19571.zip_inverter_Design It!_其他书籍下载-pudn.com

<html xmlns="http://www.w3.org/1999/xhtml"> <head> <meta charset="utf-8"> <meta name="generator" content="pdf2htmlEX"> <meta http-equiv="X-UA-Compatible" content="IE=edge,chrome=1"> <link rel="stylesheet" href="https://static.pudn.com/base/css/base.min.css"> <link rel="stylesheet" href="https://static.pudn.com/base/css/fancy.min.css"> <link rel="stylesheet" href="https://static.pudn.com/prod/directory_preview_static/626b80ee1e41a87e8aa4e7f5/raw.css"> <script src="https://static.pudn.com/base/js/compatibility.min.js"></script> <script src="https://static.pudn.com/base/js/pdf2htmlEX.min.js"></script> <script> try{ pdf2htmlEX.defaultViewer = new pdf2htmlEX.Viewer({}); }catch(e){} </script> <title></title> </head> <body> <div id="sidebar" style="display: none"> <div id="outline"> </div> </div> <div id="pf1" class="pf w0 h0" data-page-no="1"><div class="pc pc1 w0 h0"><img class="bi x0 y0 w1 h1" alt="" src="https://static.pudn.com/prod/directory_preview_static/626b80ee1e41a87e8aa4e7f5/bg1.jpg"><div class="c x0 y1 w0 h2"><div class="t m0 x1 h3 y2 ff1 fs0 fc0 sc0 ls0 ws0">0</div><div class="t m0 x2 h4 y3 ff1 fs1 fc0 sc0 ls1 ws0">Electrical Vehicle Design and Modeling</div><div class="t m0 x3 h5 y4 ff2 fs2 fc0 sc0 ls2 ws0">Erik Schaltz</div><div class="t m0 x4 h6 y5 ff3 fs3 fc0 sc0 ls3 ws0">Aalborg University</div><div class="t m0 x5 h6 y6 ff3 fs3 fc0 sc0 ls4 ws0">Denmark</div><div class="t m0 x6 h7 y7 ff1 fs4 fc0 sc0 ls5 ws0">1. Introduction</div><div class="t m0 x6 h8 y8 ff2 fs5 fc0 sc0 ls6 ws0">Electric vehicles are by many seen as the cars of the future as they are high efﬁcient, produces</div><div class="t m0 x6 h8 y9 ff2 fs5 fc0 sc0 ls7 ws0">no local pollution, are silent, and can be used for power regulation by the grid operator.</div><div class="t m0 x6 h8 ya ff2 fs5 fc0 sc0 ls8 ws0">However, electric vehicles still have critical issues which need to be solved. The three main</div><div class="t m0 x6 h8 yb ff2 fs5 fc0 sc0 ls8 ws0">challenges are limited driving r ange, long charging time, and high cost. The three main</div><div class="t m0 x6 h8 yc ff2 fs5 fc0 sc0 ls6 ws0">challenges are all related to the battery package of the car. The battery package should both</div><div class="t m0 x6 h8 yd ff2 fs5 fc0 sc0 ls9 ws0">contain enough energy in order to have a certain driving range and it should also have a</div><div class="t m0 x6 h8 ye ff2 fs5 fc0 sc0 lsa ws0">sufﬁcient power capability for the accelerations and decelerations. In order to be able to</div><div class="t m0 x6 h8 yf ff2 fs5 fc0 sc0 ls7 ws0">estimate the energy consumption of an electric vehicles it is very important to have a proper</div><div class="t m0 x6 h8 y10 ff2 fs5 fc0 sc0 lsb ws0">model of the vehicle (Gao et al., 2007; Mapelli et al., 2010; Schaltz, 2010). The model of an</div><div class="t m0 x6 h8 y11 ff2 fs5 fc0 sc0 lsc ws0">electric vehicle is very complex as it contains many different components, e.g., transmission,</div><div class="t m0 x6 h8 y12 ff2 fs5 fc0 sc0 lsc ws0">electric machine, power electronics, and battery. Each component needs to be modeled</div><div class="t m0 x6 h8 y13 ff2 fs5 fc0 sc0 lsd ws0">properly in order prevent wrong conclusions. The design or rating of each component is a</div><div class="t m0 x6 h8 y14 ff2 fs5 fc0 sc0 lse ws0">difﬁcult task as the parameters of one component affect the power level of another one. There</div><div class="t m0 x6 h8 y15 ff2 fs5 fc0 sc0 lsc ws0">is therefore a risk that one component is rated inappropriate which might make the vehicle</div><div class="t m0 x6 h8 y16 ff2 fs5 fc0 sc0 lse ws0">unnecessary expensive or inefﬁcient. In this chapter a method for designing the power system</div><div class="t m0 x6 h8 y17 ff2 fs5 fc0 sc0 lsf ws0">of an electric vehicle is presented. The method insures that the requirements due to driving</div><div class="t m0 x6 h8 y18 ff2 fs5 fc0 sc0 ls10 ws0">distance and acceleration is fulﬁlled.</div><div class="t m0 x6 h8 y19 ff2 fs5 fc0 sc0 ls6 ws0">The focus in this chapter will be on the modeling and design of the power system of a battery</div><div class="t m0 x6 h8 y1a ff2 fs5 fc0 sc0 ls11 ws0">electric vehicle. Less attention will therefore be put on the selection of each component</div><div class="t m0 x6 h8 y1b ff2 fs5 fc0 sc0 lse ws0">(electric machines, power electronics, batteries, etc.) of the power system as this is a very big</div><div class="t m0 x6 h8 y1c ff2 fs5 fc0 sc0 lsc ws0">task in it self. This chapter will therefore concentrate on the methodology of the modeling and</div><div class="t m0 x6 h8 y1d ff2 fs5 fc0 sc0 lsc ws0">design process. However, the method presented here is also suitable for other architectures</div><div class="t m0 x6 h8 y1e ff2 fs5 fc0 sc0 ls12 ws0">and choice of components.</div><div class="t m0 x6 h8 y1f ff2 fs5 fc0 sc0 ls13 ws0">The chapter is organized as follows: After the introduction Section 2 describes the modeling</div><div class="t m0 x6 h8 y20 ff2 fs5 fc0 sc0 ls14 ws0">of the electric vehicle, Section 3 presents the proposed design method, Section 4 provides a</div><div class="t m0 x6 h8 y21 ff2 fs5 fc0 sc0 ls6 ws0">case study in order to demonstrate the proposed method, and Section 5 gives the conclusion</div><div class="t m0 x6 h8 y22 ff2 fs5 fc0 sc0 ls15 ws0">remarks.</div><div class="t m0 x6 h7 y23 ff1 fs4 fc0 sc0 ls16 ws0">2. Vehicle modeling</div><div class="t m0 x6 h9 y24 ff1 fs6 fc0 sc0 ls17 ws0">2.1 Architecture</div><div class="t m0 x6 h8 y25 ff2 fs5 fc0 sc0 lsc ws0">Many different architectures of an electric vehicle exist (Chan et al., 2010) as there are many</div><div class="t m0 x6 h8 y26 ff2 fs5 fc0 sc0 ls18 ws0">possibilities, e.g., 1 to 4 electric machines, DC or AC machines, gearbox/no gearbox, high or</div><div class="t m0 x1 ha y27 ff4 fs7 fc1 sc0 ls0 ws0">1</div></div><div class="t m0 x7 hb y28 ff5 fs8 fc2 sc0 ls0 ws0">www.intechopen.com</div></div><div class="pi" data-data='{"ctm":[1.992156,0.000000,0.000000,1.992156,0.000000,0.000000]}'></div></div> </body> </html>

<div id="pf2" class="pf w0 h0" data-page-no="2"><div class="pc pc2 w0 h0"><img class="bi x0 y0 w1 h1" alt="" src="https://static.pudn.com/prod/directory_preview_static/626b80ee1e41a87e8aa4e7f5/bg2.jpg"><div class="c x0 y1 w0 h2"><div class="t m0 x6 hc y29 ff6 fs9 fc0 sc0 ls0 ws0">2 Will-be-set-by-IN-TECH</div><div class="t m0 x6 h8 y2a ff2 fs5 fc0 sc0 ls6 ws0">low battery voltage, one or three phase charging, etc. However, in this chapter the architecture</div><div class="t m0 x6 h8 y2b ff2 fs5 fc0 sc0 ls1a ws0">in Fig. 1 is chosen.</div><div class="t m0 x6 h8 y2c ff2 fs5 fc0 sc0 ls1b ws0">The purpose of the different components in Fig. 1 will here shortly be explained: The traction</div><div class="t m0 x6 h8 y2d ff2 fs5 fc0 sc0 ls14 ws0">power of the wheels is delivered by the three phase electric machine. The torque of the left</div><div class="t m0 x6 h8 y2e ff2 fs5 fc0 sc0 ls8 ws0">and right wheels are provided by a differential with also has a gear ratio in order to ﬁt the high</div><div class="t m0 x6 h8 y2f ff2 fs5 fc0 sc0 ls1c ws0">speed of the electric machine shaft to the lower speed of the wheels. The torque and speed</div><div class="t m0 x6 h8 y30 ff2 fs5 fc0 sc0 ls9 ws0">of the machine are controlled by the inverter which inverts the battery DC voltage to a three</div><div class="t m0 x6 h8 y31 ff2 fs5 fc0 sc0 ls1d ws0">phase AC voltage suitable for the electric machine. When analyzing the energy consumption</div><div class="t m0 x6 h8 y32 ff2 fs5 fc0 sc0 lsb ws0">of an electric vehicle it is important also to include the losses due to the components which</div><div class="t m0 x6 h8 y33 ff2 fs5 fc0 sc0 ls1e ws0">not are a part of the power chain from the grid to the wheels. These losses are denoted as</div><div class="t m0 x6 h8 y34 ff2 fs5 fc0 sc0 ls1f ws0">auxiliary loss and includes the lighting system, comfort system, safety systems, etc. During</div><div class="t m0 x6 h8 y35 ff2 fs5 fc0 sc0 lsc ws0">the regenerative braking it is important that the maximum voltage of the battery is not</div><div class="t m0 x6 h8 y36 ff2 fs5 fc0 sc0 ls1f ws0">exceeded. For this reason a braking resistor is introduced. The rectiﬁer rectiﬁes the three</div><div class="t m0 x6 h8 y37 ff2 fs5 fc0 sc0 ls7 ws0">phase voltages and currents of the grid to DC levels and the boost converter makes it possible</div><div class="t m0 x6 h8 y38 ff2 fs5 fc0 sc0 lsf ws0">to transfer power from the low voltage side of the rectiﬁer to the high voltage side of the</div><div class="t m0 x6 h8 y39 ff2 fs5 fc0 sc0 ls6 ws0">battery.</div><div class="t m0 x8 hd y3a ff7 fsa fc0 sc0 ls20 ws0">Gngevtke"</div><div class="t m0 x9 hd y3b ff7 fsa fc0 sc0 ls21 ws0">ocejkpg</div><div class="t m1 xa hd y3c ff7 fsa fc0 sc0 ls22 ws0">Vtcpuokuukqp</div><div class="t m0 xb hd y3d ff7 fsa fc0 sc0 ls23 ws0">Kpxgtvgt</div><div class="t m0 xc he y3e ff7 fsb fc0 sc0 ls0 ws0">y</div><div class="t m0 xc he y3f ff7 fsb fc0 sc0 ls0 ws0">y</div><div class="t m0 xd he y40 ff7 fsb fc0 sc0 ls0 ws0">y</div><div class="t m0 xd he y41 ff7 fsb fc0 sc0 ls0 ws0">y</div><div class="t m0 xe he y42 ff7 fsb fc0 sc0 ls0 ws0">u</div><div class="t m0 xf he y43 ff7 fsb fc0 sc0 ls0 ws0">u</div><div class="t m0 x10 hf y44 ff8 fsa fc0 sc0 ls0 ws0">k</div><div class="t m0 x11 he y45 ff7 fsb fc0 sc0 ls0 ws0">C</div><div class="t m0 x10 hf y46 ff8 fsa fc0 sc0 ls0 ws0">k</div><div class="t m0 x11 he y47 ff7 fsb fc0 sc0 ls0 ws0">D</div><div class="t m0 x10 hf y48 ff8 fsa fc0 sc0 ls0 ws0">k</div><div class="t m0 x11 he y49 ff7 fsb fc0 sc0 ls0 ws0">E</div><div class="t m0 x12 hf y4a ff8 fsa fc0 sc0 ls0 ws0">k</div><div class="t m0 x13 he y4b ff7 fsb fc0 sc0 ls24 ws0">Kpx</div><div class="t m0 x14 hf y4c ff8 fsa fc0 sc0 ls0 ws0">k</div><div class="t m0 x15 he y4d ff7 fsb fc0 sc0 ls24 ws0">Dcv</div><div class="t m0 x16 hd y4e ff7 fsa fc0 sc0 ls25 ws0">Cwzk/</div><div class="t m0 x17 hd y4f ff7 fsa fc0 sc0 ls26 ws0">nkct{</div><div class="t m0 x18 hd y50 ff7 fsa fc0 sc0 ls23 ws0">nqcfu</div><div class="t m0 x19 hf y51 ff8 fsa fc0 sc0 ls0 ws0">k</div><div class="t m0 x1a he y52 ff7 fsb fc0 sc0 ls27 ws0">Cwz</div><div class="t m0 x1b hd y4e ff7 fsa fc0 sc0 ls28 ws0">Dqquv"</div><div class="t m0 x1c hd y4f ff7 fsa fc0 sc0 ls29 ws0">eqp/</div><div class="t m0 x1b hd y50 ff7 fsa fc0 sc0 ls2a ws0">xgtvgt</div><div class="t m0 x1d hf y4a ff8 fsa fc0 sc0 ls0 ws0">k</div><div class="t m0 x1e he y4b ff7 fsb fc0 sc0 ls2b ws0">DE</div><div class="t m0 x1f hf y53 ff8 fsa fc0 sc0 ls0 ws0">k</div><div class="t m0 x20 he y54 ff7 fsb fc0 sc0 ls2b ws0">TH</div><div class="t m0 x21 hd y3d ff7 fsa fc0 sc0 ls2c ws0">Tgevkhkgt</div><div class="t m0 x1f h10 y55 ff8 fsb fc0 sc0 ls0 ws0">-</div><div class="t m0 x22 hf y56 ff8 fsa fc0 sc0 ls0 ws0">x</div><div class="t m0 x23 he y57 ff7 fsb fc0 sc0 ls2b ws0">TH</div><div class="t m0 x23 he y58 ff7 fsb fc0 sc0 ls0 ws0">/</div><div class="t m0 x24 hd y59 ff7 fsa fc0 sc0 ls25 ws0">Itkf</div><div class="t m0 x25 hf y5a ff8 fsa fc0 sc0 ls0 ws0">k</div><div class="t m0 x26 he y5b ff7 fsb fc0 sc0 ls0 ws0">W</div><div class="t m0 x25 hf y5c ff8 fsa fc0 sc0 ls0 ws0">k</div><div class="t m0 x26 he y5d ff7 fsb fc0 sc0 ls0 ws0">X</div><div class="t m0 x27 hf y5e ff8 fsa fc0 sc0 ls0 ws0">k</div><div class="t m0 x28 he y5f ff7 fsb fc0 sc0 ls0 ws0">Y</div><div class="t m0 x29 hf y60 ff8 fsa fc0 sc0 ls2d ws0">/x</div><div class="t m0 x2a he y61 ff7 fsb fc0 sc0 ls2e ws0">X-</div><div class="t m0 x29 hf y62 ff8 fsa fc0 sc0 ls2d ws0">/x</div><div class="t m0 x2a he y63 ff7 fsb fc0 sc0 ls2e ws0">W-</div><div class="t m0 x2b hf y64 ff8 fsa fc0 sc0 ls2d ws0">/x</div><div class="t m0 x2c he y65 ff7 fsb fc0 sc0 ls2f ws0">Y-</div><div class="t m0 x2d hd y3a ff7 fsa fc0 sc0 ls30 ws0">Dtcmkpi"</div><div class="t m0 x2e hd y3b ff7 fsa fc0 sc0 ls31 ws0">tgukuvqt</div><div class="t m0 x2f hf y66 ff8 fsa fc0 sc0 ls0 ws0">k</div><div class="t m0 x30 he y67 ff7 fsb fc0 sc0 ls2b ws0">DT</div><div class="t m0 x31 hd y3d ff7 fsa fc0 sc0 ls20 ws0">Dcvvgt{</div><div class="t m0 x32 hf y68 ff8 fsa fc0 sc0 ls0 ws0">x</div><div class="t m0 x33 he y69 ff7 fsb fc0 sc0 ls32 ws0">Dcv</div><div class="t m0 x34 hf y6a ff8 fsa fc0 sc0 ls0 ws0">-</div><div class="t m0 x33 hd y6b ff7 fsa fc0 sc0 ls0 ws0">/</div><div class="t m0 x6 h8 y6c ff2 fs5 fc0 sc0 ls1b ws0">Fig. 1. Architecture of the battery electric vehicle. In the ﬁgure the main components of the</div><div class="t m0 x6 h8 y6d ff2 fs5 fc0 sc0 ls7 ws0">vehicles which have an inﬂuence on the energy consumption of the vehicle is shown.</div><div class="t m0 x6 h9 y6e ff1 fs6 fc0 sc0 ls33 ws0">2.2 Force Model</div><div class="t m0 x6 h8 y6f ff2 fs5 fc0 sc0 ls7 ws0">The forces which the electric machine of the vehicle must overcome are the forces due to</div><div class="t m0 x6 h8 y70 ff2 fs5 fc0 sc0 ls18 ws0">gravity, wind, rolling resistance, and inertial effect. These forces can also be seen in Fig. 2</div><div class="t m0 x6 h8 y71 ff2 fs5 fc0 sc0 ls34 ws0">where the forces acting on the vehicle are shown.</div><div class="t m2 x35 h11 y72 ff3 fsc fc0 sc0 ls0 ws0">f</div><div class="t m2 x36 h12 y73 ff2 fsd fc0 sc0 ls35 ws0">wind</div><div class="t m2 x37 h11 y74 ff3 fsc fc0 sc0 ls0 ws0">f</div><div class="t m2 x38 h12 y75 ff2 fsd fc0 sc0 ls0 ws0">t</div><div class="t m2 x31 h11 y76 ff3 fsc fc0 sc0 ls0 ws0">f</div><div class="t m2 x39 h12 y77 ff2 fsd fc0 sc0 ls36 ws0">rr</div><div class="t m2 x3a h11 y78 ff3 fsc fc0 sc0 ls0 ws0">f</div><div class="t m2 x3b h12 y79 ff2 fsd fc0 sc0 ls0 ws0">I</div><div class="t m2 x32 h11 y7a ff3 fsc fc0 sc0 ls0 ws0">v</div><div class="t m2 x3c h12 y7b ff2 fsd fc0 sc0 ls37 ws0">car</div><div class="t m3 x18 h13 y7c ff3 fse fc0 sc0 ls0 ws0">f</div><div class="t m4 x3d h14 y7d ff2 fsf fc0 sc0 ls0 ws0">g</div><div class="t m2 x3e h11 y7e ff3 fsc fc0 sc0 ls0 ws0">f</div><div class="t m2 x3f h12 y7f ff2 fsd fc0 sc0 ls0 ws0">n</div><div class="t m5 x30 h15 y80 ff9 fs10 fc0 sc0 ls0 ws0">α</div><div class="t m0 x6 h8 y81 ff2 fs5 fc0 sc0 ls38 ws0">Fig. 2. Free body diagram of the forces (thick arrows) acting on the car.</div><div class="t m0 x6 h16 y82 ff6 fs11 fc1 sc0 ls0 ws0">2</div><div class="t m0 x2d hb y83 ff6 fs8 fc1 sc0 ls0 ws0">Electric Vehicles – Modelling and Simulations</div></div><div class="t m0 x7 hb y28 ff5 fs8 fc2 sc0 ls0 ws0">www.intechopen.com</div></div><div class="pi" data-data='{"ctm":[1.992156,0.000000,0.000000,1.992156,0.000000,0.000000]}'></div></div>

<div id="pf3" class="pf w0 h0" data-page-no="3"><div class="pc pc3 w0 h0"><img class="bi x0 y0 w1 h1" alt="" src="https://static.pudn.com/prod/directory_preview_static/626b80ee1e41a87e8aa4e7f5/bg3.jpg"><div class="c x0 y1 w0 h2"><div class="t m0 x6 hc y29 ff6 fs9 fc0 sc0 ls39 ws0">Electrical Vehicle Design and Modeling 3</div><div class="t m0 x6 h8 y2a ff2 fs5 fc0 sc0 ls3a ws0">The traction force of a vehicle can be described by the following two equations (Ehsani et al.,</div><div class="t m0 x6 h8 y84 ff2 fs5 fc0 sc0 ls7 ws0">2005):</div><div class="t m0 x40 h17 y85 ff3 fs5 fc0 sc0 ls0 ws0">f</div><div class="t m0 x41 h18 y86 ff2 fs12 fc0 sc0 ls0 ws0">t</div><div class="t m0 x42 h19 y87 ffa fs13 fc0 sc0 ls0 ws0">= M</div><div class="t m0 x43 h18 y86 ff2 fs12 fc0 sc0 ls37 ws0">car</div><div class="t m0 x44 h8 y88 ff2 fs5 fc0 sc0 ls0 ws0">˙</div><div class="t m0 x45 h17 y89 ff3 fs5 fc0 sc0 ls0 ws0">v</div><div class="t m0 x46 h18 y8a ff2 fs12 fc0 sc0 ls37 ws0">car</div><div class="t m0 x47 h1a y8b ffb fs5 fc0 sc0 ls0 ws0"></div><div class="t m0 x48 h1a y8c ffb fs5 fc0 sc0 ls3b ws0"> </div><div class="t m0 x49 h1b y8d ff3 fs12 fc0 sc0 ls0 ws0">f</div><div class="t m0 x4a h1c y8e ff2 fs14 fc0 sc0 ls0 ws0">I</div><div class="t m0 x4b h19 y8f ffa fs13 fc0 sc0 ls0 ws0">+ M</div><div class="t m0 x4c h18 y90 ff2 fs12 fc0 sc0 ls37 ws0">car</div><div class="t m0 x4d h1d y8f ffc fs13 fc0 sc0 ls0 ws0">· g</div><div class="t m0 x4e h1a y91 ffb fs5 fc0 sc0 ls0 ws0"></div><div class="t m0 x4f h1a y92 ffb fs5 fc0 sc0 ls3b ws0"> </div><div class="t m0 x50 h1b y93 ff3 fs12 fc0 sc0 ls0 ws0">f</div><div class="t m0 x16 h1c y94 ff2 fs14 fc0 sc0 ls0 ws0">g</div><div class="t m0 x51 h1d y95 ffc fs13 fc0 sc0 ls0 ws0">·sin(α)+sign(v</div><div class="t m0 x52 h18 y96 ff2 fs12 fc0 sc0 ls37 ws0">car</div><div class="t m0 x53 h19 y95 ffa fs13 fc0 sc0 ls0 ws0">)</div><div class="t m0 x12 h1b y97 ff3 fs12 fc0 sc0 ls0 ws0">f</div><div class="t m0 x13 h1c y98 ff2 fs14 fc0 sc0 ls0 ws0">n</div><div class="t m0 x54 h1a y99 ffb fs5 fc0 sc0 ls0 ws0"></div><div class="t m0 x55 h1a y9a ffb fs5 fc0 sc0 ls3b ws0"> </div><div class="t m0 x54 h17 y9b ff3 fs5 fc0 sc0 ls0 ws0">M</div><div class="t m0 x56 h18 y9c ff2 fs12 fc0 sc0 ls37 ws0">car</div><div class="t m0 x57 h1d y9d ffc fs13 fc0 sc0 ls0 ws0">· g ·cos(α) ·c</div><div class="t m0 x58 h18 y9c ff2 fs12 fc0 sc0 ls36 ws0">rr</div><div class="t m0 x54 h1a y9e ffb fs5 fc0 sc0 ls0 ws0"></div><div class="t m0 x59 h1a y92 ffb fs5 fc0 sc0 ls3b ws0"> </div><div class="t m0 x5a h1b y93 ff3 fs12 fc0 sc0 ls0 ws0">f</div><div class="t m0 x5b h1c y94 ff2 fs14 fc0 sc0 ls40 ws0">rr</div><div class="t m0 x47 h19 y9f ffa fs13 fc0 sc0 ls0 ws0">+ sign(v</div><div class="t m0 x4b h18 ya0 ff2 fs12 fc0 sc0 ls37 ws0">car</div><div class="t m0 x5c h19 y9f ffa fs13 fc0 sc0 ls0 ws0">+ v</div><div class="t m0 x17 h18 ya1 ff2 fs12 fc0 sc0 ls41 ws0">wind</div><div class="t m0 x5d h19 y9f ffa fs13 fc0 sc0 ls0 ws0">)</div><div class="t m0 x5e h8 ya2 ff2 fs5 fc0 sc0 ls0 ws0">1</div><div class="t m0 x5e h8 ya3 ff2 fs5 fc0 sc0 ls0 ws0">2</div><div class="t m0 x5f h1e ya4 ff9 fs5 fc0 sc0 ls0 ws0">ρ</div><div class="t m0 x60 h18 ya5 ff2 fs12 fc0 sc0 ls42 ws0">air</div><div class="t m0 x61 h17 y9f ff3 fs5 fc0 sc0 ls0 ws0">C</div><div class="t m0 x62 h18 ya1 ff2 fs12 fc0 sc0 ls43 ws0">drag</div><div class="t m0 x63 h17 y9f ff3 fs5 fc0 sc0 ls0 ws0">A</div><div class="t m0 x2e h18 ya1 ff2 fs12 fc0 sc0 ls44 ws0">front</div><div class="t m0 x30 h19 ya6 ffa fs13 fc0 sc0 ls0 ws0">(</div><div class="t m0 x64 h17 ya7 ff3 fs5 fc0 sc0 ls0 ws0">v</div><div class="t m0 x65 h18 ya8 ff2 fs12 fc0 sc0 ls37 ws0">car</div><div class="t m0 x66 h19 ya7 ffa fs13 fc0 sc0 ls0 ws0">+ v</div><div class="t m0 x55 h18 ya9 ff2 fs12 fc0 sc0 ls41 ws0">wind</div><div class="t m0 x67 h19 yaa ffa fs13 fc0 sc0 ls0 ws0">)</div><div class="t m0 x68 h18 yab ff2 fs12 fc0 sc0 ls0 ws0">2</div><div class="t m0 x3e h1a yac ffb fs5 fc0 sc0 ls0 ws0"></div><div class="t m0 x52 h1a yad ffb fs5 fc0 sc0 ls3b ws0"> </div><div class="t m0 x69 h1b yae ff3 fs12 fc0 sc0 ls0 ws0">f</div><div class="t m0 x52 h1c yaf ff2 fs14 fc0 sc0 ls45 ws0">wind</div><div class="t m0 x6a h8 yb0 ff2 fs5 fc0 sc0 ls46 ws0">(1)</div><div class="t m0 x21 h17 yb1 ff3 fs5 fc0 sc0 ls0 ws0">c</div><div class="t m0 x40 h18 yb2 ff2 fs12 fc0 sc0 ls36 ws0">rr</div><div class="t m0 x42 h19 yb3 ffa fs13 fc0 sc0 ls0 ws0">= 0.01</div><div class="t m0 x6b h1a yb4 ffb fs5 fc0 sc0 ls0 ws0"></div><div class="t m0 x6c h19 yb3 ff2 fs5 fc0 sc0 ls0 ws0">1 +</div><div class="t m0 x1e h8 yb5 ff2 fs5 fc0 sc0 ls7 ws0">3.6</div><div class="t m0 x6d h8 yb6 ff2 fs5 fc0 sc0 ls7 ws0">100</div><div class="t m0 x6e h17 yb7 ff3 fs5 fc0 sc0 ls0 ws0">v</div><div class="t m0 x16 h18 yb8 ff2 fs12 fc0 sc0 ls37 ws0">car</div><div class="t m0 x6f h1a yb9 ffb fs5 fc0 sc0 ls0 ws0"></div><div class="t m0 x5d h8 yba ff2 fs5 fc0 sc0 ls47 ws0">,(2)</div><div class="t m0 x7 h17 ybb ff2 fs5 fc0 sc0 lsf ws0">where f</div><div class="t m0 x70 h18 ybc ff2 fs12 fc0 sc0 ls0 ws0">t</div><div class="t m0 x49 h19 ybd ffa fs13 fc0 sc0 ls0 ws0">[</div><div class="t m0 x4a h8 ybe ff2 fs5 fc0 sc0 ls0 ws0">N</div><div class="t m0 x71 h19 ybd ffa fs13 fc0 sc0 ls0 ws0">]</div><div class="t m0 x72 h8 ybe ff2 fs5 fc0 sc0 ls48 ws0">Traction force of the vehicle</div><div class="t m0 x26 h17 ybf ff3 fs5 fc0 sc0 ls0 ws0">f</div><div class="t m0 x70 h18 yc0 ff2 fs12 fc0 sc0 ls0 ws0">I</div><div class="t m0 x49 h19 yc1 ffa fs13 fc0 sc0 ls0 ws0">[</div><div class="t m0 x4a h8 yc2 ff2 fs5 fc0 sc0 ls0 ws0">N</div><div class="t m0 x71 h19 yc1 ffa fs13 fc0 sc0 ls0 ws0">]</div><div class="t m0 x72 h8 yc2 ff2 fs5 fc0 sc0 lsb ws0">Inertial force of the vehicle</div><div class="t m0 x26 h17 yc3 ff3 fs5 fc0 sc0 ls0 ws0">f</div><div class="t m0 x70 h18 yc4 ff2 fs12 fc0 sc0 ls36 ws0">rr</div><div class="t m0 x49 h19 yc5 ffa fs13 fc0 sc0 ls0 ws0">[</div><div class="t m0 x4a h8 yc6 ff2 fs5 fc0 sc0 ls0 ws0">N</div><div class="t m0 x71 h19 yc5 ffa fs13 fc0 sc0 ls0 ws0">]</div><div class="t m0 x72 h8 yc6 ff2 fs5 fc0 sc0 ls13 ws0">Rolling resistance force of the wheels</div><div class="t m0 x26 h17 yc7 ff3 fs5 fc0 sc0 ls0 ws0">f</div><div class="t m0 x70 h18 yc8 ff2 fs12 fc0 sc0 ls0 ws0">g</div><div class="t m0 x49 h19 yc9 ffa fs13 fc0 sc0 ls0 ws0">[</div><div class="t m0 x4a h8 yca ff2 fs5 fc0 sc0 ls0 ws0">N</div><div class="t m0 x71 h19 yc9 ffa fs13 fc0 sc0 ls0 ws0">]</div><div class="t m0 x72 h8 yca ff2 fs5 fc0 sc0 ls11 ws0">Gravitational force of the vehicle</div><div class="t m0 x26 h17 ycb ff3 fs5 fc0 sc0 ls0 ws0">f</div><div class="t m0 x70 h18 ycc ff2 fs12 fc0 sc0 ls0 ws0">n</div><div class="t m0 x49 h19 ycd ffa fs13 fc0 sc0 ls0 ws0">[</div><div class="t m0 x4a h8 yce ff2 fs5 fc0 sc0 ls0 ws0">N</div><div class="t m0 x71 h19 ycd ffa fs13 fc0 sc0 ls0 ws0">]</div><div class="t m0 x72 h8 yce ff2 fs5 fc0 sc0 lsb ws0">Normal force of the vehicle</div><div class="t m0 x26 h17 ycf ff3 fs5 fc0 sc0 ls0 ws0">f</div><div class="t m0 x70 h18 yd0 ff2 fs12 fc0 sc0 ls41 ws0">wind</div><div class="t m0 x49 h19 yd1 ffa fs13 fc0 sc0 ls0 ws0">[</div><div class="t m0 x4a h8 yd2 ff2 fs5 fc0 sc0 ls0 ws0">N</div><div class="t m0 x71 h19 yd1 ffa fs13 fc0 sc0 ls0 ws0">]</div><div class="t m0 x72 h8 yd2 ff2 fs5 fc0 sc0 ls48 ws0">Force due to wind resistance</div><div class="t m0 x73 h1e yd3 ff9 fs5 fc0 sc0 ls0 ws0">α</div><div class="t m0 x20 h19 yd4 ffa fs13 fc0 sc0 ls0 ws0">[</div><div class="t m0 x49 h8 yd5 ff2 fs5 fc0 sc0 ls49 ws0">rad</div><div class="t m0 x1c h19 yd4 ffa fs13 fc0 sc0 ls0 ws0">]</div><div class="t m0 x72 h8 yd5 ff2 fs5 fc0 sc0 ls4a ws0">Angle of the driving surface</div><div class="t m0 x73 h17 yd6 ff3 fs5 fc0 sc0 ls0 ws0">M</div><div class="t m0 x74 h18 yd7 ff2 fs12 fc0 sc0 ls37 ws0">car</div><div class="t m0 x75 h19 yd8 ffa fs13 fc0 sc0 ls0 ws0">[</div><div class="t m0 x76 h8 yd9 ff2 fs5 fc0 sc0 ls4b ws0">kg</div><div class="t m0 x77 h19 yd8 ffa fs13 fc0 sc0 ls0 ws0">]</div><div class="t m0 x72 h8 yd9 ff2 fs5 fc0 sc0 ls4c ws0">Mass of the vehicle</div><div class="t m0 x73 h17 yda ff3 fs5 fc0 sc0 ls0 ws0">v</div><div class="t m0 x70 h18 ydb ff2 fs12 fc0 sc0 ls37 ws0">car</div><div class="t m0 x1f h19 ydc ffa fs13 fc0 sc0 ls0 ws0">[</div><div class="t m0 x48 h8 ydd ff2 fs5 fc0 sc0 ls4d ws0">m/s</div><div class="t m0 x78 h19 ydc ffa fs13 fc0 sc0 ls0 ws0">]</div><div class="t m0 x72 h8 ydd ff2 fs5 fc0 sc0 lsa ws0">Velocity of the vehicle</div><div class="t m0 x79 h8 yde ff2 fs5 fc0 sc0 ls0 ws0">˙</div><div class="t m0 x73 h17 ydf ff3 fs5 fc0 sc0 ls0 ws0">v</div><div class="t m0 x70 h18 ye0 ff2 fs12 fc0 sc0 ls37 ws0">car</div><div class="t m0 x22 h1a ye1 ffb fs5 fc0 sc0 ls0 ws0"></div><div class="t m0 x23 h8 ye2 ff2 fs5 fc0 sc0 ls4d ws0">m/s</div><div class="t m0 x1c h18 ye3 ff2 fs12 fc0 sc0 ls0 ws0">2</div><div class="t m0 x38 h1a ye1 ffb fs5 fc0 sc0 ls0 ws0"></div><div class="t m0 x72 h8 ye2 ff2 fs5 fc0 sc0 ls3a ws0">Acceleration of the vehicle</div><div class="t m0 x73 h17 ye4 ff3 fs5 fc0 sc0 ls0 ws0">g</div><div class="t m0 x7a h19 ye5 ffa fs13 fc0 sc0 ls0 ws0">= 9.81</div><div class="t m0 x22 h1a ye6 ffb fs5 fc0 sc0 ls0 ws0"></div><div class="t m0 x23 h8 ye5 ff2 fs5 fc0 sc0 ls4d ws0">m/s</div><div class="t m0 x1c h18 ye7 ff2 fs12 fc0 sc0 ls0 ws0">2</div><div class="t m0 x38 h1a ye8 ffb fs5 fc0 sc0 ls0 ws0"></div><div class="t m0 x72 h8 ye9 ff2 fs5 fc0 sc0 ls4c ws0">Free fall acceleration</div><div class="t m0 x73 h1e yea ff9 fs5 fc0 sc0 ls0 ws0">ρ</div><div class="t m0 x70 h18 yeb ff2 fs12 fc0 sc0 ls42 ws0">air</div><div class="t m0 x7b h19 yec ffa fs13 fc0 sc0 ls0 ws0">= 1.2041</div><div class="t m0 x7c h1a yed ffb fs5 fc0 sc0 ls0 ws0"></div><div class="t m0 x22 h8 yec ff2 fs5 fc0 sc0 ls4e ws0">kg/m</div><div class="t m0 x7d h18 yee ff2 fs12 fc0 sc0 ls0 ws0">3</div><div class="t m0 x4b h1a yed ffb fs5 fc0 sc0 ls0 ws0"></div><div class="t m0 x72 h8 yec ff2 fs5 fc0 sc0 ls11 ws0">Air density of dry air at 20</div><div class="t m0 x7e h1f yee ffc fs15 fc0 sc0 ls0 ws0">◦</div><div class="t m0 x7f h8 yec ff2 fs5 fc0 sc0 ls0 ws0">C</div><div class="t m0 x73 h17 yef ff3 fs5 fc0 sc0 ls0 ws0">c</div><div class="t m0 x70 h18 yf0 ff2 fs12 fc0 sc0 ls36 ws0">rr</div><div class="t m0 x49 h19 yf1 ffa fs13 fc0 sc0 ls0 ws0">[</div><div class="t m0 x4a h1d yf2 ffc fs13 fc0 sc0 ls0 ws0">−</div><div class="t m0 x71 h19 yf1 ffa fs13 fc0 sc0 ls0 ws0">]</div><div class="t m0 x72 h8 yf3 ff2 fs5 fc0 sc0 ls1f ws0">Tire rolling resistance coefﬁcient</div><div class="t m0 x73 h17 yf4 ff3 fs5 fc0 sc0 ls0 ws0">C</div><div class="t m0 x80 h18 yf5 ff2 fs12 fc0 sc0 ls43 ws0">drag</div><div class="t m0 x49 h19 yf6 ffa fs13 fc0 sc0 ls0 ws0">[</div><div class="t m0 x4a h1d yf7 ffc fs13 fc0 sc0 ls0 ws0">−</div><div class="t m0 x71 h19 yf6 ffa fs13 fc0 sc0 ls0 ws0">]</div><div class="t m0 x72 h8 yf8 ff2 fs5 fc0 sc0 ls4f ws0">Aerodynamic drag coefﬁcient</div><div class="t m0 x73 h17 yf9 ff3 fs5 fc0 sc0 ls0 ws0">A</div><div class="t m0 x7a h18 yfa ff2 fs12 fc0 sc0 ls44 ws0">front</div><div class="t m0 x20 h1a yfb ffb fs5 fc0 sc0 ls0 ws0"></div><div class="t m0 x49 h8 yfc ff2 fs5 fc0 sc0 ls0 ws0">m</div><div class="t m0 x46 h18 yfd ff2 fs12 fc0 sc0 ls0 ws0">2</div><div class="t m0 x1c h1a yfb ffb fs5 fc0 sc0 ls0 ws0"></div><div class="t m0 x72 h8 yfc ff2 fs5 fc0 sc0 ls50 ws0">Front area</div><div class="t m0 x73 h17 yfe ff3 fs5 fc0 sc0 ls0 ws0">v</div><div class="t m0 x70 h18 yff ff2 fs12 fc0 sc0 ls41 ws0">wind</div><div class="t m0 x1f h19 y100 ffa fs13 fc0 sc0 ls0 ws0">[</div><div class="t m0 x48 h8 y101 ff2 fs5 fc0 sc0 ls4d ws0">m/s</div><div class="t m0 x78 h19 y100 ffa fs13 fc0 sc0 ls0 ws0">]</div><div class="t m0 x72 h8 y101 ff2 fs5 fc0 sc0 ls51 ws0">Headwind speed</div><div class="t m0 x6 h9 y102 ff1 fs6 fc0 sc0 ls52 ws0">2.3 Auxiliary loads</div><div class="t m0 x6 h8 y103 ff2 fs5 fc0 sc0 lsb ws0">The main purpose of the battery is to provide power for the wheels. However, a modern car</div><div class="t m0 x6 h8 y104 ff2 fs5 fc0 sc0 lse ws0">have also other loads which the battery should supply. These loads are either due to safety,</div><div class="t m0 x6 h8 y105 ff2 fs5 fc0 sc0 lsf ws0">e.g., light, wipers, horn, etc. and/or comfort, e.g., radio, heating, air conditioning, etc. These</div><div class="t m0 x6 h8 y106 ff2 fs5 fc0 sc0 ls53 ws0">loads are not constant, e.g., the power consumption of the climate system strongly depend on</div><div class="t m0 x6 h8 y107 ff2 fs5 fc0 sc0 ls10 ws0">the surrounding temperature. Even though some average values are suggested which can be</div><div class="t m0 x6 h8 y108 ff2 fs5 fc0 sc0 ls7 ws0">seen in Table 1. From the table it may be understood that the total average power consumption</div><div class="t m0 x6 h17 y109 ff2 fs5 fc0 sc0 ls1f ws0">is p</div><div class="t m0 x81 h18 y10a ff2 fs12 fc0 sc0 ls54 ws0">Aux</div><div class="t m0 x28 h19 y10b ffa fs13 fc0 sc0 ls0 ws0">= 857 W.</div><div class="t m0 x82 h8 y10c ff2 fs5 fc0 sc0 ls14 ws0">Radio 52 W</div><div class="t m0 x82 h8 y10d ff2 fs5 fc0 sc0 ls1d ws0">Heating Ventilation Air Condition (HVAC) 489 W</div><div class="t m0 x82 h8 y10e ff2 fs5 fc0 sc0 ls56 ws0">Lights 316 W</div><div class="t m0 x82 h17 y10f ff2 fs5 fc0 sc0 ls7 ws0">Total p</div><div class="t m0 x38 h18 y110 ff2 fs12 fc0 sc0 ls54 ws0">Aux</div><div class="t m0 x83 h8 y10f ff2 fs5 fc0 sc0 ls7 ws0">857 W</div><div class="t m0 x6 h8 y111 ff2 fs5 fc0 sc0 ls1f ws0">Table 1. Average power level of the auxiliary loads of the vehicle. The values are inspired</div><div class="t m0 x6 h8 y112 ff2 fs5 fc0 sc0 lsb ws0">from (Ehsani et al., 2005; Emadi, 2005; Lukic & Emadi, 2002).</div><div class="t m0 x84 h16 y82 ff6 fs11 fc1 sc0 ls0 ws0">3</div><div class="t m0 x6 hb y113 ff6 fs8 fc1 sc0 ls0 ws0">Electrical Vehicle Design and Modeling</div></div><div class="t m0 x7 hb y28 ff5 fs8 fc2 sc0 ls0 ws0">www.intechopen.com</div></div><div class="pi" data-data='{"ctm":[1.992156,0.000000,0.000000,1.992156,0.000000,0.000000]}'></div></div>

<div id="pf4" class="pf w0 h0" data-page-no="4"><div class="pc pc4 w0 h0"><img class="bi x0 y0 w1 h1" alt="" src="https://static.pudn.com/prod/directory_preview_static/626b80ee1e41a87e8aa4e7f5/bg4.jpg"><div class="c x0 y1 w0 h2"><div class="t m0 x6 hc y29 ff6 fs9 fc0 sc0 ls0 ws0">4 Will-be-set-by-IN-TECH</div><div class="t m0 x6 h9 y2a ff1 fs6 fc0 sc0 ls57 ws0">2.4 Transmission</div><div class="t m0 x6 h8 y114 ff2 fs5 fc0 sc0 lsc ws0">From Fig. 1 it can be understood that the torque, angular velocity, and power of the</div><div class="t m0 x6 h8 y115 ff2 fs5 fc0 sc0 ls1b ws0">transmission system are given by the following equations:</div><div class="t m0 x3f h1e y116 ff9 fs5 fc0 sc0 ls0 ws0">τ</div><div class="t m0 x5f h18 y117 ff2 fs12 fc0 sc0 ls0 ws0">t</div><div class="t m0 x39 h19 y116 ffa fs13 fc0 sc0 ls0 ws0">= f</div><div class="t m0 x62 h18 y117 ff2 fs12 fc0 sc0 ls0 ws0">t</div><div class="t m0 x85 h17 y116 ff3 fs5 fc0 sc0 ls0 ws0">r</div><div class="t m0 x86 h18 y117 ff2 fs12 fc0 sc0 ls0 ws0">w</div><div class="t m0 x6a h8 y116 ff2 fs5 fc0 sc0 ls46 ws0">(3)</div><div class="t m0 x87 h1e y118 ff9 fs5 fc0 sc0 ls0 ws0">τ</div><div class="t m0 x88 h18 y119 ff2 fs12 fc0 sc0 ls0 ws0">w</div><div class="t m0 x39 h19 y11a ffa fs13 fc0 sc0 ls0 ws0">=</div><div class="t m0 x89 h1e y11b ff9 fs5 fc0 sc0 ls0 ws0">τ</div><div class="t m0 x8a h18 y11c ff2 fs12 fc0 sc0 ls0 ws0">t</div><div class="t m0 x15 h8 y11d ff2 fs5 fc0 sc0 ls0 ws0">2</div><div class="t m0 x6a h8 y11e ff2 fs5 fc0 sc0 ls46 ws0">(4)</div><div class="t m0 x8b h1e y11f ff9 fs5 fc0 sc0 ls0 ws0">ω</div><div class="t m0 x88 h18 y120 ff2 fs12 fc0 sc0 ls0 ws0">w</div><div class="t m0 x39 h19 y121 ffa fs13 fc0 sc0 ls0 ws0">=</div><div class="t m0 x89 h17 y122 ff3 fs5 fc0 sc0 ls0 ws0">v</div><div class="t m0 x8a h18 y123 ff2 fs12 fc0 sc0 ls37 ws0">car</div><div class="t m0 x62 h17 y124 ff3 fs5 fc0 sc0 ls0 ws0">r</div><div class="t m0 x85 h18 y125 ff2 fs12 fc0 sc0 ls0 ws0">w</div><div class="t m0 x6a h8 y126 ff2 fs5 fc0 sc0 ls46 ws0">(5)</div><div class="t m0 x3f h17 y127 ff3 fs5 fc0 sc0 ls0 ws0">p</div><div class="t m0 x5f h18 y128 ff2 fs12 fc0 sc0 ls0 ws0">t</div><div class="t m0 x39 h19 y129 ffa fs13 fc0 sc0 ls0 ws0">= f</div><div class="t m0 x62 h18 y128 ff2 fs12 fc0 sc0 ls0 ws0">t</div><div class="t m0 x85 h17 y129 ff3 fs5 fc0 sc0 ls0 ws0">v</div><div class="t m0 x32 h18 y128 ff2 fs12 fc0 sc0 ls37 ws0">car</div><div class="t m0 x3a h8 y129 ff2 fs5 fc0 sc0 ls58 ws0">,(6)</div><div class="t m0 x7 h8 y12a ff2 fs5 fc0 sc0 lsf ws0">where τ</div><div class="t m0 x70 h18 y12b ff2 fs12 fc0 sc0 ls0 ws0">t</div><div class="t m0 x8c h19 y12c ffa fs13 fc0 sc0 ls0 ws0">[</div><div class="t m0 x8d h8 y12d ff2 fs5 fc0 sc0 ls59 ws0">Nm</div><div class="t m0 x42 h19 y12c ffa fs13 fc0 sc0 ls0 ws0">]</div><div class="t m0 x8e h8 y12d ff2 fs5 fc0 sc0 ls5a ws0">Traction torque</div><div class="t m0 x73 h1e y12e ff9 fs5 fc0 sc0 ls0 ws0">τ</div><div class="t m0 x70 h18 y12f ff2 fs12 fc0 sc0 ls0 ws0">w</div><div class="t m0 x8c h19 y130 ffa fs13 fc0 sc0 ls0 ws0">[</div><div class="t m0 x8d h8 y131 ff2 fs5 fc0 sc0 ls59 ws0">Nm</div><div class="t m0 x42 h19 y130 ffa fs13 fc0 sc0 ls0 ws0">]</div><div class="t m0 x8e h8 y131 ff2 fs5 fc0 sc0 lsd ws0">Torque of each driving wheel</div><div class="t m0 x73 h17 y132 ff3 fs5 fc0 sc0 ls0 ws0">r</div><div class="t m0 x8f h18 y133 ff2 fs12 fc0 sc0 ls0 ws0">w</div><div class="t m0 x90 h19 y134 ffa fs13 fc0 sc0 ls0 ws0">[</div><div class="t m0 x21 h8 y135 ff2 fs5 fc0 sc0 ls0 ws0">m</div><div class="t m0 x91 h19 y134 ffa fs13 fc0 sc0 ls0 ws0">]</div><div class="t m0 x8e h8 y135 ff2 fs5 fc0 sc0 ls8 ws0">Wheel radius</div><div class="t m0 x73 h1e y136 ff9 fs5 fc0 sc0 ls0 ws0">ω</div><div class="t m0 x92 h18 y137 ff2 fs12 fc0 sc0 ls0 ws0">w</div><div class="t m0 x93 h19 y138 ffa fs13 fc0 sc0 ls0 ws0">[</div><div class="t m0 x94 h8 y139 ff2 fs5 fc0 sc0 ls49 ws0">rad/s</div><div class="t m0 x95 h19 y138 ffa fs13 fc0 sc0 ls0 ws0">]</div><div class="t m0 x8e h8 y139 ff2 fs5 fc0 sc0 ls5b ws0">Angular velocity of the wheels</div><div class="t m0 x73 h17 y13a ff3 fs5 fc0 sc0 ls0 ws0">p</div><div class="t m0 x96 h18 y13b ff2 fs12 fc0 sc0 ls0 ws0">t</div><div class="t m0 x8d h19 y13c ffa fs13 fc0 sc0 ls0 ws0">[</div><div class="t m0 x21 h8 y13d ff2 fs5 fc0 sc0 ls0 ws0">W</div><div class="t m0 x91 h19 y13c ffa fs13 fc0 sc0 ls0 ws0">]</div><div class="t m0 x8e h8 y13d ff2 fs5 fc0 sc0 ls5a ws0">Traction power</div><div class="t m0 x6 h8 y13e ff2 fs5 fc0 sc0 ls9 ws0">It is assumed that the power from the shaft of the electric machine to the two driving wheels</div><div class="t m0 x6 h8 y13f ff2 fs5 fc0 sc0 ls5c ws0">has a constant efﬁciency of η</div><div class="t m0 x38 h18 y140 ff2 fs12 fc0 sc0 ls5d ws0">TS</div><div class="t m0 x4e h19 y141 ffa fs13 fc0 sc0 ls0 ws0">= 0.95 (Ehsani et al., 2005). The shaft torque, angular velocity,</div><div class="t m0 x6 h8 y142 ff2 fs5 fc0 sc0 ls5e ws0">and power of the electric machine are therefore</div><div class="t m0 x97 h1e y143 ff9 fs5 fc0 sc0 ls0 ws0">τ</div><div class="t m0 x98 h18 y144 ff2 fs12 fc0 sc0 ls0 ws0">s</div><div class="t m0 x99 h19 y145 ffa fs13 fc0 sc0 ls0 ws0">=</div><div class="t m0 x5e h1a y146 ffb fs5 fc0 sc0 ls0 ws0"></div><div class="t m0 x9a h1e y147 ff9 fs5 fc0 sc0 ls0 ws0">η</div><div class="t m0 x9b h18 y148 ff2 fs12 fc0 sc0 ls5d ws0">TS</div><div class="t m0 x9c h20 y149 ff9 fs12 fc0 sc0 ls0 ws0">τ</div><div class="t m0 x8a h1c y14a ff2 fs14 fc0 sc0 ls0 ws0">t</div><div class="t m0 x9c h1b y14b ff3 fs12 fc0 sc0 ls0 ws0">G</div><div class="t m0 x32 h17 y14c ff2 fs5 fc0 sc0 ls0 ws0">, p</div><div class="t m0 x3a h18 y14d ff2 fs12 fc0 sc0 ls0 ws0">t</div><div class="t m0 x2e h8 y14c ffd fs13 fc0 sc0 ls0 ws0">< 0</div><div class="t m0 x9d h20 y14e ff9 fs12 fc0 sc0 ls0 ws0">τ</div><div class="t m0 x9e h1c y14f ff2 fs14 fc0 sc0 ls0 ws0">t</div><div class="t m0 x60 h20 y150 ff9 fs12 fc0 sc0 ls0 ws0">η</div><div class="t m0 x9b h1c y151 ff2 fs14 fc0 sc0 ls5f ws0">TS</div><div class="t m0 x9f h1b y150 ff3 fs12 fc0 sc0 ls0 ws0">G</div><div class="t m0 x32 h17 y152 ff2 fs5 fc0 sc0 ls0 ws0">, p</div><div class="t m0 x3a h18 y153 ff2 fs12 fc0 sc0 ls0 ws0">t</div><div class="t m0 x2e h1d y152 ffc fs13 fc0 sc0 ls0 ws0">≥ 0</div><div class="t m0 x6a h8 y154 ff2 fs5 fc0 sc0 ls46 ws0">(7)</div><div class="t m0 x16 h1e y155 ff9 fs5 fc0 sc0 ls0 ws0">ω</div><div class="t m0 x98 h18 y156 ff2 fs12 fc0 sc0 ls0 ws0">s</div><div class="t m0 x99 h19 y157 ffa fs13 fc0 sc0 ls0 ws0">= Gω</div><div class="t m0 xa0 h18 y156 ff2 fs12 fc0 sc0 ls0 ws0">w</div><div class="t m0 x6a h8 y157 ff2 fs5 fc0 sc0 ls46 ws0">(8)</div><div class="t m0 x97 h17 y158 ff3 fs5 fc0 sc0 ls0 ws0">p</div><div class="t m0 x98 h18 y159 ff2 fs12 fc0 sc0 ls0 ws0">s</div><div class="t m0 x99 h19 y15a ffa fs13 fc0 sc0 ls0 ws0">= τ</div><div class="t m0 x88 h18 y159 ff2 fs12 fc0 sc0 ls0 ws0">s</div><div class="t m0 x5f h1e y15a ff9 fs5 fc0 sc0 ls0 ws0">ω</div><div class="t m0 xa1 h18 y159 ff2 fs12 fc0 sc0 ls0 ws0">s</div><div class="t m0 xa2 h8 y15a ff2 fs5 fc0 sc0 ls60 ws0">,(9)</div><div class="t m0 x7 h8 y15b ff2 fs5 fc0 sc0 lsf ws0">where τ</div><div class="t m0 x70 h18 y15c ff2 fs12 fc0 sc0 ls0 ws0">s</div><div class="t m0 xa3 h19 y15d ffa fs13 fc0 sc0 ls0 ws0">[</div><div class="t m0 x8c h8 y15e ff2 fs5 fc0 sc0 ls59 ws0">Nm</div><div class="t m0 xa4 h19 y15d ffa fs13 fc0 sc0 ls0 ws0">]</div><div class="t m0 x35 h8 y15e ff2 fs5 fc0 sc0 ls1b ws0">Shaft torque of electric machine</div><div class="t m0 x73 h1e y15f ff9 fs5 fc0 sc0 ls0 ws0">ω</div><div class="t m0 x92 h18 y160 ff2 fs12 fc0 sc0 ls0 ws0">s</div><div class="t m0 xa5 h19 y161 ffa fs13 fc0 sc0 ls0 ws0">[</div><div class="t m0 x93 h8 y162 ff2 fs5 fc0 sc0 ls49 ws0">rad/s</div><div class="t m0 xa6 h19 y161 ffa fs13 fc0 sc0 ls0 ws0">]</div><div class="t m0 x35 h8 y162 ff2 fs5 fc0 sc0 ls11 ws0">Shaft angular velocity of electric machine</div><div class="t m0 x73 h17 y163 ff3 fs5 fc0 sc0 ls0 ws0">p</div><div class="t m0 x96 h18 y164 ff2 fs12 fc0 sc0 ls0 ws0">s</div><div class="t m0 x8c h19 y165 ffa fs13 fc0 sc0 ls0 ws0">[</div><div class="t m0 x8d h8 y166 ff2 fs5 fc0 sc0 ls0 ws0">W</div><div class="t m0 xa7 h19 y165 ffa fs13 fc0 sc0 ls0 ws0">]</div><div class="t m0 x35 h8 y166 ff2 fs5 fc0 sc0 ls61 ws0">Shaft power of electric machine</div><div class="t m0 x73 h17 y167 ff3 fs5 fc0 sc0 ls0 ws0">G</div><div class="t m0 xa8 h19 y168 ffa fs13 fc0 sc0 ls0 ws0">[</div><div class="t m0 x90 h1d y169 ffc fs13 fc0 sc0 ls0 ws0">−</div><div class="t m0 xa9 h19 y168 ffa fs13 fc0 sc0 ls0 ws0">]</div><div class="t m0 x35 h8 y16a ff2 fs5 fc0 sc0 ls48 ws0">Gear ratio of differential</div><div class="t m0 x6 h9 y16b ff1 fs6 fc0 sc0 ls62 ws0">2.5 Electric machine</div><div class="t m0 x6 h8 y16c ff2 fs5 fc0 sc0 ls63 ws0">For propulsion usually the induction machine (IM), permanent magnet synchronous machine</div><div class="t m0 x6 h8 y16d ff2 fs5 fc0 sc0 ls8 ws0">(PMSM), and switched reluctance machine (SRM) are considered. The "best" choice is</div><div class="t m0 x6 h8 y16e ff2 fs5 fc0 sc0 ls13 ws0">like many other components a trade off between, cost, mass, volume, efﬁciency, reliability,</div><div class="t m0 x6 h8 y16f ff2 fs5 fc0 sc0 ls5a ws0">maintenance, etc. However, due to its high power density and high efﬁciency the PMSM is</div><div class="t m0 x6 h8 y170 ff2 fs5 fc0 sc0 ls8 ws0">selected. The electric machine is divided into an electric part and mechanic part. The electric</div><div class="t m0 x6 h8 y171 ff2 fs5 fc0 sc0 ls1f ws0">part of the PMSM is modeled in the DQ-frame, i.e.,</div><div class="t m0 x38 h17 y172 ff3 fs5 fc0 sc0 ls0 ws0">v</div><div class="t m0 xaa h18 y173 ff2 fs12 fc0 sc0 ls0 ws0">d</div><div class="t m0 x4e h19 y174 ffa fs13 fc0 sc0 ls0 ws0">= R</div><div class="t m0 x17 h18 y175 ff2 fs12 fc0 sc0 ls0 ws0">s</div><div class="t m0 xab h17 y174 ff3 fs5 fc0 sc0 ls0 ws0">i</div><div class="t m0 xac h18 y173 ff2 fs12 fc0 sc0 ls0 ws0">d</div><div class="t m0 xad h19 y174 ffa fs13 fc0 sc0 ls0 ws0">+ L</div><div class="t m0 xae h18 y173 ff2 fs12 fc0 sc0 ls0 ws0">d</div><div class="t m0 x60 h17 y176 ff3 fs5 fc0 sc0 ls64 ws0">di</div><div class="t m0 xaf h18 y177 ff2 fs12 fc0 sc0 ls0 ws0">d</div><div class="t m0 xa0 h17 y178 ff3 fs5 fc0 sc0 ls65 ws0">dt</div><div class="t m0 x62 h1d y179 ffc fs13 fc0 sc0 ls0 ws0">−ω</div><div class="t m0 xb0 h1b y17a ff3 fs12 fc0 sc0 ls0 ws0">e</div><div class="t m0 x3b h17 y179 ff3 fs5 fc0 sc0 ls0 ws0">L</div><div class="t m0 xb1 h18 y17a ff2 fs12 fc0 sc0 ls0 ws0">q</div><div class="t m0 x69 h17 y179 ff3 fs5 fc0 sc0 ls0 ws0">i</div><div class="t m0 xb2 h18 y17a ff2 fs12 fc0 sc0 ls0 ws0">q</div><div class="t m0 xb3 h8 y179 ff2 fs5 fc0 sc0 ls7 ws0">(10)</div><div class="t m0 x38 h17 y17b ff3 fs5 fc0 sc0 ls0 ws0">v</div><div class="t m0 xaa h18 y17c ff2 fs12 fc0 sc0 ls0 ws0">q</div><div class="t m0 x4e h19 y17d ffa fs13 fc0 sc0 ls0 ws0">= R</div><div class="t m0 x17 h18 y17c ff2 fs12 fc0 sc0 ls0 ws0">s</div><div class="t m0 xab h17 y17d ff3 fs5 fc0 sc0 ls0 ws0">i</div><div class="t m0 xac h18 y17c ff2 fs12 fc0 sc0 ls0 ws0">q</div><div class="t m0 x1a h19 y17d ffa fs13 fc0 sc0 ls0 ws0">+ L</div><div class="t m0 xae h18 y17c ff2 fs12 fc0 sc0 ls0 ws0">q</div><div class="t m0 xb4 h17 y17e ff3 fs5 fc0 sc0 ls64 ws0">di</div><div class="t m0 xb5 h18 y17f ff2 fs12 fc0 sc0 ls0 ws0">q</div><div class="t m0 xb6 h17 y180 ff3 fs5 fc0 sc0 ls65 ws0">dt</div><div class="t m0 x15 h19 y181 ffa fs13 fc0 sc0 ls0 ws0">+ ω</div><div class="t m0 x63 h1b y182 ff3 fs12 fc0 sc0 ls0 ws0">e</div><div class="t m0 xb7 h17 y181 ff3 fs5 fc0 sc0 ls0 ws0">L</div><div class="t m0 xb8 h18 y183 ff2 fs12 fc0 sc0 ls0 ws0">d</div><div class="t m0 x69 h17 y181 ff3 fs5 fc0 sc0 ls0 ws0">i</div><div class="t m0 x52 h18 y183 ff2 fs12 fc0 sc0 ls0 ws0">d</div><div class="t m0 xb9 h19 y181 ffa fs13 fc0 sc0 ls0 ws0">+ ω</div><div class="t m0 xba h18 y182 ff2 fs12 fc0 sc0 ls0 ws0">e</div><div class="t m0 xbb h1e y181 ff9 fs5 fc0 sc0 ls0 ws0">λ</div><div class="t m0 xbc h1b y182 ff3 fs12 fc0 sc0 ls66 ws0">pm</div><div class="t m0 xb3 h8 y181 ff2 fs5 fc0 sc0 ls7 ws0">(11)</div><div class="t m0 x71 h17 y184 ff3 fs5 fc0 sc0 ls0 ws0">p</div><div class="t m0 x78 h18 y185 ff2 fs12 fc0 sc0 ls43 ws0">EM</div><div class="t m0 x4e h19 y186 ffa fs13 fc0 sc0 ls0 ws0">=</div><div class="t m0 x4f h8 y187 ff2 fs5 fc0 sc0 ls0 ws0">3</div><div class="t m0 x4f h8 y188 ff2 fs5 fc0 sc0 ls0 ws0">2</div><div class="t m0 x3d h1a y189 ffb fs5 fc0 sc0 ls0 ws0"></div><div class="t m0 xac h17 y18a ff3 fs5 fc0 sc0 ls0 ws0">v</div><div class="t m0 xbd h18 y18b ff2 fs12 fc0 sc0 ls0 ws0">d</div><div class="t m0 xbe h17 y18c ff3 fs5 fc0 sc0 ls0 ws0">i</div><div class="t m0 x8b h18 y18b ff2 fs12 fc0 sc0 ls0 ws0">d</div><div class="t m0 x3f h19 y18c ffa fs13 fc0 sc0 ls0 ws0">+ v</div><div class="t m0 xa2 h18 y18d ff2 fs12 fc0 sc0 ls0 ws0">q</div><div class="t m0 x9f h17 y18c ff3 fs5 fc0 sc0 ls0 ws0">i</div><div class="t m0 x89 h18 y18d ff2 fs12 fc0 sc0 ls0 ws0">q</div><div class="t m0 xbf h1a y18e ffb fs5 fc0 sc0 ls0 ws0"></div><div class="t m0 x32 h8 y18f ff2 fs5 fc0 sc0 ls7 ws0">, (12)</div><div class="t m0 x6 h16 y82 ff6 fs11 fc1 sc0 ls0 ws0">4</div><div class="t m0 x2d hb y83 ff6 fs8 fc1 sc0 ls0 ws0">Electric Vehicles – Modelling and Simulations</div></div><div class="t m0 x7 hb y28 ff5 fs8 fc2 sc0 ls0 ws0">www.intechopen.com</div></div><div class="pi" data-data='{"ctm":[1.992156,0.000000,0.000000,1.992156,0.000000,0.000000]}'></div></div>

<div id="pf5" class="pf w0 h0" data-page-no="5"><div class="pc pc5 w0 h0"><img class="bi x0 y0 w1 h1" alt="" src="https://static.pudn.com/prod/directory_preview_static/626b80ee1e41a87e8aa4e7f5/bg5.jpg"><div class="c x0 y1 w0 h2"><div class="t m0 x6 hc y29 ff6 fs9 fc0 sc0 ls39 ws0">Electrical Vehicle Design and Modeling 5</div><div class="t m0 x7 h17 y190 ff2 fs5 fc0 sc0 lsf ws0">where v</div><div class="t m0 x70 h18 y191 ff2 fs12 fc0 sc0 ls0 ws0">d</div><div class="t m0 xc0 h19 y192 ffa fs13 fc0 sc0 ls0 ws0">[</div><div class="t m0 x40 h8 y193 ff2 fs5 fc0 sc0 ls0 ws0">V</div><div class="t m0 xc1 h19 y192 ffa fs13 fc0 sc0 ls0 ws0">]</div><div class="t m0 xc2 h8 y193 ff2 fs5 fc0 sc0 ls10 ws0">D-axis voltage</div><div class="t m0 x73 h17 y194 ff3 fs5 fc0 sc0 ls0 ws0">v</div><div class="t m0 x70 h18 y195 ff2 fs12 fc0 sc0 ls0 ws0">q</div><div class="t m0 xc0 h19 y196 ffa fs13 fc0 sc0 ls0 ws0">[</div><div class="t m0 x40 h8 y197 ff2 fs5 fc0 sc0 ls0 ws0">V</div><div class="t m0 xc1 h19 y196 ffa fs13 fc0 sc0 ls0 ws0">]</div><div class="t m0 xc2 h8 y197 ff2 fs5 fc0 sc0 ls10 ws0">Q-axis voltage</div><div class="t m0 x73 h17 y198 ff3 fs5 fc0 sc0 ls0 ws0">i</div><div class="t m0 xc3 h18 y199 ff2 fs12 fc0 sc0 ls0 ws0">d</div><div class="t m0 xc0 h19 y19a ffa fs13 fc0 sc0 ls0 ws0">[</div><div class="t m0 x40 h8 y19b ff2 fs5 fc0 sc0 ls0 ws0">A</div><div class="t m0 xc1 h19 y19a ffa fs13 fc0 sc0 ls0 ws0">]</div><div class="t m0 xc2 h8 y19b ff2 fs5 fc0 sc0 ls14 ws0">D-axis current</div><div class="t m0 x73 h17 y19c ff3 fs5 fc0 sc0 ls0 ws0">i</div><div class="t m0 xc3 h18 y19d ff2 fs12 fc0 sc0 ls0 ws0">q</div><div class="t m0 xc0 h19 y19e ffa fs13 fc0 sc0 ls0 ws0">[</div><div class="t m0 x40 h8 y19f ff2 fs5 fc0 sc0 ls0 ws0">A</div><div class="t m0 xc1 h19 y19e ffa fs13 fc0 sc0 ls0 ws0">]</div><div class="t m0 xc2 h8 y19f ff2 fs5 fc0 sc0 ls67 ws0">Q-axis current</div><div class="t m0 x73 h17 y1a0 ff3 fs5 fc0 sc0 ls0 ws0">R</div><div class="t m0 x80 h18 y1a1 ff2 fs12 fc0 sc0 ls0 ws0">s</div><div class="t m0 x21 h19 y1a2 ffa fs13 fc0 sc0 ls0 ws0">[</div><div class="t m0 xc4 h21 y1a3 ffe fs5 fc0 sc0 ls0 ws0">Ω</div><div class="t m0 xc1 h19 y1a2 ffa fs13 fc0 sc0 ls0 ws0">]</div><div class="t m0 xc2 h8 y1a3 ff2 fs5 fc0 sc0 lse ws0">Stator phase resistance</div><div class="t m0 x73 h17 y1a4 ff3 fs5 fc0 sc0 ls0 ws0">L</div><div class="t m0 x96 h18 y1a5 ff2 fs12 fc0 sc0 ls0 ws0">d</div><div class="t m0 xc0 h19 y1a6 ffa fs13 fc0 sc0 ls0 ws0">[</div><div class="t m0 x40 h8 y1a7 ff2 fs5 fc0 sc0 ls0 ws0">H</div><div class="t m0 xc1 h19 y1a6 ffa fs13 fc0 sc0 ls0 ws0">]</div><div class="t m0 xc2 h8 y1a7 ff2 fs5 fc0 sc0 ls11 ws0">D-axis inductance</div><div class="t m0 x73 h17 y1a8 ff3 fs5 fc0 sc0 ls0 ws0">L</div><div class="t m0 x96 h18 y1a9 ff2 fs12 fc0 sc0 ls0 ws0">q</div><div class="t m0 xc0 h19 y1aa ffa fs13 fc0 sc0 ls0 ws0">[</div><div class="t m0 x40 h8 y1ab ff2 fs5 fc0 sc0 ls0 ws0">H</div><div class="t m0 xc1 h19 y1aa ffa fs13 fc0 sc0 ls0 ws0">]</div><div class="t m0 xc2 h8 y1ab ff2 fs5 fc0 sc0 ls11 ws0">Q-axis inductance</div><div class="t m0 x73 h1e y1ac ff9 fs5 fc0 sc0 ls0 ws0">λ</div><div class="t m0 x96 h18 y1ad ff2 fs12 fc0 sc0 ls68 ws0">pm</div><div class="t m0 x90 h19 y1ae ffa fs13 fc0 sc0 ls0 ws0">[</div><div class="t m0 xc5 h8 y1af ff2 fs5 fc0 sc0 ls18 ws0">Wb</div><div class="t m0 xc6 h19 y1ae ffa fs13 fc0 sc0 ls0 ws0">]</div><div class="t m0 xc2 h8 y1af ff2 fs5 fc0 sc0 ls69 ws0">Permanent magnet ﬂux linkage</div><div class="t m0 x73 h1e y1b0 ff9 fs5 fc0 sc0 ls0 ws0">ω</div><div class="t m0 x92 h18 y1b1 ff2 fs12 fc0 sc0 ls0 ws0">e</div><div class="t m0 x8c h19 y1b2 ffa fs13 fc0 sc0 ls0 ws0">[</div><div class="t m0 x8d h8 y1b3 ff2 fs5 fc0 sc0 ls49 ws0">rad/s</div><div class="t m0 xc7 h19 y1b2 ffa fs13 fc0 sc0 ls0 ws0">]</div><div class="t m0 xc2 h8 y1b3 ff2 fs5 fc0 sc0 ls7 ws0">Angular frequency of the stator</div><div class="t m0 x73 h1e y1b4 ff9 fs5 fc0 sc0 ls0 ws0">λ</div><div class="t m0 x96 h18 y1b5 ff2 fs12 fc0 sc0 ls37 ws0">pm</div><div class="t m0 x90 h19 y1b6 ffa fs13 fc0 sc0 ls0 ws0">[</div><div class="t m0 xc5 h8 y1b7 ff2 fs5 fc0 sc0 ls18 ws0">Wb</div><div class="t m0 xc6 h19 y1b6 ffa fs13 fc0 sc0 ls0 ws0">]</div><div class="t m0 xc2 h8 y1b7 ff2 fs5 fc0 sc0 ls69 ws0">Permanent magnet ﬂux linkage</div><div class="t m0 x73 h17 y1b8 ff3 fs5 fc0 sc0 ls0 ws0">p</div><div class="t m0 x96 h18 y1b9 ff2 fs12 fc0 sc0 ls43 ws0">EM</div><div class="t m0 x21 h19 y1ba ffa fs13 fc0 sc0 ls0 ws0">[</div><div class="t m0 xc4 h8 y1bb ff2 fs5 fc0 sc0 ls0 ws0">W</div><div class="t m0 x42 h19 y1ba ffa fs13 fc0 sc0 ls0 ws0">]</div><div class="t m0 xc2 h8 y1bb ff2 fs5 fc0 sc0 lsd ws0">Electric input power</div><div class="t m0 x6 h8 y1bc ff2 fs5 fc0 sc0 ls1d ws0">The mechanical part of the PMSM can be modeled as follows:</div><div class="t m0 xc8 h1e y1bd ff9 fs5 fc0 sc0 ls0 ws0">τ</div><div class="t m0 xc9 h18 y1be ff2 fs12 fc0 sc0 ls0 ws0">e</div><div class="t m0 xca h19 y1bf ffa fs13 fc0 sc0 ls0 ws0">= J</div><div class="t m0 xbd h18 y1be ff2 fs12 fc0 sc0 ls0 ws0">s</div><div class="t m0 x51 h17 y1c0 ff3 fs5 fc0 sc0 ls0 ws0">dω</div><div class="t m0 xae h18 y1c1 ff2 fs12 fc0 sc0 ls0 ws0">s</div><div class="t m0 x8b h17 y1c2 ff3 fs5 fc0 sc0 ls65 ws0">dt</div><div class="t m0 x60 h19 y1c3 ffa fs13 fc0 sc0 ls0 ws0">+ B</div><div class="t m0 x62 h18 y1c4 ff2 fs12 fc0 sc0 ls0 ws0">v</div><div class="t m0 xcb h1e y1c3 ff9 fs5 fc0 sc0 ls0 ws0">ω</div><div class="t m0 x3c h18 y1c4 ff2 fs12 fc0 sc0 ls0 ws0">s</div><div class="t m0 xb0 h19 y1c3 ffa fs13 fc0 sc0 ls0 ws0">+ τ</div><div class="t m0 xcc h18 y1c4 ff2 fs12 fc0 sc0 ls0 ws0">c</div><div class="t m0 xcd h19 y1c3 ffa fs13 fc0 sc0 ls0 ws0">+ τ</div><div class="t m0 xce h18 y1c4 ff2 fs12 fc0 sc0 ls0 ws0">s</div><div class="t m0 xb3 h8 y1c3 ff2 fs5 fc0 sc0 ls7 ws0">(13)</div><div class="t m0 xc8 h17 y1c5 ff3 fs5 fc0 sc0 ls0 ws0">p</div><div class="t m0 xc9 h18 y1c6 ff2 fs12 fc0 sc0 ls0 ws0">s</div><div class="t m0 xca h19 y1c7 ffa fs13 fc0 sc0 ls0 ws0">= τ</div><div class="t m0 xbd h18 y1c6 ff2 fs12 fc0 sc0 ls0 ws0">s</div><div class="t m0 x51 h1e y1c7 ff9 fs5 fc0 sc0 ls0 ws0">ω</div><div class="t m0 x87 h18 y1c6 ff2 fs12 fc0 sc0 ls0 ws0">s</div><div class="t m0 x3f h8 y1c7 ff2 fs5 fc0 sc0 ls7 ws0">, (14)</div><div class="t m0 x7 h17 y1c8 ff2 fs5 fc0 sc0 lsf ws0">where J</div><div class="t m0 x8f h18 y1c9 ff2 fs12 fc0 sc0 ls0 ws0">s</div><div class="t m0 x8c h1a y1ca ffb fs5 fc0 sc0 ls0 ws0"></div><div class="t m0 x90 h8 y1cb ff2 fs5 fc0 sc0 ls4b ws0">kgm</div><div class="t m0 x95 h18 y1cc ff2 fs12 fc0 sc0 ls0 ws0">2</div><div class="t m0 xcf h1a y1ca ffb fs5 fc0 sc0 ls0 ws0"></div><div class="t m0 x1f h8 y1cb ff2 fs5 fc0 sc0 ls10 ws0">Shaft moment of inertia</div><div class="t m0 x73 h1e y1cd ff9 fs5 fc0 sc0 ls0 ws0">τ</div><div class="t m0 x70 h18 y1ce ff2 fs12 fc0 sc0 ls0 ws0">e</div><div class="t m0 xd0 h19 y1cf ffa fs13 fc0 sc0 ls0 ws0">[</div><div class="t m0 xc5 h8 y1d0 ff2 fs5 fc0 sc0 ls59 ws0">Nm</div><div class="t m0 xd1 h19 y1cf ffa fs13 fc0 sc0 ls0 ws0">]</div><div class="t m0 x1f h8 y1d0 ff2 fs5 fc0 sc0 ls5b ws0">Electromechanical torque</div><div class="t m0 x73 h1e y1d1 ff9 fs5 fc0 sc0 ls0 ws0">τ</div><div class="t m0 x70 h18 y1d2 ff2 fs12 fc0 sc0 ls0 ws0">c</div><div class="t m0 xd0 h19 y1d3 ffa fs13 fc0 sc0 ls0 ws0">[</div><div class="t m0 xc5 h8 y1d4 ff2 fs5 fc0 sc0 ls59 ws0">Nm</div><div class="t m0 xd1 h19 y1d3 ffa fs13 fc0 sc0 ls0 ws0">]</div><div class="t m0 x1f h8 y1d4 ff2 fs5 fc0 sc0 ls6a ws0">Coulomb torque</div><div class="t m0 x73 h17 y1d5 ff3 fs5 fc0 sc0 ls0 ws0">B</div><div class="t m0 x96 h18 y1d6 ff2 fs12 fc0 sc0 ls0 ws0">v</div><div class="t m0 xa5 h19 y1d7 ffa fs13 fc0 sc0 ls0 ws0">[</div><div class="t m0 x93 h8 y1d8 ff2 fs5 fc0 sc0 ls6b ws0">Nms/ rad</div><div class="t m0 xd2 h19 y1d7 ffa fs13 fc0 sc0 ls0 ws0">]</div><div class="t m0 x1f h8 y1d8 ff2 fs5 fc0 sc0 ls63 ws0">Viscous friction coefﬁcient</div><div class="t m0 x6 h8 y1d9 ff2 fs5 fc0 sc0 lsa ws0">The coupling between the electric and mechanic part is given by</div><div class="t m0 xd3 h1e y1da ff9 fs5 fc0 sc0 ls0 ws0">τ</div><div class="t m0 xd4 h18 y1db ff2 fs12 fc0 sc0 ls0 ws0">e</div><div class="t m0 xd5 h19 y1dc ffa fs13 fc0 sc0 ls0 ws0">=</div><div class="t m0 x16 h8 y1dd ff2 fs5 fc0 sc0 ls0 ws0">3</div><div class="t m0 x16 h8 y1de ff2 fs5 fc0 sc0 ls0 ws0">2</div><div class="t m0 x98 h17 y1df ff3 fs5 fc0 sc0 ls0 ws0">P</div><div class="t m0 xac h8 y1de ff2 fs5 fc0 sc0 ls0 ws0">2</div><div class="t m0 xd6 h1a y1e0 ffb fs5 fc0 sc0 ls0 ws0"></div><div class="t m0 x8b h1e y1e1 ff9 fs5 fc0 sc0 ls0 ws0">λ</div><div class="t m0 x3f h1b y1e2 ff3 fs12 fc0 sc0 ls66 ws0">pm</div><div class="t m0 x39 h17 y1e3 ff3 fs5 fc0 sc0 ls0 ws0">i</div><div class="t m0 x9b h18 y1e2 ff2 fs12 fc0 sc0 ls0 ws0">q</div><div class="t m0 x9f h19 y1e3 ffa fs13 fc0 sc0 ls0 ws0">+</div><div class="t m0 xd7 h1a y1e4 ffb fs5 fc0 sc0 ls0 ws0"></div><div class="t m0 xd8 h17 y1e5 ff3 fs5 fc0 sc0 ls0 ws0">L</div><div class="t m0 xd9 h18 y1e6 ff2 fs12 fc0 sc0 ls0 ws0">d</div><div class="t m0 x3b h1d y1e7 ffc fs13 fc0 sc0 ls0 ws0">− L</div><div class="t m0 xcd h18 y1e8 ff2 fs12 fc0 sc0 ls0 ws0">q</div><div class="t m0 x30 h1a y1e9 ffb fs5 fc0 sc0 ls0 ws0"></div><div class="t m0 xda h17 y1ea ff3 fs5 fc0 sc0 ls0 ws0">i</div><div class="t m0 x65 h18 y1eb ff2 fs12 fc0 sc0 ls0 ws0">d</div><div class="t m0 xdb h17 y1ec ff3 fs5 fc0 sc0 ls0 ws0">i</div><div class="t m0 x56 h18 y1ed ff2 fs12 fc0 sc0 ls0 ws0">q</div><div class="t m0 xdc h1a y1ee ffb fs5 fc0 sc0 ls0 ws0"></div><div class="t m0 xb3 h8 y1ef ff2 fs5 fc0 sc0 ls7 ws0">(15)</div><div class="t m0 x4b h1e y1f0 ff9 fs5 fc0 sc0 ls0 ws0">ω</div><div class="t m0 xd4 h18 y1f1 ff2 fs12 fc0 sc0 ls0 ws0">e</div><div class="t m0 xd5 h19 y1f2 ffa fs13 fc0 sc0 ls0 ws0">=</div><div class="t m0 x16 h17 y1f3 ff3 fs5 fc0 sc0 ls0 ws0">P</div><div class="t m0 x18 h8 y1f4 ff2 fs5 fc0 sc0 ls0 ws0">2</div><div class="t m0 x98 h1e y1f5 ff9 fs5 fc0 sc0 ls0 ws0">ω</div><div class="t m0 xad h18 y1f6 ff2 fs12 fc0 sc0 ls0 ws0">s</div><div class="t m0 xbe h8 y1f7 ff2 fs5 fc0 sc0 ls7 ws0">, (16)</div><div class="t m0 x7 h17 y1f8 ff2 fs5 fc0 sc0 lsf ws0">where P</div><div class="t m0 xdd h19 y1f9 ffa fs13 fc0 sc0 ls0 ws0">[</div><div class="t m0 xde h1d y1fa ffc fs13 fc0 sc0 ls0 ws0">−</div><div class="t m0 x94 h19 y1f9 ffa fs13 fc0 sc0 ls0 ws0">]</div><div class="t m0 xd0 h8 y1fb ff2 fs5 fc0 sc0 ls6c ws0">Number of poles</div><div class="t m0 x6 h9 y1fc ff1 fs6 fc0 sc0 ls6d ws0">2.6 Inverter</div><div class="t m0 x6 h8 y1fd ff2 fs5 fc0 sc0 ls67 ws0">A circuit diagram of the inverter can be seen in Fig. 3. The inverter transmits power between</div><div class="t m0 x6 h17 y1fe ff2 fs5 fc0 sc0 lse ws0">the electric machine (with phase voltages v</div><div class="t m0 x31 h18 y1ff ff2 fs12 fc0 sc0 ls0 ws0">A</div><div class="t m0 xdf h17 y200 ff2 fs5 fc0 sc0 ls0 ws0">, v</div><div class="t m0 x15 h18 y1ff ff2 fs12 fc0 sc0 ls0 ws0">B</div><div class="t m0 xd7 h17 y200 ff2 fs5 fc0 sc0 ls6e ws0">,andv</div><div class="t m0 x52 h18 y1ff ff2 fs12 fc0 sc0 ls0 ws0">C</div><div class="t m0 x2f h8 y200 ff2 fs5 fc0 sc0 lsc ws0">) and the battery by turning on and</div><div class="t m0 x6 h17 y201 ff2 fs5 fc0 sc0 ls6f ws0">off the switches Q</div><div class="t m0 xc6 h18 y202 ff2 fs12 fc0 sc0 ls70 ws0">A+</div><div class="t m0 xc2 h17 y203 ff2 fs5 fc0 sc0 ls0 ws0">, Q</div><div class="t m0 x48 h18 y202 ff2 fs12 fc0 sc0 ls70 ws0">A-</div><div class="t m0 x44 h17 y203 ff2 fs5 fc0 sc0 ls0 ws0">, Q</div><div class="t m0 xe0 h18 y202 ff2 fs12 fc0 sc0 ls43 ws0">B+</div><div class="t m0 x72 h17 y203 ff2 fs5 fc0 sc0 ls0 ws0">, Q</div><div class="t m0 x6e h18 y202 ff2 fs12 fc0 sc0 ls43 ws0">B-</div><div class="t m0 x17 h17 y203 ff2 fs5 fc0 sc0 ls0 ws0">, Q</div><div class="t m0 xad h18 y202 ff2 fs12 fc0 sc0 ls71 ws0">C+</div><div class="t m0 x3e h17 y203 ff2 fs5 fc0 sc0 ls72 ws0">,andQ</div><div class="t m0 xd7 h18 y202 ff2 fs12 fc0 sc0 ls71 ws0">C-</div><div class="t m0 x33 h17 y203 ff2 fs5 fc0 sc0 lsf ws0">. The switches has an on-resistance R</div><div class="t m0 xe1 h18 y202 ff2 fs12 fc0 sc0 ls73 ws0">Q,Inv</div><div class="t m0 xe2 h8 y203 ff2 fs5 fc0 sc0 ls0 ws0">.</div><div class="t m0 x6 h8 y204 ff2 fs5 fc0 sc0 ls6 ws0">The diodes in parallel of each switch are creating a path for the motor currents during the</div><div class="t m0 x6 h8 y205 ff2 fs5 fc0 sc0 lsf ws0">deadtime, i.e., the time where both switches in one branch are non-conducting in order to</div><div class="t m0 x6 h8 y206 ff2 fs5 fc0 sc0 lsa ws0">avoid a shoot-through.</div><div class="t m0 x6 h17 y207 ff2 fs5 fc0 sc0 ls74 ws0">The average power losses of one switch p</div><div class="t m0 xaf h18 y208 ff2 fs12 fc0 sc0 ls73 ws0">Q,Inv</div><div class="t m0 x63 h17 y209 ff2 fs5 fc0 sc0 ls53 ws0">and diode p</div><div class="t m0 xe3 h18 y208 ff2 fs12 fc0 sc0 ls42 ws0">D,Inv</div><div class="t m0 xe4 h8 y209 ff2 fs5 fc0 sc0 ls50 ws0">in Fig. 3 during one</div><div class="t m0 x6 h8 y20a ff2 fs5 fc0 sc0 lsf ws0">fundamental period are (Casanellas, 1994):</div><div class="t m0 xe5 h17 y20b ff3 fs5 fc0 sc0 ls0 ws0">p</div><div class="t m0 x40 h18 y20c ff2 fs12 fc0 sc0 ls75 ws0">Q,Inv</div><div class="t m0 xc2 h19 y20d ffa fs13 fc0 sc0 ls0 ws0">=</div><div class="t m0 x48 h1a y20e ffb fs5 fc0 sc0 ls0 ws0"></div><div class="t m0 x44 h8 y20f ff2 fs5 fc0 sc0 ls0 ws0">1</div><div class="t m0 x44 h8 y210 ff2 fs5 fc0 sc0 ls0 ws0">8</div><div class="t m0 x1c h19 y211 ffa fs13 fc0 sc0 ls0 ws0">+</div><div class="t m0 x6d h17 y212 ff3 fs5 fc0 sc0 ls0 ws0">m</div><div class="t m0 x5c h18 y213 ff2 fs12 fc0 sc0 ls0 ws0">i</div><div class="t m0 x1d h8 y210 ff2 fs5 fc0 sc0 ls0 ws0">3π</div><div class="t m0 xe6 h1a y214 ffb fs5 fc0 sc0 ls0 ws0"></div><div class="t m0 x16 h17 y215 ff3 fs5 fc0 sc0 ls0 ws0">R</div><div class="t m0 x4d h18 y216 ff2 fs12 fc0 sc0 ls73 ws0">Q,Inv</div><div class="t m0 xe7 h8 y217 ff2 fs5 fc0 sc0 ls0 ws0">ˆ</div><div class="t m0 x5e h17 y218 ff3 fs5 fc0 sc0 ls0 ws0">I</div><div class="t m0 xe8 h18 y219 ff2 fs12 fc0 sc0 ls0 ws0">2</div><div class="t m0 xe9 h18 y21a ff2 fs12 fc0 sc0 ls0 ws0">p</div><div class="t m0 xb4 h19 y21b ffa fs13 fc0 sc0 ls0 ws0">+</div><div class="t m0 x61 h1a y21c ffb fs5 fc0 sc0 ls0 ws0"></div><div class="t m0 xcb h8 y21d ff2 fs5 fc0 sc0 ls0 ws0">1</div><div class="t m0 x8a h8 y210 ff2 fs5 fc0 sc0 ls0 ws0">2π</div><div class="t m0 x63 h19 y211 ffa fs13 fc0 sc0 ls0 ws0">+</div><div class="t m0 xea h17 y212 ff3 fs5 fc0 sc0 ls0 ws0">m</div><div class="t m0 xeb h18 y213 ff2 fs12 fc0 sc0 ls0 ws0">i</div><div class="t m0 x69 h8 y210 ff2 fs5 fc0 sc0 ls0 ws0">8</div><div class="t m0 xb9 h8 y21e ff2 fs5 fc0 sc0 ls3f ws0">cos</div><div class="t m0 xec h19 y21f ffa fs13 fc0 sc0 ls0 ws0">(φ</div><div class="t m0 xdc h18 y220 ff2 fs12 fc0 sc0 ls43 ws0">EM</div><div class="t m0 xed h19 y21f ffa fs13 fc0 sc0 ls0 ws0">)</div><div class="t m0 x12 h1a y221 ffb fs5 fc0 sc0 ls0 ws0"></div><div class="t m0 x5b h17 y222 ff3 fs5 fc0 sc0 ls0 ws0">V</div><div class="t m0 xee h18 y223 ff2 fs12 fc0 sc0 ls76 ws0">Q,th,Inv</div><div class="t m0 x58 h8 y224 ff2 fs5 fc0 sc0 ls0 ws0">ˆ</div><div class="t m0 x58 h17 y225 ff3 fs5 fc0 sc0 ls0 ws0">I</div><div class="t m0 xef h18 y226 ff2 fs12 fc0 sc0 ls0 ws0">p</div><div class="t m0 xb3 h8 y227 ff2 fs5 fc0 sc0 ls7 ws0">(17)</div><div class="t m0 xe5 h17 y228 ff3 fs5 fc0 sc0 ls0 ws0">p</div><div class="t m0 x40 h18 y229 ff2 fs12 fc0 sc0 ls42 ws0">D,Inv</div><div class="t m0 xc2 h19 y22a ffa fs13 fc0 sc0 ls0 ws0">=</div><div class="t m0 x48 h1a y22b ffb fs5 fc0 sc0 ls0 ws0"></div><div class="t m0 x44 h8 y22c ff2 fs5 fc0 sc0 ls0 ws0">1</div><div class="t m0 x44 h8 y22d ff2 fs5 fc0 sc0 ls0 ws0">8</div><div class="t m0 x1c h1d y22e ffc fs13 fc0 sc0 ls0 ws0">−</div><div class="t m0 x6d h17 y22f ff3 fs5 fc0 sc0 ls0 ws0">m</div><div class="t m0 x5c h18 y230 ff2 fs12 fc0 sc0 ls0 ws0">i</div><div class="t m0 x1d h8 y22d ff2 fs5 fc0 sc0 ls0 ws0">3π</div><div class="t m0 xe6 h1a y231 ffb fs5 fc0 sc0 ls0 ws0"></div><div class="t m0 x16 h17 y232 ff3 fs5 fc0 sc0 ls0 ws0">R</div><div class="t m0 x4d h18 y233 ff2 fs12 fc0 sc0 ls42 ws0">D,Inv</div><div class="t m0 xe7 h8 y234 ff2 fs5 fc0 sc0 ls0 ws0">ˆ</div><div class="t m0 x5e h17 y235 ff3 fs5 fc0 sc0 ls0 ws0">I</div><div class="t m0 xe9 h18 y236 ff2 fs12 fc0 sc0 ls0 ws0">2</div><div class="t m0 xe9 h18 y237 ff2 fs12 fc0 sc0 ls0 ws0">p</div><div class="t m0 xb4 h19 y238 ffa fs13 fc0 sc0 ls0 ws0">+</div><div class="t m0 x61 h1a y239 ffb fs5 fc0 sc0 ls0 ws0"></div><div class="t m0 xcb h8 y23a ff2 fs5 fc0 sc0 ls0 ws0">1</div><div class="t m0 x8a h8 y22d ff2 fs5 fc0 sc0 ls0 ws0">2π</div><div class="t m0 x63 h1d y22e ffc fs13 fc0 sc0 ls0 ws0">−</div><div class="t m0 xea h17 y22f ff3 fs5 fc0 sc0 ls0 ws0">m</div><div class="t m0 xeb h18 y230 ff2 fs12 fc0 sc0 ls0 ws0">i</div><div class="t m0 x69 h8 y22d ff2 fs5 fc0 sc0 ls0 ws0">8</div><div class="t m0 xb9 h8 y23b ff2 fs5 fc0 sc0 ls3f ws0">cos</div><div class="t m0 xec h19 y23c ffa fs13 fc0 sc0 ls0 ws0">(φ</div><div class="t m0 xdc h18 y23d ff2 fs12 fc0 sc0 ls43 ws0">EM</div><div class="t m0 xed h19 y23c ffa fs13 fc0 sc0 ls0 ws0">)</div><div class="t m0 x12 h1a y23e ffb fs5 fc0 sc0 ls0 ws0"></div><div class="t m0 x5b h17 y23f ff3 fs5 fc0 sc0 ls0 ws0">V</div><div class="t m0 xee h18 y240 ff2 fs12 fc0 sc0 ls77 ws0">D,th,Inv</div><div class="t m0 x58 h8 y241 ff2 fs5 fc0 sc0 ls0 ws0">ˆ</div><div class="t m0 xf0 h17 y242 ff3 fs5 fc0 sc0 ls0 ws0">I</div><div class="t m0 xef h18 y243 ff2 fs12 fc0 sc0 ls0 ws0">p</div><div class="t m0 xb3 h8 y244 ff2 fs5 fc0 sc0 ls7 ws0">(18)</div><div class="t m0 x42 h17 y245 ff3 fs5 fc0 sc0 ls0 ws0">m</div><div class="t m0 xc7 h18 y246 ff2 fs12 fc0 sc0 ls0 ws0">i</div><div class="t m0 xc2 h19 y247 ffa fs13 fc0 sc0 ls0 ws0">=</div><div class="t m0 x48 h8 y248 ff2 fs5 fc0 sc0 ls0 ws0">2</div><div class="t m0 xf1 h8 y249 ff2 fs5 fc0 sc0 ls0 ws0">ˆ</div><div class="t m0 x4a h17 y248 ff3 fs5 fc0 sc0 ls0 ws0">V</div><div class="t m0 x6c h18 y24a ff2 fs12 fc0 sc0 ls0 ws0">p</div><div class="t m0 x20 h17 y24b ff3 fs5 fc0 sc0 ls0 ws0">V</div><div class="t m0 x4a h18 y24c ff2 fs12 fc0 sc0 ls78 ws0">Bat</div><div class="t m0 x37 h8 y24d ff2 fs5 fc0 sc0 ls7 ws0">, (19)</div><div class="t m0 x84 h16 y82 ff6 fs11 fc1 sc0 ls0 ws0">5</div><div class="t m0 x6 hb y113 ff6 fs8 fc1 sc0 ls0 ws0">Electrical Vehicle Design and Modeling</div></div><div class="t m0 x7 hb y28 ff5 fs8 fc2 sc0 ls0 ws0">www.intechopen.com</div></div><div class="pi" data-data='{"ctm":[1.992156,0.000000,0.000000,1.992156,0.000000,0.000000]}'></div></div>