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Title Analytical models for wind power investment
Advisor(s) Wu, FF; Zhong, J
Author(s) Cheng, Mang-kong.; ‘ [_ [.
Citation
Issued Date 2011
URL http://hdl.handle.net/10722/174453
RightsThe author retains all proprietary rights, (such as patent rights)and the right to use in future works.
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Analytical Models for Wind Power Investment
by
Henry Mang-kong Cheng
B.Eng. HKU; M.Econ. HKU
A thesis submitted in partial fulfillment of the requirements forthe Degree of Doctor of Philosophy
at the University of Hong Kong
September 2011
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evaluation. The applications of the probabilistic wind power model to these topics are
outlined in this chapter.
In Chapter 4, investment of fixed tariff wind power project is analyzed. Operation
of wind farm is very passive and as long as wind keeps blowing, such wind power
investment has minimal risk in annual revenue. The low-risk profile facilitates debt
financing. This leads to the attempt to manipulate the project capital structure to
maximize the project levered value. Yet the default probability is raised and associated
with a subjective value of default probability there is a value-at-risk debt level. I therefore
propose an optimization formulation to maximize the wind power project valuation with
debt as decision variable subject to the value-at-risk debt constraint.Apart from independent wind power producers, many policy and market factors
driving wind power development are actually put on the utility side, e.g. Renewable
Portfolio Standard (Renewable Energy Target) in U.S. (Europe) and Green Power
Programs. It implies that utility has to have wind power (or other renewable) capacity
ready by a certain date. In practice, utility may take action earlier if conditions are
favorable or optimal. The conditions considered here are fossil fuel prices or in more
general setting, electricity contract prices. Define the total fuel cost saving from
conventional units as the benefit of wind power. If fuel prices are high enough,
substituting load demand by wind energy is profitable, vice versa. The investment
decision is analogous to premature exercising of an American option, in which the wind
power project is modeled as real option. Chapter 5 offers detailed formulation of this idea.
(485 words)
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DECLARATION
I declare that this thesis represents my own work, except where due
acknowledgement is made, and that it has not been previously included in a thesis,
dissertation or report submitted to this University or to any other institution for a degree,
diploma or other qualification.
Signed ……………………………………………….
Henry Mang-kong Cheng
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LIST OF ORIGINAL IDEAS
The following highlights in particular are original contribution of this thesis:
A new probabilistic wind power generation model furnished with analytical
formulae of any higher order moment/cumulant. It can be used in conjunction with
reliability evaluation and production costing in power system literature.
A stochastic optimisation framework of levered firm valuation for the investment
modelling of wind power project under feed-in tariff, subject to value-at-risk debt
constraint. It points to an optimal debt level for maximizing the firm valuation.
Application of a bivariate real option model to determine the optimal investment
timing and value of a wind power project undertaken by utility for meeting the
requirement of renewable energy target. The financial model successfully
incorporates probabilistic production costing result as a power system consideration.
Any error and omission are my own responsibility.
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Table of Contents
DECLARATION................................................................................................................ 3
ACKNOWLEDGMENT..................................................................................................... 4
LIST OF ORIGINAL IDEAS............................................................................................. 5
List of Tables .................................................................................................................... 10
List of Figures ................................................................................................................... 11
List of Notations ............................................................................................................... 13
List of Abbreviations ........................................................................................................ 15
1
Overview of Generation Planning and Investment................................................... 16
1.1
Introduction...................................................................................... 16
1.2
Conventional Generation Planning.................................................. 17
1.3 Distributed Generation Planning...................................................... 19
1.4 Generation Investment ..................................................................... 20
1.4.1 Financial risk management of generator profit...... ........... ............ ......... ........ 20
1.4.2 Valuation of generator in spot market............................................................21
1.5
Research Motivations....................................................................... 22
1.6
Objective and Expected Contribution.............................................. 23
1.7
Thesis Outline .................................................................................. 24
1.8 References........................................................................................ 25
2 Market Scenarios for Wind Power Investment......................................................... 29
2.1
Background and Scope .................................................................... 29
2.2
Feed-in Tariff ................................................................................... 30
2.2.1 German wind tariffs........................................................................................31
2.2.2
German photovoltaic tariffs ........................................................................... 32
2.2.3 Concluding remark for investment modeling ................................................. 33
2.3
Obligation – American Experiences ................................................ 33
2.3.1 Renewable Portfolio Standard ......... .......... .......... ........... ......... ........... .......... . 34
2.3.2 Integrated Resource Planning .......... .......... .......... ........... ......... ........... .......... . 34
2.3.3 Green Power Programs..................................................................................35
2.3.4 Tax Credits and Production Incentives ..........................................................36
2.3.5 Concluding remark for investment modeling ................................................. 37
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2.4 Obligation – European Experiences................................................. 37
2.4.1 EU Energy and Climate Package ........... ......... ........... .......... .......... .......... ...... 38
2.4.2
EU Emission Trading System .......... ......... ............ ........... ......... ........... .......... . 38
2.4.3 Nordic Energy Perspectives .......... .......... .......... .......... ........... ......... ........... .... 39
2.4.4 NEP Modelling Methodology .......... ......... ............ ........... ......... ........... .......... . 40
2.4.5 Concluding remark for investment modeling ................................................. 44
2.5
Wind Power in Spot Market ............................................................ 45
2.6
Auction and Tendering .................................................................... 46
2.7 Summary.......................................................................................... 46
2.8 References........................................................................................ 47
3
Probabilistic Wind Power Generation Model........................................................... 49
3.1
Introduction...................................................................................... 49
3.2
Wind Speed Distribution.................................................................. 50
3.3 Wind Turbine ................................................................................... 51
3.3.1 Ideal Power Curve........ .......... .......... ........... ......... ........... ......... ........... ......... .. 51
3.3.2 Aerodynamic principle ......... ........... ......... ............ ........... ......... ........... ......... .. 52
3.3.3 Wind turbine generator type........................................................................... 53
3.3.4 Power regulation............................................................................................55
3.3.5
Empirical power curve ......... ........... ......... ............ ........... ......... ........... ......... .. 55
3.4 Wind Power Distribution ................................................................. 56
3.4.1 Analytical Formulae of Wind Power Statistics..... ........... ......... ........... ......... .. 58
3.5 Wake Effect and Wind Direction..................................................... 59
3.6 Evaluating Production Cost and Reliability with Wind Power ....... 60
3.7
Data Source...................................................................................... 61
3.7.1 Royal Netherlands Meteorological Institute......... ........... ......... ........... ......... .. 62
3.7.2 Vermont Small-scale Wind Energy Demonstration Program........ ......... ........ 62
3.8
Data Pre-processing ......................................................................... 62
3.8.1 Wind speed measuring height......................................................................... 62
3.8.2 Wind speed partitions and the parameter lambda..........................................63
3.8.3 Empirical power curve ......... ........... ......... ............ ........... ......... ........... ......... .. 63
3.8.4 Wake effect .....................................................................................................65
3.9
Simulated and Empirical Results..................................................... 66
3.9.1 Historical wind speed analysis ......... .......... .......... ........... ......... ........... .......... . 67
3.9.2 Mean and standard deviation of annual average wind power ........ ........... .... 74
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3.9.3 Monte Carlo simulation for wind power statistics .......... ......... ........... .......... . 76
3.9.4 Comparison between analytical and empirical wind power PDF....... ......... .. 77
3.9.5
Regional wind power distribution .......... ......... ........... .......... .......... .......... ...... 79
3.10 Remarks ........................................................................................... 83
3.11 References........................................................................................ 83
4
Fixed Tariff Wind Power Investment Model............................................................ 88
4.1
Introduction...................................................................................... 88
4.1.1 Scope .............................................................................................................. 90
4.2
Accounting Preliminaries................................................................. 91
4.2.1 Definition of cash flow ......... ........... ......... ............ ........... ......... ........... ......... .. 92
4.2.2
Net present value .......... .......... .......... ........... ......... ........... ......... ........... ......... .. 93
4.2.3 Other discount rates .......................................................................................94
4.2.4 Capital structure.............................................................................................96
4.3 Model Formulation for FIT Wind Power Investment...................... 98
4.4
Trial Data for the Model ................................................................ 102
4.4.1 Base case financial parameters......... ............ ......... ........... ............ ......... ...... 103
4.5 Numerical Example ....................................................................... 104
4.5.1 Base case .......... ........... ......... ........... ......... ............ ........... ......... ........... ......... 104
4.5.2 Sensitivity analysis .......................................................................................106
4.6
Summary........................................................................................ 108
4.7
References...................................................................................... 108
5 Real Option Wind Power Investment Model.......................................................... 110
5.1 Introduction.................................................................................... 110
5.2
Literature Review and Comparison ............................................... 112
5.2.1 Review of selected real option applications in energy sector ......... .......... .... 112
5.2.2 Comparison with existing works................................................................... 114
5.2.3
Preliminaries of option pricing theory......................................................... 115
5.3
Contingent Claim and Real Option................................................ 117
5.3.1 Contingent claim and justification for delta hedging...................................118
5.3.2 Solution of contingent claim as project valuation ........................................121
5.3.3 Real option accounting delay of investment ......... ........... ......... ........... ......... 122
5.4
Bivariate Binomial Lattice for two Fuel Prices ............................. 125
5.4.1 Univariate binomial model........................................................................... 126
5.4.2 Bivariate binomial model ........... .......... .......... .......... ......... ............ ......... ...... 128
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5.4.3 Risk neutral valuation ......... .......... .......... .......... .......... ........... ......... ........... .. 128
5.4.4 Extension to multi-fuel displacements ........... ......... ........... ............ ......... ...... 130
5.5
Categorization of Parameters......................................................... 131
5.5.1 Annual average wind energy production........ .......... ......... ............ ......... ...... 131
5.5.2 Fuel displacement......................................................................................... 132
5.5.3 Wind turbine capital and maintenance costs................................................ 134
5.5.4 Choice of discount rate.................................................................................134
5.5.5 Carbon price and renewable credit..............................................................136
5.6 Parameters Estimation ................................................................... 139
5.6.1 Fossil fuel price drift and volatility .............................................................. 139
5.6.2 Fossil fuel price correlation......................................................................... 141
5.6.3
Risk-free rate .......... ........... .......... ........... ......... ........... .......... .......... .......... .... 141
5.6.4 Risk-adjusted discount rate by CAPM........... ......... ........... ............ ......... ...... 142
5.6.5 Wind turbine costs........................................................................................ 143
5.6.6 Fuel consumption by PPC............................................................................ 144
5.7 Numerical Example ....................................................................... 147
5.7.1 Base case results .......... .......... .......... ........... ......... ........... ......... ........... ......... 147
5.7.2 Sensitivity analysis .......................................................................................148
5.8
Summary and future works............................................................ 153
5.9
References...................................................................................... 155
6
Conclusion .............................................................................................................. 160
7 Appendices.............................................................................................................. 162
I. Wind Power Probability Distribution ..................................................................... 162
II. M&M Propositions I and II with Corporate Taxes................................................. 168
III.
Solution of an Ordinary Second Order Non-homogenous Differential
Equation 170
IV. Solving Ordinary Second Order Homogenous Differential Equation
with Boundary Conditions.............................................................................................. 172
V. Matching Mean and Variance of a Bivariate Binomial Lattice with Geometric
Brownian Motions .......................................................................................................... 173
VI.
Moment/Cumulant and Gram-Charlier series................................ 176
8
Publications............................................................................................................. 179
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List of Tables
Table 2.1 Summary of German feed-in tariffs for land and sea wind power ... 32
Table 2.2 Summary of feed-in tariffs for various photovoltaic installations.... 32
Table 2.3 EUA prices for various scenarios in Nordic Energy Perspectives.... 43
Table 2.4 Summary of attributes of groups of NEP models ............................. 44
Table 3.1 Summary of distribution parameters of selected wind speed data.... 68
Table 3.2 Annual figures of the 3.2M wind turbine placed at Station 225
IJmuiden.................................................................................................... 70
Table 3.3 Comparison between simulated and empirical average powers of the3.2MW wind turbine placed at various locations. .................................... 71
Table 3.4 Average wind power and its standard deviation............................... 74
Table 3.5 Statistical properties of residuals ...................................................... 75
Table 3.6 Statistical properties of residuals (monthly basis) ............................ 76
Table 3.7 Wind power statistics: analytic vs simulation................................... 76
Table 3.8 Wind turbine breakdown by capacities in Denmark 2009................ 80
Table 4.1 Financial parameters for fixed tariff wind power project ............... 103
Table 5.1 Drifts and volatilities derived from fossil fuel prices ..................... 140
Table 5.2 Correlations between three pairs of fossil fuel ............................... 141
Table 5.3 U.S. Treasury bond yields (Dec 2010) ........................................... 142
Table 5.4 Beta for wind power project ........................................................... 143
Table 5.5 Assumed cost data for wind turbines.............................................. 143
Table 5.6 One-area generator data .................................................................. 144
Table 5.7 Generator outage cumulants ........................................................... 145
Table 5.8 Wind power under-capacity cumulants .......................................... 145
Table 5.9 Expected energy productions before and after wind capacity addition
................................................................................................................. 147
Table 5.10 Annual fuel reductions to an IEEE-RTS96 area by 28.5MW wind
capacity ................................................................................................... 147
Table 5.11 Base case valuation of a 28.5MW wind power project ................ 148
Table V.1 Discretization outcomes of two correlated GBMs......................... 173
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List of Figures
Fig. 3.1 An ideal wind turbine power curve ..................................................... 52
Fig. 3.2 Wind turbine characteristics for maximum power extraction (Courtesy
of [59]) ...................................................................................................... 54
Fig. 3.3 Comparison between power curves of fixed speed and variable speed
wind turbine generators (Courtesy of [65]) .............................................. 54
Fig. 3.4 Comparison between power curves of pitch control and stall control
wind turbine generators (Courtesy of [64]) .............................................. 55
Fig. 3.5 Visual comparison between three-segment and four-segment power
curve.......................................................................................................... 57
Fig. 3.6 Empirical power curve determined by regressing real data ................ 64
Fig. 3.7 Waked wind speed density function (b) compared with its original
Rayleigh source (a) ................................................................................... 65
Fig. 3.8 Effective average power of waked wind turbine ................................. 66
Fig. 3.9 Average powers along specific months of all years ............................ 72
Fig. 3.10 Annual average wind power, Station I.D. 210, Valkenburg.............. 73
Fig. 3.11 Annual average wind power, various Dutch locations...................... 73
Fig. 3.12 Normality test for residuals (differences between global mean and
annual averages)........................................................................................ 75
Fig. 3.13 Wind power PDF synthesized from simple power curve.................. 77
Fig. 3.14 Wind power PDF synthesized from improved power curve ............. 77
Fig. 3.15 Modeling empirical wind power by analytical PDF.......................... 78
Fig. 3.16 Successive convolution of individual wind turbine outputs.............. 81
Fig. 3.17 Standardized PDF of correlated cumulant method of 7 variables.... 82
Fig. 3.18 Standardized PDF of correlated cumulant method of 31 variables.. 82
Fig. 4.1 Project NPV and levered NPV of one MW onshore wind capacity
investment ............................................................................................... 105
Fig. 4.2 The VaR debt level of one MW onshore wind capacity investment . 105
Fig. 4.3 Sensitivity analysis of VaR debt to debt interest rate and default
probability for onshore wind farm.......................................................... 106
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Fig. 4.4 Sensitivity analysis of VaR debt to debt interest rate and default
probability for offshore wind farm ......................................................... 107
Fig. 4.5 Sensitivity analysis of maximum levered NPV to debt interest rate and
return on unlevered equity for onshore wind farm ................................. 107
Fig. 4.6 Sensitivity analysis of maximum levered firm value to debt interest rate
and return on unlevered equity for offshore wind farm.......................... 108
Fig. 5.1 A time step of a binomial model ....................................................... 115
Fig. 5.2 Bivariate binomial lattice and iteration of its option value ............... 130
Fig. 5.3 Fuel prices for electric power use in U.S........................................... 141
Fig. 5.4 S&P 500 and Dow Jones Utility Average since 1980 ....................... 143
Fig. 5.5 Sensitivity analysis of land wind project NPV over fuel prices ........ 149
Fig. 5.6 Sensitivity analysis of land wind project IRR over carbon price ...... 150
Fig. 5.7 Sensitivity analysis of land wind project NPV over carbon price and
emission policy arrival rate..................................................................... 150
Fig. 5.8 Sensitivity analysis of sea wind project NPV over fuel prices.......... 151
Fig. 5.9 Sensitivity analysis of sea wind project IRR over carbon price........ 151
Fig. 5.10 Sensitivity analysis of sea wind project NPV over carbon price and
emission policy arrival rate..................................................................... 152
Fig. 5.11 Synthetic trading values of wind power investment real options.... 153
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List of Notations
A Area swept by wind turbine rotor; constant in contingent claim analysis
a Probability of default
B Constant in real option solution
c Call option; central moment
C Wind turbine operating cost
C co2 Carbon dioxide content of fossil fuel (lbs/MBtu)
C P Power coefficient
C T Thrust coefficient
D Debt
d Debt instalment
D p Depreciation
dq Poisson process
dz Wiener process
E Equity
E W Annual wind energy production
f(.) In general means a function or a PDF
F(.) In general means a CDF
F(S,t), F Wind power investment (real) option
g Dummy for growth rate, e.g. g C means growth rate of wind turbine operating cost
g m Rated power of wind turbine net of electrical loss H Fuel heat (MBtu), e.g. H o means heat content of oil
h Wind turbine hub height
i D Debt interest
K Option strike price
k Shape parameter of Weibull distribution; wake decay constant
LK i System load cumulant to the order i
m Moment
O CF Operating cash flow
O i Operating income
OK i Generator outage cumulant to the order i
p Probability of price evolution in binomial model, have subscript u or d
P air Power in free wind speed
P wt Power extracted by wind turbine
q Risk-neutral probability
R Radius of wind turbine blade
r, r f Risk-free rate
R A Cost/return of asset
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List of Notations (cont’d)
R co2 Carbon saving/revenue
R D Cost/return of debt
r DSC Debt service coverage ratio
R E Cost/return of equity
r i Return of an individual stock i
r m Return of market portfolio
RU Unlevered cost of capital
S Price in GBM in general, e.g. S c means coal price ($/MBtu)
S co2 Carbon price (€/ton)S RC Renewable credit price
T Terminal time period
t C Corporate tax rate
T C Corporate tax
t W Wind energy tariff
v The drift of additive Brownian motion
V Dummy for firm value
V(S,t),V Contingent claim of wind power project
V* Optimal project value
V L Levered firm value
V U Unlevered firm value
w Dummy variable of wind speed
WK i Wind power cumulant to the order i
y D Debt coupon rate
z Roughness length
α Drift rate of GBM
β Beta coefficient in CAPM; Constant in real option solution
∆ The delta of hedging
δ Convenience/dividend yield, in general meansμ
α ∆t Infinitesimal time period
κ
Cumulant
λ Parameter of exponential distribution; scale parameter of Weibull distribution; tip
speed ratio
μ
Risk-adjusted discount rate by CAPM
π
Net cost saving (profit function) of wind turbine
ρ
Correlation between two GBM; air density
σ
Volatility rate of GBM; standard deviation
ω Angular speed of wind turbine
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List of Abbreviations
BS Black ScholesBSDE Black Scholes differential equation
CAPM Capital Asset Pricing Model
CDF cumulative distribution function
CDM clean development mechanism
CER certified emission reductions
CPUC California Public Utilities Commission
DFIG doubly-fed induction generator
DG distributed generation
Dp depreciation
DSC debt service coverageEBIT earning before interest and tax
EENS expected energy not served
EIA Energy Information Administration
ETS Emissions Trading Scheme
EUA European Union allowance
FIT feed-in tariff
GBM geometric Brownain motion
GHG greenhouse gas
IPP independent power producer
IRP Integrated Resources Planning
IRR internal required rate of return
LDC load duration curve
LOLP loss-of-load probability
M&M Modigliani and Miller
NEP Nordic Energy Perspectives
NPV net present value
NREL National Renewable Energy Laboratory
NWC net working capital
OCF operating cash flow
PDF probability density function
PPC probabilistic production costingPTC production tax credit
PURPA Public Utility Regulatory Policies Act
PV photovoltaic
REC renewable energy certificate
RET Renewable Energy Target
RPS Renewable Portfolio Standard
Tc corporate tax
VaR value-at-risk
WACC weighted average cost of capital
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Chapter 1
1 Overview of Generation Planning and Investment
Abstract
This thesis works on investment modeling of wind power, and theoretically
photovoltaics as well. Under the broad umbrella of generation planning and investment,three topics, namely, conventional generation expansion planning, distribution generation
planning and the more contemporary generation investment are first identified and
discussed. Historical developments of modeling approaches to these topics are reviewed.
Then, in my opinion, the ways of constructing wind power investment model should
consider two aspects. On one hand, renewable energy investment may be recognized as
part of the overall generation investment; coherency with existing modeling works has to
be strived for. On the other hand, renewable generation may have unique characteristics
that could only be catered by new modeling techniques; in this case consistency with its
own technical specifics is more desirable. It is this special orientation of renewable
generation that requires careful justification of the choice of investment modeling
methodology.
1.1 Introduction
In power system literature, wind power investment analysis is relatively scarce. It
seldom exists as standalone, comprehensive investment model. Rather, wind, together
with other renewable, appears only as component in generation planning model. It can
also be grouped under distributed generation planning. However, both planning cases are
not readily transformable into the open market scenario if investment modeling is
required. Although there is a breakthrough of evaluating profit of conventional generator
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in spot market by real option methodology, wind power or other renewable investment
does not readily utilize this approach. The dilemma of positioning wind power investment
analysis is further explained in Section 1.5 Research Motivations of this chapter. Here I
intentionally start the thesis by reviewing conventional generation planning and
investment, so as to give a preliminary for wind power investment to come in place. Then
I briefly discuss the approach of modeling and expected contribution in Section 1.6
Objective and Expected Contribution.
1.2 Conventional Generation Planning
Conventional generation planning or generation expansion planning is the electric
utility’s decision on generating capacity additions to meet future load demand. The task
composes of a series of questions of when, where, what type and capacity of generators to
be built in long run. In the past, electric utility was vertically integrated with generation,
transmission and distribution together, essentially monopolistic in its own geographical
area. Therefore electricity tariff necessitated a cap or regulation. The business model or
objective of electric utility is to minimize total cost without jeopardizing reliable supply
to customers. This translates generation planning into a constrained optimization problem:
to minimize total costs subject to some constraints.
There are many applications of optimization in power systems; economic dispatch
is probably the most common one. It is a non-linear optimization (programming) problem
as the input-output characteristics of condensing generators, hence the objective cost
function, is nonlinear [1]. Power balance is the equality constraint. Economic dispatch is
run every moment, e.g. a couple of minutes, throughout system operation. During suchperiod of time, system load may be regarded as constant or deterministic, therefore
economic dispatch tells the optimal generator outputs corresponding to the load of that
moment. Later we will see situations that the load cannot be treated as deterministic but
has a few random scenarios, e.g. long-term load forecast, so that when optimization is
applied the problem becomes stochastic optimization.
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Economic dispatch yields optimal solution for a particular moment. On the other
hand, unit commitment calculates multi-period generator outputs that are as a whole
optimal for the time period concerned. As a generator has “on” and “off” states, binary
variables “1” and “0” respectively are needed in the objective cost function. Hence the
optimization becomes a multi-period, mixed-integer, and nonlinear programming
problem. The optimal sequence of generator states is chronological in nature in order to
minimize the total operating cost.
Multi-period optimization technique has been extended to the context of
generation planning, which takes the following features. First, the basic objective
function to be minimized is the present value of total cost. Total cost comprises ofinvestment costs of all types of generator at any capacity incurred throughout the whole
timeline and the corresponding operating costs, primarily fuel costs. It is sufficient to
approximate the generator input-output curves by linear segments because the level of
details of non-linear objective function is not necessary for long-term planning. Therefore
generation planning can be as simple as a linear programming problem with annual
capacity additions and energy outputs as decision variables. In terms of constraints, the
most important one is reliability. The common reliability criterion is the loss-of-load
probability (LOLP). Since all generators have outage probability, the total cost is
minimized subject to a pre-defined value of LOLP as constraint. Furthermore, concepts
of load duration curve and probabilistic production costing capture economic dispatch in
generation planning by loading units according to their incremental costs. An example of
generation planning in simple linear programming setting is called sequential linear
programming [32].
The formulation of [32] has catered unit forced outage and loss-of-load
probability by probabilistic production costing and reliability evaluation respectively, but
still it has limited capability to handle other broader planning uncertainties, such as load
growth rate and fuel cost growth rates, as they are only represented as deterministic
parameters. The set of parameters could be describing a particular scenario, or average
value of a few scenarios. Essentially, the resultant expansion plan is optimal only to a
particular set of deterministic equivalent parameters. Reference [3] made quite a precise
description on the limitations of deterministic linear programming applied to generation
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planning, and also on the solution approach by decision analysis and min-max strategy
for multi-objective function. Subsequently multi-period mixed integer stochastic
optimization was proposed [3]. The resultant objective function is divided into two sub-
problems and solved by Benders’ decomposition technique. Its numerical technique is not
explored further here. Apart from linear or non-linear programming, generation planning
can also be done by dynamic programming, either deterministically [23] or stochastically
[5]. For completeness, emerging techniques on generation planning other than
conventional mathematical programming are also reported [17]. Up to here a gentle
review on generation planning and its optimization techniques is completed.
1.3 Distributed Generation Planning
Optimization techniques have also been applied in distribution planning. Very
generic mixed-integer programming models for distribution planning, in terms of
substation capacity and feeder capacity, are presented in [30]. A major subset of
distribution planning is distributed generation (DG) planning, including renewable energy.
DG faces a number of technical constraints in the distribution network, such as short
circuit level and voltage level; optimal allocation (location and rating) of DG can be
formulated as an optimization problem. Linear programming to determine the maximum
DG capacity with respect to the network constraints is reported in [2]. Mathematical
programming is a good formulation to cover as many constraints as possible, but it limits
the problem nature as a planning model. What may be more contemporary, as mentioned
in [31], is DG investment, which describes distribution utility considering DG as an
alternative to meet future load demand. In competitive electricity market wheredistribution utility acts as a buyer, it bids in the spot market or purchases electricity
directly from other generators through bilateral contracts. But in principle, both
distribution utility and end customers can own DG [31]. The optimal DG investment
decision, again in terms of location and capacity, is determined from a proposed heuristic
approach to minimize total cost, which consists of DG investment and operating costs,
network upgrade cost, electricity purchase (spot or contract) and unserved load.
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In course of literature review of distributed generation, one widely mentioned
attribute is the so-called economic benefit. The benefits recognized are network upgrade
deferral, reduced network loss and avoidance of electricity purchase. The authors of [15]
believe that “efficient economic systems require that those who create a benefit to
someone else be economically compensated”. If DG is found good to a system, it is
necessary to quantify its benefits and make them visible to regulators for the development
of incentives or commercial mechanisms that can allocate those benefits back to DG
owners and improve the profitability of their investment. In turn this encourages
implementation of DG that is valuable to the system and society as a whole. Specifically,
the same authors have offered a quantification of the deferral value (benefits of deferringsubstation and feeder investments) of a hypothetical DG in a testing system [16].
1.4 Generation Investment
The unbundling of generation assets from the grid has fundamentally abolished
the traditional concept of generation planning. There is no such entity as the vertically
integrated utility that could look for a least-cost generation expansion plan anymore.
Instead, generation companies sell electricity in competitive wholesale or spot market,
and through bilateral contracts. Their common objective is to maximize individual profits.
Generation investment models are very often evaluated in the context of bidding in day-
ahead spot market. Two main research areas that are under the hierarchy of generation
investment are identified: financial risk management of generator profit and valuation of
such generator.
1.4.1 Financial risk management of generator profit
Risk management and assessment of generator profit in contemporary electricity
markets is very broad, comprehensive survey papers [19] and [25] serve as good
introduction. Selected topic, for example, is the optimization of portfolio of contacts hold
by generation company. A portfolio of contracts comprises of revenue contracts and fuel
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contracts. A utility function, defined in terms of expected return of the portfolio, is
maximized subject to a stated level of risk denoted in standard deviation of the expected
return. A very general setting of portfolio comprising revenue contracts, including futures
contracts, and fuel contracts is constructed and then the tradeoff between return and risk
is illustrated by efficient frontier [26]. A slight modification to incorporate multi-market
conditions, both spot market and bilateral contract, is also found [20]. Other topics
include hedging generator operations with forward contracts [21] and futures contracts
[10]. Nevertheless, there is argument from the economist’s point of view that hedging by
electricity futures is not the same as other commodities [24]. A spot transaction in the
future can be hedged by the next-to-expire futures (futures with expiration date right afterthe transaction). The difference between the prospective spot price and the futures price,
called basis risk, would be normally small and stable as it is affected by delivery force
only. This is true for most commodities. However, electricity is non-storable, so
electricity price can fluctuate greatly with no guarantee that the price now would be
similar to the next hour’s due to, e.g. sudden forced outage. Hence basis risk would still
be large. More recently, with the prerequisite that the probability distribution of generator
profit in spot market is available [33], analytical formulae of common risk assessment
tools such as standard deviation, value-at-risk and conditional value-at-risk are also
derived [34]. References on financial risk management in electricity markets are made
very selectively and stopped here. In the next section, valuation of generator in spot
market will be carried on.
1.4.2 Valuation of generator in spot market
As a broad classification, generator valuation can be separated into price-based
unit commitment approach [7][8][9] and real option approach [27][28][29]. The
application of option theory for generator valuation by Deng et al. has received most
attentions. In their work, generator profit is modeled by a spark spread option, in which
its value is solved to be the expected value of a derivative (the derivative takes a
probability distribution) according to the Black-Scholes theory. However, the key
argument in option pricing, i.e., the formation of riskless portfolio leading to risk-
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neutrality is not valid for electricity price because electricity is non-storable. In view of
this, two works have been proposed. First, probability distributions of generator profit
based on two stochastic processes of electricity price, namely geometric Brownian
motion and geometric mean-reverting process [18], are analytically derived without
resorting to Black-Scholes theory [33]. Its simulation counterpart is also done [11].
Second, risk-adjusted valuation, instead of risk-neutral valuation of generator is
attempted [12]. These references collectively complete the literature review of the
development of generator valuation by real option approach.
1.5 Research Motivations
This thesis is concerned with wind power investment and development of its
analytical models. Yet, I start the thesis introduction by writing the conventional and
distributed generation planning, for a few reasons as below.
1. Problem formulations of generation planning in the framework of mathematical
programming or optimization are more or less the same and saturated, merely adding
renewable components such as wind power does not bring too much breakthrough.
2. Centralized generation planning has simply become obsolete in restructured
electricity markets. Generation investment should take place, yet how should
renewable investment be formulated remains as a research question. Renewable
investment could be a direct extension from conventional generation investment or
radically viewed from a new perspective.
3. Mathematical programming or optimization for distributed generation (includingrenewable) planning is reasonable, but its capability to analyze long-term DG
investment is questionable.
4. Optimization itself has some inherent weaknesses in handling financial aspects of
generation planning. Discount rates (fuel and electricity price expected returns,
project required return, etc.) are usually exogenously assumed, without inferring
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concrete reasoning to finance theories. In particular, fuel price volatilities are left
completely unattended, implying no measurement of financial risk.
5. Generation projects are huge and carry large projected cash flows. Discount rate is
very sensitive to project valuation, but its importance is usually overlooked [14].
6. It is believed that the financial approach, which can consistently accommodate
return and risk, is needed for renewable and wind power investment. Also, the
formulation has to be able to consider technical specific of renewable generation as
much as possible.
Generally speaking, there is no simple and readily available framework for windpower investment to be analysed by optimization or financial model. The problem
formulation has to be vetted from its underlying scenario, which mostly depends on the
market and regulatory rules for wind power. For example, wind energy could be paid at
spot market price, fixed feed-in tariff or its tender price. Meanwhile, wind power is
driven by national renewable energy target to various extents. All these market and
regulatory factors determine the right type of investment models and subsequent
valuation result of wind project. In Chapter 2, details of the market scenarios for wind
power will be described.
One clear policy driver of wind power is the renewable portfolio or target so that
wind power project has to be deployed before a certain deadline. It is not impossible for
wind power investment having no profit if it is built for political and environmental
concerns rather than actual cost-benefit consideration. Nevertheless, the investment
timing of renewable projects to comply the renewable target deadline is flexible before
the deadline. It may be better to build later rather than now. Hence there is a distinct
motivation to model wind power investment as a real option because the flexibility of
investment timing can be captured. Real option evaluation of wind power project based
on an appropriate scenario is the main theme of this work.
1.6 Objective and Expected Contribution
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The goal of this work is to create analytical models for wind power investment
analysis. Models would vary according to market scenarios, but the common objective is
to give assessment of the valuation of wind power projects, in course of the following
high-level considerations (not in order):
1. Investment models are formulated in consistence to finance theories, which apply
for any but not limited to generation projects.
2. Electricity market and regulatory rules should be properly addressed in the models.
3. Benefit of wind power to the society as a whole should be assessed, in particular, its
value should depend on how much fossil fuel saved [6][13][22]4. Economic viability of wind power itself is more appealing than the subsidized case.
5. Effects of wind variability can only be assessed in conjunction with the specifics of
individual power system where the wind farm is connected [4]. Generic investment
model applicable for different power system structures is preferred.
6. Sufficient technical or power system considerations should be incorporated into the
wind power investment models.
Investment models fulfilling the above considerations are expected to contribute to
investors a set of comprehensive and accurate valuation tools for wind power projects in
various market scenarios.
1.7 Thesis Outline
This thesis composes of six chapters. As we have gone through, Chapter 1 is anintroduction of generation planning and investment, which serves as a platform for
renewable investment to come into discussion. Research motivations and objectives are
also stated in this chapter. Chapter 2 is an overview of market scenarios for wind power
investment. In particular, it highlights four scenarios in which each scenario shall lead to
unique investment methodology. Out of the four, two scenarios will be further explored
in subsequent chapters, which collectively explain the development of the proposed
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analytical models of wind power investment. Chapter 3 is about the derivation of a
probabilistic wind power generation model. Chapter 4 is concerned with investment
analysis and capital structuring of wind power project under feed-in tariff. Chapter 5
offers a real option model of wind power investment from the perspective of utility.
Finally, conclusion is made in Chapter 6 to affirm accomplishment of the overall
objective of this research study. Every chapter, except this one, has a short summary or
future work. References are included at the end of each chapter. Derivations of formulae
are mostly kept in Appendix.
1.8 References
[1] Allen J. Wood and Bruce F. Wollenberg, Power Generation Operation and Control,
New York: Wiley, 1996.
[2] Andrew Keane and Mark O’Malley, "Optimal Allocation of Embedded Generation on
Distribution Network," IEEE Trans. Power System, Vol. 20, No. 3, pp. 1640-1646,
Aug 2005.
[3] B. G. Gorenstin, N. M. Campodonico, J. P. Costa and M. V. F. Pereira, "Power
System Expansion Planning under Uncertainty," IEEE Trans. Power System, Vol. 8,
No. 1, pp. 129-136, Feb 1993.
[4] Bart C. Ummels, Madeleine Gibescu, Engbert Pelgrum, Wil L. Kling, and Arno J.
Brand, “Impacts of Wind Power on Thermal Generation Unit Commitment and
Dispatch,” IEEE Trans. Energy Conversion, vol. 22, No. 1, pp. 44-51, March 2007.
[5] Birger Mo, Jan Hegge and Ivar Wangensteen, "Stochastic Generation Expansion
Planning by means of Stochastic Dynamic Programming," IEEE Trans. PowerSystem, Vol. 6, No. 2, pp. 662-668, May 1991.
[6] Brendan Fox, Damian Flynn, Leslie Bryans, Nick Jenkins, David Miborrow, Mark
O’Malley, Richard Watson, and Olimpo Anaya-Lara, Wind Power Integration,
Connection and System Operation Aspects, London: IET Power and Energy Series,
2007.
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[7] Chung-Li Tseng and Graydon Barz, “Short-Term Generation Asset Valuation,” in
Proc. the 32nd
Hawaii International Conference on System Sciences, 5-8 Jan 1999.
[8] Chung-Li Tseng and Graydon Barz, “Short-Term Generation Asset Valuation: A Real
Options Approach,” Operations Research, vol. 50, no. 2, pp. 297-310, Mar-Apr 2002.
[9] Erjiang Sun and Edwin Liu, “Generation Asset Valuation under market
Uncertainties,” in Proc. 2007 IEEE Power Engineering Society General Meeting,
Tampa.
[10] Eva Tanlapco, Jacques Lawarree and Chen-Ching Liu, "Hedging with Futures
Contracts in a Deregulated electricity Industry," IEEE Trans. Power Syst., Vol. 17,
No. 3, pp. 577-582, Aug 2002.[11] Felix F. Wu, Jifeng Su, Hui Zhou and Yunhe Hou, “Valuation of Generator Profit
from Spot Market: Simulation Approach,” submitted to IEEE Trans. Power System.
[12] Felix F. Wu, Yang, He Zhou and Yunhe Hou, “Risk-adjusted Valuation of
Generator Asset,” submitted to IEEE Trans. Power System.
[13] Hannele Holttinen and Jens Pedersen, "The Effect of Large Scale Wind Power on
a Thermal System Operation," in Proc. the 4th International Workshop on Large
Scale Integration of Wind Power and Transmission Networks for Offshore Wind
Farms, pp. E1-E7, 20-22 Oct. 2003.
[14] Hisham Khatib, Economic Evaluation of Projects in the Electricity Supply
Industry, IEE Power and Energy Series 44.
[15] Hugo A. Gil and Geza Joos, “Models for Quantifying the Economics Benefits of
Distributed Generation,” IEEE Trans. Power System, Vol. 23, No. 2, pp. 327-335,
May 2008.
[16] Hugo A. Gil and Geza Joos, “On the Quantification of the Network Capacity
Deferral Value of Distributed Generation,” IEEE Trans. Power System, Vol. 21, No.
4, pp. 1592-1599, Nov 2006.
[17] Jinxiang Zhu and Mo-yuen Chow, "A Review of Emerging Techniques on
Generation Expansion Planning," IEEE Trans. Power System, Vol. 12, No. 4, pp.
1722-1728, Nov 1997.
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[18] Julio J. Lucia and Eduardo S. Schwartz, “Electricity Prices and Power
Derivatives: Evidence from the Nordic Power Exchange,” Review of Derivatives
Research, 5, pp. 5-50, 2002.
[19] Min Liu, Felix F. Wu and Yixin Ni, “A Survey on Risk Management in
Electricity Markets,” in Proc. 2006 IEEE Power Engineering Society General
Meeting, Montreal.
[20] Min Liu and Felix F. Wu, “Managing Price Risk in a Multimarket Environment,”
IEEE Trans. Power Syst., Vol. 21, No. 4, pp. 1512-1519, Nov 2006.
[21] R. J. Kaye, H. R. Outhred and C. H. Barmister, “Forwards Contracts for the
Operation of an Electricity Industry under Spot Pricing,” IEEE Trans. Power Syst.,Vol. 5, No. 1, pp. 46-52, Feb 1990.
[22] R. N. Allan and Avella Corredor, “Reliability and economic assessment of
generating systems containing wind energy sources,” IEE Proc. C , Vol. 132, No. 1,
pp. 8-13, Jan 1985.
[23] R. R. Booth, "Optimal Generation Planning considering Uncertainty," IEEE
Trans. PAS , Vol. PAS-91, No. 1, pp. 70-77, 1972.
[24] Robert A. Collins, “The Economics of Electricity Hedging and a Proposed
Modification for the Futures Contract for Electricity,” IEEE Trans. on Power
Systems, vol. 17, no.1, pp. 100-107, Feb 2002.
[25] Robert Dahlgren, Chen-Ching Liu and Jacques Lawarree, "Risk Assessment in
energy Trading," IEEE Trans. Power Syst., Vol. 18, No. 2, pp. 503-511, May 2003.
[26] Roger Bjorgan, Chen-Ching Liu and Jacques Lawarree, "Financial Risk
Management in a Competitive Electricity market," IEEE Trans. Power Syst., Vol. 14,
No. 4, pp. 1285-1291, Nov 1999.
[27] Shijie Deng, “Financial methods in competitive electricity markets,” Ph.D.
dissertation, University of California, Berkeley, CA, 1998.
[28] Shijie Deng, Blake Johnson and Aram Sogomonian, “Spark Spread Options and
the Valuation of Electricity Generation Assets,” in Proc. the 32nd Hawaii
International Conference on System Sciences, 5-8 Jan 1999.
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[29] Shijie Deng, Blake Johnson and Aram Sogomonian, “Exotic electricity options
and the valuation of electricity generation and transmission assets,” Decision Support
Systems, 30, pp. 383-392, Jan 2001.
[30] Suresh K. Khator and Lawrence C. Leung, "Power Distribution Planning: A
Review of Models and Issues," IEEE Trans. Power System, Vol. 12, No. 3, pp. 1151-
1159, Aug 1997.
[31] Walid El-Khattam, Kankar Bhattacharya, Yasser Hegazy and M. M. A. Salama,
“Optimal Investment Planning for Distributed Generation in a Competitive Electricity
Market,” IEEE Trans. Power System, Vol. 19, No. 3, pp. 1674-1684, Aug 2004.
[32] William Rutz, Martin Becker, Frank E. Wicks and Stephen Yerazunis,"Sequential Objective Linear Programming for Generation Planning," IEEE Trans.
PAS , Vol. PAS-98, No. 6, pp. 2015-2021, Nov/Dec 1979.
[33] Yunhe Hou and F. F. Wu, “Valuation of Generator Profit from Spot Market:
Analytical Approach,” submitted to IEEE Trans. Power System.
[34] Yunhe Hou and F. F. Wu, “Risk Assessment of Generator Asset in Electricity
Markets: Analytical Approach,” submitted to IEEE Trans. Power System.
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Chapter 2
2 Market Scenarios for Wind Power Investment
Abstract
For any investment analysis, it is necessary to identify the relevant market
background before choosing the proper analytical tool or model. In this chapter, a numberof wind power investment scenarios are identified in accordance to modern electricity
market regimes. The two main scenarios are fixed tariff wind project by independent
power producers and wind power project undertaken by utility. Details of market
structure and regulation are discussed as far as investment modeling is concerned. It has
to be emphasized that different market scenarios would lead to different modeling
methodologies for best representing the reality. This chapter serves as introduction of the
rationale of modeling approaches chosen for the two highlighted scenarios that will be
further explored in subsequent Chapter 4 and 5.
2.1 Background and Scope
Chapter 1 has already outlined three topics in generation planning or investment,
namely, traditional generation expansion planning, distributed generation planning, and
generation investment in deregulated markets. They are problems corresponding to theirmarket regimes. It is important to recognize the type of market structure before inferring
to any planning or investment modeling methodology. Therefore in this chapter a survey
on modern electricity market rules and regulations for wind power development in some
major regions is first conducted. The survey is based on materials from a couple of
government regulatory issues, technical reports and internet resources rather than
academic papers, because the nature of materials is rather informative than research-
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oriented. Most importantly, the survey is classified into four different scenarios of wind
power investment: feed-in tariff, obligation for wind generation, wind power in spot
market, and auctioning, as follow in the remaining sections of this chapter. Some
contents in the survey are not limited to wind power but apply to the more general
renewable energy. Based on feed-in tariff and obligation, wind power investment models
will be derived and presented in subsequent chapters.
Several points were recognized and paid attention to when this survey was written.
First, market rules and regulations could be detailed and have many special cases, the
merit is to capture essential and generic parts but avoid unnecessary extensions. Second,
proper scenarios are identified for investment modeling with emphasis on the subject ofmaking the investment, i.e. who the investor is. Third, it should be borne in mind that
wind power development is not new upon the restructuring of electricity market. Rules
and regulations for wind power were there for some time and have also been evolving in
parallel to electricity market restructuring. In short, I try to capture and consolidate the
links between wind power pricing and modern electricity market in order to create a
starting point for further investment analysis.
2.2 Feed-in Tariff
Tariffs for renewable generation are mostly feed-in and fixed. Feed-in could be
understood as dispatch with higher priority. Since wind and solar are intermittent and
their powers non-dispatchable, and also for the purpose of promoting renewable, they are
dispatched before conventional generation. Tariffs are usually fixed for many years of
operation of the renewable installations, and are differentiated among different renewabletechnologies. Each unit of electricity generated is paid fixed throughout the whole period.
Such fixed tariffs usually have premium to provide guarantee return for the expensive
renewable investment, in which the premium is carefully assessed to balance between
investment incentive and consumer welfare.
Wind power development has a long history and was well before restructuring of
electricity markets in most regions. The wholesale generation bidding mechanism, on the
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other hand, is designed for big conventional generators. For two reasons wind power
producers do not find spot market an attractive platform to sell electricity. First the spot
price is low compared with wind power initial cost. Second, the mechanism of bidding
does not favour intermittent wind power radically. Therefore, something different is
needed to promote wind power, and feed-in tariff is observed to be prevalent.
An introduction of feed-in tariffs is found in [42]. Apart from the two basic
features of feed-in tariff (fixed and priority dispatch), very often the later the renewable
installation is built, the smaller is the tariff, whereas the already existed installations are
not affected. Such mechanism is called tariff degression, which creates an incentive to
boost renewable investment early and at the same time takes into account the generaldropping trend of renewable technology costs. The rate of degression is in annual
percentage reduction.
Two advocates of feed-in tariff are Germany and Spain, in particular German
feed-in tariff has been very aggressive. I try to highlight the German Renewable Energy
Sources Act [47] on both wind power and photovoltaics, and extract some of their tariff
structures for discussion in the coming two sub-sections. Readers who do not need
specific figures may jump over directly to the concluding remark of the suitable
investment modeling approach for feed-in tariff wind power.
2.2.1 German wind tariffs
The level of degression for wind energy commissioning in 2000 and 2004 are 1%
and 2% respectively, to recognize the cost reductions in manufacturing of wind turbines.
However, for offshore wind energy, the tariff remains the same as in 2000 and degression
comes only in 2008 at 2%. Tariffs are different for onshore and offshore wind turbines,
and furthermore there are two levels of tariffs for each type of turbine. The basic tariff for
onshore wind turbine commissioning in 2007 is €5.17 cents/kWh for 20 years. If, in the
first 5 years, the wind farm generates more than expected and reaches 150% of a
reference installation, the tariff for the corresponding period is increased to €8.19
cents/kWh. The 150% reference is not a target but only a reference. For every 0.75% the
generation falls short of the reference, the increased tariff period will be extended by two
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months. Such remedy tries to prevent excessive demand of windy site because less windy
site can enjoy longer period of higher tariff. However, there would be no fee if the
generation turns out to be less than 60% of the reference. After all, the degression still
applies. Table 2.1 summarizes the tariffs for both onshore and offshore wind farms.
Tariff (€ cents /
kWh)
Conditions for increased tariff
Type Start-up year 2004 2007
Basic tariff 5.9 5.17Onshore
Increased tariff 8.8 8.19
For the first 5 years if output reaches 150% of
reference, yet the period is extended 2 months for
every 0.75% falls short of 150%
Basic tariff 6.19 6.19Offshore
Increased tariff 9.1 9.1
For the first 12 years if site is 3 nautical miles off
the coast, extended half a month for every further
mile. Concurrently, high tariff period extended by
1.7 months for every metre in depth of water
deeper than 20m where turbines sit.
Table 2.1 Summary of German feed-in tariffs for land and sea wind power
2.2.2 German photovoltaic tariffs
Tariffs for photovoltaic (PV) installations are quite diversified, with classification
into installation methods (on buildings or open space) and capacities. Tariff degression
for open space PV (6.5%) is higher than that of building PV (5%). For easy reference,
Table 2.2 is a summary of feed-in tariffs for various photovoltaic installations.
Tariff (€ cents / kWh)
Start-up year 2004 2005 2006 2007
PV on buildings
100kWp 54 51.3 48.74 46.3
Façade bonus 5 5 5 5
Open space PV 45.7 43.42 40.6 37.96
Table 2.2 Summary of feed-in tariffs for various photovoltaic installations
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2.2.3 Concluding remark for investment modeling
Electricity market deregulation, as well as the environmental concern, provide
marketplace for independent renewable power producers. It is straightforward to analyze
wind power project by net present value (NPV) if the tariff structure is fixed and flat [38].
Apparently, the value of such a project is a simple annuity because both the price and
quantity of wind energy are passively fixed. There shall be no simple way to boost
project value in the level of operation. However, in terms of finance, capital structure has
something to do on firm value. Considering the minimal risk nature of such wind power
project, it should permit high leverage of the initial investment capital. I try to determine
the optimal debt level that maximizes firm value subject to operational characteristics of
wind power.
After all, evaluation of wind power investment under feed-in tariff is simple in
which NPV criterion is sufficient. By observing the regulatory and market factors for
wind power projects in contemporary electricity markets, it indeed leads to more
complicated investment scenarios. Specifically, I try to grasp the idea of large-scale wind
power project invested by distribution utility under certain types of policy obligations.
Policy obligations undertaken by two major parties, the US and the EU, will be explored
in coming sections.
2.3 Obligation – American Experiences
American support on renewables can be referenced from a National Renewable
Energy Laboratory (NREL) technical report [40], which encompasses wide coverage of
experiences of wind power development in US. The experiences are in the context of
policy drivers and market factors state by state. I try to summarize those attributes as
renewable portfolio standard (RPS), integrated resource planning (IRP), green power
programs and tax credit & production incentives as follow. While the technical report
illustrates each attribute by real scenarios involving the actual utilities and states, I would
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not completely exclusive from competitive electricity markets. For example, Xcel Energy
in Colorado was once required by the state utility commission to build large-scale wind
farms because wind power was cost-effective compared with gas-fired generation. It also
supplied wholesale wind power to other utilities. Deregulation could limit the ownership
right of wind power projects by utilities. Still, there was case that, e.g. utility in Oregon
called for wind power projects and purchasing agreement to meet its load growth, amid
high wholesale electricity prices. After all, whether an utility directly owns or contracts
wind power project is not important, the point is the utility is given an option to procure
electricity other than in wholesale bidding market. In short, IRP remains a driver of wind
power in some states.
2.3.3 Green Power Programs
There are a lot of green power programs across states. Basically green power
programs are options given to customers to buy electricity, or attribute their electricity
consumptions from renewable. Nowadays, provisions of such options are increasingly
compulsory across states. Green power programs are primarily realized by wind power.
The options are usually fixed-tariff contracts for some years. For a few reasons end-use
customers would switch to green power programs. It is not surprising that customers are
willing to pay more simply because of their environmental awareness. In states where the
standard or base electricity rates are higher, at the same time with large wind resources,
wind power price is actually cheaper by itself. Or some consumers may find slightly
elevated but fixed green power prices are reasonable hedge over the volatile retail
electricity prices.
Ownership of wind power project is an issue of green power program. In most
cases, wind power projects are owned by independent power producers (IPPs) or utilities.
If wind power project is owned by utility, corresponding green power program can be
marketed by the utility itself, or make it non-discriminative with the base rate. If it is
owned by IPP, implementation of green power program could depend on the extent of
deregulation. Power retailers market green power programs if there is retail competition.
Or the utility contracts wind power by power purchasing agreements, in which the wind
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capacity becomes part of its generation portfolio, and then offers its own green power
program.
2.3.4 Tax Credits and Production Incentives
1. Production tax credit
The production tax credit is a federal policy giving a tax credit for each unit of
electricity sold by qualified renewable facilities. The policy was originally created under
the 1992 Energy Policy Act, and has been extended and expanded quite a few times. The
up-to-date tax credit for wind power is (inflation-adjusted) $2.2 US¢/kWh and the wind
power facility has to be available by 31 Dec 2012 [46]. The duration of tax credit is 10
years counting from the facility in-service date. For renewable facilities owned by
utilities that do not have federal tax liabilities, the Renewable Energy Production
Incentive may support them alternatively.
2. Other tax and financial incentives
Other taxes, such as sales, investment and property taxes, may have abatements
subject to various states. Tax credit and financial incentive are the most straightforward
way to boost and subsidize renewable investment. Yet they are the least market-based
approaches and their extents may lack justification.
3. PURPA
Public Utility Regulatory Policies Act (PURPA) is another federal policy driver,
which was strongly implemented by California in 1980s. Under PURPA, the California
Public Utilities Commission (CPUC) required its utilities to procure electricity from
qualifying renewable facilities at the utility’s avoided cost. The purchasing contracts are
approved long-term and at high prices and included capacity as well as energy payments.
Properly because the offer is too generous, the PURPA contract was too popular and was
subsequently suspended in 1985. Mid-1990s was a short sluggish period of wind power
when previous PURPA contracts began to expire.
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4. System/Public benefits funds
Following the sunset of PURPA contracts, California’s 1996 electric industry
restructuring legislation (AB 1890) mandated the three major investor-owned utilities to
collect surcharge on all electricity consumption to create a fund pool, known as
System/Public Benefits Funds, for supporting renewable development. Simply put, the
public benefits funds are like production incentive on each unit of electricity generated
from renewable facilities along a pre-defined period. Wind power is one of the qualifying
renewable facilities. The funds may need to be auctioned. Again the legislation has been
revised and extended, the latest version could be found in [44].
2.3.5 Concluding remark for investment modeling
The renewable portfolio standard leads to a unique scenario of utility wind power
investment. The investment decision is somehow passive because it has to conform to the
renewable target and deadline. Modeling the valuation of wind power project by
American real option is suggested. Furthermore, availability of green power program
allows distribution utility to attribute wind power production to other renewable IPP.
Although distribution utility may not directly own generation assets after deregulation,
one can still analyze the economic performance of a wind power project in terms of
bilateral contracts, as if the project an indirect investment of the utility.
2.4 Obligation – European Experiences
The European commitments on climate change can be referenced from a series of
measures stipulated by the European Union. Similar to the US renewable portfolio
standard, EU also has a target percentage of renewable shares in total energy
consumption. Furthermore EU has a target on emissions reduction. Collectively the
targets are so-called the EU energy and climate package. Apart from setting targets, EU
introduced an Emissions Trading Scheme (ETS) in which the industrial and power
generating parties from all its member states trade European Union Allowances (EUAs),
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commonly known as emission allowances to compensate for emissions produced.
Background of EU ETS is widely available on the Internet or in paper’s introduction such
as [50]. Nevertheless, both the EU energy and climate package and the ETS will be
briefly mentioned in the following sections.
2.4.1 EU Energy and Climate Package
The EU energy and climate package is a bundle of policy targets on energy and
emission issues binding on all its member states. The three targets, so-called 20-20-20,
are as follow.
1. To reduce emission of greenhouse gases by at least 20% compared to the level in
1990 by 2020.
2. To increase the share of renewables in the total energy consumption (including
transport systems) to 20% by 2020.
3. To achieve energy efficiency of 20% improved over the current status by 2020.
For convenience, the following simplifications on those targets are assumed:
1. The emission target means the same for carbon dioxide.
2. How the renewable burden sharing on all EU member states are ignored.
3. The transport sector is neglected.
4. A fixed percentage of wind power is assumed out of the 20% target.
2.4.2 EU Emission Trading System
A. Background of Kyoto Protocol
The aim of Kyoto Protocol is to reduce global greenhouse gas (GHG) emissions
by a certain date. Governments who have ratified this treaty can be separated into two
categories: developed countries (Annex 1) and developing countries (Non-annex 1). As
of January 2008, Annex 1 countries have to reduce their GHG emissions by a collective
average of 5% below their 1990 levels by December 2012. The levels of reduction are
specified for each party who ratified the Protocol. This figure actually corresponds to
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some 15% below the GHG emissions in 2008 for many EU member states. Among EU
member states, the actual emissions reduction may range from an average of 8%
(compared to 1990’s) to an emission increase from some less-developed EU countries.
Non-annex 1 countries do not have any restrictions on GHG emissions, but may
participate in the clean development mechanism (CDM) in which when a GHG emission
reduction project is implemented within them, certified emission reductions (CER) would
be earned and can be sold to Annex 1 countries. Annex 1 countries could meet the
emissions caps by purchasing emission allowances from other parties (presumably one
allowance is granted for one permissible tonne of GHG emissions for all Annex 1
countries). Failing to comply will be penalized by having to submit 1.3 emissionallowances for every tonne of GHG emissions in the second commitment period starting
from 2013. International talks have started on matters of second commitment period.
B. European Union Emission Trading Scheme (EU ETS)
EU ETS is a trading system especially for EU member states to trade emission
allowances. Its existence is closely related to the fulfilment of Kyoto Protocol for EU
member states but in fact it had started before Kyoto Protocol was kicked off. European
Union Allowances (EUA), the formal name of emission allowances, are granted to plant
operators for free (grandfathering) according their historical emission levels with
reductions. The allowances are given out for a sequence of several years at once so that
plant operators can neutralize annual irregularities in GHG emissions. The first phase of
EU ETS ended in December 2007 and it was found that the verified emissions between
2005 and 2007 still experienced an increase. The reason is that individual countries
granted the allowances loosely and as a result the price of allowances also dropped to
nearly zero by the end of 2007. Working closely with the Kyoto Protocol, changes
proposed for 2013 onwards (second commitment period of Kyoto Protocol) include
centralized allocation, a migration to auctioning a greater share of allowances instead of
grandfathering and also potentially, a more stringent emissions cap.
2.4.3 Nordic Energy Perspectives
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Nordic Energy Perspectives (NEP) is an interdisciplinary research project on the
Nordic energy systems. It has a number of energy system models, collectively known as
NEP model toolbox. The models are able to analyse relevant policy instruments and
market factors, then demonstrates their influence and impact on energy markets and
systems. Electrical system is the main subset of the broader sense energy system. The
targets of the EU energy and climate package constitute a few main scenarios for NEP
models to work on. The development of Nordic energy sector is analysed and forecasted
through these scenarios. Results of the NEP analysis are projected based on targets of the
package. The main objective of the NEP project is to demonstrate to stakeholders of the
Nordic energy sector any anticipated effect of following the EU as well as global energyand climate policies.
The NEP project has gone through its first phase during 2005-2006. Results of its
second phase carried out during 2007-2010 have been recently released. The results
compose of three main documents. The first one is an offprint known as Ten
Opportunities and Challenges for Nordic Energy [51], the second one is a full report
called Towards a Sustainable Nordic Energy System [52] and the third one is about
model toolbox descriptions called Coordinated use of Energy system models in energy
and climate policy analysis [37].
The full report of NEP contains very comprehensive analysis and projected results
based on various scenarios. By no means I extract and compare any results here again.
Instead I am going to highlight a few parts of the modeling methodology in the NEP
project for discussion as follow.
2.4.4 NEP Modelling Methodology
Reference [37] is a standalone book written on the modeling methodology
employed by the NEP project. It serves the following important purposes. First, it
describes the energy-systems modeling methodology in general and the use of different
approaches in NEP in particular. Second, it presents how various models within the NEP
model toolbox are coordinated through synchronization of model assumptions and input
parameters. Third, it illustrates how the models of the NEP project function, their
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performance and model output achieved. The aim of writing [37] is not to pinpoint model
result in itself; insights and model results of the broader sense energy issue should be
obtained from the main NEP report [52]. For simulation results specific to the Nordic
electricity market, such as electricity production, investments, electricity prices, cross-
border transactions, carbon dioxide emitted from power industry, etc., [39] is a good
reference.
A. Energy-systems modelling
Energy-systems modelling deals with models on energy issues. It may cover theentire energy system including transports and heating systems, or just a subset of the
energy system, notably the electrical system. The key function of modelling is the ability
to transform complex reality into simpler and yet representative enough model that is
suitable to analyse and able to predict, here matters in relation to the energy issues.
Energy-systems modelling can differ in a few ways. In terms of mathematical
formulation, models can be descriptive (simulating models) or normative (optimization
models). They can also be classified into bottom-up models and top-down models. For
bottom-up electrical system models, they are mostly technology-oriented and treat
demand forecast as exogenously given. Energy demand is supplied by various generation
technologies, and technological change takes place through phasing out of existing
technologies by new technologies according to cost performance. Effectively bottom-up
electrical system models belong to optimization problem. If the energy demand is a
function of other parameters, say electricity price, then the model may be regarded as
partial-equilibrium model. The original electrical system model becomes part of the
macro-economy only and the relationship between its energy demand and other economic
variables is governed by elasticity of substitution. It then becomes the so-called top-
bottom model, in which it endogenizes the macroeconomic development through changes
on parameters of the energy system. Naturally, top-down models have little technological
explicitness compared to bottom-up models.
Energy system models can also be grouped by modeling approaches in which two
main types are techno/engineering-economic model and general/partial equilibrium
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model. Concise descriptions and comparisons of the two are included in [37]. Here I only
make a little supplement. In power system literature, generation expansion planning
problems of various complexities and depths are solved by optimization or linear
programming methods. They belong to the type of techno/engineering-economic model.
For energy system models as part of the macro economy, they could be dynamic with
time and belong to general/partial equilibrium model. Using equilibrium models to
describe energy systems generally contains less technological detail.
In NEP model toolbo
