Wireless Ev Charging Matlab

Coordination For The Voltage Regulation

Abstract—This paper investigates a decentralized optimization methodology to coordinate Electric Vehicles (EV) charging in order to contribute to the voltage control on a residential electrical distribution feeder. This aims to maintain the voltage level in function of the EV’s power injection using the sensitivity matrix approach. The decentralized optimization is tested with two different methods, respectively global and local, when EV take into account their impact on all the nodes of the network or only on a local neighborhood of their connection point. EV can also update their decisions asynchronously or synchronously.

While only the global approach with asynchronous update is theoretically proven to converge, using results from game theory, simulations show the potential of other algorithms for which fewer iterations or fewer informations are necessary. Finally, us- ing Monte Carlo simulations over a wide range of EV localization configurations, the first analysis have also shown a promising performance in comparison with uncoordinated charging or with a ”voltage droop charging control” recently proposed in the literature.

Index Terms—Voltage control - Decentralized algorithms - EV

V

OLTAGE regulation is one of the significant ancillary services in distribution systems. In the evolution towards a ”smarter grid”, it has to become more flexible to deal with the variation of consumer’s need and distributed generations .

In this context, smart grid is envisioned to make the most of potential interactions between power systems and electric vehicles (EV). A large part of literature has been devoted to a centralized approach (see ) to perfectly schedule EV charging according to various objectives (power losses, voltage deviations, charging costs...) while the behavior of end users is less considered. Thus, a decentralized approach could contribute to the further development of practical coordination mechanisms, the next step before real implementation.

recently gave an overview of smart mechanisms explored in EV smart charging literature comparing centralized and decentralized results. Some of the distributed methods leading to promising results are based on game theory, which is a powerful tool to study their properties . This comes from the fact that Nash equilibria may be attractors for many distributed mechanisms designed in coordination problems. Consequently, these equilibria, and particularly the study of their efficiency, nault SAS, in Paris, France, Y. He PhD student at Supelec Power System De- partment, M. Hennebel researcher and professor at Supelec Power System De-

Manuscript Received June 19, 2013

may play a major role in this context. Recent literature in this field contains which optimizes the interaction between a transformer and a group of EVs and in the context of wind power integration. To the best of our knowledge, our work is the first to apply this framework to the issue of voltage control.

A. Ev Charging Modeling

The availability of EV charging is concerned with a wild research on user’s behavior. In this work, it will be considered that most of users park their car at home during the night hours and require that it is enough charged to travel next day.

The EV charging in this context can be simply modeled as a controllable power-constant load in the band of [0, Pmax], where Pmax is the maximal charging power of EV. The value of Pmax is varied from 3kW to 48kW, depending on different technologies of EV charging. With the state-of-charge (SoC) representing the charging state of EV batteries, the constraints

(1)

where SoCinit is the initial value when EV parks at home, SoCmin is the minimal acceptable value for the user’s next day traveling, SoCmax the maximal value limited by the battery of EV and Pt the EV charging power during time slot t.

Given the SoC at time t, and SoCmin (respectively SoCmax), the minimal (respectively maximal) charging power at time t, denoted by P t (respectively P t), can be calculated, providing P t ≤Pt ≤P t .

(2)

As known, cables on distribution systems have a great R/X ratio (close to 1). Hence the active power delivery to EV chargers can generate voltage drops, and a charging power modulation can contribute to the voltage control, as is highlighted hereafter. In the following, time indexes will be omitted given that the proposed methodology is repeated at each time slot.

B. Voltage Control With A Sensitivity Analysis

The sensitivity analysis is used to evaluate the changes of some quantity η of interest if changes of some parameter p take place in electric systems. In this work, the changes of bus voltage magnitude ∆V will be evaluated and the parameters of concern are bus power injections P, Q.

2

The concerned sensitivity matrix comes from the network’s

(3)

where Pi, Qi, Vi and δi are respectively the active and reactive power injection, bus voltage magnitude and angle at bus i; Yij and θij are respectively the module and argument of the element (i, j) of the network admittance matrix.

By calculating the partial derivatives of (3), its Jacobian

(4)

The coupling of V -P and V -Q can be expressed from the

(5)

where p is the notation of the set of pilot nodes whose voltage profile should be maintained, while c is the notation of the set of nodes where load injection is controlled. The matrices SV p,P c and SV p,Qc are called sensitivity matrices respectively for the coupling V -P and V -Q.

Considering active power control is concerned in EV charg- ing, only the matrix SV p,P c will be used for this study. The charger converter could also allow a reactive power control.

Before presenting the decentralized algorithms to control

V

V

Fig. 1.

Objective Concerning Voltage Regulation

This will permit to quantify how efficient is the voltage regulation. In practice, this must be determined according to the penalties paid by the Distribution Network Operator (DNO) to keep the voltage within its standard limits. With this definition, while the voltage is between its standard limits (0.9 and 1.1 pu), the DNO has no penalty, and these penalties are quadratic out of this interval. As a comparison and as presented in dashed in Fig.1, a second metric will be considered here, called ”crenel” function: 0 between 0.9 and 1.1 pu, 1 otherwise. This is a first step to analyze the sensibility of the results to the metric used.

C. Decentralized Algorithm For Voltage Control

The decentralized algorithm used in this work is an iterative algorithm which is called the best response dynamics (BRD) in game theory . This implements a communication phase taking place off-line, before charging begins, to coordinate charging decisions of all the EV connected to the same network. Note that an online application of the proposed methodology could also be considered : if the charging at time t has already begun but if there is a need for updating the charging decisions (for example, a new EV has just connected to the network) before time t + 1, the decentralized process could be applied again, having updated the charging needs of all the EV which were charging at this time. As soon as a new charging configuration is obtained, then it is applied.

By default, without knowing the state of the voltage on the pilot nodes, each EV (with an automaton) initially chooses a charging power (for example Prated). Receiving all the EV charging decisions, an aggregator calculates the voltage on all the pilot nodes and feedbacks EV with this information.

Therefore each EV updates its charging decision to minimize an objective and reports this change to the aggregator. This procedure is then repeated while a stopping criterion is not reached.

Observe that EV can update their decisions synchronously or asynchronously (EV 1 updates its choice, then the aggregator calculates and send the pilot nodes’ voltage to all the EV, then EV 2 updates and reports its charging power...). Once this communication phase is finished, each EV knows its charging power.

Using the sensitivity matrix, two decentralized approaches for the voltage regulation will be distinguished according to the objective used by EV to update their charging decisions.

In the first one, all EV follow the same objective which concerns all pilot nodes. Setting ∆Pi and supposing ∆P−i = (∆P1, ∆P2, ..., ∆Pi−1, ∆Pi+1..., ∆PI) fixed, EV i minimizes

(7)

where Vp is the actual voltage measurement and Vref the setpoint for voltage control. In the second one, EV i is more particularly concerned with the voltage on its neighborhood, denoted by Vi, and defined by the electrical network topology (typically, a single feeder or a part of this feeder) given that its charging choice can more directly influence the state of these nodes. To update its

(8)

It should be noted that one key advantage of the local approach in comparison to the global one is that only the local

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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