Param e tric Mod e lin g of Compon e nts for S e l e ction and Sp e cification of Hybrid V e hicl e Dri ve trains

Driv e train hybridi z ation impli e s adding a s e condary pow e r sourc e ( e l e ctric machin e /batt e ry) to a primary pow e r sourc e ( e ngin e /fill e d fu e l tank) in ord e r to improv e: fu e l e conomy, e missions, drivability (p e rformanc e ), comfort and saf e ty. D e signing a hybrid v e hicl e driv e train fulfilling th e r e quir e d v e hicl e driving functions is th e r e for e a compl e x task. Many r e s e arch e rs hav e put e ffort formulating and d e v e loping ov e rall hybrid driv e train analysis, d e sign and optimi z ation mod e ls including top-l e v e l v e hicl e control strat e gy for optimal fu e l e conomy. This pap e r s ee ks to inv e stigat e th e possibility of ov e rall mod e l simplification for th e hybrid driv e train syst e m including th e control strat e gy. This is p e rform e d by d e scribing th e compon e nt e ffici e nci e s and control rul e s with only a f e w charact e ristic param e t e rs that captur e th e total syst e ms fu e l e ffici e ncy with suffici e nt accuracy ( ~ 1%). Using th e s e param e t e rs th e mod e ling and simulation proc e ss can b e don e v e ry quickly. Th e m e thod has b ee n d e monstrat e d on a s e ri e s -, a parall e l - and a s e ri e s-parall e l hybrid driv e train with sp e cifi e d compon e nt t e chnologi e s, v e hicl e param e t e rs and driv e cycl e . Th e fu e l e conomy and control strat e gy r e sults ar e compar e d with Simulink/Advisor and Dynamic Programming.


INTRODUCTION
Ongoing emission legislation and increasing fuel prices pursue many leading vehicle manufactures, and their suppliers to put effort in developing and manufacturing new efficient though cost-effective drivetrain technologies. On nowadays passenger vehicle market, hybrid vehicles are readily available, e.g., the Honda Civic IMA, Toyota Prius, Ford Escape, Lexus RX400h, etc. All these vehicles fulfill almost the same hybrid functions, e.g., energy recuperation during braking, motor-assisting, engine off during standstill. Despite of this, their drivetrain topology, transmission technology and control are completely different. The objectives of a hybrid drivetrain are to some extend improving the driving functions of a vehicle: fuel economy, emissions, drivability (performance), comfort and safety. Due to the complexity of hybrid vehicle drivetrains, the design of topologies, component technologies and the control strategy forms a considerable challenge for engineers. Therefore, many researchers have devoted their attention to develop different hybrid drivetrain modeling and simulation tools [1][2][3][4][5][6]. The tools are usually based on predefined drivetrain topologies, specific component technologies and control strategies. In [4][5] a more flexible modeling and simulation tool (QSS toolbox) is discussed, with which user-defined drivetrain topologies can be build quite easily. In [6][7] the research is focused on developing system design tools for optimizing component sizes and vehicle design parameters, whereby ADVISOR [2] is used as vehicle modeling and simulation platform. Other system design optimization approaches use globally optimal control strategy based on Dynamic Programming (DP) [8]. However, an integral system design approach is usually characterized by large computational times, complex design problem (optimization) formulations, multiple subsystem simulations, non-smooth or non-continuous models. In addition, insights into the design problem at hand are lost when a single final design proposal is presented as a result of a complex integral design process. Interactions between the different drivetrain components, topology and control are then difficult to investigate.

OBJECTIVES AND APPROACH
This paper presents a "modeling approach" in characterizing the component technologies in order to select topologies and for designing the control strategy of hybrid vehicle drivetrains (see Fig. 1 for an overview). Thereby, a generic "hybrid topology model" is introduced, whereby the main power sources, i.e., Primary power source (P) (engine), Secondary power source (S) (battery/electric machine) and Transmission technology (T) (depicted as "black box models") are modeled by simplified parametric "power-based efficiency fit functions". If an affine relationship is assumed, then the input power P in as a function of the output power P out becomes P in = c 1 ⋅P out + c 0 . The static power losses are represented by c 0 and the reciprocal of the inner efficiency by c 1 respectively. Furthermore, the variable P max represents the output power limitation of the component. In order to capture the high power-loss effects of the engine a second order approximation gives better-fit results [9]. The operation points of P, S and T determine the characteristic parameters (c 1 , c 0 ) of the power-based efficiency functions. The main assumptions to speed up the modeling/simulation process are the operation points determined by driving a vehicle over a drive cycle: (i) during regenerative braking and pure electric driving have been used to fit linear functions describing the S efficiency. If S is coupled at engine-side of the transmission, then S is operated at the highest efficiency points by selecting the optimal transmission ratios. If S is coupled at the wheel-side, then the transmission ratio is fixed. (ii) With a battery power equal to zero has been used to fit a linear function describing the T efficiency, whereby P is operated at the highest efficiency points. It will be shown, that operating S during hybrid driving modes has effect on the transmission efficiency, but that the change in transmission efficiency has a negligible effect on the overall fuel economy. The modeling approach discussed in this paper is a step forwards in developing a quick modeling and simulation tool for component sizing and topology selection whereby the fuel economy is calculated very quickly and with sufficient accuracy. Thereby, a target is to find answers to the underlying research questions: Can the component efficiency models and the control model be described with sufficient accuracy by a limited set of characteristic parameters? (ii) What is the influence of the drivetrain component technology and the topology on the fuel economy and emissions? The first research question studies the influence of the operation points on the component efficiency. Thereby, ADVISOR and DP are used as reference "control models/algorithms". In addition, a novel "Rule-Based Energy Management Strategy" (RB EMS) is used with which the fuel economy and control Fig. 1 Classification overview of different hybrid drivetrains and modeling approach strategy can be calculated very quickly and with the same accuracy as DP (~1%) (see [10]). The second research question studies if a generic hybrid topology model can be used independently on the type of hybrid transmission. Therefore, the influence of three typical different hybrid drivetrain topologies, i.e., "series", "parallel" and a "series-parallel" hybrid transmission with different component technologies on fuel economy and emissions is investigated. The maximum vehicle power specification consisting of the engine and the electric machine power is kept constant, such that the acceleration performance of the vehicle is not compromised. Furthermore, for comparison the main vehicle parameters and the drive cycle describing the vehicle load are also kept constant.
The topology -and the rule-based control model are discussed in the Sections 3 and 4 respectively. The simulation results of the topology and the parametric component modeling study are discussed in Section 5. Finally, the conclusions are described in Section 6.

HYBRID TOPOLOGY MODEL
A drivetrain topology defines the possible connections and puts constraints on the transmission ratios between P, S, and V. For the series -and the series-parallel transmission the advantage is that S is integrated with T. However, looking at a higher abstraction level for both transmission types S is functionally coupled to the wheel-side of the transmission, as is shown in Fig. 1 (top-right). Thereby, the intrinsic functions for S are defined as performing recuperation of brake energy (BER) and propulsion only by S while P is shut-off (eliminating the engine drag -and friction losses). In addition, for the parallel and series-parallel transmission Charging (CH) or Motor-Assisting (MA) during driving is possible with S. In case of the series -or the series-parallel transmission this will or can also be done with the electric machine connected at the engine-side respectively. However, most of the charged energy with the electric machine at the engine-side is directly transmitted to electric machine at the wheel side (avoiding additional battery losses). In Section 4 the hybrid modes will be discussed in more detail. For the parallel transmission S is connected at the engine-side of T. The variator of the series -and the parallel transmission consists respectively of two electric machines and a push-belt Continuously Variable Transmission (CVT). One of the major advantages of the series transmission is the infinitely variable transmission ratio. Thereby, it is possible to operate the engine and the generator intermediately, but continuously at its highest efficiency point(s). However, at higher requested vehicle loads, the transmission losses of the electrical variator are typically larger than compared to a mechanical variator. The CVT losses in the parallel transmission are lower at higher vehicle loads, but due to the overdrive constraint not all optimal operating points of the engine can be reached. The series-parallel transmission combines the electrical -and mechanical paths with its advantages, which consists of a planetary gear set combined with two electric machines, which form the electrical variator part of T. The advantages of a series-parallel transmission, compared to a series transmission are: • The transmission efficiency is higher, because most of the power is transmitted over the mechanical branch; • An electrical variator with a lower maximum power specification can be used. However, a disadvantage is the possible occurrence of re-circulation of power flow thereby reducing the transmission efficiency. The operation of the variator and the influence of the battery power on the power flows and the overall efficiency are discussed in more detail in [11].

Energy Management Optimization Problem
The optimization problem is finding the optimal control power flow P s (t) of the power source S given a certain power demand at the wheels P v (t), while the fuel energy, denoted as the variable J, over a certain drive cycle with time length t f is minimized subjected to several constraints, i.e., J G , where the fuel power P f is the product of the fuel rate (g/s) and the lower heating value h lv (J/g) for fuel. The main constraints are energy conservation balance of E s over the drive cycle, constraints on the power P s and the energy E s :

The Rule-Based Energy Management Strategy
The control model used in this paper is based on a Rule-Based (RB) Energy Management Strategy (EMS) as is described in [10]. Thereby, the hybrid drivetrain can be operated in certain distinct driving modes. In Fig.  2, a block diagram is shown for the power distribution between the different energy sources, i.e., fuel tank with stored energy E f , power source S with stored energy E s and the vehicle driving over a drive cycle represented by a required energy E v . The efficiencies of the fuel combustion in the engine, the storage and electric motor S, and the Transmission (T) are described by the variables η p , η s , and η t respectively. The energy exchange between the fuel tank, S and the vehicle can be performed by different driving modes. The engine power at the crankshaft is represented by P p . The power demand at the wheels (P v ), and the power flow to and from the power source S (P s ) determines which driving mode is active. The following operation modes are defined: • M: Motor only mode, the vehicle is propelled only by the electric motor and the battery storage supply S up to a certain discharge power level P o M , which is not necessary equal to the minimum discharging power P s,min . The engine is off, and has no drag -, and idle losses.
• BER: Brake Energy Recovery mode, the brake energy is recuperated up to the maximum generative power limitation P s,max , and stored into the accumulator of S. The engine is off, and has no drag -, and idle losses. • CH: Charging mode, the instantaneous engine power is higher than the power needed for driving. The redundant energy is stored into the accumulator of S. • MA: Motor-Assisting mode, the engine power is lower than the power needed for driving. The engine power is augmented by power from S. • E: Engine only mode, only the engine power is used for propulsion of the vehicle. S is off, and generates no losses. During the M, and the BER mode the engine is off, and as a consequence uses no fuel. This is also referred to as the Idle-Stop (IS) mode. In order to fulfill the integral energy balance constraint over the drive cycle, the energy required for the M and the MA mode needs to be regenerated during the BER mode, or charged during the CH mode. To explain the basic principles of the RB EMS, which is a trade-off between energy balance and fuel consumption, consider the following two cases. Either case represents a different choice for P o M , whereby the recuperated brake energy (BER) is: (i) not sufficient, and (ii) more than sufficient for supplying the energy during the motor only mode (M) over a given drive cycle. (i) The additional required energy for the M mode has to be charged during the CH1 mode resulting in additional fuel cost. (ii) The redundant energy of the BER mode can be used for motor-assisting during the MA1 mode resulting in additional fuel savings. Both cases are schematically shown in the Fig. 3. Referring to case (i), if -P o M is lowered, then the additional fuel cost becomes lower due to decrease of the required charging energy. However, the fuel saving due to the M mode is also reduced, and vice-versa, if -P o M is increased. The same holds for case (ii): the fuel saving during the MA1 mode is increased if -P o M is lowered, but the fuel saving due to the M mode is reduced. For both cases, additional charging (CH2 mode) during driving and using for motor-assisting (MA2 mode) can be beneficial, if the energy is charged at a lower driving power, and this energy is used for motor-assisting at a higher driving power. However, the additional fuel saving is relatively small, because the drive energy at higher powers is relatively small. For more details concerning calculation of P o M is referred to [10].
The iteration is repeated until the error e(i) between the iteration steps at a certain time instant becomes sufficiently small (i.e., e(i)≤ε). In Fig. 4 the iterative procedure is schematically shown. A mathematical condition to prevent the iteration loop from instabilities, in terms of the estimation P o This condition implies that error e of each estimate decreases in each iteration step i. If the ratio of the error between the previous and the subsequent step becomes equal to 1 the estimates will not further improve. the requested P v is divided by the computed η t . Using the modified T o p and ω o p prescribed by the EOOL, which are stored-in look-up tables, the optimal power flow out P s is calculated using DP or the RB EMS given the drive cycle and the vehicle parameters.

Reference Control Models: ADVISOR and DP
For comparison the control strategies as are implemented in ADVISOR are compared with the results from DP and the RB EMS. In Table 1 the rule-based conditions that define which hybrid mode is active for the different hybrid transmission types are given. Thereby, the battery is allowed to operate within a certain defined state-of-charge ξ window, i.e., ξ ∈ [ξ min , ξ max ]. The control parameters as implemented in ADVISOR were optimized to achieve the highest fuel economy while the final ξ(t f ) is maintained within a certain zero change in ξ(t f ) +/-0.5% tolerance band.
The optimizing torque fraction parameters f 1,j , power fraction parameters f 0,j with j ∈ {1,2} and the vehicle electric launch speed threshold value v 0 are intrinsic parameters of the control strategy. The parameters are used to assure that the engine is operated in the relative high efficiency areas. For details on these parameters and the functions for calculating the amount of charging/discharging power for the different topologies is referred to [2].
Using DP the finite horizon optimization problem is translated into a finite computation problem [10], [12]. Note that in principle the technique results in an optimal solution for the EMS, but that the grid step size also influences the accuracy of the result.
Furthermore, the engine and the generator of the series transmission are operated at the System Optimal Operation Line (SOOL). For the parallel transmission the electric machine and the engine are operated separately at the maximum efficiency points during the BER, M and the E mode (EOOL). During the CH and the MA mode the engine and the electric machine are operated at the SOOL. For the series-parallel transmission the engine is operated at the EOOL alone.

RESULTS
All simulations presented in this paper have been done on the JP10-15 drive cycle. The inertias of the electric machines, engine and auxiliary loads are, for simplicity, assumed to be zero. During braking energy is partially recuperated up to the maximum generative power limitation of the electric machine. In addition, some of the braking energy is dissipated between the front -and the rear-wheels in the wheel-brake discs. The braking energy distribution is prescribed by a non-linear function which is dependent on the vehicle speed [2]. During braking the engine is assumed to be shut-off or disengaged eliminating the engine drag losses. The Reference Vehicle (RV) is equipped with a 74-kW 1.6-L SI engine and a push-belt CVT as is used in the parallel transmission. In Table 6 an overview of the component data is given. The total power specification for every hybrid drivetrain configuration is kept constant at approximately 74 kW. The battery pack is sized to meet the power specifications. In this way the dynamic performance of the vehicle is not compromised.

Fuel Economy and Emissions
In Table 2 the fuel economy and emission results for the different hybrid topologies and control models are listed. In Table 4 the characteristic parameters describing the P, S and T efficiency, which are used with the RB EMS to calculate the fuel economy (test 12-14), are listed. Although the cost function consists only of the fuel consumption, for all hybrid drivetrains the HC, CO and NO x emissions are reduced, except regarding the NO x emissions for the series transmission. This can be solved by using a weighted cost function consisting of the sum of the fuel use and emissions and increasing the weight factor regarding the NO x emissions. However, this has not been investigated in this paper. The relative influence of engine downsizing (without a battery), topology choice and hybridization (adding an S) on the fuel economy results is shown in Table 3. The lowest fuel economy is realized with the series-parallel transmission. Due to coupling of S at the wheel-side of T for the series-parallel transmission (maximizing the regenerative brake efficiency) the fuel [T p > T p,max (ω p )]*,**} Additionally, in case of the *parallel transmission with CVT or the **series-parallel transmission economy is lower than for the parallel hybrid transmission. In the Fig. 5 and Fig. 6 the energy distribution between different hybrid modes and the relative energy ΔE s over time for the different topologies and strategies are shown respectively. Although, S is coupled at the wheel-side of the transmission for both the series-parallel -and the series hybrid transmission, it can be seen, that the energy recuperation during braking (BER) for the series-parallel is larger than for the series. Since the S efficiency of the series-parallel is higher than the S efficiency of the series transmission. The series transmission has the highest fuel economy mainly due to the lowest transmission efficiency.

Control Models Parameters -ADVISOR
The fuel economy is mainly determined by the control constraints or rules, which determine where the engine is allowed to be turned off (BER and M mode). Therefore, the main control parameters within ADVISOR are f 0,1 , f 1,1 or v 0 (see Table 1). The calibrated f 0,1 for each topology is also listed in Table 4. Thereby, f 1,1 ≥ f 0,1 and v 0 is larger than the maximum cycle speed. The calibrated f 0,1 for the series transmission is 0.51 (equivalent to P o M = -32.5 kW). At this power fraction the engine and generator are operated at the "sweet spot" of the engine (highest efficiency) and energy is charged with minimum fuel cost. However, with DP it was found that the fuel consumption could be reduced if the electric machine at the wheel-side is partially supplied by the battery up to a drive power of approximately 6.1 kW. At higher power demands the battery power is augmented by power from the engine that is a function of the drive power P v and the state-of-chargeξ. It appeared to be not straightforward to adapt the defaults rules within ADVISOR by changing the main control parameters to the preferred optimal control settings. This explains the relative large discrepancy between DP and ADVISOR for the series transmission. Using the results from DP it showed that for the parallel and the series-parallel transmission the optimized f 0,1 are 0.10 (equivalent to P o M = -6.1 kW) and 0.12 (equivalent to P o M = -7.5 kW) respectively. With the default control parameters as implemented in ADVISOR for series-parallel transmission (Toyota Prius 1998) it was found that in the high-speed areas the engine was not allowed to shut off at relative low P v resulting in less Idle-Stop. In addition, generative torque of the motor during braking is reduced due to additional engine drag torque. Since, the vehicle speed was then larger than v 0 . If v 0 is set to a larger value than the maximum cycle speed effectively more (free) energy is charged during the BER mode, which reduces the additional charging fuel cost. Furthermore, it was found that the optimal EMS is focused on charging during driving in the low-speed areas (v < 40 km/h) by the generator (15-kW) and in the high-speed areas by the motor (30-kW) respectively. This has influence on the optimal P o M as will be discussed in the following section.

Parametric Efficiency Functions and Generic Hybrid Topology Model
Although the static-efficiency map of the engine is very non-linear, the EOOL is well approximated by a quadratic fit function, i.e., P f = c 2 ⋅P 2 p + c 1 ⋅P p + c 0 (for reasons of space this is not shown in this paper, e.g., see also [11]). In the Fig. 7 and Fig. 8 the linear functions fitted through the operation points for S (BER and M mode) and T (only E mode) are shown. For sake of clarity, the S efficiency for the parallel transmission as shown in Fig. 7 includes the T efficiency. The found component parameters including the calculated optimal control parameter P o M used in the RB EMS are shown in Table 4. In Fig. 7 also P o M is shown of tests 9, 10 and 11. Due to uncertainty on the found fit coefficients the static losses c 0 for S can be negative for positive output power and vice-versa.
The electric machines at the engine-side for the series -and the series-parallel transmission are assumed to be part of T. Furthermore, charging and motor-assisting during driving is only possible with the electric machines at the wheel side (S). For the parallel transmission charging and motor-assisting during driving is done at the SOOL, which causes that the S efficiency is not similar to the S efficiency during the BER and M mode. These assumptions cause that the optimal P o M with the fit functions used with the generic hybrid topology model is higher than P o M with the actual drivetrain topology and component technology (see Table 4). Thereby, the energy charged and discharged during driving (CH and M mode) is reduced (compare test 9-11 with test 12-14 in Fig. 5). However, the higher value for P o M for every hybrid drivetrain topology has a very small influence (~1%) on the overall fuel economy (compare test 9-11 with test 12-14 in Table 2).
The battery power influences the transmission efficiency. In Fig. 9, as example, the engine input power as function of the vehicle drive power for different battery powers calculated with DP for the series-parallel transmission is shown. However, the assumption of modeling the transmission efficiency used only in the E mode ("pure transmission efficiency") is allowable. The reason for this is: if the transmission input power is corrected with the battery power during the CH and the MA mode, then it can be seen that the "corrected hybrid transmission efficiency" is slightly better than the "pure transmission efficiency" (no battery power). However, the discrepancy is very small. Therefore, the difference in fuel economy is very small. This holds for every investigated topology (see Table 5). It can be concluded that the implicit sensitivity of the fit coefficients to battery power for T is small.

CONCLUSIONS
The results show that overall model simplification for the hybrid drivetrain topology, component technology and control strategy regarding fuel economy can be done with sufficient accuracy (~1%). Thereby, the component efficiencies and the control model are only described by P+S+T+C = 3+4+2+1 = 10 characteristic parameters. In contrary to the relative large amount of required static component efficiency data and different control rules used in ADVISOR or the relative long computation time with DP. Determining the component parameters can be done in advance independent on the hybrid control strategy, but dependent on the choice of engine -or wheel-side coupling of S to the drivetrain (topology choice), the vehicle load and speed. Reversibly, if realistic characteristic parameters for P, S and T are determined fulfilling a certain fuel economy improvement; then component specifications (size and efficiency) can be derived and consequently the technology and topology can be selected or specified. In this way, control design, optimization, component and topology selection and specification are merged in a single methodology framework. In future work the design of a hybrid vehicle drivetrain (a passenger car -and a distribution truck case study) using the modeling approach as discussed in this paper will be investigated.