Application of multi objective optimisation to MRT systems optimisation

... discusses the application of multi- objective optimisation to MRT systems 4.2 Mathematical Definition Given a set of objective functions, the multiple -objective optimisation aims to find a solution... vector so that all the objectives can be optimised in a compromise 30 Chapter Literature Review of Multi- Objective Optimisation Approaches way Generally, the vector of F(x) in multi- objective optimisation. .. the entire global Pareto-optimal set through a one-time solution of the multi- objective optimisation problem, avoiding the need to solve a multitude of single -objective optimisation problems

Founded 1905

APPLICATION OF MULTI-OBJECTIVE OPTIMISATION TO MRT SYSTEMS

BY

TIAN LIFEN DEPARTMENT OF ELECTRICAL ENGINEERING

Acknowledgements

The author genuinely appreciates the help from her supervisor, Professor C S Chang, who has provided invaluable guidance to the author while the author works on the projects and writes this thesis

Sincere thanks and gratitude are also extended to Mr Seow Hung Cheng of Power System laboratory for his support throughout this research project

This thesis is dedicated to the author’s family and friends They always have the unreserved understanding and great support to the author

Table of Contents

ACKNOWLEDGEMENTS I TABLE OF CONTENTS II LIST OF FIGURES V LIST OF TABLES VI LIST OF ABBREVIATIONS VII LIST OF PUBLICATIONS RELATED TO THIS THESIS VIII SUMMARY OF THE THESIS IX

CHAPTER 1 INTRODUCTION 1

1.1 B ACKGROUND 1

1.2 M OTIVATION OF THE R ESEARCH 2

1.2.1 Go-Circuit Optimisation 3

1.2.2 Return-Circuit Optimisation 4

1.3 O BJECTIVE AND S COPE OF THE R ESEARCH 5

1.4 M ULTI -O BJECTIVE O PTIMISATION A LGORITHMS 6

1.5 O RGANISATION OF THE T HESIS 8

CHAPTER 2 OUTLINE OF GO-CIRCUIT OPTIMISATION 11

2.1 I NTRODUCTION 11

2.2 M ATHEMATICAL M ODEL 12

2.2.1 System Model 12

2.2.2 Objective Functions 13

2.2.3 Impact of Operational Timetable 15

2.3 L AYOUT OF T HREE -S TAGE S CHEME 16

2.4 S IMULATION O UTLINE 18

2.5 S UMMARY 19

CHAPTER 3 OUTLINE OF RETURN-CIRCUIT OPTIMISATION 21

3.1 I NTRODUCTION 21

3.2 M ATHEMATICAL M ODEL 22

3.2.1 Return-Circuit Model 22

3.2.2 Objective Functions 23

3.2.3 Impact of Earthing and Bonding Arrangements 24

3.3 L AYOUT OF T WO -S TAGE S CHEME 25

3.4 S IMULATION O UTLINE 27

3.5 S UMMARY 28

CHAPTER 4 LITERATURE REVIEW OF MULTI-OBJECTIVE OPTIMISATION

APPROACHES 30

4.1 I NTRODUCTION 30

4.2 M ATHEMATICAL D EFINITION 30

4.3 P REFERENCE S TRUCTURE 32

4.4 R EVIEW OF M ULTI -O BJECTIVE O PTIMISATION M ETHODS 33

4.4.1 Traditional Approaches 34

4.4.2 Evolutionary Approaches 35

4.4.2.1 Vector Evaluated Genetic Algorithm 35

4.4.2.2 Pareto-Based Genetic Algorithm 36

4.4.2.3 Multi-Attribute Genetic Algorithm 37

4.4.3 Discussions 37

4.5 S UMMARY 39

CHAPTER 5 EVOLUTIONARY MULTI-OBJECTIVE OPTIMISATION APPROACHES 40

5.1 I NTRODUCTION 40

5.2 M ULTI -O BJECTIVE G ENETIC A LGORITHM 41

5.2.1 Selection Processing with Rank Assignment 41

5.2.2 Fitness Sharing 42

5.2.3 Variable Recombination Operators 43

5.2.4 Treatment of Preferred Priorities among Objectives 43

5.3 M ULTI -O BJECTIVE P ARTICLE S WARM A LGORITHM 45

5.3.1 Search Strategy 45

5.3.2 Rank-Based Selection 47

5.3.3 Weight Update 47

5.3.4 Pareto-Optimal Set Update 48

5.4 M ULTI -O BJECTIVE D IFFERENTIAL E VOLUTION A LGORITHM 49

5.5 S UMMARY 49

CHAPTER 6 RESULTS OF GO-CIRCUIT OPTIMISATION 50

6.1 O PTIMAL T RACTION -S UBSTATION P LACEMENTS 50

6.2 W ORST -C ASE S CENARIOS OF O PERATIONAL D EVIATIONS 53

6.3 P ERFORMANCE C HECK FOR F AILURE C ONDITIONS 56

6.4 S UMMARY 58

CHAPTER 7 RESULTS OF RETURN-CIRCUIT OPTIMISATION 60

7.1 M ULTI -O BJECTIVE O PTIMISATION FOR N ORMAL C ONDITIONS 60

7.2 P ERFORMANCE C HECK FOR F AILURE C ONDITIONS 68

7.3 S UMMARY 69

CHAPTER 8 CONCLUSIONS 71

8.1 S UMMARY AND C ONCLUSIONS 71

8.2 S UGGESTIONS FOR F UTURE W ORK 74

REFERENCES 75

APPENDIX A EVOLUTIONARY ALGORITHMS 79

A.1 I NTRODUCTION 79

A.2 G ENETIC A LGORITHM 79

A.3 P ARTICLE S WARM AND D IFFERENTIAL E VOLUTION A LGORITHM 80

A.3.1 Particle Swarm Algorithm 81

A.3.2 Differential Evolution Algorithm 82

APPENDIX B FLOWCHART OF PROPOSED EVOLUTIONARY MULTI-OBJECTIVE OPTIMISATION APPROACHES 84

B.1 F LOWCHART OF M ULTI -O BJECTIVE G ENETIC A LGORITHM 84

B.2 F LOWCHART OF M ULTI -O BJECTIVE P ARTICLE S WARM AND M ULTI -O BJECTIVE D IFFERENTIAL E VOLUTION 85

APPENDIX C PRELIMINARY TESTING OF MULTI-OBJECTIVE OPTIMISATION ALGORITHMS 86

C.1 I NTRODUCTION 86

C.2 C ONCAVE P ROBLEM 87

C.3 D ISCONTINUOUS P ROBLEM 89

C.4 S UMMARY 91

List of Figures

Figure 1-1: Schematic of Singapore MRT system 1

Figure 2-1: Sectional network representation of double-track MRT system 13

Figure 2-2: Three-stage scheme for go-circuit optimisation 18

Figure 2-3: Flowchart for go-circuit simulation 19

Figure 3-1: Return-circuit model 22

Figure 3-2: Simple case study of touch voltage and stray current 25

Figure 3-3: Two-stage procedure for touch voltage and stray current 27

Figure 3-4: Flowchart of return-circuit simulation 28

Figure 4-1: Pareto front for bi-criterion minimisation problem 32

Figure 4-2: Nonconvex solution boundary 35

Figure 4-3: Outline of VEGA evolution results 36

Figure 4-4: Rank assignment for Pareto-based genetic algorithm 37

Figure 5-1: Rank assignments for different priorities among objectives 44

Figure 6-1: Optimised configurations 51

Figure 6-2: Energy consumption convergence curve 52

Figure 6-3: Load sharing convergence curve 52

Figure 6-4: Pareto-optimal set for Configuration 1 54

Figure 6-5: Pareto-optimal set for Configuration 2 55

Figure 7-1: Layout of study system 61

Figure 7-2: Touch voltage distribution with different earthing arrangement 63

Figure 7-3: Pareto-optimal sets for Configuration 1 65

Figure 7-4: Pareto-optimal sets for Configuration 2 66

Figure C-1: MOPS results for Test1 89

Figure C-2: MODE results for Test 1 89

Figure C-3: MOPS results for Test 2 91

Figure C-4: MODE results for Test 2 91

List of Tables

Table 6-1: Improvement of optimised energy consumption and load sharing 53

Table 6-2: Parameter limits for bi-criterion optimisation 54

Table 6-3: Maximum deviation for energy consumption 55

Table 6-4: Maximum deviation for load sharing 55

Table 6-5: Performance check results for case 1.1 57

Table 6-6: Performance check results for case 2.2 58

Table 7-1: Typical arrangements of earthing and bonding 62

Table 7-2: Multi-objective optimisation of earthing & bonding for configuration 1 67

Table 7-3: Multi-objective optimisation of earthing & bonding for configuration 2 68

Table 7-4: Performance check for case 2.1 69

Table C-1: Non-dominated solution numbers for Test 1 88

Table C-2: Non-dominated solution numbers for Test 2 90

List of Abbreviations

TSS: Traction Substation

GA: Genetic Algorithm

DE: Differential Evolution algorithm

PS: Particle Swarm algorithm

MOGA: Multi-Objective Genetic Algorithm

MODE: Multi-Objective Differential Evolution algorithm

MOPS: Multi-Objective Particle Swarm algorithm

List of Publications Related to this Thesis

[1] C.S Chang and L Tian,” Worst-case identification of touch voltage and stray

current of DC railway system using genetic algorithm”, IEE Proceedings, Electric Power Applications, Vol 146, No 5, 1999

Summary of the Thesis

MRT system design can be formulated as a problem of three-stage optimisation In the first stage, the basic design of a MRT section is optimised by extensively searching through a large set of design alternatives Only the key or primary variables are optimised in this stage The second stage evaluates the worst-case performance of the basic design using secondary variables arising from operational deviations and other random variables The need for changing the basic design to cater for both the normal condition and failure conditions is ascertained and implemented in the third stage

MRT supply networks can be divided into the traction substation, the go-circuit and the return-circuit At traction substations, AC supply voltage is stepped down and converted to DC Catenary wires or third rails are used in the go-circuit while running rails and return cables are the main components of return-circuit In this work, the go-circuit and return-circuit are each optimised with the procedure as outlined above

Energy consumption and load sharing are two important issues in the go-circuit Energy consumption calculates the total energy consumed at all the traction substations, and load sharing measures the load distribution among all traction substations They are influenced by many factors and their optimisation cannot be obtained simultaneously In the proposed first-stage optimisation, a previously developed algorithm is incorporated for configuring the traction placements by optimising either energy consumption or load sharing During operation, train timetables deviate continually from the predefined train despatch frequency due to variations of train headway, synchronisation delay and dwell time This work focuses

on the second-stage optimisation, which implements the bi-criterion optimisation of energy consumption and load sharing under normal condition The system performance is evaluated under failure conditions in the third stage

With running rails used as part of the traction current return-circuit, the main concerns

in the return-circuit are the touch voltage and stray current Touch voltage is the voltage between the running rail and the ground Excessive instantaneous touch voltage jeopardises safety Stray current is the leakage current between the running rail and the ground The stray current is likely to be picked up by the underground structures in the vicinity and cumulative stray current may accelerate their corrosion The earthing and bonding strategy within the system has a profound impact on the control of touch voltage and stray current Meanwhile, the improvement of touch voltage or stray current tends to deteriorate the other The return-circuit optimisation is thus composed of two-stage implementation In the first stage, different earthing and bonding arrangements at passenger stations or traction substations are extensively explored under normal operation The second stage conducts performance check on each appropriate earthing and bonding arrangement with the list of credible failure conditions such as rectifiers and inverters out-of-service

The technique of Pareto-optimal set is developed for the above go-circuit and circuit optimisations The solutions are often multi-objective and seldom unique, as they usually comprise a finite set of non-dominated or Pareto-optimal points Three evolutionary algorithms are applied, which are namely: the Multi-Objective Genetic Algorithm (MOGA) for discrete problems, Multi-Objective Particle Swarm (MOPS) algorithm and Multi-Objective Differential Evolution (MODE) algorithm for

return-continuous problems MOPS and MODE are proposed to solve MRT problems for the first time

The three proposed algorithms are based on the concepts of population, rank-based selection and competitive evolution During optimisation, a population of candidate solutions is evolved in the feasible space to search for the Pareto-optimal set Ranking

of the population is accomplished through Pareto ranking, where all points in the Pareto-optimal set are successively placed on different Pareto fronts Competitive evolution consists of selecting subsets of points with respect to their ranks and moving them toward the Pareto-optimal set Test analysis of the proposed algorithms is made

on each of the go-circuit and return-circuit simulations Numerical comparisons of MOPS and MODE against the Multi-Attribute Genetic Algorithm (MAGA) favour the former two algorithms

Earthing device Go-circuit

Transformer

Go-circuit

Return-circuit

Rectifier TSS 1

Earthing device

Figure 1-1: Schematic of Singapore MRT system

• Traction substation: In Singapore MRT system, several traction substations (TSSs) are located at passenger stations due to construction convenience and cost consideration From the viewpoint of electrifying the MRT systems, TSSs function

as energy sources, transferring power between the AC side and the DC side The

66 kV supply voltage is stepped down to 22 kV at intake substations via the transformer Rectifiers installed at TSSs convert power from the 22 kV AC into

DC so as to provide the go-circuit with traction current While trains are usually equipped with the regenerative braking, some TSSs are configured with inverters

to increase line receptivity As a result, power released during regenerative braking

is either consumed by nearby accelerating trains or returned to supply through inverters The 22 kV AC is also stepped down to furnish service loads, such as lighting, air-conditioning and other auxiliary devices at passenger stations

• Go-circuit: This contains the catenary wires or third rails and positive feeders In most MRT systems, running rails are used as traction return paths Hence the traction current, distributed from the TSSs, flows along the catenary wires or third rails to supply trains with power and then flows back to the TSSs through the running rails

• Return-circuit: Running rails, rail bonds and negative feeders are the main components of the return-circuit Running rails are often lightly insulated from the ground so a fraction of the traction currents may leak into the earth whereas the bulk of traction currents return to the TSSs via the negative feeders

1.2 Motivation of the Research

Single-objective optimisation techniques have long been applied in MRT system Nevertheless, there are needs for multi-objective optimisation Energy consumption and load sharing in go-circuit, influenced by many aspects, cannot be optimised simultaneously Likewise, the mitigation of touch voltage and stray current in return-circuit are not likely to be achieved at the same time Practical solutions for multi-objective optimisation are seldom unique, as they comprise a finite set of non-dominated or Pareto-optimal points In this thesis, the technique of Pareto-optimal set (Section 4.2) is developed for the go-circuit and return-circuit optimisations in MRT system Three evolutionary algorithms are explored, namely: the Multi-Objective Genetic Algorithm (MOGA, Section 5.2) for return-circuit optimisation, Multi-Objective Particle Swarm (MOPS) algorithm (Section 5.3) and Multi-Objective Differential Evolution (MODE) algorithm (Section 5.4) for go-circuit optimisation MOPS and MODE are proposed to solve MRT problems for the first time

1.2.1 Go-Circuit Optimisation

In MRT systems, TSSs supply train power via the rectifiers and receive the regenerated power via the inverter The energy consumption, which is calculated as the sum of the power flowing through the rectifiers and the inverters installed at each TSS,

is quite crucial to the efficiency of the MRT system In addition to energy flows through rectifiers and inverters, load sharing among TSSs is also of importance As trainloads are highly fluctuating, the TSS loads can be unevenly distributed Some TSSs are overloaded but others are under-loaded In case of some traction substations outage, the power flowing through the nearby traction substations could exceed their

capacity Therefore, energy consumption and load sharing are selected as optimisation objectives in go-circuit optimisation

Energy consumption and load sharing are dependent on the instantaneous train positions and control status (accelerating, coasting, dwelling or braking) These are influenced by the service schedule (declared train despatch frequency or headway) and operational deviations (synchronisation delay and train dwell times) Traction substation placements also have profound impact on the energy consumption and load sharing

At the first stage of go-circuit optimisation, a previously developed algorithm [3] is incorporated to configure the traction substation placements by optimising either energy consumption or load sharing Energy consumption and load sharing are not consistent with each other The same train running timetable will probably lead to their different regulation direction At the second stage, the effect of operational timetable is discussed, and the competing nature of energy consumption and load sharing is investigated The optimisation variables, namely headway, synchronisation delay and dwell times, vary continually during the simulation period In order to solve this continuous problem, MOPS and MODE algorithms are proposed and applied for the first time to generate a variety of Pareto-optimal solutions The compromise between worst-case energy consumption and load sharing is then identified for performance margin specification, which is implemented at the third stage of go-circuit optimisation

1.2.2 Return-Circuit Optimisation

Running rails are usually used as the traction current return paths Owing to the ground and rail resistance, there will be a voltage difference caused by the return current flows from between the rails and the local ground known as touch voltage Excessive touch voltages jeopardises safety As running rails are often lightly insulated, the traction current flowing back to the substations may partly take the ground Known as stray current, it is likely to be picked up by the underground structures in the vicinity and through the ground to enter another structure before returning to the TSS Accumulative stray currents may accelerate the structures’ corrosion Accurate evaluation and effective control of touch voltage and stray currents are therefore the consideration factors in the return-circuit

rail-to-Simulations and field tests reveal that both touch voltage and stray current are greatly influenced by the earthing strategy and bonding arrangement adopted in MRT system However, the improvement of touch voltage or stray current tends to deteriorate the other A two-stage scheme is thus proposed for return-circuit optimisation At the first stage, Multi-Objective Genetic Algorithm (MOGA) is developed to extensively explore earthing and bonding arrangements so that the compromising mitigation of touch voltage and stray current is obtained under normal running condition At the second stage, the most appropriate earthing and bonding patterns are then picked up for performance check under credible failure conditions

1.3 Objective and Scope of the Research

MRT systems are complex and highly integrated The scope of this research is confined to the electrification subsystem and focused on the DC side In particular,

effects of operational parameters rather than design parameters are investigated for the safety and efficiency of MRT system Two sets of objectives are defined for the problem of energy consumption and load sharing in the go-circuit, and the problem of touch voltage and stray current in the return-circuit Variables governing these two sets

of objectives can either be discrete or continuous The nature of competing objectives

in these two problems is explored Evolutionary algorithms are then applied for attaining satisfactory trade-offs within these sets of objectives

Although the use of rectifiers and inverters does introduce harmonic in the MRT system, harmonic can be minimized by employing appropriate type of power converters and by placing active harmonic filters [29] This thesis focuses on the application of multi-objective optimization of primary variables to MRT systems The harmonic effects on go-circuit and return-circuit optimisation are not addressed in this thesis, but will be discussed by other researchers [30]

1.4 Multi-Objective Optimisation Algorithms

Multi-objective optimisation problems involve in simultaneous optimisation of multiple non-commensurable objectives The solution to such problems is not unique but a family of non-dominated points (Pareto-optimal set) In traditional methods of multi-objective optimisation, different criteria are linearly blended into a composite scalar objective This requires pre-establishment of the weights of different criteria As

it is never a simple task to specify an appropriate set of weights, optimal solutions are individually obtained for a range of weights and the so-called trade-off curves are

generated [5] The computing time required for generating the trade-off curves is high and it is also difficult to apply such techniques to non-convex problems

The need for an improved multi-objective optimisation method to seek the optimal solutions is evident, and such a method should have the following characteristics [23]:

Pareto-• Efficiency: It can approximate or identify the entire global Pareto-optimal set through a one-time solution of the multi-objective optimisation problem, avoiding the need to solve a multitude of single-objective optimisation problems

• Objectivity: It does not require the priori assessment of preferences to objective functions in the generation of the Pareto-optimal set

• Reliability: It can facilitate the evaluation of candidate non-dominated solutions in

a quick and reliable fashion

The search processes of evolutionary algorithms, using a population of candidates, suggest their application to multi-objective optimisation problems for finding a number

of Pareto-optimal solutions in parallel In this thesis, Genetic Algorithm (GA), Particle Swarm (PS) algorithm and Differential Evolution (DE) algorithm are appropriately refined for multi-objective optimisation

The performance of GA is mostly determined by its selection operation In order to deal with multiple conflicting objectives, a degree of control should be exerted over the selection process With the employment of rank assignment method [16], MOGA selects individuals for survival according to their mutual dominance as well as their fitness values It attempts to trace all the non-dominance individuals in the present

population as far as possible and each objective function is utilised separately rather than collectively When all the non-dominated individuals in the current generation are picked, the recombination operators are then applied to produce the next generation The above procedure is iterated to locate the Pareto-optimal points and produce subsequent populations until convergence is met At the end of MOGA evolution, the final non-dominated set represents the collection of compromising solutions among all the objectives

Encoding brittleness in GA has degraded its performance in continuous problem domain Contrary to GA, MOPS and MODE avoid parameter encoding and work directly on real-value parameter vectors to search for the optimal solutions The concept of scalarising function is also introduced to replace the global and individual best solutions with compromise solutions respectively The behaviour of each individual in the population is influenced not only by its own historical performance but also by its peers Moreover, rank-based selection is applied in MOPS and MODE

to determine the individual’s likelihood of producing offspring and distribute the population towards the promising areas

By modifying the individuals’ ranks, the specification of preferences among objectives

is allowed in MOGA, MOPS and MODE The technique of fitness sharing is adopted

to maintain the population diversity With the treatment of dominance properties among individuals, these evolutionary algorithms possess a more exploitative mechanism to obtain the Pareto-optimal set

1.5 Organisation of the Thesis

This thesis is organised as follows:

• Chapter 1 describes briefly the background and the objective of the research Two kinds of multi-objective problems, i.e., touch voltage versus stray current (discrete problem) and energy consumption versus load sharing (continuous problem) are introduced by outlining their corresponding optimisation approaches

• Chapter 2 defines the energy consumption and load sharing in go-circuit After presenting the DC-powered two-track MRT system model, this chapter formulates

a three-stage scheme for optimising energy consumption and load sharing and checking system performance

• Chapter 3 defines the touch voltage and stray current in return-circuit The concepts of return-circuit modelling and load referral solution method are explained A two-stage scheme is also put forward to attain the trade-off between touch voltage and stray current, and to evaluate the system performance under failure conditions

• Chapter 4 categorises multi-objective optimisation methods and identifies their specific advantages and disadvantages

• Chapter 5 develops a Pareto-based multi-objective genetic algorithm A particle swarm algorithm based as well as a differential evolution based multi-objective optimisation approach is also proposed for the first time to solve the continuous problems

• Chapter 6 discusses mainly the impact of actual operational timetable on energy consumption and load sharing calculation The traction substation placements are

first configured by obtaining either minimal load sharing or equal load sharing Then the proposed continuous multi-objective optimisation methods are applied to explore the compromise nature of energy consumption and load sharing against varying operational timetable Simulation results indicate the effectiveness of the proposed three-stage scheme for fulfilling the design objective

• Chapter 7 discusses the influence of earthing and bonding policies, and, employs the proposed discrete multi-objective algorithm to achieve trade-off between the touch voltage and the stray current The priority assigned to different objectives allows the decision-maker’s preference to be attained during optimisation Simulation results for different earthing and bonding arrangements are compared and the promising solutions are further checked under failure conditions

• Chapter 8 summarises the research with final conclusion and some suggestions for future work

Chapter 2 Outline of Go-Circuit Optimisation

2.1 Introduction

Energy consumption by TSSs and load sharing among TSSs in go-circuit are influenced by diverse factors such as station spacing, service schedule, firing angles of rectifiers and inverters, and transformer tap positions The impact of traction substation placements and firing angles of rectifiers and inverters were investigated in [3,5] In [3], the energy consumption and load sharing were treated as two separate objective functions, and Tabu Search (TS) algorithm was applied to explore different combinations of traction substation placements For simplicity of optimisation, the energy consumption and load sharing were combined linearly in [5] to form a single objective The conventional Genetic Algorithm (GA) was then employed to examine the effect of firing angles of rectifiers and inverters The performance curves were plotted against the objective weights reflecting the relative significance among objectives, and the so-called trade-off was made between energy consumption and load sharing

The competing nature between energy consumption and load sharing is not fully discussed in the above work The traction substation placements and train operational timetable have great influence on the MRT system, which runs under normal conditions or failure conditions Therefore, the go-circuit optimisation in this thesis presents normal and failure conditions, and is carried out in three stages Stage I uses the algorithm of [3] to optimise the traction substation placements, so that minimum

energy consumption or equal load sharing is attained At Stage II, the train operational timetable varies continuously Two novel multi-objective optimisation methods (Multi-Objective Particle Swarm and Multi-Objective Differential Evolution algorithm) are developed for the first time in this work to obtain the Pareto-optimal set, and achieve the trade-off between energy consumption and load sharing under normal running conditions At Stage III, the worst-case solutions are picked up from Pareto-optimal set and the performance check is implemented under failure conditions

2.2 Mathematical Model

2.2.1 System Model

Figure 2-1 schematically shows a two-track DC-powered MRT system The components are modelled in terms of resistances and current sources, and the interconnection of these components constitutes a nodal electrical circuit

From the viewpoint of circuit theory, the DC-fed MRT system can be divided into circuit and return-circuit In go-circuit, the traction power provided by TSS flows through the catenary wire or third rail, supplies trains and passes back to TSS via running rails TSS is represented by a Thevenin equivalent voltage source (constant voltage in series with a resistance) or a Norton equivalent current source (constant current in parallel with a resistance) Trains are modelled as a voltage-dependent resistance and the running rail is represented by lumped parameters in go-circuit

go-The return-circuit deals with the touch voltage and leakage current Its simulation is explained in Chapter 3

Negative Busbar

Up Track Feeders

Positive Busbar Substation

Earth

Train

Rails

Catenary or Third Rail

systems, the harmonic effects can be minimized by employing appropriate types of power converters and by placing active harmonic filters [29] Therefore, the harmonic effects are not addressed in this thesis and will be covered by other researchers [30] The energy consumption here is defined as the sum of traction energy contributed by all the TSSs, i.e the total power flows through the rectifiers and the inverters installed

at the TSSs

headway dt

t P EC

headway t

t

N i

i tss

tss

/)(

where EC represents the energy consumption P tss i (t)stands for the power flow through

the i-th TSS at time t N tss is the total number of TSS t 0 is the simulation start time

Considering the respective rectifier loading and inverter loading, load sharing is formulated as the sum of the deviation power of each rectifier and inverter from their mean values

headway dt

t P

t P t

P t P LS

headway

t

t

N j

N

k inv mean

rec j

rec

/)()

()

()

where LS represents the load sharing P rec j (t) stands for the power flow through the

j-th rectifier and P inv k (t) stands for the power flow through the k-th inverter N rec and N inv

are the number of rectifiers and inverters installed at TSSs respectively The mean rectifying power P rec,mean(t) and the mean inverting power P inv,mean(t)are computed as

N i

inv i

inv mean

inv

N i

rec i

rec mean

rec

N t P t

P

N t P t

P

1

1

/)()

(

/)()

(

2.2.3 Impact of Operational Timetable

Power network of MRT system is a complex combination of substations, feeding trains with dynamically varying demand Energy consumption and load sharing, which are functions of the instantaneous net power drawn from TSSs, largely depend on the operational timetable being used

Operational timetable variations can be described with three time variables in units of second: headway, synchronisation delay and dwell time Headway and synchronisation delay variables determine the distance between two adjacent trains running in the same direction and in the opposite (up- or down-) directions respectively Dwell time, also known as the station-waiting period, leads to deviation of each train schedule from the prescribed timetable

Under ideal operating condition, trains travel along the track in accordance with established train movement profile and schedule Trains in the same direction are dispatched at a prescribed headway and the corresponding trains in opposite directions are run with certain synchronisation delay Headway varies with the time of the day, being shorter during rush hours and longer during late-evening and early-morning hours When trains stopover at stations, regardless of how passengers are crowded, trains are ideally assumed to leave for the next station after fixed dwell time Due to

repeatable nature of MRT systems, each train follows ideally the same movement pattern

Under actual operating conditions, however, headway, synchronisation delay and train dwell time will deviate from the prescribed pattern due to variations in passenger load and the state of the track ahead Therefore, the net power drawn from the TSSs, which

is governed by the relative positions and demands of trains both in the same direction and in the opposite direction, will be inevitably affected Energy consumption and load sharing are in turn influenced by the varying operational timetable

2.3 Layout of Three-Stage Scheme

Considering the impacts of substation placements and system operational timetable, the go-circuit optimisation is divided into three stages as Figure 2-2

At Stage I, Tabu Search (TS) algorithm is applied to explore different possible combinations of traction substation placements, and optimise energy consumption or load sharing under predefined operational timetable By guiding the local search descent method to avoid bad local optima, TS leads to the appropriate traction substation placements for either minimum energy consumption or equal load sharing

In practical operation conditions, the actual operational timetable may deviate continuously from the predefined value due to unpredictable emergency such as an abruptly increased number of passengers At Stage II, the operational timetable is taken as the optimisation variable, and the compromise worst cases between energy consumption and load sharing are identified Multi-Objective Particle Swarm (MOPS) algorithm and Multi-Objective Differential Evolution (MODE) algorithm proposed in

Section 5.3 are applied to exploit the competing nature of energy consumption and load sharing with varying headway, synchronisation delay and dwell times The Pareto-optimal set is obtained to reflect the trade-off between energy consumption and load sharing

Performance check with the list

of credible failure conditions

Add to the forbidden timetable Set

Performance accepted ?

Relocate the

traction substation

placements

Figure 2-2: Three-stage scheme for go-circuit optimisation

In the failure conditions, some rectifiers and inverters at the TSSs or even the TSS are out-of-service The MRT system should sustain from such credible failure scenarios Stage III conducts the performance check for solutions picked up from the Pareto-optimal set If the system performance is undesirable, the corresponding operational timetable should be avoided A list of avoidable operational timetable is generated after all the Pareto-optimal solutions are checked In case that all the worst cases fail in the performance check, the traction substation placements derived from Stage I need some adjustments to ensure the reliability of system operation

In this way, the power flow in go-circuit is deduced, and the energy consumption and load sharing are obtained

Implement load referral to form the network nodal admittance matrix Solve eqn [V]=[Y][I] to derive power flow

Calculate energy consumption and load

sharing Return-circuit simulation

timetable deviation A three-stage scheme is accordingly put forward to implement criterion optimisation of energy consumption and load sharing under normal condition and evaluate the system performance under failure conditions

bi-Chapter 3 Outline of Return-Circuit Optimisation

3.1 Introduction

In MRT systems, running rails are used as the traction current return conductor, which causes concern for touch voltage and stray current In order to realise the computer-based simulation of touch voltage and stray current, the finite-cell idea in power system was introduced for return-circuit modelling By dividing the track into a number of equal-length cells, a multi-conductor shunt energised model was accordingly set up to calculate the touch voltage [7] The follow-on work [8] then examined and discussed the relative merits of four earthing schemes, namely: float earth, float earth with rail potential control device, direct earth and diode earth, on the rail potential and stray current The control of touch voltage and stray current were also addressed in [11,12,13] from the viewpoint of engineering rather than from computer simulation

The monitoring and mitigation of touch voltage and stray current are receiving increasing attention while their computer simulation is well done The problem of reducing the touch voltage and stray current in DC railways is multi-objective and conflicting It is affected by many factors such as the earthing and bonding design as well as the normal and failure operating conditions Therefore, the return-circuit optimisation in this thesis is performed in two stages At Stage I, a multi-objective optimisation method, Multi-Objective Genetic Algorithm, is applied to search among various earthing and bonding arrangements to obtain Pareto-optimal set for touch

voltage and stray current The worst cases are then picked up for performance check at Stage II

3.2 Mathematical Model

3.2.1 Return-Circuit Model

In the return-circuit, trains inject traction currents into the running rails, and, TSSs absorb the return currents from the running rails All these currents are actually injected currents with appropriate (positive or negative) signs Since the running rail is represented as a single conductor with distributed leakage resistance, i.e., a transmission line in Figure 3-1(a), the return-circuit can be modelled as a transmission line under shunt energisation at multiple points [7]

: Conductors

(b) A multi-conductor system

Figure 3-1: Return-circuit model

When the four running rails in double track MRT systems are not bonded together, the four running rails cannot be treated as a single conductor Instead, a multi-conductor system model as in Figure 3-1(b) will be used This model is based on the multi-conductor theory given in [1]

to the product of the magnitude of stray current and the time duration, stray current used in this thesis is represented by the stray-current integral collected from all earthing points The stray-current integral, independent of the simulation duration, is defined as [8]:

=

=

2 1 )

)/(

)),((t t N t

where i re ( k t, )is the current flow from running rail to the earth at electrical node k and

at time t, and N(t) is the total number of electrical nodes at time t The simulation spans from time t 1 to t 2

3.2.3 Impact of Earthing and Bonding Arrangements

Touch voltages and stray current are influenced under normal condition by factors, such as the traction substation spacing, rail resistance and rail conditions, headway interval, synchronisation delay, weather condition, soil resistivity, and earthing and bonding design Among these factors, a close TSS spacing decreases the go-circuit voltage drops but the spacing is determined by other considerations such as the ease of construction and commercial benefit Once the MRT system is designed, the rail resistance is fixed and cannot be changed easily The headway depends on the passenger traffic flow It usually takes constant values during certain periods, e.g., rush hours, normal hours and evening hours The synchronisation delay varies during the actual train run from zero to the headway specified at that time In addition, the touch voltage and stray current are affected by operational abnormality (or failure), which can be results of track paralleling switched off, substations out of service etc

To briefly estimate the impact of earthing and bonding arrangement on the circuit, a simplified single-TSS and single-train model for DC transit system is shown

return-in Figure 3-2 The impacts of harmonics are not shown return-in the model, as they can be minimized by employing appropriate power converters and by placing active harmonic filters The harmonic effects on MRT systems are discussed in [30] The stray current

of this model is:

S R T

T R

R R R

I R Is

++

where I T is the train current R R is the running rail resistance R is the earth S

resistance at the TSS and R Tis the earth resistance as seen at the train

Catenary wire+

-

Train Substation

Figure 3-2: Simple case study of touch voltage and stray current

In Equation (3-3), the train current I T is largely affected by the train schedule and

passenger flow As the running rail resistance R R is decided at the design stage of the

MRT system, R and S R T are the only variables to be investigated In general, low R S

and R T give rise to a high stray current but a relatively low rail potential Regular bonding of the rails equalises the rail-to-earth potentials of all rails along the return-circuit It also reduces the return resistance because of parallel rail paths constituting the return-circuit The earthing and bonding arrangements hence play a significant role

in determining the touch voltages and stray current

3.3 Layout of Two-Stage Scheme

To provide accurate modelling of stray current, the peak loading condition should be studied On the other hand, touch voltage tends to be higher under failure conditions Meanwhile, improvement of the stray current or touch voltage tends to deteriorate the other For instance, high rail-to-ground insulation is liable to present large touch voltages but small stray currents Therefore, a two-stage scheme is proposed as in Figure 3-3 to represent the normal and failure conditions

At Stage I of return-circuit optimisation, the method of Pareto-optimal set is developed

to best improve the objectives of touch voltages and stray current for normal running condition The Multi-Objective Genetic Algorithm (MOGA) described in Section 5.2

is applied to obtain a set of Pareto-optimal solutions In each solution, the earthing and bonding design is optimised and therefore represents a different degree of trade-off between touch voltages and stray current The Pareto-optimal set from Stage I contains

a large collection of optimal designs This is also a source of reference for different design variations Because the specific times at which initiating events that cause failure conditions are unpredictable, any optimal design taken from Stage I must be operated at all times, in such a way that the system will not be endangered, should any credible failures occur

At Stage II, the decision-maker picks one optimal design from the Pareto-optimal set, and performs performance-check with the list of credible failure conditions The worst-case touch voltage and stray-current integral is identified during checking The decision-maker prepares his/her own list of credible failures from predefined events such as substation out-of-service, broken or deteriorating bonding and joints etc Should the worst case be unsatisfactory, the decision-maker is prompted to pick another optimal design from the Pareto-optimal set for further performance-check

Obtain Pareto Optimal Set by using MOGA for normal running condition

Select one solution from the Set

Performance check with the list of credible failure conditions

Performance Accepted ?

StartSet load configurationTrain movement moduleCreate current-distance andvelocity-distance profiles

Calculate load flow to producesystem operation parameters

Apply Gauss elimination to

Solve eqn [I]=[Y][V] to obtaininstantaneous values of touchvoltage and stray current

Search the minimumtouch voltage andcalculate the straycurrent integral