In the following the two HEV models under optimization are detailed and their parameters are explained.
Model A
The first model — Model A further on — has been developed by the first author of [30] and has the ability to act both as a series and a power-split hybrid. The vehicle relies on a single ICE and two electric machines — termed “generator” and “motor” further on – for propulsion.
The ICE and the “generator” are directly coupled via a shaft, but may be detached by opening a clutch. Though the distribution of the required power between the machines is variable and is determined by the operation strategy. The ICE/generator unit and the “motor” are coupled to the driving shaft by a planetary gear set. Although the ICE/generator unit can be mechanically decoupled from the planetary gear set.
By using the above setup the following modes of operation are enabled.
• EV1is a pure-electric mode for low vehicle velocities where only the electric “motor” is used for propulsion. The ICE/generator unit is deactivated and detached from the plane-tary gear set.
• EV2is a pure-electric mode for high vehicle velocities where both electric machines are used for propulsion. The “generator” is attached to the gear set, but the ICE is deactivated and detached from the “generator”.
• ER1is the first range-extension mode where the HEV is operated in a series hybrid setup.
Therefore the ICE/generator unit is decoupled from the planetary gear set and is used to generate electrical power for the “motor” and for charging the battery. This range-extension mode is typically used for low velocities.
• ER2 is the second range-extension mode where the HEV is operated in a power-split setup. All clutches are closed and all machines are active and thereby the power output of the ICE is split into a mechanical and electrical path. This mode is typically used for high velocities.
The selection of the proper mode of operation is determined by the vehicle’s operation strat-egy, which is pre-determined for the HEV. The behaviour of the strategy is parametrized by the parameters explained in the next section.
Parameters
• ringteethdetermines the number of teeth for the ring gear of the planetary gear set. The domain of the parameter is integer. Further the parameter has been limited to the values {70,80,90,100,110,120,130}as using a finer grained domain is considered redundant.
• sunteethdetermines the number of teeth for the sun gear of the planetary gear set. The domain of the parameter is restricted to the values{20,30,40,50,60}. Letrbe the num-ber of ring teeth andsbe the number of sun teeth. Then the following constraints have to hold s.t.ringteethandsunteethform a valid parameter tuple.
– (r−s) mod 2 = 0 – r > s
The both constraints are enforced by the domains chosen for the parameters.
• generatorpowermin determines the minimal power output of the electric “generator”.
The domain of the parameter is integer and limited to[3,20].
• torqueev1up ∈ [200,800] determines the torque on the driving shaft above which no switching from mode EV1 to EV2 is performed. The domain of the parameter is integer as fractional values are not considered significant.
• speedev1up∈[60,140]determines the vehicle speed required to switch from mode EV1 to EV2. The domain of the parameter is integer as fractional values are not considered significant.
• torqueer1up ∈ [200,1000]determines the axle torque above which no switching from mode ER1 to ER2 is performed. The domain of the parameter is integer as fractional values are not considered significant.
• speeder1up∈[40,140]determines the vehicle speed required to switch from mode ER1 to ER2. The domain of the parameter is integer as fractional values are not considered significant.
• speedermin ∈ [0,80]determines the minimal vehicle speed required to switch from a pure-electric mode to ER1. The domain of the parameter is integer as fractional values are not considered significant. Further its value is required to be less than or equal to the value ofspeeder1up.
• socband ∈ [0.01,0.1]determines the allowed percental deviation of the battery’s initial SOC — in both directions. Low values lead to higher rates of starting/stopping the ICE as it is tried to keep the SOC nearly constant. Higher values lead to may lead to larger deviations at the end of the simulated driving cycle and to a penalization of the solution in sequence (as described in the next section). Further thesocbanddetermines when the switch from pure-electric to range-extension modes is performed.
• chargepowerhigh ∈ [20,100]is the maximum power used to charge the battery. This amount of power has to be generated if the SOC is far lower than the initial SOC.
• chargepowerlow∈[0,30]is the minimum power used to charge the battery. This amount of power has to be generated if the SOC is higher or only a bit lower than the initial SOC.
The domain is integer and the parameter’s value has to be lower thanchargepowerhigh.
The actual power generated by the “generator” is determined by interpolating between chargepowerlowandchargepowerhigh, depending on the SOC’s level in comparison to the initial SOC.
• usepowerdemandcharge∈ {0,1}is boolean and indicates if the “generator” should try to cover the current power requirement of the electric “motor”.
Objective function
Model A is evaluated on the EPA US06 driving cycle, as it is short driving cycle and as it is designed to resemble “real” driving behaviour. As objective function the single case objective function — as described in Section 4.2 — is used with a single target value. Thefuelconsvalue measures the fuel consumption in L/100km on the driving cycle plus a penalization for SOC deviation. The penalization for a negative deviating SOC is calculated by estimating how much fuel would be needed to charge the battery to its original state using the ICE/generator combo at stop. It is possible that the penalization is negative if the SOC deviation is positive. The lower bound
Model B (IFAHEV)
Model B is a version of the IFAHEV model in [31], but a larger set of parameters has been chosen for the optimization. The operation strategy for Model B is specifically designed for the NEDC as described in Section 2.2. As this model is protected by an NDA it is not allowed to detail the achieved results as well as the model itself. Therefore the model serves mainly for verification for some aspects of the evaluated methods.
Parameters
• GearRPMi, i∈ {2,3,4,5,6,7}determines the RPM whiche the ICE needs to reach to switch from geari−1to geari.
• LPSx, x ∈ {ECE-15,EUDC} determines the percental load-point shifting during the constant speed phases of the ECE-15 and EUDC parts of the NEDC respectively.
• LPSi,i∈ {2,3,4,5}determines the percental load-point shifting during different accel-eration phases. LPS2and LPS3control the load-point shifting during the second and third acceleration phase in the ECE-15 parts of the NEDC. LPS4controls the load-point shift-ing durshift-ing the first two acceleration phases in the EUDC part of the NEDC and LPS5 in the last two acceleration phases of the EUDC part.
• EMVehicleSpeedx, x ∈ {ECE-15,EUDC} determines the vehicle speed up to which acceleration is handled by the electric machine solely. The ECE-15 and EUDC variants control this parameter for the respective phases of the driving cycle.
Objective function
As fitness function the single case objective function with two parameters has been used. The first parameter is the fuel consumption and the second parameter is the SOC deviation. The SOC deviation has been modified s.t. a deviation less than one percent does not contribute to the fitness function. The weights of the parameters have been split 70/30. The estimated lower/upper bounds chosen for the parameters, as well as the exact calculation of the fuel consumption with SI units, cannot be given. Doing so would allow to reverse the fitness calculation giving insight in protected data.