Cascaded H Bridge Inverter Matlab

International Journal of Power Electronics and Drive System (IJPEDS)

617

Journal homepage: http://iaescore.com/journals/index.php/IJPEDS MATLAB/simulink modelling and simulation of 9-level cascaded H-bridge multilevel inverter with mismatched

Dc Sources

W. V. Yong1, M. S. Chye2, Y. C. Tan3, S. L. Ong4, and J. H. Leong5 1,2,3,5 School of Electrical System Engineering, Universiti Malaysia Perlis, Malaysia 4 School of Microelectronic Engineering, Universiti Malaysia Perlis, Malaysia

Accepted Feb 8, 2019

This paper presents a MATLAB/Simulink model for a 9-level cascaded H- bridge multilevel inverter with mismatched DC voltage sources. The impact of mismatched DC voltage sources on the performance of the 9-level CHBMI is investigated. Due to the mismatched voltages among DC voltage sources, the output fundamental voltage is different from the input reference voltage. To address this problem, a switching-angle calculation technique that accounts for mismatched as well as varying DC voltage sources is demonstrated. The switching angles obtained using this technique is able to produce the desired output fundamental voltage for a wide range of input reference voltages. Since this switching-angle calculation technique does not require complex iterative computation, it has the potential for real-time implementation.

Total Harmonic Distortion

Copyright © 2019 Institute of Advanced Engineering and Science. All rights reserved.

Universiti Malaysia Perlis,

Pauh Putra Campus, 02600, Arau, Perlis, Malaysia. 1.

Introduction

The power quality of the AC output voltage produced by a 9-level cascaded H-bridge inverter (CHBMI) shown in Figure 1 is determined by the harmonic contents of the output voltage waveform which can be measured as total harmonic distortion (THD) . The presence of harmonics in the output voltage waveform is due to the stepped output voltage levels, given by an example of a staircase waveform in Figure 2. Both the output fundamental voltage and the harmonic contents are related to the switching angles applied to the active power semiconductor switches in the H-bridge (HB) modules. Therefore, it is necessary to calculate the switching angles in order to obtain an output voltage waveform with the desired fundamental voltage and the lowest possible THD .

Switching angles are usually calculated off-line and kept in lookup tables for real-time control due to the complex iterative switching-angle calculations involved. The main drawback of this method is that distinct lookup tables are required for each distinct value of output fundamental voltage . Also, large sets of lookup tables result in higher cost associated with the hardware required for real-time calculation.

In practice, battery characteristics such as internal resistance and self-discharge rate are different among units . Consequently, for battery powered H-bridge cells, the voltages among batteries used as DC voltage sources are mismatched. Several researchers developed various strategies to compensate the mismatch among the batteries. However, the compensation circuits require additional components that increase the circuit complexity.

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In this work, a switching-angle calculation technique based on a geometric approach that accounts for mismatched voltages among DC voltage sources for a 9-level CHBMI is described in Section 2. The impact of mismatched voltages among DC voltage sources on the performance of the system is highlighted in Section 3. Also, the effectiveness of the presented switching-angle calculation technique validated via a 9- level CHBMI MATLAB/Simulink model is demonstrated in Section 3.

Figure 1. A Typical 9-Level Chbmi

Figure 2. Staircase voltage waveform produced by 9-level

Mismatched Dc Voltage Sources

2.

Switching-Angle Calculation Technique

Figure 3 shows the block diagram of the control algorithm, which includes a gain compensation for a 9-level CHBMI. The switching angles are determined from the reference voltage, Vref_pk, as follows:

(1)

where VDC is the nominal voltage of the individual DC voltage sources, ΔVDC is the variation of the individual DC voltage sources, and αn is the n-th switching angle. The relation between the output



MATLAB/simulink modelling and simulation of 9-level cascaded H-bridge … (W. V. Yong)

619

fundamental voltage, V1, and the switching angles can be obtained by analysing the output voltage using Fourier series. The expression of the fundamental voltage can be written as:









The limitation of (1) to produce the switching angles needed to produce the desired output fundamental voltage can be proofed by using (2). The conditions are set as follows: All the DC voltage sources are set to 10 V and the input reference voltage is set to 37.2 V. By using (1), the switching angles obtained for a 9-level CHBMI shown in Figure 1 are: α1=7.73º, α2=23.79º, α3=42.26º and α4=70.30º. Using (2), the output fundamental voltage, V1, obtained from these switching angles is 38.0 V, which is different from the input reference voltage. To obtain the desired output fundamental voltage with minimal error, it is necessary to perform a gain compensation, as shown by the control algorithm given in Figure 3. The expression of the output fundamental voltage with compensation can be obtained by rewriting (2):

(3)

where V1_out is the corrected output fundamental voltage after gain compensation and Δα is compensation of switching angles to produce the desired output fundamental voltage. From the equations above, the corrected output fundamental voltage can be rewritten in terms of input reference voltage and the switching angles as



To produce the desired output fundamental voltage while considering the mismatched voltages among the DC voltage sources, the switching angles are first obtained by using (1) and then, compensation is performed by using (4).

3. Simulation Results

The system has been verified using MATLAB for normalized output fundamental voltage range from 0.00 to 1.00. To verify the impact of mismatched voltages among the DC sources on the performance of the system and the effectiveness of the algorithm to account for mismatched voltages among DC voltage sources, the algorithm is tested for a 9-level CHBMI with mismatched DC voltage sources. The switching angles are first calculated using Equation (1) and (4), assuming that all DC voltage sources are equal and perfectly matched to a 10 V nominal voltage. The switching angles are then used to calculate the output fundamental voltage of 9-level CHBMI with DC voltage sources mismatched to ±20% of the nominal voltage to investigate the impact of the mismatched DC voltage sources onto the performance of the system.

Figure 4 shows the normalized output fundamental voltage versus the normalized input reference voltage for 9-level CHBMI. From the results obtained, without taking into consideration the mismatched DC voltage sources, the output fundamental voltage differs from the desired output fundamental voltage defined by the input reference voltage. After considering the mismatched voltages among the DC voltage sources, the

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output fundamental voltage is very close to the desired output fundamental voltage given by the input reference voltage. Figure 4. Comparison between normalized output fundamental voltage without and with mismatched DC voltage sources (MDCVS) consideration for 9-level CHBMI Figure 5 shows the switching angles versus normalized output fundamental voltage for a 9-level CHBMI, whilst Figure 6 shows the THD versus normalized output fundamental voltage for a 9-level CHBMI. At the lowest range of output fundamental voltage, the THD increases due to reduced available output voltage levels. Whilst at the highest range of the output fundamental voltage, the THD increases due to the output voltage waveform approaches a square wave.

Figure 5. Switching angle trajectories after gain compensation for 9-level CHBMI with ± 20% voltage mismatch from the nominal voltage of the DC voltage sources Figure 6. THD of output voltage waveform for 9-level CHBMI with ±20% voltage mismatch from the

Deployment In Out-Of-Position Situations

D. Bendjaballah1, A. Bouchoucha1, M. L. Sahli1,2* and J-C. Gelin2

Abstract

Side-impact collisions represent the second greatest cause of fatality in motor vehicle accidents. Side-impact airbags have been installed in recent model year vehicle due to its effectiveness in reducing passengers’ injuries and fatality rates. In meeting these requirements, simulations of folding and deploying airbags are very useful and are widely used. The paper presents a simulation method for the deploying airbags using three materials in different working conditions. Finite element analysis is primarily used to evaluate this concept. In these simulations, the gas flow is described by the conservation laws of mass, momentum, and energy. The numerical results indicate that the FE method in this paper is capable of capturing airbag deploying process accurately.

Keywords: Airbag simulations, Out-of-position, Crash, Modeling, Out-of-position

Background

The passive safety of cars has become a very high prior- ity issue for the automotive industry. Today, there are not only one or two airbags in a car; certain models have ten times more than that. With the increasing usage of airbags, the number of accidents where the airbag itself can cause an injury to the occupant also increases

(Augenstein Et Al. 2003; Gabauer And Gabler 2010;

Audrey et al. 2011). As is well known, safety belts are also now devices designed to provide protection to the users of vehicles during crash events, minimizing the loads necessary to adapt their movement to the move- ment of the car (Freesmeier and Butler 1999; Schmitt et al. 1997). In general, the seat belt is designed to restrain the occupant in the vehicle and prevent the

Occupant From Having Harsh Contacts With Interior

surfaces of the vehicles. The airbag acts to cushion any impact with vehicle structure and has positive internal pressure, which can exert distributed restraining forces over the head and face. As a safety component of auto- mobile, an airbag decreases occupants’ injury likelihood effectively in case of an accident (Ruff et al. 2007). These safety elements can reduce the death rates on the roads, and its protection effects have been widely approved (Crandall et al. 2001; Teru and Ishikawa 2003). With computational tools such as finite element methods designed for dynamic contact problems, crashworthiness simulations can now be used with reliable accuracy to evaluate occupant protection in various collision condi- tions with safety metric/parameters such as acceleration, head injury criteria, intrusion distance, intrusion vel- ocity, and neck forces (neck injury risk or whiplash).

Thus, new types of airbag products are being developed to handle different collision scenarios.

Become Standard Equipment On Most New Passenger

vehicles (Braver and Kyrychenko 2004; Teng et al. 2007; Yoganandan et al. 2007). The airbag cushion is com- posed of a woven fabric which is rapidly inflated during a car crash. The airbag dissipates the passenger’s kinetic energy thereby reducing injury through biaxial stretching of the fabric bag and escaping gas through vents. There- fore, the performance of the airbag is greatly influenced by the mechanical properties of the fabric. Generally, air bags are designed to deploy in a crash that is equivalent to a vehicle crashing into a solid wall at 8 to 14 mph.

Air bags most often deploy when a vehicle collides with another vehicle or with a solid object like a tree. There are various types of airbags: frontal, side-impact, and curtain airbags. In general, the passenger side airbags are usually larger than the driver airbags (see Fig. 1).

Besançon, France

© The Author(s). 2017 Open Access This article is distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.

Bendjaballah et al. International Journal of Mechanical

Doi 10.1186/S40712-016-0070-2

Extensive studies have shown that the airbag deploy- ment in load cases consists of two occupant loading phases: a punch-out effect where the airbag bursts out of its container with the airbag and airbag module cover accelerating towards the occupant and a second loading phase during which the airbag is taking on its deployed shape and volume (membrane-loading effect). Bankdak et al. (2002) developed an experimental airbag test system to study airbag-occupant interactions during close proximity deployment. The results provided insight for simulating the effect of inflation energy and mass flow on target response. Bedard et al. (2002) found that while left-side (driver-side) impacts accounted for only 13.5% of all crashes, the fatality rate among these

Crashes Was 68.3% In Comparison To Front Impact

(48.3%), right-side impact (31.3%), and rear impact (38.4%). These studies underscore the importance of oc- cupant safety during side-impact collisions. In the last years, the current market requested to reduce the time and cost airbag development. In order to achieve this result, virtual simulations play an important role since they allow to minimize the number of experimental tests (Pei et al. 2013; Cao et al. 2014). Several simulation models of airbag were established (Wang et al. 2007). It is feasible to optimize the parameters of airbag deploy- ment using simulation technology. Experimental and numerical studies have quantified injury risks to close- proximity occupants from deploying side airbags. These studies have focused on the prevention of the most ad- verse effects of airbag deployment (Duma et al. 2003).

Other studies have proposed airbag characteristics to minimize particular biomechanical responses (Haland and Pipkorn 1996). In a more recent study, Marklund and Nilsson (2003) compared deformation patterns with experimental data as well as the computational costs associated with three different airbag deployment simu- lation methods; they concluded that the SPH method is relatively inexpensive and produces incremental deform- ation patterns that compare most closely to the experi- mental results. The process of inflation of an airbag is one of the determining factors in saving lives. The duration from the initial impact of the crash to the full inflation of an airbag is about 40 ms, and during this time, the airbag goes from being in a folded state to a fully inflated state, with a high internal pressure. After achieving this state, the airbag begins to deflate, thus providing a nice cushion for the body impacting it.

Ideally, the person in the crash should come into contact with the airbag at this time. In the present study, a large volume passenger side airbag model is developed to handle different collision scenarios. The main aim is evaluate the performance of deploying of passenger side airbag using finite element methods (FEM).

Materials

The tensile specimens were made in different airbags (P: Peugeot, R: Renault, and VW: Volkswagen) with a length of 200 mm long and a width of 40 mm. Table 1 shows the mechanical properties of the airbag.

Tensile Tests

To determine the mechanical properties of the material of airbag used in the test pieces, tensile tests were performed on Lloyd EZ20 universal testing machine in Constantine. These tests were conducted using rect- angular samples. The axial force and axial displacement acquired during a test are converted into stress and the strain in order to be used for the fabric material model.

The continuous recording of the stress-strain data was performed during both the load and unload phases. A minimum of five samples were made in order to check the repeatability of the measurements. All the data was collected by using a PC-based data acquisition system and analyzed by commercial software. The picture frame test device that is made for this study is shown in Fig. 2.

Fig. 1 a Frontal and side airbags. b Oblique view of facet occupant model in sitting posture following airbag deployment (Lim et al. 2014)

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Bendjaballah et al. International Journal of Mechanical and Materials Engineering (2017) 12:12

Page 2 Of 9

Figure 3 shows the stress-strain relationship of the airbag sample under axial tensile loads. The results are showing a linear increase in extension with the increas- ing stresses. This is an expected output and it confirms with the theoretical behavior of a sample subjected to tensile stress. The rupture strain values for different airbags (R/P/VW) were 0.322, 0.441, and 0.472, respect- ively. The measured elastic parameters (i.e., Young’s modulus E and initial yield strength) and Poisson’s ratio are summarized in Table 2. The tensile tests of the woven fabrics can show differences on mechanical prop- erties because woven fabrics can resist in-plane shear loads once the yarn lock-up angle has been reached. The differences of material property on material direction can affect the shape of fully deployed bag (see Fig. 3b).

Theoretical Background

Numerical simulations of airbags use very complex and techniques such as an orthotropic model to identify the mechanical behaviors during the airbag inflation and the fluid mechanics (gas flow) to describe the inflator gas flow (pressure gradient) and improve the representation of the pressures within the airbag. To model the airbag as an orthotropic model, three material constants have to be provided. Assuming a plane stress condition, the

Ð1Þ

where σ is the normal stress and τ is the shear stress, the subscript refers to the principal material directions, i.e., the fill and warp directions. Also, ε and γ are the strain components. The material elastic constants Qij are

Ð2Þ

where E1 and E2 are the Young’s modulus in the fill and wrap directions and G12 is the shear modulus of the fabric material. νij is the Poisson ratio of the material.

The gas exerts a pressure load on the airbag causing it to expand. This expansion puts the airbag under tensile stress lowering the expansion rate. In this study, heat conduction and heat transfer is not taken into account.

Fig. 2 A photograph of Lloyd EZ20 universal testing Fig. 3 Stress versus strain using Lloyd EZ20 machine for a three different airbags at 0° and 90° and b VW airbag test specimens at

Different Angles

Table 2 Physical and mechanical properties of the airbag

Page 3 Of 9

In the deployment of an airbag, an inflator supplies high velocity gas into an airbag causing it to expand rapidly. The gas inside the airbag is assumed to be ideal, to be of constant entropy, and to satisfy the equation of state:

Ð3Þ

Here p, ρ, and e are respectively the pressure, density, and specific internal energy, and γ is the ratio of the heat capacities of the gas. The gas flow is described by the conservation laws for mass, momentum, and energy that

Ð4Þ

here, V is a volume, A is the boundary of this volume,

N Is The Normal Vector Along The Surface A, And U

denotes the velocity vector in the volume. Applying Bernoulli’s equation in the case of an ideal gas with

Ð5Þ

Here, the subscript ex denotes quantities at the throat of the tube. Furthermore u, p, and ρ denote the quan- tities inside that part of the tube that is supplying mass.

Materials And Boundary Conditions

The airbag system mainly consists of three parts: the airbag itself, the inflator unit, and the crash sensor or diagnostic unit. Thus, to study the behavior of the airbag using FE simulations, we need to have an FE model of the airbag in the folded position. A FE model of the airbag was used to simulate the test condition as shown in Fig. 5. LS-DYNA® material model FABRIC (MAT_34) is used to simulate the airbag material. It is a variation of the layered orthotropic material model. Additionally, in the LS-DYNA® material model, fabric leakage can be accounted for. However, for this CAB material, the leak- age is almost negligible and therefore no leakage is specified. The mechanical properties can be determined from the physical test. Typical material properties for airbag fabrics are taken as given in Chawla et al. (2004a) (Table 3). These properties are used to simulate inflation process of airbag (see Table 1). The car dashboard is modeled as the rectangular thin plate using a MAT_RI-

Gid Material, And The Degrees Of Freedom Are Con-

strained in all the directions. The similar properties of thermoplastic polymer are assigned for contact purposes. The porosity of the fabric is assumed zero. The nitro- gen gas is taken for inflating the airbag. Properties of nitrogen gas and initial bag conditions are shown in Table 4. The example on which we perform the study is a typical passenger side airbag. The geometric de- tails have been measured from a commercially avail- able airbag. The initial state of the airbag is a closed rectangular whose sides are to be finished to 482 × 635 mm2 and is shown in Fig. 4.

Table 3 Material properties of airbag and rigid plate used in FE

–

Table 4 Initial values used for FE simulation of the swelling of

3.33 × 10−4

Fig. 4 The initial airbag geometry in the form of a rectangular Bendjaballah et al. International Journal of Mechanical and Materials Engineering (2017) 12:12

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