Hedging the Risk of Renewable Energy Sources in Electricity

Outline
RES penetration
Case study
Modeling
Results
Conclusions
Hedging the Risk of Renewable Energy Sources
in Electricity Production
Giorgia Oggioni1
Cristian Pelizzari2
Mercati energetici e metodi quantitativi:
un ponte tra Università e Aziende
Padova
October 8th, 2015
1
University of Brescia, Department of Economics and Management, 25122 Brescia, Italy. E-mail:
giorgia.oggioni@unibs.it.
2
University of Brescia, Department of Economics and Management, 25122 Brescia, Italy. E-mail:
cristian.pelizzari@unibs.it.
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Outline
RES penetration
Case study
Modeling
Results
Conclusions
Outline
1
Effects of renewable energy sources penetration
2
Wind strategies
3
Modeling wind penetration in a risk neutral world
Reference equilibrium model: no wind energy production
Modeling wind energy production
4
Results
5
Conclusions
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Outline
RES penetration
Case study
Modeling
Results
Conclusions
The 20-20-20 European targets
Europe 2020, the 2020 climate and energy package, sets demanding climate and
energy targets to be met by 2020, known as the “20-20-20” targets:
20% reduction of GHG emissions by 2020 compared to 1990 through the EU
Emissions Trading System (Directives 2003/87/EC and 2009/29/EC);
20% share of renewable energy sources (RES) based energy in final energy
consumption by 2020 (Directive 2009/28/EC);
20% reduction in EU primary energy consumption by 2020, compared with
projected levels, to be achieved by improving energy efficiency.
In addition, Europe 2030, 2030 framework for climate and energy policies, and
Europe 2050, Roadmap for moving to a low-carbon economy in 2050, set more
ambitious objectives, to the aim of a full decarbonization of the energy sector.
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Outline
RES penetration
Case study
Modeling
Results
Conclusions
Effects of RES penetration
BUT RES penetration implies:
1
Intermittence of energy production;
2
Reduction of electricity prices that implies a significant revenue drop and
thus:
reduction of incentives to invest in conventional power plants;
mothballing and/or dismantling of existing power plants,
with the result that the security of supply becomes riskier and riskier.
RES penetration has some side effects that need to be quantified in relation to the
relevant market design!
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0
Outline
RES penetration
Case study
BULGARIA
690.5
Modeling
ITALY
8,662.9
PORTUGAL*
4,914.4
Results
Conclusions
FYROM**
37
SPAIN
22,986.5
TURKEY
3,762.5
GREECE
1,979.8
Wind installed capacity in Europe
MALTA
0
Installed End 2013 Installed
2013
2014
EU Capacity (MW)
Austria
308.4
1,683.8
411.2
Belgium
275.6
1,665.5
293.5
Bulgaria
7.1
681,1
9.4
Croatia
81.2
260.8
85.7
Cyprus
146.7
Czech Republic
8
268.1
14
Denmark*
694.5
4,807
67
Estonia
10.5
279.9
22.8
Finland
163.3
449
184
France
630
8,243
1,042
Germany
3,238,4 34,250.2 5,279,2
Greece
116.2
1,865,9
113.9
Hungary
329.2
Ireland
343.6
2,049.3
222.4
Italy
437.7
8,557.9
107.5
Latvia
2.2
61.8
Lithuania
16.2
278.8
0.5
Luxembourg
58.3
Malta
Netherlands
295
2,671
141
Poland
893.5
3,389.5
444.3
Portugal*
200
4,730.4
184
Romania
694.6
2,599.6
354
Slovakia
3.1
Slovenia
2.3
2.3
0.9
Spain
175.1 22,959.1
27.5
Sweden
689
4,381.6 1,050.2
UK
2,075
10,710.9 1,736.4
12,440.3
Total EU-28
128,751.4
11,357.3
117,383.6 11,791.4
End
2014
2,095
1,959
690.5
346.5
146.7
281.5
4,845
302.7
627
9,285
39,165
1,979.8
329,2
2,271.7
8,662.9
61.8
279.3
58.3
2,805
3,833.8
4,914.4
2,953.6
3.1
3.2
22,986.5
5,424.8
European Union: 128,751.4 MW
Candidate Countries: 3,799.5 MW
EFTA: 882.6 MW
Total Europe: 133,968.2 MW
Installed 2013
Candidate Countries (MW)
FYROM
Serbia
Turkey
646.3
Total
646.3
EFTA (MW)
Iceland
1.8
Liechtenstein
Norway
110
Switzerland
13.3
Total
Other (MW)
Belarus
Faroe Islands
Russia
Ukraine
Total
Total Europe
End 2013
CYPRUS
146.7
Installed 2014
End 2014
2,958.5
2,958.5
37
804
841
37
3,762.5
3,799.5
1.8
771.3
60.3
1.2
48
-
3
819.3
60.3
125.1
833.4
49.2
882.6
4.5
95.3
99.8
12,228.5
3.4
6.6
15.4
371.2
396.7
11.7
126.3
138.0
12,819.6
3.4
18.3
15.4
497.5
534.7
133,968.2
121,572.2
* Provisional data
** Former Yugoslav Republic of Macedonia
Note: due to previous year adjustments, 423.5 MW of project decommissioning, repowering and
rounding of figures, the total 2014 end-of-year cumulative capacity is not exactly equivalent to
the sum of the 2013 end-of-year total plus the 2014 additions.
EWEA (2015). Wind in Power - 2014 European Statistics. Available at http://www.ewea.
THE EUROPEAN WIND ENERGY ASSOCIATION
org/fileadmin/files/library/publications/statistics/EWEA-Annual-Statistics-2014.pdf.
4
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Outline
RES penetration
Case study
Modeling
Results
Conclusions
Wind strategies
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Outline
RES penetration
Case study
Modeling
Results
Conclusions
Wind policies and assumptions
Wind penetration levels
1
2
No wind penetration (reference case without wind production);
Wind penetration (priority dispatch).
Load and wind electricity production uncertainty
1
Load and wind-power scenarios.
Wind derivatives (in a risk neutral world)
1
2
3
Call option (hedge of “too strong” wind);
Put option (hedge of “too weak” wind);
Monte Carlo pricing based on wind speed scenarios.
Link between wind speed scenarios and load/wind-power scenarios
1
2
3
closeness of simulated wind-power duration curves to observed wind-power
duration curve;
probability distribution of observed distances;
probabilistic assignment of wind speed scenarios to wind-power scenarios.
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Outline
RES penetration
Case study
Modeling
Results
Conclusions
Reference equilibrium model:
no wind energy production
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Modeling
Results
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Notation
Sets
m ∈ M : Set of plant types. M = res ∪ conv, where res and conv respectively
indicate wind and conventional power plants;
b ∈ B: Set of demand blocks.
Parameters
Gm : Capacity of plant type m (MW);
db : Power consumed in block b (MWh);
cm : Variable costs of plant type m (e/MWh);
em : Emission factor associated to plant type m (ton/MWh);
pCO2 : Allowance price (e/ton);
pc: Price cap (e/MWh);
Hb : Duration in hours of each block b.
Variables
gb,m : Power generated in block b by plant type m (MWh);
gsb : Power sold in block b (MWh);
nb : Shortage in block b (MWh);
pb : Electricity price in block b (e/MWh).
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Outline
RES penetration
Case study
Modeling
Results
Conclusions
Reference equilibrium model
Generator’s profit maximization problem
"
X
X
Max
Hb · pb · gsb −
cm · gb,m − pCO2 ·
b
m∈conv
#
X
em · gb,m
m∈conv
subject to:
Gm − gb,m ≥ 0
(ϕb,m )
X
gb,m = gsb
∀b
∀m ∈ conv
(ηb )
∀b
m∈conv
gb,m ≥ 0
∀b
∀m ∈ conv
gsb ≥ 0
∀b
Clearing of the energy market
Min
X
Hb · pc · nb
b
subject to:
gsb + nb − db = 0
nb ≥ 0
(pb )
∀b
∀b
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Outline
RES penetration
Case study
Modeling
Results
Conclusions
Complementarity formulation of the reference equilibrium model
0 ≤ cm + em · pCO2 + ϕb,m − ηb ⊥gb,m ≥ 0
0 ≤ −pb + ηb ⊥ gsb ≥ 0
∀b
∀m ∈ conv
∀b
0 ≤ Gm − gpb,m ⊥ ϕb,m ≥ 0 ∀ b ∀m ∈ conv
X
gb,m − gsb = 0 (ηb f ree) ∀ b
m∈conv
gsb + nb − db = 0
(pb
0 ≤ pc − pb ⊥ nb ≥ 0
f ree)
∀b
∀b
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RES penetration
Case study
Modeling
Results
Conclusions
Modeling wind energy production
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Outline
RES penetration
Case study
Modeling
Results
Conclusions
Notation
Additional Sets
s ∈ S: Set of scenarios considered in each block b.
Additional Parameters
θs,b : Wind power capacity factor in scenario s and block b (%);
ds,b : Power consumed in scenario s and block b (MWh);
τs,b : Probability of scenario s associated to block b;
α: Wind derivative (call/put option) price (e/MWh);
βs,b : Wind derivative (call/put option) payoff in scenario s and block b (e/MWh).
Variables
gs,b,m : Power generated in scenario s and block b by existing plant of type m (MWh);
gss,b : Power sold in scenario s and block b (MWh);
ns,b : Shortage in scenario s and block b (MWh);
ps,b : Electricity price in scenario s and block b (e/MWh).
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Outline
RES penetration
Case study
Modeling
Results
Conclusions
Generator’s profit maximization problem
Max
X
τs,b · Hb · pb · gss,b −
s,b
−
X
τs,b · Hb ·
τs,b · Hb · pCO2 ·
X
X
em · gs,b,m
m∈conv
s,b
+
cm · gs,b,m
m
s,b
X
X
τs,b · Hb · (βs,b − α) ·
X
gs,b,m
m∈res
s,b
subject to:
Gm − gs,b,m ≥ 0
(ϕs,b,m )
∀s, b
∀m ∈ conv
Gm · θs,b − gs,b,m ≥ 0
(ϕs,b,m ) ∀s, b ∀m ∈ res
X
gs,b,m = gss,b
(ηs,b ) ∀s, b
m
gs,b,m ≥ 0
gss,b ≥ 0
∀s, b, m
∀s, b
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Outline
RES penetration
Case study
Modeling
Results
Conclusions
Clearing of the energy market
Min
X
τs,b · Hb · pc · ns,b
s,b
subject to:
gss,b + ns,b − ds,b = 0
ns,b ≥ 0
(ps,b )
∀s, b
∀s, b
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RES penetration
Case study
Modeling
Results
Conclusions
Complementarity formulation of the wind equilibrium model
0 ≤ cm + em · pCO2 + ϕs,b,m − ηs,b ⊥gs,b,m ≥ 0
∀ s, b
∀m ∈ conv
0 ≤ cm + ϕs,b,m − ηs,b + α − βs,b ⊥gs,b,m ≥ 0
∀ s, b
∀m ∈ res
0 ≤ −ps,b + ηs,b ⊥ gss,b ≥ 0
0 ≤ Gm − gs,b,m ⊥ ϕs,b,m ≥ 0
∀ s, b
∀ s, b
∀m ∈ conv
0 ≤ Gm · θs,b − gs,b,m ⊥ ϕs,b,m ≥ 0 ∀ s, b ∀m ∈ res
X
gs,b,m − gss,b = 0 (ηs,b f ree) ∀ s, b
m
gss,b + ns,b − ds,b = 0
(ps,b
0 ≤ pc − ps,b ⊥ ns,b ≥ 0
f ree)
∀s, b
∀ s, b
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Outline
RES penetration
Case study
Modeling
Results
Conclusions
Wind derivatives
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Outline
RES penetration
Case study
Modeling
Results
Conclusions
Wind derivatives: call and put option payoffs
t: hour of the reference year, t ∈ {1, ..., 8760}
Wt : wind speed at hour t, measured in m/s
Wind call option
designed to hedge “too strong” wind: it pays for hours with wind speed
higher than a “strike price”
strike price x × w̄t,Y : for each hour t, it is a factor x of the average wind
speed w̄t,Y of the previous Y years
χ: conversion coefficient from m/s to e/MWh
expiration: end of the reference year
Asian style option: the option sums the excess wind speeds of each hour of
the reference year
payoff:
8760
X
payof fc =
χ max(0, Wt − x × w̄t,Y )
t=1
Wind put option
hedging of “too weak” wind
payoff:
payof fp =
8760
X
χ max(0, x × w̄t,Y − Wt )
t=1
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Modeling
Results
Conclusions
Wind derivatives: call and put option prices
Pricing of wind options
Call option fair price:
αc = e
−r
EQ (payof fc )
assumptions: r (continuously compounded interest rate on an annual basis),
Q ≡ P (risk neutral world)
Monte Carlo method:
generate N wind speed scenarios
evaluate the option payoff for each wind speed scenario
average the N option payoffs
take the previous average as an approximation of EQ (payof fc )
PN
i=1 payof fc,i
,
EQ (payof fc ) ≈
N
where payof fc,i is the call payoff (in e/MWh) associated to wind speed
scenario i
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RES penetration
Case study
Modeling
Results
Conclusions
Wind derivatives: wind speed scenarios
Input data: Hourly wind speeds of Germany in 2014
Data from NCAR are u-components and v-components of wind collected
every 6 hours at 10 metre heights on a grid of 48 intersection points between
parallels and meridians, transformed into wind speeds and then made hourly
N = 100
Scenarios are based on Weibull distributions fitted on the 6-hour 48-point grid
data, then made hourly
Dependence of data is indirectly taken into account because scenarios are
composed of wind speeds with the same time order of the input data
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Wind derivatives: other settings
Strike price:
w̄t,Y : hourly average of German wind speeds in the last 12 years
(2002 − 2013)
call option: x is set equal to 1.01, 1.03, 1.05, 1.10, 1.15, and 1.20
put option: x is set equal to 0.99, 0.97, 0.95, 0.90, 0.85, and 0.80
r = 0.05%
Conversion coefficient χ based on the slope coefficient of a linear regression
model fitted to the 2014 data of wind speeds and wind electricity productions
in Germany
100 wind speed scenarios (and corresponding option payoffs) assigned
probabilistically to the 36 load/wind-power scenarios based on their closeness
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Link between wind speed scenarios
and load/wind-power scenarios
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RES penetration
Case study
Modeling
Results
Conclusions
Load/Wind-power scenarios
1.00
0.80
0.90
0.70
0.80
0.60
0.70
0.50
Wind factor
Demand factor
0.60
0.50
0.40
0.40
0.30
0.30
0.20
0.20
0.10
0.10
0.00
0.00
1
501
1001
1501
2001
2501
3001
3501
4001
4501
Hour
5001
5501
6001
6501
7001
7501
8001
8501
1
501
1001
1501
2001
2501
3001
3501
4001
4501
Hour
5001
5501
6001
6501
7001
7501
8001
8501
Figure: Load and wind-power capacity factor duration curves of Germany in 2014 - 3
levels for each of the 4 blocks of the load and wind-power duration curves.
Scenarios based on the load and wind-power capacity factor duration curves
of Germany in 2014.
A total of 36 scenarios, 3 levels of wind-power capacity factors times 3 levels
of load capacity factors times 4 load blocks.
Baringo, L., A.J., Conejo (2013). Correlated wind-power production and electric load
scenarios for investment decisions, Applied Energy, 101, 475–482.
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Case study
Modeling
Results
Conclusions
Link between wind speed scenarios and load/wind-power scenarios (1)
IDEA
assess the similarity of each wind speed scenario generated for the wind
derivatives to the wind-power scenarios of the equilibrium model
assign wind speed scenarios to wind-power scenarios in a probabilistic way,
in particular option payoffs payof fc,i and payof fp,i , with i = 1, ..., 100
do this for each of the 4 load blocks
calculate the option payoffs, βs,b,c and βs,b,p for the call and the put
respectively, for each wind-power scenario and load block as the average of
the option payoffs assignments
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Link between wind speed scenarios and load/wind-power scenarios (2)
35000
30000
Wind electricity production (MWh)
25000
20000
15000
10000
5000
0
0
1
2
3
4
5
Wind speed (m/s)
6
7
8
9
Figure: Wind electricity production against wind speed in Germany in 2014.
Lydia, M., Kumar, S.S., Selvakumar, A.I., and G.E.P., Kumar (2015). Wind resource
estimation using wind speed and power curve models, Renewable Energy, 83, 425–434.
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Modeling
Results
Conclusions
Link between wind speed scenarios and load/wind-power scenarios (3)
Sigmoid regression model fitted to the 2014 data of wind speeds and wind
electricity productions in Germany
Each wind speed scenario transformed into a wind electricity production
scenario
Sigmoid function value altered by a normally distributed number accounting
for variability of production at different speeds
Wind-power capacity factors calculated for each wind electricity
production scenario
Assessment of closeness of capacity factors of wind electricity production
scenarios to capacity factors of wind-power scenarios (capacity factors
adjusted by their standard deviation)
Probability distribution estimation with higher probability to lower
absolute differences
Probabilistic assignment of wind electricity production scenarios to
wind-power scenarios
The last 3 steps repeated for each load block
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Modeling
Results
Conclusions
Model additional assumptions
Input data of the equilibrium model
Electricity market: Germany
Reference year: 2014
EU-ETS
No EU-ETS: CO2 price 0 e/ton
EU-ETS: CO2 price 40 and 50 e/ton
Available technologies
RES based plants: wind
Conventional plants: nuclear, lignite, coal, CCGT, oil
Conventional plant dismantling/mothballing
Dismantling of 30% of the available nuclear capacity
Mothballing of 30% of the available CCGT capacity
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Results
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Outline
RES penetration
Case study
Modeling
Results
Conclusions
No wind penetration
Production per block and technology in MWh (reference capacity)
80,000 70,000 60,000 50,000 Electricity produc.on (MWh) Oil Gas 40,000 Coal Lignite Nuclear 30,000 Wind 20,000 10,000 0 No EU-­‐ETS EU-­‐ETS 40 EU-­‐ETS 50 No EU-­‐ETS EU-­‐ETS 40 EU-­‐ETS 50 No EU-­‐ETS EU-­‐ETS 40 EU-­‐ETS 50 No EU-­‐ETS EU-­‐ETS 40 EU-­‐ETS 50 Block 1 Block 2 Block 3 Block 4 29/ 38
Outline
RES penetration
Case study
Modeling
Results
Conclusions
No wind penetration
Profits (Ke)
No EU-ETS
Revenues
Costs
Reference capacity
70% nuclear
70% CCGT
70%-70%
21,525,027
169,904,105
180,108,829
831,852,306
8,928,503
9,578,034
8,978,623
10,000,624
-
-
-
-
12,596,524
160,326,071
171,130,206
821,851,683
Emissions
Profits
EU-ETS CO2 40 e/ton
Revenues
Costs
Emissions
Profits
33,501,692
180,059,147
193,309,454
837,123,275
8,957,224
9,594,775
9,007,344
10,017,365
14,519,622
15,054,114
14,450,594
14,982,118
10,024,845
155,410,259
169,851,516
812,123,792
EU-ETS CO2 50 e/ton
Revenues
37,172,267
183,274,317
196,989,411
Costs
11,480,140
10,407,480
11,748,578
Emissions
15,393,016
16,458,072
16,528,039
Profits
10,299,110
155,067,667
170,053,892
838,820,818
11,219,308
17,408,326
810,193,183
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No Wind vs. Wind penetration
Prices e/MWh, no EU-ETS
Wind
No wind
1600.00
1400.00
1200.00
1000.00
800.00
600.00
400.00
200.00
0.00
Initial capacity
70% nuclear
70% CCGT
70%-70%
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Wind penetration
Production per block and technology in MWh (reference capacity)
80,000 70,000 Electricity produc.on (MWh) 60,000 50,000 Oil Gas 40,000 Coal Lignite Nuclear 30,000 Wind 20,000 10,000 0 No EU-­‐ETS EU-­‐ETS 40 EU-­‐ETS 50 No EU-­‐ETS EU-­‐ETS 40 EU-­‐ETS 50 No EU-­‐ETS EU-­‐ETS 40 EU-­‐ETS 50 No EU-­‐ETS EU-­‐ETS 40 EU-­‐ETS 50 Block 1 Block 2 Block 3 Block 4 32/ 38
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RES penetration
Case study
Modeling
Reference capacity
70% nuclear
70% CCGT
70%-70%
21,135,150
38,868,742
105,009,753
327,265,260
Wind revenues
1,640,170
2,184,352
4,932,441
20,060,014
Costs
7,080,919
7,661,617
7,170,246
7,825,957
-
-
-
-
15,694,402
33,391,476
102,771,947
339,499,317
Results
Conclusions
Wind penetration
Profits (Ke)
No EU-ETS
Revenues
Emissions
Profits
EU-ETS CO2 40 e/ton
Revenues
32,857,787
49,625,557
117,120,313
335,587,664
Wind revenues
3,535,022
3,892,320
6,873,776
21,629,047
Costs
7,211,097
7,753,520
7,300,424
7,917,860
12,694,553
13,403,830
12,684,668
13,370,863
32,360,527
104,008,997
335,927,989
Emissions
Profits
16,487,159
EU-ETS CO2 50 e/ton
Revenues
36,272,524
52,866,220
120,522,051
338,189,507
4,030,516
4,368,912
7,396,694
22,083,426
Costs
10,282,913
10,615,683
9,263,817
9,715,466
Emissions
12,530,962
13,639,757
13,715,935
14,750,785
Wind revenues
Profits
17,489,166
32,979,692
104,938,993
335,806,682
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Results
Conclusions
Introducing call options
Wind electricity production (MWh)
Call payoff net of call price (e)
100,000,000
30,000
29,000
50,000,000
28,000
Call 1%
Call 3%
Call 5%
Call 10%
Call 15%
Call 20%
27,000
No EU-ETS
No EU-ETS
-50,000,000
EU-ETS
EU-ETS
26,000
-100,000,000
25,000
24,000
-150,000,000
23,000
No Call
Call 1%
Call 3%
Call 5%
Call 10%
Call 15%
Call 20%
-200,000,000
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Introducing put options
Wind electricity production (MWh)
Put payoff net of put price (e)
300,000,000
35,000
30,000
250,000,000
25,000
200,000,000
20,000
No EU-ETS
No EU-ETS
150,000,000
EU-ETS
EU-ETS
15,000
100,000,000
10,000
50,000,000
5,000
No Put
Put 1%
Put 3%
Put 5%
Put 10%
Put 15%
Put 20%
Put 1%
Put 3%
Put 5%
Put 10%
Put 15%
Put 20%
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Outline
RES penetration
Case study
Modeling
Results
Conclusions
Both call and put options
Call and put payoffs net of
corresponding call and put prices (e)
Wind electricity production (MWh)
29,200
180,000,000
29,000
160,000,000
140,000,000
28,800
120,000,000
No EU-ETS
28,600
EU-ETS
100,000,000
No EU-ETS
EU-ETS
80,000,000
28,400
60,000,000
40,000,000
28,200
20,000,000
28,000
No Call-Put Call-Put 1% Call-Put 3% Call-Put 5% Call-Put 10% Call-Put 15% Call-Put 20%
Call-Put 1%
Call-Put 3%
Call-Put 5%
Call-Put 10%
Call-Put 15%
Call-Put 20%
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Outline
RES penetration
Case study
Modeling
Results
Conclusions
Conclusions and further steps
Options can be beneficial, with exceptions (that could be the reason of a
small (and OTC) market of wind derivatives)
Design of scenarios to favor an integration between a financial approach and
an (economic) equilibrium approach
Consider a risk averse world by introducing a Value-at-Risk-based objective
function on the side of the electricity producer in the equilibrium model and a
market price of risk for the underlying asset (wind speed) of the wind
derivatives
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Outline
RES penetration
Case study
Modeling
Results
Conclusions
Thank you for your attention!
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