Indirect Matrix Converter Matlab

Journal of Engineering Science and Technology Review 15 (5) (2022) 145 - 152

Research Article

Indirect Matrix Converter Controlled with ANFIS-based Modulation Murikipudi Nagaraju1,*, G. Durga Sukumar1 and M. Ravindrababu2 1Vignan Institute of Technology and Science, Deshmuki, Yadadri, Bhuvanagiri, Telengana, 508284, India

Received 19 July 2022; Accepted 15 November 2022

___________________________________________________________________________________________

Abstract

A matrix converter is a one level converter; it converts from AC input to AC output without an intermediate circuit capacitor. An indirect matrix converter has more advantages and performs better with space vector modulation (SVM) techniques. This article proposed an ANFIS-based SVM technique for the rectifier stage of an Indirect Matrix Converter.

The data used to train the ANFIS-based SVM is generated from the traditional SVM. The training methods used for training are the combination of backpropagation and least squares methods. The angle and delay angle are inputs to the proposed scheme and outputs are switching times. Because of this technique; The converter output voltage is improved and THD (Total Harmonic Distortion) of voltage and currents are reduced compared to the traditional SVM. The performance of the converter with ANFIS-based SVM is compared with conventional and the changed SVM by using MATLAB/Simulink.

Keywords: Space vector modulation (SVM), ANFIS (Adaptive Neuro Fuzzy Inference System)-based SVM, Total Harmonic Distortion (THD), Indirect Matrix Converter (IMC), Converter side modulation modified matrix converter, Virtual DC link. ____________________________________________________________________________________________

1. Introduction:

The converter that converts from direct AC input power to AC output power is a matrix converter. The matrix converter has various advantages such as: Allowing current flow in both directions, no need for a large intermediate circuit capacitor, the life of the converter is extended due to the lack of a capacitor and it is economical. The matrix converters are grouped such as Direct Matrix converter (DMC) and Indirect Matrix Converter (IMC). The IMC has more advantages than the DMC, such as generating pulses to turn the devices ON (switching) is easy, and turning them OFF (commutating) is also easy. Due to these advantages of an IMC and with bidirectional power flow current source rectifier stage and unidirectional voltage source inverter, it is used in various applications such as electric drives such as controlling an asynchronous motor , as an active filter and also in FACT's device for power factor correction and power quality improvement [ 2.3]. The performance of an IMC depends on the type of modulation scheme used to switch the power electronic devices.

The indirect matrix converter is controlled using a carrier- based modulation method and a space vector method. The carrier based modulation methods are used to control the output voltage with the load of the motor and the slope of the carrier and the voltage offset to get the unity power factor on the input side . Phase Shift and Phase Disposition Carrier based modulation scheme is applied to control the output voltage.

Advantages,

e.g.

Simple

implementation by using digital controllers like DSP or microprocessor, output current quality, dynamic performance and performance under unbalance conditions are also good .

Space vector modulation is applied separately for the rectifier stage and the combination of booster and inverter stages, the rectifier is controlled with the current reference based SVPWM and the inverter is controlled with the voltage reference . In the modulation techniques for IMC are SVPWM and Sinusoidal PWM (SPWM), the rectifier stage is controlled with the SVPWM and an inverter stage is controlled with the SPWM. Carry-based PWM is used to control the IMC, the pulses are generated by comparing the modulation signal with the same triangle for rectifier and inverter, this IMC is used to drive the five-phase motor .

Controller

powered induction motor with current control is presented. This PI technique is replaced by a neuro-fuzzy controller to improve voltage levels and self-tune against speed command fluctuations and load disturbances . In order to reduce the common mode voltage by space vector pulse width modulation of matrix converters, the correct selection of the active vectors and the switching sequence is explained .

The neuro-fuzzy based SVM powered induction motor is presented. The neuro-fuzzy provides better drive performance with reduced torque ripple compared to neural network and traditional SVM methods . An alternative space vector modulation applied to a matrix converter based induction motor to reduce the common mode voltage. By analysing SVM switching patterns and matrix converter zero vectors replaced by rotating to reduce leakage current and increase motor life . The matrix converter based on space vector modulation offers better performance compared to a traditional matrix converter . The induction motor based on a matrix converter allows better control of torque, flux ripple and low reactive power delivered to the grid at unity power factor .

With conventional SVPWM for the rectifier stage, the output is the result of mains input voltages, with this PWM,

______________

Murikipudi Nagaraju, G Durga Sukumar and M Ravindrababu/Journal of Engineering Science and Technology Review 15 (5) (2022) 145 - 152

146

the virtual intermediate circuit shows more fluctuations. However, if the SVPWM for the rectifier stage is changed, the utilization of the DC link increases and the fluctuation of the DC link voltage also decreases. In this work, the modified SVPWM for the rectifier stage is implemented and compared to the ANFIS-based SVPWM for the rectifier stage. The THD of the output current and mains voltages is reduced in ANFIS- based SVPWM.

The paper is structured as follows: Section II explains IMC’s modified SVPWM at the rectifier stage and SVPWM for the inverter stage. The implementation of ANFIS-based SVPWM is described in Section III. In section IV, the simulation results are evaluated. Conclusions are presented in Section V.

2. Control Of An Indirect Matrix Converter

The schematic diagram of an IMC is shown in Fig 1 and has two conversion levels, one is the rectifier and the other is an inverter levels.

A) Switching Of Rectifier Stage

The IMC rectifier stage is a bidirectional power flow current source rectifier and the block diagram is shown in Figure 2. Fig 2. Rectifier stage of an Indirect matrix converter The rectifier has six bidirectional switches represented from Nap to Ncn as shown in Fig 2. The device with the suffix p indicates connection to the positive pole when they are on, and the suffix n indicates the negative pole when they are on.

The suffix a, b and c indicates the connected phase. The three- phase AC input voltages that enter the rectifier are VR, VY, and

(1)

Where the maximum or peak value of the sinusoidal input voltage is represented by Vmax and the frequency is represented by ω. The rectifier stage of IMC is controlled by SVM. The hexagon of the space vector is divided into six sectors, the duration of each sector is 600 and is shown in Figure 3.

Fig 3. Space vector diagram with different sectors

Process Of Space Vector Modulation (Svm):

1. Three phase voltages are converted into two axis – α and β components.

2. Calculate Vref And Θin From Vα And Vβ

3. The location of Vref in space vector Hexagon is identified with the help of θin and the modulation index considered as unity.

4. The Switching times Tp and Tn are calculated and there active vector are responsible to produce the required current in the sector.

5. Switching time of active vectors are calculated using

(3)

Where Ts is sampling time. 6. Sector and active voltage vector with variation of

Shown In Table 1 And The Turn-On Time Of Each

switch in each sector is given Table.2.

147

Table 1. Active Voltage Vectors of modified SVPWM at

Vry

Table 2. Switching times of modified SVPWM at rectifier

B) Switching Of Inverter Stagey:

At the inverter side also SVM method is used. Space vector hexogen diagram and six active vectors V1 to V6 and two Zero vectors V0 and V7 are shown Fig 4. The voltage-time balance method is used to determine the switching times T1 and T2. In Fig 5, the operational switching times are shown along with active vectors for Sector-1.

(4)

Where the reference voltage is represented as Vref, the operational switching time of V1 is T1, T2 is the operational time of V2 and T0 is the operational time of zero vectors (V0

(7)

Where the virtual output voltage at the rectifier level is

Represented As Vdc

The operational switching times of the IMC inverter level are a combination of the switching times of rectifier and conventional inverter operation.

(8)

The operational switching sequence of IMC inverter level in sector-1 is shown in Fig 5. Fig. 5. Switching sequence of IMC inverter level of sector-1

I. Anfis Based Svpwm For Rectifier Stage:

The ANFIS controller is trained by taking angle α, and α are input and output are switching timings T1 &T2 are outputs. The α, and α are rectifier input voltage angle and derivative of the an angle respectively.

A) Structure Of Adaptive Neuro-Fuzzy Controllers

Fig. 6. Structure of five-layer ANFIS for T1 Switching time Fig. 7. Structure of five-layer ANFIS for T2 Switching time The structure of five-layer ANFIS for switching time T1 and T2 is shown in fig. 3 and 4.

Layer 1: Let Z′ j be the response of jth node in first layer and input is αj of jth node of the ANFIS, j = 1, 2, …, q, let a node function N be associated with each node.

(9)

Here, N1, N2, …, Nq are the node functions, which are same as the regular fuzzy system membership functions and q is the number of nodes for each input. The Gaussian shieled membership function is used.

Layer 2: The response of each node in layer 2 is the product of all input signals. Each node response represents the trigger strength of a rule.

(10)

Layer 3: The normalized triggering strengths are determining in this Layer.

(11)

Layer 4: It executes Sugeno-type inference system, i.H. the

Linear Input Variables Of Anfis, Α1, Α2,……,Αq And

constant term, d1, d2, …, dq. The weighted response sum of an intermediate is the node’s response.

Where Q1, Q2, …, Qq And D1, D2, …, Dq, Are

consequent parameters in this layer. Layer 5: This layer response is similar to the defuzzification processor of a fuzzy system using weighted average

Method. It Generates The Output By Summing Its

input signals.

This Output

is the T1 for this example.

B) Learning Algorithm

The ANFIS controller is initially taken as a fuzzy model and tuned using a backpropagation least squares combinatorial algorithm. In each epoch the difference between an actual response and a required response is measured, it is an error.

The error size is reduced. The training process ends when either the error rate or the specified number of epochs is reached.

Simulation Results

When the changes of SVPWM for rectifier stage is changed the virtual DC voltage magnitude variations are reduced and distortion in DC voltage is reduce. Fig. 8 shows the DC virtual link voltage with the conventional SVPWM. The magnitude is varied from 400 V to 740 V and have distortions. Fig.9 and 10 show the DC virtual link voltage waveform of changed SVPWM for rectifier stage and ANFIS SVPWM for rectifier stage respectively. The voltage magnitude is varied from 640V to 740V and waveform is smooth.

Fig. 8. Virtual DC link voltage waveform with conventional SVPWM Fig. 9. Virtual DC link voltage with modified SVPWM at rectifier stage Fig. 10. Virtual DC link voltage waveform with ANFIS SVPWM

Fig. 12. Fuzzy Rules Of Switching Time T2

Fig. 11 and 12 show the funny rules of switching times T1 &T2 in ANFIS SVPWM. 13, 14 and 15 show the supply current waveforms in

Svpwm

respectively, the magnitude is varied from 30 A to -30 A peak to peak. The supply side current waveform has more

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)

0.150

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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