Dc Microgrid Control Matlab

03 October 2026

______________________________________________________________________________________________________________ Adaptive Neural Network-Based Control of a Hybrid AC/DC Microgrid / Nadjwa, C., Adel, M., Sulligoi, G.,

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Adaptive Neural Network-Based Control of a Hybrid AC/DC Microgrid

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This version is available at: 11368/2885747 since: 2018-09-04T08:57:06Z This is the peer reviewed (post-print) version of the following article:

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Abstract — In this paper, the behavior of a grid-connected hybrid AC/DC Microgrid has been investigated. Different Renewable Energy Sources – photovoltaics modules and a wind turbine generator - have been considered together with a Solid Oxide Fuel Cell and a Battery Energy Storage System. The main contribute of this work is the design and the validation of an innovative online-trained artificial neural network based control system for a hybrid microgrid. Adaptive Neural Networks are used to track the Maximum Power Point of renewable energy generators and to control the power exchanged between the Front-End Converter and the electrical grid. Moreover, a fuzzy logic based Power Management System is proposed in order to minimize the energy purchased from the electrical grid. The operation of the hybrid microgrid has been tested in the

Operating

conditions. The obtained results demonstrate the effectiveness, the high robustness and the self-adaptation ability of the proposed control system.

Index Terms — Adaptive interaction, fuel cells, microgrid, neural networks, photovoltaics, predictive control, wind energy, battery energy storage system.

Sofc Solid Oxide Fuel Cell

SN-RBFN Single Neuron Radial Basis Function Network

I. Introduction

OWADAYS, the wide diffusion of distributed RES presents a new scenario for the regulation of distribution networks and the availability of new technologies for storage systems encourages their use in power systems . In general, a hybrid AC/DC MG integrates different Distributed Generators (e.g.

solar power sources, wind power generators, cogenerators, etc.), a energy storage system and a number of AC and DC loads. A FEC can interface the MG with the electric grid and can operate either in a grid-connected or islanded mode. The use of a PMS is crucial to optimize the power flow through the different components of the MG and the exchange of energy with the electric grid. Moreover, since the power produced by RESs depends on the climatic conditions, MPPT algorithms are needed in order to harvest the maximum available energy.

The intermittent nature of RESs with the time-varying loads demand make the use of advanced control structures fundamental in order to make the operation of the MG reliable, economic, and secure under different operating conditions. The MG must also guarantee a high quality power supply to both local loads and electrical grid.

Many works have focused on hybrid microgrids and have proposed a number of control schemes for different mode of operations -. A multiagent-based energy management system to optimizes the economic operation of a MG is presented in . A reactive power sharing algorithm in hierarchical droop control is developed in . A novel coordinated voltage control scheme with islanding capability for a MG is proposed in . For highly nonlinear and complex AC/DC MGs, control schemes based on artificial intelligence techniques such as Fuzzy Logic (FL), Neural Network (NN), and evolutionary algorithms are gaining widespread interest.

Intelligent controllers are very promising because they can

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adapt to uncertainties and they can be used also when the model of the system to be controlled is not available. Recently, the NNs with the learning capability are widely applied for the control of complex power systems. In , a back-propagation NN is applied for the real-time estimation of the wind speed. A novel discrete-time NN controller for the control of DC distribution system is designed in . In ,

A Rbfn And An Improved Enn Are Proposed As Mppt

controllers for different types of RES. A RBFN with an ENN have been also analyzed in for the wind speed prediction in a wind farm.

The different NNs based techniques proposed in the literature can be classified, according to the training algorithm, into two categories : offline and online trained NN.

Offline learning of a neuro-controller is usually accomplished using a training dataset coming from the system model or from experimental data. When the controlled system is too complex to be modeled and/or experimental datasets are not available, it is more adequate to use online trained NNs that respond dynamically to the system uncertainties resulting from nonlinearities, parameters changing and exterior perturbations.

In this paper, a grid-connected hybrid MG which consist of a PV source, a WT generator, a SOFC, a BESS and two equivalent DC and AC loads is studied. A PMS based on FL is proposed to supervise the power flow in the MG. Online- trained NNs based MPPT for the RESs in addition to ADALINE based linear controllers for both SOFC stack and BESS are introduced. Moreover, a simplified deadbeat based predictive control scheme is applied for the WEGS. Further, a VF-DPC strategy for the bidirectional FEC is adopted. A FFNN is proposed for the regulation of the DC-bus voltage.

Two ENNs based controllers are adopted to ensure the control of the bidirectional flow of the active power as well as the compensation of the AC load reactive power. An AI based algorithm is applied for the online weights adaptation of the proposed FFNN and ENNs. The investigated MG is simulated in the Matlab/Simulink environment. Then, the effectiveness of the proposed controllers is verified for different test cases.

The paper is organized as follows: the next Section in on the configuration and the modeling of the MG, Section III deals with the control scheme, the simulation results are given in Section IV, and Section V is on Conclusions and Perspectives.

Ii. System Configuration And Modeling

As shown in Fig.1, the investigated MG is connected to the electric grid though a FEC, while the DC-Bus is fed by four energy sources: a 21kWp PV generator, a 10kW WEGS, a 10kW SOFC, and a 20Ah Lithium-Ion BESS. A bidirectional buck-boost converter interfaces the BESS with the DC link.

Whereas, boost converters are used for coupling the PV source and SOFC with the DC-bus. A filter capacitor Cdc is connected to the DC-bus to minimise the DC voltage ripples. Moreover, the MG includes also AC and DC loads. The circuit model of the converters used in the MG is shown in Fig.2.

Fig. 1. Hybrid Microgrid configuration. 2. Circuit model of the considered converters.

A. Modeling The Pv Generator

The equivalent circuit used to model a PV module is shown in Fig.3 and is represented by the following equation :

𝑛𝑠+ 𝐼𝑃𝑉𝑅𝑆) −1] (1)

Where IPV and VPV are the PV module’s output current and voltage, RS is the series resistance, IPH is the photocurrent, IS is the saturation current, q is the electron charge, K is the Boltzman constant, A is the diode ideality factor, T is the temperature, while nP and nS are the numbers of series and parallel-connected solar cells.

Fig. 3. Single diode equivalent circuit of PV module.

B. Modeling The Wind Energy Generation System

The WEGS consists of a WT coupled to a PMSG, where an AC-DC Rectifier is used for the interfacing with the DC-bus. The mathematical model of the PMSG implemented in the synchronous rotating frame dq is given as [15, 16]:

(2)

Where Vsd, Vsq, Isd and Isq are the d and q-axis components of the stator voltages and currents; Lsd and Lsd are the d and q- axis inductance, ωe is the generator speed defined as : 𝜔𝑒= 𝑝. 𝜔𝑡 such that p is the number of pole pairs and ωt is the angular velocity of WT, ϕ is the permanent magnet flux, and Rs is the stator resistance. The electromagnetic torque Te

(3)

Considering that for nonsalient PMSG Lsd = Lsq=Ls, Eq.3

(4)

Since the magnetic flux is constant, the electromagnetic torque and the q-axis stator current component Isq are directly proportional. Whereas, the reactive power may be controlled depending on the d-axis current component Isd. The motion

(5)

Where F is the viscous friction factor, J is the moment of inertia. The aerodynamic torque of WT is defined as the ratio between the aerodynamic power Pt and the WT angular

(6)

Where ρ, VW, R, CP are the air density, the wind speed, the radius of turbine blade and the power coefficient, respectively.

The Dynamic Model Adopted For The Sofc Is Based

on the relationship between the FC output voltage Vfc and the partial pressures of hydrogen, oxygen, and water PH2, PO2, PH2O, respectively. The SOFC terminal voltage Vfc is determined using the Nernst’s equation and Ohm’s law as

(7)

Where N0 is the number of series connected cells, E0 is the free reaction voltage, R is the universal gas constant, T is the temperature, F is the Faraday’s constant, Ifc is the FC output current, and r is the ohmic resistance.

D. Modeling The Battery Energy Storage System

The Matlab/Simulink module used for the BESS simulation consists of a controlled voltage source series-connected with an internal resistance . The battery output voltage and the

(9)

Where Vb and Ib are the BESS terminal voltage and current, E0 is the BESS no-load voltage, Rin is the internal resistance, K is the polarization voltage, Q is the BESS capacity, A is the exponential zone amplitude, and B is the inverse exponential zone time constant. In this paper, a 20 Ah Lithium-Ion battery bank is used.

Iii. Control Strucure Of The Hybrid Microgrid

The main tasks of the control system of a hybrid MG are: to minimize the amount of power purchased from the electric grid, to make the RESs based generators operate at their MPPs and to ensure a high-quality power supply to local loads and to electric grid. Being motivated by the benefits of learning ability, robustness against uncertainties and adaptability, a number of intelligent NN controllers have been designed and used instead of the conventional controllers, in order to satisfy the above requirements.

A. Mppt Control Of Pv Generator

The PV source exhibits a nonlinear behavior depending upon the variable operating conditions, and the maximum output power is generated at an unique operating point.

Several Mppt Algorithms Heva Been Proposed In The

litherature to extract the maximum energy from PV modules. One of them is the well-known incremental conductance

(Inccond) Algorithm . This Method Consists In The

regulation of the PV voltage according to the MPP voltage reference. At each iteration, the PV voltage reference is adjusted based on the comparison of the incremental conductance (dI/dV) of the PV source with the negative instantaneous conductance (-I/V). The position of the operating point with respect to the MPP on the PV power

(10)

The IncCond method is simple and easy to implement. But, the convergence speed and the steady state power oscillations depend mainly on the size of the step change in the reference voltage. In this paper, a SN-RBFN based controller is applied to overcome the nonlinear issues arising with such MPPTs.

The aim is to enhance the dynamic performance and the tracking accuracy of the IncCond algorithm. The MPP of the studied PV generator is tracked through a DC-DC boost converter. As shown in Fig.4a, a PI voltage controller generates the gate signal of the power switch, while the SN- RBFN based controller generates the PV voltage reference.

The proposed MPPT regulator is based on the principle of the IncCond technique. The learning ability of the SN-RBFN tracker ensures the self-adaptation to any change of operating conditions.The adopted SN-RBFN contains a single hidden

(11)

Where c is the central point of the Gaussian function f(x), b is the width value of f(x), and x=[x1,x2,x3] is the input vector

(12)

Where a0 and a1 are the bias and the weight of the SN-RBFN respectively, and Vpvref is the PV voltage reference at the output of MPPT controller. The SN-RBFN’s inputs are: the instantaneous conductance (I/V), the incremental conductance (ΔI/ΔV), and the reference voltage error (ΔVpvref(k)=Vpvref(k)- Vpvref(k-1)). In this paper, a supervised learning rule based gradient descent method is adopted for the online update of the SN-RBFN parameters. The objective function

(13)

Where ey is the output error, and yd is the desired output voltage. The goal of the online learning process of the SN-

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RBFN is to minimize the performance index function σ(k). Thus, the adaptation laws of the SN-RBFN gains are given according to the gradient descent method as follows:

(14)

𝑐𝑗1(𝑘+ 1) = 𝑐𝑗1(𝑘) + ∆𝑐𝑗1(𝑘) + 𝛼(𝑐𝑗1(𝑘) −𝑐𝑗1(𝑘−1))

(16)

Where α is the momentum factor, k is the k-th iteration, i=0,1, and j=1,2,3. According to the BP algorithm based on the gradient descent rule, the SN-RBFN parameters ai, cj1 and b are adjusted by computing the gradient of the error function σ(k) with respect to the SN-RBFN coefficients, so that σ(k) is eliminated. The derivative of the error function σ(k) against each SN-RBFN’s gain is evaluated by propagating the error term back through the NN. Thus, the SN-RBFN parameters

(20)

Where μ denotes the learning rate. We define the variable Gin(k)= (I(k)/V(k))+(ΔI(k)/ΔV(k)) that has to be equal to zero at the MPP. Since the desired output of SN-RBFN based MPPT controller (yd) is unknown, the error eG(k)=(0 - Gin(k)) is used instead of ey(k) in Eq.17-20. Thus, the iterative learning algorithm of the SN-RBFN based MPPT controller is

𝑎0(𝑘+ 1) = 𝑎0(𝑘) + 𝜇𝐺𝑖𝑛(𝑘) + 𝛼(𝑎0(𝑘) −𝑎0(𝑘−1))

𝑎1(𝑘+ 1) = 𝑎1(𝑘) + 𝜇𝐺𝑖𝑛(𝑘)𝑓(𝑥) + 𝛼(𝑎1(𝑘) −𝑎1(𝑘−1))

(21)

Once the term Gin(k) converges to zero, the SN-RBFN stabilizes at the reached operating power point that correspond to the MPP of PV source at the given climatic condition.

B. Predictive Torque Control For The Pmsg

The block diagram of the control scheme of the AC-DC converter used for the PMSG is depicted in Fig.4.b. A DPCM based on the Deadbeat approach is applied to drive the AC-DC rectifier in order to improve the dynamic performance of the classical direct torque control scheme of PMSG. Besides, an ADALINE based MPPT controller is proposed for the tight regulation of the rotating speed of WT.

The Main Tasks Of The Pmsg Control System Are To

instantaneously follow the MPP of WT generator, to track the electromagnetic torque reference, and to maintain the direct stator current component close to zero.

The basic idea of the adopted DPCM is to compute, at each sampling period, and apply the optimal stator voltage vector that ensures the minimization, at the next sampling instant, of the tracking errors between the predicted and the reference values of the controlled variables . Using the calculated voltage vector, the proper switching pulses for rectifier are generated through the Space-Vector Modulator (SVM).

Discrete Time Model

The model of the PMSG developed in the rotating dq frame is used to predict the future values of the controlled variabes, which are the electromagnetic torque Te and the direct stator current Isd. Then, the reference stator voltage components Vsd and Vsq that should be generated during one sampling period are calculated in function of the tracking errors of the regulated quantities Te and Isd. The stator flux magnitude of PMSG is indirectly controlled using the d-axis current component.

Thus, the continuous-time model represented by Eq.2 is discretized using the Euler forward method, such that the

(22)

Where TS is the sampling period, k and k+1 are the actual and future sampling instants, respectively. The future values of d-axis and q-axis components of stator current are

(23)

The linear relationship between the q-axis stator current and

(25)

According to deadbeat principle , the predictive control target here is to get, at the next sampling instant (k+1), both predicted values of the generator torque and d-axis current component ideally equal to their respective references:

(27)

Since the d-axis current reference Isd* is constantly zero, it can be assumed that the present setpoint of d-axis current is

(28)

On the other hand, as shown in Fig 4.b, the external speed control loop provides the actual torque set point Te*(k). Assuming that the tracking error of the rotational speed is constant during two successive sampling period, the future reference value of Te at the instant (k+1) is estimated using the linear Lagrange extrapolation as presented in Fig4.c.

Thus, the future torque reference is calculated as :

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Substituting Eq.29 and Eq.28 in Eq.27, the d-axis and q-axis components of the required stator voltage vector are given as:

(30)

Where ΔTe(k) and ΔIsd(k) are the instantaneous tracking errors of the torque and the d-axis current, respectively. While, dTe*(k) is the current variation in the torque reference:

Adaline Based Speed Controller

Traditionally, a Proportional Integral (PI) controller is used to regulate the rotating speed of WT in order to extract the maximum wind energy. However, a PI controller with fixed gains for a time-varying WEGS, which is subject to random wind speed and parameters variations, can yield to poor dynamic performance. To overcome this drawback, an

Adaptive Adaline (Adaptive Linear Neuron) Network

based controller is adopted in this paper, to control the rotational speed by producing the reference for the electromagnetic torque. The ADALINE based speed controller consists of a single neuron with linear activation function,

(32)

Where wi is the ith weight coefficient (i=1,2,3), xi is the ith input signal and n is the number of inputs. Xω and Wω are the inputs and weights vectors, respectively. The ADALINE output is the electromagnetic torque reference Te*(k), while the inputs are the measured speed at the instant k ωe(k), the actual speed error eω(k)=ωe*(k)-ωe(k), and the previous error eω(k-1).

Such that ωe*(k) is the speed reference. The Widrow–Hoff Least Mean Square (LMS) learning algorithm is used for the online update of the ADALINE’s weights. Where, the goal of the self-learning process of the ADALINE based speed controller is to minimize the mean square of the instantaneous error eω(k). Using the transformation 𝑋′ = 0.5 𝑠𝑔𝑛(𝑋𝜔) +

(33)

Where Wω(k+1) and Wω(k) are the weight vectors at the next and present iteration, k+1 and k, respectively. 𝜆 is a correction

2 Is The Squared Norm Of

the input vector 𝑋′. The learning coefficient αω which has a value in the interval [0.1,1] affect considerably the speed of convergence to the optimal weighting factors of the

Adaline’S Weights Using The Normalized Lms Law Of

Equ.33, ensures the self-adaptation of the adopted speed controller to any change of working conditions unlike the PI regulator with fixed gains .

As Depicted In Fig.4.D, An Adaline Based Power

controller with two adaptive weights regulates the SOFC’s output power to follow the power reference provided by the central power supervisor. The inputs of the ADALINE controller are the power error (efc(k) =Pfc (k)-P*fc(k)), and the change of error (defc(k)=efc(k)-efc(k-1)). Such that, Pfc*(k) and Pfc(k) are the power reference and the output power generated by the SOFC stack, respectively. Whereas, the output is the duty cycle Dfc(k) that controls the commutation time of the switching device of the boost converter. The control error Efc(k) used for the online learning process of the SOFC’s power controller is defined in function of the sliding surface

(34)

Where 𝜆1 is a positive constant. According to the SMC principle , the control goal here is to maintain the trajectory of the state variable, which is the SOFC’s output power, on the sliding surface Sfc(k)=0 for the whole time. With reference to the LMS algorithm , the weight vector (Wfc) of the SOFC’s controller is updated at each iteration of the

(35)

Where Xfc is the input vector and α2 is the learning rate of the SOFC’s controller. In this case, the connective weights are adapted in such way that the sliding surface Sfc(k) tend to zero, so that the power tracking error will be eliminated.

Fig. 4. a) SNRBN based PV controller, b) control scheme of WEGS, c) Estimation of future value of torque , d) SOFC’s controller, and e) BESS’s controller.

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

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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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