1. Introduction
DAM/RTM Dynamic model
Multi-settlement Electricity Market
Who Commands the Wind?
Numerical Results
Concluding Remarks
The Value of Volatile Resources
in Electricity Markets
Sean P. Meyn
Joint work with: Matias Negrete-Pincetic, Gui Wang, Anupama Kowli, Ehsan
Shafieeporfaard, and In-Koo Cho
Coordinated Science Laboratory
and the Department of Electrical and Computer Engineering
University of Illinois at Urbana-Champaign, USA
May 5, 2010
1 / 50

2. Introduction
DAM/RTM Dynamic model
Multi-settlement Electricity Market
Who Commands the Wind?
Numerical Results
Concluding Remarks
Outline
1 Introduction
2 DAM/RTM Dynamic model
3 Multi-settlement Electricity Market
4 Who Commands the Wind?
5 Numerical Results
6 Concluding Remarks
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3. Introduction
DAM/RTM Dynamic model
Multi-settlement Electricity Market
Who Commands the Wind?
Numerical Results
Concluding Remarks
Introduction
Increased deployment of renewable energy can lead to
significant environmental benefits
3 / 50

4. Introduction
DAM/RTM Dynamic model
Multi-settlement Electricity Market
Who Commands the Wind?
Numerical Results
Concluding Remarks
Introduction
Increased deployment of renewable energy can lead to
significant environmental benefits
However, the characteristics of renewable resources are very
different from those of conventional resources
3 / 50

5. Introduction
DAM/RTM Dynamic model
Multi-settlement Electricity Market
Who Commands the Wind?
Numerical Results
Concluding Remarks
Introduction
Increased deployment of renewable energy can lead to
significant environmental benefits
However, the characteristics of renewable resources are very
different from those of conventional resources
It is imperative to understand their characteristics to fully
harness the benefits of renewable resources
3 / 50

6. Introduction
DAM/RTM Dynamic model
Multi-settlement Electricity Market
Who Commands the Wind?
Numerical Results
Concluding Remarks
Introduction
Renewable Portfolio Standards
www.dsireusa.org / February 2010
VT: (1) RE meets any increase ME: 30% x 2000
WA: 15% x 2020* New RE: 10% x 2017
MN: 25% x 2025 in retail sales x 2012;
MT: 15% x 2015 (Xcel: 30% x 2020) (2) 20% RE & CHP x 2017 NH: 23.8% x 2025
OR: 25% x 2025 (large utilities)* ND: 10% x 2015 MI: 10% + 1,100 MW MA: 15% x 2020
5% - 10% x 2025 (smaller utilities) x 2015* + 1% annual increase
(Class I RE)
SD: 10% x 2015 WI: Varies by utility; NY: 29% x 2015
10% x 2015 goal RI: 16% x 2020
NV: 25% x 2025* CT: 23% x 2020
IA: 105 MW
W O
OH: 25% x 2025†
CO: 20% by 2020 (IOUs) PA: 18% x 2020†
10% by 2020 (co-ops & large munis)*
IL: 25% x 2025 WV: 25% x 2025*† NJ: 22.5% x 2021
CA: 33% x 2020 UT: 20% by 2025* KS: 20% x 2020 VA: 15% x 2025* MD: 20% x 2022
MO: 15% x 2021
DC DE: 20% x 2019*
AZ: 15% x 2025
NC: 12.5% x 2021 (IOUs) DC: 20% x 2020
0
10% x 2018 (co-ops & munis)
NM: 20% x 2020 (IOUs)
10% x 2020 (co-ops)
TX: 5,880 MW x 2015
HI: 40% x 2030
State renewable portfolio standard Minimum solar or customer-sited requirement 29 states +
*
State renewable portfolio goal Extra credit for solar or customer-sited renewables DC have an RPS
Solar water heating eligible † (6 states have goals)
6
Includes non-renewable alternative resources
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7. Introduction
DAM/RTM Dynamic model
Multi-settlement Electricity Market
Who Commands the Wind?
Numerical Results
Concluding Remarks
Wind power
Wind power is currently favored over all renewables
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8. Introduction
DAM/RTM Dynamic model
Multi-settlement Electricity Market
Who Commands the Wind?
Numerical Results
Concluding Remarks
Wind power
Wind power is currently favored over all renewables
Its deployment presents major challenges in system operations
due to its:
limited control capabilities
forecasting uncertainty
uncertainty and intermittency
5 / 50

9. Introduction
DAM/RTM Dynamic model
Multi-settlement Electricity Market
Who Commands the Wind?
Numerical Results
Concluding Remarks
Balancing Authority Load (MW)
7000 January 16-22, 2010
6000
5000
Wind generation (MW)
1000
0
Sun Mon Tues Weds Thurs Fri Sat
Figure: Example of load and wind generation data
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10. Introduction
DAM/RTM Dynamic model
Multi-settlement Electricity Market
Who Commands the Wind?
Numerical Results
Concluding Remarks
Different opinions...
“The Value of Wind - why more renewable energy means lower electricity bills,” Adam
Bruce, Chairman, British Wind Energy Association
“Wind is a free source of fuel. When the wind blows the UK’s electricity system
has access to this free source and the power generated is automatically accepted
onto the system”
“Wind energy means lower bills; it’s as simple as that”
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11. Introduction
DAM/RTM Dynamic model
Multi-settlement Electricity Market
Who Commands the Wind?
Numerical Results
Concluding Remarks
Different opinions...
“The Value of Wind - why more renewable energy means lower electricity bills,” Adam
Bruce, Chairman, British Wind Energy Association
“Wind is a free source of fuel. When the wind blows the UK’s electricity system
has access to this free source and the power generated is automatically accepted
onto the system”
“Wind energy means lower bills; it’s as simple as that”
“Wind power’s dirty secret? Its carbon footprint”
“Wind power is touted as the cleanest and greenest renewable energy resource”
“You’ve got a non-carbon-emitting source of energy that’s free,” said Doug
Johnson of the Bonneville Power Administration
“However, Todd Wynn of the Cascade Policy Institute says it’s not as clean as
advocates claim. He says it’s simply because the wind is volatile and doesn’t
blow all the time”
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12. Introduction
DAM/RTM Dynamic model
Multi-settlement Electricity Market
Who Commands the Wind?
Numerical Results
Concluding Remarks
Scope
Goal of this work
Understand how volatility impacts the value of wind generation
Focus: Competitive market setting
8 / 50

13. Introduction
DAM/RTM Dynamic model
Multi-settlement Electricity Market
Who Commands the Wind?
Numerical Results
Concluding Remarks
Scope
Goal of this work
Understand how volatility impacts the value of wind generation
Focus: Competitive market setting
Beyond mean energy...
We evaluate impacts of wind resources by focussing on two
parameters: penetration and volatility of wind generation.
8 / 50

14. Introduction
DAM/RTM Dynamic model
Multi-settlement Electricity Market
Who Commands the Wind?
Numerical Results
Concluding Remarks
Scope
Goal of this work
Understand how volatility impacts the value of wind generation
Focus: Competitive market setting
Beyond mean energy...
We evaluate impacts of wind resources by focussing on two
parameters: penetration and volatility of wind generation.
Vehicle
Dynamic electricity market model,
Multi-settlement structure
Captures wind volatility
Ramping constraints
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15. Introduction
DAM/RTM Dynamic model
Multi-settlement Electricity Market
Who Commands the Wind?
Numerical Results
Concluding Remarks
Day-ahead market motivations
The day-ahead market (DAM) is cleared one day prior to the
actual production and delivery of energy.
Economic world...
Forward markets for electricity which improve market efficiency and
serve as a hedging mechanism
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16. Introduction
DAM/RTM Dynamic model
Multi-settlement Electricity Market
Who Commands the Wind?
Numerical Results
Concluding Remarks
Day-ahead market motivations
The day-ahead market (DAM) is cleared one day prior to the
actual production and delivery of energy.
Economic world...
Forward markets for electricity which improve market efficiency and
serve as a hedging mechanism
...Physical world
Facilitate the scheduling of generating units
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17. Introduction
DAM/RTM Dynamic model
Multi-settlement Electricity Market
Who Commands the Wind?
Numerical Results
Concluding Remarks
Real-time market (RTM)
At close of the DAM: The ISO generates a schedule of generators
to supply specific levels of power for each hour over the next 24
hour period.
RTM = Balancing Market
As supply and demand are not perfectly predictable, the RTM
plays the role of fine-tuning this resource allocation process
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18. Introduction
DAM/RTM Dynamic model
Multi-settlement Electricity Market
Who Commands the Wind?
Numerical Results
Concluding Remarks
DAM/RTM
32000
30000 Available Resources Forecast
Megawatts
28000
Day Ahead Demand Forecast
26000 Actual Demand
24000
22000
20000
00 01 02 03 04 05 06 07 08 09 10 11 12 13 14 15 16 17 18 19 20 21 22 23 Hour Beginning
Figure: March 4, 2010 CAISO forecast and real-time supply and demand
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19. Introduction
DAM/RTM Dynamic model
Multi-settlement Electricity Market
Who Commands the Wind?
Numerical Results
Concluding Remarks
DAM/RTM
Notation
Total demand at time t, Dttl (t) = dda (t) + D(t),
Total capacity at time t, Gttl (t) = g da (t) + G(t)
Total reserve at time t,
Rttl (t) = Gttl (t) − Dttl (t) = G(t) − D(t) + rda (t)
DAM Reserve policy
rda (t) ≡ r0
da
is constant.
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20. Introduction
DAM/RTM Dynamic model
Multi-settlement Electricity Market
Who Commands the Wind?
Numerical Results
Concluding Remarks
RTM Model
RTM model of Cho & Meyn consists of the following components:
Volatility
Deviation in demand D is modeled as a driftless Brownian motion
with instantaneous variance σ 2 .
Friction
Generation cannot increase instantaneously: There exists
ζ ∈ (0, ∞) such that,
G(t ) − G(t)
≤ζ, for all t ≥ 0, and t > t.
t −t
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21. Introduction
DAM/RTM Dynamic model
Multi-settlement Electricity Market
Who Commands the Wind?
Numerical Results
Concluding Remarks
RTM Model
Write dG(t) = ζdt − dI(t), with I non-decreasing, to model the
upper bound on the rate of increase in generation.
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22. Introduction
DAM/RTM Dynamic model
Multi-settlement Electricity Market
Who Commands the Wind?
Numerical Results
Concluding Remarks
RTM Model
Write dG(t) = ζdt − dI(t), with I non-decreasing, to model the
upper bound on the rate of increase in generation.
Reserve process regarded as a controlled stochastic system,
Reserve process
dR(t) = ζdt − dI(t) − dD(t)
with control I.
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23. Introduction
DAM/RTM Dynamic model
Multi-settlement Electricity Market
Who Commands the Wind?
Numerical Results
Concluding Remarks
Market Analysis
Market analysis assumptions:
Cost
The production cost is a linear function of G(t),
of the form cG(t) for some constant c > 0.
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24. Introduction
DAM/RTM Dynamic model
Multi-settlement Electricity Market
Who Commands the Wind?
Numerical Results
Concluding Remarks
Market Analysis
Market analysis assumptions:
Cost
The production cost is a linear function of G(t),
of the form cG(t) for some constant c > 0.
Value of power
Consumer obtains v units of utility per unit of power consumed:
Utility to the consumer = v min(D(t), G(t)).
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25. Introduction
DAM/RTM Dynamic model
Multi-settlement Electricity Market
Who Commands the Wind?
Numerical Results
Concluding Remarks
Market Analysis
Disutility from power loss
The consumer suffers utility loss if demand is not met:
Disutility to the consumer = cbo |R(t)| whenever R(t) < 0.
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26. Introduction
DAM/RTM Dynamic model
Multi-settlement Electricity Market
Who Commands the Wind?
Numerical Results
Concluding Remarks
Market Analysis
Disutility from power loss
The consumer suffers utility loss if demand is not met:
Disutility to the consumer = cbo |R(t)| whenever R(t) < 0.
Perfect competition
The price of power P (t) in the RTM is assumed to be exogenous
(it does not depend on the decisions of the market agents).
16 / 50

27. Introduction
DAM/RTM Dynamic model
Multi-settlement Electricity Market
Who Commands the Wind?
Numerical Results
Concluding Remarks
Market Analysis
Disutility from power loss
The consumer suffers utility loss if demand is not met:
Disutility to the consumer = cbo |R(t)| whenever R(t) < 0.
Perfect competition
The price of power P (t) in the RTM is assumed to be exogenous
(it does not depend on the decisions of the market agents).
“price-taking assumption”
16 / 50

28. Introduction
DAM/RTM Dynamic model
Multi-settlement Electricity Market
Who Commands the Wind?
Numerical Results
Concluding Remarks
Market Analysis
The objectives of the consumer and the supplier are specified by
the respective welfare functions,
Welfare functions
WS (t) := P (t)G(t) − cG(t)
WD (t) := v min(D(t), G(t))
− cbo max(0, −R(t)) − P (t)G(t)
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29. Introduction
DAM/RTM Dynamic model
Multi-settlement Electricity Market
Who Commands the Wind?
Numerical Results
Concluding Remarks
Market Analysis
The consumer and supplier each optimize the discounted
mean-welfare
Discounted mean-welfare expressions
For given initial values of generation and demand g = G(0),
d = D(0), the respective discounted rewards are denoted
KS (g, d) := E e−γt WS (t) dt ,
KD (g, d) := E e−γt WD (t) dt ,
γ > 0 is the discount rate.
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30. Introduction
DAM/RTM Dynamic model
Multi-settlement Electricity Market
Who Commands the Wind?
Numerical Results
Concluding Remarks
Market Analysis
The social planner’s problem is defined as the maximization of the
total discounted mean welfare,
Social planner’s objective
K(g, d) = E e−γt WS (t) + WD (t) dt .
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31. Introduction
DAM/RTM Dynamic model
Multi-settlement Electricity Market
Who Commands the Wind?
Numerical Results
Concluding Remarks
Market Analysis
The optimal reserve process is a reflected Brownian motion (RBM)
on the half-line (−∞, r∗ ], with
¯
Reserve threshold
1 cbo + v
r∗ =
¯ log .
θ+ c
where θ+ is the positive solution to the quadratic equation
2 σ θ − ζθ − γ = 0
1 2 2
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32. Introduction
DAM/RTM Dynamic model
Multi-settlement Electricity Market
Who Commands the Wind?
Numerical Results
Concluding Remarks
Market Analysis
The equilibrium price functional is a piecewise constant function of
the equilibrium reserve process,
Equilibrium price functional
pe (re ) = (v + cbo )I{re < 0}
The sum cbo + v is in fact the maximum price the consumer is
willing to pay, often called the choke-up price.
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33. Introduction
DAM/RTM Dynamic model
Multi-settlement Electricity Market
Who Commands the Wind?
Numerical Results
Concluding Remarks
A little bit of technical details...
On substituting the price into the respective welfare functions:
Expected welfare values
E[WS (t)] = (v + cbo ) E[D(t)I{Re (t) ≤ 0}]
∗
+ E[Re (t)I{Re (t) ≤ 0}] − cE[Re (t)]
E[WD (t)] = −(v + cbo )E[D(t)I{Re (t) ≤ 0}]
∗
where R = Re is the equilibrium reserve process.
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34. Introduction
DAM/RTM Dynamic model
Multi-settlement Electricity Market
Who Commands the Wind?
Numerical Results
Concluding Remarks
How does this look?...
Prices
Reserves
Normalized demand
v + cbo
r∗
0
Figure: Model price dynamics
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35. Introduction
DAM/RTM Dynamic model
Multi-settlement Electricity Market
Who Commands the Wind?
Numerical Results
Concluding Remarks
Familiar, right?
Illinois, July 1998 California, July 2000
Spinning reserve prices PX prices $/MWh
5000 Purchase Price $/MWh 70
250
Previous week 60
4000 200
50
3000 150 40
2000 30
100
20
1000 50
10
0 0
Mon Tues Weds Thurs Fri Weds Thurs Fri Sat Sun Mon Tues Weds
Ontario, November 2005 APX Power NL, April 23, 2007
Forecast Demand
Demand in MW Last Updated 11:00 AM Predispatch 1975.11 Dispatch 19683.5
Current Week Volume Current Week Price
21000 7000 400
Prev. Week Volume Prev. Week Price
18000 6000
300
Price (Euro/MWh)
5000
Volume (MWh)
15000
4000
Hourly Ontario Energy Price $/MWh Last Updated 11:00 AM Predispatch 72.79 Dispatch 90.82
200
2000
Forecast Prices
3000
1500
2000 100
1000
500 1000
0 3 6 9 12 15 18 21 3 6 9 12 15 18 21 3 6 9 12 15 18 21 Time 0 0
Tues Weds Thurs Tues Wed Thus Fri Sat Sun Mon
Figure: Real-world price dynamics
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36. Introduction
DAM/RTM Dynamic model
Multi-settlement Electricity Market
Who Commands the Wind?
Numerical Results
Concluding Remarks
Coupling DAM/RTM
Multi-settlement market model: A coupling of the DAM and RTM.
Consumers’ welfare in the multi-settlement market
WD (t) := v min(Dttl (t), Gttl (t)) − cbo max(0, −R(t))
ttl
− P e (t)G(t) − pda (t)g da (t)
25 / 50

37. Introduction
DAM/RTM Dynamic model
Multi-settlement Electricity Market
Who Commands the Wind?
Numerical Results
Concluding Remarks
DAM/RTM Consumer’s welfare
Principle of optimality =⇒ Formulae for total discounted mean
welfare,
Consumers’ mean welfare in the multi-settlement market
KD = KD (r) + γ −1 (r − G(0))(pe (r) − pda )
ttl ∗
∞
+ (v − p(t))dda (t) e−γt dt .
0
in which KD (r) corresponds to the RTM welfare.
∗
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38. Introduction
DAM/RTM Dynamic model
Multi-settlement Electricity Market
Who Commands the Wind?
Numerical Results
Concluding Remarks
Coupling DAM/RTM
Total supplier welfare: Through similar and simpler arguments,
Suppliers’ welfare in the multi-settlement market
WS (t) = WS (t) + pda (t) − cda g da (t)
ttl
(1)
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39. Introduction
DAM/RTM Dynamic model
Multi-settlement Electricity Market
Who Commands the Wind?
Numerical Results
Concluding Remarks
DAM/RTM Supplier’s Welfare
Principle of optimality =⇒ Formulae for total discounted mean
welfare,
Supplier’s mean welfare in the multi-settlement market
KS = KS (r) + γ −1 (r − G(0))(pda − cda )
ttl ∗
∞
+ p(t) − cda dda (t) e−γt dt .
0
in which KS (r) corresponds to the RTM welfare.
∗
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40. Introduction
DAM/RTM Dynamic model
Multi-settlement Electricity Market
Who Commands the Wind?
Numerical Results
Concluding Remarks
Integrating Wind...
Figure: Who Commands the Wind?
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41. Introduction
DAM/RTM Dynamic model
Multi-settlement Electricity Market
Who Commands the Wind?
Numerical Results
Concluding Remarks
Extending the dynamic model
Goal
Extend the DA/RT market model to differentiate power generated
by wind and by conventional generation units
30 / 50

42. Introduction
DAM/RTM Dynamic model
Multi-settlement Electricity Market
Who Commands the Wind?
Numerical Results
Concluding Remarks
Extending the dynamic model
Goal
Extend the DA/RT market model to differentiate power generated
by wind and by conventional generation units
Assumption
All the wind power available is injected into the system
30 / 50

43. Introduction
DAM/RTM Dynamic model
Multi-settlement Electricity Market
Who Commands the Wind?
Numerical Results
Concluding Remarks
Extending the dynamic model
Goal
Extend the DA/RT market model to differentiate power generated
by wind and by conventional generation units
Assumption
All the wind power available is injected into the system
Key issue
Conventional generators serve residual demand.
30 / 50

44. Introduction
DAM/RTM Dynamic model
Multi-settlement Electricity Market
Who Commands the Wind?
Numerical Results
Concluding Remarks
Extending the dynamic model
Goal
Extend the DA/RT market model to differentiate power generated
by wind and by conventional generation units
Assumption
All the wind power available is injected into the system
Key issue
Conventional generators serve residual demand.
Volatility of the residual demand will result in higher reserves in
the dynamic market equilibrium
30 / 50

45. Introduction
DAM/RTM Dynamic model
Multi-settlement Electricity Market
Who Commands the Wind?
Numerical Results
Concluding Remarks
Emerging issues
Not only mean energy
The details depend on both volatility of wind and its proportion of
the overall generation
What about now?
If the penetration of wind resources is low, then the increase in
load volatility will be negligible, and hence there will be negligible
impact on the market outcomes
31 / 50

46. Introduction
DAM/RTM Dynamic model
Multi-settlement Electricity Market
Who Commands the Wind?
Numerical Results
Concluding Remarks
Emerging issues
Not only mean energy
The details depend on both volatility of wind and its proportion of
the overall generation
What about now?
If the penetration of wind resources is low, then the increase in
load volatility will be negligible, and hence there will be negligible
impact on the market outcomes
What about in 2020?
Potential negative market outcomes are possible with a
combination of high wind generation penetration and high
volatility of wind
31 / 50

47. Introduction
DAM/RTM Dynamic model
Multi-settlement Electricity Market
Who Commands the Wind?
Numerical Results
Concluding Remarks
Who Commands the Wind?
Approach
To quantify the impact of volatility we obtain expressions for the
total welfare in two market models, differentiated by who
commands the wind generating units
32 / 50

48. Introduction
DAM/RTM Dynamic model
Multi-settlement Electricity Market
Who Commands the Wind?
Numerical Results
Concluding Remarks
Who Commands the Wind?
Approach
To quantify the impact of volatility we obtain expressions for the
total welfare in two market models, differentiated by who
commands the wind generating units
Main finding
Volatility can have tremendous impact on the market outcomes
32 / 50

49. Introduction
DAM/RTM Dynamic model
Multi-settlement Electricity Market
Who Commands the Wind?
Numerical Results
Concluding Remarks
Who Commands the Wind?
Approach
To quantify the impact of volatility we obtain expressions for the
total welfare in two market models, differentiated by who
commands the wind generating units
Main finding
Volatility can have tremendous impact on the market outcomes
Asymmetric and surprising result
The supplier can achieve significant gains,
even when the consumer commands the wind
32 / 50

50. Introduction
DAM/RTM Dynamic model
Multi-settlement Electricity Market
Who Commands the Wind?
Numerical Results
Concluding Remarks
Consumers command the wind
Wind generating units are commanded by the demand side:
Consumers’ and suppliers’ welfare expressions
WD,W (t) = v min(Dttl (t), Gttl (t) + Gttl (t))
ttl
W
− cbo max(0, −R(t))
− P (t)G(t) − p(t)g da (t)
WS,W (t) = P (t) − crt G(t) + p(t) − cda g da (t)
ttl
33 / 50

51. Introduction
DAM/RTM Dynamic model
Multi-settlement Electricity Market
Who Commands the Wind?
Numerical Results
Concluding Remarks
Consumers command the wind
Welfare expressions: DAM/RTM decomposition
WD,W (t) = WD,W (t)
ttl rt
+ vdda (t) − p(t)(dda (t) − gW (t))
da
+ (P (t) − p(t))r0 + vGW (t)
da
WS,W (t) = WS,W (t) + p(t) − cda g da (t)
ttl rt
WD,W (t), WS,W (t): Welfare obtained in the RTM
rt rt
with residual demand Dnet (t).
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52. Introduction
DAM/RTM Dynamic model
Multi-settlement Electricity Market
Who Commands the Wind?
Numerical Results
Concluding Remarks
Suppliers command the wind
The other alternative is to consider wind as part of the supply side,
Consumers’ welfare
WD,W (t) = v min(Dttl (t), Gttl (t) + Gttl (t))
ttl
W
− cbo max(0, −R(t))
− P (t)(G(t) + GW (t)) − p(t)(g da (t) + gW (t))
da
= WD,W (t)
rt
+ (v − p(t))dda + (P (t) − p(t))r0
da
+ (v − P (t))GW (t)
35 / 50

53. Introduction
DAM/RTM Dynamic model
Multi-settlement Electricity Market
Who Commands the Wind?
Numerical Results
Concluding Remarks
Suppliers command the wind
Suppliers’ welfare
WS,W (t) = P (t) − crt G(t) + P (t)GW (t)
ttl
+ p(t) − cda g da (t) + p(t)gW (t)
da
= WS,W (t)
rt
+ p(t) − cda g da (t) + P (t)GW (t) + p(t)gW (t)
da
The welfare gain p(t)gW (t) is now taken by the suppliers
da
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54. Introduction
DAM/RTM Dynamic model
Multi-settlement Electricity Market
Who Commands the Wind?
Numerical Results
Concluding Remarks
Numerical Results: Setting the stage I
Parameters used in all of our experiments:
Parameters [$/MWh]
Cost of blackout and value of consumption:
cbo = 200, 000 v = 50
Cost and prices of generation: crt = 30, and
cda = 0.75 ∗ crt , pda = 0.85 ∗ crt
Discount factor: γ = 1/12 (12 hour time horizon).
37 / 50

55. Introduction
DAM/RTM Dynamic model
Multi-settlement Electricity Market
Who Commands the Wind?
Numerical Results
Concluding Remarks
Numerical Results: Setting the stage II
Parameters (physical)
Ramp limit: ζ = 200 MW/min
¯
Mean demand: D = 50, 000 MW
Standard deviation: σ = 500 MW.
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56. Introduction
DAM/RTM Dynamic model
Multi-settlement Electricity Market
Who Commands the Wind?
Numerical Results
Concluding Remarks
Numerical Results: Setting the stage III
Penetration and volatility
Coefficient of variation to capture the relative volatility of wind:
σw
cv =
E[Gttl (t)]
W
Percentage of wind penetration:
¯
k = 100 ∗ E[Gttl (t)]/D
W
.
39 / 50

57. Introduction
DAM/RTM Dynamic model
Multi-settlement Electricity Market
Who Commands the Wind?
Numerical Results
Concluding Remarks
Numerical Results: Volatility Impacts
3
x 10
140
120 Optimal Reserve Level k = 20
100
k = 15
80
60
k = 10
40
20 k=5
0 k=0
0 0.1 0.2 0.3 0.4
cv
Figure: Optimal reserves depend on penetration and coefficient of
variation.
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58. Introduction
DAM/RTM Dynamic model
Multi-settlement Electricity Market
Who Commands the Wind?
Numerical Results
Concluding Remarks
Numerical Results: Volatility Impacts
6
x 10
18
Total Welfare ζ = 200
16
ζ=
500
14
12 ζ
=
0.
1
10
0 200 400 600 800 1000
σ
Figure: Social planner’s welfare.
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59. Introduction
DAM/RTM Dynamic model
Multi-settlement Electricity Market
Who Commands the Wind?
Numerical Results
Concluding Remarks
Numerical Results: Consumers command the wind
6 6
x 10 x 10
15 k = 20
Consumer Welfare Supplier Welfare
k = 15
5
k=0
k = 10
10
k=5 4
k=5
5
k = 10 3 k=0
k = 15
0 k = 20
0 0.1 0.2 0.3 0.4 0 0.1 0.2 0.3 0.4
cv
Figure: Consumer and supplier welfare when consumer owns wind for
different coefficient of variation cv and cda < pda < crt .
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60. Introduction
DAM/RTM Dynamic model
Multi-settlement Electricity Market
Who Commands the Wind?
Numerical Results
Concluding Remarks
Facing wind volatility
The results of this paper invite many questions:
C1
The impact of demand management and storage on the market
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61. Introduction
DAM/RTM Dynamic model
Multi-settlement Electricity Market
Who Commands the Wind?
Numerical Results
Concluding Remarks
Facing wind volatility
The results of this paper invite many questions:
C1
The impact of demand management and storage on the market
C2
The impact of supply management and storage on the market.
e.g., modern wind turbines allow pitch angle control.
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62. Introduction
DAM/RTM Dynamic model
Multi-settlement Electricity Market
Who Commands the Wind?
Numerical Results
Concluding Remarks
Facing wind volatility
C3
Mechanisms to reduce consumers and suppliers exposure to
supply-side volatility.
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63. Introduction
DAM/RTM Dynamic model
Multi-settlement Electricity Market
Who Commands the Wind?
Numerical Results
Concluding Remarks
Facing wind volatility
C3
Mechanisms to reduce consumers and suppliers exposure to
supply-side volatility.
C4
How to create policies to protect participants on both sides of the
market, while creating incentives for R&D on renewable energy?
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64. Introduction
DAM/RTM Dynamic model
Multi-settlement Electricity Market
Who Commands the Wind?
Numerical Results
Concluding Remarks
The main messages...
It is not so easy...
The main message of this paper is that consumer welfare may fall
dramatically as more and more wind generation is dispatched
A beautiful world...
This is true even under the most ideal circumstances:
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65. Introduction
DAM/RTM Dynamic model
Multi-settlement Electricity Market
Who Commands the Wind?
Numerical Results
Concluding Remarks
The main messages...
It is not so easy...
The main message of this paper is that consumer welfare may fall
dramatically as more and more wind generation is dispatched
A beautiful world...
This is true even under the most ideal circumstances:
consumers own all wind generation resources and
price manipulation is excluded
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66. Introduction
DAM/RTM Dynamic model
Multi-settlement Electricity Market
Who Commands the Wind?
Numerical Results
Concluding Remarks
The main messages...
It is not so easy...
The main message of this paper is that consumer welfare may fall
dramatically as more and more wind generation is dispatched
A beautiful world...
This is true even under the most ideal circumstances:
consumers own all wind generation resources and
price manipulation is excluded
No “ENRON games” – no “market power”
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67. Introduction
DAM/RTM Dynamic model
Multi-settlement Electricity Market
Who Commands the Wind?
Numerical Results
Concluding Remarks
Concluding remarks
Volatility and mean energy are key parameters for new energy
sources. Our results show that resource volatility can have
tremendous impacts on the market outcomes
Currently adopted wind integration schemes can be harmful
for consumers with larger wind penetration
Suppliers can achieve significant gains even when the
consumer commands the wind
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68. Introduction
DAM/RTM Dynamic model
Multi-settlement Electricity Market
Who Commands the Wind?
Numerical Results
Concluding Remarks
Concluding remarks
Who faces the uncertainty and risk associated to volatile
resources is a big challenge from an economic viewpoint
Under certain conditions consumers are better off not
dispatching wind
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69. Introduction
DAM/RTM Dynamic model
Multi-settlement Electricity Market
Who Commands the Wind?
Numerical Results
Concluding Remarks
Concluding remarks
Who faces the uncertainty and risk associated to volatile
resources is a big challenge from an economic viewpoint
Under certain conditions consumers are better off not
dispatching wind
Storage and demand management emerge as solutions for a
smooth integration of wind power
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70. Introduction
DAM/RTM Dynamic model
Multi-settlement Electricity Market
Who Commands the Wind?
Numerical Results
Concluding Remarks
Concluding remarks
Market analysis requires dynamic rather than snapshot
models
Greater wind penetration will require redesigns of both
power system operations and electricity markets
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71. Introduction
DAM/RTM Dynamic model
Multi-settlement Electricity Market
Who Commands the Wind?
Numerical Results
Concluding Remarks
Thanks!
Figure: Celebrating with Dutch Babies after finishing part of this work
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72. Introduction
DAM/RTM Dynamic model
Multi-settlement Electricity Market
Who Commands the Wind?
Numerical Results
Concluding Remarks
Bibliography
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I.-K. Cho and S. P. Meyn. Efficiency and marginal cost pricing in dynamic
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M. Chen, I.-K. Cho, and S. Meyn. Reliability by design in a distributed power
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I.-K. Cho and S. P. Meyn. A dynamic newsboy model for optimal reserve
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D. J. C. MacKay. Sustainable energy : without the hot air. UIT, Cambridge,
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