Development Mechanics Michigan Technological University Houghton, MI 49931

of mode selection map for multi-mode powersplit hybrid electric vehicle based
on offline optimization


Huanqing Wang

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of Mechanical Engineering_Engineering Mechanics

Technological University

MI 49931 USA

[email protected]












of Mechanical Engineering_Engineering Mechanics

Technological University

MI 49931 USA


Bo Chen

of Mechanical Engineering_Engineering Mechanics

of Electrical & Computer Engineering

Technological University

MI 49931 USA

[email protected]

Abstract—This paper presents an
offline optimization strategy to be used for multi-mode hybrid electric vehicle
powertrain control. A novel method of using equivalent consumption minimization
strategy (ECMS) to determined best mode is explained and a mode selection map
is created. The performance of offline optimized map control is compared with
rule based control from data provided by Argonne national lab.

electric vehicle; optimal control; powersplit; 

I.      Introduction

With higher regulations
on emission and fuel economy, electric vehicle and hybrid electric vehicle are
taking over the market quickly. With EV charging infrastructure and battery
technology takes time to develop, internal combustion engine is still the
dominate force. Electrification could significantly reduce the inefficient use
of engine, for example, during low speed, and city stop and go situation.
Electric motor can do the majority of the work during low speed situation,
avoiding running engine at low BSFC point. Motor is also capable of regenerate
braking where charge can be brought back to the battery. The powersplit vehicle
is capable of being a series or parallel, it can used one motor as a propelling
motor the other used as generator. The combination aims to use engine at most
efficient point, whether directly propelling the vehicle or charged battery for
future use.


control strategy for hybrid electric vehicles are: rule based control, instantaneous
optimization, model predictive control and global optimization. Rule based
control are widely applied in automotive industries where rule extraction are
based on calibration tasks. Instantaneous optimization is suitable for real
time control since the algorithm try to minimize the cost at each time step.
Equivalent consumption minimization strategy would fall in the category of
instantaneous optimization. Dynamic programming is a global optimization
method, where it determines the state trajectory of a given solution. It
utilizes bellman principle of optimality and the cost is calculated backwards,
therefore prior knowledge of entire drive cycle is require. Model predictive
control is a dynamic programming break in shorter intervals, instead of
requiring entire drive cycle; it could uses only short predicted speed chunks
of 5 seconds or 10 seconds to perform dynamic programing for optimal control.


ECMS has
been a popular method for instantaneous optimization in single mode series,
parallel and powersplit vehicle, but not for multi-mode vehicle control. This
paper proposes of method applying ECMS for multi-mode vehicle powertrain
control. The powersplit is generated in a lookup table offline for each mode.
All modes are compared for all driving conditions and the mode with lowest
equivalent fuel cost would be selected. The best mode map is generated offline
but it can be used for online application. The control strategy is tested in
UDDS drive cycle and optimized map based control is compared with rule based
control data by Argonne national lab.


Section II introduces the
specs of vehicles and kinematic relationship in each operating mode. Section
III explains the problem formulation, powersplit optimization, and mode
optimization and control strategy. Section IV compares the results with
experimental data from Argonne national lab. Section V concludes this paper.

II.    Vehicle

A.    Vehicle

GM volt 2 uses a 1.4-liter engine and two motors and two
planetary gear set. Different operating modes can be achieved by opening and
closing of the two clutches 3. MGB is ideal for low speed high torque
application where MGA is more suitable for high-speed low torque. There is a
one way clutch on connected to the engine to prevent engine spinning backwards
during EV mode. Clutch one connects sun gear of PG1 and ring gear of PG2.

Architecture of Chevy Gen II Volt


B.    Mode

There are five modes introduced by GM. Different mode can
be achieved by opening and clutches. The summary and equations are presented
for each mode. The governing equation for speed relation is Willis’ equation.


Where  is the angular velocity of the ring gear,  is the angular velocity of the sun gear,  is the angular velocity of the planetary
carrier. S is the teeth number of sun gear and R is the teeth number of sun

1EV: During one motor EV mode, clutch 1 is open and
clutch2 is closed. Motor A and Motor B both spins and react to vehicle speed,
but only Motor B provides torque.

EV2: During two motor EV mode, clutch 1 is open and
clutch2 is closed. Both Motor and Motor can provide torque. This mode can
provide maximum amount of torque.

LER: During LER mode, clutch 1 is open and clutch 2 is
closed. Part of engine power is used to charge the battery. Motor A acts as a
generator and motor A torque is directly coupled to engine torque.

FER: During fixed extended range, clutch 1 and clutch 2
are both closed. Only in this mode. Motor A is grounded and it does not provide
torque. All engine power is used to propel the vehicle. The engine speed is
directly proportional to vehicle speed since the gear ratio between engine and
wheels is fixed. Motor B can assist propelling the vehicle when large axle
torque is required.

HER: During high extended range, clutch 1 closes and
clutch 2 is open. By closing clutch 1, sun gear of PG1 is connected to ring
gear of PG2. This gives a higher ratio and makes it efficient for high speed
driving. Engine speed is independent from wheel speed. By adjusting motor A and
motor B rpm, the engine rpm can run at efficient operating points.

Where  is the angular velocity of motor A,  is the angular velocity of motor B,  is the angular velocity before final drive. S1
is number of teeth of the sun in the first planetary gearset. R1 is the number
of teeth of the ring in the first planetary gearset. S2 is number of teeth of
the sun in the second planetary gearset. R2 is the number of teeth of the ring
in the second planetary gearset. is the torque of motor A, is the torque of motor B, is the torque of engine.

III.   optimal

Instantaneous optimization is used for this equivalent
minimization strategy approach. At every operating point, the cost of fuel and
cost of electricity is being minimized. Since electric and fuel is not directly
comparable, electric consumption is converted to equivalent fuel1. Brute
force algorithm is used to determine best motor and engine operating
combinations and results are stored in maps.

best operating points

During EV operation, the goal is to reduce battery energy consumption.
It is achieved by using both motors at the most efficient combination.The cost
function is defined:

 Where  is the battery power consumption;  is the Motor A torque, is the Motor A angular speed, is the Motor B torque, is the Motor B angular speed, is the Motor A efficiency, is the Motor A efficiency , is the Motor A power electronics efficiency, is  the
Motor B power electronics efficiency. All driving condition can considered in
terms of axle torque and speed4. For each, torque and speed combination, all motor
operating conditions are examed, and the control with lowest cost is recorded
and shown in the graph.


Fig.2 Motor
B best operating torque for EV mode.

Fig.3 Motor
A best operating torque for EV mode.


mode best operating points

During hybrid
operation, the equivalent fuel consumption

is being minimized at each
instant. The equivalent fuel consists of instantons fuel consumption and
electricity converted into fuel by multiply average bsfc factor. The equivalent
fuel factor is a BSFC equivalent factor, represent how efficient engine would
operate if those motor power are provided by engine. For every speed and torque
point, all engine and motor operating combinations are examed and control with
the lowest operating cost is selected.

 is the equivalent fuel
consumption, which is the sum of engine fuel consumption  and equivalent fuel consumption from electric
motor  . is the equivalence factor of
converting battery power to fuel consumption, it represents how efficient the
engine would operate if those electric power are otherwise provided by engine,
the detailed of determination of this factor can be found in 2. is the Motor A power, is the Motor B power.  is -1 when MGA acts as generator and 1 when
acts a motor. is -1 when MGB acts as generator and 1 when
acts a motor.


All driving condition can be
mapped into axle torque and speed combination, sweeping through all
combinations, the best control in terms engine speed, engine torque, motor B
torque, motor B speed, motor A torque, and motor A speed are shown in Fig.4-9.


Fig.4 Engine
best operating torque for LER mode.

Fig.5 Engine
best operating rpm for LER mode.




Fig.6 Motor
B best operating torque for LER mode.

Fig.7 Motor
B best operating speed for LER mode.


Fig.8 Motor
A best operating torque for LER mode.


Fig.9 Motor
A best operating speed for LER mode.


mode map

For each mode, the equivalent fuel cost can be determined for
all operating conditions and is generated in map with respect to axle torque and
speed. The fuel consumption map for LER mode is shown in Fig.10.

Equivalent fuel consumption for LER mode.


There are total of four maps (EV, LER, FER, HER), after
overlay 4 modes fuel consumption together, for each axle torque and speed, the
mode with the lowest fuel cost is selected. The mode selected will be recorded
into our new map best mode map. The results are shown in Fig.11. It shows EV
mode is most efficient during low speed operation. During extreme high torque
requirement, it is also selected since it exceeds other mode’s torque capability.

Fig.11 best
operating mode map.


A.     Control strategy

When determining best operating
points and extracting mode map, all control combinations are examined; it is
computationally expensive and the map is developed offline. Although the mode
map and operating map are generated offline, it is suitable for online
application. In Fig.12, any drive cycle can be discretized into vehicle’s axle
torque requirement and speed. At each discrete time step, the pair goes through
mode selection lookup first. Then, the two points going into the mode selection
table to select the mode. The according best operating points from that mode is
looked up and send to the vehicle model.



Fig.12 the control strategy from
best mode map

IV.   Results

The drive cycle being used is UDDS and it is compared with
experimental data of the same cycle from Argonne National Lab5. The offline
optimized map method uses the best mode map and best operating points, where
rule based control method used experimentally recorded mode shift and
powersplit. Both control strategies are used and fed into the model and results
are recorded. Fig.13 shows the engine operating points of the optimized map
method. The inefficient use of engine is avoided in this method whereas there
are low BSFC points recorded in rule-based control in Fig.15.

Engine operating points in UDDS cycle from offline optimization map.

Fig.14 Simulation
results of UDDS cycle from offline optimization map.

Fig.14 shows that by running engine at low BSFC point,
lower fuel consumption can be obtained. The mode shift of the optimized map
eliminated the use of two motor EV mode, since it is determined there are less
loss using one motor during UDDS driving, which is a relative low torque
requirement driving cycle. Rule based control almost has a charging and
depleting behavior. As shown in Fig.15, when battery state of charge becomes
relatively high, it uses EV to drain the battery for the next 250s.

Engine operating points in UDDS cycle from ruled based control.

Fig.16 Simulation
results of UDDS cycle from ruled based control.

After the drive cycle, the simulation shows the rule based
control strategy control strategy consumes 0.304 gallons of gasoline and the
optimized map control strategy consumes 0.246 gallons of gasoline. The fuel
saving is achieved by running the engine at efficient point where BSFC values
are low.

V.    Conclusions

This paper introduces the architecture of Chevy gen2 volt,
explained an offline optimization strategy to determine vehicle best operating
points and best mode map. The offline optimized map control strategy compared
with rule based control strategy from data provided by Argonne National Lab.


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