Models of Electric and
Hybrid-Electric
Propulsion Systems
Chapter 4
From the book: ” Vehicle Propulsion Systems”
Lino Guzella – Antonio Sciarretta
Outline
• Discussion about Electric Vehicles (EV).
• Introduction of Hybrid Electric Vehicles (HEV).
• Description of quasi-stationary and dynamic models of:
– Electric components
– Electric power bus
– Energy consumption
Electric Propulsion Systems
• Composed of :
– An Electricity Storage System.
– An Electric Motor.
Battery
Electric Motor
• The resulting vehicle is not
autonomous.
Transmission
Hybrid-Electric Propulsion Systems
• Characterized by two or more prime movers and power sources.
• In general a HEV includes:
–
–
–
–
An engine as fuel converter or irreversible prime mover.
Electric prime mover (different type of motors).
A second electric machine (generator).
Electric storage system (electrochemical battery, supercapacitors).
Hybrid-Electric Propulsion Systems
•
Motivations for developing HEVs:
– downsize the engine and still fulfill the maximum power requirements of the
vehicle;
– recover some energy during deceleration instead of dissipating it in friction
braking;
– optimize the energy distribution between the prime movers;
– eliminate the idle fuel consumption by turning off the engine when no power is
required (stop-and-go); and
– eliminate the clutching losses by engaging the engine only when the speeds match.
•
These improvements are counteracted by the fact that HEV are 10-30%
heavier than ICE based vehicles.
Configuration of Hybrid-Electric Vehicles
• There exists three different main types:
– Parallel Hybrid: both prime movers operate in the same drive
shaft, thus they can power individually or simultaneously.
– Series Hybrid: The electric motor drives the vehicle. Electricity is
provided by the battery or by the engine – driven generator.
– Series-Parallel or Combined Hybrid: has both a mechanical link
and electrical link.
Series HEVs
•
Needs three machines:
–
–
–
•
Engine
Electric generator
Electric traction motor
The gasoline engine turns a generator,
and the generator can either charge the
batteries or power an electric motor that
drives the transmission. Thus, the
gasoline engine never directly powers the
vehicle.
Parallel HEVs
•
Have a fuel tank, which supplies gasoline
to the engine.
•
They also have a set of batteries that
supplies power to an electric motor.
•
Both the engine and the electric motor
can turn the transmission at the same
time, and the transmission then turns the
wheels.
Combined HEVs
•
Act mostly as a parallel but have the
features of a hybrid series.
•
They introduced the usage of a planetary
gear set (PGS).
•
They introduced as well the combination
of a chain driven generator of mild parallel
hybridds and a crankshaft-mounted motor
as in full parallel hybrids coupled at the
DC link level.
Power Flow
Series Hybrid
Parallel Hybrid
Power Flow in Combined hybrid Vehicles
Combined Hybrid
•
In recent years the models that
have already entered to the
market in mass production are
the combined hybrids preferably
with planetary gear set.
•
Some Parallel hybrid have been
also produced.
•
The most common:
–
–
–
Gasoline engines
Permanent magnet synchronous
AC motor/generator
Nickel metal hybride batteries.
Modeling of Hybrid Vehicles
• How to model HEVs:
– Subsystem analysis: modeling of components (submodels).
– System synthesis: Integration of submodels by power flow.
• With this approach of submodelling the system and designing a
“library” of components it becomes easy to represent series, parallel
and combined hybrids models.
Quasistatic and dynamic modeling
Flow of power factors
Series Hybrid
Parallel Hybrid
Quasistatic and dynamic modeling
Flow of power factors
Combined Hybrid
Electric Motors
•
•
•
•
Convert electricl power from battery into
mechanical power.
Convert mechanical power from the
engine into electrical power to recharge
the battery.
Recuperate mechanical power available
at the drive train to recharge the battery.
Good HEV motors:
–
–
–
–
–
–
–
High efficiency
Low cost
High specific power
Good controllability
Fault tolerance
Low noise
Low torque fluctuation
Electric motor
Quasistatic Modeling of Electric Motors
•
•
Input: T2(t) and ω2(t) requiered at the shaft.
Output: P1(t)=I1(t) · U1(t)
– If P1(t) > 0, acting as a motor (absorbing)
– If P1(t) < 0, acting as a generator(delivering)
Motor Efficiency
Causality representation
Quasistatic Modeling of Electric Motors
Motor Efficiency
•
•
•
The efficiency map ηm(ω2(t), T2(t)) is ususally
defined for the first quadrant (motor mode).
To extend the data to the second quadrant(generator)
two methods can be applied.
–
Mirroring the efficiency:
–
Mirroring the power losses
The two methods yield different results.
Quasistatic Modeling of Electric Motors
DC Motor
•
The Kirchoff voltage equation:
•
For the field circuit:
•
•
In common expression:
•
In the quasy-stationary limit the system can
be described as:
•
Giving a linear dependency:
Newton’s second law:
•
The induced voltage (emf):
•
The armature torque:
Quasistatic Modeling of Electric Motors
DC Motor
•
•
The dependency between Ua(t), Ia(t) and
U1(t), I1(t) is determined by the controller.
Mostly DC-DC choppers converters are
used.
For the field circuit, the balance of power
is:
•
The input power:
•
The efficiency:
•
The power losses P1-P2 will be:
Quasistatic Modeling of Electric Motors
AC Motor
•
•
–
Compose of three-phase windings.
The Kirchoff voltage laws for the stator
and roto d-q axes are:
–
Rotor
stator
•
By Newton’s second law
Quasistatic Modeling of Electric Motors
AC Motor
•
By a balance of power:
•
The efficiency will be:
•
The power losses
Quasistatic Modeling of Electric Motors
Permanent Magnet Synchronous Motors & DC Motor
•
The Kirchoff voltage equation:
•
The torque at the shaft:
•
Newton’s second law:
•
The torque T2 at steady – state limit:
•
The efficiency:
Dynamic Modeling of Electric Motors
•
•
•
Dynamic models are used mainly for
specific control and diagnostics purposes.
In dynamic models, the correct physical
causality should be used.
The voltage Ua is in function of U1 and it
depends on the type of chopper used.
–
Single-quadrant or step-down
• α(t) is the chopper duty cycle
–
Two-quadrant
–
Step-up
Batteries
•
•
•
Transform chemical energy into
electrical energy and vice versa.
They represent a electrical energy storage
system.
Three main components:
– Cathode (reduction-gain of electrones)
– Anode (oxidation-loss of electrones)
– The medium ion transport.
•
Categories:
– Ambient-temperature operating battery.
– High-temperature operating battery.
•
Technologies:
– Lead-acid, Lithium-ion, Nickelcadmium, Nickel-metal hydride, Sodium
sulfur.
Battery
Quasistatic Modeling of Batteries
Causality representation
Capacity and state of Charge
•
Ideally the charge can be expressed as:
•
Due to parasitic effects in the battery the charge can
be expressed considering the coulombic efficiency:
•
In tests the discharge time expresses when the voltage
has reached a desired voltage
•
If the capacity Qo* for a given I2* is known, then the
capacity at a different current will be
•
More sophisticated models have been
developed, ex.
Quasistatic Modeling of Batteries
Capacity and state of Charge
•
According to Kirchooff’s voltage law:
•
Uoc is a function of the battery charge:
•
•
κ2 and κ1 depend on the battery construction.
The Resistance is a contribution of the ohmic, chargetransfer and diffusion resistance.
•
Instead of modeling the various electrochemical
processes of a battery, often experimental data from a
constant – current discharge test are used to derive a
black box.
Equivalent circuit
Quasistatic Modeling of Batteries
Capacity and state of Charge
•
The resistance during the discharge test can be
expressed as:
•
U2 will have the form:
•
The power as a function of voltage is
calculated as:
Quasistatic Modeling of Batteries
•
The maximum current and voltage
for the discharge state of the battery
can be expressed as:
•
The maximum current and voltage
for the charge state of the battery can
be expressed as:
Battery Efficiency
•
•
The global efficiency is defined on the basis of a full charge/discharge cycle as the ratio
of total energy delivered to the energy that is necessary to charge up the device.
The discharge energy is:
•
Charging the battery with a current of the same intensity, I2 = - |I2|, requieres an energy
that is evaluated as:
•
The artio of Ed to Ec is by definition the global efficiency which is a function of I2:
Dynamic Modeling of Batteries
•
•
•
The dynamical model will describe the transient
behavior of the battery.
The simplest model is the Randles or Thevenin
model.
The dynamic equations derived from Kirchhoff
are:
Dynamic Modeling of Batteries
•
•
Another approach consists of representing the battery transient behavior by means of
black box dynamic circuits.
The state equations are:
Supercapacitors
•
Hold significantly more charge.
•
Supercapacitors are well suited to replace batteries because of their scale.
•
Batteries have a limited number of charge/discharge. Supercapacitors can be charged and
discharged almost an unlimited number of times.
•
They can discharge in matters of milliseconds and are capable of producing enormous
currents.
•
Supercapacitors have a very long lifetime.
Quasistatic Modeling of Supercapacitors
•
By the Kirchooff’s voltage law
•
And the relationship:
•
The resulting equation for the voltage is:
•
The global efficiency can be defined as:
Torque Couplers
Planetary Gear Sets
•
The Schematic representation (as in toyota prius) :
Quasistatic Modeling of Planetary Gear Sets
•
The ratio of the relative speeds of the sun and ring can be written as:
•
Assuming ω1(t) = ωc(t), ω4(t) = ωs(t), ω2(t) = ω3(t) = ωr(t)
•
The balance of power applied to the four ports:
•
Combining equations we find: