Upfc Unified Power Flow Controller Matlab

Integration In Unit Commitment

Jia Lia, Feng Liua,∗, Zuyi Lib, Shengwei Meia, Guangyu Hec bRobert W. Galvin Center for Electricity Innovation at Illinois Institute of Technology,

Chicago, Il 60616 Usa

cSchool of Electronic Information and Electrical Engineering, Shanghai Jiao Tong

Abstract

Unified Power Flow Controller (UPFC) is recognized as the most powerful flexi- ble AC transmission systems (FACTS) device for power system operation. This paper addresses how UPFC explores the transmission flexibility and facilitates the integration of uncertain and volatile wind power generation. To this end, a comprehensive unit commitment (UC) model with UPFC and uncertain wind power generation is proposed. Then, some metrics are introduced to evaluate the impacts of UPFC on the reliability, security and economy of power sys- tem operation. Further, different dispatch strategies of UPFC are compared to provide helpful guidances on making full use of UPFC to hedge against uncer- tainties. In addition, facing the challenging mixed-integer non-linear non-convex problems, approximate models are proposed to provide a starting point to solve the problems efficiently. All these models are easy to adapt to other types of FACTS devices. Illustrative numerical results are provided.

Keywords:

UPFC, unit commitment, transmission flexibility, wind power,

I, J, K

Index of system buses.

S

Index of wind power generation scenarios.

T

Index of time periods.

N/N L/N G/N W

Set of all buses/load buses/thermal unit buses/wind farm buses.

S

Set of wind power generation scenarios.

T

Set of time periods.

Αls/Αw C

Price of load shedding/wind power curtailment.

I

Susceptance/conductance/ shunt conductance.

Ps

Probability of scenario s.

Ij

Limitation of active power transferred through the con- verters of UPFC.

I,T

Active/reactive load.

I

Maximum active/reactive power output of unit i.

I

Minimum active/reactive power output of unit i.

Ij

Capacity of line ij.

S,I,T

Active wind power generation forecast/scenarios.

S,I,T

Reactive load forecast/scenarios of wind farm.

Rt

Spinning reserve requirement.

Rdi/Rui

Ramp-down/ramp-up limit of unit i.

Sdi/Sui

Shutdown/startup ramp limit of unit i.

Ij

Thermal limitation of series/shunt converter.

V Max/V Min

Maximum/minimum voltage magnitude.

Xij

Reactance of line ij.

Ij

Re-dispatch limit of active/reactive power injection of UPFC.

I,T

Shutdown/startup cost of a thermal unit.

S,I,T

Fuel cost of a thermal unit in the second stage.

S,I,T

Active power generation of a thermal unit in the first/second stage.

S,I,T

Maximum available active power generation of a thermal unit in the first/second stage.

Pij/Ps,Ij

Branch power flow in the first/second stage.

S,Ij,T

Active power injection of UPFC in the first/ second stage.

S,I,T

Load shedding in the second stage.

S,I,T

Wind power curtailment in the second stage.

S,I,T

Reactive power generation of a thermal unit in the first/second stage.

S,Ij,T

Shunt reactive power injection of UPFC in the first/second stage.

S,Ij,T

Series reactive power injection of UPFC in the first/second stage.

S,Ij,T

Equivalent non-control reactive power injection of UPFC in the first/second stage.

S,I,T

Reactive load shedding of wind farm.

Ui,T

Thermal unit status.

Vi,T/Vs,I,T

Voltage magnitude in the first/second stage.

Θij,T/Θs,Ij,T

Voltage angle in the first/second stage.

1. Introduction

The uncertainty of wind power generation has posed new challenges to power systems. The inherent volatility of wind power generation may impact the security and economy of power system operation, causing voltage violation and congestion.

In order to deal with the increasing penetration of wind power generation, there is an urgent need to take full advantage of power system flexibility.

Generally, the flexibility of power system operation can be divided into three categories: generation side, transmission network and demand side. In genera- tion side and demand side, a lot of efforts have been devoted to addressing the

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uncertainty of wind power generation. Different kinds of methods have been ap- plied in unit commitment (UC) and economic dispatch to enhance generation- side flexibility, such as stochastic optimization [1, 2], chance-constrained opti- mization , robust optimization [4, 5], minimax regret . In order to improve the computational efficiency and tractability, a scenario tree approach and a scenario selection algorithm inspired by importance sampling [8, 9, 10, 11] have been applied to characterize the uncertainty of wind power generation with a few scenarios in stochastic UC problems. A practical adaptive robust UC solu- tion methodology has been proposed in , highlighting the scalability of the proposed formulation. In demand side, demand response, including price-based and incentive-based methods has been introduced to improve demand-side flex- ibility.

Although flexible AC transmission systems (FACTS) and high-voltage direct current (HVDC) provide transmission flexibility, few studies have been made to analyze their impacts on wind power integration in power system operation.

In terms of FACTS, a control scheme is proposed in to determine the op- timal steady-state settings of thyristor controlled series capacitor (TCSC) in order to improve the usage of the existing transmission network. A two-stage method based on regression analysis is applied using a collection of offline sim- ulations. A scenario-based optimal power flow (OPF) model is proposed in to minimize wind power spillage with TCSC. The decision making method is formulated as a two-stage stochastic programming model while the control of TCSC are considered in the second stage. It has been proved that a series com- pensation may reduce the wind power spillage, unserved load, and total active power losses of the network . In , nodal and angular sensitivities are used for coordinating phase shifting transformers (PSTs) to deal with contingencies and to increase wind power penetration. It has been shown that the coordina- tion in operation of these devices helps to bring the system into a secure state from an overload situation. The flexibility of HVDC lines and HVDC grid is exploited in security-constrained OPF frameworks so as to minimize the oper- ating cost under wind power uncertainty [16, 17]. In those papers, the problems are formulated as chance constrained optimization programs and scenario-based methodologies are applied, which offer a strong solution with a-priori constraint violation guarantees. It has been shown that HVDC lines can be used to handle the fluctuating in-feed from renewable energy sources . In , a stochas- tic multi-period OPF model is presented which consists of an offshore wind farm connected to the grid by a line-commutated converter HVDC link. The obtained results demonstrate that the availability of transmission network ca- pacity at the interface of AC/DC network is a key factor affecting the utilization of wind power generation.

Though efforts have been devoted to introducing FACTS devices into eco- nomic dispatch [19, 20, 21, 22], the references with regard to unit commitment with FACTS devices are still limited. Reference focuses on solving security constrained UC problem using artificial bee colony (ABC) algorithm incorpo- rating FACTS devices. The results show that the installation of FACTS de- vices can improve power flow and reduce transmission line losses. A UC model

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considering FACTS devices for corrective operation is proposed in . The original mixed-integer non-linear problem is reformulated as an mixed-integer linear problem. In this context, though optimality is not guaranteed, the sim- ulation studies show that the method finds the optimal solution in most cases.

However, these references all focus on using FACTS devices to improve power system reliability considering contingency, other than using FACTS devices to promote the integration of wind power generation. In addition, no evaluation process is developed for comparing different ways of using FACTS devices. In , different types of FACTS devices are modeled in detail. In this paper, though only one type of FACTS devices, i.e., UPFC is considered, the power injection model is applied. It is more general and can easily be used to model other types of FACTS devices. In , a linear programming approach is pro- posed to reduce computational complexity. However, only DC power flow is considered. In this context, the flexibility of FACTS device may not be fully exploited. In this paper, both active and reactive power flow are taken into account in order to take full advantage of FACTS devices.

Compared with generation-side and demand-side flexibility, using FACTS devices may be faster and cheaper, making it an appropriate tool to cope with the uncertainty of wind power generation in UC. FACTS devices can be initiated quickly and frequently, since the power electronics allows very short reaction time down to far below one second . Moreover, FACTS devices are capable of controlling the interrelated parameters that govern the operation of transmission systems including series impedance, shunt impedance, current, voltage, phase angle .

Among the converter-based FACTS devices, Unified Power Flow Controller (UPFC) [27, 28] is a versatile FACTS device, which is capable of controlling circuit impedance, voltage angle and power flow simultaneously for optimal operation performance of power system .

This paper is focused on analyzing the impacts of UPFC on wind power integration in UC, so as to provide new insights into the utilization of UPFC. In the context, two issues need to be addressed. First, how to assess the impacts of UPFC? Second, how to use UPFC in an appropriate way? To lay the foundation for evaluation, a comprehensive UC model with UPFC and uncertain wind power generation is proposed. Then, some metrics are introduced to evaluate the impacts of UPFC. Further, different dispatch strategies of UPFC are compared to facilitate wind power integration. Additionally, facing the challenging mixed- integer non-linear non-convex problems, approximate models are proposed to provide a starting point to solve the problems efficiently. Thus, the contributions

Of This Paper Are Threefold:

(1) A comprehensive evaluation process based on a two-stage stochastic UC model with UPFC and uncertain wind power generation is proposed. The con- trol variables of UPFC are incorporated in both stages, while AC power flows are taken into account. In addition, power injection model of UPFC is used, which can be extended easily to incorporate different types of FACTS devices, such as static var compensator (SVC), static synchronous compensator (STATCOM), thyristor-controlled phase-shifter (TCPS).

(2) Different ways of applying UPFC in UC are comprehensively compared

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to fully exploit the flexibility of UPFC. Numerical results show that using UPFC only in the first stage helps to make a more economic UC schedule, but may bring adverse effects on wind power integration. On the other hand, the expectation of wind power curtailment and load shedding are largely reduced with the help of UPFC in the second stage. Meanwhile, the voltage profile is improved and the expected total cost is reduced even within a more rigid voltage limit. Moreover, the lowest expected total cost is achieved when UPFC is dispatched in both stages. The results provide new insights for the use of UPFC in UC so as to address uncertain wind power generation.

(3) A DC model and a mixed model are proposed to find an approximate solution with lower computational burdens. Since the proposed AC model is a mixed-integer non-linear non-convex problem which is challenging to solve, a good starting point is identified to solve it. The DC model is computationally efficient but it cannot make full use of UPFC. Meanwhile, the mixed model obtains relatively accurate solutions with less computational burdens than the AC model, when the UC schedule derived from the DC model is feasible.

The rest of the paper is organized as below. Section 2 incorporates UPFC into the two-stage stochastic UC model, and proposes the approximate DC and mixed models. Section 3 proposes the different strategies of using UPFC. Section 4 presents the evaluation process and introduces various metrics.

Section 5

provides the comprehensive analysis of the impacts of UPFC. Finally, in Section 6, some relevant conclusions are drawn.

2.1. Two-Stage Stochastic Uc Model

The UC problem is formulated as a two-stage stochastic programming model. The UC schedule is determined in the first stage, while wind power curtailment and load shedding are only allowed in the second stage.

The objective is to minimize the total cost, which consists of two parts: the UC cost in the first stage, including startup cost and shutdown cost, and the expected cost in the second stage, including fuel cost, wind power curtailment cost and load shedding cost (1).

2.1.1. First-Stage Problem

The first-stage problem represents the here-and-now decision making process before knowing the actual values of stochastic variables. Therefore, the decisions

6

are made based on forecast data. The constraints are formulated with reference to , including active and reactive power balance constraints (2)-(3), voltage magnitude limits (4), voltage angle limits (5), spinning reserve requirements (6), transfer capacity limits (7)-(8), thermal unit generation limits (9)-(11), ramping constraints (12)-(14), minimum up and down time constraints .

2.1.2. Second-Stage Problem

The second-stage problem makes the wait-and-see decisions, based on wind power generation scenarios. Latin hypercube sampling (LHS) technique is employed to generate a set of scenarios in order to form a discrete approximation of wind power generation.

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the associated stochastic optimization problem intractable. Thus, a scenario reduction technique based on probability metric [31, 32] is applied to reduce the number of scenarios, while preserving most of the stochastic information.

In each scenario, the power system operation constraints are satisfied, in- cluding active and reactive power balance constraints (15)-(16), wind power curtailment limits (17), load shedding limits (18), voltage magnitude limits (19), voltage angle limits (20), spinning reserve requirements (21), transfer ca- pacity limits (22)-(23), thermal unit generation limits (24)-(26), and ramping constraints (27)-(29).

U

Figure 1: Power injection model of UPFC. The steady-state models of FACTS devices can be formulated as a series and/or shunt-inserted voltage (-current) source(s), which is called voltage source model (VSM) . The VSM is intuitive but it destroys the symmetric charac- teristics of the admittance matrix . Derived from VSM, the power injection model (PIM) [35, 36], as shown in Fig. 1, keeps the symmetry of the admit- tance matrix. The PIM of UPFC is applied in both first and second stages.

Both active and reactive power flows are taken into account, so that not only the impacts on active power but also voltage can be analyzed. For brevity, only the integration of UPFC into the first stage of UC is shown. UPFC is included in the second stage analogously. Then, re-dispatch constraints are introduced between the two stages to formulate different dispatch strategies.

Let L be the set of branches with UPFC installed. For any branch ij ∈L, the PIM of UPFC in the first stage is formulated as below .

(37)

The impacts of UPFC on active power flow are incorporated into the active power balance constraint (2) as two inverse active power injections at bus i (30) and bus j (32), respectively. Similarly, The impacts of UPFC on reactive power flow are included in the reactive power balance constraint (3) as reactive power injections at bus i (31) and bus j (33), respectively. It should be noted that the two reactive power injections have different physical meanings. According to

Ij,T

is injected by the shunt synchronous voltage source (SVS) directly

Is Generated By The Series Svs,

flowing via line ij for reactive line flow control.

Moreover, The Formulation

with two reactive power injections is more versatile, which can be extended to represent shunt or series controllers. Equality (34) represents the line flow with UPFC power injections. Inequality (35)-(37) denote the thermal limitations and the limit of active power transferred through converters. The details of UPFC injection model can be found in .

The model of UPFC in the second stage is formulated similarly to the above constraints (30)-(37) with second-stage variables. In addition, the re-dispatch constraints are added as below, so that the power injections of UPFC are dis- patched within an acceptable level between the two stages to accommodate wind power uncertainty.

2.3. Dc And Mixed Models

The proposed AC problem above is mixed-integer, nonlinear, and non-convex. Due to its complexity and lack of efficient computational tools, some approx-

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imate models are proposed, which may be served as alternatives to solve the problem. If only DC power flows are considered, the model can be simplified to reduce computational burdens. However, it is worth mentioning that the impacts of UPFC on voltage are ignored, yielding the flexibility of UPFC can- not be fully exploited. Compared with the AC model, the objective function is the same as (1), while the constraints related to voltage and reactive power are removed in the DC model. Moreover, the power balance constraints and line flow equations in the first (41)-(45) and second stage (46)-(50) are changed, while the other constraints remain unchanged.

(50)

Since the integer variables largely increase computational complexity, the mixed model performs an AC economic dispatch based on the UC solution of the aforementioned DC model. First, the DC problem is solved to obtained the UC schedule. Second, the binary variables in the AC model, which indicate the unit status, are fixed with the UC schedule of the DC model. Third, the AC problem is solved with economic dispatch constraints. On one hand, the

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computational burden is reduced compared with the full AC model. On the other hand, the solution to the DC-only model may violate the AC economic dispatch constraints, since reactive power flow constraints are ignored in the DC model.

3. Different Dispatch Strategies Of Upfc

In the first stage, the setpoints of thermal unit outputs and UPFC are de- termined according to wind power generation forecast minimizing the UC cost, while in the second-stage, the expected total cost is minimized with the re- dispatch of thermal units and UPFC to accommodate uncertain wind power generation in different scenarios. According to the stage where the control of UPFC is employed, different dispatch strategies are proposed as follows, aimed at seeking the best way to utilize UPFC for wind power integration in UC. All the models are implemented in GAMS and solved by DICOPT .

(1) DM: Deterministic UC model without UPFC, based on wind power gen- eration forecast. (2) NOM: Non-optimal model with UPFC, where only wind power genera- tion forecast is used, and no optimization is made for the second stage.

(3) NM: No UPFC model. (4) FSM: UPFC controllable in the first stage model. (5) SSM: UPFC controllable in the second stage model.

(6) FSSM: UPFC controllable in the first stage and second stage model.

3.1. No Upfc Model (Nm)

In NM, all of UPFC associated variables are set to zero as below.

The

objective function and other constraints remain unchanged. As a result, it is a basic two-stage stochastic UC model with uncertain wind power generation, serving as a benchmark.

3.2. Upfc In The First Stage Model (Fsm)

When employed only in the first stage, the UPFC cannot be re-dispatched in the second stage. In other words, the setpoints of UPFC are determined in the first stage and remain unchanged in the second stage. Thus, the re-dispatch constraints of UPFC are set to zero as below.

3.3. Upfc In The Second Stage Model (Ssm)

When employed only in the second stage, the UPFC has zero setpoints in the first stage as below, and is re-dispatched in the second stage with respect to wind power generation scenarios.

(54)

3.4. UPFC in the First and Second Stage Model (FSSM) When used in the both stages, the UPFC is set up in the first stage and then re-dispatched in the second stage based on wind power generation scenarios, while the re-dispatch constraints (38)-(40) are satisfied.

It is worth noting that compared with NM, FSM has extra controllable variables in the first stage which may help to reduce operating cost, while SSM has extra controllable variables in the second stage which may contribute to reducing the expected wind power curtailment cost and load shedding cost.

Further, FSSM has the most controllable variables among the proposed models, making it the most flexible one.

4. Evaluation And Metrics

As stated in Section 2.1.2, a large quantity of possible wind power gener- ation scenarios are generated using LHS, then reduced to a few scenarios by scenario reduction technique. The optimization problems are formulated based on the reduced scenarios. Therefore, evaluations are required to test the opti- mal solutions in each of the original generated scenario, as well as to analyze metrics reflecting the impacts of UPFC on wind power integration. In this pa- per, 1000 scenarios are generated then reduced to 10 for optimization. With the first-stage decisions fixed as the optimal solutions, including thermal unit status and UPFC setpoints, economic dispatch is performed according to each wind power generation scenario as a simulation of the second-stage decision making process aimed at minimizing operating cost, including fuel cost, wind power curtailment cost and load shedding cost. After all the scenarios are evaluated, various metrics are calculated based on all the evaluation results. The whole process is shown in Fig. 2.

The expected costs are calculated as below, including expected fuel cost (EFC), expected wind power curtailment cost (EWC), expected load shedding cost (ELC) and expected total cost (ETC).

(58)

where ˆS denotes the set of all generated scenarios. CF

Are The

fuel cost, wind power curtailment cost, and load shedding cost of each scenario, respectively. UC cost (UCC) includes the startup and shuntdown cost of thermal units.

Change rate (CR) of expected costs compares the difference of the EFC, EWC, ELC, ETC before and after UPFC is employed. In other words, it shows the rate of change of the expected costs in FSM, SSM and FSSM, compared with NM. For instance, the change rate of EFC (CREF C) in FSSM is calculated as below.

(59)

where the superscript of EFC denotes the type of model. The change rate of EWC (CREW C), ELC (CRELC) and ETC (CRET C) can be obtained similarly. The loss of load probability (LOLP) is also introduced to evaluate the prob- ability of load shedding (60).

Where Hl

t equals to 1 if there is load shedding at hour t, otherwise hL

T Is 0. 24

indicates the dispatch horizon is 24 hours. Similarly, the wind power curtail- ment probability (WPCP) is proposed to quantify the probability of wind power curtailment (61).

T

equals to 1 if there is wind power curtailment at hour t, otherwise

T

is 0.

5. Case Studies

A 6-bus system , as shown in Fig. 3, is used for testing the proposed models and analyzing the impacts of UPFC. The system contains three thermal units, one wind farm and one UPFC. The transmission line data are listed in Table 1. The spinning reserve requirements are assumed to be 5% of the load.

The wind farm, which is assumed to be controlled with a constant power factor of 0.96, is located at bus 4, with the capacity of 150MW. The UPFC is installed in line 4-5 and paralleled at bus 4. The parameters of UPFC are given in Table 2. The price of wind power curtailment is considered as the levelized cost of electricity , which is $73.6/MWh, and the price of load shedding is assumed to be $300/MWh. In Appendix, the characteristics of thermal units are given in Table 17 and Table 18, while the hourly load and wind power generation forecast are listed in Table 19.

W

Figure 3: Six-bus system. Table 1: Transmission line data.

50

Table 2: UPFC data.

200

200

200

Without loss of generality, the hourly wind power generation forecast error is assumed to follow a normal distribution N(0, σ), and the standard deviation σ is set as 20MW. This normal distribution assumption is an approximate and

15

widely used one, which has been adopted in [1, 3, 40, 41]. Since the proposed UC model is independent of the distribution of wind power generation forecast error, other distributions may also be applied. 1000 scenarios of wind power generation are generated using LHS technique, each of which is assigned a probability that is one divided by the number of total generated scenarios, i.e., 0.001. Then these scenarios are reduced to 10 scenarios using the scenario reduction technique .

It should be noted that the proposed UC models are independent of the scenario generation and reduction technique. As a result, other scenario generation and reduction methods can also be adopted. The reduced 10 scenarios are shown in Table 20 in Appendix. More detailed scenario data can be found at .

In the following sections, the impacts of UPFC on wind power integration are analyzed from different aspects, including wind power curtailment, load shed- ding, power flow, operating costs, unit status and voltage profile. Additionally, the approximate models are investigated.

5.1. Wind Power Curtailment And Load Shedding

Table 3: Evaluation results of AC models.

104636.22

Table 4: Change rate of expected costs in AC models.

-4.8%

The expected costs are shown in Table 3, while the change rates are listed in Table 4. If UPFC is not allowed to be re-dispatched in the second stage (FSM), the impact on the expected wind power curtailment cost is negligible. Addition- ally, the expected load shedding cost increases compared with NM. Otherwise, dispatching UPFC in the second stage (SSM, FSSM) yields considerable reduc- tions in the expected wind power curtailment and expected load shedding cost.

It is especially evident in SSM, where the expected wind power curtailment cost and expected load shedding cost dramatically decrease by 73.5% and 91.7%, respectively.

For further analysis, the wind power curtailment probability and loss of load probability are provided in Table 5. When observing FSM, one interesting finding is that employing UPFC may increase the probability of wind power curtailment and load shedding when the re-dispatch of UPFC is not allowed

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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