Analysis of Energetic and Traction Performances for an Electric Vehicle in Real Driving Conditions

In continuation of the studies related to the performances of electric vehicles and their optimization solutions, in this work a simulation model will be created in accordance with all the demands that appear on the vehicle during driving and the model will be adapted for urban driving conditions on a certain length of time, so that the performance of the electric propulsion system can be determined, such as: the state of charge of the battery, the consumption of electricity, the characteristics of the electric motor, as well as the variation of the autonomy of the vehicle. The simulation model made will later be correlated with a series of experimental data determined in real driving conditions so that the accuracy of the made model can be checked and validated so that it can be used on different types of electric vehicles with different performances and destinations.


Introduction
The issue related to the spread of electric vehicles worldwide and the permanent need to determine solutions to optimize dynamic and energetic performances represent aspects of heightened interest in terms of recent concerns and each completed study constitutes an additional step in the deepening of certain notions necessary to complete a numerical simulation model that can be used on several types of electric vehicles depending on destination and interest.However, in order to be able to validate the developed model, different experimental determinations are needed in certain real driving conditions through which, after validating the model, concrete valid optimization solutions can be identified and proposed.
So this paper proposes the analysis of certain performances for another electric vehicle, different in terms of characteristics from those studied in previous works, in which the already existing simulation model presented in the paper [1] suffered some changes to become more accurate and to be able to provide some more conclusive results.In addition to the model architecture, which contains the vehicle dynamic model, the driver model, the transmission model, the electric motor model and of course the battery model, this paper will also present some experimental results measured under real driving conditions for a short distance and a short time in the urban area, but in which the basic parameteres like speed and torque varied greatly.Using the data obtained through experimental measurements, the simulation model will be parameterized according to the characteristic sizes of the analyzed electric vehicle so that the main purpose of the work is the validation of the results obtained through simulation by comparison with the real, measured ones and obviously the resolution of certain inconsistencies or errors that may appear and can influence the accuracy of the model.
Finally, the performances of the studied vehicle will be presented under the conditions of the considered real cycle.

Theoretical aspects and data used for realize the study
To carry out the study, experimental data were recorded when driving in the urban area at a temperature close to that of the ambient environment in a short cycle of 320 seconds, over a distance of less than 5 km.The vehicle used was the Peugeot e-208 model, a vehicle with reduced overall dimensions, hatchback bodywork with 5 seats, extremely suitable for driving in the urban area.The e-208 model has a total weight of 1910 kg and is equipped with an electric motor on the front axle which develops a electric power of 100 kW, a maximum torque of 260 Nm and a maximum speed of 14000 rpm and the efficiency ηm=0.98.It uses a lithium-ion battery which presents the following characteristics: nominal battery voltage 400 V, usable energy 46.3 kWh and battery capacity of 115 Ah [3] and the efficiency of the battery was considered 1.Other important data about the vehicle used in the study are maximum speed: V=150 km/h, the front track: E1=1500 mm, height: Ha=1450 mm, cross-sectional area: A=2.145 m 2 , drag coefficient: cx=0.29,total reduction coefficient: it=9.701 and transmission efficiency ηt=0.98 [2] and tire rolling radius: rr=0.303m, calculated using the wheel size type of e-208: 205/45R17 [3].All these values will be used in the simulation model in the same way as in last work [1].
An Exxotest VCI-Muxdiag type device was used to realize the measurements and the program used to process the experimental data and provide the communication interface between the electric vehicle and the measuring device was the INCA program.An important observation is that the response time of the program was set to 500 ms.
Following the registrations, a series of values for the vehicle speed, torque variation of the electric motor during the actual cycle and the position of the accelerator pedal were saved.These values were later exported to Excel, where the graphs related to the variation of those parameters over time were generated, which will be used to validate the simulation results under the same conditions.
In the following paragraphs you can find the graphs obtained from the measurements recorded in real driving conditions: From figure 1 it can be seen that during the approx.313.5 seconds of driving, the vehicle speed had a large variation and there were also moments with important breakings that were recorded.The maximum speed reached by the vehicle on this proposed cycle was ~105.5 km/h.

Electric motor torque profile
In figure 2 it can be seen the variation of the electric motor torque during the approx.313.5 seconds of driving.The negative part of the obtained diagram shows us according to speed variation, the braking moments during the measurements.The maximum torque reached by the vehicle on this proposed cycle was 259.3 Nm in the second 72 and the minimum value -160.7 Nm in the second 143.To do the simulations, vehicle data will be entered into the already existing model: driving time, response time and distance will be considered as input data in the conditions in which the measurements were made and also the speed profile obtained in figure 1 will be entered.

Model used for simulation
As specified in the first part of the paper the model used for the simulation is based on the structure already presented in [1].The dynamic model of the vehicle under horizontal driving conditions, the model of the driver, the electric motor and the transmission with a single gear, the lithium-ion battery was considered for which an already existing block in the Simscape library of the Simulink program was used.Figure 3 shows the simulation model used:  Additionally, a branch was added to simulate the power consumed when running on the considered cycle and the energy corresponding to this power in order to be able to compare the results with those obtained by measurements.The following calculation relationship was used to determine the power [4]: (1) Where T is electric motor torque, [Nm] and ω is angular speed, [s -1 ] which is determined using the next relation [5]: (2) In order to obtain the energy profile by simulation, the power profile obtained with relation 1 was integrated as a function of time.So, in the next figure is presented the simulation model obtained: As for the battery once the power was determined by simulation using the model from figure 4, it was considered that its nominal voltage remains constant throughout the simulation cycle (Unom = 400 V) and the variation of the battery discharge current was determined by the ratio between the power profile and voltage (P=f(t)/U) so as to identify some performances of the battery during the driving cycle.The model used for the battery can be found in figure 5: Finally, in order to verify the model and to correlate the parameters obtained through simulation with those obtained through experimental measurements a model was developed where the measured profiles were entered from Excel using a "RepeatingSequence" type block and through the "Mux" block compared to the simulated profiles.That model took into account the units of measurement of all parameters so that the results are conclusive; it can be found below: To simplify the connections between the electric vehicle body and the other branches of the model we used the "GoTo" and "From" commands to retrieve and connect certain parameters such as: power, torque of the electric motor and energy consumed:

Results
The figures below show the results obtained from the simulations compared to the measured results:

Comments of the results
 Regarding the speed obtained by simulation compared to the profile measured in real conditions, it is observed that these two coincide and the simulated speed follows exactly the real profile.The maximum speed reached by the electric vehicle when driving in real conditions was 106.9 km/h while the maximum value resulting from the simulation was 107.4 km/h;  The acceleration profile of the electric vehicle was also obtained by simulation (figure 8) and the resulting maximum value was 4.168 m/s 2 in the 73rd second at which point the maximum torque value is also reached on the considered cycle as can be seen in figure 9;  In the upper part of the diagram (figure 9) the simulated torque follows the real profile in a very large proportion but in the negative part, where the regenerative brakes are important, it is constant that the torque values are lower from the simulation which can be caused by the settings from "Braking Command" where the set lower limit is not enough for braking to occur exactly as in reality.The maximum value of the real torque was 259.6 Nm, and the measured one of 260 Nm, which causes an error of 0.15% between the two;  Regarding the simulated power (figure 10), it shows some limitations of the maximum points in the positive part of the diagram, never managing to reach the nominal value of 100 kW as it happens in the case of the measured profile.This can also be determined by the "Motor Command" settings but also by the type of solver used which can introduce different errors in this regard.The maximum value reached by simulation was 83.25 kW compared to 100 kW in the real case, thus resulting in an error of 16.5%, which determines the identification of problems and the optimization of the simulation model;  In figure 11 can see the variation of the energy consumed on the considered cycle in the two analyzed cases, which resulted in a real value of 1.248 kWh and a simulated value of 1.328 kWh so that an error can be calculated:  = |1.248−1.328| 1.248 • 100 = 6.41%.In this case, an energy consumption of 7.63 kWh/100 km was recorded by simulation under the imposed driving conditions compared to the measured one of 7.167 kWh/100 km;  The state of charge of the battery changed by 2.87% in the 320 seconds during the simulation, the distance traveled being 4,172 km, which means that if the vehicle traveled 100 km, the state of charge would reach 68.8%.Thus, if we compare the theoretical autonomy mentioned by the manufacturer of 340 km [3], when running in the regime of the considered cycle, the vehicle could cover a maximum of 300 km.

Conclusions
The simulation model developed and obtained in this work and in the previous paper [1] can be used to determine the performances of an electric vehicle according to certain imposed driving conditions.Use of measured data as input led to results that are extremely close to reality, which proves that the model is valid and ready for future optimizations that lead to even more accurate results.
Finally in order to eliminate the errors that were detected in the torque and power profiles obtained by simulation, other types of solvers will be tried and the modification of certain basic settings will be considered so that the model is no longer limited by the program.
It is very important to know that the Results obtained by simulation are very useful as a validation key.

Figure 1 .
Figure 1.Speed profile obtained during the considered driving cycle for Peugeot e-208.

Figure 2 .
Figure 2. Torque profile obtained during the considered driving cycle for Peugeot e-208.

Figure 3 .
Figure 3. Simulation model for electric vehicle.

Figure 4 .
Figure 4. Simulation model for power and energy profiles.As for the battery once the power was determined by simulation using the model from figure4, it was considered that its nominal voltage remains constant throughout the simulation cycle (Unom = 400 V) and the variation of the battery discharge current was determined by the ratio between the power profile and voltage (P=f(t)/U) so as to identify some performances of the battery during the driving cycle.The model used for the battery can be found in figure5:

Figure 5 .
Figure 5. Simulation model for lithium-ion battery.Finally, in order to verify the model and to correlate the parameters obtained through simulation with those obtained through experimental measurements a model was developed where the measured profiles were entered from Excel using a "RepeatingSequence" type block and through the "Mux" block compared to the simulated profiles.That model took into account the units of measurement of all parameters so that the results are conclusive; it can be found below:

Figure 6 .
Figure 6.Simulation model for comparing the simulated results with the measured results.The final model obtained in MatLAB-Simulink is presented in figure below.To simplify the connections between the electric vehicle body and the other branches of the model we used the "GoTo" and "From" commands to retrieve and connect certain parameters such as: power, torque of the electric motor and energy consumed:

Figure 8 .
Figure 8. Acceleration profile during the simulation.