Universitat Rovira i Virgili – Energy Conversion and Storage
Assignment 1 - Lecture 1
Problem 1 - Energy Storage for a HWFET Driving Cycle.
This homework is based on the speed, force and power profiles of an electric vehicle. These profiles
are provided as one dimensional vectors in a MATLAB file named 'assignment1_L1.mat'. The file
can be found in the course website.
The force vector simply shows the overall net force applied in the vehicle, expressed in [N]. This
force is the result of tractive and braking actions in the vehicle.
The speed of the vehicle is based on the Highway Fuel Economy Driving Schedule (HWFET),
which represents highway driving conditions under 100 km/h (60 mph), for a period of
approximately 12 minutes. Since this is a US driving cycle, the speed vector is given in [mph].
The power vector shows the effort done by the propulsion/braking system, in [W].
These three vectors do not take into account efficiency in any of the parts of the vehicle.
Finally, the time vector accounts for the time in seconds. Note that the time step for the profiles is
one second, so each column in the vectors corresponds directly to the speed, force and power at a
time t = [column index -1] seconds, starting at t = 0 s.
On Energy and Power Measurements (Efficiency of power conversion stages is 100%).
a) Plot the speed [km/h], force [N] and power [W] against time. Point out the average speed and the
length of the trip. Can you estimate the mass of the vehicle?
b) What is the required tractive average power if braking is dissipative? How much energy is
required? What is the liters per 100 km equivalent?
c) Now find out the average power and the liters per 100 km equivalent if braking is regenerative.
d) Plot the energy against time [kWh] from the instantaneous power and compare it to the energy
from the average power if braking is regenerative. What is the total energy required to complete the
trip [kWh]? What is the required energy storage in the case of a hybrid vehicle [kWh]?
On Efficiency.
e) Consider the data used in the previous problem. How could efficiency of the system be taken into
account to measure how much power goes in and out the battery? Positive and negative power must
go through the electric drive. The AC machine efficiency in both directions is 90 %. The inverter is
95 % efficient in tractive mode, and 90 % efficient during braking, when it operates as a rectifier.
f) Plot the new power versus time function and compare it with the original data. Find out the
average power and the liters per 100 km equivalent if regenerative braking is active. What is the
energy required in this case?
C. Olalla
ECE 2022/2023
1
Universitat Rovira i Virgili – Energy Conversion and Storage
Problem 2 - Specific Energy and Power
You are a fan of the movie 'Back to the Future'. According to the movie, by 2019 we should have
hoverboards that 'float' (or levitate) in the air. You have developed a prototype based on a powerful
fan that blows air directly to the ground (just like a hovercraft) and now you are planning to do a
demonstration. In order to be successful, you must design the battery appropriately.
- The blades of the fan in the hoverboard are 1
meter long (r = 1 m).
- The weight of the hoverboard, with no batteries is
4 kg (mass_h = 4 kg).
- The specific energy of the batteries is 100 Wh/kg.
- Your first demo is near the Delta de l'Ebre near
Tarragona. You will need to jump over the sea, from platja del trabucador to the coast. The distance
that the hoverboard should run is 2500 m.
The thrust force (vertical) that the hoverboard can produce is as follows:
, where is the air density (1.2 kg/m3), A is the area of the circle drawn by the blades of
the fan and is the speed of the propelled air.
The power consumed by the motor in the hoverboard to produce this force is:
In order to make your derivations, you should consider only the force of gravity as a braking force.
No drag or any other negative force should be taken into account. You can also assume that only
vertical thrust is required, to 'hold you' in the air, for enough time to go through 2500 m (remember,
there is no drag!). It is estimated that your traveling speed in the air will be 1 m/s.
Besides to analytical derivations, it may be a good idea to use MATLAB to obtain numerical results.
a) Find out the force to sustain yourself in the air. How long should this force be maintained? How
much energy is required to sustain yourself for 2500 m?
b) Design the battery pack, according to your weight, the weight of the hoverboard, the weight of
the battery and the specific energy (Wh/kg), in order to do the jump. Plot the time the hoverboard
will be flying with respect to the mass of the battery. Will you be able to make it? If you can, how
much weight will you need to carry with you?
c) Find the specific energy required to be able to do the jump with a battery pack weighting only 10
kg. Do a quick search and find out what kind of energy storage technology can provide the required
specific energy (Wh/kg).
C. Olalla
ECE 2022/2023
2
Universitat Rovira i Virgili – Energy Conversion and Storage
Assignment 1 - Lecture 2
Problem 3 – EV Battery Sizing.
An electric vehicle has the following requirements: eight years of operation at an average of 24000
km per year, averaged out over 365 days per year. Assume an average requirement of 204 Wh/km
and a rated cell voltage of 3.6 V, a capacity of 3.4 Ah @ 1 h, and a lifetime index of L = 1.
a) Determine the beginning of life energy storage, assuming the battery is charged only once every
day.
b) How many cells do you need and what is the beginning of life range?
c) What is the beginning of life storage and how many cells are required for a larger pack in order to
increase the range (beginning of life) to 425 km?
d) Considering the previous point, how many parallel strings are required if the pack has 96 cells in
series?
e) With the 425 km range, what is the battery pack mass, assuming a battery with a pack density of
150 Wh/kg?
f) If the peak power is 100 kW, what is the power/energy ratio of the battery for the larger pack?
Problem 4 – HEV Battery Sizing.
A NiMH HEV battery pack is sized according to the following requirements: 10000 cycles of 60
Wh per year for 10 years, using a 6.5 Ah cell with a rated voltage of 1.2 V and a lifetime index of L
= 1.5.
a) What is the beginning of life battery pack energy storage?
b) What is the total number of cells required?
c) What is the pack voltage if the cells are all in series?
d) If the peak power is 30 kW, what is the power/energy ratio of this battery system?
C. Olalla
ECE 2022/2023
3
Universitat Rovira i Virgili – Energy Conversion and Storage
Problem 5 – Large Vehicle Battery Technology
The new mayor of Tarragona is considering replacing all its fuel-based buses with clean electric
vehicles. Buses have a mass of approximately 10.000 kg. The energy need per km is 500 Wh. The
average trip length between stops is 600 m, and the longest trip length is 1 km. Average speed is 30
km/h. At every stop, the bus waits for approximately 20 seconds. Buses run 365 days a year and
they should be operated with no maintenance during 8 years at least.
Full trips have an average length of 4 km, but the longest trip is 8 km long. Buses typically do these
full trips 12 times a day. At the end of every trip, the bus waits for 10 minutes.
a) Consider recharging the buses at the end of the day, at the end of every full trip, or at every stop.
What is the required energy capacity in every case? What is the required power capability of the
charger/s in every case?
b) According to the previous point and the slides in Lecture 2, choose one of the specific energy
storage types and justify its use in the application with a detailed explanation. You should consider
weight, size, safety, environmental impact, cost and lifetime.
C. Olalla
ECE 2022/2023
4