OPTIMORE Optimised Modular Range Extender for every day customer usage

Transcription

1 EUROPEAN COMMISSION DG RTD SEVENTH FRAMEWORK PROGRAMME THEME 7 TRANSPORT - SST GC.SST : Integration and optimisation of range extenders on Electric Vehicles GA No OPTIMORE Optimised Modular Range Extender for every day customer usage Deliverable No. OPTIMORE D6.2 Final version Deliverable Title Driving cycles for robust optimization of range Dissemination level extender vehicles Written By Victor Judez/Jonas Sjöberg (Chalmers) Checked by Jonas Sjöberg WP leader (Chalmers) Approved by Theodor Sams (AVL) Accepted by EC Issue date Date Date

2 1. Introduction Series Powertrain Sizing Description of a RE-vehicle Power requirements: Battery Power and Range Extender Power Transient power requirements: Battery SoC swing Energy requirements: Battery Size Relation between Battery power and Battery energy content Discharging Strategies Blended mode: possibility when driving distance is known in advance Blended mode for improved efficiency Blended mode for smaller RE or improved performance Optimal Range Extender Size Effect of average speed and accelerations on RE Size Effect of road gradients Range Extender Size using a Blended discharging strategy Smaller Range Extender Size Improved performance for a given RE size Optimal battery size Optimal battery size for a given set of drivers Improved cost function including speed dependency on the battery size optimization Energy management and Simulations Convex Optimization for controlling and sizing of the powertrain Matlab Files Conclusions References /36

3 1. Introduction This milestone report concerns the sizing of the combustion engine and the battery of a range extender vehicle (RE-vehicle). The idea of a RE-vehicle is a hybrid electric vehicle which can be charged from the grid and driven purely electrical on short distances. The combustion engine (the range extender) is used to make trips longer than the All Electric Range (AER) of the vehicle. This concept offers the advantages of electric vehicles (cheap, environmental, electric driving) on short distances at the same time as long distance driving is possible thanks to the range extender. Since short trips dominate the driving for most drivers this makes sense. The range extender reduce the vehicle price since the expensive battery can be made smaller. To make the RE-vehicle economically competitive, the appropriate sizing of the driveline is of importance so that no component is over-sized. At the same time, the performance requirements are important to meet customer acceptance. The following sizing problems are covered in this report: Battery sizing: - Energy sizing influences AER and the cost effectiveness of the powertrain. - Power sizing influences if the vehicle can meet power demand peaks (for example accelerations) purely electric or if the RE must be started. The RE sizing is influenced by: - Power performance requirements at long trips, when the battery is empty and all energy comes from the RE. - The discharging strategy at trips longer than AER. Chapter 2 describes the example vehicle used to generate the results and also explains the requirements on the RE-engine and the battery. Chapter 3 describes the two main strategies of how to use the electric energy at trips longer than the AER when the trip distance is known in advance. Charge Depletions means that the electric energy is used first, and when the battery is empty one shifts to Charge Sustainable Mode where the vehicle is used as a normal hybrid. The alternative is to operate the vehicle in Blended Mode which means that the electric energy usage is distributed over the whole trip. This gives lower losses and makes downsizing possible. Chapter 4 presents the results on RE size for different driving conditions and the two discharging strategies. Chapter 5 describes an estimate of the optimal battery size for individual drivers, and how this estimate can be improved. Chapter 6 describes the calculations to obtain the results and the Matlab files which contains the code. Finally in Chapter 7 conclusions are given. 3/36

4 2. Series Powertrain Sizing This chapter starts with a description of the RE-vehicle used to obtain the results in this report in Section 2.1. The rest of the chapter describes requirements on the vehicle. The power requirements on the RE-engine and on the battery are explained in Section 2.2. When the battery is empty (or more correctly, almost empty), the vehicle is operated like a normal hybrid where excess energy can be temporally stored in the battery. The SoC swing needed is investigated in Section 0. Finally, in Section 2.3 the energy requirements on the battery are explained Description of a RE-vehicle In a series hybrid powertrain an Electric Machine (EM) drives the wheels, while the electricity can be provided by a battery or by an engine-driven generator. Using a generator the mechanical power output of the engine is converted into electricity that can either feed directly the motor or charge the battery. Since the engine/generator unit is mechanically decoupled from the driven wheels the operating point is independent of vehicle speed and torque demand, and the engine can be controlled to operate in its most efficient points. Vehicle performance (in terms of acceleration, gradeability and maximum speed) is completely determined by the size and characteristics of the electric motor. This traction motor used as a generator also allows for regenerative braking storing the energy in the battery. Figure 1. Series hybrid powertrain 4/36

5 The vehicle characteristics used to perform all the simulations presented in the rest of the report can be seen in Table 1. Vehicle Data Vehicle mass without battery [kg] 1280 Frontal area [m2] 2 Aerodynamic drag coefficient 0.30 Rolling resistance coefficient 0.01 Wheel radius [m] Gear ratio motor to wheel 5.7 Power used by auxiliary devices [kw] 0.75 Battery Size (When not sizing the battery) [kwh] 14 Table 1. Vehicle Characteristics The modelling of the powertrain components as well as the simulation/optimization tool used in this study is explained in Chapter 6. 5/36

6 2.2. Power requirements: Battery Power and Range Extender Power As explained in previous section 2, the electric power needed to supply the electric motor can be provided by the battery, by the RE or by a combination of both sources. To fully utilize the traction capability of the electric motor the sum of the power of the RE and battery should be greater than, or at least equal to, the maximum power demanded by the electric motor: (1) Where: Maximum EM electric power. Maximum RE electric power. Maximum battery power. A second requirement must be imposed to the RE power. When the battery is depleted the RE is the only energy source on board, thus it must able to deliver the average power demanded by the electric motor: ( ) (2) where Total driving cycle time. ( ) = Electric power demanded by the electric motor. It must be noted that this equation is not totally accurate. For transient driving cycles the RE has to provide also for the losses in the charging/discharging battery cycles. In section 4 the size of the RE will be studied in detail by simulation of the complete powertrain model in real world driving. In section 4.3 it will be discussed that this requirement can be lowered if the energy contained in the battery is used simultaneously with the RE from the beginning of the trip. An extra power requirement must be added to the battery if the REV is designed to provide full performance in pure battery mode. In this case the battery maximum power must be equal to the maximum possible power demanded by the electric motor: (3) These 3 requirements are illustrated in Figure 2. The shadowed areas represent nonpermitted RE-Battery power combinations. In this example the maximum electric power required by the EM is 100 kw. 6/36

7 Pegu(kW) P RE (kw) OPTIMORE D6.2 Driving cycles for robust optimization of range extender Pbat (kw) Figure 2. Power requirements for battery and RE Of all the possible battery-re combinations in Figure 2, some special cases are shown in Figure 3 and explained in Table Pbat (kw) Figure 3. Specific battery-re power combinations 7/36

8 1 Dual powertrain Either battery or RE can provide all possible power demanded by the EM. Although technically possible, this solution would not be competitive in view of package, weight and cost. 2 RE only 3 Minimum Possible RE All the power demanded by the EM is directly provided by the engine-generator. This means that requirements are met with by the RE and there is no battery. The RE unit is sized to only fulfill the average power requirements and battery power is needed to fulfill requirements, eg, at accelerations and slopes. If the RE is downsized below this level the vehicle cannot meet the performance requirements at long distance trips when the battery is depleted. 4 Full Performance Electric Mode. The battery is able to deliver all the power demanded by the electric motor. The RE is sized to deliver the average power used by the powertrain. In comparison to design 3, the vehicle does not have any performance decrease for long trips. Table 2. Some special design cases of sizing of the battery-re power combinations shown in Figure 3. In addition to the 3 requirements presented above, we must also ensure that the battery is able to absorb the power transients, so the RE can be sized to only cover the average power demand. A short investigation of de battery SoC swing needed is done in section /36

9 Transient power requirements: Battery SoC swing When the battery is depleted and the vehicle is operated in charge sustaining mode, the battery must still be able to absorb power transients, like accelerations and short slopes. As a first approximation it is possible to calculate how much energy is stored in the vehicle due to kinetic energy and potential energy. The kinetic energy stored in the vehicle when driving at 110 km/h is approximately 0.25 kwh, which for a 14 kwh battery corresponds to only a SoC swing of 1.8 %. Changes in altitude of 100 m (vertically) correspond to about 0.5 kwh. As an example of real world driving an ARTEMIS motorway driving cycle have been chosen. Figure 4 shows the speed profile and SoC profile when simulating this driving cycle with a 25 kw RE. Figure 4. Speed and SoC profile of the ARTEMIS motorway driving cycle. From Figure 4 can be seen that the SoC swing needed is of around 1.5%, which can be easily absorbed by the battery. However is complicated to give a specific number to the SoC swing needed since in general this depends on several factors like: The driving cycle. The RE size. A smaller RE will take longer to compensate for transients. The control strategy used. An earlier activation of the RE can be required by the control strategy in order not to deplete the battery too much. 9/36

10 To have a more robust answer of the SoC swing needed more driving cycles should be simulated. However the results indicate that the SoC variations are small compared with the battery sizes considered. 10/36

11 2.3. Energy requirements: Battery Size The energy content in the battery (KWh), commonly called battery size can be sized in different ways. Some relevant design scenarios are: What in this report is called Optimal Battery Size, which is the battery size that minimizes the total cost of ownership of the vehicle (buying the vehicle + running the vehicle). This is the approach chosen to size the battery in this report. The Optimal battery size for different drivers is presented in Section 5. Other alternatives to size the energy content of the battery are: Size the energy content of the battery in order to fulfil a predefined AER. Note that the AER depends on the driving cycle this is defined. In order to achieve a predefined combined fuel consumption (CO 2 emissions) homologation. In the case of Europe the Hybrid procedure for calculating fuel consumption is as follows: where: FC= Homologated Fuel consumption. FC CS = Fuel consumption in charge sustaining mode. Storage device in minimum stage of charge. FC CD = Fuel consumption charge depleting mode. Storage device fully charged. D E = Vehicle s electric range (km) = AER D AV = 25 km (assumed average distance between two battery recharges). For a REV FC CD =0, which leads to For a given (Fuel consumption in fuel mode) a desired Homologated Fuel Consumption can be achieved by adapting the AER (D E ) of the vehicle. 11/36

12 Relation between Battery power and Battery energy content Another phenomenon that can affect the battery size decision is the power to energy ratio of the battery. The price per kwh of battery is not linear, but depends on the power-to energy ratio. For a given battery power vehicles with larger batteries, like EV, can use less powerful and thus cheaper (per kwh) cells since the required battery power will be achieve by packing more battery cells. Figure 5 shows how the battery price depends on the power-to-energy ratio. Figure 5. Specific cost ($/KWh) depending on Power-to-Energy Ratio (W/Wh) PHEV Discharge Strategies. 12/36

13 3. Discharging Strategies This chapter describes the two main strategies of how to use the electric energy available in the battery. Charge Depletions means that the electric energy is used first, and when the battery is empty one shifts to Charge Sustainable Mode where the vehicle is used as a normal hybrid. The alternative is to operate the vehicle in Blended Mode, which means that the electric energy usage is distributed over the whole trip, or, more precisely, over the distance to the next charging opportunity for the case that the vehicle is not charged after each trip Blended mode: possibility when driving distance is known in advance PHEV, as is the case of REV, have rather big batteries which can be charged from the grid providing All Electric Range (AER). For trips exceeding the AER of the vehicle there is a degree of freedom concerning the how the battery is discharged. Discharging strategies for PHEV can be divided in two main categories: Charge depletion charge sustaining (CDCS) strategy Blended Mode strategy In CDCS strategy the vehicle operates as an electric vehicle until the usable energy of the battery is depleted (CD Mode). Once the SoC reaches the charge-sustaining region the strategy changes to Charge Sustaining (CS) Mode, in which the RE is switched on and maintain the SoC level within the desired SoC window (the vehicle is driving as a HEV). In Blended Mode both power sources, combustion engine and battery, are used during the whole trip and the minimum SoC is only reached at the end of trip. In Figure 6 both discharging strategies are shown.

14 Figure 6. Discharging strategies. CDCS strategy/ Blended strategy For trips shorter than the All Electric Range (AER) the optimal discharge strategy is simply to operate in CD mode (i.e. as an electric vehicle), since electricity is considerably cheaper than gasoline. However when driving distances longer than the AER it is energy and cost efficient to turn on the engine at early stage and blend power from the battery with power from the combustion engine from the beginning of the trip. Blended strategy avoids the CD phase, thus reducing the mean power (current) demanded from the battery and thereby the electric losses (which are approximately proportional to square of the current). The blended strategy has several additional advantages compared to the CSCD strategy. It depletes the battery more slowly and evenly, causing less battery wear. Moreover, in cold climates where the cabin needs heating, an early engine activation might be favourable, using the engine losses to provide heating, instead of using energy from the battery for this purpose. The main disadvantage of the blended strategy is the dependency the control strategy has on the drive length until the next charging possibility, since it would not be cost optimal finishing with an unnecessary high battery State of Charge (SoC). There are several ways to anticipate the required energy to complete the trip, for example: By predefining the driving route via GPS. Based on the altitude profile, expected vehicle speed and even other factors like individual driving style or auxiliaries energy consumption the energy reserve is permanently adjusted to the expected energy requirement. A more sophisticated one, but transparent for the driver, would be trying to guess the route the driver will take by using route recognition or similar technics. 14/36

15 3.2. Blended mode for improved efficiency As explained in previous section using a Blended discharging strategy for drives longer than the AER of the vehicle can improve the efficiency by lowering the following losses: Lowering the average battery current Avoiding that the RE is used to charge the battery during CS operation The potential improvement in fuel efficiency for the case where there is full information compared with the case where is illustrated in Figure 7. Results show that a blended discharging strategy can improve the fuel economy up to 16 % compared to CDCS. However, the gain depends on several factors like the length and the aggressiveness of the cycle, with higher reductions possible for trip lengths somewhat longer than the AER. For more detailed studies about the potential savings of blended control and the influence of different information levels look at [1][2][3]. Figure 7. The improvement in fuel consumption when using blended control compared to CDCS 15/36

16 3.3. Blended mode for smaller RE or improved performance Using Blended control instead of CDCS is also beneficial from a performance perspective or sizing perspective. Making use of battery and RE in a combined way can allow for improvements in performance or for the same levels of performance with a smaller RE. The reason for the previous statement is easier explained making use of Figure 8 and Figure 9. Figure 8 shows how when driving in CSCD mode the RE size is determined by the average power demanded in the CS region, independently of the driving distance. On the other hand, when driving in blended mode the energy in the battery is distributed over the complete distance up to the next charging possibility (Figure 9) the RE only have to provide for the rest of the average power. informa on CD CS P RE,CDCS E b Figure 8. Battery energy and RE energy use in CDCS mode. Same long term performance with smaller RE P RE, Blended E b!!!!!! Figure 9. Battery energy and RE energy use in Blended mode. 16/36

17 The relation explained both in words and with the help of Figure 8 and Figure 9 could also be expressed with the following mathematic expression: (4) where: E b = Energy in the battery (kwh) P RE, CSCD = Range Extender Power required when driving in CSCD mode. P RE, Blended = Range Extender Power required when driving in Blended mode. T d = duration up to the next charging opportunity, typical one or several trips. Equation (4) is only an approximation, and for more accurate calculation the charging/discharging losses on the battery shall be taken into account. The benefits of a smaller RE are several and should be taken into account: Cheaper: The first and more obvious advantage is that a less powerful engine should be cheaper to produce. According with the cost estimations made in [4] a 35 kw RE would cost around 2800 while the cost of a 15 kw RE would be in 1500 level. Smaller: A less powerful RE should be also smaller in size. Packaging is always a concern, but even more in PHEV where since we need to allocate a bulky battery pack, an electric machine and the engine. Lighter: A smaller RE should be also lighter, which will increase the energy efficiency of the vehicle (both on electricity and fuel). The possibilities of downsizing the RE by using a Blended discharging strategy are investigated in Section /36

18 P RE (kw) OPTIMORE D6.2 Driving cycles for robust optimization of range extender 4. Optimal Range Extender Size This chapter contains results on the sizing problems explained in Chapter 2 and discharging strategies discussed in Chapter 3. Section 4.1 describes the RE-engine sizing and its dependence on speed and acceleration requirements. The effect of road gradients is discussed in Section 4.2 and the possibility to downsize the RE by using blended discharging, as described in Chapter 0 is described in Section 4.3. The mathematical optimization used to obtain the results presented in this chapter is described in Chapter Effect of average speed and accelerations on RE Size The main factor influencing the average power demand is the possible speed of the vehicle. Figure 10 shows the minimum RE power needed to drive in CS mode for constant speed driving (red line) and different real world driving cycles (blue dots). The values of power shown in Figure 10 correspond to electric power of the RE, once all the powertrain efficiencies have been taken into account by simulation. The RE is maintained ON always that the speed of the vehicle is greater than Artemis Cycles Cte speed Average Speed (km/h) Figure 10. Range extender power The exact mean speed and Minimum RE sizes needed for the different drive cycles are given in Table 3. 18/36

19 Mean Speed (km/h) Range Extender Size (kw) ARTEMIS12 122,46 24,22 ARTEMISmotorwayb 120,338 23,38 ARTEMISmotorway 99,59 18,31 ARTEMISmotorway130 96,86 16,9 ARTEMIS ,18 ARTEMISroad 57,46 6,82 NEDC 33,35 4,19 ARTEMISurban 17,65 3,18 Table 3. RE power needed to fulfil different Artemis driving cycles in CS mode. Several conclusions can be derived from Figure 10: The driving cycle average speed has a strong influence in the minimum RE power needed. Real driving cycles demand more power than constant speed driving. Real driving cycles present dynamics. During accelerations the power demand is higher than at constant speed, and during braking part of the energy can be recuperated by regenerative braking. However, due to not perfect regeneration and efficiency of the battery charging/discharging cycles the power required to drive real world driving cycles is higher than driving at constant speed. The results in Figure 10 also show that a 35 kw RE could maintain an average speed of over 145 km/h. A less powerful 25 kw RE is able to maintain an average speed of almost 130 km/h and fulfill the all the simulated driving cycles shown in Table 3. 19/36

20 P RE (kw) OPTIMORE D6.2 Driving cycles for robust optimization of range extender 4.2. Effect of road gradients Until now only flat roads have been considered in the simulations. However gradients are also influencing the average power requirements. Figure 11 shows the size of the RE power needed to maintain constant speed for 0, 2, 5 and 10 % gradients % slope 2% slope 5% slope 10% slope Average Speed (km/h) Figure 11. Range Extender power for different slopes. Figure 11 shows that a 35 kw RE can maintain 100 km/h at 5% in CS mode. Even with a 10% slope the vehicle could be driven at 70 km/h indefinitely. If the RE is downsized to 25 kw the performance of the vehicle will be suffering limitations, being the speed limited to 80 km/h in a 5% slope and only 50 km/h in a 10% slope. This reasoning is based on the average slope over a long climb. It will still be possible with higher gradients for short times, as the battery can even out the power demand for short and steep gradients. It is only the long average gradient that requires a certain RE power. The following example shows what slopes and average speed mean in real world driving. Due to the lack of real data with high altitude drops, a driving cycle consisting on the ARTEMIS Rural driving cycle with the addition of an 8% average slope has been created. The driving cycle is around 18 km long and with an 8 % average slope the altitude climb is almost 1300 m. The speed and altitude profiles are shown in Figure 12. The average slope and altitude drop would be comparable to some of the greatest mountain passes in the Alps. 20/36

21 Figure 12. Speed and Altitude profile of Artemis Rural driving cycle with an 8% average slope. For this quite demanding driving cycle the minimum RE power needed when driving in CS mode is 25,65 kw. 21/36

22 P RE (kw) Savings ( ) OPTIMORE D6.2 Driving cycles for robust optimization of range extender 4.3. Range Extender Size using a Blended discharging strategy As explained in Section 0 the use of a Blended discharging strategy compared with a conventional CDCS strategy can lead to smaller RE sizes or improved performance for a given RE size. In the following sections two examples of how the RE can be downsized are given Smaller Range Extender Size In this section an example of how the RE can be downsized by using a Blended discharging strategy is presented. The comparison is the following: RE power needed to complete motorway driving cycles of different distances in CSCD mode. RE power needed to complete motorway driving cycles of different distances in Blended mode. Motorway driving is represented by an Artemis motorway driving cycle. The battery size in this example is of 14kWh battery, which allows for approximately 47 km AER in an Artemis Motorway driving cycle. The RE sizes needed as well as the savings (RE cost in CDCS mode compared with Blended mode) depending on maximum trip distance are shown in Figure Blended Mode CSCD Distance (km) Figure 13. RE power required in CDCS mode and Blended mode function of trip distance. From Figure 13 several conclusions can be derived: 22/36

23 The RE size for CSCD mode is independent on the distance of the driving cycle. It only depends on the average power demanded in the CS part of the driving. The reduction in RE size when driving in Blended mode is proportional to the ratio between the driving cycle distance and the AER of the vehicle Improved performance for a given RE size A blended discharging strategy can also be used as a way to improve long distance performance for a given RE size. In this example a comparison between a 35 kw RE operated in CS mode and a 25 kw operated in Blended mode is done for climbing driving. Table 4 shows the extra energy needed from the battery in order to climb 1000 meters with a 25 kw RE but maintaining the performance level of a 35 kw RE meters climb at: Charge Sustaining Mode Blended Mode 120 km/h-2% slope 35 kw 25 kw kwh 100 km/h-5% slope 35 kw 25 kw + 2 kwh 70 km/h-10% slope 35 kw 25 kw kwh Table 4. Extra energy from the battery to climb 1000 meters when downsizing the RE power from 35 kw to 25 kw. If the vehicle is able to anticipate and save that extra energy in the battery a 25 kw RE could offer similar performance than a more expensive, heavier 35 kw RE. As shown in previous Section 4.1 when driving in flat roads the 25 kw EGU can maintain more than 120 km/h constant speed, and when driving in mountain regions this RE size could perform as well as a 35 kw EGU with just some information about the route and anticipation of the control system. For a 14 kwh battery 2kWh represent 22% of the usable energy (assuming that 65% of the total energy is usable). Charging the battery with RE power will be possible in many driving situations. Driving the vehicle in an Artemis motorway driving cycle a 25 kw RE is able to recharge 2kWh into the battery in around 18 minutes, and if the vehicle is driving a less power demanding rural environment (Artemis Rural) the same 2 kwh can be charged into the battery in just 10 minutes. According with the cost estimations made in [4] a 35 kw RE would cost around 2800 while the cost of a 15 kw RE would be in 1500 level. Assuming a linear dependency between power and cost a 25 kw RE would cost approximately 2150, which represent 650 savings from a 35 kw RE. 23/36

24 5. Optimal battery size The optimal battery size was investigated in previous deliverable 6.1, however further understanding and refinements have been included in this report. In Section 5.1 a better explanation of how the optimal battery size depends on cost and driving parameters is given. In Section 0 an extension of the method presented in deliverable 6.1 that allows for including speed dependency in the optimization is explained. To illustrate the methodology developed, a real world movement database with more than 400 drivers is used. Detailed description about the information contained in the database and how the data was acquired can be found in [5]. The examples shown in this section make use of this database Analytical optimal battery size for a given set of drivers In previous deliverable 6.1 an analytical expression of the Total cost of ownership as a function of AER was derived: ( ) [ ( ( ) ) ( ( ) ) ( ) ( ( ) )] (5) Taking the derivative of TCO with respect of AER and simplifying the following expression for the Optimal AER was found: ( ) ( ) (6) Further detail of how these expressions were derived can be found in Deliverable 6.1. An additional version of equation (6) can be re-written as (this was not included in previous deliverable), ( ) ( ) (7) 24/36

25 Although (7) is only a manipulation of (6) in which the integration is done from the longest trips, this new version allows us for a better graphical representation and understanding of how the different equation parameters relates to the Optimal AER (AER OPM ). This relation can be seen in following Figure 14. ( ) ( ) Figure 14. Relation between Optimal AER, distance distribution, fuel and electricity efficiencies and battery price. From Figure 14 it can be seen that the optimal battery size is defined when the integral ( ) reach a number of trips equal to ( ). This horizontal line depends on set prices (battery, fuel and electricity) and the fuel and electricity efficiencies, and the optimal battery size is given by the intersection. The advantage of this new representation is that now is possible to compare in a single figure different drivers, being all the parameters visible in the same figure. An interesting observation is that once that level is reached the rest of the cumulative driver distribution does not influence the optimal battery size. Another insight is that in order to have a battery a minimum number of trips is needed. If that minimum number of trips is never reached in the lifetime of the vehicle having a battery wont be interesting from a Total Cost of Ownership point of view. Hence, the figure gives a simple illustration of the optimal choice. It also illustrates the sensitivity of the optimal choice by changed conditions by how much the intersection change. The sensitivity of the Optimal Battery Size towards driving and cost parameters will be investigated in following Deliverable /36

26 When computing the optimal battery size for the 400 drivers contained in the database and grouping them in vehicle niches is now easier to visualize which drivers are group together. An example is shown in Figure 15. AEROPM Figure 15. Driver statistics showing the distributions of trip lengths for each driver and indicating preferred battery size with colour. From Figure 15 it can be seen that the groups are approximately made around the crossing with the horizontal line. However for an exact solution the cost function for every driver and not only their optimal battery size must be taken into consideration. 26/36

27 5.2. Improved cost function computation including speed dependency on the battery size optimization The results presented so far used the simplified assumption of a constant cost per kilometer. This section describes a way to obtain a more accurate result by including speed dependency cost. The optimization results have not yet been re-computed using this compensation, it is only the method which is described. One of the main simplifications made in Deliverable 6.1 when computing the TCO function and the Optimal AER from data for individual driver is the assumption of a single/average electricity and fuel consumptions per kilometre for all the drivers. However, the energy consumption per kilometre can vary a lot, depending on speed and other factors. As an example, speed distribution for two different drivers is shown in Figure 16. Figure 16. Speed distribution for two different drivers. Moreover, there is also correlation between the trip distance and average speed of the trip. Longer trips are usually driven at higher average speeds, since are usually driven on motorways or high-speed roads. This correlation can be seen in Figure 17. Here we also see a large variability around the average. 27/36

28 Electricity Consumption (kwh/km) OPTIMORE D6.2 Driving cycles for robust optimization of range extender Figure 17. Relation between trip distance and average trip speed. To improve the result on the sizing of the components a speed dependent kilometre cost is suggested. This is done by calculating the electricity consumption and fuel consumption for different driving cycles with different average speeds. The results are shown in Figure 18 and Figure 19, respectively. 0,25 0,2 0,15 0,1 0, Average Speed (km/h) Figure 18. Electricity consumption (KWh/km) in charge depletion mode function of average driving cycle speed 28/36

29 Fuel Consumption (l/100 km) OPTIMORE D6.2 Driving cycles for robust optimization of range extender Average Speed (km/h) Figure 19. Fuel Consumption (l/100km) in charge sustaining mode function of average speed The computation of the optimal battery size, including the speed dependency is just a modification to the earlier case, described in Deliverable 6.1, with a constant cost. Here follows a description of the main algorithm, with the necessary change indicated. The algorithm delivers the cost for each driver as a function of the battery size. This information can be used to generate all kind of interesting results, as was shown in Deliverable 6.1. The algorithm requires a vehicle model and a data base of driver statistics from a number of drivers. The diver statistics should include, for each driver, the information of their driving divided into trips with specified distance and speed profile. Also charging possibilities is needed. The most evident assumptions for charging is to assume charging only at nights which means that all trips on one day only get one charging, or charging after each trip. For each driver For every battery size For every charging opportunity for the specific driver - Start with SoC 100% For all trips up till next charging opportunity 1. An electricity or/and a fuel efficiency (depending on the SoC of the battery) is calculated depending on the average speed of the trip (using Figure 18 and Figure 19). This is the step that has been upgraded from Deliverable The calculated efficiency is multiplied by the distance of the trip (energy used) and translated into a monetary unit. 3. The cost of the trip is added to the total cost of operation for this battery size. 29/36

30 4. The SoC on the battery is updated (deplete the electricity consumed and charge if possible) End (For all trips) End (For every charging opportunity) This gives the operational cost for a specific battery size. The Total Cost for the battery size is obtained by adding the cost of the battery. End (every battery size) End (each driver) The reason that the result in Deliverable 6.1 has not been re-calculated as described is that the relations in Figure 18 and Figure 19 need to be calculated more accurately. Both Figures have been created by simulation of six driving cycles with different average speeds (and only one driving cycle per average speed). In order to validate the results more driving cycles with the same average speeds need to be simulated. Depending on the spread in the efficiencies, either a confidence interval or additional explanatory variables (acceleration, number of stops ) can be included. The results on how the average speed influences the optimal battery size will be included in next deliverable /36

31 6. Energy management and Simulations for sizing of the RE In this section the methods used to obtain the results in Section 4 are explained. The energy management problem is formulated as a convex optimization problem where the total fuel and electricity consumption and component cost (in this case RE size) over a driving cycle is being minimized. The main challenge in using convex optimization is to formulate it as convex optimization problem. Once the problem is convex effective solvers can solve it in a fast and straightforward way. Important efforts have been done at Chalmers University of Technology to further develop this method. The optimization problem is presented in Section 6.1 while in Section 6.2 the Matlab tool developed to perform the optimizations is explained Convex Optimization for control and sizing of the RE For a given driving cycle the optimization tool provides two main results: The optimal RE size. The optimal energy management strategy. These two results are obtained by minimization of an objective function with two components: The operational, or equivalently, the energy cost consisting of the costs for electric energy and fuel: ( ( ) ( )) (8) where and are price parameters ( /W) and the driving mission lasts for t f seconds. ( ) and ( ) are the electric power and fuel power in every time instant. The component cost is the size dependent part of the cost for the powertrain components. In this case: (9) where is the RE price ( /kw) and is a sizing factor that modifies the power of the RE. By discretizing the variables in (8) in time, with interval, the integral is approximated as a sum, and the optimization problem can formally be stated as: 31/36

32 Minimize ( ( ) ( )) (10) subject to: Components equations and limits: These constrains represents the components governing equations as well as their limits (Maximum torque, speed, current ). Connection equations: These constrains represent the mechanical and electrical links between the different powertrain components. Other constrains like sustained battery Charge or performance requirements The minimization is with respect to the split of the power flows ( ( ) time instant and the component sizing ( ). ( )) at every A detailed explanation of the powertrain components models (Electric motor, Battery and Range Extender), vehicle model, as well as the main steps to formulate the energy management and sizing problem (10) as a convex problem can be found in [6]. For further examples of the possible uses of this approach consult [7] [8]. The Matlab code used to perform the simulations and optimizations is described in following Section Matlab Files The convex optimization tool used in Section to 4 to size the RE has been implemented in Matlab. This section describes the structure of the Matlab tool and its different options, for other partners to use it. The files are available in a file named Convex Optimization Matlab tool_6_2.zip. For any question regarding the tool please contact Victor Júdez (judezv@chalmers.se). The tool is composed of three folders: cvx: This folder contains the convex solver data: This folder contains the structures for driving cycles, range extender, battery, electric motors.. test_cvx: This folder contains the scripts from where the optimization is run. Before running the optimization two steps several steps must be done: 1. Within cvx folder run the m-file cvx_setup.m 32/36

33 2. Within the folder test_cvx open the m-file cvx_addpath.m, and change the following line with your own path where the folfer cvx/cvx_v1.21_b781' is: root='/users/victorjudez/documents/matlab/cvx/cvx_v1.21_b781'; 3. Add the three folders to the path you are working on. In the test_cvx folder several functions and scripts can be found, but only two m-files need interaction by the user: start_optimization.m and init.m: start_optimization.m: It is the main script from where the tool is run. To run the tool is enough to press or F5. Several case studies can be selected in this script: o Charge Depleating /Charge Sustaining Mode o Blended Mode o Fixed/ Optimal Range Extender Size init.m: In this script the driving cycle, components models and other parameters (prices, cost of the components, payback time and other options) are defined according to the desired case study. Apart from these two main files there are a number of Matlab scripts and functions that perform the optimization and preparation of the data: prethreat_data.m: prepares the inputs to the optimization functions. cvx_solve_sizingre_blended: Perform the convex optimization for Blended control. cvx_solve_sizingre_cs: Perform the convex optimization for CS control. When the optimization is finished the following information is shown in the command window: Elapsed time is seconds: It s the time the optimization has taken. Solved (P RE =18.31 kw, soc=5%, fuelcon=5.54 l/100km): Status of the Optimization (Optimal RE size, SoC deviation, fuel consumption). The results are stored in a structure in the workspace called out. The main variables stored in that structure are: P_RE_max = Optimal Range Extender Power for the cycle. soc = State of Charge profile during the driving cycle. P_dem: Power demanded by the wheels at every time instant. P_bat: Power provided by the battery at every time instant. P_egu: Power provided by the RE at every time instant. 33/36

34 7. Conclusions This report has illustrated the following issues: Battery sizing: - Energy sizing influences AER and the cost effectiveness of the powertrain. - Power sizing influences if the vehicle can meet power demand peaks (for example accelerations) purely electric or if the RE must be started. The sizing of the RE is set by - The power performance requirements at long trips, when the battery is empty and all energy comes from the RE. For long trips, longer than AED, and with trip information the RE can be down-sized by using the RE and the battery energy in a blended mode. In such a scenario a performance decrease due to the down size of the RE will occur first at a distance many times larger than the AER. 34/36

35 8. References [1] M. Pourabdollah, PHEV Energy Management: A Comparison of Two Levels of Trip Information, [2] V. Larsson, L. Johannesson, and B. Egardt, Impact of Trip Length Uncertainty on Optimal Discharging Strategies for PHEVs, in IFAC Advances in Automotive Control, [3] V. Larsson, Benefit of Route Recognition in Energy Management of Plug-in Hybrid Electric Vehicles, Am. Control Conf., [4] A. Grauers, FUEREX D2.2. Range Extender Requirements and comparison, [5] L. H. Kullingsjö and S. Karlsson, The Swedish car movement data project, in EEVC Brussels, 2012, pp [6] N. Murgovski, Electromobility Studies Based on Convex Optimization, no. april, [7] N. Murgovski, L. Johannesson, and J. Hellgren, Convex optimization of charging infrastructure design and component sizing of a plug-in series HEV powertrain, IFAC WC, [8] N. Murgovski, L. Johannesson, J. Sjöberg, and B. Egardt, Component sizing of a plug-in hybrid electric powertrain via convex optimization, Mechatronics, vol. 22, no. 1, pp , /36

36 Acknowledgment This project is co-funded by the 7th FP (Seventh Framework Programme) of the EC - European Commission DG Research Disclaimer The FP7 project has been made possible by a financial contribution by the European Commission under Framework Programme 7. The ation as provided reflects only the authors view. Every effort has been made to ensure complete and accurate information concerning this document. However, the author(s) and members of the consortium cannot be held legally responsible for any mistake in printing or faulty instructions. The authors and consortium members retrieve the right not to be responsible for the topicality, correctness, completeness or quality of the information provided. Liability claims regarding damage caused by the use of any information provided, including any kind of information that is incomplete or incorrect, will therefore be rejected. The information contained on this website is based on author s experience and on information received from the project partners. 36/36