Energy Management Strategies for Diesel Hybrid Electric Vehicle

This paper focuses on hybrid energy management for a Diesel Hybrid Electric Vehicle (HEV) with a parallel architecture. The proposed strategy focuses on the reduction of Nitric Oxides (NOx) emissions that represents a key issue to meet Diesel emissions standards. The strategy is split in two separated functions aiming at limiting the NOx in steady-state and transient operating conditions. The first functions, control the torque split between the engine and the electric motor. This energy management is based on the Equivalent Consumption Minimization Strategy (ECMS) where an additional degree of freedom is introduced to tune the optimization trade-offs from the pure fuel economy case to the pure NOx limitation case. The second function adapts the torque split ratio between the motor and the engine, initially computed from the optimal control strategy during transient operations where NOx are produced. The engine torque correction relies on mean value models for the EGR system dynamics and for the NOx formation. This paper applies a methodology based on Software in the Loop (SiL) and Hardware in the Loop (HiL) simulations in order to understand the system performance according to the powertrain configurations and also to tune the proposed energy management strategy. The simulation results are confirmed by experiments performed on Hybrid-Hardware in the Loop (Hy-HiL) test bench. This work shows the potential of using the hybrid architecture to limit NOx emissions by choosing the best operating point and by limiting the engine dynamics. The NOx reduction has limited impact on fuel consumption. Résumé — Lois de gestion de l’energie pour le véhicule hybride Diesel — Cet article présente une stratégie de gestion de l’énergie pour un véhicule hybride parallèle muni d’une motorisation Diesel. Cette stratégie est consacrée à la réduction des émissions d’oxydes d’azote (NOx) dont la dépollution constitue une problématique majeure pour l’homologation des véhicules Diesel. La stratégie comporte deux fonctions distinctes visant à limiter les émissions de NOx en régime stabilisé et en régime transitoire. La première fonction agit sur la répartition de couple entre le moteur thermique et la machine électrique. L’approche ECMS (Equivalent Consumption Minimization Strategy, ou stratégie de minimisation de la consommation équivalente) est utilisée pour gérer la réparation de couple et dans notre cas elle intègre dans la fonction coût un compromis entre la consommation et les émissions de NOx. La seconde fonction corrige la répartition de couple issue de l’ECMS mais uniquement en régime transitoire et afin de réduire les pics d’émissions de NOx. L’adaptation de la répartition de couple repose sur des modèles moyens du système EGR et de la formation des NOx. Cet article présente le principe de ces stratégies et leur comportement est analysé grâce à un simulateur représentatif des émissions polluantes. Ces résultats sont complétés par des essais expérimentaux sur un banc moteur HiL Oil & Gas Science and Technology – Rev. IFP Energies nouvelles, Vol. 70 (2015), No. 1, pp. 125-141 O. Grondin et al., published by IFP Energies nouvelles, 2014 DOI: 10.2516/ogst/2013215 This is an Open Access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. (Hardware in the Loop). Ce travail montre qu’il est possible de limiter les émissions de NOx par le biais de l’hybridation en adaptant le choix du point de fonctionnement du moteur et en réduisant les sollicitations transitoires pendant lesquelles les NOx sont produits. La réduction des émissions de NOx n’est pas obtenue au détriment de la consommation.

Re´sume´-Lois de gestion de l'energie pour le ve´hicule hybride Diesel -Cet article pre´sente une strate´gie de gestion de l'e´nergie pour un ve´hicule hybride paralle`le muni d'une motorisation Diesel.Cette strate´gie est consacre´e a`la re´duction des e´missions d'oxydes d'azote (NO x ) dont la de´pollution constitue une proble´matique majeure pour l'homologation des ve´hicules Diesel.La strate´gie comporte deux fonctions distinctes visant a`limiter les e´missions de NO x en re´gime stabilise´et en re´gime transitoire.La premie`re fonction agit sur la re´partition de couple entre le moteur thermique et la machine e´lectrique.L'approche ECMS (Equivalent Consumption Minimization Strategy, ou strate´gie de minimisation de la consommation e´quivalente) est utilise´e pour ge´rer la re´paration de couple et dans notre cas elle inte`gre dans la fonction couˆt un compromis entre la consommation et les e´missions de NO x .La seconde fonction corrige la re´partition de couple issue de l'ECMS mais uniquement en re´gime transitoire et afin de re´duire les pics d'e´missions de NO x .L'adaptation de la re´partition de couple repose sur des mode`les moyens du syste`me EGR et de la formation des NO x .Cet article pre´sente le principe de ces strate´gies et leur comportement est analyse´graˆce a`un simulateur repre´sentatif des e´missions polluantes.Ces re´sultats sont comple´te´s par des essais expe´rimentaux sur un banc moteur HiL (Hardware in the Loop).Ce travail montre qu'il est possible de limiter les e´missions de NO x par le biais de l'hybridation en adaptant le choix du point de fonctionnement du moteur et en re´duisant les sollicitations transitoires pendant lesquelles les NO x sont produits.La re´duction des e´missions de NO x n'est pas obtenue au de´triment de la consommation.

INTRODUCTION
In a context of increasing demand for cleaner vehicles, hybrid electric vehicles are recognized as an effective way to reduce fuel consumption and emissions.The most common hybrid powertrains usually combine a gasoline engine with an electric motor with different architectures and several degrees of hybridization.The pollutant emissions of the gasoline engine are treated by the three-way catalytic converter.For the gasoline hybrid vehicle, the energy efficiency improvement is the main objective.Thus, the energy supervisor improves the fuel economy rather than the emissions in warm conditions while the thermal management is the main issue in cold conditions [1].If we consider hybrid powertrains with a Diesel engine, the Nitrogen Oxide (NO x ) emissions must be considered because the operating regions of maximum efficiency and minimum NO x emissions are generally not the same.For this purpose, the energy management strategy must be adapted to maximize the use of the engine within its low NO x emissions operating points.This control issue was studied in the literature mainly in simulation.Early work from Johnson et al. [2] deals with heuristic supervision strategies for a Diesel HEV.The latter takes into account fuel consumption weighted with the four main pollutants (NO x , PM, HC, CO).Other heuristic strategies are proposed in [3].On the other hand, model-based techniques have already been proposed by Lin et al. [4] (ECMS) and Musardo et al. [5,6] (dynamic programming).More recently, Dextreil and Kolmanovsky [7] propose an energy management controller based on the application of game theory.The simulation and experimental results from these papers indicate that a significant NO x reduction is possible at the price of a slight drop in fuel consumption.These papers confirm the feasibility of integrating emission constraints into heuristic or model-based supervision strategies.
These solutions can be applied for Euro 6 engines but new constraints will arise from the transient nature of the upcoming Worldwide harmonized Light vehicles Test Procedures (WLTP).Indeed if we consider only the current European driving cycle, the transient part of the total NO x emissions can clearly be neglected.But these transient emissions are actually significant with the new driving cycle which is more representative of real world conditions.In this context, the current strategies applying optimal control based on static maps are not sufficient and NO x transient emissions should be taken into account.
The goal of this paper is to propose a global energy management strategy for Diesel HEV taking into account both static and transient NO x emissions in addition to the fuel consumption objective.In our approach, the steady-state and transient parts are treated separately as described in Figure 1.The steady state optimal torque splits are found using the optimal control theory.The engine torque T sp eng;ss and motor torque T sp mot;ss setpoints are computed from an ECMS-based strategy including the steady-state NO x emission maps into the cost function.The second function consists of a modelbased strategy that adapts the static torque split during the transient phases where NO x peaks can occur.This leads to a computation of two trajectories for the engine torque (T sp eng;t ) and the motor torque (T sp mot;t ).The paper is organized as follows: the vehicle architecture is presented in the first part of the paper (Sect.1.1) with the modeling aspects (Sect.1.2) and the presentation of the EMS based on the equivalent consumption minimization strategy (Sect.1.3).The steady-state strategy performances are analysed in simulation and some experimental results are shown in Section 1.4.In the second part of the paper, we highlight the transient NO x emissions problem in Diesel engines (Sect.2.1).The principle of the engine torque setpoint control and the NO x trajectory definition are detailed in Section 2.2.The strategy is validated in simulation and the results are discussed in Section 2.3.Finally, this paper ends up with conclusions.

ADAPTATION OF THE EMS FOR DIESEL ENGINE:
MINIMIZATION OF NO X ALONG WITH FUEL CONSUMPTION

System Description
In this paper, we consider the vehicle architecture depicted in Figure 2.This is a parallel hybrid architecture that uses a Separated Starter Generator (SSG) in the pre-transmission side (only allowed to start the engine) and the post-transmission Electric Machine (EM) allows for power assist, full electric drive, regenerative braking and battery recharge.More details about the hybrid parallel vehicle can be found in [8].The Diesel engine is a 1.6 liter, four-cylinder, direct-injection engine with a maximum power of 50 kW and a maximum torque of 150 Nm. the exhaust gases downstream after the treatment system -composed of a Diesel Oxidation Catalyst (DOC) and a Diesel Particulate Filter (DPF) -to upstream the compressor.In this paper, we consider only the LP EGR operations.In this configuration, the system has a slower burned gas settling time compared to the HP EGR mode.The engine transients are then more drastic according to the NO x emission peaks since they are mostly caused by EGR time lag.This is a fancy case study to develop and validate a transient NO x limitation strategy using the power assist from the electric machine (Sect.2).In this work, we perform a parametric study of the electric machines power.We adopt a basic rule to adapt the battery size in order to keep the battery energy to motor power ratio constant and close to 35 Wh/kW.This value is chosen according to the reference hybrid system where the electric motor has a rated power of 42 kW and the battery an energy of 1.5 kWh [9].The vehicle mass is also adapted to account for the electric machine and battery size.This leads to the configuration detailed in Table 1.

System Modeling
The aim of this section is to introduce the mathematical model of the parallel hybrid powertrain shown in Figure 2. The model has a backward causality and it is of the quasi-static type.All the dynamics except for the vehicle longitudinal dynamics and the battery accumulator dynamics are neglected.These models equations are accepted to be relevant for optimization tasks.They are physically based, they capture the dominant phenomena and they can be implemented online.In backward modeling, the vehicle speed profile and the driver's torque demand are the main model inputs.The torque request at wheel, T sp pwt , depends on the driving conditions (speed and acceleration) and can be evaluated from drivers demand (throttle and brake pedal positions).Moreover: where R gb is the gear ratio and R 1 is the front axle ratio.
The torque setpoint can be positive or negative depending on the vehicle operating conditions (traction or braking).T sp mot;ss is the requested electric motor torque and the engine torque is the control input: The electric motor power, P elec , is usually described by a map as a function of the motor torque and speed N mot : The engine Fuel Consumption (FC) and the NO x emissions are provided by steady state maps that depend on the engine torque and speed N e : These two maps describe the quasi-static performances resulting from the engine calibration.They will be introduced in the energy management strategy.
The fuel mass injected _ m f is transformed into a fuel power using the lower heating value of the fuel Q lhv which is a constant for a given fuel: The battery pack is modeled as a basic equivalent circuit comprising a voltage source U 0 placed in series with a resistance R 0 .These two variables vary according to the battery State of Charge ðSOCÞ.The battery current and voltage are given by: where the battery power is P bat ¼ P elec ¼ U bat I bat .The variation of battery SOC is computed from the battery current and power: where Q 0 is the battery capacity and g bat represents its Faradic efficiency.In the next section, the battery SOC

Supervisory Control Strategy
For hybrid electric vehicle, the total power delivered to the wheels comes from two energy sources: the fuel and a battery.The energy management strategy computes the best power split between these two sources.The proposed strategy is based on the ECMS previously developed [10][11][12] and is already implemented on a gasoline hybrid electric vehicle [1,13].In previous studies considering SI engines, the main optimization criterion was the overall fuel consumption.Thus, the problem formulation was to determine the command uðtÞ that minimizes the cost function expressed as: For a Diesel HEV, this objective is modified and we chose to minimize a compromise between fuel consumption and NO x emission.Then, the integral cost of the fuel is defined to be the integral of the weighted sum of the fuel consumption and the NO x emission over the driving cycle.The idea is to merge the fuel map and the NO x map in order to replace the fuel consumption-based cost by a weighted average of NO x and fuel consumption.Thus, the fuel power defined by Equation ( 6) becomes: where the parameter k fc=NO x is used to set the trade-off between fuel consumption and NO x emission.In order to ease the tuning of this parameter, the two maps must be comparable.Thus, the NO x map is normalized such that its mean value remains close to the mean value of the fuel maps.The fuel mass flow rate and the NO x emission strongly depend on the engine operating condition.As a first approximation, we use two static maps depending on engine speed and torque (Eq.4, 5) and the optimal control problem is then: The state of the system is the State of Charge.Its dynamics writes: where a and b depend on the battery equivalent circuit characteristics (resistance R 0 , voltage U 0 , efficiency g bat ) and the SOC as described in Equations (7)(8)(9).The optimization problem has a state constraint such that the final value of the SOC xðt f Þ should be equal to its initial value xðt 0 Þ.The system input is the engine torque request that belongs to an admissible space such that U ¼ ½T eng min T eng max .This optimization problem can be solved using the Pontryagin's Minimum Principle (PMP) where the optimal command writes: HðxðtÞ; kðtÞ; uðtÞ; tÞ ð 15Þ where the Hamiltonian function is defined as: HðxðtÞ; kðtÞ; uðtÞ; tÞ In first approximation, if U 0 and R 0 are constant (the SOC does not vary so much), the Hamiltonian can be rewritten as: HðxðtÞ; kðtÞ; uðtÞ; tÞ The equivalence factor s weighs the electrochemical power.Its value modifies the balance between the electrochemical power use and the equivalent fuel power use.The equivalence factor is chosen such that the constraint on the final SOC is fulfilled xðt f Þ ¼ xðt 0 Þ.In this paper, we assume the drive cycle is known and, under this assumption, the equivalence factor is a constant determined off-line.The sensitivity of this parameter and the online adaptation rule was studied by Chasse et al. for a SI engine in [13].The robustness of this energy management for a Diesel HEV was studied by Thibault and Leroy in [14].The method to determine the equivalence factor off-line according is described in [15].In the next section, we present the influence of the weight between the fuel consumption and the NO x emissions.

Results
The simulation results are presented in Figure 3.These simulations are performed from the fuel economy optimization to the NO x abatement optimization.The weighting parameter k fc=NO x ranging from 0 (minimum of fuel consumption) to 1 (minimum of NO x emission).The trends are clear for all the driving cycles considered (FTP, WLTP and ARTEMIS Urban): the weighting parameter set the trade-off between FV and NO x emission.For a pure NO x optimisation, the Fuel Consumption (FC) penalty can be very high.However a fine tuning of k fc=NO x provides a great potential for limiting NO x emission at a price of a very small increase of fuel consumption.The achievable NO x reduction is close to 40% for FTP.On the other hand, the fuel penalty is small and does not exceed 5%.This behaviour can be observed for several values of the electric machine power.
Figure 4 shows the instantaneous values of some powertrain quantities during the experimental tests.The comparison concerns the HEV with a 20 kW electric motor.Two cases are presented: the fuel-economy optimization and the NO x reduction optimization.The test results are summarized in Table 2 and in Figure 5.For the optimization of the fuel consumption, the electric motor is mostly used for traction during the urban part of the cycle while the Diesel engine is mostly used at high loads during the extra-urban part to recharge the battery.The ECMS allows to run the ICE mostly for high efficiency setpoints.For the NO x reduction case, the instantaneous values of torque are limited and the optimal NO x strategy avoids the high torque values (especially during the extra-urban part of the drive cycle).When the NO x emissions are not considered (k fc=NO x ¼ 0), the Diesel engine operates mostly at high loads where the engine efficiency is high.The selected operating points are close to the border limit of the LTC region where the amount of EGR is reduced compared to the NO x optimal region.For the NO x optimization case (k fc=NO x ¼ 0:5), most of the selected operating conditions are located at middle engine loads.This region of the engine mapping represents a good compromise between NO x emissions and fuel consumption.The pure engine mode or the recharging mode is limited to the middle torque operating conditions.These results prove that the adapted ECMS is suitable for the Diesel HEV and the optimal behavior is modified compared to the optimization policy applied for gasoline HEV.

Analysis of the Transient NO x Emisssions
The pollutant emission behaviour of an engine is not purely quasi-static.Thus, the assumption that the emissions can be modeled using static maps can be inadequate.An example of transient NO x emissions for a portion of a NEDC is displayed in Figure 6.This test was performed on a high dynamic test bench and the NO x emissions were recorded with a gas analyzer.At each gear change, the injection cut-off decreases the exhaust equivalence ratio.This limits the availability of burned gas at the engine intake.During the transient, the intake Burned Gas Ratio (BGR) drops dramatically.
When the driver re-accelerates, the intake BGR target cannot be reached instantaneously due to burned gas transport from the exhaust to the intake plenum.During this transient, the intake gas composition and thus the cylinder burned gas ratio are not in steady-state operating conditions leading to spikes in measured NO x .
The transient part of the pollutant emission may vary according to the engine, its calibration and the driving cycle considered.In the experimental data presented in Figure 5, the instantaneous NO x levels can be twice the   steady state values during transients.Table 3 recaps the transient NO x contribution on the engine performances during driving cycles.These results correspond to a NECD and a FTP driving cycles performed in conventional engine-driven operations.For the NEDC, the transient NO x contribution is lower than 9%.However, for the FTP cycle, the transient contribution rises up to 42%.
For the next generation Euro 7 vehicles, a new driving cycle (WLTC) is going to be defined.This latter is more representative of real driving conditions (such as the FTP) and imposes more drastic transient solicitations compared to the actual NEDC.Thus, a higher transient part of the total NO x emissions is expected.This paper addresses this issue and aims at developing a suitable control strategy for Diesel HEV.

Transient Torque Control
NO x peaks occurring during engine transients account for an important part of the total NO x emissions.The reduction of the transient part of NO x can be achieved by further improvements of the air system architecture (shorter LP EGR system, combination of HP and LP EGR systems, internal EGR using Variable Valve Actuation (VVA)) or by including a combustion control strategy to adapt injection settings according to air system errors (as proposed by [16]).Here, we consider a Diesel engine with a LP EGR system and without transient combustion control strategy.The goal is to take the advantage of the additional degree of freedom provided by the hybridization only.The idea is to use the electric machine to limit the internal combustion engine dynamics.Some preliminary solutions of transient emission limitation by means of electric boost are proposed in the literature.The limitation of the transient NO x emissions by an adaptation of the transient torque demand is proposed by [17].A similar approach, called  phlegmatising, was developed by [18].Recently, Nue¨sch et al. [19] investigate the influence of considering transient emissions in Diesel hybrid electric vehicles.They consider nitrogen oxide and particulate matter using empirical emissions models.

Key Idea and Principle of the Strategy
Figure 7 shows the influence of the torque demand on the amplitude of a NO x peak obtained with our experimental setup.The NO x peak amplitude is higher for fast torque transient and these peaks decrease as far as the torque gradient decreases.Also, the NO x peaks are well correlated with the BGR error (eF . This figure demonstrates that the NO x emissions are strongly linked with the torque demand and the amplitude of the peak increases with the torque gradient.
These results confirm the conclusion drawn by [17] and [18] who proposed heuristic methods consisting in a limitation of the engine torque setpoint dynamics.In this paper, we apply a similar principle while introducing models of the system to compute the limited engine torque demand.The principle of this strategy is illustrated in Figure 8.
The transient consists in an increasing engine torque step from point A to point B. In this case, the EMS proposes a torque step noted T sp eng;ss .This choice is the solution of Equation (15) (respecting (1)) computed from purely static maps without any consideration for the Diesel engine constraints.The principle of the strategy is to keep the same torque setpoint B requested by the EMS but the trajectory followed to reach this value is adapted.The torque setpoint control consists in defining a new torque trajectory T sp eng;t from point A to point B 0 (in red in Fig. 8) such that the transient NO x peak is avoided or reduced.The torque request at wheel, T sp pwt , depends on the driving conditions (speed and acceleration) and can be evaluated from driver's demand (throttle and brake pedal positions).This demand can be satisfied using the engine, the electric motor or any combination of these two torque sources: where R gb is the gear ratio and R 1 is the front axle ratio.
The torque setpoint can be positive or negative depending on the vehicle operating conditions (traction or braking).T sp mot;ss is the electric motor torque setpoint and T sp eng;ss is the engine torque setpoint.The steady-state split ratio is chosen by the EMS and the principle of the strategy is to modify its value during the engine transients only.In steady-state, the torque split ratio is maintained.In transient, Equation ( 18) is not modified but the steady-state engine and motor torques become two trajectories: In both cases, the torque request at wheel is not modified.The command uðtÞ is defined as the motor torque correction uðtÞ ¼ ÁT mot .Then, the dynamic motor torque request corresponding to the corrected motor torque setpoint is: The command uðtÞ is a portion of the motor torque that compensates for the engine torque during transients.The command u is deduced from Equation ( 19) and (20) and it writes: The command uðtÞ is directly linked to the static motor and powertrain torque setpoints and the dynamic torque setpoint T sp eng;t .This latter is a key variable and it is computed such that the NO x peak generated during a transient is limited.The computation of the corrected engine torque demand T sp eng;t (or trajectory) is explained in the next section.Following this approach, this strategy is applied in cascade with the EMS displayed in Figure 1.The ECMS determines the optimal operating points at some (relatively large) time scale, while a faster controller determines the engine and motor trajectories that minimize the NO x emissions.

NO x Modeling
Nitrogen oxides produced by Diesel engines mainly consist of Nitric Oxides (NO) and, to a lesser extent, of nitrogen dioxides (NO x ).In standard Diesel combustion conditions, NO is essentially produced by the extended Zeldovich mechanism.According to [20], under the equilibrium assumption, the initial NO x formation rate (in mol.cmÀ3 .sÀ1 ) may be written: where h represents the crank angle, N e is the engine speed, H b the temperature in the burned gases and [X] e refers to the equilibrium concentration of the species X. NO x formation is thus promoted by high O 2 concentrations and elevated temperatures in the post-combustion gases.Moreover, [21] experimentally shows that the critical time period is when burned gas temperatures are at a maximum.The complexity level of the model employed in the present study to predict NO x emissions has to be compatible with its integration in the transient torque control strategy, preventing the use of a crank angle resolved thermodynamical model.As the torque trajectory is determined a priori, the use of measured values as input variables of the model is also banned.A semiphysical mean value model proposed by [22], and inspired by NO x kinetics, has been chosen to estimate NO x emissions.A detailed analysis of this model is proposed by [23].NO x concentration in the output of the cylinders is expressed as a function of the engine speed N e , the intake manifold burned gas ratio F 1 and the maximum value of in-cylinder temperature Ĥcyl , according to the following expression: The coefficients a i are calibration parameters learnt on experimental data.The values obtained for the Diesel engine considered in this paper are given in Table 4.In this model, the temperature in the burned gases has been replaced by the maximum value of the mean temperature in the cylinder for sake of simplicity, as the temperature in the burned gases is not measurable for control applications.In spite of this simplification, the model predicts NO x emissions with a good accuracy over the whole engine operating range as well as for variations of BGR, as shown in [23].An example of the NO x model sensitivity according to a BGR variation is displayed in Figure 9. Principle of the control strategy to limit the amplitude of the NO x peak during a torque step.During transients, the intake manifold gas compositions are not in steady-state operating conditions.The maximum in-cylinder temperature reaches its steadystate values much faster, and as a result, is considered to be quasi-static.A simplified model is used to represent the dynamics of the intake manifold burned gas ratio (Eq.24).It consists of a delayed first order filter of the BGR static value: where the time constant s and the time delay t d are parametrized as a function of the engine speed: The BGR map F 1 has the general form: The burned gas ratio dynamic model is compared with experimental results in Figure 12.The model is in good agreement the observed test data and can be used as a reference EGR system model into the torque control strategy.
Table 5 compares the estimated cumulated emissions and the NO x transient contribution on these emissions during driving cycles with the corresponding experimental results given in Table 3.The model correctly predicts both the cumulated NO x emissions and the transient part.It is employed to validate the NO x limitation strategy in simulation.

Engine Torque Setpoint Correction
This section explains how to compute the corrected engine torque trajectory.The transient correction of

Experimental data Model
Comparison between measured and estimated intake manifold burned gas fraction (top) and NO x emission (bottom) during a gear change.
O. Grondin et al. / Energy Management Strategies for Diesel Hybrid Electric Vehicle the torque setpoint requested by the EMS relies on a Mean Value Model (MVM) of the engine NO x emissions presented in the previous subsection.This model links the NO x emissions with the engine speed (N e ), the intake BGR (F 1 ) and the maximum cylinder temperature ( Ĥcyl ).These variables are recognized as first order variables of NO x formation in compression-ignition engines.The NO x model, has the general form: The steady-state NO x level is: The BGR sepoint F ss 1 is computed from a static map (27).Temperature setpoint, Ĥss cyl is also mapped according to engine speed and torque (Fig. 13): During a transient, the BGR is not equal to its setpoint due to the EGR system lag (as displayed in Fig. 6).For the engine control, an online estimation of the BGR is used [24].This estimation is valid for the actual BGR value, however, we need to determine the expected BGR value before the transient has occurred.Then, this estimation cannot be used for the high level torque control strategy.Here, the burned gas transport delay from exhaust manifold to intake manifold is modeled using the MVM detailed previously.This model provides the estimated BGR (F est 1 ) assuming a first order dynamics and a pure delay applied to the BGR map as described in Equation (24).The function / appearing in Equation ( 28) is invertible and a cylinder temperature setpoint can be computed from this BGR estimation and from the target NO sp x (Fig. 8): The NO x target computation is explained in the next subsection.Knowing Ĥsp cyl , the cylinder temperature map w 1 can be inverted in order to find the corrected value of the engine torque (or torque trajectory): For sake of simplicity, we assume that the static maximum temperature map w 1 , established for the nominal BGR setpoint, is representative of the actual BGR condition.A dependency of the temperature map according to the actual BGR would provide acceptable results.For that, the cylinder temperature map w 1 can be modified as follows: Adding this dependency into a modified function w 2 will increase the calibration part of the strategy.We are currently investigating a model-based approach to reduce the experimental tests needed for the calibration Maximum cylinder temperature map.
of the maximum temperature function w 2 .This work is not the purpose of this paper and will be reported in a further paper with the justification for the BGR dependency simplification in map w 1 .

NO x Target Definition
This section explains how to compute the NO x trajectory used for torque trajectory computation.The NO x target definition is purely heuristic and relies on a tunable reduction factor of the maximum NO x peak amplitude.The achievable NO x target NO sp x (Fig. 8) is supposed to be included between the actual (or estimated) value and the steady-state value: The target NO x is tuned empirically with a reduction factor n such that: where ÁNO x is the amplitude of the NO x peak referred as the steady NO x value as shown in Figure 8: This method is simple and allows to flexibly tune the level of NO x reduction.However, the ability for the system to achieve this target is not guaranteed because the system saturation is not considered.Moreover, the reduction factor n value is constant for each transient.Including the system saturation to define what can be the reachable NO x target is a necessary improvement to make the transient torque controller more generic and easy to tune.This will lead to define a limiting factor n according to a feasible NO x target instead of an empirical one.This is the main perspective of this work.

Actuator Limitation and System Saturation
The torque control strategy must account for the actuator limitation that depends on the maximum motor torque T max mot and the static motor torque defined by: T sp mot;ss ðtÞ ¼ T sp pwt ðtÞ À R gb T sp eng;ss ðtÞ R 1 Then the command uðtÞ is bounded such that: From Equations (21,37) The notation satðu; u m ; u M Þ is used for the function defined by: T f eng is the feasible torque trajectory that defines the achievable transient NO x emissions.This latter corresponds to the existing minimum value of the NO x emissions that can be performed during transient conditions where the cylinder oxygen content (i.e.BGR) is not in steady-state condition.The system saturation is not included in this paper and is an ongoing work at IFP Energies nouvelles.Thus, the transient engine torque setpoint writes: T sp eng;t ¼ sat T t eng ; T sp;min eng ; T sp;max eng ð42Þ

Results
This section presents the simulation results of the transient torque control strategy.The objective is to determine whether limiting the Transient Part (TP) of the total NO x emissions is possible or not.We also would like to characterize the influence of the strategy on the Steady-State Part (SSP) of the total NO x emissions as well as the Fuel Consumption (FC).
A simulation platform modelling the complete hybrid vehicle has been developed to simulate driving cycles.In this paper, we consider the FTP.The idea is to simulate the system for several values of the NO x reduction factor n ranging from 0% (baseline case) to 100%.This latter case corresponds to a limitation of all the NO x emissions TP.In order to compare these simulations, the equivalence factor is adapted (dotted line in Fig. 1).The value of the equivalence factor was found by dichotomy in order to satisfy the constraint on the final battery state of charge: t 0 and t f are the initial and final times of the considered driving cycle.The simulations are made for three hybridization levels defined by the power of the electric motor: To be realistic, the battery capacity and vehicle mass are adapted to the electric motor power as described in [15].Pure electric driving is only enabled in the 20 kW case.The EMS finds the steady-state optimal torque split repartition which minimizes a trade-off between quasi-static NO x and fuel consumption.The results displayed are obtained for a constant value of the parameter k fc=NO x ¼ 0:4 in Equation (15).The impact of the hybridization level and this setting variable on NO x emissions and fuel consumption for a Diesel HEV is not the purpose of this paper since it affects only the static balance between NO x and FC.A sensitivity analysis was done by [25].
The strategy acts on transient phases involving increasing BGR setpoint.Figure 14 illustrates its action on two torque transients belonging to the FTP (Fig. 15).n ¼ 0% corresponds to the reference case, without transient strategy; the two others cases (50% and 90%) illustrate the impact of the adjustable transient NO x reduction parameter.For the second torque transient (t ¼ 203 s), the NO x peak can be completely avoided and the tuning parameter allows a flexible reduction of the peak's amplitude.This reduction is made by limiting the maximal cylinder temperature until enough burned gas is available.In the first torque transient (t ¼ 199 s), a saturation on NO x reduction is observed between the 50% and 90% cases.This saturation can be easily explained looking at the motor torque setpoint which has already reached its maximal value (T max mot ) for n ¼ 50%.As a consequence, NO x abatement is not achievable without increasing the electric motor maximum torque (i.e. the motor size).We can notice that the strategy does not affect the steady-state engine and motor torque setpoints as claimed in the previous section.They are equal to the one chosen by the EMS once the transient is over (T sp mot;ss ¼ T sp mot;t and T sp eng;ss ¼ T sp eng;t ).The impact of the transient strategy on the battery SOC during a complete FTP is illustrated in Figure 16.When the strategy is enabled, the SOC decreases progressively because of the electric energy spent to cut NO x peaks during each transient phase.The missing energy must be recuperated in order to complete the driving cycle with a final SOC constraint respected.This was done by adjusting the equivalence factor in the energy management strategy which slightly modifies the static operating point choice.
The effect of the strategy on the cumulated NO x emissions and fuel consumption is illustrated in Figure 17.Due to transient peak reduction, the total NO x emissions significantly drop at the price of a slight increase of fuel consumption.This demonstrates the interest of choosing a partial NO x reduction instead of a total elimination.Indeed in this case, the most interesting case is n ¼ 50% since it allows a global NO x reduction of 17% with a fuel penalty of only 2%.
The transient part of NO x emissions can be controlled with the damping factor n as illustrated in Figures 18,19 and 20.The TP of NO x emissions is defined as the    difference between total and steady-state emissions.The total emissions are computed from the model (28): NO est x ¼ /ðN e ; w 1 ðN e ; T sp eng;t Þ; F est 1 Þ ð 45Þ The steady-state NO x emissions are computed with the same NO x model.But, instead of using the estimated BGR as input, we use its steady-state value computed from the map (27): NO ss x ¼ /ðN e ; w 1 ðN e ; T sp eng;t Þ; 0ðN e ; T sp eng;t ÞÞ ð46Þ They represent what the emissions would be if the exhaust gas recirculation loop had an instantaneous settling time.Even if the static part of the cumulated NO x emissions increases slightly with n due to the slight modification of static operating points, the total NO x emissions are decreasing.The strategy allows to divide the transient part by two (from 49% to 24%) while the cumulated NO x emissions are reduced by 26%.For n ¼ 90%, the remaining transient part corresponds to the saturation of the electric motor which is not able to provide enough torque.
For lower hybridization levels (14 kW and 8 kW), the electric torque available to allow transient NO x reduction is lower and the emissions can not be reduced as much as in the full hybrid case.In the 8 kW, the electric motor saturation is quickly reached.As a consequence the transient NO x is limited (Fig. 20).
As a conclusion, the transient strategy allows to control the NO x transient emissions as long as the maximal electric motor torque is not reached.With a 20 kW electric motor, a spectacular NO x reduction is achievable with a reasonable increase in fuel consumption.The value of the damping factor n tunes the trade-off between the NO x TP and the FC.

CONCLUSION
In Diesel hybrid vehicles, steady-state and transient NO x emissions must be considered in the supervision strategy.First, we adapted the ECMS-based energy management strategy to account for the steady NO x .An additional tuning parameter was introduced into the ECMS and allows to tune the trade-off between NO x abatement and fuel consumption reduction.These results clearly demonstrate that model-based strategy (ECMS) allows an easy integration of the NO x objective.In addition to the simulation results, the adapted ECMS is validated on the experimental hybrid test bench.The trend observed using the simulator was experimentally reproduced leading to a substantial reduction of the NO x emissions.In addition, we introduced a torque control cascaded with the EMS in order to correct the torque split ratio computed by the ECMS.This strategy focuses on transient NO x emissions and adapts the torque split ratio during transient operations where NO x peaks are produced.The strategy tends to smooth the engine torque using the motor torque as torque compensator.This controller uses a mean value model for the intake manifold burned gas ratio dynamics and for the NO x production.Using such models into a vehicle supervision level is the novelty of the approach.The simulation results have shown that the transient part of the NO x emissions can be reduced.The strategy allows to limit the transient part of the emissions without modifying the steady-state part.Also, the use of the electric motor during transients has a price and the transient NO x reduction slightly increases fuel consumption.This trade-off can be tuned with the reduction factor.The proposed strategy can be valuable to deal with driving cycles presenting more transient phases.This will be the case for Euro 7 vehicles with the new worldwide harmonized light-duty transient cycle.

nO.
Grondin et al. / Energy Management Strategies for Diesel Hybrid Electric Vehicle

Figure 3
Figure 3Evolution of the tradeoff betweeen NO x emissions and fuel consumption for a parametric variation of the electric machine power and the weighting parameter k fc=NOx .From top to bottom: FTP, WLTP and ARTEMIS Urban.

Figure 5
Figure 5 exhibits several peaks in NO x during the first acceleration of the extra-urban part of the driving cycle.At each gear change, the injection cut-off decreases the exhaust equivalence ratio.This limits the availability of burned gas at the engine intake.During the transient, the intake Burned Gas Ratio (BGR) drops dramatically.When the driver re-accelerates, the intake BGR target cannot be reached instantaneously due to burned gas transport from the exhaust to the intake plenum.During this transient, the intake gas composition and thus the cylinder burned gas ratio are not in steady-state operating conditions leading to spikes in measured NO x .

5 Figure 4
Figure 4Experimental results for NEDC with the HEV with a 20 kW electric motor.Comparison of two optimisation trade-offs: fuel consumption oriented optimisation with k fc=NOx ¼ 0:2 (red line) and NO x -oriented optimisation with k fc=NOx ¼ 0:5 (black dotted line).

Figure 5
Figure 5 Summary of the experimental results.The gains are relatives to the stand-alone Diesel engine.Three configurations are displayed: Stop and Start, HEV with k fc=NOx ¼ 0:2 and HEV with k fc=NOx ¼ 0:5.

Figure 6 First
Figure 6First acceleration of the extra-urban part of the NEDC.a) Vehicle speed, b) engine speed (dotted line) and fuel mass flow, c) BGR and d) NO x emissions.The steady state NO x value is calculated from a static map depending on engine speed and torque.The measured NO x value is delayed and filtered due to the gas analyzer dynamics.

Figure 7
Figure 7Experimental results of a transient representing an engine cut-off followed by a tip-in with a torque gradient limitation.a) Engine torque, b) BGR error and c) NO x emissions.

Figure 9 Comparison 11 Comparison
Figure 9Comparison between the NO x model and experimental data for a BGR variation.

Figure 14 Impact
Figure 14 Impact of the transient strategy parameter n -FTP Full Hybrid 20 kW.a) Engine torque, b) motor torque, c) maximal cylinder temperature, d) burned gas ratio and e) NO x emissions.

Figure 16 Impact
Figure 16Impact of the transient strategy on the battery SOC -FTP Full Hybrid 20 kW.

Figure 17 ImpactFigure 18 ImpactFigure 15 FTP
Figure 17 Impact of the transient strategy parameter n on the tradeoff between NO x emissions and fuel consumption -FTP Full Hybrid 20 kW.

Figure 19 Impact
Figure 19 Impact of the transient strategy parameter n on the NO x transient part -FTP Mild Hybrid 14 kW.

Figure 20 Impact
Figure 20 Impact of the transient strategy parameter n on the NO x transient part -FTP Mild Hybrid 8 kW.

TABLE 3
Engine performances measured during NEDC and FTP driving cycles.The Transient Part (TP) contribution (in %) of the FC (in L/100 km) and NO x (in mg/km) emissions are computed from the experimental measures and the engine static maps

TABLE 5
Comparison between measured and estimated NO x emissions during NEDC and FTP driving cycle.The experimental Steady-State Part (SSP) of the emissions are computed from the static map.The estimated steady-state emissions are calculated from the model using the intake BGR setpoint F sp and (38), the minimum and maximum engine torque values write: