# Novel-efficient-rule-based-controller-for-electric-vehicles-switch-mode-battery-charger

Battery Charging Power Electronics Converter and Control for Plug-in Hybrid Electric Vehicle Sharanya Jaganathan, Wenzhong Gao Electrical and Computer Engineering Department Tennessee Technological University Cookeville, Tennessee sjaganath21@tnetch.edu , wgao@tntech.edu Abstract— Plug-in hybrid electric vehicles are gaining popularity because of the environmental consideration “Go green” factor. In this paper a battery charging system based on a three level ac-dc converter and bidirectional dc-dc converter has been proposed and associated control strategy for the battery charging/discharging has been presented. It has been shown that with direct duty cycle calculation technique that unity power factor is achieved and total harmonic distortion is minimized. The simulation has been performed using simulink. The plots are presented to show the battery charging/discharging and the converter characteristics. Keywords- Plug-in hybrid electric vehicle, three level neutral point clamped converter, unity power factor, battery control strategy. I. INTRODUCTION With the increase in demand for environment-friendly automobile, plug-in hybrid electric vehicle (PHEV) becomes a preferred choice as automotive industries are focusing on hybrid electric vehicle (HEV) and electric vehicle (EV) development. A plug-in hybrid electric vehicle can be defined as any hybrid electric vehicle which contains: a higher capacity of battery storage system used for powering the vehicle and a battery charger for recharging the battery system from an external outlet and has an ability to drive in all-electric range without consuming gasoline [1]. The conversion from hybrid electric vehicle to plug-in hybrid electric vehicle can be done by adding a high energy density battery pack in order to extend the all-electric-range (AER). The main challenge for PHEVs is the battery, but compared to pure EVs, battery size and cost issues are much less pronounced. The battery requirements are determined by the energy needed for the desired AER. The battery pack of PHEV must be able to store energy from external charging as well as from regenerative braking and preferably be able to supply stored energy back to the utility if necessary. PHEV requires an AC outlet charging system for charging the battery. AC-DC converters are used in a number of applications such as power supply, household electric appliances, battery charger, etc. Depending on the switching frequency they are classified as converters with low switching frequency and those with high switching frequency [2]. Conventional uncontrolled rectifiers and line commutated phase controlled rectifiers so far have dominated the AC to DC power conversion. Such converters have inherent drawbacks such as harmonics in the input current and output voltage; low input power factor especially at low output voltage since these conventional rectifiers draw non-sinusoidal currents from the grid [3]. Since power devices demand reactive power in addition to active power, a charger with low power factor increases burden on the utility system. On the other hand, harmonics have a negative effect in the operation of the electrical system and therefore, an increasing attention is paid to their mitigation and control. The problems due to harmonics in conventional rectifiers have resulted in the establishment of standards such as IEC 61000-3-2 [4]. Thus, a PHEV battery charger with a Power Factor Correction (PFC) based AC-DC converter is desirable. Voltage source converter or synchronous link converter is the best solution under such situation, which has both rectification and regeneration capability [5]. The input current in these converters flows through the inductor which can be wave shaped with appropriate current mode control. These converters have high efficiency and inherent power quality improvement at the ac input and dc output. In this paper a three level ac-dc converter and bidirectional dc- dc converter have been implemented for a PHEV battery charger. In Fig. 1 the block diagram of the battery charger is shown. A three level neutral point clamped (NPC) converter and dc- dc converter topology have been explained in section II. In the section III PI controller design for maintaining the dc link voltage and PI controller design for the current control have been described. In section IV pulse charging technique for battery has been described. In section V direct duty cycle calculation method and bidirectional nature of the charger has been illustrated with simulation results. Conclusion section describes the advantages of the proposed PHEV charging system and the future work. Figure 1. Block diagram of battery charger for plug-in hybrid electric vehicle 978-1-4244-2601-0/09/$25.00 ©2009 IEEE 440Authorized licensed use limited to: University of Electronic Science and Tech of China. Downloaded on January 28, 2010 at 02:08 from IEEE Xplore. Restrictions apply. II. THREE LEVEL NPC CONVERTER Multilevel converters have gained attention in the recent years. Of the many topologies of multilevel converters, the most popular topology used is the three level diode clamped converter also known as neutral point clamped (NPC) voltage source converter, topology as the serial power switch connection reduces the device voltage stress. The three level NPC voltage source converter is also known as diode clamped converter. This topology results in three level line voltages which reduces the input current harmonics. In this paper single phase three level NPC topology and simple topology of dc-dc converter has been considered for design of the PHEV battery charger. A. AC-DC converter One of the many advantages of using a multilevel converter as compared to two level converter is that they have lower dtdv per switching. In a three-level converter there are two additional diodes per phase leg. The three level diode clamped converter has two capacitors (Cd1and Cd2) in series with a center tap at O as shown in Fig. 2. Each phase of the three level converter has two pair of switching device ()6521, SSSS and ()8743, SSSS in series. The center of each pair is clamped to the neutral of the center-tapped capacitor through clamping diodes (D1, D2, D3 and D4). In phase sinusoidal Pulse Width Modulation (IPSPWM) technique has been used for three-level converter [6]. Figure 2. Single phase three level NPC converter. B. DC-DC converter The bidirectional dc-dc converter shown in Fig. 3 is used for the battery charging topology [7]. There are two switches S1 and S2 and two diodes D1 and D2. When the battery is charged by the dc-dc converter, switch S1and diode D2conduct current alternately. The inductor current ILis positive in this case. When the battery is being discharged switch S2 and D1 conduct current alternately. During this time the inductor current IL is negative. Figure 3. Bidirectional DC-DC converter. The model equations of the system are derived below. During the system equations when state switch S1 is on and S2 is switched off, based on Kirchhoff’s laws: cccdcrIVV += (1) LdccIICpV −= (2) wheredtdp = LcdcIII += (3) LbattLbattcccLpIRIVrIV ++=+ (4) Equation (4) can be written as: battLbattcccLRIVrIVLpI −−+= (5) The equations (1), (2) and (3) can be rearranged as: CrVVpVCcdcc−= (6) Equations (1), (3) and (5) can be rearranged as: ()battLbattdcLRIVVLpI −−=1(7) During off state when S1 off and S2 is on the equations for the converter is given by: cccdcrIVV += (8) dccICpV = (9) wheredtdp = cdcII = (10) LbattLbattLpIRIV ++=0 (11) The equations (8), (9) & (10) can be rearranged as: CrVVpVCcdcc−= (12) Equation (11) can be arranged as: 441Authorized licensed use limited to: University of Electronic Science and Tech of China. Downloaded on January 28, 2010 at 02:08 from IEEE Xplore. Restrictions apply. ()battLbattLRIVLpI −−=1(13) III. CONVERTER CONTROLLER DESIGN This section focuses on the PI controller design of ac- dc converter and dc-dc converter. The ac-dc converter is connected to dc-dc converter whose output is connected to the battery such that it charges the battery when the state of charge of the battery goes below 85%. The dc-link voltage of the ac- dc converter is maintained at 500V. The primary objective is to regulate the dc bus voltage within a narrow band thus proportional integral (PI) controller is the obvious design as the voltage control loop need not be very fast in response. Fig. 4 shows the schematic of the voltage control design. Linear controller has been designed in the following section, which explains the choice of the values of Kpand Ki. Also in the later part of this section the PI controller for dc-dc converter is also designed with explanation of the choice of values of Kpand Kifor pulse charging technique. Figure 4. Control strategy for dc link volatge. Finally, complete content and organizational editing before formatting. Please take note of the following items when proofreading spelling and grammar: A. Linear controller design for ac-dc converter The model equations of the converter and the switching function for the three level NPC converter can be found in [8]. The dc side current of the converter in terms of the switching function can be written as follows: acacdiSSiSSi65211−= (14) acacdiSSiSSi87432−= (15) The average output power must be equal to the average input power according to the law of conservation of energy. Also it is assumed that voltage across the two capacitors is balanced. The power balance equation for the converter can be written as follows which are derived from the model equations: ()LcaccdRViSSSSdtdVC1652111−−= (16) where RLis the resistive load. Multiplying both the sides of equation (16) by 2dcVwe get: ()⎟⎟⎠⎞⎜⎜⎝⎛×−−×=×⎟⎠⎞⎜⎝⎛LcdcacdcdccdRVViSSSSVVdtdVC1652111222(17) The term ()acdciSSSSV65212−× is nothing but output power equation and as per the law of conversation of energy the output power term can be replaced by the input power term. Thus equation (17) changes to the following equation: ()⎟⎟⎠⎞⎜⎜⎝⎛×−+−=×⎟⎠⎞⎜⎝⎛ ∗∗LcdcacacacdccdRVViVRiVdtdVC121122(18) where the term ()∗∗+−acacaciVRi2is the power equation P. ∗refers to the reference term and Z is the impedance of the load connected to the converter. Neglecting the loss term ()( )Riac2∗as R is very low, from equation (18) we get: ⎟⎟⎠⎞⎜⎜⎝⎛⎟⎟⎠⎞⎜⎜⎝⎛×−×=⎟⎟⎟⎟⎠⎞⎜⎜⎜⎜⎝⎛⎟⎠⎞⎜⎝⎛∗LcdcacacdcdcdRVViVVdtVdC11222(19) Let dtdp = ()LdcdcddcdcRVpVCVVK +=−∗1(20) where K is the compensator used for the system. In this case K is a PI compensator. ⎟⎠⎞⎜⎝⎛++=∗KZpCVKVddcdc11(21) The transfer function of a PI controller is given by equation (22), thus K can be written as function of Kpof and KisKKsGipc+=)( (22) addcdcZKsCKVV11++=∗(23) aipdipZsKsKsCKsK++++=21(24) Equation (24) can be expressed as a 2ndorder Butterworth (filter) equation. 0222=++nnss ωξω (25) Where nω is the natural frequency in radians/sec. ξ (damping factor) to be chosen is 0.5 for a critically damped system. The values of Kpand Ki- 0.05 and 5.5 respectively are found by the following equation: 442Authorized licensed use limited to: University of Electronic Science and Tech of China. Downloaded on January 28, 2010 at 02:08 from IEEE Xplore. Restrictions apply. 21ndiCKω= (26) ξ21111didpCKCZK =⎟⎟⎠⎞⎜⎜⎝⎛+ (27) Accordingly design parameter is found out using bode plot and root locus. Fig. 5 shows the bode plot of the system. In general a linear time invariant (LTI) system is said to be stable if the Gain margin (GM) and Phase margin are positive. The stability of the system is decided by the phase margin. It can be seen from the figure a stable design bode plot of the system with a phase margin of 110 degree. Also the results are confirmed using the root locus which is shown in Fig. 6. For a system to be stable the poles of the system should lie on the left hand side of the plane. As seen from the figure the poles lie on the left hand side of -500 making the system stable. Apart from maintaining the dc-link voltage, the unity power factor is also maintained at the grid side of the converter which is shown in the later section. Figure 5. Bode plot of the system (stability study). Figure 6. Root locusof the system (stability study). B. DC-DC converter controller design The dc-dc converter design has been described in this part. Referring to the model equations in the section II the state space f the two subsystems can be written as follows. The state space equation in the matrix form for the converter during on state is given by: ⎥⎦⎤⎢⎣⎡⎥⎥⎥⎦⎤⎢⎢⎢⎣⎡+⎥⎦⎤⎢⎣⎡⎥⎥⎥⎦⎤⎢⎢⎢⎣⎡−−=⎥⎦⎤⎢⎣⎡battdcccLcbattcLcVVLLrCrIVLRCrpIpV1101001(28) The state space equation in the matrix form for the converter during off state is given by: ⎥⎦⎤⎢⎣⎡⎥⎥⎦⎤⎢⎢⎣⎡+⎥⎦⎤⎢⎣⎡⎥⎥⎥⎦⎤⎢⎢⎢⎣⎡−−=⎥⎦⎤⎢⎣⎡battdccLcbattcLcVVLCrIVLRCrpIpV1001001(29) Combining the two subsystems the averaged state space equation can be written as: battdceVbVAxX ++=•)1(21dAdAA −+= )1(21dbdbB −+= ()dedeE −+= 121Where ⎥⎥⎥⎦⎤⎢⎢⎢⎣⎡−−= dLRCrdAbattc0011()⎥⎥⎥⎦⎤⎢⎢⎢⎣⎡−−−−=LRdCrdAbattc1001)1(2⎥⎥⎥⎦⎤⎢⎢⎢⎣⎡=LrdCrdbcc111()⎥⎥⎦⎤⎢⎢⎣⎡−=0112Crdb c⎥⎥⎦⎤⎢⎢⎣⎡=Lde101()⎥⎥⎦⎤⎢⎢⎣⎡−=Lde1102The state space equation for the output can be written as: DuCxY += )1(21dCdCC −+= )1(21dDdDD −+= Where d is the duty cycle and the matrices are given by: ⎥⎦⎤⎢⎣⎡=01101C ⎥⎦⎤⎢⎣⎡=01102C []TD 0,01= []TD 0,02= 443Authorized licensed use limited to: University of Electronic Science and Tech of China. Downloaded on January 28, 2010 at 02:08 from IEEE Xplore. Restrictions apply. The input to output transfer function can be written as: []avavavavDBAsICsusy+−=−1)(~)(~(30) where )(~sy is the output and )(~su is the input in Laplace form. Also the averaged matrices are given by: ⎥⎦⎤⎢⎣⎡=0110avC ⎥⎥⎥⎦⎤⎢⎢⎢⎣⎡−−=LRCrAbattcav001⎥⎥⎥⎦⎤⎢⎢⎢⎣⎡=LLrdCrBccav1101⎥⎦⎤⎢⎣⎡=00avD The final input to output transfer function can be written as: 8346.0102108.84574.0326+∗+∗=−−ssTF (31) Proportional- integral compensator is a special phase lag compensator used for ensuring good stability margin. To ensure good stability margin the desired phase margin is chosen between °−° 7545 . This is to ensure that in root locus no poles enter the right half of the complex plane. The transfer function of PI controller is given by: sKKsGIpc+=)( (32) Following the steps of PI compensator design the bode plot and the step response of the compensated and uncompensated system is plotted in Matlab. From Fig. 7 it can be seen that the uncompensated system has an infinite phase margin and it is desired that the system has good steady state performance and achieves the desired phase margin of 60 degree. The thick line waveform refers to the uncompensated system while the dashed line refers to compensated system wherein the desired phase margin of 60 degrees is achieved at gain crossover