.
• Modulation index Mi = 0.9,
• Inverter output power 1.14 MW, R = 60 Ω, L =
20mH.
• IGBT of blocking voltage 3.3 kV [8].
Based on the required output voltage and selected
power switches, the inverter is designed at 13-level
CHB-MLI. To control this inverter with SHE, GA has
been applied to solve for the switching angles which
found to be:
∝1 =3.04°, α2 =8.65°, ∝3 =13.35°
α4 =23.09°,α5 =28.88°, α6 =42.06°
Fig. 8
Inverter total power losses.
The %THD at the output voltage is 2.1 which is a
small value as a result of operating at 13-level. The GA
was found to be very powerful and efficient to solve the
problem of SHE which not only find the switching
angles and eliminating the low order harmonics, but
also minimizes the THD. Fig. 7 shows the performance
of GA in the optimization to find global minimum
objective functions based on the given constrains.
Operating at the above parameters, the inverter
losses have been evaluated applying the proposed
model. It was found that the total loss of the inverter is
3.765 kW. Majority of this losses results from
conduction loss which represents around 89% of the
total inverter losses. This is shown in the pie chart in
Fig. 8. The switching loss is 11% of total inverter
losses. This is justifiable as normally when controlling
the multilevel inverter with SHE, the power switches
237
Power L
Loss Investiga
ation for 13-le
evel Cascaded
d H-Bridge Mu
ultilevel Invertter
Conductio
on
Switching
Conducttion
700
600
Totaal
4
Losses ( kW )
500
Losses ( W )
Switcching
5
3
400
300
2
200
100
1
0
Cell-1
Fig. 9
Cell-2 Celll-3 Cell-4 Cell-5
Cascadedd H-Bridge Cells
Cell-6
0
0.0
00
0.20
Switch
hing losses per H
H-bridge cell.
Conductionn
Switching
160
Fig. 12
0.40
0.60
Load Power Facctor
0.80
1.00
Inverter lossees at different power
p
factors.
betweeen the cascad
ded H-brides when applyinng SHE
controll technique. In
n Figs. 10-11,, the losses aree shown
120
Losses ( W )
per eacch switch. In 13-level CH
HB-MLI, theree are 24
80
power switches requ
uired.
In order
o
to study
y and analyzee the inverterr power
40
losses at different po
ower factors, the
t load was cchanged
0
Fig. 10
graduaally from purely resistive looad, mixed RL
L load to
S1 S2
S S3 S4 S5 S6 S7 S8 S9
9 S10 S11 S12
Pow
wer Switches
highly inductive load changingg the powerr factor
Switcching losses perr power switch (S1-S12).
betweeen the value of
o 0 and 1. The
T inverter lloss was
Condcutio
on
Switching
presentted here in Fiig. 12. In all cases the connduction
200
loss is much higher than the swittching loss whhich due
150
Losses ( W )
compuuted at each time at variious loads annd it is
c
using SHE as explaained before. IIt is also
to the control
can be noticed that as
a the load beccome more innductive,
100
the invverter loss inccreases signifficantly. The analysis
50
shows that the in
nverter lossess depends onn many
factorss such as contrrol technique, switching freequency,
0
S13 S14 S15 S16 S17 S18 S19 S20 S21
1 S22 S23 S24
wer Switches
Pow
Fig. 11
voltagee applied, po
ower switch selected,
s
and type of
load.
Switcching losses perr power switch (S13-S24).
are kept condducting for loong time com
mpared to otheer
control techhniques andd hence geenerates morre
conduction looss. On the otther hand, pow
wer switches is
switched onee time only w
within one period
p
and this
results in minnimum switchhing losses ass the switchinng
frequency in this case is 500 Hz.
Fig. 9 demonstrates tthe losses asssociated witth
each H-bridgge. The simullation results shows almosst
the inverter loosses in CHB--MLI are distrributed equallly
7. Con
nclusions
The use of multtilevel inverters has beenn grown
significcantly in maany industriaal and utilityy power
applicaations as they add more tecchnical and ecconomic
benefitts and improve the power quality to the end
custom
mer. CHB-ML
LI, NPC-MLI and FC-MLII are the
basic topologies off multilevel inverters whhich are
commeercially avaiilable and well
w
establisshed in
industrry. Precise evaluation
e
off multilevel inverter
238
Power Loss Investigation for 13-level Cascaded H-Bridge Multilevel Inverter
losses is an up to date subject in research. This paper
proposes a simple, efficient and easy to implement
on-line model for conduction and switching losses
calculation in multilevel inverters. A 13-level
CHB-MLI has been chosen as a case study as these
losses are the main inverter loss. The model evaluates
the losses by calculating the conduction and switching
losses in each device separately. Then, adding the
losses together. The model use accurate voltage and
energy curves as per power switch device datasheet. It
was found that most of the loss is coming from
conduction which represents around 90% of total
inverter loss. On the other hand, switching loss is
representing a small portion of inverter loss as the
inverter has been controlled with very low switching
frequency. Applying SHE in CHM-MLI control
results in equal distribution of losses among the
cascaded H-bridges. AS expected, the inverter loss
increases as the power factor decreases. The analysis
shows that several factors affect the loss performance
in multilevel inverter such as: operating voltage,
applied control, selected switching device and type of
load. The study recommends solving the problem of
SHE using GA as this results in minimum THD,
eliminate the low order harmonics and can solve high
number of inverter levels.
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