Design Optimization of a Parallel Hybrid
Electric Vehicle
Design Optimization Report
Mahmoud Al-Zahrani, Andrew Carlile, Nikhil Ramaswamy, and Hao Chen
Table of Contents
Design Optimization Report ......................................................................................................................... 1
Solving the Design Problem Deterministically .............................................................................................. 3
Solve the Design Problem Under Uncertainty .............................................................................................. 5
Lessons Learned ............................................................................................................................................ 8
Website Update .......................................................................................................................................... 10
Solving the Design Problem Deterministically
In order to determine the optimum design parameters for our parallel hybrid vehicle, we linked our
QuickWrap, Cost Script, and Survey with the Design Explorer Optimization Tool. This layout is shown in
Figure 1. The following figures show the variation of the design variables to obtain the optimum
configuration for maximum value. From the results obtained, the deterministic optimum design
variables are shown in Table 1.
Figure 1 ModelCenter model for the deterministic optimization
Figure 1 shows the ModelCenter arrangement for the optimization tool linked to the excel file and the
cost script. It converged quickly and gave reasonable values outlined in the following figures.
Figure 2 Change in the optimum value of AmpHr
Figure 2 shows the value of the battery in AmpHr varying in different runs. The optimal value of 10.5
converged after approximately 100 runs. This value is slightly larger than a Civic Hybrid (6 AmpHr) but
that can be expected as battery prices have fallen and the MPG is at a premium in our survey results.
Figure 3 Change in the optimum value of engine power
Figure 3 displays the values of the engine power during the optimization. The final value of 164.5 kW is
convergent after approximately 105 runs. Although the value is a bit higher than other hybrid vehicles
(75 kW approximately) our survey results emphasized acceleration, and the larger engines would
provide quicker acceleration.
Figure 4 Change in the optimum value of motor power
Figure 4 shows the optimum value of the motor power converging. After approximately 100 runs, it
converged to 31.45 kW. This value is higher than most hybrid vehicles (15 kW approximately). The
reason for this is that our survey results emphasized acceleration a great deal. The large motor and
battery allow the vehicle to compensate for the large engine with more power being delivered by the
more efficient electrical drivetrain components.
Table 1 Optimum design variables
Parameter
Optimum
Engine power (kW)
164.5
Motor power (kW)
31.45
Battery size (AmpHr)
10.5
The obtained results are reasonable, since they show that the battery size required is not that large
(which would increase the total weight) and is comparable to other vehicles on the market. The motor is
small compared to the engine and the engine is not significantly large which could lead to more fuel
consumption. The obtained results are not at a constraint, which means the constraints are not active
constraints. The maximum utility obtained from these variables is 4.014 x 106. For our analysis, these
values correspond with reasonable values and a positive utility indicates that our vehicle will be
profitable.
Solve the Design Problem under Uncertainty
To evaluate the optimum design variables, a surrogate model was developed in order to reduce
computational time for the analysis. Figure 5 shows the ModelCenter layout for creating the Surrogate
model. 1000 LHS samples were used in creating the model. Figure 6 shows the Kriging model developed
from the analysis. The accuracy of the model is almost high in all outputs, except the output for mileage
per gallons (MPG), but that value was still around 80%. This Kriging model should be sufficient to work
with the optimization process. The surrogate model was then used in the optimization loop shown in
Figure 7. All uncertain parameters are being fed to the model via the inverse of the CDF from the excel
files, while the other uncertain parameters are given through the LHS model.
Figure 5 Creating the Surrogate model
Figure 6 Kriging model of the simulation
Figure 7 Surrogate model optimization
The optimization was run at different numbers of samples for the LHS model. The model converged
after 100 samples and the optimum design parameters are shown in Table 2. The optimum parameters
from the stochastic analysis are a bit different from the ones obtained from the deterministic analysis,
but the difference is not that great. The constraints are not active constraints even in the stochastic
analysis. Figures 8-10 show the convergence of the parameters. Under uncertainty, a large engine and
smaller electrical powertrain components were optimal. This is likely due to the variance of the
uncertain parameters affecting the performance and price of the vehicle in a way that encourages a
larger engine. For example, a larger mass of the vehicle would require more power, and the cheapest
way to add power to the vehicle is to increase the size of the engine while keeping smaller electrical
components. In addition, these values are closer to the values of vehicles currently on the market. That
suggests that the uncertainty calculation aids in the development of a new vehicle because it gave
results that are more likely to be successful (Since hybrid vehicles are selling well, this is a safe
assumption).
Figure 8 Change in the optimum value of AmpHr
The optimal value for the AmpHr of the motor converged after approximately 125 runs. Its value of 6.75
closely matches hybrid vehicles currently on the market and is very likely to be a good value for a vehicle
in the current car market.
Figure 9 Change in the optimum value of engine power
The engine power value also converged after approximately 125 runs. The final value of 200.2 kW is
significantly larger than the Civic Hybrid (75 kW), but as our survey had a large bias for acceleration and
the optimum value of the motor power is lower, this value makes sense.
Figure 10 Change in the optimum value of motor power
The value of the optimum motor power for our system converged after approximately 125 runs. The
value of 25 kW is still larger than hybrid vehicles currently on the market, but is still a reasonable size
given that our survey had an acceleration bias. This motor power also allows the vehicle to receive a
substantial amount of power from the electrical powertrain components, which aids with the miles per
gallon.
Table 2 Stochastic optimum design variables
Parameter
Optimum
Engine power (kW)
Motor power (kW)
Battery size (AmpHr)
200.2
25.02
6.75
Our uncertainty optimization arrived at very plausible values of design parameters. This helps to validate
our utility functions, survey results, and the surrogate’s ability to model the system. With uncertainty
included in the modeling, the optimum parameters were closer to vehicles currently on the market than
when our analysis did not include uncertainty. This suggests a few things: First, our model is able to give
very reasonable design parameters for our vehicle. Second, the uncertainty analysis is most likely a
valuable task because it pushed our design closer to values that we assume are valid. All of these
indicators point to a successful modeling of our parallel hybrid vehicle, the cost and survey models, the
utility, uncertainty, and the surrogate model.
Lessons Learned
The main lesson learned was the importance of working deliberately and properly. Trying to work
quickly would result in sloppy or unusable results. The best strategy for modeling in Dymola was to
make everything modular and scalable. When this was done properly, it was very easy to get results
from the simulation and link it inside of Model Center. When the Dymola models were not created in a
deliberate manner, they could be difficult to link with other models and difficult to get results from. This
general principle was true for Model Center as well.
Understanding the behavior of the vehicle we were trying to simulate (even if it was not detailed) was
hugely important. The Dymola model would not just work if components were placed. Looking up hybrid
car’s performance parameters and components was a huge help, especially for pricing. We knew the
general behavior of a hybrid vehicle, but being able to compare our results with cars on the market,
such as the Prius or Civic Hybrid, was extremely helpful. In short, historical data was very helpful.
The area we struggled with the most was creating an accurate Dymola model of our system. Initially, we
separated the system into three main areas: electrical components, mechanical components, and the
control system. The plan was to connect those pieces and have our vehicle simulated. As it turned out,
the best method to creating a valid model was to build up the components in an integrated way to
ensure that they would function as a single system.
Another thing that we struggled with was creating a good Surrogate model that could mimic the Dymola
model. At first, we wanted to create the Surrogate model so that it produces the utility as an output,
and then use it in the optimizer. The problem was that the Kriging model had an accuracy of 80%, which
produced results that were different from what the original model would give. To overcome this
problem, we only created the Kriging model for the outputs of the Dymola model. All of them had high
accuracy (above 97%) except the mileage, which was 80%. However, the overall accuracy was sufficient
for the model to mimic the Dymola model.
If we were assigned a new problem, the process would have been slightly different but have some
similarities. Initially (as with this project), we would likely begin with the historical data and decide on a
few general assumptions for how our system would be simulated. Different from our current project, we
would integrate the Dymola models as we went to ensure all of the pieces worked together. Our Model
Center analysis would be completed in a similar manner to this project, as we did not have any
significant problems.
Website Update