Blended Power Management Strategy Using Pattern Recognition for a Plug-in Hybrid Electric Vehicle Nicolas Denis, Maxime R. Dubois, Renaud Dubé & Alain Desrochers
International Journal of Intelligent Transportation Systems Research ISSN 1348-8503 Int. J. ITS Res. DOI 10.1007/s13177-014-0106-z
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Author's personal copy Int. J. ITS Res. DOI 10.1007/s13177-014-0106-z
Blended Power Management Strategy Using Pattern Recognition for a Plug-in Hybrid Electric Vehicle Nicolas Denis & Maxime R. Dubois & Renaud Dubé & Alain Desrochers
Received: 26 February 2014 / Revised: 20 October 2014 / Accepted: 23 October 2014 # Springer Science+Business Media New York 2014
Abstract The dual power source of a plug-in hybrid electric vehicle (PHEV) requires a high level control strategy in order to establish a power split decision that will minimize fuel consumption while taking full advantage of the embedded source of electrical energy. Literature shows that the optimal control of the power split is greatly influenced by the future trip to be made and that blended strategies are more appropriate regarding battery usage throughout a trip. This paper proposes a blended strategy for a PHEV which uses a driving pattern recognition scheme that allows control adaptation in real-time regarding current driving conditions.
Keywords Plug-in hybrid electric vehicles . Energy management . Blended strategy . Genetic algorithm . Driving pattern recognition . Supervised classification
N. Denis (*) Centre de Technologies Avancées, Université de Sherbrooke, Sherbrooke, Canada e-mail:
[email protected] M. R. Dubois : R. Dubé Département de Génie Électrique et Génie Informatique, Université de Sherbrooke, Sherbrooke, Canada M. R. Dubois e-mail:
[email protected] R. Dubé e-mail:
[email protected] A. Desrochers Département de Génie Mécanique, Université de Sherbrooke, Sherbrooke, Canada e-mail:
[email protected]
1 Introduction Environmental concerns and fuel cost increase lead manufacturers and governments to develop alternative technologies to replace conventional internal combustion engine (ICE) vehicles. One possibility consists in developing vehicle electrification and particularly hybrid powertrain technology. The architectures of hybrid electric vehicles (HEV) and plug-in hybrid electric vehicles (PHEV) need a specific controller in order to take full advantage of their additional power source. More precisely, an energy management system (EMS) is implemented in order to carefully choose the power distribution between the internal combustion engine and the electric motor (EM). An optimal power distribution will minimize fuel consumption while maintaining battery state of charge (SOC) within a safe range. This is especially the case in a parallel hybrid configuration, where the internal combustion engine and electric motor are coupled together on a common mechanical shaft. Energy management systems for PHEVs can be classified in two categories which are rule-based and optimization-based [1]. The external plug of the PHEV allows the embedded battery pack to be recharged when the vehicle is stopped. Consequently, the battery SOC at the final time of a trip can be much lower than the SOC at the beginning of the trip. Unlike an HEV that runs only in charge sustaining (CS) operation, control strategies of PHEVs can adopt different kinds of charge depleting (CD) strategies. Global optimization techniques are part of the optimization-based strategies and perform mathematical optimizations over a complete predefined driving cycle. In particular, dynamic programming (DP) can optimize the powertrain control while constraining the initial and final SOC. DP applied to a PHEV shows that the best strategy is to use the ICE before the low SOC is reached, resulting in a gradual discharge of the battery pack [2, 3]. This means that when the trip exceeds the all electric range
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(AER), a blended strategy is preferred in order to use the engine punctually throughout the whole trip. However DP cannot be applied in real-time because solving needs lengthy computations as well as the complete speed profile of the trip. Authors propose different alternatives for the real-time control that overcome these difficulties. The rule-based strategies offer computational simplicity, reliability and robustness but cannot reach global optimality because the control decisions do not take the entire trip information into account. Literature proposed both deterministic [4, 5] and fuzzy [6, 7] rule-based strategies for PHEVs, that generally make the vehicle run only with the EM during the first part of the trip and then enter CS operation when the battery SOC is low. Contrarily to a blended strategy, these strategies reach the low SOC level before the end of the trip whenever its length exceeds the AER. Yan et al. propose a rule-based blended strategy that constrains the SOC to follow a decreasing reference that is constructed based on the knowledge of the current driven distance and the total trip length obtained with a GPS [8]. They manage to decrease fuel consumption by avoiding inefficient CS operation. However, constraining the SOC to follow a reference independently from the driving conditions could be non-optimal. Zhu et al. propose to use DP on a predefined driving cycle and then to design simple real-time control rules on the basis of DP optimality observation [9]. Computational complexity of DP leads authors to propose various meta-heuristic optimization techniques to optimize a selected set of rules or control parameters on predefined driving cycles [10–13]. Compared to DP, they generally allow faster convergence towards optimum parameters values that can be used in real-time. Another alternative consists in using optimal control theory in order to break the global optimization problem into an equivalent consumption minimization strategy (ECMS) [14, 15] which is a local optimization problem that requires less computational effort. Using this method, optimality can be reached as long as the Lagrangian multiplier of the problem is carefully chosen. The latter, however, depends on the driving cycle to be made. A similar approach proposes to translate the driving cycle into a probability density function of the required power and then to design a blended strategy using optimal control parameters computed by a gradient-based optimization technique [16]. The previous techniques need the knowledge of the future driving cycle which is likely to be unknown, or subject to uncertainties, in the case of a real-time application. That is why some authors propose speed prediction techniques using live-streamed data or historical traffic data available on a geographical area. Different traffic models were developed, from simple models using speed limits and traffic signals information [17] to more advanced models using gas-kinetic traffic flow model [18] or neural networks [19]. Zhang et al. benefited from these speed predictions techniques and
combined them with ECMS in order to build a blended strategy for a PHEV [20, 21]. However, lack of available data can make speed prediction difficult so some authors propose driving pattern recognition. In these techniques, a past speed frame of the current trip is analyzed in order to extract meaningful features and realize a adaptive powertrain control. Different supervised classification techniques were employed for this purpose [22–25]. In general, the choice of a classification technique has to satisfy a tradeoff between classification accuracy and computation requirement. This paper proposes a novel real-time blended strategy for a PHEV that uses a driving pattern recognition module based on the k-nearest neighbor (KNN) algorithm. Carefully selected control parameters are optimized offline from a collection of predefined driving patterns that represent different driving conditions. The proposed driving pattern recognition associates a past speed-frame acquisition of the current trip with one of the known patterns. Finally the recognition is used for the real-time selection of the appropriate pre-optimized control parameters, thus adapting the powertrain control to the current driving conditions. Existing control parameters optimization techniques need the knowledge of the full driving cycle and often, no solution is provided for the real-time use, where the driving cycle is not previously known. In this paper, an original set of control parameters is defined, optimized on different driving cycles and used in combination with driving pattern recognition for the real-time use. Naturally, speed pattern recognition has been widely studied in literature. However, it has not been associated with the type of control parameters optimization technique proposed in this paper. Moreover, the KNN classification accuracy for speed pattern recognition has been evaluated but its potential in terms of fuel savings has not been investigated. It will be seen that, despite its simplicity, it leads to interesting fuel economy. Finally, unlike HEV charge sustaining strategies, real-time blended strategies for PHEV, although advantageous, has seldom been proposed. In this paper, it is proposed to associate speed pattern recognition with the knowledge of the trip length, to form an original blended strategy. Section 2 introduces the powertrain architecture and its complete model, section 3 exposes the analysis made on the dynamic programming results, section 4 presents the design and choices for the proposed EMS and finally section 5 and 6 present simulation results and experimental tests.
2 Powertrain Mathematical Model The approach for the control design described in this paper can be applied for a wide range of PHEV with parallel architecture. To illustrate this approach, a three-wheel plug-in hybrid electric roadster is considered. Its powertrain architecture is described in Fig. 1. The ICE and the EM are combined
Author's personal copy Int. J. ITS Res. Table 1 Vehicle specifications Characteristic
Value
PMSM Maximum speed Number of pole pairs d-axis inductance q-axis inductance Stator windings resistance per phase Magnet flux amplitude Inverter IGBT Rated collector current Rated On-state collector-emitter voltage Threshold voltage Diode Rated forward current Rated forward voltage Threshold voltage Battery Embeddable energy Rated output voltage
Fig. 1 Powertrain architecture
in a parallel hybrid configuration. The gearbox is composed of six gears. The battery pack can be regenerated by electrically braking the vehicle or by overpowering the engine. Negative engine output power is not allowed for efficiency consideration. In all cases, power contributions of the two power sources have to satisfy the driver demand. The electrical powertrain can be seen in Fig. 2. It is composed of a Li-Ion technology battery pack, a voltage source inverter using IGBTs and a permanent magnet synchronous motor (PMSM). The vehicle specifications are listed in Table 1. For a matter of space in our vehicle, the electrical powertrain does not include any DC/DC converter that would stabilize the bus voltage. Hence, the inverter will see a variable bus voltage depending on the voltage drop caused by the internal resistance of the battery cells. This affects the whole powertrain efficiency. Moreover, there is no clutch on the electrical motor shaft which means that the electrical motor will always be coupled to the wheel. A backward mathematical model of the vehicle has been built and is described in the following sections.
Fig. 2 Electrical powertrain configuration
Cell capacity ICE 4 strokes – 2 cylinders Engine displacement Idle speed Vehicle dynamics Mass Drag coefficient Frontal area First order rolling resistance coefficient Second order rolling resistance coefficient Third order rolling resistance coefficient
8,000 rpm 5 90 μH 90 μH 15 mΩ 0.0543 Wb 550 A 1.35 V 0.8 V 550 A 1.35 V 0.9 V 2.5 kWh 360 V 2.3 Ah
600 cm3 1,600 rpm 565 kg 0.537 1.19 m2 0.0155 7.93×10−4 s/m 3.17×10−6 s2/m2
2.1 Estimation of the Wheel Required Torque In this paper, the torque required at the wheel Treq is calculated based on the speed profile using: T req ¼ Rw
Jtot dvveh F drag þ F roll þ M v þ M d þ 2 ; ð1Þ dt Rw
where Rw is the rear wheel radius, Fdrag is the drag force, Froll is the rolling resistance, Mv is the vehicle mass, Md is the driver mass, Jtot is total inertia of the rotating parts brought back to the rear wheel and vveh is the vehicle speed. Both drag force and rolling resistance depend on the speed. The expression of the drag force is given by: F drag ¼
1 ρ A f C d v2veh ; 2 a
ð2Þ
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where ρa is the air density, Af is the frontal area and Cd is the drag coefficient. The drag coefficient depends on the vehicle geometry and has been calculated through numerical simulations developed in [26, 27]. The expression of the rolling resistance is based on the general form that can be found in [28]. In addition, a quadratic evolution has been supposed, giving: F roll ¼ ðM v þ M d Þgcosα f r1 þ f r2 vveh þ f r3 v2veh ; ð3Þ where g is the gravity constant, α is the road slope and fr1, fr2 and fr3 are respectively the first, second and third order rolling resistance coefficients that have been estimated through experimental tests. In our simulations, no wind and no slope have been considered. In theory, it is possible to take the slope effect into account by adding an extra force in (1). It is also possible to model the wind effect by adding the wind speed into (2). 2.2 Internal Combustion Engine Model The ICE is modeled by a map that gives its instantaneous consumption for every possible values of delivered torque TICE and rotational speed NICE. Figure 3 illustrates this map along with the maximum torque that the ICE is able to deliver. It should be noted that the total delivered torque TICE is not completely transmitted to the rear wheel because a fraction of it is used to power the different accessories of the vehicle. 2.3 Electric Motor Model The PMSM used in this paper has three-phase, star-connected stator windings. The back electromotive force (EMF) is assumed to be sinusoidal. The PMSM uses vector control and it is proposed to write its mathematical equations in the rotor frame (d-q), following the Concordia-Park transformation
Fig. 3 ICE instantaneous consumption (g/h)
standard [29]. The rotor is assumed to be non-salient. However, a non-negligible magnetic saturation of the iron appears at high current. Based on this analysis, it is preferable to write the steady-state electrical equations as: V d ¼RI d −pωEM ψtq ðI d ;I q Þ ; ð4Þ V q ¼RI q þpωEM ψtd ðI d ;I q Þ where Vd, Vq are respectively the d-axis and q-axis stator voltages, R is the per phase stator windings resistance, Id, Iq are respectively the d-axis and q-axis stator currents, p is the number of pole pairs, ωEM is the EM rotational speed in rad/s and ψtd, ψtq are respectively the d-axis and q-axis total flux linkage. Due to the magnetic saturation phenomenon, ψtd and ψtq are non-linear functions of the stator currents, as illustrated in Figs. 4 and 5. The mathematical model aims at calculating the stator currents and voltages along with the input active electrical power Pelec based on the information of the commanded torque TEM and the rotational speed ωEM. Based on (4), Pelec can be written: Pelec ¼ R I 2d þ I 2q þ pωEM ψtd I q −ψtq I d : ð5Þ The first term of (5) represents the copper losses and the second is the electromagnetic power Pe. The electromagnetic torque Te can be derived from the expression of Pe: ð6Þ T e ¼ p ψtd I q −ψt q I d : The electromagnetic power is not completely converted into output mechanical power because a fraction of it is dissipated through the core losses Pc (hysteresis and eddy current losses): Pe ¼ Pc þ ωEM T EM :
Fig. 4 d-axis total flux linkage (Wb)
ð7Þ
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2.4.1 Conduction Losses When in the on state, IGBTs and diodes see a small voltage drop that leads to energy dissipation. Based on the forward characteristic of the switch, this voltage drop can be approximated by a linear function of the current going through the device. For example, the collector-emitter voltage of the IGBT VCE is a linear function of the collector current IC:
V CE ¼
Fig. 5 q-axis total flux linkage (Wb)
The core losses can be written mathematically as: Pc ¼ K h ωEM þ K e ω2EM ψ2t ;
ð8Þ
where Kh and Ke are respectively the hysteresis and eddy current coefficients [29] that can be estimated by a no load experimental test. ψt is the peak total flux linkage whose expression is given in (9), according to the Concordia-Park transformation standard: ψ2t ¼
2 2 ψtd þ ψ2tq : 3
ð9Þ
The model is completely defined by the above equations in which only Id, Iq are still unknown. In the case of this paper, the currents are closed-loop controlled through the inverter. At low speed, since the rotor is assumed non-salient, it is preferable to command Id = 0 [29]. Iq is imposed using (6), knowing the torque that must be applied (in the control architecture, Te and TEM are taken equal for a matter of simplification). At high speed, the peak stator voltage reaches its saturation value, which is half of the bus voltage. In this situation, Id cannot be maintained to zero and Iq and Id are imposed to satisfy both (6) and the voltage constraint. It is the flux weakening operation [29].
2.4 Inverter Model The three-phase voltage source inverter is controlled by pulse width modulation (PWM). The model estimates the input electrical power of the inverter based on the stator currents and voltages and the input active electrical power of the PMSM. In order to do this, conduction and switching losses in IGBTs and diodes are calculated.
V CEN −V CEO I C þ V CEO ; I CN
ð10Þ
where VCEN is the rated On-state collector-emitter voltage, ICN is the rated collector current and VCE0 is the threshold voltage. The diode forward voltage can be approximated by a similar function. The conduction losses can be obtained by integration of the dissipated energy over the whole electrical period [30]. For the IGBT, it gives:
Pcon ¼
1 2M V CEN −V CEO 2 þ I 4 3π I CN pffiffiffi 1 M þ cosðφi −φv Þ V CEO I 2; þ 2π 8
ð11Þ
where M is the amplitude modulation ratio of the PWM, I is the rms phase current and φi, φv are respectively the phases of the stator current and voltage. Since the inverter is composed of six IGBTs, the conduction losses of all IGBTs is six times the value obtained with (11). The conduction losses of the diodes can be found using the same approach. 2.4.2 Switching Losses Switching losses are non-negligible in IGBTs since they are controlled switches. For better accuracy of the switching losses estimation, manufacturers advise to use their experimental characterization [31]. IGBT switching losses characterization gives the dissipated energies during turn-off Eoff and turn-on Eon as functions of the collector current. For the inverter used in this paper, this characterization is illustrated in Fig. 6. The total switching losses are then calculated by integration of the dissipated energies over the whole electrical period. Diode switching losses are mainly caused by their recovery current. They are also characterized as a function of the forward current so they can be estimated using the same approach.
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For the model to be closer to the reality, some coefficients have been added into the calculation of it and the cell voltage Vcell [34]. These coefficients, named k1, k2 and k3, allow taking cell temperature Tc and current effects into account: Z t it ¼ k 1 ðicell Þk 2 ðT c Þicell ðuÞdu; ð13Þ o
V cell ¼ E cell −Rinticell þ k 3 ðT c Þ:
ð14Þ
The global calculation process is illustrated in Fig. 8, in which Nc is the total number of cells in the battery pack and Pinv is the input electrical power of the inverter. Calculation of the battery output current and voltage are based on icell, Vcell and the battery cells configuration.
3 General Form of the Power Split Rules Based on DP Results Fig. 6 Switching losses in IGBT. Source: [32]
3.1 The Dynamic Programming Algorithm 2.5 Battery Model The battery model calculates the battery output current and voltage along with its SOC, based on the input electrical power of the inverter. A battery cell is modeled by a variable voltage source Ecell in series with a variable internal resistance Rint [33], as illustrated in Fig. 7. Ecell is the no load cell voltage and follows: E cell ¼ E o −K
Q þ Ae−B it ; Q−it
ð12Þ
where Q is the cell capacity, it is the used capacity and E0, K, A, B are constants evaluated experimentally. Rint is experimentally characterized for a range of temperature, SOC and cell current.
Fig. 7 Cell model
In this paper, the DP theory [35] will not be detailed since it is well known and extensively used in the literature. The DP algorithm was used to find the optimal values of the engine torque TICE and the gear number k of the gearbox at each time of a predefined driving cycle. The optimal value of the EM torque TEM is computed from TICE and k knowing the value of the required torque Treq at the considered time. In this paper, the minimization objective is the total fuel consumption over the given driving cycle and the exhaust emissions have not been taken into account. Since there is no clutch on the EM shaft, the vehicle can be run in only two main modes which are 1) pure electric where only the EM propels the vehicle 2) hybrid where both motors are combined for the propulsion. DP performs an exhaustive search and tests the two modes at each iteration. In pure electric, k and TICE are null and in hybrid mode a range of values for the control variables has to be tested regarding the problem constraints. The constraints on k and TICE are defined at each time step regarding Treq and the wheel speed Nw along with the speed
Fig. 8 Calculation process in the battery model
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and torque limitations of both motors. In order to avoid hazardous operation of the battery pack, the SOC is constrained to be into the range of 20–95 %. The initial and final SOC are then imposed depending on the situation to be simulated. 3.2 General Form of the Power Split Rules The first objective is to observe the optimal torque split given by DP for different driving conditions. Consequently we decided to run the DP algorithm on 11 facility-specific driving cycles developed by Sierra Research Inc. [36]. These driving cycles describe vehicle operation over different types of roadway (arterial, local and freeway) with several traffic and facility levels called level of service (LOS). The different driving cycles are listed in Table 2. Letter “A” indicates a low LOS while letter “G” indicated a high LOS. As a general rule, a high LOS implies heavy traffic and facility density that lead to a low average speed. On the contrary, a low LOS leads to higher average speed. The observation of the optimality will allow finding two control laws that mimic the optimal behavior; one that rules the power split decision during hybrid mode and one that rules the decision for transition between pure electric and hybrid mode. Since a PHEV can begin a trip with any possible initial SOC values, DP was run for each of the 11 facility-specific driving cycles with a few different values for the initial SOC. The obtained results would provide the general form of the control laws. Moreover, since the target is to minimize the fuel consumption, it is better to end a trip with the lower possible final SOC in order to maximize the electrical energy contribution. It is considered that the degradation of the battery is accelerated when the SOC is under 30 %. Thus a final SOC value of 30 % for every case is imposed. However DP allows the SOC to temporarily evolve between 20 and 30 % during a driving cycle. Among the several DP results that have been
obtained, this paper illustrates the case of ART LOS AB beginning with a 50 % full battery pack. In order to find the first control law, the engine load points coming from the DP results were plotted. In each speed cycle and for each defined initial SOC, it was observed that the engine always worked around its maximum efficiency in the hybrid mode. The illustration of this observation on ART LOS AB is shown in Fig. 9. Consequently it was decided to design a control law that always makes the ICE work at its maximum efficiency during hybrid mode. This is made possible by an accurate real-time computation of the ICE torque and gear number based on the vehicle speed, required torque and physical limits of the ICE. For the second control law, the EM load points obtained with DP were plotted and compared with the wheel torque/ speed load points brought down to the electric motor shaft. The example of ART LOS AB is given in Fig. 10. During DP optimization, DP identifies the pure electric mode as the optimal mode of operation when it makes the EM provide the entire required torque. This case appears when the EM load points from DP (dots) match the wheel torque/speed load points (circles). On the contrary, the DP algorithm identifies the hybrid mode as optimal in the cases where the compared load points are separated (dots and circles do not coincide). For each driving cycle, it was observed that the vehicle works in hybrid mode as soon as relatively high power is required. The resulting conclusion is that a transition threshold can be used above which the EM should not operate alone, in order to stay close to optimality. At low speed, where the ICE speed is below the idle speed, the vehicle always runs in pure electric mode. The absence of a DC/DC converter and the need for flux weakening current increase the power losses in the whole electrical powertrain, especially when high mechanical power is required. This can explain why the EM operates in a
Table 2 Facility-specific driving cycles Number
Name
Acronym
1 2 3 4 5 6 7 8 9 10 11
Freeway high-speed Freeway LOS A-C Freeway LOS D Freeway LOS E Freeway LOS F Freeway LOS G Arterial LOS A-B Arterial LOS C-D Arterial LOS E-F Local Freeway ramp
FW HS FW LOS AC FW LOS D FW LOS E FW LOS F FW LOS G ART LOS AB ART LOS CD ART LOS EF LOCAL FW RAMP
Fig. 9 ICE load points obtained with the DP algorithm on ART LOS AB (circles) and maximum efficiency curve (solid line)
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Fig. 11 Real-time management of the mode transition Fig. 10 Required torque brought to the EM shaft (circles), EM load points from DP optimization (dots) and transition threshold (solid line)
4.1 Parameter Optimization using GA relatively low range of power in DP results. The different DP results show that the threshold curve is a good way to separate pure electric mode from hybrid mode for every considered driving cycle and initial SOC. It was observed that the curves were different for each driving cycle but always parabolic or linear shaped. Increasing the initial SOC means that a higher amount of electrical energy is available for use, consequently this makes the threshold level to increase in order to favor electric mode and battery depletion. The real-time controller will adopt a control law that will try to recreate and adapt this threshold based on the current driving condition and the initial SOC.
4 Design of the Real-Time Controller The threshold curve in Fig. 10, which results from the DP calculation, may easily be implemented in a real-time controller. However, the DP algorithm cannot be used for a real-time control of the power split estimation. The assessment of the optimized power split ratio based on a DP calculation may take several hours on a powerful computer. Moreover the DP algorithm gives only the shape of the transition threshold curve. Consequently, it must be described by introducing real-time control parameters. In this section, these parameters are optimized offline on the predefined driving cycles using a genetic algorithm (GA). The optimized parameters are used in conjunction with a driving pattern recognition system for an appropriate real-time control of the operating mode transition. An overview of the real-time controller described in this section is illustrated in Fig. 11. The blended strategy is performed using the instantaneous vehicle speed, the current SOC and total trip distance as control inputs.
The threshold curve in Fig. 10 can be interpreted as a torque threshold, which depends on the EM speed NEM (in rpm). From the work presented in section 3, the DP analysis has shown that the optimal threshold, called Tth, can be described by a function of the following general form: T th ðN EM Þ ¼ αN 2EM þ bN EM þ c:
ð15Þ
The three coefficients a, b and c forms the real-time control parameters. As DP provides the shape of the Tth function, a GA is now used to provide optimized a, b, and c values. The GA is also found to be much faster than DP with only a few minutes against several hours. The GA minimizes both SOC deviation and fuel consumption and is based on the fitness function ffit:
f fit ða; b; cÞ ¼ f uel cost þ γ SOC tar −SOC f ; ð16Þ where fuelcost is the fuel consumption over the trip, SOCtar is the targeted final SOC of 30 % and SOCf is the obtained final SOC which depends on the speed and required torque profiles as well as the transition decision ruled by a, b and c. The state of charge constraint and the fuel consumption minimization create a multi-objective optimization problem which is here reduced to a single-objective minimization one using the weight factor γ. For a given speed profile, this factor is responsible for the balance of the two objectives and is iteratively selected to give a final SOC sufficiently close to 30 % while allowing quasi-optimal results in terms of fuel consumption. The GA works on two subpopulations of 50 individuals which are randomly initialized into the search space. An individual is formed by coding the values of the parameters
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a, b and c. An iteration of the GA consists in a first step called improvement step which uses probabilistic tools to modify the current population with the aim to find better individuals which will form the next generation. The second step is called evaluation step in which each individual of a population is evaluated using the fitness function and then ranked based on their fitness values. During the improvement step, a random selection is made among the individuals of the current population, the best-ranked individuals having a higher probability to be selected. A certain number of selected individuals (called parents) are “crossovered” in order to create potential better individuals (called children) that will compose the next generation. The crossover process, illustrated in Fig. 12, is of random-heuristic type in which a child is created by averaging the two parents with random weights. In addition to crossover, some children are created by a parent mutation that consists in randomly modifying an individual. The mutation process helps to maintain a good exploration of the search space and avoid a too fast convergence. The GA optimization has been made for several initial SOC values on the 11 driving cycles, each having a defined length. However, the optimal control parameters also depend on the trip distance. In order to deal with the variability of the trip distance, it is proposed to introduce the concept of global discharge rate, noted disrate, which is the SOC depletion that has to be performed over a trip considering its length: disrate ¼
SOC init −SOC tar : dist
ð17Þ
The global discharge rate is in %/km, SOCinit is the SOC of the battery pack at the beginning of the trip and dist is the total distance in km. The global discharge rate casts the influence of the distance and initial SOC into one single trip characteristic. It represents charge sustaining operation when equal to 0 and charge depleting operation when positive. Above a certain value, the electrical energy in the battery pack is sufficient for the vehicle to perform the entire speed cycle only with the
Fig. 12 Random-heuristic crossover of the developed GA
electric motor. Above this value, the global discharge rate is not considered since there is no need for transition management. The maximum global discharge rate is about 4.8 %/km for low speed profiles (high LOS) and 8 %/km for high speed profiles (low LOS). Since different initial SOC levels on a given driving cycle corresponds to different global discharge rates, it is proposed to optimize the set of parameters with GA for the whole range of global discharge rates with a fixed step of 0.1 %/km. Thus the optimized parameters are associated with their respective global discharge rates rather than only the initial SOC in order to take distance variability into account. Finally, the values of the optimized parameters are known for every global discharge rate and driving condition, forming a reference table. As indicated in Fig. 11, the real-time controller compares the current position and the total expected distance as well as the current SOC with the targeted final SOC. This provides the necessary information to select an accurate set of parameters by invoking the reference table. More details will be provided in section 4.2. Going back to the example in section 3, a GA optimization can be performed on ART LOS AB with an initial SOC of 50 %. The length of the trip is 8.24 km and the corresponding global discharge rate is 2.43 %/km. The result of the optimization gives the optimized parameters: a ¼ −7:36 10−6 ; b ¼ 2:65 10−2 ; c ¼ 30:94:
ð18Þ
The SOC evolution obtained with these optimized parameters has been compared to the optimal SOC path provided by DP. The comparison is illustrated in Fig. 13. DP gives a consumption of 2.31 L/100 km and GA gives 2.37 L/ 100 km. The difference can be partly explained by the delay
Fig. 13 SOC comparison between DP (black) and GA (grey) for ART LOS AB
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in mode transitions. Once the engine is started, it cannot be shut down immediately after and a necessary delay of 5 s has to be imposed. This extra constraint cannot be taken into account in DP but can be factored in the GA optimization process. From this, it can be concluded that the obtained results can be considered as quasi-optimal.
Table 3 Feature selection
4.2 Driving Pattern Recognition
Acceleration standard deviation Average deceleration Deceleration standard deviation Percentage of time between 0 and 15 km/h Percentage of time between 15 and 30 km/h
As illustrated in Fig. 14, the driving pattern recognition module makes a real-time analysis of the speed profile on a past time frame of the current driving cycle. This analysis consists in extracting some speed features which are then associated to a specific driving pattern by a KNN classifier. The different driving patterns are the facility-specific driving cycles in our case. The first step is to extract the speed features from the facility-specific driving cycles for the KNN supervised learning process. The feature selection is based on the work presented in [24]. Based on the statistical distribution of the features for every driving cycle, some of them were found irrelevant or too noisy for the KNN classification. Other relevant features were also added. The 11 selected features are listed in Table 3. For each driving cycle, features were extracted on 200 windows uniformly selected in the whole cycle. The window length is an important classification parameter that has to be defined carefully. If the length is too small, the window will not contain enough information to perform an accurate recognition. Moreover, some authors observed that the larger the window, the worse the classification accuracy [22, 24]. In this paper, the k-fold cross validation technique has been used to evaluate the influence of the window length on the classification accuracy. Figure 15 shows the cross validation loss for several values of window length. In Fig. 15, a number of neighbors of 20 and the Mahalanobis distance were used for the KNN classification. These choices will be justified later in this section. The observation made in [22] and [24] are confirmed by Fig. 15. However, choosing a
Fig. 14 Real-time feature extraction
Maximum speed Minimum speed Average speed Speed standard deviation Maximum acceleration Average acceleration
too big length may cause some problems when it comes to the real-time use. A too big window may contain obsolete information leading to a slow and delayed adaptation to changes in the driving conditions [25]. It is also computationally less efficient. As a tradeoff, a window length of 60s is used in this paper. It is well known that classification becomes more difficult with the increasing number of classes (the facility-specific driving cycles in this case). However, keeping as many classes as possible allow the controller to deal with many situations. After several iterations, it has been decided to keep 10 driving cycles among the 11. Only FW RAMP has been discarded. This choice offers better results even if the fraction of misclassification increases. Consequently, a database of 2,000 feature sets, each labeled with one of the 10 driving cycles, is obtained. This database is then submitted to the KNN algorithm to train the controller which will in turn be able to label the real-time feature set coming from the current driving cycle. Using the k-fold cross validation technique again, it was found that the cross validation loss increases with the number
Fig. 15 KNN classifier cross validation loss versus the window length
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of neighbor k. Nevertheless, choosing a high k reduces the problem of irrelevant classifications caused by sparse training data in the feature space. A value of 20 for k was found to be a good tradeoff. The same kind of analysis was made to choose the most appropriate distance. The “Mahalanobis” distance was chosen as it exhibited the smallest cross validation loss. This distance has the advantage of selecting the nearest neighbors based on the training data structure by explicitly taking the training data correlation into account. The choices detailed above lead to a KNN classifier that has 20 % cross validation loss, meaning that it is 80 % accurate. Another measure of the classification accuracy is to simulate a real-time recognition on the 10 facility-specific driving cycles. In real-time, the feature extraction is made every 5 s on the last 60 s of the current trip. For a given facility-specific driving cycle, a perfect recognition would, at each time, associate the past speed frame to this particular facility-specific driving cycle. In reality, the classification is not perfectly accurate, which leads to some error in the recognition. Table 4 shows the percentage of correct recognition through every facility-specific driving cycle. In addition to the driving pattern recognition, the real-time controller computes the current discharge rate using the remaining distance of the trip and the difference between the current SOC and the targeted final SOC as illustrated in Fig. 11. The computation of the remaining distance needs the knowledge of the trip distance which can be provided by a GPS. At a given time during the current trip, the controller sees the remaining part of the trip as a new trip with a given discharge rate. On the basis of the discharge rate and the detected driving pattern, the controller is able to select the suitable control parameters by searching in the reference table introduced previously. The transition threshold is then computed and the operating mode choice is done by comparing the required torque with the torque threshold.
5 Simulation Results The proposed controller was integrated in the simulation tool and the fuel consumption performance was evaluated on the urban dynamometer driving schedule (UDDS) which is a complete test driving cycle that represents different operations in an urban area. The fuel consumption was compared to the achievable minimum obtained by DP and also the consumption obtained from a basic rule-based controller. The rule-based strategy is the power follower [28]. Adapted to a PHEV, this strategy depletes the SOC by maximizing the EM contribution during the first part of the trip and enters a charge sustaining operation when the SOC falls down to 30 %. During the charge sustaining operation, the pure electric mode is only used for low speed operation and regenerative braking. In other cases, the engine provides the most part of the required power and works at high efficiency whenever possible. If the SOC drops too low the engine provides additional power to replenish the battery. Conversely, if the SOC is too high, the engine reduces its power to keep SOC close to 30 %. The SOC comparison can be seen in Fig. 16. The SOC evolution obtained with the proposed controller was found to be close to the results obtained with DP. Moreover it gives a fuel consumption of 2.14 L/ 100 km, which represents a non-negligible improvement over the rule-based strategy that gives 2.58 L/100 km. The minimum fuel consumption obtained with DP was 1.89 L/100 km. Finally, the proposed controller has the advantage of not requiring any previous knowledge of the trip apart from the total distance, while providing performances close to optimality.
Table 4 Recognition accuracy for the 10 facility-specific driving cycles Facility-specific driving cycles
Percentage of correct recognition
FW HS FW LOS AC FW LOS D FW LOS E FW LOS F FW LOS G ART LOS AB ART LOS CD ART LOS EF LOCAL
81.6 65.4 81.8 75.5 85.6 82.3 62.6 66.2 86.9 78.3
% % % % % % % % % %
Fig. 16 SOC comparison between DP (black), the proposed EMS (red) and the rule-based strategy (blue)
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6 Experimental Results The controller was embedded in a prototype for a real-world test drive. A 12.7 km trip composed of a little portion of freeway followed by urban roadways was performed. The test drive was done at approximately 10 am on a working day with medium traffic. The corresponding speed cycle is illustrated in Fig. 17. The driving pattern recognition module was found to be difficult to implement in the prototype because its computational requirement was too demanding for the capability of the embedded processor. Since the computational requirement was mainly influenced by the number of labeled feature sets, it was decided to reduce this number to 200 (20 per driving patterns) for the embedded processor to be able to perform the calculation in real-time. From the point of view of the controller, the different driving patterns were numbered as shown in Table 2. The consequence of reducing the number of samples in the KNN classifier is illustrated in Fig. 18. This figure shows a comparison between the sequence of driving patterns recognized by the real-time controller and the sequence that should have been obtained with all the 2,000 feature sets. The lack of samples makes the real-time controller to miss some detection or to be less accurate in the recognition process. It is now interesting to observe the consequences of this weaker recognition in terms of SOC evolution throughout the trip and overall fuel consumption. The trip was started with an 80 % full battery pack and the targeted final state of charge was 50 % in order to make sure that a significant portion of hybrid mode operation happens. Figure 19 illustrates the SOC evolution obtained in three cases. The first case is the experimental SOC measurement which shows a final state of charge of 51 %. Despite the weaker recognition, the final SOC in experiment remains close to the targeted final SOC of 50 %. In the second case the experimental driving cycle was submitted to the simulation tool which benefits from all the 2,000 feature
Fig. 17 Speed profile of the test drive
Fig. 18 Sequence of recognized driving patterns. All samples recognition (top) and real-time recognition (bottom)
sets. In the latter case, the SOC reaches a final value of 49 %. The last case is the optimal SOC path obtained with DP for which the final state of charge was constrained to be strictly 50 %. It can be observed that DP found it more efficient to make the SOC go a bit under the value of 50 % just before the end of the trip and then make it increase to reach the targeted SOC. This is however unlikely to happen with the proposed controller since the future driving cycle is not known in advance. Nonetheless, the fuel consumption comparison gave good results. The experimental test gave 2.71 L/100 km while 2.53 L/100 km was expected by simulation. The DP algorithm showed a minimum fuel consumption of 2.48 L/100 km. It can be seen that the controller with a higher number of samples in the KNN classifier (expected by simulation) gives a better fuel economy compared to the controller used in realtime.
Fig. 19 SOC comparison on the experimental drive test. DP (black), pure experimental (red) and expected by simulation (blue)
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7 Conclusion In this paper, a complete real-time energy management system for a PHEV has been proposed. Based on the feedback on the current position and the current SOC, the controller is able to adopt a suitable blended strategy. The only required previous knowledge is the total trip distance. Moreover, a driving pattern recognition system makes the controller adapt the power split control to the current driving conditions. It has been shown by simulation and experiment that the controller can lead to fuel consumption close to the achievable minimum by efficiently benefiting from the available electrical energy. Acknowledgments The authors wish to thank the BRP Corporation and the Automotive Partnership Canada (APC) for supporting and funding this work.
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Author's personal copy Int. J. ITS Res. N. Denis received a Master degree and the French engineer diploma in electrical engineering from the École Nationale Supérieure d’Électricité et de Mécanique of Nancy, France, in 2010. He obtained a PhD degree in electrical engineering from the Université de Sherbrooke, Canada, in 2014. His PhD research was focused on intelligent energy management of PHEVs and was performed at the Centre de Technologies Avancées BRP (Bombardier Recreational Products) – Université de Sherbrooke, a joint research center with a focus on motorized sports.
Maxime R. Dubois obtained his B. Sc. in Electrical Engineering from the Université Laval, Québec, Canada in 1991. He received a PhD cum laude from Delft University of Technology in The Netherlands in 2004. Between 1993 and 1999 he has worked in the industry as a power electronics engineer. Between 2004 and 2011, he has been with the Université Laval. Since 2011, Prof. Dubois has been Associate Professor at the department of Electrical Engineering at Sherbrooke University, Canada. He is the founder of Eocycle Technologies Inc., a company specialized in the development of TFPM. He is also the founding professor of the company AddEnergie Technologies. His fields of interest are electrical machines and power electronics applied to the field of wind energy, energy storage and electric vehicles.
R. Dubé received his Bachelor and Master degrees in electrical engineering from the Université de Sherbrooke, Québec, Canada in 2011 and 2013. Since 2014, he is a PhD candidate at the Université de Sherbrooke with the Laboratory on Intelligent Vehicles.
Pr. Alain Desrochers holds an engineering degree from École Polytechnique de Montréal, an M.Sc. from the University of California in Los Angeles and a Ph.D. from École Centrale Paris. Prof. Desrochers is the NSERC Chair in Design for Aluminum in addition to being Director of University Affairs at the Centre de Technologies Avancées BRP (Bombardier Recreational Products) – Université de Sherbrooke, a joint research center with a focus on motorized sports. Prior to this, Pr. Desrochers was Associate Dean Resource at the Engineering Faculty from 2005 to 2009 and Bombardier Chair in modeling and design of mechanical systems and complex structures from 1999 to 2004.
