Energy Management of Parallel Hydraulic Hybrid Wheel Loader

INOM TEKNIKOMRÅDET EXAMENSARBETE

TEKNISK FYSIK

OCH HUVUDOMRÅDET ELEKTROTEKNIK,

AVANCERAD NIVÅ, 30 HP STOCKHOLM SVERIGE 2018 ,

Energy Management of Parallel Hydraulic Hybrid Wheel Loader

with Focus on Fuel Consumption Minimization

HOANG THAI DO

Abstract

Hybridization of driveline system is one possible solution to increase fuel efficiency.

In this thesis a parallel hybrid hydraulic wheel loader concept was studied. A high

pressure accumulator was added to the system and acted as a second source of en-

ergy. By adding the high pressure accumulator, regenerative braking energy can

be stored for later utilization. A backward facing simulation model was developed

where the high pressure accumulator’s State Of Charge (SOC) as state variable

and hydraulic pump/motor’s displacement as control input. Furthermore, differ-

ent energy management strategies: Dynamic Programming (DP), rule-based and

Equivalent Consumption Minimization Strategy (ECMS) were developed. These

strategies were evaluated and compared to each other all with respect to the fuel

consumption. The result from conventional machine acted as the benchmark for

other strategies to compare with. From simulation results, rule-based strategies

showed to be the most robust, resulted in lower fuel consumption in every tested

driving cycle. For ECMS, the performance varied from cycle to cycle. A reduction

in fuel consumption was observed for short-loading cycles. Especially in one cycle,

ECMS result outclassed rule-based and was almost the same as DP. However, a

small increment was observed for long-carry cycle. Here the introduction of lock-up

feature in the torque converter yielded instead the most fuel saving. These valuable

conclusions acted perfectly as a good starting point for future product development.

Sammanfattning

Hybridisering av drivlinan ¨ ar en m¨ ojliga l¨ osning f¨ or ¨ okad br¨ ansleeffektivitet. En par- allell hybrid hydraulik hjullastare koncept unders¨ oktes i detta arbetet. Genom att s¨ atta en extra h¨ ogtrycksackumulator till systemet kunde regenerativ bromsningsen- ergi lagras f¨ or senare anv¨ andning. En bak˚ at simuleringsmodell med ackumulators laddningstillst˚ and som tillst˚ andsvariabel och hydraulisk pumps/motors f¨ orflyttning som reglering signal utvecklades tillsammans med olika energy regleringstrategier s˚ a som: dynamisk programmering (DP), regelbaserad (RB) och Ekvivalent Konsum- tion Minimering Strategi (engelska - ECMS). Strategierna evaluerades och j¨ amf¨ ordes med h¨ ansyn till br¨ anslef¨ orbrukningen d¨ ar resultaten fr˚ an konventionella maskinen anv¨ andes som referens. Regelbaserad strategier visades vara mest robusta d¨ ar br¨ anslef¨ orbrukning minskades f¨ or alla testade k¨ orcyklar. F¨ or ECMS varierades re- sultatet mellan olika k¨ orcyklar. En minskning av br¨ ansle f¨ orbrukning noterades f¨ or alla kortcyklar. F¨ or en cykel utklassade ECMS RB och var n¨ astan lika bra som DP.

F¨ or l˚ angcyklar resulterade ECMS i en liten ¨ okning av br¨ anslef¨ orbrukning. Att intro- ducera ”l˚ asa-in” funktion i momentomvandlare gavs den st¨ orta br¨ ansleminskningen.

Slutsatserna var mycket v¨ ardefulla till framtidens utveckling.

Contents

1 Introduction 1

1.1 Background . . . . 1

1.2 Problem description . . . . 1

1.3 Energy Management Strategy . . . . 2

1.4 Purpose and project aim . . . . 3

1.5 Method . . . . 3

1.6 Thesis Outline . . . . 4

2 Hydraulic Hybrid Vehicle 5 2.1 Parallel Hybrid Hydraulic Vehicle . . . . 6

2.2 Series Hybrid Hydraulic Vehicle . . . . 6

2.3 Power-split Hybrid Hydraulic Vehicle . . . . 7

2.4 Studied Wheel Loader Hybrid Configuration . . . . 8

3 Theory 9 3.1 Driving cycles . . . . 9

3.1.1 Short Loading Cycle . . . . 9

3.1.2 Load and Carry Cycle . . . 10

3.2 Torque Converter . . . 11

3.3 Energy storage . . . 13

3.4 Accumulators . . . 14

4 System Modeling 15 4.1 Backward simulation model . . . 15

4.1.1 Propeller shaft . . . 16

4.1.2 Transmission Gear ratios . . . 16

4.1.3 Add-on Hydraulic Hybrid Pump/motor . . . 17

4.1.4 Transmission . . . 17

4.1.5 Torque Converter . . . 18

4.1.6 Work Hydraulic Machine . . . 18

4.1.7 Internal Combustion Engine . . . 18

4.2 Lock-up Activation . . . 19

5 Control Strategies 20

5.1 Dynamic Programming . . . 20

5.1.1 Theory . . . 20

5.1.2 Mathematical Problem Formulation . . . 23

5.2 Rule-based Strategies . . . 24

5.2.1 Working moment based . . . 24

5.2.2 Power and Torque based . . . 24

5.3 Equivalent Consumption Minimization Strategy . . . 25

5.3.1 Mathematical Problem Formulation . . . 28

5.3.2 Optimal equivalent factor . . . 28

6 Result and Analysis 29 6.1 Fuel consumption . . . 29

6.2 Additional Lock-up Feature . . . 30

6.3 Simulation parameters - ECMS . . . 30

6.4 Strategies analysis . . . 31

7 Conclusions and Future Work 34 7.1 Conclusion . . . 34

7.2 Future Work . . . 34

List of Figures 1.1 Energy Management Strategies overview of classification . . . . 2

2.1 A schematic illustration of a parallel HHV. . . . 6

2.2 A Schematic illustration of serie HHV. . . . 7

2.3 A Schematic illustration of power-split HHV. . . . 7

2.4 Driveline components for hydraulic hybrid wheel loader concept . . . 8

3.1 Short loading cycle. [11] . . . . 9

3.2 Load & carry cycle [11] . . . 10

3.3 Schematic presentation of a TC together with fluid flow direction [12] 11 3.4 Specific power and specific energy for different short-term energy stor- age systems [7] . . . 13

3.5 Common types of hydropneumatic accumulator [13] . . . 14

4.1 Simple version of backward simulation model with one control signal

and one state variable. . . 15

5.1 The red arc is the optimal trajectory. Any problem initiated from a point on the optimal trajectory will have the remaining trajectory as the optimal trajectory. . . 21 5.2 The DP algorithm. The red arc is the optimal path with lowest cost-

to-go . . . 22 5.3 The energy flow in ECMS for recharging and discharging phase . . . 25 5.4 Weight function W _SOC for different exponent a with SOC _min = 0,

SOC _max = 1 and SOC _{f inal} = 0.5 . . . 27 5.5 The algorithm of the bisection method for optimal equivalent factor

searching. . . 28 6.1 DP and ECMS SOC trajectory for the short loading cycle 1. . . 31 6.2 DP and ECMS SOC trajectory for load carry cycle without lock-up. . 32 6.3 DP and ECMS SOC trajectory for load carry cycle with lock-up. . . . 32 6.4 Rule-based 1 and 2 SOC trajectory for short loading cycle 1. . . 33

List of Tables

6.1 Fuel consumption comparison for different EMS and driving cycles with fuel consumption for conventional machine as baseline . . . 29 6.2 Fuel consumption comparison (in % ) for load and carry cycle be-

tween no lock-up and lock-up with fuel consumption for conventional

machine without lock-up as baseline. . . 30

6.3 Simulation parameter in ECMS for different driving cycle. . . . 30

Nomenclature

Acronyms

DP Dynamic Programming

ECMS Equivalent Consumption Minimization Strategy EMS Energy Management System

FD Final Drive FWD Forward

HV Hybrid Vehicle

HEV Hybrid Electric Vehicle HHV Hybrid Hydraulic Vehicle ICE Internal Combustion Engine

KD Kick Down

REV Reverse

SOC State of Charge

TC Torque Converter

Symbols

η _axle Axle efficiency [-]

λ Equivalent factor [-]

µ Torque converter slip [-]

ν Torque multiplication factor [-]

 _hyb Relative displacement setting hybrid hydraulic system [-]

 _{W H} Relative displacement setting work hydraulic system [-]

γ Polytropic index [-]

D _hyb Maximum hybrid machine displacement [ml/rev]

D _{W H} Maximum work hydraulic displacement [ml/rev]

f uel _ICE Engine consumed fuel [l]

F _wheel Vehicle wheel traction force [Nm]

J _ICE Engine moment of inertia [kgm ² ]

i _axle Gear ratio for drive [-]

i _hyb Gear ratio propulsion axle - hybrid machine axle [-]

i _tra Gear ratio transmission [-]

i _{W H} Gear ratio work hydraulic - engine crankshaft [-]

n _hyb Rotational speed of hybrid machine [rpm]

n _ICE Engine speed [rpm]

n _prop Rotational speed of propulsion axle [rpm]

n _turb Rotational speed of torque converter turbine [rpm]

n _imp Rotational speed of torque converter impeller [rpm]

n _{W H} Rotational speed of work hydraulic [rpm]

p Accumulator pressure [bar]

p ₀ Accumulator initial charge pressure [bar]

p _max Accumulator maximum pressure [bar]

p _min Accumulator minimum pressure [bar]

p _{W H} Work hydraulic pressure [bar]

P _aux Auxiliary power [W]

P _prop,lim Propulsion axle power limit [W]

p _eng Engine power [W]

Q _{W H} Work hydraulic pump flow [m ³ /s]

Q _lvh Diesel lower heating value [MJ/kg]

r _tire Tire radius [m]

T s Simulation time step [s]

T _ICE Engine torque [Nm]

T _ICE,load Engine load torque [Nm]

T _imp Torque converter impeller torque [Nm]

T _hyb Hybrid hydraulic machine torque [Nm]

T _prop Propulsion axle torque [Nm]

T _prop,lim Propulsion axle torque limit [Nm]

T _turb Torque converter turbine torque [Nm]

Chapter 1 Introduction

1.1 Background

Higher fuel efficiency has been one of the biggest goal in automotive industry for decades. Reasons are many: more restrictive emission legislation, high fuel prices and the fact the fossil fuel is a limited resource are some of the examples. In the past few years, the trend towards hybridization of driveline is easier to observe than ever.

In the field of off-road machinery, the same trend can be observed. Volvo CE, as one of the biggest player in the construction equipment industry has always strive for higher fuel efficiency by investigating of new driveline configurations. Again, hybridization is one of the possible solution.

Wheel loaders are heavy machines where a typical operating cycle contains many starts and stops. Large amount of energy is wasted as heat when the tradition friction brakes are used [1]. If these energy can somehow be recuperated and stored for later utilization, significant improvement in term fuel efficiency can be achieved.

It raises the questions of how to recuperate and store these energy and when is the best occasion to use the stored one.

1.2 Problem description

In the concept studied in this thesis, the first problem for recuperating the energy is solved by introducing hydropneumatic accumulators and a hydraulic pump/motor mounted on a transmission shaft to enable regenerative braking.

In order to deal with the second question, it is important to have adequate simulation models and suitable energy management strategies. The stored energy in the high pressure accumulator must be used in an efficient way to maximize the fuel efficiency.

As an example, automatic transmission is used to increase the driving comfort where

the torque converter (as a driveline component) is known to have a low efficiency

in low speeds when the demanded torque is high (when accelerating from stops or

filling the bucket). Here, as one of the occasion when the stored energy can be used to compensate for low torque converter efficiency.

1.3 Energy Management Strategy

In the area of energy management strategy (EMS) for hybrid vehicle (HV), exten- sive researches have been made by many researchers [2]. An EMS can be designed in many ways where different objectives are taken into consideration. Complexity of the EMS, optimization category or prior knowledge of the driving cycle are some of the examples. The thing that they share in common is the fact that at each time instant, a suitable torque split between different propulsion actuators is determined [3],[4],[5]. Each of the actuators can therefore work in their higher efficiency regions and thus lower the total fuel consumption [6].

Control Strategies 

Rule-based Model-based Optimization

Numerical Analytical

Figure 1.1: Energy Management Strategies overview of classification

In general, EMS for HV can be divided into two categories: heuristic/rule-based and model-based optimization. These categories can further be divided into several sub- categories. A classification overview of the control strategies is given in figure 1.1. In rule-based strategies, no explicit minimization nor optimization are involved. The values of the control signals at each time instant relied instead on a set of predefined rules based on heuristic, intuitions, or from the characteristic of the optimal global solution. These controllers are easy to implement and to understand. They can be trimmed to wanted behaviours where each component can be optimized individually.

In model-based optimization category, optimal controls are calculated by minimiza-

tion of a cost/objective function. The driving cycle is often fixed and known in ad-

vance where a global optimal solution can be obtained [3]. However, when the knowl-

edge of future driving information is required, the solution is non-causal [7],[3],[8].

implementation where they serve as a valuable tool for online implementation. Set of rules can be designed from the characteristic of the solution [9]. Furthermore, the solution can be used as benchmark for other control strategies.

Optimization based strategies can in turn be divided into two subcategories: nu- merical and analytical. In numerical subcategory, the entire driving cycle is taken into consideration in the process of finding the global optimal solution numerically.

Dynamic programming, stochastic dynamic programming and simulated annealing are some of the examples.

On the other hand, an analytical problem formulation is used in analytical subcat- egory to find the solution in closed, analytical form. The original problem is be divided to subproblems where each one of them is optimized locally. Equivalent consumption minimization strategy (ECMS) based on Pontryagin’s minimum prin- ciple (PMP) [10] and model predictive control (MPC) are some of the examples.

Since the knowledge of the driving mission is not necessarily required in advance, these strategies are more suitable for online implementation [1].

1.4 Purpose and project aim

The thesis aims to develop different EMS using known driving cycles. The sequence of control policy close to optimal is obtained from the EMS to minimize the fuel consumption. The following questions will be investigated and answered:

• How much fuel can be saved from different EMS?

• How lock-up feature in the torque converter affect the fuel consumption?

• Which EMS is most suitable for the studied wheel loader in term of fuel effi- ciency and implementation complexity?

1.5 Method

As mentioned, the driving cycles are known. Several variables are given directly from the driving cycle such as vehicle velocity, traction force, flow and pressure in the work hydraulic, etc... Backward facing simulation model starting from the wheel to the engine will be developed as well as different EMS. The idea is to have at least one EMS corresponds to each category mentioned earlier.

First of all, dynamic programming (DP) is used to obtain the global optimal solution.

Based on the characteristic of the control sequence from DP, simpler rule-based strategies will be developed. Later on, ECMS based on PMP will be implemented.

Finally, these EMS:s are evaluated using the model with respect to fuel consumption

and complexity.

1.6 Thesis Outline

In the remaining of this thesis report, the following chapters are presented:

Chapter 2: Different types of hydraulic hybrid vehicle in general are pre- sented and compared to each other. Furthermore, the studied wheel loader configuration will be presented together with the characteristic of the driving cycles used in the simulation model.

Chapter 3: Fundamental background theories with focus on physical hard- ware components will be presented. The goal is to have a better understanding and make it easy to follow the simulation model.

Chapter 4: The backward simulation model with one state variable and one control signal is presented. In the end of this chapter, the lock-up feature in the torque converter is presented with all the changes in the simulation model when the feature is introduced.

Chapter 5: A deeper explanation for each EMS will be presented. Mathe- matical problem formulations are presented together with the motivation of why each EMS is implemented in a certain way.

Chapter 6: The fuel consumption result when utilizing each EMS is presented and compared against each other for each driving cycle. A deeper analysis of the results as well as the answers for the investigated question will be presented.

Chapter 7: Final chapter about the conclusions can be drawn from the thesis

work together with the recommendations for future work.

Chapter 2

Hydraulic Hybrid Vehicle

Hybrid vehicle (HV) is developed to increase the fuel efficiency of the power train and decrease emissions from the vehicle. In a conventional machine without any add-on hybrid system, there is only one power source that is responsible for all required power during operations. While in a HV there are at least two energy sources, one primary (irreversible) and one secondary (reversible). The primary energy source is usually a combustion engine or Fuel Cell while the secondary energy acts as a buffer and varies from application to applications.

With the secondary reversible energy storage, regenerative braking is possible, where the braking energy that otherwise is wasted in form of heat losses in traditional fric- tion brake can now be stored. The fuel efficiency can therefore increases. Further- more, in some hybrid configuration, more than one propulsion actuators can coop- erate and split the required power. This allows better dimensioning of the driveline where components can be downsized while the power requirements are still satisfied.

In the case of hybrid hydraulic vehicles (HHV), hydropneumatic accumulators are used where pressure energy can be extracted from, acting like a secondary power source. Based on the power-train topologies, three types of HHV can be categorized:

parallel, serial and power-split HHV.

2.1 Parallel Hybrid Hydraulic Vehicle

In a parallel hybrid hydraulic vehicle, the engine provides power to the wheel through standard driveline components. The hydraulic add-on components are attached to the drive shaft or to one transmission’s axle. The parallel HHV is also known assist HHV since the engine still takes care of the propulsion while the hybrid components only assist in stopping (by regenerative braking) and when high power are required.

Figure 2.1 illustrates a schematic view of a parallel HHV.

Engine

Hydraulic Pump/motor

Driveshaft

Low pressure reservoir High pressure

Accumulator

Figure 2.1: A schematic illustration of a parallel HHV.

During regenerative braking, the hydraulic pump/motor is activated and acting as a pump. The rotational energy from the wheel is used to pump the fluid from the low pressure reservoir to the high pressure accumulator. The pressure energy is stored and can later be used to assist the vehicle. In this case the pump/motor acts as a motor and the fluid flows in the opposite direction.

2.2 Series Hybrid Hydraulic Vehicle

In serie HHV, only the hydraulic pump/motor is connected to the drive shaft. The

vehicle is moved only by pressure energy from the high pressure accumulator. In this

configuration, the ICE is connected to a hydraulic pump and its only purpose is to

charge the high pressure accumulator. The principle of regenerative breaking is the

same as in parallel HHV. The illustration of a serie HHV can be seen from figure 2.2.

Engine

Hydraulic Pump/motor

Driveshaft

Engine Crankshaft

Hydraulic pump

High pressure Accumulator

Low pressure reservoir

Figure 2.2: A Schematic illustration of serie HHV.

2.3 Power-split Hybrid Hydraulic Vehicle

In power-split HHV (also called combined HHV), both advantages of parallel and serie hybrid concepts are combined. Depending on the driving condition, the engine can propel the vehicle through physical connection to drive-shaft or act as a pump to charge the high pressure accumulator. The vehicle can be driven only by the engine or only by the hydraulic pump/motor or a combination of both, hence the name power-split. An illustration of a power-split HHV is given in figure 2.3.

Engine

Hydraulic Pump/motor

Driveshaft

Engine Crankshaft Hydraulic pump

Clutch

High pressure Accumulator

Low pressure reservoir

Figure 2.3: A Schematic illustration of power-split HHV.

2.4 Studied Wheel Loader Hybrid Configuration

Conventional Wheel Loader

In a conventional wheel loader, the engine is the only energy source that is respon- sible to all required energy during operation. The power from the engine to the driving wheels is delivered through the driveline which consisted of the following components:

An diesel engine as power source.

A torque converter.

A transmission box A drive axle.

A final drive.

Parallel Hydraulic Hybrid Concept

The wheel loader hybrid concept studied in this thesis is of parallel type. As men- tioned earlier, a hydraulic pump/motor and hydropneumatic accumulators are in- troduced. They are located in one transmission’s axle. When needed, the engine can be assisted by the high pressure accumulator through the hydraulic pump/motor. It results in lower power demand from the engine. The fuel consumption is therefore decreased. Figure 2.4 illustrates the driveline components of the studied configura- tion.

FD

Transmission Engine

Hydraulic Pump/motor

Driveshaft

Torque Converter WH

Working Hydraulic

Low pressurereservoirLow pressure reservoir High pressure Accumulator

Figure 2.4: Driveline components for hydraulic hybrid wheel loader concept

Chapter 3 Theory

This chapter aims to make the thesis easier to understand. Two types of driving cycles used in the simulation will be explained in details, both the similarities and differences. Furthermore, the driveline components presented in previous chapter will be explained.

3.1 Driving cycles

In the remaining part of the thesis, two types of driving cycle are examined. The first one is called ”short loading” while the second one as ”load-carry”. Worth to mention, they might also be called for short and long cycle in the following chapters.

The differences between these two types are presented below.

3.1.1 Short Loading Cycle

Gravel Pile

Hauler

1 4

3 2

Start position

Figure 3.1: Short loading cycle. [11]

Figure 3.1 illustrates the short loading cycle. As can be seen, a short loading cycle is consisted of four following phases:

1 - Bucket filling: from the initial starting position at the gravel pile, the wheel loader fills the bucket and use reverse gear to move away from the gravel pile.

2 - Bucket emptying: using the forward gear, the wheel loader approaches the (close by) hauler and empties the bucket.

3 - Reversing from hauler: using the reverse gear, the wheel loader move away from the hauler and is ready to the last phase.

4 - Approaching gravel pile: again, forward gear is used for the wheel loader to move to the starting position at the gravel pile.

Since the distance between the gravel pile and the hauler is short, the maximum speed of the wheel loader in a short loading cycle is limited. Therefore, the brakes are not used frequently and the driver often flips the gear to change direction with- out braking.

3.1.2 Load and Carry Cycle

Similar to short loading cycle, the load and carry cycle is consisted of four phases.

However the transportation distances in bucket emptying and approaching gravel pile phase are significantly longer. The vehicle speed can reach high values which required more braking to slow down the machine in the end of each transportation phase. Figure 3.2 illustrates the load and carry cycle.

Gravel Pile

Hauler

1 4

3

2

Start position

Figure 3.2: Load & carry cycle [11]

3.2 Torque Converter

In a manual transmission vehicle, the engine is connected to the transmission by clutch. Utilizing this connection, the vehicle is able to completely stop without killing the engine. In the case of an automatic transmission vehicle, there is no clutch that disconnect the transmission from the engine. Instead a torque converter (TC) is used.

There are three main components in a TC: an impeller, a turbine and a stator.

These components are surrounded by transmission fluid/oil - the power transferring medium. See figure 3.3 for an schematic overview of a TC. The impeller is connected directly to the engine and rotates at the same speed as the engine crankshaft. When rotating, the impeller acts as a centrifugal pump and pushes the fluid away from the center to the turbine by centrifugal force. Because of the directional change of the fluid when enters and exits the turbine, the turbine is rotated. Since there is always losses, the turbine speed in most cases is lower than the impeller speed.

The exiting fluid flows back to the impeller center through the stator. The stator’s main purposes is to slow down the fluid and change its direction to the same as the rotating direction of the impeller. By doing that, the loss is reduced, resulting in a higher efficiency.

Figure 3.3: Schematic presentation of a TC together with fluid flow direction [12]

Two useful ratios in a TC are slip and torque multiplication:

Slip ν is defined as the ratio between output (turbine) and input (impeller) speeds:

ν = n _out

n _in = n _turb

n _imp (3.1)

ν is normally a positive number 0 ≤ ν ≤ 1. However when the driver quickly flips gear from forward to reverse or vice verse, negative slip can occurs due to the turbine in a brief moment rotates in the opposite direction of the impeller.

Torque multiplication factor µ is the ratio between output (turbine) and input (impeller) torques:

µ = T _out

T _in = T _turb

T _imp (3.2)

µ can have value larger than 1. When µ > 1, The TC acts as a reduction gear where the input torque is multiplied.

A torque converter has three stages of operations:

Stall (start-up): the engine applies power to the impeller but the turbine cannot rotate. As mentioned earlier, it can occur when the driver continuously applies the brake to keep the vehicle from moving. At stall, maximum torque multiplication µ _max can be achieved with sufficient input power.

Acceleration: the load is accelerating, the turbine starts to rotate but there is large difference between impeller and turbine speed n _turb << n _imp . The input torque are amplified µ > 1. However the torque multiplication is less than µ _max in stall phase.

Coupling phase: now the vehicle is reaching a higher speed, the impeller and

turbine speed are almost the same. The torque multiplication is ceased. Usu-

ally at this stage, an optional lock-up clutch can be applied to keep identical

turbine/impeller speed/torque. In this case µ = ν = 1

3.3 Energy storage

Additional energy storage plays a fundamental role in hybrid vehicle. Depending on the application, different types of energy storage are used. There are two terms that are central to any energy storage, namely:

Specific Energy: a term describes the amount of energy stored per unit of mass.

Specific Power: a term describes flow of power that can be extracted from the medium in an instant for a specific mass.

For most types of energy storage, these two properties do not go hand in hand.

With another words, a energy storage with high specific energy has often low spe- cific power and vice verse.

Energy storages can be divided into two groups: long term and short term. Fossil fuel and electrochemical battery are examples of long term energy storage due to high specific energy. These long term energy storage can act alone as a energy source while short term energy storage with low specific energy is often used in a combination with a long term energy storage to increase the overall fuel efficiency. Figure 3.4 presents specific power versus specific energy for various short term storages.

Figure 3.4: Specific power and specific energy for different short-term energy storage

systems [7]

3.4 Accumulators

The hydropneumatic accumulators belong to the group of energy storage with high specific power but low specific energy. Compare to an electrochemical battery, hy- dropneumatic accumulators have much higher specific power where higher power flows can be extracted from or put into. At the same time, frequent complete charg- ing and depleting do not impact the component’s lifespan significantly. Furthermore hydropneumatic accumulators are easy to integrate to the existing system and have low component cost.

Figure 3.5 illustrates two of the most common type of hydropneumatic accumulators:

Bladder och Piston type.

Figure 3.5: Common types of hydropneumatic accumulator [13]

The working principle is the same for both types. When charging, the fluid (oil) flows into the accumulator, the gas (often nitrogen gas) is compressed and pressure is build up. The pressure energy is now stored. When discharging, the fluid flows out, the gas is expanded and the pressure is decreased.

To sum up, this chapter has presented two types of driving cycles used in this thesis

together with short descriptions about some of the driveline components. The next

chapter will be about the backward simulation model where these components are

modelled.

Chapter 4

System Modeling

Backward-facing simulation is used to simulate the wheel loader system. In this chapter, the simulation model used to evaluate all the developed EMS in this thesis is presented. Similar model has been developed earlier [14].

4.1 Backward simulation model

Wheel/axel

∑

Transmission Torque

Converter Pump/

Motor Accumulator

Work Hydraulics

Pump 

Engine Operating Cycle

Tturb

∑ Operating Cycle

u TWH

Fwheel KD

Tprop Ttra

nprop

vwheel

nturb

TPM

QPM p

nice

Timp Tice

x

Operating Cycle

pWH

QWH

Taux ^Text

Figure 4.1: Simple version of backward simulation model with one control signal and one state variable.

The simulation model is presented in figure 4.1. In this model, there is only one con- trol signal u controlling the displacement of the hydraulic pump/motor and one state variable x, which represents the state of charge of the accumulator corresponding to the pressure level p. x is defined as:

x = p − p ₀

p _max − p ₀ (4.1)

where p ₀ is the pre-charge minimum accumulator pressure, p _max is the maximum

accumulator pressure. The model updates for each time step as follow:

x _k+1 = f (x _k , u _k , t _k ) (4.2) In the following sections, the simulation model is explained. The signals propagate backwardly from the wheels to the engine.

4.1.1 Propeller shaft

The torque and rotational speed from the transmission are transferred to the pro- pelling wheels via a propeller shaft connected to the final driver. The force F _wheel and speed v _wheel of the wheels are specified from given driving cycle for each time step. With the assumption of stiff tires without slippage, the propeller shaft speed n _prop and torque T _prop can be calculated using eq. 4.3 and 4.4 below:

n _prop = v _wheel r _tire

60

2π (4.3)

T _prop = F _wheel r _tire

η _axle i _axle (4.4)

where r _tire is wheel radius, i _axle is axle ratio and η _axle is axle efficiency due to losses occur between the final drive axle and the propulsion axle.

4.1.2 Transmission Gear ratios

A multi-gears transmission is used in the studied wheel loader. Depending on the driving condition, proper gear choice must be made and used resulting in a need of a gear shifting strategy [15],[16],[17]. In this model, gear shifting at fixed vehicle speeds is used. Furthermore, the gear is assumed to be shifted instantaneously without any delay. The reason is to eliminating the need of additional input signal to the model.

The gear shifting strategy is presented below together with the transmission gear ratio i _tra :

i _tra =



 

 

 

 

 

 

 

 

 

 

 

 

i _{F 1} for KD = 1

i _{F 2} for 0 < v _wheel < v ₂₃ and KD = 0 i _{F 3} for v ₂₃ < v _wheel < v ₃₄ and KD = 0 i _{F 4} for v ₃₄ < v _wheel and KD = 0

i _R2 for − v ₂₃ < v _wheel < 0 and KD = 0 i _R3 for − v ₃₄ < v _wheel < −v ₂₃ and KD = 0 i _R4 for v _wheel < −v ₃₄ and KD = 0

(4.5)

KD is the binary signal and is activated (KD = 1) when the wheel loader requires

extra high traction force (often during bucket filling) indicating the first forward

fact that the hydraulic pump/motors is mounted in one of the transmission shaft and therefore the gear ratio to the propeller shaft is also speed dependent.

4.1.3 Add-on Hydraulic Hybrid Pump/motor

In this model, the only available control signal is the displacement of the hydraulic pump/motor  hyb :

 _hyb = u (4.6)

The rotational speed of the hydraulic pump/motor axle n hyb is calculated as:

n _hyb = −i _hyb n _prop (4.7)

The pump/motor torque of the hybrid system T _hyb and flow Q _hyb are given by equations below:

T _hyb =  _hyb D _hyb p

20π ∓ T _loss (4.8)

Q _hyb =  _{P M} D _{P M} n _hyb

1000 − Q _loss (4.9)

where D _hyb is the maximum hydraulic machine displacement, p is the current ac- cumulator pressure. Q loss and T loss are the flow and torque loss obtained from two look-up tables where:

Q _loss = f _Q (p, n _hyb ,  _hyb ) (4.10) T _loss = f _T (p, n _hyb ,  _hyb ) (4.11) Assuming an ideal adiabatic gas compression and expansion (no heat transfers to the surrounding), the accumulator pressure p is calculated as follow:

p = p ₀ V ₀ ^γ V γ

(4.12) where V ₀ is the maximum accumulator volume and γ is the polytropic index. The gas volume V is given by:

V = V ₀ − Z

Q _hyb η ^j _acc dt (4.13)

where η acc is the accumulator efficiency, j = 1 correspond for charging while j = −1 for discharging of the high pressure accumulator.

4.1.4 Transmission

To satisfy the propeller shaft’s torque requirement, the transmission need to supply the remaining torque T _tra :

T _tra = T _prop − i _hyb T _hyb (4.14)

The mechanical transmission transfer torque from the TC’s turbine shaft to the gearbox’s output shaft. Now when the transmission torque are available, the turbine torque T turb and speed n turb can be calculates as:

T _turb = T _tra

i _tra η _tra (4.15)

n _turb = n _prop i _tra (4.16)

where η tra is the transmission efficiency and i tra is the transmission gear from eq 4.5.

4.1.5 Torque Converter

The torque converter is placed between the engine and the transmission and it’s purpose is to transfer a torque based on the speed ratio µ of the impeller and the turbine. The impeller’s speed and torque are directly related to the turbine speed and torque as:

T _imp = f (n _turb , T _turb ) (4.17) n imp = f (n turb , T turb ) (4.18) Note that these functions are given by the component supplier and are specific to each converter design. By using two look-up tables, T imp and n imp is obtained.

4.1.6 Work Hydraulic Machine

The impeller side of the TC is directly connected to the engine crankshaft. Therefore the engine speed is given by:

n _ICE = n _imp (4.19)

The work hydraulic machine (not to confuse with the hybrid hydraulic pump/motor) is connected directly to the engine crankshaft using a gear with ratio i _W H. The pump speed of the work hydraulic machine is therefor:

n _{W H} = n _ICE i _{W H} (4.20)

Using the pump flow Q _{W H} and pressure p _{W H} given from driving cycle together with equations similar to eq 4.8 and 4.9, the relative displacement and required torque of the working hydraulic can be calculated.

4.1.7 Internal Combustion Engine

The engine must now provide enough torque T _ICE to satisfy the torque requirement

of the working hydraulic, the impeller side of the TC as well as other needed auxiliary

T _ICE = T _imp + T _{W H} + P _aux n _ICE

60

2π (4.21)

where P _a ux is the auxiliary power required for fans, generator etc and assumed to be constant. With known value of engine speed and torque, the consumed fuel flow is obtained from a look-up map of the engine brake specific fuel consumption (BSFC) where:

Q _{f uel,ICE} = F _{f uel} (T _ICE , n _ICE ) (4.22)

4.2 Lock-up Activation

At the coupling phase of the TC, the turbine and the impeller rotate almost at the same speed. However, there is still a small difference in speed where small losses are unavoidable. By introducing the lock-up feature, the turbine and the impeller are locked to each other and rotate at the same speed. In this thesis, lock-up feature is investigated as a way to further improve the fuel efficiency.

As mentioned earlier, the choice of transmission gear is based on the vehicle speed.

At any time, the gear is known and can be used to define the lock-up strategy. The following simple strategy for the lock-up feature is used:

The lock-up is activated in 3:rd and 4:th gear, ie:

i _tra ∈ {i _{F 3} , i _{F 4} , i _R3 , i _R4 }

Back to the simulation models in figure 4.1, when the lock-up is activated, the Torque Converter block’ effects are neglected and the following equations are valid instead:

T _turb = T _imp (4.23)

n _turb = n _imp = n _ICE (4.24)

Chapter 5

Control Strategies

5.1 Dynamic Programming

5.1.1 Theory

As mentioned in the introduction part, Dynamic programming (DP) belongs to numerical model-based categories of EMS. In general, DP can be used for solving problems involve multistage decisions-making. It is based on the Bellman’s principle of optimalily (Bellman (1957), page 83):

”An optimal policy has the property that whatever the initial state and initial deci- sion are, the remaining decisions must constitute an optimal policy with regard to the state resulting from the first decision.”

In other words, from any point on a problem’s optimal trajectory, the remaining is the optimal trajectory for the corresponding problem initiated at that point. For example, if a problem is initiated at A and has the optimal trajectory A − B − C − D − E − F (see fig. 5.1) then the corresponding problem initiated at B will have B − C − D − E − F as the optimal trajectory.

Consider a discrete time system:

x k+1 = f k (x k , u k ) (5.1)

Where x _k is the state and u _k is the control signal at time k, both are discretized and bounded. If there are N time steps then k takes integer values k = 0, 1, 2, ...N . For a control policy over N time steps:

u = {u ₀ , u ₁ , ..., u _{N −1} } (5.2)

the corresponding cost, starting at initial condition x ₀ is:

t ₀ t N−4 t N−3 t N−2 t N−1 t N

x

A B

C D

E F

Text

t

Figure 5.1: The red arc is the optimal trajectory. Any problem initiated from a point on the optimal trajectory will have the remaining trajectory as the optimal trajectory.

Where L _k is the instantaneous cost function, also called as arc-cost. For the optimal solution, the cost function obtained is:

J ^min (x ₀ ) = arg min

u J (x ₀ , u) (5.4)

The corresponding optimal control policy is now:

u ^min = {u ^min ₁ , u ^min ₂ , ..., u ^min _{N −1} } (5.5) For a ”tail sub-problem” starting from time i and state x _i , the cost-to-go C that need to minimized is:

C(x i , i) = L N (x N ) +

N −1

X

k=i

L k (x k , u k ) (5.6)

From Bellman’s principle of optimality, {u ^min _i , u ^min _i+1 , ..., u ^min _{N −1} } is the optimal ”tail”

control policy for the ”tail sub-problem”. Utilizing Bellman’s principle of optimality,

DP starts from the time step N − 1 and propagates backward using the sequence of

controls that minimizes the cost-to-go.

The DP algorithm is explained below:

DP algorithm procedure:

Step 1 : Set k = N − 1.

Step 2 : Find the control signal that minimizes the cost-to-go:

u _k = arg min

u (L _k (x _k , u) + C _k+1 (f _k (x _k , u _k ), u _k )) (5.7) Step 3 : If k = 0, return the sequence of control signals (the solution), otherwise set k = k − 1 and return to Step 2

The illustration of the DP algorithm can be seen in figure 5.2. In this explanatory example, for simplification, there is only one state variable discretized to five values - five nodes. There is another assumption of the control signal to be large enough to move from a node at a time step to any other node at the next time step. Once again, only six time instances are illustrated for simplification.

t 0 t N−4 t N−3 t N−2 t N−1 t N

u

A B

C D

E F

Text

t

Figure 5.2: The DP algorithm. The red arc is the optimal path with lowest cost-to-

go

time t = t _{N −1} and calculates the cost-to-go from each nodes to reach node F . When all the costs are available, the node with lowest cost (node E) is chosen. The control signal to move between E and F is also saved.

The same procedure is repeated for t _{N −2} ,t _{N −3} and t _{N −4} . When t _{N −4} is reached, the optimal trajectory (A − B − C − D − E − F ) and the optimal control policy are obtained.

5.1.2 Mathematical Problem Formulation

With  hyb for the hybrid hydraulic pump/motor displacement control, the mathe- matical formulations of the optimization problem is formulated as follow:

min 

Z t

t

˙

m _f (t)dt (5.8)

S.t

SOC min ≤ SOC ≤ SOC _max (5.9)

 hyb,min ≤  hyb ≤  hyb,max (5.10)

Where ˙ m _f (t) is the instantaneous fuel flow consumption of the engine, t ₀ and t _f is the start and end time of the time interval.

A developed generic DP function solver for MATLAB is adapted for the DP part in

this thesis. For the interested reader, more info can be found from [18],[19],[20].

5.2 Rule-based Strategies

Simple control strategies can still yield a great improvement in term of fuel efficiency for (on and off-road) hybrid vehicles [21],[22]. Based on DP solution’s characteris- tics, simple control strategies can be implemented online where state variables are directly involved in the decision-making.

In the scope of this thesis, two simple rule-based strategies are implemented and evaluated. The common between these strategies is the fact that both utilize the extra add-on hydraulic when high load are required. However, the decision-making variables are different. More detailed descriptions for each of them are following:

5.2.1 Working moment based

Knowing from previous chapter, the signal are (manually) activated when the wheel loader required extra high traction force, usually when filling the bucket. In this EMS, the kick-down signal is directly involved in the decision-making. The following rules are used:

- Charge the accumulator whenever regenerative braking energy is available.

- Discharge when KD signal is activated.

- Stop discharging when the accumulator pressure is under a minimum limit p _min .

- Stop charging when the accumulator pressure is above a maximum limit p _max .

5.2.2 Power and Torque based

In this EMS, the required propeller shaft’s power and torque are used to determine charging and discharging of the energy storage. Similar to working moment based strategy, regenerative braking energy is stored for later usage. The following rules are used:

- Charge if the required propeller shaft power under a (designed) limit P _prop,lim or whenever regenerative braking energy is available.

- Discharge if the required propeller shaft torque over a (designed) limit T _prop,lim . - Stop discharging when the accumulator pressure is under a minimum limit

p _min .

- Stop charging when the accumulator pressure is above a maximum limit p _max .

5.3 Equivalent Consumption Minimization Strat- egy

Instead of solving the global minimization problem as in DP, ECMS reduces the problem to an instantaneous minimization problem to be solved at each time in- stant where arguments based on the actual energy flow are taken into consideration.

In ECMS, an equivalent factor λ is assigned and indicates the cost of using energy from the reversible storage. The equivalent factor’s optimal value is highly cycle- dependent and can only be found when the whole drive cycle is known a priori.

However, as many other works has suggested, a look up table can be obtained from offline simulation and used online. In this case, the vehicle adapts the equivalent factor after the past and predicted driving conditions [23],[24],[25].

In a hybrid vehicle in general, there are several energy storages which can perform useful work. At least one of them is reversible and the energy flow can be either from or into the storage. The usage of reversible storage is made equivalent to using (or saving) a certain quantity of fuel in irreversible energy storage. Fig 5.3 illustrates the idea of ECMS.

Fuel Tank

Engine Engine

Hydraulic Accumulator

Vehicle

Fuel  Consumption

Accumulator Discharge Virtual fuel

consumption for future recharge

(a) Discharge Phase

Fuel Tank

Engine Engine

Hydraulic Accumulator

Fuel  Consumption

Accumulator Recharge Virtual fuel

saving for future discharge

Vehicle

(b) Recharging Phase

Figure 5.3: The energy flow in ECMS for recharging and discharging phase At each time step, the equivalent fuel consumption ˙ m _f,eqv (t) that need to minimized is:

˙

m _f,eqv (t) = ˙ m _f (t) + ˙ m _hyb (t) (5.11) where ˙ m _f (t) is the instantaneous fuel consumption by the engine and ˙ m _hyb (t) is the equivalent fuel consumption (or saving) in the future when using the energy storage.

˙

m f (t) is given by:

˙

m _f (t) = P _eng (t)

η _eng Q _lhv (5.12)

where Q _lhv is the fuel lower heating value which indicate the energy content per unit of mass. Analogously, the simplest expression of ˙ m _hyb (t) can be given by:

˙

m _hyb (t) = λ P _hyb

Q _lhv (5.13)

where λ is the equivalent factor that represents efficiency through which fuel is trans- formed into (in our case) hydraulic power and vice-verse.

Depending on the sign of P hyb , ˙ m hyb (t) can either have positive and negative value, the equivalent consumption is therefore higher or lower than the actual fuel con- sumption. To better adapt the ECMS to the characteristics of the DP solution (see the motivation in result section), two multiplicative weight functions W SOC and W _KD are introduced where W _SOC :

W _SOC = 1 − SOC − SOC _{f inal}

SOC

−SOC

2

! a

Values of W _SOC for different exponent a are illustrated in figure 5.4. As can be seen, the effective equivalent factor is increased i.e W _SOC > 1 when SOC < SOC _{f inal} and decreased i.e W SOC < 1 when SOC > SOC f inal . The exponent a decides how big SOC interval around SOC _{f inal} with (almost) unity weighting and serves as an extra design parameter for the optimization problem.

Once again the KD signal plays an important role in the development of a EMS.

For ECMS it is not an exception. KD signal indicates high torque requirement of the machine. The idea is to prepare the high pressure accumulator before the KD signal kicks in by charging it. It can be done by increasing the equivalent factor temporarily by introducing the second weight function W _KD :

W _KD =

( w _KD if Activation = 0

1 if Activation = 1 (5.14)

Where w KD > 1, Activation = 0 initially and Activation = 1 the first time KD signal kicks in.

Another weight function W N (SOC) is implemented to help the ECMS obtains the charge sustainability after each driving cycle by introducing an additive penalty in the last simulation time step:

( ∞ if |SOC − SOC | > 

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 SOC [-]

0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2

W

W

vs exponent a

a = 1 a = 3 a = 5

Figure 5.4: Weight function W _SOC for different exponent a with SOC _min = 0, SOC _max = 1 and SOC _{f inal} = 0.5

Where K >> 1 and  _{SOC,f inal} > 0 is the acceptable deviation margin from the SOC _{f inal} . To sum up, the new expression of ˙ m _hyb (t) is now:

˙

m _hyb (t) = λ P _hyb

Q _lhv W _SOC W _KD + W _N (SOC) (5.16) And the equivalent fuel consumption ˙ m _f,eqv :

˙

m _f,eqv = ˙ m _f + λ P _hyb

Q _lhv W _SOC W _KD + W _N (SOC) (5.17) The ECMS algorithm is explained below:

At each time instant:

Step 1 : Discretize the control interval into finite number of equidistant candidates.

Step 2 : Calculate the equivalent fuel consumption ˙ m _f,eqv corresponding to each con- trol value. Save the candidates which satisfy system constraints.

Step 3 : Select the control value yielding the lowest equivalent fuel consumption and

apply to the system.

5.3.1 Mathematical Problem Formulation

The minimization problem has the following mathematical formulations in ECMS.

Z t

t

min 

˙

m _f,eqv (t)dt (5.18)

S.t (5.19)

SOC _min ≤ SOC ≤ SOC _max (5.20)

 _hyb,min ≤  _hyb ≤  _hyb,max (5.21)

5.3.2 Optimal equivalent factor

In order to have a ECMS yielding charge sustainability property, the optimal value of the equivalent factor must be defined. From researches in this field have shown, the optimal equivalent factor is known to be cycle-dependent. Charge sustainability for one cycle can lead to charge depleting for another cycle. Therefore, it is im- portant to have a systematic searching algorithm for finding the optimal equivalent factor for each driving cycle. In this thesis, the bisection method is used to obtain the optimal equivalent factor by successive halving the searching interval. Figure 5.5 illustrates the algorithm of the bisection method.

Text

λ

λ

=

λ

λ

+ λ

2

Simulation Model

SO C

= SO C

SO C

< SO C

SO C

> SO C

= λ

λ

= λ

λ

= λ

λ

Figure 5.5: The algorithm of the bisection method for optimal equivalent factor

searching.

Chapter 6

Result and Analysis

6.1 Fuel consumption

In Appendix A, the torque and speed profiles for different studied simulation cycles are shown while the simulation results for all simulated cycles are presented in Ap- pendix B. In total there are three short loading cycles and one load-carry cycle. The following analysis is more focus on the first short loading cycle and the load-carry cycle.

For rule-based strategies described in Chapter 5, there are no specific constrains for the final SOC. Therefore the final SOC value can be higher or lower than the initial value. In order to have a fair comparison between different EMS:s, correction must be made if the final SOC is different from the wanted one. See Appendix B for the SOC trajectory for different driving cycles and EMS. In table 6.1, the comparison of fuel consumption for different EMS:s is presented together with the correction of final SOC value.

EMS Short 1 Short 2 Short 3 Long Long & LU

Conventional 100 100 100 100 100

Rule-based 1 96.67 93.31 96.51 98.95 97.89

Rule-based 2 98.79 96.21 96.36 100.16 98.89

ECMS 98.23 94.96 93.46 101.78 100.45

DP 93.67 91.19 93.38 97.58 97.65

Table 6.1: Fuel consumption comparison for different EMS and driving cycles with fuel consumption for conventional machine as baseline

Table 6.1 shows that all tested EMS:s have better performance in short than in long

cycle. Even when the global solution can be obtained from DP, there is only more

than 2 % reduction in fuel consumption in the long cycle.

6.2 Additional Lock-up Feature

As describes in earlier chapters, the lock-up feature is activated only when the vehicle speed is high enough where the third or fourth gear is used. For short loading cycle, the maximum speed is under the threshold for the third gear. Therefor, the lock- up feature is never activated which in turn result in no difference in fuel efficiency.

However for load and carry cycle, the lock-up is activated. The result of adding the lock-up feature to the TC can be seen in table 6.2.

EMS Long Long & Lock-up

Conventional 100 84.27

Rule-based 1 99.24 82.71

Rule-based 2 100.16 83.56

ECMS 101.78 84.65

DP 97.58 82.29

Table 6.2: Fuel consumption comparison (in % ) for load and carry cycle between no lock-up and lock-up with fuel consumption for conventional machine without lock-up as baseline.

As can be seen, the total fuel consumption is decrease by more than 17 % when the lock-up feature is available, even for the case of conventional machine without any hybrid system. This result confirms the fact that significant losses occurs in the TC, even when the vehicle speed are high where the turbine and the impeller are rotating at almost same speed.

6.3 Simulation parameters - ECMS

The optimal simulation parameters for each driving cycle in ECMS are presented in table 6.3. Despite the same characteristics between three short loading cycles, different optimal equivalent factor for different driving cycle are observed. This con- firm the theory about the cycle dependency of equivalent factor in ECMS. In reality, there are rare occasions where certain knowledge of the future driving condition is known at the moment.

Parameter Short 1 Short 2 Short 3 Long Long & LU

λ 3.10 2.66 3.46 3.44 3.43

a 3 3 3 3 3

W KD 2 2 2 2 2

Table 6.3: Simulation parameter in ECMS for different driving cycle.

6.4 Strategies analysis

In this section, deeper analysis for each strategy will be presented. For DP, When- ever the wheel loader requires high torque, for example when accelerating from stationary point or filling the bucket, the hybrid machine will assist the engine by discharging the high pressure accumulator. For short loading cycles with four pos- sible regenerative braking occasions (as mentioned in Chapter 3), the DP tries to charge the accumulator in each of these braking occasions. This can be seen in figure 6.1. Since the DP has the knowledge of the entire driving cycle in advance.

DP knows extra high torque is needed when filling the bucket. Therefore, beside the regenerative braking energy recuperated when approaching the gravel pile, the engine is also used to charge the accumulator to make sure that the accumulator has sufficient pressure for the bucket filling. In the end of the bucket filling phase after assisting the engine, the accumulator is completely depleted.

0 5 10 15 20 25 30 35

Time [s]

0 0.2 0.4 0.6 0.8 1

SOC [-]

SOC trajectory for different EMS

Dynamic Programming ECMS

Figure 6.1: DP and ECMS SOC trajectory for the short loading cycle 1.

In the case of load and carry cycle without lock-up (figure 6.2), until the first re-

versing phase, the same accumulator charging and discharging characteristic can be

observed. However, when reversing from the gravel pile, instead of just recuperat-

ing the regenerative braking energy, the accumulator is charged by the engine to

almost maximum pressure. By doing it, DP prepares the accumulator for the accel-

eration in the transport phase which is significantly longer where the wheel loader

reaches much higher speed than in short loading cycle. Higher speed results in a

larger amount of energy which can be recuperated by regenerative braking. Inter-

estingly, in the start of second transport from the dumping site, the accumulator is

only discharged slightly. According to DP, it is more fuel efficient to fully deplet-

ing the accumulator in the later part of the transport before taking the advantage

of the final regenerative braking to recharge the accumulator to the wanted pressure.

0 10 20 30 40 50 60 70 80 Time [s]

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

SOC [-]

SOC trajectory for different EMS

KD*0.9

Dynamic Programming ECMS

Figure 6.2: DP and ECMS SOC trajectory for load carry cycle without lock-up.

When the lock-up feature is activated (see Figure 6.3). Once again, the SOC profile changes. Instead of keeping the accumulator pressure close to zero after assisting the acceleration in the first transport phase as in the case without the lock-up, the accumulator is charged successive. Here in the second transportation phase, again the accumulator assists the wheel loader in acceleration by fully discharging.

0 10 20 30 40 50 60 70 80

Time [s]

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

SOC [-]

SOC trajectory for different EMS

KD*0.9

Dynamic Programming ECMS

Figure 6.3: DP and ECMS SOC trajectory for load carry cycle with lock-up.

The SOC profile for ECMS can be seen from Figure 6.1. Same characteristics of the

torque is needed. The hybrid machine will assist the wheel loader. Furthermore, the accumulator is charged whenever the regenerative energy is available.

The most interesting ECMS result is obtained in the third short cycle. Here, the ECMS outperforms all rule-based ones with great margins. The total fuel consump- tion obtained from ECMS is almost identical to DP. A solution that is so closed to the optimal one can never be achieved from any proposed rule-based strategy.

For short loading cycle 1 (Figure 6.4), both rule-based strategies seems to perform well. Especially in the case of the first rule-based strategy. In this strategy, lower fuel consumption is observed in all tested cycles. This result is as expected due to how the strategy is implemented. Regenerative braking energy is stored in the accumulator whenever it is available and it is used when the wheel loader requires extra high power.

0 5 10 15 20 25 30 35

Time [s]

0 0.2 0.4 0.6 0.8 1

SOC [-]

SOC trajectory for different EMS

KD*0.9 Rule-based 1 Rule-based 2 DP

Figure 6.4: Rule-based 1 and 2 SOC trajectory for short loading cycle 1.

Chapter 7

Conclusions and Future Work

7.1 Conclusion

From the analysis av result, the following conclusions can be drawn:

The second simple logic rule-based strategy is adequate for the current studied wheel loader configuration to reduce the fuel consumption despite its simple nature. A rec- ommendation is to further refine the control logic for better strategy.

Huge improvement in term of fuel efficiency can be achieved by introducing addi- tional lock-up feature. This result confirms the fact that significant losses occurs in both low and high vehicle speed.

ECMS works better for short loading cycles where a reduction in fuel consumption is observed. For the third short loading cycle, ECMS has almost the same fuel efficiency as the DP solution. However for load and carry cycle, a small increment is observed. ECMS results in SOC trajectories with most characteristic similarities as in DP. For small energy storage as in here, ECMS cannot utilize all of its advantages over rule-based. If the energy storage is much bigger, ECMS is a better choice of EMS.

7.2 Future Work

To improve the control strategy further, more analysis and development has to be made. At the current state, some physical effects are simplified or neglected which should be taken more into consideration when making model that better describes the real machine.

One of the example is the transition between transmission gears. In the models

used, gear changes are assumed to happen instantly without any delay time. At

not modelled. Furthermore, when the lock-up feature is activated, there is no cost in term of additional fuel usage assigned. As a result, a very high fuel efficiency is observed. By introducing a cost, the fuel efficiency result will be closer to the reality.

With one value of equivalent factor used throughout this thesis, the costs of dis- charging and recharging the accumulator are assumed to be the same. In order to have a more control over the ECMS in HHV, these two factors can have different values. However by differentiating the charge and discharge equivalent factors, the bisection searching method for optimal values will no longer function (at least at its current form). The algorithm must be modified or another and more complex method must be used instead.

The high pressure accumulator used throughout this thesis has a very limited vol- ume which results in low total energy storage. One suggestion is to compare how these EMS:s behave with bigger accumulator volumes. From theory, higher volume should yield closer result between ECMS and DP.

In the current ECMS algorithm used, at each time instant, the control interval

is discretized into equidistant candidates where equivalent fuel consumption corre-

sponding for the control values are calculated. Another possible approach could be

as follow: at each time instant, control interval is dicretized with non-equidistant

steps where more weight is put in a smaller suitable control interval that satisfy the

system constrains.