Energy Management Control Of Plug-in Hybrid Electric .
IEEE TRANSACTIONS ON INTELLIGENT TRANSPORTATION SYSTEMS, VOL. XX, NO. X, XX1Energy Management Control of Plug-in HybridElectric Vehicle using Hybrid Dynamical SystemsHarpreetsingh Banvait, Student Member, IEEE, Jianghai Hu, Member, IEEE, andYaobin Chen, Senior Member, IEEEAbstract—This paper presents a supervisory energy management control system design of power-split Plug-in HybridElectric Vehicles (PHEV). The power-split PHEV operates invarious discrete operating modes. The dynamics of the systemare continuous within each of these discrete modes. This powersplit PHEV system consisting of discrete operational modesand continuous dynamics can be modelled using the hybriddynamical system framework. In this paper, the vehicle andpowertrain dynamics of power-split PHEV are introduced. Usingthese dynamics, a hybrid system model of the PHEV is proposed,and a nonlinear constrained energy minimization problem issolved using the dynamic programming approach. Furthermore,sub-optimal strategies for the energy minimization problem areobtained using model predictive hybrid control method. Simulation results show that, compared to the dynamic programmingapproach, the model predictive hybrid control provides good suboptimal results and can be implemented in real-time.Index Terms—PHEV, MPC, Dynamic Programming, Hybridsystem. Non-linear.N �RwmFresisa0 , a1 , a2ρQMoment of inertia of engine and carrier gear.Moment of inertia of ring gear.Moment of inertia of generator and sun geargear.Engine speedRing gear speedSun gear speedEngine torqueGenerator torqueMotor torqueSun gear torqueRing gear torqueDrivetrain from drive shaft to wheelsPlanetary gear ratioNumber of teeth on sun gearNumber of teeth on ring gearVehicle speedEffective wheel radiusMass of vehicleResistive forces acting on vehicleResistive co-efficientsState of charge of batterySet of discrete statesH. Banvait and Y. Chen is with is with the Department of Electrical andComputer Engineering, Purdue School of Engineering and Technology, IUPUI(e-mail: {hbanvait, ychen}@iupui.edu)J. Hu is with the School of Electrical and Computer Engineering, PurdueUniversity, West Lafayette, IN 47907 USA (email: jianghai@purdue.edu).XSet of continuous statesVSet of discrete inputsDomDomain of modefContinuous dynamicsESet of EventsGSet of guard conditionsRSet of resetsInitSet of initial statesEVElectric vehicle modeRegenRegenerative Braking modeHybridHybrid vehicle modeBatterychg Battery charging modeωeidleEngine idle speedMaximum engine speedωemaxVocOpen circuit voltage of batteryPbatPower used from batteryRintInternal resistance of batteryCMaximum capacity of batteryIBattery CurrentηmMotor efficiencyηgGenerator efficiencyηeEngine efficiencyVkValue function at time kσModeI. I NTRODUCTIONIN today’s world air pollution and dependence on fossil fuelhave become huge problems. United States accounts for22.6 % of the total oil consumption in the world and 42% ofpetroleum used in the US comes from foreign countries. In theUS, 69% of the petroleum is used for transportation and the UStransportation sector is heavily dependent on petroleum: 96%of total energy use in transportation comes from petroleum.Moreover, harmful gases like CO and CO2 are emitted fromtransportation applications which accounts for 42% of airpollution in the US (96% of which comes from petroleum).Thus, reducing the petroleum usage for transportation purposescan reduce the depletion of fossil fuels, air pollution andreliance on external resources significantly.One way to reduce the dependence on conventional sourcesof energy in transportation is by deploying Electric Vehicles(EVs) whose electrical energy is obtained from renewableenergy sources. Due to technological limitations in batterytechnology, the development of EVs is confined. Hybridelectric vehicles, which use both internal combustion engineand battery as two different power sources, have been in the
IEEE TRANSACTIONS ON INTELLIGENT TRANSPORTATION SYSTEMS, VOL. XX, NO. X, XX150323212081510503620010250300Engine speed (rad/sec)10350400450Engine Torque (Nm)Fig. 1. Engine efficiency map contour.Energy management system can be designed as rule-basedstrategies using heuristic knowledge. They are easy to implement and have been researched vastly. In [3], a rule basedalgorithm was used to solve the fuel minimization problem.[4] proposed a rule-based control strategy for a parallel PHEVbus model which showed better performance and higher engineefficiency. Sharer et al. compared EV and charge depletionstrategy option using PSAT for different control strategies ofpower split HEVs [5]. Similarly, in [6] Gao et al. presented9085908085708590859093909370808590Motor Torque (Nm)85 1009090 200 400 600 400 2007080 3000Motor speed 53560 3340353610090373536802007080858537050122365380321 353410030090Engine Efficiency map120Motor efficiency map40090market since late 1990s. Next step towards the transistion toEVs is Plug-in Hybrid Electric Vehicles (PHEVs), where thebattery is the major power source as compared to the internalcombustion engine.In PHEVs both energy sources, a small onboard engine anda bigger battery pack, provide energy to drive the vehicle. Thebigger battery pack cannot be charged from onboard internalcombustion engine and must be charged from external powersupply. Fig. 1 and Fig. 2 show the maximum torque curveand the efficiency countours of a typical engine and a motor,respectively. It can be seen from the figures that at high speedsthe overall efficiency of the engine is low (at 20-22%) but itcan produce large torque. The motor can produce very hightorque at low speeds with very high efficiency around 85-90%;the Li-ion batteries and the motor combined have 80-90%efficiency. Battery and motor are highly efficient but motorcan provide torque only at low speeds whereas engine can beefficient for high power demands. Using these two differentenergy sources together, an energy efficient vehicle can bedesigned. Hence, it has been of interest to researchers. In [1],Karbowski investigated a control strategy for pre-transmissionparallel PHEVs using a global optimization technique basedon the Bellman principle, with the main objective of increasingefficiency by reducing losses.Additionally, the fuel economy of the vehicle can be improved by selecting optimal sizing of key vehicle drivingcomponents like motor, battery and engine. In [2], Baumannused a fuzzy logic controller for the nonlinear controller,presented system integration and component sizing techniquesof the HEV, and simulated the system design and controlstrategy in an actual vehicle.2200400600Fig. 2. Motor efficiency map contour.various rule-based strategies for PHEV passenger cars andanalyzed them in terms of fuel consumption. These rule-basedenergy management systems can be optimized by tuning itsparameters. [7] did a parameteric optimization to optimizethe control parameters using the Divided Rectangles (so-calledDIRECT) method. They also analyzed the impact of distancetravelled by PHEVs with these parameters. Similarly, Wu [8]employed a control parameter optimization for parallel PHEVusing unconstrained PSO, with the target objective of theproblem being the fuel economy along with the performance.Design of energy management system of Power-split drivetrain PHEV requires a detailed Vehicle model. In [9] Cao et al.validated the PSAT model for the Toyota Prius PHEV whichis a Power-split drivetrain; implemented control strategies toreduce the ON/OFF frequency of the engine by tuning someparameters, and also made the engine to operate in moreefficient regions in the charge depletion (CD) state. Similarly,In [10], a detailed model of power-split HEVs was presentedand the model was validated with test data. But in these vehiclemodels, discrete mode transitions were discarded and onlycontinuous system models were considered.Optimal Energy management system can be designed usingdynamic programming. Several authors have used dynamicprogramming to design such system. [11] used a neuralnetwork to detect highway on/off ramps patterns throughtraining from data sets. In [12] Moura et al. used a stochasticdynamic programming (DP) technique to obtain the optimalpower management of a power split PHEV, implemented it forboth blended fuel use strategy and charge depletion/chargesustaining modes, and studied the impact of battery size onthese control strategies. His results showed that the blendingstrategy is significantly better for smaller batteries but its effectdiminishes for large batteries. [13] used dynamic programmingto get optimum energy distribution for certain drive cycles.Here the DP was implemented in the spatial domain while thedrive cycle was approximated which showed that the time forthe DP calculations can be reduced to get suboptimal results.Gong et al. Liu [14] obtained the vehicle dynamics for powersplit HEV and designed energy management using stochasticdynamic programming and ECMS strategy and compared
IEEE TRANSACTIONS ON INTELLIGENT TRANSPORTATION SYSTEMS, VOL. XX, NO. X, XXthe results with those using dynamic programming. Additionally, Energy management system can be designed usingother optimal theories. In [15] Stockar designed a supervisoryenergy manager by applying Pontryagin’s minimum principleto minimize the overall carbon dioxide emissions. Borhan[16] employed model predictive control strategy to designa power management system of power-split HEVs. Musardo[17] designed a real-time Adaptive Equivalent ConsumptionMinimization Strategy (A-ECMS) for energy managementsystem of HEV, whereas in [18] a Particle Swarm Optimization(PSO) based solution is proposed.The optimal energy management system cannot always beapplied in real-time. Hence, several authors have proposedsub-optimal energy mangement systems. Xiao [19] also usedPSO to obtain optimal solutions and subsequently used Artifical Neural Network (ANNs) to produce sub-optimal results. In [20] Mohebbi et al. showed that a neural networkbased adaptive control method can be used for controllingPHEVs. This leads to an online controller that can maximizethe output torque of the engine while minimizing the fuelconsumption. [21] used artificial neural networks and fuzzylogic to implement a load leveling strategy for intelligentcontrol of a parallel HEV powertrain. [22] developed andtested a highly efficient energy management system for HEVswith ultracapacitors using neural networks. They first obtainedan optimal control model and then obtained its numericalsolution. Gong [23] used dynamic programming along withintelligent transport system GPS, Geographical InformationSystem (GIS) and advanced traffic flow modeling technique toobtain an optimized power management strategy for a parallelPHEV. Moreno et al.In PHEVs, the vehicle operates in various modes such asthe EV mode, the Battery charging mode, the Regenerativemode, etc. In each of these modes, the vehicle dynamics isdifferent. Furthermore, the inputs of engine and motor in thesemodes are also different. Such a system which consists ofboth discrete and continuous states can be modelled by hybriddynamical systems. Yuan [24] demonstrated the applicationof hybrid dynamical systems to HEVs, where sequentialquadratic programming and dynamic programming were usedto obtain an optimal solution to the problem before using fuzzyapproximation to obtain sub-optimal ones.The contributions of this paper consists of the following:i) a model of the power-split PHEV using hybrid dynamicalsystem; ii) the design of an energy management strategy basedon the dynamic programming approach of hybrid systems; iii)a sub-optimal strategy using model predictive hybrid control.This paper is organized as follows. Section II presents vehiclemodel of the power-split PHEVs. It the provides detaileddynamics of the power-split drivetrain; and using these dynamics vehicle dynamics, a hybrid dynamical system framework model of the power-split PHEV is presented. SectionIII formulates the energy minimization problem of PHEV,and presents the detailed design of the supervisory energymanagement strategy. The dynamic programming and modelpredictive hybrid control based solutions are also presented.Finally, Section IV presents the simulation results of theproposed strategies and compares their performances.3II. N ONLINEAR PHEV M ODELThe drivetrain of conventional vehicles consists of gearbox,clutch and engine; and there is only one path for energy toflow and one degree of freedom. In comparison, power-splitdrivetrain has two paths of energy flow, i.e. electrical pathand mechanical path. Hence, power-split drive train has twodegrees of freedom: engine speed and engine torque. Thepower-split drivetrain has a continuously varying transmissionconsisting of planetary gear set. Fig. 3 shows a detailedstructure of the power-split drivetrain. The PHEV consists of aspeed coupling between the engine and the generator (MG2);and a torque coupling between the planetary gear output andthe motor (MG1). The engine is connected to the carrier gearof the planetary gear set and the generator is connected to thesun gear of the planetary gear set. The output of this planetarygear set, ring gear, is connected to the motor (MG1) via torquecoupling. The output of this torque coupling is connectedto the drive shaft, the final drive, the axle and the wheels,respectively. Fig. 4 shows the energy flow in PHEV power-Fig. 3. Power split Drive train configuration.Fig. 4. Energy flow in Power split drivetrain.split drivetrain. The power delivered by the engine is split intothe electrical path and the mechanical path. Part of the powerdelivered by engine PE is converted into electrical power PEGdue to the reaction torque provided by the generator. The
IEEE TRANSACTIONS ON INTELLIGENT TRANSPORTATION SYSTEMS, VOL. XX, NO. X, XXremaining power PEW is delivered mechanically directly tothe wheels using the ring gear of the planetary gear set. Theelectrical power from the generator Pg is provided to the powerconverter which routes it to the motor Pm and the rest of theelectrical power Pbat is deposited into the battery.By applying the Newtons second law on the engine weobtain the equation (1) below which relates the engine speedωe with the engine torque τe , the sun gear torque τs and thering gear torque τr :(1)Similarly, applying the Newtons law at the ring gear we obtainthe equation (2) which relates the ring gear speed ωr with thering gear torque τr , the motor torque τm and wheel torque τw :Jm ωr τr τm γτw .(2)The generator speed ωg is related to the generator torque τgand the sun gear torque asJg ωg τg τs .(3)In equations (1), (2) and (3), Je , Jm , Jg are the moment ofinertia of the engine, the motor, and the generator, respectively,and γ is the gear ratio.Due to the kinematic property of the planetary gear set, thesun gear, the carrier gear and ring gear are linearly related toeach other. Since the sun gear is connected to the generator(MG2), the carrier gear is connected to the engine and the ringgear is connected to the output shaft, the engine speed ωe , thegenerator speed ωg and the ring gear speed ωr are related by:ωr (1 ̺)ωe ̺ωg .(4)In the above speed coupling relation, ̺ is the planetary gearratio defined by̺ N s/N r,(5)where Ns and Nr are the numbers of gear teeth on the sun gearand the ring gear, respectively. Note that since the moment ofinertia of the pinions gears is very small, they are neglectedwhen compared with the moments of inertia of the engine, themotor, and the ring gears.The sun gear torque τs and the ring gear torque τr arerelated by:τs ̺τr .(6)For this drivetrain, the motor is on the driveshaft connectedby the ring gear. Thus, the ring gear speed ωr is the same asthe motor (MG1) speed ωm . The relation between the motorspeed ωm and the vehicle speed υ is given byυ.(7)ωm Rw γBy applying the Newton’s second law to the vehicle dynamics,the following equation is obtained which relates the vehiclespeed υ, the wheel torque τw and the losses Fres as:Rw mυ τw mFres .In this equation, Rw and m are the wheel radius and thevehicle mass, respectively.The vehicle has to overcome resistance from aerodynamicforces and rolling resistance losses. To account for this, aresistive force Fres is introduced, which can be approximatedas a quadratic function of the vehicle speed υ as:Fres a0 a1 υ a2 υ 2 .A. PHEV Vehicle DynamicsJe ωe τe τr τs .4(8)(9)Here, the parameters a0 , a1 and a2 have been obtained fromexperimental results of the PSAT software.The PHEV battery is modelled as an equivalent open circuitmodel. The current drawn from the battery is given byp2 4RVoc Vocint Pbat.(10)I 2RintA negative current I implies that the current goes into thebattery. In this equation, C is the maximum capacity of thebattery, Rint is its internal resistance, Voc is the open circuitvoltage of the battery and Pbat is the battery power.Power Pbat drawn from the battery is further given byωm τmPbat ωg τg ηg (ωg , τg ).(11)ηm (ωm , τm )Here, ηm is the motor efficiency as a function of the motortorque τm and the motor speed ωm . Similarly, the generatorefficiency ηg depends on the generator torque τg and thegenerator speed ωg .Using the battery current I in (10), differential equation ofthe State of Charge (SOC) ρ of the battery is obtained as:q1dρ(12) { Voc Voc 2 4Rint Pbat }.dt2Rint CThe engine power is split into the mechanical power andthe electrical power by the generator speed. The generatorspeed is changed using the reaction torque provided to theengine through the generator torque. This generator torque isthen transmitted to the wheels via the planetary gear set. Thegenerator (MG2) acts as the motor when both the speed and thetorque are acting in the same direction; otherwise it acts as agenerator. When the generator (MG2) is acting as a generator,absorbing mechanical power of the engine and converting itinto electrical power, the drivetrain is operated as a positivesplit mode, which occurs when the battery (or the driver)demands more power from the vehicle. Generator (MG2) canalso act as a motor by providing reaction torque to the engineand delivering power to the wheels using the planetary gearset. This mode of operation is called the negative split mode,which occurs when the demanded power is suddenly reduced.B. Hybrid System Model of PHEVPower-split Plug-in Hybrid Electric Vehicle (PHEV) operates in different modes. When the power demand is low andthe vehicle speed is low, PHEV can be operated in the EVmode because it is more efficient for the energy to flow fromthe battery to the motor. Fig. II-B shows the energy flow in theEV mode. When the vehicle is decelerating rapidly, the kineticenergy of the vehicle can be recovered by operating the motor(MG1) as a generator to recover maximum electrical energy
IEEE TRANSACTIONS ON INTELLIGENT TRANSPORTATION SYSTEMS, VOL. XX, NO. X, XXfrom the vehicle deceleration. This operation of the vehicle iscalled the regenerative braking mode. The energy flow duringthe regenerative braking mode is shown in Fig. II-B. It canbe seen that the motor (MG1) recovers the energy and storesit back into battery. When the power demand is high so thatthe motor (MG1) alone cannot supply it, the vehicle can beoperated in the hybrid drive mode. Fig. II-B shows that duringthis mode the motor (MG1) gets power from the battery todrive the wheel and at the same time the generator (MG2)is also acting as a motor and provides the reaction torque tothe engine and powers the wheels usingthe planetary gear set.When the battery power is not sufficient, the battery can becharged using the onboard engine. To do this, the generator(MG2) stores energy into the battery. At the same time, themotor (MG1) can provide power to the wheels if the batteryhas sufficient power. Fig. II-B shows the ener
Energy Management Control of Plug-in Hybrid Electric Vehicle using Hybrid Dynamical Systems Harpreetsingh Banvait, Student Member, IEEE, Jianghai Hu, Member, IEEE, and Yaobin Chen, Senior Member, IEEE Abstract—This paper presents a supervisory energy man-agement control system design of power-split Plug-in Hybrid Electric Vehicles (PHEV).
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