Models of Electric andHybrid-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.

• The resulting vehicle is not autonomous.

BatteryBattery

Electric MotorElectric Motor

TransmissionTransmission

• 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.

Hybrid-Electric Propulsion Systems

• 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.

Configuration of Hybrid-Electric Vehicles

• 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.

Series 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.

Parallel 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.

Combined HEVs

Power Flow

Series HybridSeries Hybrid Parallel HybridParallel Hybrid

Power Flow in Combined hybrid Vehicles

• 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.

Combined HybridCombined Hybrid

• 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.

Modeling of Hybrid Vehicles

Quasistatic and dynamic modelingFlow of power factors

Series HybridSeries HybridParallel HybridParallel Hybrid

Quasistatic and dynamic modelingFlow of power factors

Combined HybridCombined Hybrid

• 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 Motors

Electric motorElectric motor

• 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)

Quasistatic Modeling of Electric Motors

Causality representationCausality representation

Motor EfficiencyMotor 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 MotorsMotor Efficiency

• The Kirchoff voltage equation:

• For the field circuit:

• Newton’s second law:

• The induced voltage (emf):

• The armature torque:

Quasistatic Modeling of Electric MotorsDC Motor

• In common expression:

• In the quasy-stationary limit the system can be described as:

• Giving a linear dependency:

• 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:

Quasistatic Modeling of Electric MotorsDC Motor

• The power losses P1-P2 will be:

• Compose of three-phase windings.

• The Kirchoff voltage laws for the stator and roto d-q axes are:

– stator

Quasistatic Modeling of Electric MotorsAC Motor

– Rotor

• By Newton’s second law

• By a balance of power:

• The efficiency will be:

• The power losses

Quasistatic Modeling of Electric MotorsAC Motor

Quasistatic Modeling of Electric MotorsPermanent 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 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

– Two-quadrant

– Step-up

Dynamic Modeling of Electric Motors

• α(t) is the chopper duty cycle

• 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, Nickel-cadmium,

Nickel-metal hydride, Sodium sulfur.

Batteries

BatteryBattery

• 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

Quasistatic Modeling of Batteries

Causality representationCausality representationCapacity and state of ChargeCapacity and state of Charge

• More sophisticated models have been developed, ex.

• 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, charge-transfer 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.

Quasistatic Modeling of Batteries

Equivalent circuitEquivalent circuitCapacity and state of ChargeCapacity 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

Capacity and state of ChargeCapacity and state of Charge

• The maximum current and voltage for the discharge state of the battery can be expressed as:

Quasistatic Modeling of Batteries

• The maximum current and voltage for the charge state of the battery can be expressed as:

• 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:

Battery Efficiency

• 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:

Dynamic Modeling of Batteries

• 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.

Supercapacitors

• By the Kirchooff’s voltage law

• And the relationship:

• The resulting equation for the voltage is:

• The global efficiency can be defined as:

Quasistatic Modeling of Supercapacitors

• The Schematic representation (as in toyota prius) :

Torque CouplersPlanetary 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:

Quasistatic Modeling of Planetary Gear Sets