Table of Contents
Preface v
1 Introduction 1
1.1 Transportation networks . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
1.2 Control structures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3
1.2.1 Control structure design . . . . . . . . . . . . . . . . . . . . . . . 6
1.2.2 Assumptions for design and analysis . . . . . . . . . . . . . . . . . 7
1.3 Model predictive control . . . . . . . . . . . . . . . . . . . . . . . . . . . 8
1.3.1 Single-agent MPC . . . . . . . . . . . . . . . . . . . . . . . . . . 8
1.3.2 Multi-agent MPC . . . . . . . . . . . . . . . . . . . . . . . . . . . 11
1.4 Power networks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14
1.4.1 Physical power networks . . . . . . . . . . . . . . . . . . . . . . . 14
1.4.2 Future power networks . . . . . . . . . . . . . . . . . . . . . . . . 15
1.4.3 Opportunities for multi-agent control . . . . . . . . . . . . . . . . 15
1.5 Overview of this thesis . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16
1.5.1 Thesis outline . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16
1.5.2 Road map . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17
1.5.3 Contributions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18
2 Serial versus parallel schemes 19
2.1 Network and control setup . . . . . . . . . . . . . . . . . . . . . . . . . . 19
2.1.1 Network dynamics . . . . . . . . . . . . . . . . . . . . . . . . . . 19
2.1.2 Control structure . . . . . . . . . . . . . . . . . . . . . . . . . . . 20
2.2 MPC of a single subnetwork . . . . . . . . . . . . . . . . . . . . . . . . . 21
2.3 Interconnected control problems . . . . . . . . . . . . . . . . . . . . . . . 22
2.3.1 Types of information exchange . . . . . . . . . . . . . . . . . . . . 24
2.3.2 Timing of information exchange . . . . . . . . . . . . . . . . . . . 25
2.4 Lagrange-based multi-agent single-layer MPC . . . . . . . . . . . . . . . . 27
2.4.1 Combined overall control problem . . . . . . . . . . . . . . . . . . 28
2.4.2 Augmented Lagrange formulation . . . . . . . . . . . . . . . . . . 28
2.4.3 Distributing the solution approach . . . . . . . . . . . . . . . . . . 29
2.4.4 Serial versus parallel schemes . . . . . . . . . . . . . . . . . . . . 31
2.5 Application: Load-frequency control . . . . . . . . . . . . . . . . . . . . . 33
2.5.1 Benchmark system . . . . . . . . . . . . . . . . . . . . . . . . . . 34
2.5.2 Control setup . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36
2.5.3 Simulations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37
2.6 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 44
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viii Contents
3 Networked hybrid systems 47
3.1 Transportation networks as hybrid systems . . . . . . . . . . . . . . . . . . 47
3.2 Modeling of hybrid systems . . . . . . . . . . . . . . . . . . . . . . . . . 49
3.2.1 Models for MPC control . . . . . . . . . . . . . . . . . . . . . . . 50
3.2.2 From discrete logic to linear mixed-integer constraints . . . . . . . 50
3.2.3 Mixed-logical dynamic models . . . . . . . . . . . . . . . . . . . . 52
3.3 Application: Household energy optimization . . . . . . . . . . . . . . . . . 52
3.3.1 Distributed energy resources . . . . . . . . . . . . . . . . . . . . . 52
3.3.2 System description . . . . . . . . . . . . . . . . . . . . . . . . . . 53
3.3.3 MPC problem formulation . . . . . . . . . . . . . . . . . . . . . . 59
3.3.4 Simulations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 61
3.4 Control of interconnected hybrid subnetworks . . . . . . . . . . . . . . . . 66
3.4.1 Hybrid subnetwork models . . . . . . . . . . . . . . . . . . . . . . 67
3.4.2 Non-convergence due to the discrete inputs . . . . . . . . . . . . . 68
3.4.3 Possible extensions of the original schemes . . . . . . . . . . . . . 68
3.4.4 Serial and parallel single-layer hybrid MPC approaches . . . . . . . 70
3.5 Application: Discrete-input load-frequency control . . . . . . . . . . . . . 71
3.5.1 Network setup . . . . . . . . . . . . . . . . . . . . . . . . . . . . 71
3.5.2 Control setup . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 71
3.5.3 Simulations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 72
3.5.4 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 72
3.6 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 75
4 Multi-layer control using MPC 77
4.1 Multi-layer control of transportation networks . . . . . . . . . . . . . . . . 77
4.1.1 Multi-layer control . . . . . . . . . . . . . . . . . . . . . . . . . . 78
4.1.2 Multi-layer control in power networks . . . . . . . . . . . . . . . . 78
4.1.3 MPC in multi-layer control . . . . . . . . . . . . . . . . . . . . . . 79
4.2 Constructing prediction models with object-oriented modeling . . . . . . . 81
4.2.1 Object-oriented modeling . . . . . . . . . . . . . . . . . . . . . . 81
4.2.2 Modeling tools . . . . . . . . . . . . . . . . . . . . . . . . . . . . 82
4.2.3 Object-oriented prediction models . . . . . . . . . . . . . . . . . . 82
4.2.4 Linearized object-oriented prediction models . . . . . . . . . . . . 85
4.3 Supervisory MPC control problem formulation . . . . . . . . . . . . . . . 88
4.3.1 Nonlinear MPC formulation . . . . . . . . . . . . . . . . . . . . . 89
4.3.2 Direct-search methods for nonlinear optimization . . . . . . . . . . 90
4.3.3 Linear MPC formulation . . . . . . . . . . . . . . . . . . . . . . . 92
4.4 Application: Voltage control in a 9-bus power network . . . . . . . . . . . 93
4.4.1 The 9-bus dynamic benchmark network . . . . . . . . . . . . . . . 94
4.4.2 Object-oriented model of the network . . . . . . . . . . . . . . . . 96
4.4.3 Control problem formulation for the higher control layer . . . . . . 100
4.4.4 Control using the nonlinear MPC formulation . . . . . . . . . . . . 103
4.4.5 Control using the linear MPC formulation . . . . . . . . . . . . . . 105
4.5 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 108
Contents ix
5 Overlapping subnetworks 109
5.1 Steady-state models of transportation networks . . . . . . . . . . . . . . . 109
5.2 Subnetworks and their properties . . . . . . . . . . . . . . . . . . . . . . . 111
5.2.1 Properties of subnetworks . . . . . . . . . . . . . . . . . . . . . . 111
5.2.2 Defining subnetworks . . . . . . . . . . . . . . . . . . . . . . . . 111
5.3 Influence-based subnetworks . . . . . . . . . . . . . . . . . . . . . . . . . 113
5.3.1 Using sensitivities to determine subnetworks . . . . . . . . . . . . 113
5.3.2 Computing the sensitivities . . . . . . . . . . . . . . . . . . . . . . 114
5.3.3 Control of influence-based subnetworks . . . . . . . . . . . . . . . 114
5.4 Multi-agent control of touching subnetworks . . . . . . . . . . . . . . . . . 115
5.4.1 Internal and external nodes . . . . . . . . . . . . . . . . . . . . . . 115
5.4.2 Control problem formulation for one agent . . . . . . . . . . . . . 116
5.4.3 Control scheme for multiple agents . . . . . . . . . . . . . . . . . 118
5.5 Multi-agent control for overlapping subnetworks . . . . . . . . . . . . . . 120
5.5.1 Common nodes . . . . . . . . . . . . . . . . . . . . . . . . . . . . 120
5.5.2 Control problem formulation for one agent . . . . . . . . . . . . . 122
5.5.3 Control scheme for multiple agents . . . . . . . . . . . . . . . . . 124
5.6 Application: Optimal flow control in power networks . . . . . . . . . . . . 124
5.6.1 Steady-state characteristics of power networks . . . . . . . . . . . 125
5.6.2 Control objectives . . . . . . . . . . . . . . . . . . . . . . . . . . 128
5.6.3 Setting up the control problems . . . . . . . . . . . . . . . . . . . 128
5.6.4 Illustration of determination of subnetworks . . . . . . . . . . . . . 129
5.6.5 Simulations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 129
5.7 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 133
6 Conclusions and future research 137
6.1 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 137
6.2 Future research . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 139
Bibliography 143
Glossary 155
TRAIL Thesis Series publications 159
Samenvatting 165
Summary 169
Curriculum vitae 173
Abstract
Transportation networks, such as power networks, road traffic networks, water distribution networks, railway networks, etc., are the corner stones of our modern society. As transportation networks have to operate closer and closer to their capacity limits and as the dynamics of these networks become more and more complex, control of these networks has to be advanced to a higher level using state-of-the-art control techniques. Such control techniques should be able to deal with the large size and distributed nature of the control problems encountered, and should in addition be able to anticipate undesired behavior at an early stage. In this PhD thesis several novel control techniques for the control of transportation networks are proposed. Each of the techniques proposed is based on a combination of ideas from the fields of multi-agent systems and model predictive control. Control problems from the domain of power networks are used to illustrate and assess the performance of the proposed techniques.
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