Electric Vehicle Modeling Utilizing DC Motor Equations

Clay S. Hearn, Damon A. Weeks, Richard C Thompson, and Dongmei Chen

2010 IEEE/ASME International Conference on Advanced Intelligent Mechatronics

July 6 – 9, 2010, Montreal, Quebec

Introduction

• Previous electric and hybrid electric vehicle modeling experience and demonstrations at UT-CEM

• PSAT modeling toolbox and motor models– Acausal modeling– Steady state efficiency maps

• Development of causal electric vehicle model– Account for transient dynamics

and other constraints– Requires feed-forward control

design

Vehicle Modeling at UT-CEM

• Plug-In Hybrid Fuel Cell Shuttle Bus– On road evaluations– 3 different routes– PSAT models matched energy

consumption data to within 5%

• Columbia ParCar utility vehicle conversion– Upgrading with 8.5 kW fuel cell

and ultracapacitor energy storage– PSAT modeling used in design

process– Base vehicle modeling with DC

motor used for model development

Advantages and Limitations of PSAT

• Large library of component models derived from testing for engines, motors, batteries, etc…

• Quickly evaluate different component options and hybrid configurations

• Development of supervisory control strategies• Acausal modeling techniques

– Static power converters with efficiency transfers power between batteries, motors, and auxiliaries

• Steady state efficiency maps used for motors and engine models

– Validity of efficiency map– Loss of transient dynamics– Loss of other limitations such as current limits

or thermal limits• Inaccuracies in transient dynamics and

performance limitations

Model Development• Base vehicle model is ParCar SUV-LN

– 48V lead acid batteries– 12.9 kW DC motor

• Model vehicle with DC motor equations and causal modeling techniques

• Bond graph and equation formulation• Develop control strategies for route

following– Feed-forward Torque demand estimation– Field and armature voltage control

Bond Graph Model Development

• Bond graph tracks power flow and causality

• Idealized DC converters modeled as transforming elements

• Nonlinearities included in motor constant

Derived Equations from Bond Graph Model• Battery SOC is a quasi-

state based on Voc – R battery model

• Main model states– If = field current

– Ia = armature current– V = Linear velocity

• Controls– m = field current duty

cycle– n = armature current duty

cycle

Back EMF

EM Torque Motor Friction

Drag Grade and Roll Resistance

DC Motor Control

• Separately wound DC motors allow active control of field and armature current

• Below base speed: field current held constant and armature voltage controlled for constant torque

• Above base speed: field current is weakened to increase motor speed at constant power

Driver Model

• Driver model estimates required torque to move vehicle along given velocity profile

• Feed forward controller design– Linearize and invert vehicle equations

• Feedback PI controller included to add additional corrections to reference speed

Feed Forward Control Design

Linearize vehicle motion equations about a specified V0 and solve for steady state EM torque

Derive and invert transfer function from linearized equations. Inverted TF yields dynamic EM torque output, but requires low-pass filter

Set filter pole ~100X left of pole location

Steady state torque minus V0

torque requirement is added to dynamic estimation (above)

DC Motor Current Requirements

• Vehicle model uses separate PI controllers for armature and field loops (m and n duty outputs)

• Translate torque estimates from driver model to field and armature current demands

• Constant torque regime– Constant field current at 10 amps– Solve for the armature current

• Field weakening regime– Solve for the steady state field and armature currents from

initial state equations– Solution based on the motor speed demand

Field Weakening Current Estimate

• Above base speed, PI motor current controllers solve for these reference currents

• Current limits are set at 400 A for armature and 40 A for field

Steady state expression for armature current demand

Steady state expression for field current demand

Substitution yields quadratic equation that can be used to find required currents

Simulink Model Overview

Torque_Estimator

Speed _Demand

Grade _Profile

Speed _Veh

Tem

Motor _Speed

time

Armature _Command

Field _Command

Battery _Vout

Battery _Current

Armature _Current

Field _Current

Velocity _Out

Battery _SOC

Speed _Profile

sch_cycle

Motor_Commands

Tem _demand

speed_demand

field _current

armature _current

Vout

M_duty

N_duty

Grade _Profile

sch_grade

Electric_Vehicle

field _control

armature _control

theta

Battery _SOC

Battery _Current

Velocity

field _current

Armature _Current

Vout

Clock

Route Following Response

Comparisons to PSAT Performance

Summary

• Presented a causal model of an electric vehicle driven by separately wound DC motor

• Developed driver models and vehicle control algorithms

• Level of modeling will include transient dynamics as well as specified constraints– Current limitations– Addition of thermal modeling will allow current limits due

to thermal constraints• ParCar SUV-LN is now at UT-CEM for testing and retro-

fit