Standalone Pv System Matlab

1

Abstract - Standalone PV battery systems have great potential to power the one billion people worldwide who lack access to electricity. Due to remoteness and poverty, durable and inexpensive systems are required for a broad range of applications. However, today’s PV battery systems do not yet fully meet this requirement. Especially batteries still prove to be a hindrance, as they represent the most expensive and fastest- aging component in a PV battery system. This work aims to address this by prolonging battery life. For this purpose, a forecast-based charging strategy was developed. As lithium-ion batteries age slower in a low state of charge, the goal of the operation strategy is to only charge the battery as much as needed. The impact of the proposed charging strategy is examined in a case study using one year of historical data of 14 standalone systems in Nigeria. It was found that the proposed operation strategy could reduce the average battery state of charge by around 20% without causing power outages for the mini-grids. This would significantly extend the life of the battery and ultimately lead to a more durable and cheaper operation of standalone PV battery systems.

Index Terms

Battery storage, Photovoltaic, Operation strategy, Off-grid, Rural

1. Introduction

In Sub-Saharan Africa, 548 million people in 2018 had no access to electricity . The vast majority of them live in rural areas . It is often impossible or economically unfeasible to connect these areas to the national energy grid . Additionally, long-distance grid extensions are often unreliable, as 59% of rural households in Nigeria reported daily blackouts in 2016 . To overcome the stated deficits, the World Bank identified that mini-grid solutions are essential and wants to connect 490 million people worldwide to a total of 210,000 mini-grids by 2030 . For comparison, in 2019 47 million people worldwide were connected to 19,000, mini-grids .

Half of the planned mini-grids are announced to be built in Africa . Historically, diesel generators have been a common technology for standalone energy systems in sub-Saharan Africa . A shift towards renewable solutions could be achieved through continuous cost reduction of batteries, photovoltaic (PV) panels, and PV inverters . In addition, PV battery systems are more reliable, reduce air pollution, and are less noisy when compared to diesel generators [2, 4, 5].

Batteries contribute to a large part of the lifetime costs of PV battery systems [6, 7]. In addition to the already high initial cost, most of the batteries in this application have a comparatively short life of 5-10 years and therefore need to be replaced more frequently than PV panels or inverters, which nowadays can last up to 30 years. But due to difficult external conditions like high temperatures, sand, and torrential rain in Sub-Saharan Africa, a lifetime of 20 years is more realistic .

When replacing, not only the cost of the battery must be considered, but also the complicated procurement and installation in rural areas in Sub-Saharan Africa. Hence, it is desirable to maximize battery life.

For autonomous mini-grids in Sub-Saharan Africa, lithium-ion (Li-ion) batteries have overtaken lead-acid batteries and become the main battery technology . In contrast to lead-acid batteries, Li-ion batteries should be operated at a low state of charge (SOC) to decelerate aging processes. Nevertheless, most solar mini-grids in Sub-Saharan Africa charge their battery whenever there is surplus energy available from solar generation. This can lead to batteries being operated in high SOCs for most of the time, which again accelerates battery aging.

1.1 Objective

This paper proposes a forecast-based operation strategy to extend the life of Li-ion batteries in standalone PV battery systems. The objective of the operation strategy is to only charge the battery as much as needed and thereby keep the battery in lower SOC. This dynamic operation is enabled by day-ahead forecasts of PV generation and consumption. To ensure that errors in the prediction don’t lead to empty batteries, safeguards are introduced.

Pv Battery Systems In Sub-Saharan Africa

Jonathan Schulte a,b,d*, Jan Figgener a,b,c*, Philipp Woerner a,b, Hendrik Broering d, Dirk Uwe Sauer a,b,c c Juelich Aachen Research Alliance, JARA-Energy, Germany

2

This work has access to one year of historical data from 14 standalone battery systems in Sub-Saharan Africa, which are used to train a forecast model as illustrated in Fig. 1. Based on this, the operation of the systems is simulated to investigate the impact of the proposed operational strategy on the 14 energy systems.

Fig. 1. Overview of input data, ideation, and methodology This paper solely focuses on the reduction of the SOC to increase battery life. Other battery aging factors like temperature, charging rate, depth of discharge or cycle frequency are not optimized.

1.2 Literature Review

Forecast-based charging strategies are established in other PV battery applications. Especially for grid-connected PV battery systems and microgrids, they have been researched for some time and are also used in commercial applications. The following overview of existing literature on forecast-based strategies in these applications is supported by a comprehensive list in Table 1.

For grid-connected PV battery systems, forecast-based charging strategies are mainly used to reduce the utility costs and increase the battery lifetime . However, there are also strategies that neglect battery aging and only minimize utility costs [13, 14]. The latter is of no further interest for this work.

The former has been shown to prolong battery lifetime by 2-5 years on general lifetimes of 5-10 years . The strategies aim to only charge as much energy into the battery as needed . Thereby the SOC is kept relatively low, which in turn extends the calendar life of a Li-ion battery. Since full battery discharges are not a critical issue in grid-connected applications, the forecasts-based strategies here are designed in such a way that they can regularly lead to fully discharged batteries [10, 11].

In micro-grids, forecast-based charging strategies are used to optimize the interaction of PV, battery, diesel genset, and optionally wind and grid . The objective function is to optimize the operation costs by reducing the costs of fuel, genset wear, and battery wear. Most available research focuses on lead-acid batteries, which have different aging mechanisms compared to Li-ion batteries.

The forecast-based charging strategy proposed in this work is mainly inspired by the approaches for grid-tied applications in . In contrast to grid-tied systems, a full battery discharge leads to a power outage in standalone systems and consequently needs to be avoided. The proposed operation strategy addresses this risk by introducing safeguards.

1.3 Novelty And Contribution

The selected references show potential for battery aging optimization in PV battery systems. However, all references focus on either grid-connected systems with a Li-ion battery or standalone systems with a lead-acid battery.

The novelty of this paper is to propose a battery life-extending operation strategy for standalone systems with Li-ion batteries. Unlike most other work on operating strategies to extend battery life, this work has access to historical data from a large number of economically operated systems.

Table 1

Overview of existing literature on forecast-based charging strategies

Lifetime

M. Alramlawi, A.

Operation Strategies

G. Angenendt, S.

Forecast Based Operating Strategies

G. Angenendt, S.

Micro-Grid Applications

D. Tran, A. M.

To Microgrid Operation Optimization

A, Parisio, E. Rikos, L.

L. Moretti, S. Polimeni,

L. Meraldi, P. Raboni, S.

Model

R. Dufo-López, L. A. Fernández Jiménez, I. J. Ramírez-Rosado, J. S.

Artal-Sevil, J. A. Domínguez-Navarro, J.

Pv/Battery Hybrid System

H. Mahmood, D.

Aging

B. Lunz, H. Walz, D. U.

2. Methodology

This paper proposes a forecast-based operation strategy to increase the lifetime of Li-ion batteries in standalone PV battery systems. The goal of the proposed strategy is to only charge the battery as much as needed while minimizing the risk of an empty battery.

This paper has access to one year of historical data for 14 standalone PV battery systems in Sub-Saharan Africa monitored by the company AMMP. First, this data is examined to understand the historical operation and potential for optimization. Later, the historical data is used to simulate a scenario in which the systems are operated with the new proposed strategy.

Figure 2 gives an overview about the structure of this chapter, which starts with a brief description of the systems and the data set. Afterwards, the historical operation is analyzed with a focus on the potential for optimization. Further, the methods used to create PV generation and consumption forecasts are presented.

Finally, the idea and algorithm of the proposed operation strategy are outlined.

2.1 Data Set

This section describes the application and topology of the PV battery system considered in this work. It also explains how the historical time series data was collected.

Overview

All considered systems supply shops in a local market in Nigeria. This market is not connected to the national power grid. Before using PV battery systems, the market was powered by diesel generators.

Dc

All considered systems share a similar typology, which is

In

Fig. 3. The PV panels are DC coupled. Furthermore, lithium iron phosphate (LFP) batteries are used.

Fig. 3. System Topology And Measurement Point

At each site, two DC meters and one AC meter are installed, as illustrated in Fig. 3. The DC meters are integrated into the respective DC-DC converter to monitor the battery and the PV panels. For the AC meter at the load side, an external energy meter is used. Each meter measures voltage and current. Based on this, other quantities such as power, energy, and battery SOC are derived locally. Further, a temperature sensor is installed to monitor the battery temperature. Each device transmits its data to a controller device via the MODBUS protocol. From here, the data is transmitted either by a cellular or ethernet connection to a cloud database.

In this work, the following data is used in a 1-hour resolution:

Historical Operation

This section intends to give insights into the historical system operation to understand the further methodology. At first, a single system is analyzed in detail. This system is referenced as system 1. Afterwards, the other systems are included in the analysis.

The operation of system 1 is visualized for an exemplary week in Fig. 4. The upper part of the graph shows that the consumption (blue dotted line) is very similar on all days except Sunday. This is because the market is closed on Sundays.

Moreover, there is no consumption at night because the stores are closed, and electricity consumption at night is even prohibited. The figure also displays the PV generation as a yellow dotted line. In the morning, PV generation often spikes before falling back to match consumption. To understand this behavior, it is helpful to look at the SOC curve. Here, it can be observed that the battery is fully charged every day already in the morning. As the system is not connected to a grid, the surplus PV power cannot be used to charge the battery and needs to be limited to the consumption demand. Therefore, the system generates a lot less energy than theoretically possible.

In the evening, the available PV power falls below consumption demand. Hence, the batteries are used to power the loads.

5

Fig. 4. Operation of system 1 from 16th November 2019 to 23rd

November 2019

Figures 5 to 7 show the distribution of historical data for all recorded days of the given system to give a broader impression of the typical system operation. The data is presented as fan charts in such a way that each quarter hour of a day is assigned by the distribution of all values over the year in that quarter hour. Fig. 5 visualizes the consumption demand in which the median describes a typical commercial load profile. Figures 6 and 7 show the PV generation and battery SOC, respectively.

Typically, at 5:00 AM, the PV panels start to generate electricity (Fig. 6). Because no consumption is required at that time, the energy is used to charge the battery. Therefore, the battery SOC (Fig. 7) rises between 5:00 AM and 7:00 AM.

Between 7:00 AM and 8:00 AM in the morning, the SOC rises to 100%, and thus, the battery is fully charged.

Fig. 7. Fan Chart Of Battery Soc (System 1)

As soon as the battery is fully charged, the PV power (Fig. 6) is actively limited, as the PV power can only be used to meet the consumption demand. From here on, the PV generation follows the consumption curve for most of the day. Around 4 PM, the battery SOC starts to decline again. At this time, the PV power is no longer sufficient to meet the consumption demand. The battery steps in to supply the missing power. The battery reaches its minimum SOC around 5 PM and remains at the same level until the next morning.

The figures show that the battery is barely seeing any significant discharges and is kept fully charged for many hours of the day. Furthermore, the potential peak PV power of 9.75 kWp is not even closely reached on any day, as the fully charged battery leads to active curtailment of the PV power.

Table 3 shows various key performance indicators (KPIs) for each of the 14 systems. Each indicator is calculated for the whole period of 2019. The PV generation and consumption are close to each other because, with the exception of losses, only as much energy can be generated as is consumed locally in an off-grid application. The average system efficiency is calculated by dividing the consumed energy by the generated energy. The main reasons for losses in the systems are the efficiencies of inverter and battery as well as cable losses. The

6

75% SOC confidence interval describes the window in which the 75% of the SOC values were located. This interval is formed around the median value. This KPI shows that the batteries of all systems are kept in a high or full SOC for most of the time.

The direct consumption rate describes the proportion of the consumed electricity that came directly from the solar system without taking the detour via the battery. The capacity factor represents the ratio of the average PV power over the whole year and the rated peak power. A typical capacity factor for a PV system in Nigeria is 16% to 20% . The values for the examined systems tend to be much lower, as the consumption of the systems is relatively low and the PV power is often actively curtailed as soon as the battery is fully charged. Finally, the total downtime due to an empty battery describes how often the battery of each system was fully discharged while there was insufficient PV power to power the loads. This finally leads to downtimes. It can be observed that downtimes tend to be more frequent for systems with high consumption.

With only one cycle per day and the batteries not being discharge below 60% - 80% on most day, the energy throughput of the battery is rather low. Further, the maximum charging / discharging power rates of 2 kW are rather low at 10 kWh battery capacity. While the rated maximal charge / discharge rate of the LFP batteries is around 1 C, the maxima in the operation of the analyzed systems is around 0.2 C. This leads to the assumption, that cyclic aging (influenced by charging frequency, charging rate, depth of discharge) has a minor role compared to calendar aging (mainly influenced by SOC and Temperature).

Table 3

Operational key indicators for each system in 2019

2.2 Forecasts

The proposed operation strategy is based on forecasts. This chapter describes the algorithms used in this work to forecast both the day-ahead generation and consumption. Both forecasts are calculated in a resolution of 1h with a 24h time horizon.

Consumption Forecast

For the consumption forecast, a combination of a daily clustering technique and the autoregressive integrated moving average (ARIMA), as proposed in , is chosen. In contrast to , a two-level clustering method is used. At first, the weekdays are clustered based on the total energy consumption using the k-means Algorithm . This typically led to one group of working days (Monday to Saturday) and one group for Sundays. The day for which the prediction is to be made is then associated with one of the clusters based on its day of the week.

Finally, an ARIMA model is used to extrapolate the historical

7

operation of the days in the respective cluster to the forecast day. Holidays are not considered in this work, which can increase accuracy even further . It shall be noted that in

Contrast To , The Number Of Clusters K Is Not Set

automatically, but the optimal number of clusters is found as part of the algorithm using the silhouette method .

Generation Forecast

The goal of the generation forecast is to predict the theoretical PV generation power curve of the next day. Potential curtailments due to a fully charged battery are neglected. The basic idea of this forecast method is to use a horizontal irradiation forecast and convert it to a power forecast using a linear regression.

For the irradiation forecast, the publicly available historic downward short-wave radiation flux forecast from National Oceanic and Atmospheric Administration (NOAA) is used . Since NOAA provides the data in a spatial resolution of 0.25 by 0.25 degrees, the irradiation forecast can be used accordingly for the individual locations.

To perform the linear regression, a linear least square regression model (LSR) is trained using historic irradiation data from NOAA (independent variable) and historic PV power (dependent variable) as proposed in .

To take the orientation of the PV panels into account, both the historic irradiation data and the irradiation forecasts are projected to the surface normal of the PV panels with the help of the open-source tool pvlib python .

Real irradiation data from the sites for training the model or validating the data was not available. Comparisons between the prediction and the real feed-in power are presented in Fig. 18 and Fig. 19.

2.3 Proposed Operation Strategy

In this section, a forecast-based charging strategy for standalone PV battery systems with a Li-ion is proposed. Firstly, the general objective and functioning of the strategy is outlined.

Later, the exact algorithm of the proposed strategy is outlined.

Basic Idea Of Proposed Operation Strategy

The calendric aging of a Li-ion battery is accelerated by high SOCs and high ambient temperatures . The basic idea of the proposed algorithm is to keep the SOC as low as possible.

Meanwhile, the SOC shall always stay above a certain security threshold to prevent the battery from being fully discharged during an unpredicted event.

Fig. 8 illustrates the basic idea of the presented algorithm by comparing it to a conventional strategy. Two approaches are used to decrease the SOC. While in the conventional operation of a PV battery system the battery is directly charged in the morning, the proposed strategy actively decides to delay the charging period to later in the day (similarly proposed in ).

Hereby, the battery is kept longer at a low SOC. Additionally, an upper SOC cap is introduced to ensure that the battery is only charged to the maximum required SOC (similar to ).

Thereby, very high SOCs are avoided and the average SOC is decreased. The exact delay time and the exact SOC cap are dynamically calculated based on the forecasts. To prevent batteries from being fully discharged, two safety buffers have been built into the strategy. First, a conservative forecast is used instead of the mean forecast. Secondly, a buffer is kept free in the battery and is not used for the dynamic strategy.

Fig. 8. Basic principle of proposed operation strategy

Algorithm Of Proposed Operation Strategy

The proposed operation strategy requires three input parameters, which are outlined in Table 4. The adjustable

!$%$& Determines The Portion Of The

battery charge that shall not be considered for the dynamic operation strategy. The algorithm will operate the battery in such a way that the SOC should not fall below this threshold in regular operation. If the SOC should fall below this threshold due to unforeseen events, the algorithm will try to charge the battery with any surplus power until the SOC is above 𝑆𝑂𝐶!"#

!$%$&, The Operation Strategy

can be tuned to be more conservative or more dynamic. The impact of such amendments will be examined in Section III of

This

paper.

Battery

𝐸'(&& is required as input of the algorithm. Finally, η)*(+,- represents the energy efficiency from PV to battery and from battery to load. To reduce complexity, it is assumed that both are equal.

Efficiency (Assumed To Be Equal)

The algorithm defines three setpoints for the operation of the standalone system as outlined in Table 5. The exact value of each setpoint is dynamically calculated at each processing time

Are

correct.

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

Related Journal Articles & DOI Links

Selected peer-reviewed publications relevant to 12 Lead ECG Acquisition. Click the DOI to access the full paper (may require institutional access).

Why Choose Us?

Bangalore guidance for robotics, Spectre and autonomous systems projects.