market mechanisms to allow trading of impervious cover

328 Pages·2013·5.2 MB·English

MARKET MECHANISMS TO ALLOW
TRADING OF IMPERVIOUS COVER

A THESIS SUBMITTED IN PARTIAL FULFILMENT OF THE REQUIREMENTS

FOR THE DEGREE OF DOCTOR OF PHILOSOPHY IN MANAGEMENT SCIENCE

AT THE UNIVERSITY OF CANTERBURY

BY

ANTONIO A. PINTO RODRIGUEZ

UNIVERSITY OF CANTERBURY
NEW ZEALAND
2013
To Ramy my wife,
Alfonso y Raquel my parents,
Patricio Contreras my cousin and F. Dioselinda
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Acknowledgements

I am grateful to my supervisors Dr. John F. Raffensperger, Dr. Thomas A. Cochrane, Dr.
Shane Dye and Prof. E. Grant Read for their support, comments, ideas, constructive
criticisms and encouragement. In particular, I want to thank Fritz and Tom who gave me
the opportunity to do my PhD.
Thanks to the Management Department for the scholarships, as well as to the staff and
fellow students for their continuous advice, support and friendships. In the same way,
thanks to all “Water Management Research Group” for the interesting discussions and
ideas about “Operation Research” topics. In particular, thank you Peter and Stephen for
your friendship.
My deepest thanks and love to my devoted wife Rosa M. Alzamora (Ramy), for her
patience, English help and constant support in all my endeavours, “Gracias Ramita por
todo tu apoyo, soporte y comprensión, te amo”.
Thanks, Luis and Marcela, for helping us with the first steps in New Zealand and for their
friendship to my wife and I.
Lastly, I wish to acknowledge my parents Raquel and Alfonso, who led me in my first
steps and always encouraged me toward looking for knowledge.
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Abstract

Problems with storm water runoff are becoming more frequent, and the main cause is the
increase of impervious cover (IC). The imperviousness increases stream peak flows,
changes peak times, and so changes the flood distribution. Several policies are used to
manage flows and flooding; however most have been reported to be inefficient because
land owners do not have correct exposure to price incentives and risk.
The main contributions of this thesis are an investigation into market mechanisms to
price and allocate impervious cover allowances, while managing flood distribution. The
market mechanisms are based on the electricity and gas markets which use linear
programming formulations. This thesis develops three net pool market mechanisms:
Det_MarketIC is a capped and deterministic market for IC, and Sto_MarketIC and
Sto_MarketIC_Risk are stochastic market models with flood component penalties and risk
positions representing the desired risk from the community respectively. Additionally, a
gross pool market was extended under rainfall uncertainty, Gross_MarketIC.
The market design is an auction system with operational constraints and bids for IC
allowances from participants. The system relates physical routed flows at nodal or control
points to these bids.
The models clear the market by creating a demand (supply) curve for increments
(reductions) in flows at specific places, and accounts for marginal changes in the expected
flood damage and flood damage components. The market formulations estimate efficient
allocations and prices. Decomposed prices from the market models are shown based on
duality, as applied in electricity markets. The dual prices show spatial and temporal effects
of flows, which impact at flooding areas. With Sto_MarketIC and Gross_MarketIC, prices
account for changes in flood distribution.
With Sto_MarketIC_Risk, prices also account for the risk as CVaR in flooding areas.
Thus, prices increase as binding risk conditions are tightened.
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Finally, the net pool models are illustrated using hydrological and hydraulic simulators
based on a small catchment located in Canterbury, New Zealand. Allocations and prices
varied with the different models. Participants would face increasing prices in their IC
allowances due to increments in flood damage.
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Table of Contents

Acknowledgements ............................................................................................................... i
Abstract ................................................................................................................................ ii
Table of Contents ................................................................................................................ iv
List of figures ...................................................................................................................... ix
List of tables ...................................................................................................................... xiv
Terms ................................................................................................................................. xvi
1 MECHANISMS FOR MANAGING IMPERVIOUS COVER AND RUNOFF .. 1
1.1 Introduction ............................................................................................................1
1.2 The runoff-flood problem .......................................................................................2
1.3 Mechanisms to deal with flooding .........................................................................3
1.3.1 Summarising physical measures ........................................................................ 3
1.3.2 Policies to manage flooding .............................................................................. 5
1.4 Smart market ..........................................................................................................8
1.5 Scope .....................................................................................................................12
2 MODELLING FLOWS, FLOOD, AND FLOOD DAMAGE .............................. 14
2.1 Introduction ...........................................................................................................14
2.2 Smart market for IC allowances ............................................................................16
2.3 Rainfall events (Storms) ........................................................................................22
2.4 Storm water runoff ................................................................................................25
2.5 Hydraulic modelling: governing equations ...........................................................29
2.6 Linear impacting flows ..........................................................................................33
2.7 Flood modelling ....................................................................................................35
2.8 Flood damage estimation.......................................................................................40
2.9 Flood damage function ..........................................................................................48
2.10 Expected flood damage .........................................................................................50
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3 DETERMINISTIC MARKET FOR IC ALLOWANCES ................................... 53
3.1 Introduction ...........................................................................................................53
3.2 Demand and supply ...............................................................................................55
3.3 Clearing the Det_MarketIC ...................................................................................57
3.4 A LP impacting/pricing model Det_MarketIC1 ....................................................59
3.4.1 Bid formation ................................................................................................... 63
3.4.2 Settlement with market model Det_MarketIC1............................................... 63
3.4.3 Price analysis ................................................................................................... 64
3.4.4 Trading implication ......................................................................................... 67
3.4.5 Locational-nodal prices ................................................................................... 69
3.4.6 Operator revenue: Initial rights ....................................................................... 70
3.4.7 Auction period ................................................................................................. 72
3.4.8 Planning horizon .............................................................................................. 73
3.4.9 Storms to establish short and long term markets ............................................. 75
3.5 An alternative LP pricing/impacting model Det_MarketIC2 ................................77
3.6 Settlement with market model Det_MarketIC2 ....................................................82
3.7 Comparing trade condition from models...............................................................83
3.8 Market competitiveness .........................................................................................83
3.9 Final remarks and conclusion ................................................................................85
4 A MARKET FOR IC ALLOWANCES UNDER RAINFALL UNCERTAINTY
.................................................................................................................................... 87
4.1 Motivation for stochastic programming ................................................................87
4.2 The general two-stage stochastic model ................................................................92
4.3 Choosing scenarios ................................................................................................93
4.4 Overview of the Sto_MarketIC market .................................................................95
4.5 A piecewise convex approximation to flooding cost ............................................97
4.6 Market model for IC, Sto_MarketIC .....................................................................99
4.6.1 Damage and flood cost .................................................................................... 99
4.6.2 Market-clearing model Sto_MarketIC1 ........................................................ 101
4.6.3 Price analysis ................................................................................................. 107
4.6.4 Prices relating to flood costs .......................................................................... 109
4.7 Settlement ............................................................................................................ 111
4.8 Hedging against storms ....................................................................................... 111
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4.8.1 Trading cases ................................................................................................. 112
4.9 System operator revenue ..................................................................................... 124
4.9.1 Initial IC allowances and revenues ................................................................ 125
4.9.2 Operator revenue due to flood damage cost approximation .......................... 127
4.9.3 Operator revenue surplus ............................................................................... 129
4.10 Dealing with a non-convex flood damage cost in the market formulation ......... 132
4.11 Final remarks and conclusion .............................................................................. 133
5 EXTENDING PENALTIES FOR FLOOD DAMAGE ...................................... 136
5.1 Introduction ......................................................................................................... 136
5.2 Relating cost to flood damage ............................................................................. 138
5.2.1 Depth cost in floodplain areas ....................................................................... 139
5.2.2 Rapid flooding and lengthening duration ...................................................... 139
5.2.2.1 Changes in flow levels and penalty cost ................................................ 142
5.2.2.2 Alternative penalty cost for large flow increments ............................... 143
5.3 Sto_MarketIC2 model ......................................................................................... 144
5.4 Price analysis ....................................................................................................... 148
5.4.1 Maximum depth in channels and floodplains ................................................ 148
5.4.2 Depth, rapid flooding and flood duration ...................................................... 149
5.4.3 Theoretical illustration for participants’ price allowances ............................ 152
5.4.4 Initial IC allowances and the SO’s revenue .................................................. 157
5.5 Final remarks and conclusion .............................................................................. 158
6 HEDGING VIA CONDITIONAL VALUE AT RISK (CVaR) ......................... 160
6.1 Introduction ......................................................................................................... 160
6.2 Decision-making under risk ................................................................................ 163
6.2.1 Risk aversion ................................................................................................. 164
6.2.2 Stochastic dominance .................................................................................... 165
6.2.3 Risk measure ................................................................................................. 167
6.2.4 CVaR ............................................................................................................. 168
6.3 Including risk in the market clearing model ........................................................ 171
6.4 The proposed market clearing model .................................................................. 174
6.5 Price analysis ....................................................................................................... 179
6.5.1 Price analysis and CVaR ............................................................................... 179
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6.5.2 Participants’ shadow prices ........................................................................... 182
6.5.3 Hedging with a set of CVaR positions at control points ............................... 184
6.6 Example applications .......................................................................................... 186
6.7 Misestimating confidence level () and CVaR value ......................................... 195
6.8 Possible issues in hedging against changes in damage via CVaR ...................... 195
6.9 Final remarks and conclusion .............................................................................. 198
7 CASE STUDY ........................................................................................................ 200
7.1 Introduction ......................................................................................................... 200
7.2 Property, hydrological and hydraulic assumptions ............................................. 201
7.2.1 Participant properties and preferences ........................................................... 201
7.2.2 Storms ............................................................................................................ 204
7.2.3 Hydrology of properties ................................................................................ 206
7.2.4 Hydraulic flows in the network ..................................................................... 206
7.3 Initial flood condition .......................................................................................... 207
7.3.1 Flows and flow capacities ............................................................................. 207
7.3.2 Flood cost ...................................................................................................... 212
7.4 Outcomes for proposed market models ............................................................... 212
7.4.1 Det_MarketIC ................................................................................................ 213
7.4.2 Sto_MarketIC ................................................................................................ 216
7.4.2.1 Sto_MarketIC for maximum stage-flood cost ....................................... 216
7.4.2.2 Sto_MarketIC with additional flood components ................................. 218
7.4.3 Sto_MarketIC_Risk ....................................................................................... 225
7.4.4 Summary deterministic and stochastic models .............................................. 229
7.5 Final remarks and conclusion .............................................................................. 231
8 GROSS POOL MODEL WITH REVENUE ADJUSTMENT .......................... 233
8.1 Gross vs. net pool market .................................................................................... 234
8.2 A gross pool formulation, Gross_MarketIC1 ...................................................... 235
8.3 Price analysis ....................................................................................................... 239
8.4 Settlement ............................................................................................................ 240
8.5 Trading condition ................................................................................................ 240
8.6 Issues with the Gross_MarketIC1 ....................................................................... 242
8.7 Setting a reference usage ..................................................................................... 243
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8.8 Operator revenue adequacy ................................................................................. 245
8.9 Scaling initial rights to reach revenue neutrality ................................................. 247
8.10 Example applications .......................................................................................... 249
8.11 Final remarks and conclusion .............................................................................. 253
9 CONCLUSIONS AND FUTURE RESEARCH .................................................. 255
9.1 Summary ............................................................................................................. 255
9.2 Conclusions ......................................................................................................... 257
9.3 Future research .................................................................................................... 259
9.3.1 Flood damage (cost functions) and risk measures ......................................... 259
9.3.2 Insurance for disasters ................................................................................... 259
9.3.3 Transported pollutants from runoff ............................................................... 260
9.3.4 User interface and SO simulation framework ............................................... 260
9.3.5 Infrastructure investment and effects in the market ...................................... 261
10 Bibliography ........................................................................................................... 262
Appendix A ....................................................................................................................... 278
Appendix B ....................................................................................................................... 284
B.1 Linearised non-convex flood damage cost function, example ............................ 284
B.2 Approximations to the flood costs function ........................................................ 286
B.2.1 Example flood damage approximations ......................................................... 288
B.2.2 Extending convexification .............................................................................. 293
Appendix C ....................................................................................................................... 295