Optimal energy management for a diesel hybrid electric vehicle considering transient PM and...

Optimal energy management for a diesel hybrid electric vehicleconsidering transient PM and quasi-static NOx emissions

Tobias Nüesch a,n, Mu Wang a, Pascal Isenegger a, Christopher H. Onder a, Rüdiger Steiner b,Pedro Macri-Lassus b, Lino Guzzella a

a ETH Zurich, Institute for Dynamic Systems & Control, Sonneggstrasse 3, 8092 Zurich, Switzerlandb Daimler AG, Group Research & Advanced Engineering Powertrain, 019-G206 RD/RPE, 70546 Stuttgart, Germany

a r t i c l e i n f o

Article history:Received 31 May 2013Accepted 17 January 2014

Keywords:Energy managementHybrid electric vehicleDiesel engineParticulate matterNitrogen oxide (NOx)

a b s t r a c t

In this paper, optimal energy management strategies are derived to balance fuel consumption, rawparticulate matter (PM) emissions, and raw nitrogen oxide (NOx) emissions for a Diesel hybrid electricvehicle. Two methods for the derivation of these strategies are compared. One method is based ondynamic programming and steady-state engine maps only. The second method is based on dynamicprogramming, steady-state engine maps, and a validated transient PM emission model. As a result, onlythe second method allows for the generation of smooth engine set point trajectories to reduce transientPM emissions without compromising fuel consumption and NOx emissions.

& 2014 Elsevier Ltd. All rights reserved.

1. Introduction

Car manufacturers are forced to further reduce fuel consump-tion and pollutant emissions. Particularly for Diesel-poweredvehicles, pollutant emission abatement is a challenging task. Whilefor conventional vehicles the optimization of emissions takes placein reaction to operating points dictated by the driver, hybridelectric vehicles (HEVs) offer the additional degree of freedom tochoose the operating point of the engine independently of thedriver's torque request. Therefore, the hybridization of Diesel-powered vehicles offers the possibility to further reduce not onlythe fuel consumption, but potentially also pollutant emissions.

Yet, when hybridizing a Diesel engine-powered vehicle, thegain in additional fuel economy and the potential to further reduceemissions must be analyzed carefully. For example, Lindenkamp,Stöber-Schmidt, and Eilts (2009) and Filipi et al. (2006) haveshown that a Diesel hybrid electric vehicle can indeed save morefuel, but at the same time also emit much more pollutants than itsconventional counterpart. Therefore, control strategies for DieselHEVs also have to account for emissions at the energy manage-ment level. Research articles dealing with energy managementstrategies (EMS) accounting for fuel consumption and quasi-staticemissions can be found in Johnson, Wipke, and Rausen (2000), Lin,

Peng, Grizzle, and Kang (2003), Lin, Peng, and Grizzle (2004), andAo et al. (2008), to name but a few.

Further studies have shown that more than 50% of total Dieselpollutant emissions can be attributed to transient effects1 duringengine operation (Ericson, Westerberg, & Egnell, 2005; Hagena,Filipi, & Assanis, 2006; Rakopoulos & Giakoumis, 2009). Sucheffects cannot be modeled solely by taking quasi-static emissionsinto account. As a consequence, new approaches for the design ofEMSs have been proposed. One approach described in Lindenkampet al. (2009) proposes to ramp and limit the engine torque at afixed value to avoid high transients. This method was shown toyield lower transient PM emissions for a parallel HEV with aheuristic energy management strategy. The authors of Wang et al.(2011) presented an air-to-fuel-ratio-based engine transient miti-gation strategy similar to an advanced smoke limiting strategy.The type of EMS was not indicated. An approach based on optimalcontrol theory was presented by Serrao et al. (2011). The authorsformulated an optimal control problem based on Pontryagin'sMinimum Principle to account for transient emissions. However,a solution to the problem was not provided. Furthermore, theauthors of Johri, Salvi, and Filipi (2011) used neuro-dynamicprogramming in conjunction with a neuro-fuzzy dynamic emis-sion model to regulate transient PM and NOx emissions online in aseries of hydraulic hybrid vehicles.

In Nüesch, Wang, Voser, and Guzzella (2012), the authorspresented a method to benchmark energy management strategies

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n Corresponding author. Tel.: þ41 44 6320485; fax: þ41 44 6321139.E-mail addresses: [email protected] (T. Nüesch), [email protected] (M. Wang),

[email protected] (P. Isenegger), [email protected] (C.H. Onder),[email protected] (R. Steiner),[email protected] (P. Macri-Lassus), [email protected] (L. Guzzella).

1 In this paper, transient emissions are referred to effects arising mainly due tothe turbocharger lag. Any influences of engine temperature, etc. are not considered.

Please cite this article as: Nüesch, T., et al. Optimal energy management for a diesel hybrid electric vehicle considering transient PM andquasi-static NOx emissions. Control Engineering Practice (2014), http://dx.doi.org/10.1016/j.conengprac.2014.01.020i

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taking into account transient pollutant emissions. The method wasbased on dynamic programming (Bertsekas, 2005), and it includeda dynamic NOx and PM emission model adopted from theliterature. However, since the emission models were not validated,the conclusions were not supported to their full satisfaction.

In this paper, a validated transient PM emission model ispresented that is easy to use for the simulation and optimizationof energy management strategies. The NOx model is of the quasi-static type because its performance proved to be sufficient whencompared to measurement data. Simulation results are thenobtained for the energy management strategies derived withtwo different methods. One method takes into account onlyquasi-static PM and NOx emissions, while the second methodtakes into account transient PM emissions and quasi-static NOxemissions. For both methods, the relative weights of fuel con-sumption, PM emissions, and NOx emissions are varied to studytheir trade-offs for a hybrid electric vehicle on the MVEG-95homologation cycle. Furthermore, a comparison of the two meth-ods is performed and the advantages of a strategy accounting fortransient emissions are discussed in detail.

The paper is organized as follows: after explaining the meth-odology in more detail in Section 2, the emission models arepresented in Section 3. In Section 4, the two methods for thederivation of fuel- and emission-optimal energy managementstrategies are compared. In the last section, the main findings ofthis study are summarized.

2. Methodology

The energy management controller of a hybrid electric vehiclecoordinates the operating set points for the combustion engineand the electric motor. In this paper, the optimal energy manage-ment is applied such that it optimizes a cost function Jð�Þ over anentire driving cycle known in advance.

Introducing the variables fx;u;wg for the states of the system,the control signals, and the disturbance (driving cycle) of length Ntime steps of 1 s, respectively, the optimal control problem isformulated as2:

Find the sequence of controls u¼ ½u0;…;uN�1� that minimizes thecost function Jðx;u;wÞ for the entire driving cycle w, that is,

uo ¼ argminu

Jðx;u;wÞ ð1Þ

subject to the vehicle model presented in Appendix A, and subject tothe charge-sustenance condition xSOCN ¼ xSOC0 .

Identically to the definition in Nüesch et al. (2012), the costfunction Jð�Þ here represents a weighted sum of the instantaneousfuel consumption and pollutant emissions:

Jðx;u;wÞ ¼ ∑N�1

k ¼ 0ð1�αPM�αNOxÞ �

_mf ðxk;uk;wkÞ_mf ;norm

�

þαPM � _mPMðxk;uk;wkÞ_mPM;norm

þαNOx �_mNOxðxk;uk;wkÞ

_mNOx;norm

�: ð2Þ

The disturbance is a predefined driving cycle given by itsvelocity trajectory. The variables _mf ; _mNOx; _mPM stand for the massflow rates of fuel, NOx, and PM, respectively, whereas the subindex“norm” denotes a normalization constant. The positive-valuedweighting factors αNOx and αPM satisfy the inequalityð1�αNOx�αPMÞZ0, such that the fuel consumption always has asemi-positive weight.

There is at least one state variable in this problem: the batterystate of charge xSOC. The state variable for the state of charge isneeded to ensure a charge sustaining solution over the driving

cycle. Further, depending on the emission model used, the enginetorque is added as an additional state variable xTe . The enginetorque state variable is used for the transient emission modelintroduced later in Section 3. The corresponding state dynamics indiscrete time are written as

xSOCkþ1 ¼ f SOC ðxSOCk ;uk;wkÞ ð3Þ

xTekþ1 ¼ Te;k: ð4Þ

The final state constraint, ensuring charge-sustenance of thebattery, is given by xSOCN ¼ xSOC0 ¼ 0:60. For xTe , the initial conditionis assumed to be 0 N m, and no final state constraint is imposed.

The only control u of the vehicle is the torque of the internalcombustion engine. The gears are adjusted according to a heuristicgear shift table based on the transmission output speed and pedalposition. Therefore, the gearbox input speed trajectory can becalculated for the entire driving cycle prior to the optimization.This allows the time-shifted gearbox input speed trajectory to beused as an extra disturbance in the DP algorithm, withoutintroduction of another state.

Note that to account for transient emissions, the emission massflow rate of the transient emission model (5) is used. When onlyquasi-static emissions are of interest in the design of the EMS, theemission mass flow rate of a steady-state emission map is assignedand the dynamic state xTe from the problem is removed.

The above optimal control problem is solved using the deter-ministic dynamic programming algorithm provided by Sundströmand Guzzella (2009).

3. Emission models

3.1. Engine description

For the studies in this paper, measurements were taken on apassenger car Diesel engine with the nominal data listed inTable 1. The engine features exhaust gas recirculation, intake portshut-off, and a turbocharger with variable turbine geometry. Thereference maps for fuel injection, intake manifold pressure,exhaust gas recirculation, intake port shut-off, and the control ofthe turbine are different from the manufacturer's original calibra-tion. The reference maps were adjusted to custom use with regardto various research projects at the authors' research institute. Thecontroller for the air path was implemented according to Zentner,Schäfer, Fast, Onder, and Guzzella (in press).

3.1.1. Steady-state mapsFigs. 1–3 show the steady-state maps of the fuel efficiency, PM

emissions, and NOx emissions, respectively. Exhaust gas recircula-tion is mainly active in the low load and low speed area of theengine map.

Table 1Engine data.

Description Value

Engine type Research engine (custom calibration)Fuel type DieselEngine displacement 2998 ccmNumber of cylinders 6Nominal power 173 kWEmission legislation Euro 5Features Single stage turbocharger

Variable turbine geometryHigh-pressure exhaust gas recirculationPre, main, and post injectionIntake port shut-off

2 For brevity, the notation of the time dependency yðtkÞ is replaced by yk.

T. Nüesch et al. / Control Engineering Practice ∎ (∎∎∎∎) ∎∎∎–∎∎∎2





Note that the maximum torque of the engine is limited to300 N m because of limitations in the operation of the dynam-ometer of the engine test bench. The same reason holds for themaximum engine speed which is limited to 3000 rpm.

3.2. PM emission model

In the literature, many publications on modeling of PM emis-sions can be found, see for instance the overview in Kumar,Manish, and Varun (2013) or the literature survey in Ahlawat(2011). Phenomenological models, as described in Hiroyasu,Kadota, and Arai (1983), Fuso, Knox-Kelecy, and Foster (1994),and Kirchen and Boulouchos (2009), for example, are usuallyemployed to describe in detail the formation of PM emissionsduring the combustion. However, the computational complexityoften exceeds the limit for an application of such models tooptimization and control. By contrast, empirical models(Ahlawat, Hagena, Filipi, Stein, & Fathy, 2010; Benz, Onder, &Guzzella, 2010; Brahma, Rutland, Foster, & He, 2005; Hirsch &Alberer, 2008; Tschanz, Amstutz, Onder, & Guzzella, 2010) areusually better suited for those kinds of applications.

Since in this paper the PM emission model is to be used in theframework of dynamic programming in conjunction with thesimulation of a hybrid vehicle, the model has to be of lowcomputational complexity. In the literature, several modelingapproaches can be found that satisfy this requirement, see e.g.Hausberger, Ivanisin, and Riemersma (2001), Ericson et al. (2005),and Giakoumis and Lioutas (2010). Common to all these empiricalapproaches is the use of at least one state which renders the modela dynamic system. This additional state allows the turbochargerlag to be modeled. In Watson and Janota (1982) and Rakopoulosand Giakoumis (2009), this effect was identified to be the mostimportant reason for transient emissions.

From the model suggestions mentioned above, a model ischosen that is a modified version of the approach presented byGiakoumis and Lioutas (2010). Accordingly, the transient emis-sions at the discrete time step k are calculated as

_mPM;k ¼ _mPM;qs;k � 1þcðωe;k�1; Te;k�1Þ �Te;k�Te;k�1

τs

� �; ð5Þ

where _mPM;k stands for the transient emission mass flow rate,

_mPM;qs;k ¼ f PMðωe;k; Te;kÞ

stands for the quasi-static PM emissions obtained from the steady-state map, Te is the engine output torque, τs ¼ tk�tk�1 ¼ 1 s is theconstant sampling time, and cðωe;k�1; Te;k�1Þ is a positive-valuedfitting constant defined similar to the one in Giakoumis andLioutas (2010) and Giakoumis and Alafouzos (2010). The c-factorat any instant of time tk depends on the engine operatingconditions (ωe;k�1; Te;k�1) one time step before. Accordingly, theengine map is partitioned into nine regions, composed of threeengine speed intervals and three load intervals. The speed inter-vals are 0–1400 rpm, 1401–2000 rpm, and 2001–3000 rpm. Theload intervals are 0–33%, 34–66%, and 67–100%, where the load isdefined as

load ≔Te

Te;maxðωeÞ:

These regions specify the potential amounts of the transientemissions to be expected when a transient is started from one ofthose regions. For example, the c-factor for a transient starting atlow speed and low load would be relatively large because of thepronounced turbocharger lag (Giakoumis & Lioutas, 2010). Thec-values obtained for the model in this paper are listed in Table 2.

The overall correction applied to the quasi-static PM emissionmass flow _mPM;qs;k is limited to 3. Otherwise, unrealistically highemission predictions might occur.

In reality, transient emissions can also be lower than quasi-static emissions in the case of a negative torque change. For PM,for example, this is explained by the intake manifold pressurebeing higher than compared to the quasi-static pressure during

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Fig. 1. Fuel efficiency indicated in g/kW h. The maximum torque corresponds to anartificial limitation due to limited operation of the dynamometer. The same holdsfor the engine speed which is limited to 3000 rpm.

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Fig. 2. Steady-state particulate matter (PM) emissions given in mg/kW h.Pronounced PM emissions are observed in the low speed/high torque area wherethe turbocharger is limited by its surge limit.

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Fig. 3. Steady-state nitric oxide emissions given in g/kW h.

T. Nüesch et al. / Control Engineering Practice ∎ (∎∎∎∎) ∎∎∎–∎∎∎ 3





transients. Nevertheless, the influence of negative torque changesis neglected since their influence on the quasi-static correction ismuch smaller than in the case of positive torque changes.

3.3. NOx emission model

The literature on NOx emission models is vast, see e.g. theliterature survey in Asprion, Chinellato, and Guzzella (2013) orKumar et al. (2013) for an overview of physics-based, empiricaland mixed approaches. The use of physics-based or phenomen-ological models (Bazari, 1992, 1994; Hiroyasu et al., 1983; Khan &Greeves, 1973; Kyriakides, Dent, & Mehta, 1986; Shahed, Chiu, &Yumlu, 1973) or typical empirical models (e.g. Hirsch, Oppenauer,& del Re, 2010; Sequenz & Isermann, 2011 and the referencestherein) is too complex for the methodology presented in thispaper since either too many state variables or many non-availableinput variables are required. Therefore, the starting point for thedevelopment of a NOx model in this paper was a map of themeasured steady-state NOx emissions as a function of enginespeed and torque:

_mNOxðtkÞ ¼ _mNOx;qsðtkÞ ¼ f NOxðweðtkÞ; TeðtkÞÞ: ð6ÞIn fact, such a quasi-static model turned out to be sufficient due tothe observation that the transient NOx emissions are negligible forthe engine and its calibration considered in this paper. More detailon the verification of this assumption is given in the validationsection below. In a different application, where a steady-state mapis not sufficient, the models presented in Hausberger et al. (2001),Ericson et al. (2005), and Giakoumis and Lioutas (2010) or themodel structure (5) could be used. If in addition thermal influ-ences have to be considered, the reader is referred to Gao, Conklin,Daw, and Chakravarthy (2010), for instance.

3.4. Validation

For the validation of the PM model, the test bench wasequipped with a photo-acoustic soot sensor Micro Soot Sensorby AVL GmbH with an identified response time of about 0.5 s, anda DMS500 fast particle analyzer by Cambustion Ltd with aresponse time of 0.2 s (Cambustion Ltd., 2008). For both devices,the emission samples were taken after the turbine without anyaftertreatment system in-between. Moreover, the particle analyzerwas calibrated such that its calculated mass corresponds to themass measured by the soot sensor in most of the operating pointsof the engine. For the subsequent validation of the PM emissionmodel, only measurement data for the particle analyzer are shownsince this device provided a lower response time and thus moreaccurate measurements during transients.

The NOx model was validated with measurement dataobtained with a VDO/NGK UniNOx sensor by Continental AG witha response time of about 1.8 s. In addition, measurements weretaken with a fNOx400 Fast CLD, sometimes known as fast NOxanalyzer, by Cambustion Ltd. with a response time of less than0.01 s (Collier, Gregory, Rushton, & Hands, 2000).

Fig. 4 shows the instantaneous and cumulated NOx emissionsfor the quasi-static NOx model, the UniNox sensor and the fast

NOx analyzer for a load step from 0 to 50 N m and back to 0 N m at1200 rpm. This load step represents the most difficult case for theNOx model, namely low steady-state values and a relatively largepeak compared to the steady-state values (� 30% overshoot).As can be seen from the upper figure, the fast NOx analyzer showsa fast increase of NOx emissions and subsequent oscillatingbehavior due to the EGR control. By contrast, the UniNOx sensorshows a slow increase of NOx emissions, attributed to the slowsensor response time. The NOx emissions predicted by the quasi-static model increase fast and level off at the new steady-statevalues. Despite the differences observed, the cumulated emissionsof the quasi-static model, the fast NOx analyzer and the UniNOxsensor are all about the same as seen in the lower graph of Fig. 4.Similar effects, but even less significant and therefore not shownhere, are also observed at higher loads and for larger load steps.Summarized, transient NOx emissions do not contribute signifi-cantly to the total NOx emissions for the engine under investiga-tion due to the fact that the steady-state NOx emissions have amuch higher influence on the total NOx emissions. Therefore, theNOx emissions are modeled with a quasi-static approach. More-over, in the remainder of the validation, the UniNOx sensor is usedas a reference since the fast NOx analyzer suffers from a largesensor drift. As such, the fast NOx analyzer could not be used overthe duration of a typical driving cycle.

For calibration and validation, different data sets were used.The calibration data comprise steady-state data of different oper-ating conditions as well as data of transients generated withvarious torque steps, speed steps, and engine cycles. The validationwas based on data obtained from driving cycles.

Fig. 5 shows the performance of the PM and NOx models on adriving cycle. The driving cycle was repeated three times in orderto obtain an estimate of the standard deviation of the emissionmeasurements. While the quasi-static PM model (black dottedline) is unable to predict the PM peaks, the dynamic PM model(black solid line) shows a good agreement with the measurementdata of the fast particle analyzer (dark gray solid line).

The NOx model (black solid line) seems to yield slightly highervalues during transients when compared to the measurement dataobtained with the UniNOx sensor (dark gray solid line). Taking intoaccount the slow response of the NOx sensor, the model shows anacceptable performance.

Table 3 lists the cumulated emission values of three differentcycles. Each cycle was measured three times in order to determine

Table 2Correction values c for the transient PM emission model.

Speed (rpm) Load intervals

0–33% 34–66% 67–100%

0–1400 0.0870 0.0406 0.04131401–2000 0.0339 0.0382 0.10592001–3000 0.0245 0.0262 0.0088

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x[m

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x[m

g]

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ModelUniNOxfast NOx

Fig. 4. Comparison of the quasi-static NOx model, the UniNOx sensor measure-ment data and the fast NOx analyzer measurement data for a load step from 0 to50 N m and back to 0 N m at 1200 rpm.






the repeatability or the standard deviation of the measurements(7).

The cumulated PM emissions predicted by the dynamic modelstay within one standard deviation of the recorded cumulatedvalues of the PM measurements. By contrast, the performance ofthe quasi-static PM model in terms of cumulated emissions isinsufficient.

Further, the cumulated NOx emissions predicted the NOxmodel show an increase of about 3–11% compared to the mea-surements obtained with the UniNOx sensor. This deviation is adirect consequence of the relatively high response time of theUniNOx sensor which was used to obtain the measurement data.Therefore, the quality of the prediction in terms of cumulatedemissions is acceptable.

4. Comparison of the methods

In this section, two methods are compared for the derivation ofenergy management strategies including pollutant emissions forhybrid electric vehicles, namely (i) a method with the quasi-staticemission models only (referred to as the static EMS) and (ii) amethod with the dynamic PM emission model and the quasi-staticNOx model (referred to as the dynamic EMS).

First, the influence of the static EMS on fuel consumption andemissions is analyzed. Second, the same is done for the dynamicEMS. Finally, the advantages of a dynamic EMS over a static EMSare explained.

All studies are carried out on the MVEG-95 driving cycle (NewEuropean Driving Cycle, NEDC) with the hybrid vehicle modeldescribed in Appendix A.

4.1. Static EMS

The static EMS optimizes only the steady-state operating pointsof the electric motor and the engine. The strategy takes intoaccount the fuel consumption, PM emissions, and NOx emissionsdepending on the weighting factors αPM and αNOx. However, thetransitions between the operating points are not taken intoaccount in this strategy. Therefore, large transients may occurbetween any two consecutive time steps.

In this subsection, first the influence of the static EMS on theoperating points of the engine is analyzed as well as the fuelconsumption and emissions using only the predictions of thesteady-state maps. Then, the influence of the static EMS on theemissions calculated with the dynamic emission model is inves-tigated. The results show that the static EMS can generatetrajectories with large changes of the operating conditions of theengine. These changes generally result in significant transientemissions, such that the predicted emission data of the staticEMS are not valid.

4.1.1. Influence on the operating points of the engineFirst, the influence of the optimal static EMS on the operating

points of the engine is analyzed for a fuel-optimal, a PM-optimal,and a NOx-optimal choice of the weighting factors αPM and αNOx.Operating conditions for an intermediate choice of the weightingfactors are not shown because the resulting operating pointsrepresent a mix of those obtained with the extreme choices ofthe weighting factors.

Fig. 6 shows the time-based frequency distribution of theoperating points plotted in three types of engine maps. Fig. 6ashows the fuel efficiency map for a fuel-optimal choice of theweighing factors (αPM ¼ αNOx ¼ 0). The engine is mainly operated atmedium loads with occasional excursions to high loads where thebrake specific fuel consumption is reasonably good. The totalengine run-time is 189 s or 16% of the total duration of thedriving cycle.

Fig. 6b shows the PM emission mass flowmap for a PM-optimalchoice of the weighing factors (αPM ¼ 1; αNOx ¼ 0). Most of theoperating points are located at low loads, with some excursions tomedium and high loads. All operating points belong to regionswhere the brake specific PM emissions are low. The total enginerun-time is 480 s or 41%, which is more than double the run-timeof a fuel-optimal strategy.

Fig. 6c shows the NOx emission mass flow map for a NOx-optimal choice of the weighing factors (αPM ¼ 0; αNOx ¼ 1). Alloperating points are located at low to medium loads withoutany excursions to high loads. These operating points belong to theregion where the brake specific NOx emissions are lowest. Thetotal engine run-time is 329 s or 28%, which is slightly less thandouble of the run-time of a fuel-optimal strategy.

These results show that, by an appropriate choice of theweights αPM and αNOx, the energy management strategy forcesthe operation of the engine to regions where the brake specificperformance index (fuel consumption, PM, or NOx) is best. Thismeans that an optimal-control based energy management issensitive to the underlying engine maps, which can result infrequent changes of the operating conditions of the engine such

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Fig. 5. Validation of the PM and NOx emission models. The graphs show themeasured engine speed N and engine torque T, and a comparison of the emissionmodels with the corresponding measurement data.

Table 3Cumulated emissions recorded on three different driving cycles.

Data source No. 1 No. 2 No. 3

PM quasi-static model (mg) 25.5 31.1 33.1PM dynamic model (mg) 36.2 42.8 43.2PM measurement (mg) 45.5715.5 42.377.9 40.674.4NOx model (mg) 3697 2685 2758NOx measurement (mg) 33337123 2486784 26847100






as frequent engine on/off behavior or frequent changes of torqueset points.

4.1.2. Emission prediction with the quasi-static approachIn this subsection, the influence of the optimal static EMS on

the predicted fuel consumption and emissions is analyzed basedon the steady-state maps only, i.e. without any calculation oftransient PM emissions.

Fig. 7 shows the trade-offs between fuel consumption, specificPM emissions, and specific NOx emissions for various values of theweighting factors αPM and αNOx. In each graph, the fuel-optimalsolution (αPM ¼ αNOx ¼ 0) is indicated by a black square.

Fig. 7a shows the trade-off between the fuel consumption andPM emissions. For a fixed value of αNOx, increasing the weight αPMin the design of the EMS gradually decreases PM emissions. Forlow values of αNOx, the fuel consumption gradually increases at thesame time. For high values of αNOx, the fuel consumption firstdecreases before increasing again, which is due to the cross-coupling between the weights αPM and αNOx.

Fig. 7b shows the trade-off between the fuel consumption andNOx emissions. For a fixed value of αPM , increasing the weight αNOxin the design of the EMS gradually decreases NOx emissions andincreases the fuel consumption at the same time.

Fig. 7c shows the trade-off between PM and NOx emissions.Accordingly, the results indicate that the Euro 5 emission stan-dards (5 mg/km PM, 180 mg/km NOx) may potentially be met

without any emission aftertreatment for the choice αPM ¼ 0:1,αNOx ¼ 0:5 at the cost of an increase in fuel consumption of about2% compared to that obtained with the fuel-optimal static EMS.

4.1.3. Emission prediction with the dynamic PM emission modelThe influence of the static EMS on the transient emissions is

assessed by simulating the transient emission model based on thestatic strategies. The operating points of the engine are still thesame as in the previous analysis. Therefore, the influence of thetransitions between the operating points can now be analyzed.

Fig. 8 again shows the fuel consumption, PM emissions, andNOx emissions for the same choice of weights αPM and αNOx as inthe previous analysis.

Fig. 8a shows the trade-off between the fuel consumption andPM emissions. For a fixed value of αNOx, increasing the value of αPMseems to result in lower PM emissions. Compared to the predictionobtained with steady-state maps, the general level of PM emis-sions is more than 20% higher. For example, the lowest achievablePM emission level predicted by the dynamic PM model, comparedto the static prediction, has increased by 25%. Thus, the increasedamount of emissions is attributed to the transient emissions whichare observed during aggressive changes of the engine operatingset points.

With reference to the observation described in Section 4.1.2,the Euro 5 emission standards may potentially be met with thesame weighting factors for the static EMS evenwithout accounting

Fig. 6. Engine operating points for the fuel-optimal, PM-optimal, and NOx-optimal strategies obtained with the static EMS.






for transient emissions in the design of the EMS. However, the PMemission levels could be higher for a different engine where moreexhaust gas is recirculated for instance. In such a case, reducingtransient emissions can become much more important than in thecase just presented.

Another drawback of the static EMS is that it is not possible tofully control the PM emission performance in the development ofthe static EMS. Gradually increasing the value of αPM does notalways guarantee lower PM emissions as shown in Fig. 9.

4.2. Dynamic EMS

A dynamic EMS aims to compensate the drawbacks of the staticEMS by taking into account the transitions between consecutiveoperating set points of the engine. With the approach presented inNüesch et al. (2012) and in this paper, the dynamic programmingalgorithm uses a dynamic emission model to generate the infor-mation as to when transients have a large influence on PMemissions. Thus, simulation results are presented using thedynamic EMS method described in Section 2 together with thevalidated transient emission model described in Section 3. Again,the results below were obtained on the MVEG-95 driving cycle bysimulating the model of the hybrid electric vehicle described inAppendix A. The results of the optimal dynamic EMS are alsocompared to those obtained with the optimal static EMS.

4.2.1. Influence on the operating points of the engineSimilar to the analysis for the static EMS, the influence of

the dynamic EMS on the operating conditions of the engine is

analyzed first. This analysis is made for the PM-optimal strategyonly as the fuel-optimal and NOx-optimal strategies yield thesame results as for the corresponding static EMS.

Fig. 10 shows the engine operating points for the PM-optimaldynamic EMS. The distribution of the operating points is verysimilar to that of the PM-optimal static EMS. Most of the operatingpoints are located at low loads with occasional excursions to highloads, i.e. the operating conditions remain at regions where thebrake specific PM emissions are low. The total engine run-time ofthe dynamic EMS is 467 s, which is slightly lower than the 480 sobtained with the static EMS.

The difference between the PM-optimal dynamic and the staticEMS is best observed when their torque set points are comparedon a segment of the driving cycle. Fig. 11a shows the torque setpoints of both strategies on a part of the MVEG-95 driving cycle.The graph shows that the engine torque set points of the staticstrategy can vary rapidly and reach high torque set points. Also,the engine is turned on and off frequently. By contrast, thedynamic strategy generates smooth transitions between the oper-ating points without necessitating the engine to be frequentlyturned on and off.

4.2.2. Emission prediction with the dynamic PM emission modelIn this subsection, the trade-off between the fuel consumption,

PM emissions, and NOx emissions is analyzed for various values ofthe weighting factors αPM and αNOx in the design of the optimaldynamic EMS. All PM emissions indicated were obtained bysimulating the transient PM model.

4 4.2 4.4 4.6 4.8 5 5.21.5

2

2.5

3

3.5

4

4.5

5

5.5

6

6.5

7

FC [L/100km]

PM

[mg/

km]

4 4.2 4.4 4.6 4.8 5 5.2150

200

250

300

350

400

450

500

FC [L/100km]

NO

x [m

g/km

]

1.5 2 2.5 3 3.5 4 4.5 5 5.5 6 6.5 7150

200

250

300

350

400

450

500

PM [mg/km]

NO

x [m

g/km

]

αNOx

= 0

αNOx

= 0.1

αNOx

= 0.2

αNOx

= 0.5

αNOx

= 0.8

αNOx

= 1

αPM

= 0

αPM

= 0.1

αPM

= 0.2

αPM

= 0.5

αPM

= 0.8

αPM

= 1

Fig. 7. Results for the static EMS by varying the weighting factors αPM ; αNOx for the MVEG-95. The PM emission levels indicated were evaluated only based on the steady-statemaps (no dynamic correction).






Fig. 12 shows the trade-offs between the fuel consumption, PMemissions, and NOx emissions for various choices of αPM and αNOx.

Fig. 12a shows the trade-off between the fuel consumption andPM emissions. For a fixed value of αNOx, increasing the value of αPMgradually decreases the PM emissions, while it generally increasesthe fuel consumption at the same time. Only for higher values ofαNOx, the fuel consumption first decreases and then increases dueto the cross-coupling between the weights for PM and NOx. Incomparison to the static EMS evaluated with the dynamic PM

model, the fuel consumption is shifted to slightly higher values,and at the same time the PM emission levels are decreased tolower values. A more detailed comparison follows after theremaining graphs in Fig. 12 are explained.

Fig. 12b shows the trade-off between the fuel consumption andNOx emission for the dynamic EMS. In comparison to the staticEMS evaluated with the dynamic PM model, the trade-off does notchange significantly except for the slightly higher fuel consump-tion due to the shift mentioned above. Concluding, the dynamic

4 4.2 4.4 4.6 4.8 5 5.21.5

2

2.5

3

3.5

4

4.5

5

5.5

6

6.5

7

FC [L/100km]

PM

[mg/

km]

4 4.2 4.4 4.6 4.8 5 5.2150

200

250

300

350

400

450

500

FC [L/100km]

NO

x [m

g/km

]

1.5 2 2.5 3 3.5 4 4.5 5 5.5 6 6.5 7150

200

250

300

350

400

450

500

PM [mg/km]

NO

x [m

g/km

]

αNOx

= 0

αNOx

= 0.1

αNOx

= 0.2

αNOx

= 0.5

αNOx

= 0.8

αNOx

= 1

αPM

= 0

αPM

= 0.1

αPM

= 0.2

αPM

= 0.5

αPM

= 0.8

αPM

= 1

Fig. 8. Results for the static EMS by varying the weighting factors αPM ; αNOx for the MVEG-95. The PM emission levels indicated were evaluated based on the dynamicemission model (i.e. with dynamic correction).

4 4.2 4.4 4.6 4.8 51.5

2

2.5

3

3.5

4

4.5

FC [L/100km]

PM

[mg/

km]

Increasing αPM

αNOx

= 0

Fig. 9. Results for the static EMS by varying the weighting factors αPM for αNOx ¼ 0on the MVEG-95. The PM emission levels indicated were evaluated based on thedynamic emission model (i.e. with dynamic correction). The figure shows that thePM emissions do not decrease gradually when αPM is increased.

Fig. 10. Engine operating points for the PM-optimal strategy obtained with thedynamic EMS.






method does not influence NOx emissions differently from thestatic method.

Fig. 12c shows the trade-off between PM and NOx emissions forthe dynamic EMS. Due to the reduced PM emissions predictedwith the dynamic EMS compared to those of the static EMSevaluated with the dynamic PM model, the trade-offs are shiftedtowards lower PM emissions. Again, the Euro 5 emission standardsmay potentially be met without using any aftertreatment systemsby using the dynamic EMS with an appropriate choice of theweighting factors.

The dynamic and the static EMS are now compared in furtherdetail. Fig. 13 shows a comparison of the dynamic EMS with thestatic EMS evaluated with the dynamic PM model (cf. Fig. 8a).Accordingly, for small values of the weights αPM and αNOx, theperformance of the static EMS is comparable to that of thedynamic EMS. For larger weights, the dynamic EMS outperformsthe static EMS. As discussed above, the problem of the static EMSis that it does not guarantee any decreased transient emissionswhen the value of αPM is increased. On the other hand, thedynamic EMS gradually decreases the PM emissions by increasing

510 520 530 540 550 560 5700

20

40

60

80

100

120

Time [s]

v [k

m/h

]

0

50

100

150

200

250

300

T ICE [N

m]

TICE

DynT

ICE Stat

v

Fig. 11. Comparison of the engine torque set points for the PM-optimal dynamicand PM-optimal static EMS.

4 4.2 4.4 4.6 4.8 5 5.21.5

2

2.5

3

3.5

4

4.5

5

5.5

6

6.5

7

FC [L/100km]

PM

[mg/

km]

4 4.2 4.4 4.6 4.8 5 5.2150

200

250

300

350

400

450

500

FC [L/100km]

NO

x [m

g/km

]

1.5 2 2.5 3 3.5 4 4.5 5 5.5 6 6.5 7150

200

250

300

350

400

450

500

PM [mg/km]

NO

x [m

g/km

]

αNOx

= 0

αNOx

= 0.1

αNOx

= 0.2

αNOx

= 0.5

αNOx

= 0.8

αNOx

= 1

αPM

= 0

αPM

= 0.1

αPM

= 0.2

αPM

= 0.5

αPM

= 0.8

αPM

= 1

Fig. 12. Results for the dynamic EMS by varying the weighting factors αPM ;αNOx for the MVEG-95. The PM emission levels indicated were evaluated based on the dynamicemission model (i.e. with dynamic correction).

4 4.2 4.4 4.6 4.8 5 5.21.5

2

2.5

3

3.5

4

4.5

5

5.5

6

6.5

7

FC [L/100km]P

M [m

g/km

]

αNOx

= 0

αNOx

= 0.5

αNOx

= 0.8

αPM

= 0α

PM = 0.1

αPM

= 0.2α

PM = 0.5

αPM

= 0.8α

PM = 1

Fig. 13. Comparison of the optimal dynamic EMS (solid line) and the optimal staticEMS evaluated with the dynamic PM emission model (dash-dotted line).






the weight αPM . Last but not least, the maximum reduction of thePM emissions is only possible with the dynamic EMS.

As a conclusion, introducing the torque state xTe in the dynamicprogramming allows for a smoothing of the torque set pointtrajectories almost without influencing the optimal steady-stateoperating points. As a result, much lower transient emissions at aslightly increased fuel consumption are obtained. An additionalbenefit of penalizing torque variations is that it reduces thesensitivity of the optimal-control-based energy managementstrategy with respect to the driver's torque request, and thereforeimproves the driver acceptance as well.

5. Conclusions

Two methods for the derivation of energy management stra-tegies for a Diesel hybrid electric vehicle were compared. The goalwas to make an optimal trade-off between the fuel consumption,raw PM emissions and raw NOx emissions. The static methodtakes into account quasi-static engine maps, whereas the dynamicmethod additionally takes into account transient PM emissions.For both methods, the optimal energy management was derivedusing the deterministic dynamic programming approach.To account for transient influences in the dynamic method, theengine torque was added as an additional state variable.

In a detailed case study, the engine operating points wereanalyzed for both types of strategies. Moreover, the optimal trade-offs between the specific fuel consumption, the specific PMemissions, and the specific NOx emissions were calculated for ahybrid electric vehicle on the MVEG-95 homologation drivingcycle. The results show that it may be possible to meet the Euro5 emission standards without any engine aftertreatment systemsfor both types of strategies. The fuel consumption of such asolution would increase by just 2% compared to the amount of afuel-optimal strategy.

In comparison to the static method, the dynamic methodgenerates much smoother torque set point trajectories and achieveslower fuel consumption for a given level of PM and NOx emissions.

Appendix A. Vehicle model

The vehicle model used for the studies in this paper is based on aparallel hybrid electric vehicle as shown in Fig. A1. The model is of thequasi-static type. It is computed at a sampling rate of 1 Hz. A detaileddescription of the subsystems is given in the following subsections.

A.1. Road load model

Given a driving cycle described by the vehicle velocity v,acceleration a, slope angle α, the rotational speed ωw, rotational

acceleration _ωw and torque Tw at the wheels were calculated by

ωw ¼ v=rw; _ωw ¼ a=rw ðA:1Þ

Tw ¼ ðFiþFaþFrþFgÞ � rw ðA:2Þwhere rw is the radius of the wheels, Fi represents the inertialforces, Fa the aerodynamic drag, Fr the rolling friction, and Fg thegravitational forces, i.e.

Fi ¼ ðmvþmrÞ � a ðA:3Þ

Fa ¼ 1=2 � ρair � cd � Af � v2 ðA:4Þ

Fr ¼ cr �mv � g � cos ðαÞ ðA:5Þ

Fg ¼mv � g � sin ðαÞ: ðA:6ÞHere, mv and mr are the total vehicle mass and the inertial mass ofthe rotating parts in the powertrain (including the inertias of thewheels, the gear, the electric motor and the engine), respectively.For simplicity, the rolling friction coefficient cr is assumed to be aconstant. The total vehicle mass mv comprises the masses of thenominal vehicle m0, internal combustion engine me, electric motormm, and the battery mb.

Table A1 summarizes the numerical values of all constantparameters required to parameterize (A.1)–(A.6).

A.2. Gearbox model

The gearbox model represents a 7-stepped automatic gearboxincluding the final drive. The model accounts for different effi-ciencies among the gears. With nAf1;2;3;4;5;6;7g being the gearindex, i being the gear ratio, and ηg being the transmissionefficiency, the equations for the speed and the torque at thegearbox input are

ωg ¼ in � ωw; _ωg ¼ in � _ωw; ðA:7Þ

Tg ¼

Tw

in � ηg;nif TwZ0;

Tw � ηg;nin

otherwise:

8>>><>>>:

ðA:8Þ

Since the gear is controlled by a heuristic gear shift strategy, thegear selected is not influenced by the energy managementstrategy.

A.3. Torque split model

For the torque split, the torque of the combustion engineTeA ½0; Te;max� is chosen as the control variable for the energymanagement. It is used to split the torque demand Tdem ¼ Tg

between the electric motor, the engine, and the mechanical brake,i.e.,

Tm ¼maxðTdem�Te; Tm;minÞ ðA:9Þ

Tbr ¼ Tdem�Tm if Tdemo0; ðA:10Þ

Fig. A1. Schematic drawing of a full-parallel HEV as used in the case studies.

Table A1Vehicle parameters.

Parameter Description Value

rw Wheel radius 0.32 mm0 Nominal vehicle mass 1480 kgAf Effective frontal area 2.32 m2

cd Aero. drag coefficient 0.26cr Rolling friction coefficient 0.012






with Tbr and Tm being the torque of the mechanical friction brakesand the torque of the electric motor, respectively.

A.4. Internal combustion engine model

The fuel mass flow rate _mf of the Diesel internal combustionengine is determined via an engine map of the form _mf ¼ f eðωe; TeÞwith the engine torque Te and the engine speed ωe ¼ ωg if theclutch is engaged. The engine torque satisfies the speed-dependent inequality TeðωeÞrTe;maxðωeÞ. More details on theengine can be found in Section 3.1.

A.5. Electric motor model

An electric power map is used to obtain the electric powereither drawn from or supplied to the battery, i.e. Pm ¼ f mðωm; TmÞ.The motor torque is limited by a set of speed dependent torqueinequality constraints Tm;minðωmÞrTmrTm;maxðωmÞ.

A.6. Battery model

The battery with the nominal capacity Qb is modeled as anequivalent circuit model with an ideal open-circuit voltage sourceVoc in series with an internal resistance Ri. The dynamics of thestate of charge xSOC are calculated according to

xSOCkþ1 ¼ xSOCk �VocðxSOCk Þ�

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiV2ocðxSOCk Þ�4 � RiðxSOCk Þ � ðPmþPaÞ

q2 � RiðxSOCk Þ � Qb

� Ts; ðA:11Þ

with the sampling time Ts ¼ 1 s, the electric motor power Pm, andthe constant auxiliary electrical power Pa ¼ 300 W. The opensource voltage Voc and the internal resistance Ri both are afunction of the state of charge.

The electrical power supplied to or drawn from the batteryrespects the battery power limits Pb;minrPmþParPb;max.

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