dynamic models and dynamic markets for electric power … · dynamic models and dynamic markets for...
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[email protected] and Approaches
Dynamic Markets and their EquilibriaWho Commands the Wind?
Research Frontiers
Dynamic Models and Dynamic Markets
for Electric Power NetworksBased on tutorial & panel lectures at Energy Systems Week, Cambridge UK
http://www.newton.ac.uk/programmes/SCS/scsw07p.html
Sean P. Meyn
Joint work with: In-Koo Cho, Matias Negrete-Pincetic, Gui Wang,
Anupama Kowli, and Ehsan Shafieeporfaard
Coordinated Science Laboratory
and the Department of Electrical and Computer Engineering
University of Illinois at Urbana-Champaign, USA
July 16, 2010
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[email protected] and Approaches
Dynamic Markets and their EquilibriaWho Commands the Wind?
Research Frontiers
Outline
2 Issues and Approaches
3 Dynamic Markets and their Equilibria
4 Who Commands the Wind?
5 Research Frontiers
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[email protected] and Approaches
Dynamic Markets and their EquilibriaWho Commands the Wind?
Research Frontiers
TCIPG
Trustworthy Cyber Infrastructure for Power Grid
tcipg.iti.illinois.edu
The Smart Grid Can Deliver
Interoperability &
Functionality are
Key Attributes
TCIPG
3 / 48
[email protected] and Approaches
Dynamic Markets and their EquilibriaWho Commands the Wind?
Research Frontiers
TCIPG
The Challenge:
Trustworthy Smart Grid Operation, even in Hostile Environments
4 / 48
[email protected] and Approaches
Dynamic Markets and their EquilibriaWho Commands the Wind?
Research Frontiers
TCIPG
The Challenge:
Trustworthy Smart Grid Operation, even in Hostile Environments
TrustworthyA system which does what is supposed to do — nothing else.Availability, Security, Safety, ...
Hostile EnvironmentAccidental Failures, Design Flaws, Malicious Attacks
Cyber Physical Must make the whole system trustworthy:The physical & cyber components, and their interaction.
4 / 48
[email protected] and Approaches
Dynamic Markets and their EquilibriaWho Commands the Wind?
Research Frontiers
Extending the Realm of OptimizationComplex Systems: Uncertainty, Competition and Dynamics
The Challenge:
Planning & operations for the next generation ofengineering-economic systems
5 / 48
[email protected] and Approaches
Dynamic Markets and their EquilibriaWho Commands the Wind?
Research Frontiers
Extending the Realm of OptimizationComplex Systems: Uncertainty, Competition and Dynamics
The Challenge:
Planning & operations for the next generation ofengineering-economic systems
Stochastic Systems & Stochastic Games:Analysis, approximations, distributed algorithms
Dynamic optimization and games: Efficiency and reliability
What does a dynamic equilibrium look like?
What is the impact of strategic behavior?
Mean-field approximations: Model reduction, decentralized
outcomes, learning schemes
5 / 48
[email protected] and Approaches
Dynamic Markets and their EquilibriaWho Commands the Wind?
Research Frontiers
Uncertainty & Dynamics ⊕ Risk-aversionFirms bid in forward market, subject to equilibrium in spot-market
When competing firms have volatile generation assets, integrating
uncertainty and risk-aversion is crucial
6 / 48
[email protected] and Approaches
Dynamic Markets and their EquilibriaWho Commands the Wind?
Research Frontiers
Uncertainty & Dynamics ⊕ Risk-aversionFirms bid in forward market, subject to equilibrium in spot-market
When competing firms have volatile generation assets, integrating
uncertainty and risk-aversion is crucial
Contributions:
Nash equilibria:Existence, uniqueness, computation
Application: 53-node network with 6 generators(2 of whom have wind assets)
With increased risk-aversion, wind-basedgenerators participate less in forward markets
Forward bids vs. Risk Aversion
Fo
rwa
rd b
ids
Risk Aversion
Forward bids vs. Wind Penetration
Fo
rwa
rd b
ids
Wind Penetration
A. Kannan, U. Shanbhag, and H. Kim:
1. Risk-based Generalized Nash Games in Power Markets: Characterization and Computation of Equilibria, 2009
2. Strategic behavior in power markets under uncertainty, 2010
6 / 48
[email protected] and Approaches
Dynamic Markets and their EquilibriaWho Commands the Wind?
Research Frontiers
Synchronization of coupled oscillators is a gameAutonomous dynamical systems coupled by objectives
Oscillator model: dθi = (ωi + ui(t)) dt + σ dξi
Each seeks to minimize the coupled cost,
ηi(ui; u−i) = limT→∞
1
T
∫T
0
E[ c(θi; θ−i)︸ ︷︷ ︸
cost of anarchy
+ 1
2Ru2
i︸ ︷︷ ︸
cost of control
] ds �����������
7 / 48
[email protected] and Approaches
Dynamic Markets and their EquilibriaWho Commands the Wind?
Research Frontiers
Synchronization of coupled oscillators is a gameAutonomous dynamical systems coupled by objectives
Oscillator model: dθi = (ωi + ui(t)) dt + σ dξi
Each seeks to minimize the coupled cost,
ηi(ui; u−i) = limT→∞
1
T
∫T
0
E[ c(θi; θ−i)︸ ︷︷ ︸
cost of anarchy
+ 1
2Ru2
i︸ ︷︷ ︸
cost of control
] ds �����������
���������
���������
�
−0.2
0
0.2
0.4
0.6
ω = 0.95
ω = 1
ω = 1.05
Kuramoto
Population
Density
Control laws
0 π 2π θ 0 0.1 0.15 0.215
20
25
30
35
40
45
50
Incoherence
Synchrony
H. Yin, P. G. Mehta, S. P. Meyn and U. V. Shanbhag:
1. “Synchronization of coupled oscillators is a game,” American Control Conference 2010, Baltimore, MD
2. “Learning in mean-field oscillators games,” IEEE Conference on Decision and Control, 2010
7 / 48
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Dynamic Markets and their EquilibriaWho Commands the Wind?
Research Frontiers
Control Techniques for Complex NetworksBreaking the curse of dimensionality
• Convex relaxations
• Workload relaxations
• Algorithms for learning and simulation
Complex Networks FOR
Sean Meyn
Control Techniques
8 / 48
[email protected] and Approaches
Dynamic Markets and their EquilibriaWho Commands the Wind?
Research Frontiers
Control Techniques for Complex NetworksBreaking the curse of dimensionality
• Convex relaxations
• Workload relaxations
• Algorithms for learning and simulation
Complex Networks FOR
Sean Meyn
Control Techniques
w1
w2 RSTO
W+
1d
2d
Demand driven network and its workload relaxation
8 / 48
[email protected] and Approaches
Dynamic Markets and their EquilibriaWho Commands the Wind?
Research Frontiers
Pri
ce (
Au
s $
/MW
h)
Vo
lum
e (
MW
)
Demand
Demand
Prices
Prices
24:00
23:00
22:00
21:00
20:00
19:00
18:00
17:00
16:00
15:00
14:00
13:00
12:00
11:00
10:00
09:00
08:00
07:00
06:00
05:00
04:00
03:00
02:00
01:00
00:00
24:00
23:00
22:00
21:00
20:00
19:00
18:00
17:00
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15:00
14:00
13:00
12:00
11:00
10:00
09:00
08:00
07:00
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02:00
01:00
00:00
19,000
10,000
1,400
1,200
1,000
800
600
400
200
0
1,000
0
- 1,000
- 1,500
1,000
- 1,000
9,000
8,000
10,000
7,000
6,000
5,000
4,000
3,000
2,000
1,000
0
Tasmania
Victoria
Australia - January 16, 2007
Victoria
Tasmania
Issues and Approaches
9 / 48
[email protected] and Approaches
Dynamic Markets and their EquilibriaWho Commands the Wind?
Research Frontiers
Issues: Political Mandates come, and go...
6
Renewable Portfolio Standards
State renewable portfolio standard
State renewable portfolio goal
www.dsireusa.org / February 2010
Solar water heating eligible * †
Extra credit for solar or customer-sited renewables
Includes non-renewable alternative resources
WA: 15% x 2020*
CA: 33% x 2020
NV: 25% x 2025*
AZ: 15% x 2025
NM: 20% x 2020 (IOUs)
10% x 2020 (co-ops)
HI: 40% x 2030
Minimum solar or customer-sited requirement
TX: 5,880 MW x 2015
UT: 20% by 2025*
CO: 20% by 2020 (IOUs) 10% by 2020 (co-ops & large munis)*
MT: 15% x 2015
ND: 10% x 2015
SD: 10% x 2015
IA: 105 MW
MN: 25% x 2025 (Xcel: 30% x 2020)
MO: 15% x 2021
WI: Varies by utility; laog 5102 x %01
MI: 10% + 1,100 MW x 2015*
OH: 25% x 2025†
ME: 30% x 2000 New RE: 10% x 2017
NH: 23.8% x 2025
MA: 15% x 2020 + 1% annual increase
(Class I RE)
RI: 16% x 2020
CT: 23% x 2020
NY: 29% x 2015
NJ: 22.5% x 2021
PA: 18% x 2020†
MD: 20% x 2022
DE: 20% x 2019*
DC: 20% x 2020
VA: 15% x 2025*
NC: 12.5% x 2021 (IOUs)
10% x 2018 (co-ops & munis)
VT: (1) RE meets any increase in retail sales x 2012;
(2) 20% RE & CHP x 2017
KS: 20% x 2020
OR: 25% x 2025 (large utilities)*
5% - 10% x 2025 (smaller utilities)
IL: 25% x 2025 WV: 25% x 2025*†
29 states +
DC have an RPS (6 states have goals)
DC
0
OW
10 / 48
[email protected] and Approaches
Dynamic Markets and their EquilibriaWho Commands the Wind?
Research Frontiers
Issues: Dynamics Coupled generators and consumers
Time in Seconds
4600
0 20 40 60 80
4400
4200
4000
MW
Mass-spring model
Instability in the North-West U.S.
11 / 48
[email protected] and Approaches
Dynamic Markets and their EquilibriaWho Commands the Wind?
Research Frontiers
Issues: Complexity
Interconnected
network of
ENTSO-E
European Network of TransmissionSystem Operators for Electricity
12 / 48
[email protected] and Approaches
Dynamic Markets and their EquilibriaWho Commands the Wind?
Research Frontiers
Issues: Market Power Risk to consumers
Spinning reserve prices PX prices $/MWh
100
150
0
50
200
250
10
20
30
40
50
60
70
Mon Tues WedsWeds Thurs Fri Sat Sun
Enron traders openly discussed manipulating
California’s power market during profanity-laced
telephone conversations in which they merrily
gloated about ripping o! “those poor
grandmothers” during the state’s energy crunch
in 2000-01 ...
California, July 2000
[AP by Kristen Hays, 06/03/04]
NRON As Je!rey Skilling, the "rst but sadly not the last guy
to package up a big sample of nothing and sell it to a greedy
public, Samuel West oozes self-belief; his boss, Ken Lay (Tim
Piggott-Smith) and stooge, Andy Fastow (Tom Goodman-Hill)
end up smeared with it. But Lucy Prebble's play is rather more
than a simple tale ... -Time Out, London 2010
Enron traders Enron traders Enron traders
California’s power market during California’s power market during California’s power market during California’s power market during California’s power market during California’s power market during California’s power market during California’s power market during California’s power market during California’s power market during California’s power market during California’s power market during
telephone conversations telephone conversations telephone conversations telephone conversations telephone conversations telephone conversations telephone conversations telephone conversations telephone conversations telephone conversations telephone conversations telephone conversations telephone conversations telephone conversations in which they merrily telephone conversations telephone conversations telephone conversations telephone conversations telephone conversations telephone conversations telephone conversations telephone conversations telephone conversations
gloated about ripping o! “those poor gloated about ripping o! “those poor gloated about ripping o! “those poor gloated about ripping o! “those poor gloated about ripping o! “those poor gloated about ripping o! “those poor gloated about ripping o! “those poor gloated about ripping o! “those poor
grandmothers” during the state’s energy crunch grandmothers” during the state’s energy crunch grandmothers” during the state’s energy crunch grandmothers” during the state’s energy crunch grandmothers” during the state’s energy crunch
[AP by Kristen Hays, 06/03/04]in 2000-01 ... in 2000-01 ... in 2000-01 ... [AP by Kristen Hays, 06/03/04]in 2000-01 ... [AP by Kristen Hays, 06/03/04][AP by Kristen Hays, 06/03/04][AP by Kristen Hays, 06/03/04][AP by Kristen Hays, 06/03/04]
NRON NRON NRON As Je!rey Skilling, the "rst but sadly not the last guy As Je!rey Skilling, the "rst but sadly not the last guy NRON As Je!rey Skilling, the "rst but sadly not the last guy As Je!rey Skilling, the "rst but sadly not the last guy As Je!rey Skilling, the "rst but sadly not the last guy As Je!rey Skilling, the "rst but sadly not the last guy As Je!rey Skilling, the "rst but sadly not the last guy
to package up a big sample of nothing and sell it to a greedy to package up a big sample of nothing and sell it to a greedy
public, Samuel West oozes self-belief; his boss, Ken Lay (Tim
to package up a big sample of nothing and sell it to a greedy to package up a big sample of nothing and sell it to a greedy to package up a big sample of nothing and sell it to a greedy to package up a big sample of nothing and sell it to a greedy to package up a big sample of nothing and sell it to a greedy to package up a big sample of nothing and sell it to a greedy to package up a big sample of nothing and sell it to a greedy to package up a big sample of nothing and sell it to a greedy to package up a big sample of nothing and sell it to a greedy to package up a big sample of nothing and sell it to a greedy
public, Samuel West oozes self-belief; his boss, Ken Lay (Tim public, Samuel West oozes self-belief; his boss, Ken Lay (Tim public, Samuel West oozes self-belief; his boss, Ken Lay (Tim public, Samuel West oozes self-belief; his boss, Ken Lay (Tim public, Samuel West oozes self-belief; his boss, Ken Lay (Tim public, Samuel West oozes self-belief; his boss, Ken Lay (Tim public, Samuel West oozes self-belief; his boss, Ken Lay (Tim public, Samuel West oozes self-belief; his boss, Ken Lay (Tim public, Samuel West oozes self-belief; his boss, Ken Lay (Tim public, Samuel West oozes self-belief; his boss, Ken Lay (Tim public, Samuel West oozes self-belief; his boss, Ken Lay (Tim public, Samuel West oozes self-belief; his boss, Ken Lay (Tim public, Samuel West oozes self-belief; his boss, Ken Lay (Tim public, Samuel West oozes self-belief; his boss, Ken Lay (Tim public, Samuel West oozes self-belief; his boss, Ken Lay (Tim public, Samuel West oozes self-belief; his boss, Ken Lay (Tim public, Samuel West oozes self-belief; his boss, Ken Lay (Tim public, Samuel West oozes self-belief; his boss, Ken Lay (Tim public, Samuel West oozes self-belief; his boss, Ken Lay (Tim public, Samuel West oozes self-belief; his boss, Ken Lay (Tim public, Samuel West oozes self-belief; his boss, Ken Lay (Tim public, Samuel West oozes self-belief; his boss, Ken Lay (Tim public, Samuel West oozes self-belief; his boss, Ken Lay (Tim
Piggott-Smith) and stooge, Piggott-Smith) and stooge, Piggott-Smith) and stooge, Piggott-Smith) and stooge, Piggott-Smith) and stooge, Piggott-Smith) and stooge, Piggott-Smith) and stooge, Piggott-Smith) and stooge, Piggott-Smith) and stooge, Andy Fastow (Tom Goodman-Hill) Piggott-Smith) and stooge, Piggott-Smith) and stooge, Piggott-Smith) and stooge, Piggott-Smith) and stooge, Piggott-Smith) and stooge, Andy Fastow (Tom Goodman-Hill)
up smeared with it. But Lucy Prebble's play is rather more
Piggott-Smith) and stooge, Piggott-Smith) and stooge, Andy Fastow (Tom Goodman-Hill) Piggott-Smith) and stooge, Piggott-Smith) and stooge, Piggott-Smith) and stooge, Piggott-Smith) and stooge, Piggott-Smith) and stooge, Piggott-Smith) and stooge,
end up smeared with it. But Lucy Prebble's play is rather more
than a simpl
Piggott-Smith) and stooge, Piggott-Smith) and stooge, Piggott-Smith) and stooge, Piggott-Smith) and stooge, Andy Fastow (Tom Goodman-Hill) Piggott-Smith) and stooge, Piggott-Smith) and stooge,
end up smeared with it. But Lucy Prebble's play is rather more end up smeared with it. But Lucy Prebble's play is rather more up smeared with it. But Lucy Prebble's play is rather more end up smeared with it. But Lucy Prebble's play is rather more up smeared with it. But Lucy Prebble's play is rather more up smeared with it. But Lucy Prebble's play is rather more up smeared with it. But Lucy Prebble's play is rather more up smeared with it. But Lucy Prebble's play is rather more up smeared with it. But Lucy Prebble's play is rather more up smeared with it. But Lucy Prebble's play is rather more up smeared with it. But Lucy Prebble's play is rather more up smeared with it. But Lucy Prebble's play is rather more up smeared with it. But Lucy Prebble's play is rather more up smeared with it. But Lucy Prebble's play is rather more up smeared with it. But Lucy Prebble's play is rather more up smeared with it. But Lucy Prebble's play is rather more
e tale ...
up smeared with it. But Lucy Prebble's play is rather more
e tale ... than a simplthan a simple tale ... than a simple tale ... e tale ...
telephone conversations in which they merrily telephone conversations telephone conversations
California’s power market during
openly discussed manipulating
California’s power market during
Enron traders openly discussed manipulating
California’s power market during
telephone conversations in which they merrily
gloated about ripping o! “those poor
openly discussed manipulating Enron traders openly discussed manipulating
California’s power market during
telephone conversations
gloated about ripping o! “those poor
grandmothers” during the state’s energy crunch
in 2000-01 ... [AP by Kristen Hays, 06/03/04]
NRON As Je!rey Skilling, the "rst but sadly not the last guy
California’s power market during
telephone conversations
gloated about ripping o! “those poor
grandmothers” during the state’s energy crunch
in 2000-01 ...
gloated about ripping o! “those poor
Enron traders openly discussed manipulating
California’s power market during
telephone conversations
California’s power market during
telephone conversations telephone conversations
gloated about ripping o! “those poor gloated about ripping o! “those poor
grandmothers” during the state’s energy crunch
[AP by Kristen Hays, 06/03/04]
NRON to package up a big sample of nothing and sell it to a greedy
NRON As Je!rey Skilling, the "rst but sadly not the last guy
gloated about ripping o! “those poor
grandmothers” during the state’s energy crunch
in 2000-01 ...
telephone conversations
gloated about ripping o! “those poor
grandmothers” during the state’s energy crunch
telephone conversations telephone conversations
Enron traders
California’s power market during
Enron traders
California’s power market during
Enron traders Enron traders
California’s power market during
Enron traders
California’s power market during
openly discussed manipulating
California’s power market during California’s power market during California’s power market during
telephone conversations
California’s power market during California’s power market during California’s power market during
telephone conversations in which they merrily
gloated about ripping o! “those poor
California’s power market during
telephone conversations
California’s power market during
in which they merrily telephone conversations
California’s power market during
telephone conversations telephone conversations telephone conversations telephone conversations telephone conversations telephone conversations telephone conversations telephone conversations telephone conversations in which they merrily telephone conversations telephone conversations telephone conversations
gloated about ripping o! “those poor
telephone conversations
gloated about ripping o! “those poor
telephone conversations
gloated about ripping o! “those poor
telephone conversations
gloated about ripping o! “those poor
telephone conversations telephone conversations telephone conversations
gloated about ripping o! “those poor gloated about ripping o! “those poor
telephone conversations
gloated about ripping o! “those poor gloated about ripping o! “those poor
in 2000-01 ... in 2000-01 ...
gloated about ripping o! “those poor
[AP by Kristen Hays, 06/03/04][AP by Kristen Hays, 06/03/04][AP by Kristen Hays, 06/03/04][AP by Kristen Hays, 06/03/04]
gloated about ripping o! “those poor gloated about ripping o! “those poor
grandmothers” during the state’s energy crunch
in 2000-01 ...
gloated about ripping o! “those poor
grandmothers” during the state’s energy crunch
in 2000-01 ... in 2000-01 ...
gloated about ripping o! “those poor gloated about ripping o! “those poor
grandmothers” during the state’s energy crunch grandmothers” during the state’s energy crunch
in 2000-01 ... in 2000-01 ... in 2000-01 ... [AP by Kristen Hays, 06/03/04]in 2000-01 ... in 2000-01 ... in 2000-01 ... in 2000-01 ... [AP by Kristen Hays, 06/03/04]in 2000-01 ... in 2000-01 ... [AP by Kristen Hays, 06/03/04][AP by Kristen Hays, 06/03/04]
As Je!rey Skilling, the "rst but sadly not the last guy
to package up a big sample of nothing and sell it to a greedy
public, Samuel West oozes self-belief; his boss, Ken Lay (Tim
to package up a big sample of nothing and sell it to a greedy to package up a big sample of nothing and sell it to a greedy to package up a big sample of nothing and sell it to a greedy to package up a big sample of nothing and sell it to a greedy to package up a big sample of nothing and sell it to a greedy
As Je!rey Skilling, the "rst but sadly not the last guy
[AP by Kristen Hays, 06/03/04]
NRON to package up a big sample of nothing and sell it to a greedy
public, Samuel West oozes self-belief; his boss, Ken Lay (Tim
Piggott-Smith) and stooge,
public, Samuel West oozes self-belief; his boss, Ken Lay (Tim
Piggott-Smith) and stooge,
up smeared with it. But Lucy Prebble's play is rather more
than a simple tale ...
Piggott-Smith) and stooge,
public, Samuel West oozes self-belief; his boss, Ken Lay (Tim
Piggott-Smith) and stooge, Piggott-Smith) and stooge, Piggott-Smith) and stooge,
public, Samuel West oozes self-belief; his boss, Ken Lay (Tim
to package up a big sample of nothing and sell it to a greedy
NRON As Je!rey Skilling, the "rst but sadly not the last guy As Je!rey Skilling, the "rst but sadly not the last guy NRON As Je!rey Skilling, the "rst but sadly not the last guy As Je!rey Skilling, the "rst but sadly not the last guy As Je!rey Skilling, the "rst but sadly not the last guy
to package up a big sample of nothing and sell it to a greedy
NRON to package up a big sample of nothing and sell it to a greedy to package up a big sample of nothing and sell it to a greedy to package up a big sample of nothing and sell it to a greedy to package up a big sample of nothing and sell it to a greedy
public, Samuel West oozes self-belief; his boss, Ken Lay (Tim public, Samuel West oozes self-belief; his boss, Ken Lay (Tim
to package up a big sample of nothing and sell it to a greedy
public, Samuel West oozes self-belief; his boss, Ken Lay (Tim
to package up a big sample of nothing and sell it to a greedy to package up a big sample of nothing and sell it to a greedy to package up a big sample of nothing and sell it to a greedy to package up a big sample of nothing and sell it to a greedy
public, Samuel West oozes self-belief; his boss, Ken Lay (Tim
to package up a big sample of nothing and sell it to a greedy
public, Samuel West oozes self-belief; his boss, Ken Lay (Tim
Andy Fastow (Tom Goodman-Hill)
up smeared with it. But Lucy Prebble's play is rather more
to package up a big sample of nothing and sell it to a greedy to package up a big sample of nothing and sell it to a greedy
public, Samuel West oozes self-belief; his boss, Ken Lay (Tim
Andy Fastow (Tom Goodman-Hill)
up smeared with it. But Lucy Prebble's play is rather more
-Time Out, London 2010
to package up a big sample of nothing and sell it to a greedy
public, Samuel West oozes self-belief; his boss, Ken Lay (Tim
to package up a big sample of nothing and sell it to a greedy
public, Samuel West oozes self-belief; his boss, Ken Lay (Tim public, Samuel West oozes self-belief; his boss, Ken Lay (Tim public, Samuel West oozes self-belief; his boss, Ken Lay (Tim public, Samuel West oozes self-belief; his boss, Ken Lay (Tim public, Samuel West oozes self-belief; his boss, Ken Lay (Tim public, Samuel West oozes self-belief; his boss, Ken Lay (Tim public, Samuel West oozes self-belief; his boss, Ken Lay (Tim
up smeared with it. But Lucy Prebble's play is rather more
public, Samuel West oozes self-belief; his boss, Ken Lay (Tim public, Samuel West oozes self-belief; his boss, Ken Lay (Tim public, Samuel West oozes self-belief; his boss, Ken Lay (Tim
Andy Fastow (Tom Goodman-Hill) Piggott-Smith) and stooge, Piggott-Smith) and stooge, Andy Fastow (Tom Goodman-Hill)
up smeared with it. But Lucy Prebble's play is rather more up smeared with it. But Lucy Prebble's play is rather more
e ...
up smeared with it. But Lucy Prebble's play is rather more up smeared with it. But Lucy Prebble's play is rather more
Piggott-Smith) and stooge,
up smeared with it. But Lucy Prebble's play is rather more up smeared with it. But Lucy Prebble's play is rather more up smeared with it. But Lucy Prebble's play is rather more
California’s power market during
telephone conversations telephone conversations
gloated about ripping o! “those poor
in 2000-01 ...
As Je!rey Skilling, the "rst but sadly not the last guy
to package up a big sample of nothing and sell it to a greedy to package up a big sample of nothing and sell it to a greedy
public, Samuel West oozes self-belief; his boss, Ken Lay (Tim public, Samuel West oozes self-belief; his boss, Ken Lay (Tim public, Samuel West oozes self-belief; his boss, Ken Lay (Tim public, Samuel West oozes self-belief; his boss, Ken Lay (Tim public, Samuel West oozes self-belief; his boss, Ken Lay (Tim
Andy Fastow (Tom Goodman-Hill)
than a simpl
Enron traders
California’s power market during
in 2000-01 ...
to package up a big sample of nothing and sell it to a greedy to package up a big sample of nothing and sell it to a greedy
up smeared with it. But Lucy Prebble's play is rather more
than a simple tale tale ...
gloated about ripping o! “those poor
grandmothers” during the state’s energy crunch
public, Samuel West oozes self-belief; his boss, Ken Lay (Tim
up smeared with it. But Lucy Prebble's play is rather more up smeared with it. But Lucy Prebble's play is rather more up smeared with it. But Lucy Prebble's play is rather more
“Ripping off those poor grandmothers”
13 / 48
[email protected] and Approaches
Dynamic Markets and their EquilibriaWho Commands the Wind?
Research Frontiers
Issues: Risks to suppliers
Mon Tues Weds Thurs Fri SatSun0
1000
5000
6000
7000
Wind generation (MW)
Balancing Authority Load (MW) January 16-22, 2010
Who will buy my power if the wind is blowing?
14 / 48
[email protected] and Approaches
Dynamic Markets and their EquilibriaWho Commands the Wind?
Research Frontiers
Issues: Friction
Pri
ce (
Au
s $
/MW
h)
Vo
lum
e (
MW
)
Demand
Demand
Prices
Prices
24:00
23:00
22:00
21:00
20:00
19:00
18:00
17:00
16:00
15:00
14:00
13:00
12:00
11:00
10:00
09:00
08:00
07:00
06:00
05:00
04:00
03:00
02:00
01:00
00:00
24:00
23:00
22:00
21:00
20:00
19:00
18:00
17:00
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15:00
14:00
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12:00
11:00
10:00
09:00
08:00
07:00
06:00
05:00
04:00
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02:00
01:00
00:00
19,000
10,000
1,400
1,200
1,000
800
600
400
200
0
1,000
0
- 1,000
- 1,500
1,000
- 1,000
9,000
8,000
10,000
7,000
6,000
5,000
4,000
3,000
2,000
1,000
0
Tasmania
Victoria
Australia - January 16, 2007
Power flows according toKirchoff’s Laws, and subjectto constraints ...
15 / 48
[email protected] and Approaches
Dynamic Markets and their EquilibriaWho Commands the Wind?
Research Frontiers
Issues: Friction
Pri
ce (
Au
s $
/MW
h)
Vo
lum
e (
MW
)
Demand
Demand
Prices
Prices
24:00
23:00
22:00
21:00
20:00
19:00
18:00
17:00
16:00
15:00
14:00
13:00
12:00
11:00
10:00
09:00
08:00
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06:00
05:00
04:00
03:00
02:00
01:00
00:00
24:00
23:00
22:00
21:00
20:00
19:00
18:00
17:00
16:00
15:00
14:00
13:00
12:00
11:00
10:00
09:00
08:00
07:00
06:00
05:00
04:00
03:00
02:00
01:00
00:00
19,000
10,000
1,400
1,200
1,000
800
600
400
200
0
1,000
0
- 1,000
- 1,500
1,000
- 1,000
9,000
8,000
10,000
7,000
6,000
5,000
4,000
3,000
2,000
1,000
0
Tasmania
Victoria
Australia - January 16, 2007
Power flows according toKirchoff’s Laws, and subjectto constraints ...
... Mechanical andthermal constraints, rampconstraints, securityconstraints, ...
15 / 48
[email protected] and Approaches
Dynamic Markets and their EquilibriaWho Commands the Wind?
Research Frontiers
Issues: Friction
Pri
ce (
Au
s $
/MW
h)
Vo
lum
e (
MW
)
Demand
Demand
Prices
Prices
24:00
23:00
22:00
21:00
20:00
19:00
18:00
17:00
16:00
15:00
14:00
13:00
12:00
11:00
10:00
09:00
08:00
07:00
06:00
05:00
04:00
03:00
02:00
01:00
00:00
24:00
23:00
22:00
21:00
20:00
19:00
18:00
17:00
16:00
15:00
14:00
13:00
12:00
11:00
10:00
09:00
08:00
07:00
06:00
05:00
04:00
03:00
02:00
01:00
00:00
19,000
10,000
1,400
1,200
1,000
800
600
400
200
0
1,000
0
- 1,000
- 1,500
1,000
- 1,000
9,000
8,000
10,000
7,000
6,000
5,000
4,000
3,000
2,000
1,000
0
Tasmania
Victoria
Australia - January 16, 2007
Power flows according toKirchoff’s Laws, and subjectto constraints ...
... Mechanical andthermal constraints, rampconstraints, securityconstraints, ...
Market and physical system
are tightly coupled
15 / 48
[email protected] and Approaches
Dynamic Markets and their EquilibriaWho Commands the Wind?
Research Frontiers
Issues: Uncertainty
32
30
28
26
24
22
20
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
Actual Demand (GW)Day Ahead Demand Forecast
Available Resources Forecast (GW)
California ISO www.caiso.com
California ISO www.caiso.com
ISO new england Mission:
• Operate the grid reliably and efficiently• Provide fair and open transmission access• Promote environmental stewardship
• Facilitate effective markets ...16 / 48
[email protected] and Approaches
Dynamic Markets and their EquilibriaWho Commands the Wind?
Research Frontiers
Control solution: Model basedSimplest model that offers insight & leads to useful policy
Listed in order of complexity:
1. Generation is modeled via overall ramp-rate:
G(t1)−G(t0)t1−t0
≤ ζ+, 0 ≤ t0 < t1 < ∞
We may also impose lower bounds.
17 / 48
[email protected] and Approaches
Dynamic Markets and their EquilibriaWho Commands the Wind?
Research Frontiers
Control solution: Model basedSimplest model that offers insight & leads to useful policy
Listed in order of complexity:
1. Generation is modeled via overall ramp-rate:
G(t1)−G(t0)t1−t0
≤ ζ+, 0 ≤ t0 < t1 < ∞
We may also impose lower bounds.
2. Distinguish primary and ancillary service:
Gp(t1)−Gp(t0)t1−t0
≤ ζp+, Ga(t1)−Ga(t0)t1−t0
≤ ζa+
17 / 48
[email protected] and Approaches
Dynamic Markets and their EquilibriaWho Commands the Wind?
Research Frontiers
Control solution: Model basedSimplest model that offers insight & leads to useful policy
Listed in order of complexity:
1. Generation is modeled via overall ramp-rate:
G(t1)−G(t0)t1−t0
≤ ζ+, 0 ≤ t0 < t1 < ∞
We may also impose lower bounds.
2. Distinguish primary and ancillary service:
Gp(t1)−Gp(t0)t1−t0
≤ ζp+, Ga(t1)−Ga(t0)t1−t0
≤ ζa+
3. Introduce transmission constraints:Power flow on transmission lines = linear function of nodalpower values
F (t) = ∆Z(t), ∆ = distribution factor matrix
17 / 48
[email protected] and Approaches
Dynamic Markets and their EquilibriaWho Commands the Wind?
Research Frontiers
Control solution: Model basedSimplest model that offers insight & leads to useful policy
Listed in order of complexity:
1. Generation is modeled via overall ramp-rate:
G(t1)−G(t0)t1−t0
≤ ζ+, 0 ≤ t0 < t1 < ∞
We may also impose lower bounds.
2. Distinguish primary and ancillary service:
Gp(t1)−Gp(t0)t1−t0
≤ ζp+, Ga(t1)−Ga(t0)t1−t0
≤ ζa+
3. Introduce transmission constraints:Power flow on transmission lines = linear function of nodalpower values
F (t) = ∆Z(t), ∆ = distribution factor matrix
F (t) ∈ F := {x ∈ Rℓt : −f+ ≤ x ≤ f+}
17 / 48
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Dynamic Markets and their EquilibriaWho Commands the Wind?
Research Frontiers
Market Analysis: Perfect competition
A beautiful world...
In this lecture,Dynamic market equilibriaunder the most ideal circumstances:
18 / 48
[email protected] and Approaches
Dynamic Markets and their EquilibriaWho Commands the Wind?
Research Frontiers
Market Analysis: Perfect competition
A beautiful world...
In this lecture,Dynamic market equilibriaunder the most ideal circumstances:
Price manipulation is excluded
18 / 48
[email protected] and Approaches
Dynamic Markets and their EquilibriaWho Commands the Wind?
Research Frontiers
Market Analysis: Perfect competition
A beautiful world...
In this lecture,Dynamic market equilibriaunder the most ideal circumstances:
Price manipulation is excludedNo “ENRON games” – no “market power”
18 / 48
[email protected] and Approaches
Dynamic Markets and their EquilibriaWho Commands the Wind?
Research Frontiers
Market Analysis: Perfect competition
A beautiful world...
In this lecture,Dynamic market equilibriaunder the most ideal circumstances:
Price manipulation is excludedNo “ENRON games” – no “market power”
Externalities are disregardedNo government mandates
18 / 48
[email protected] and Approaches
Dynamic Markets and their EquilibriaWho Commands the Wind?
Research Frontiers
Market Analysis: Perfect competition
A beautiful world...
In this lecture,Dynamic market equilibriaunder the most ideal circumstances:
Price manipulation is excludedNo “ENRON games” – no “market power”
Externalities are disregardedNo government mandates
Consumers own available wind generation resources
18 / 48
[email protected] and Approaches
Dynamic Markets and their EquilibriaWho Commands the Wind?
Research Frontiers
Purchase Price $/MWh
Previous week
APX Power NL, April 23, 2007
Cho & Meyn, 2006Illinois, July 1998
Ontario, November 2005
0
1000
2000
3000
4000
5000
Mon Tues Weds Thurs Fri
Tues Weds ThursTime3 6 9 12 15 18 213 6 9 12 15 18 213 6 9 12 15 18 21
Demand in MW Last Updated 11:00 AM Predispatch 1975.11 Dispatch 19683.5
Hourly Ontario Energy Price $/MWh Last Updated 11:00 AM Predispatch 72.79 Dispatch 90.822000
21000
18000
15000
1500
1000
500
0Fore
cast
Pri
ces
Fore
cast
Dem
and
Pric
e (E
uro
/MW
h)
Volu
me
(MW
h)
7000
6000
5000
4000
3000
2000
1000
0
400
300
200
100
0
Fri Sat Sun MonTues Wed Thus
Prev. Week Volume
Current Week Volume
Prev. Week Price
Current Week Price
choke
0
r∗
Prices
Reserves
Normalized demand
Dynamic Markets and their Equilibria
19 / 48
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Dynamic Markets and their EquilibriaWho Commands the Wind?
Research Frontiers
Market StructureDay-ahead market
The day-ahead market (DAM) is cleared one day prior to theactual production and delivery of energy.
Economic world...
Forward markets for electricity which improve market efficiency andserve as a hedging mechanism
20 / 48
[email protected] and Approaches
Dynamic Markets and their EquilibriaWho Commands the Wind?
Research Frontiers
Market StructureDay-ahead market
The day-ahead market (DAM) is cleared one day prior to theactual production and delivery of energy.
Economic world...
Forward markets for electricity which improve market efficiency andserve as a hedging mechanism
...Physical world
Facilitate the scheduling of generating units
20 / 48
[email protected] and Approaches
Dynamic Markets and their EquilibriaWho Commands the Wind?
Research Frontiers
Market StructureReal-time market
At close of the DAM: The ISO generates a schedule of generatorsto supply specific levels of power for each hour over the next 24hour period.
RTM = Balancing Market
As supply and demand are not perfectly predictable, the RTMplays the role of fine-tuning this resource allocation process
21 / 48
[email protected] and Approaches
Dynamic Markets and their EquilibriaWho Commands the Wind?
Research Frontiers
Market StructureReal-time market
At close of the DAM: The ISO generates a schedule of generatorsto supply specific levels of power for each hour over the next 24hour period.
RTM = Balancing Market
As supply and demand are not perfectly predictable, the RTMplays the role of fine-tuning this resource allocation process
RTM is the focus here
21 / 48
[email protected] and Approaches
Dynamic Markets and their EquilibriaWho Commands the Wind?
Research Frontiers
Market AnalysisFirst Welfare Theorem
Efficient Equilibrium
max K(g, d) = E[∫
e−γt(WS(t) + WD(t)
)dt
]
.
subject to GS(t) = GD(t) for all t
22 / 48
[email protected] and Approaches
Dynamic Markets and their EquilibriaWho Commands the Wind?
Research Frontiers
Market AnalysisFirst Welfare Theorem
Efficient Equilibrium
max K(g, d) = E[∫
e−γt(WS(t) + WD(t)
)dt
]
.
subject to GS(t) = GD(t) for all t
Welfare functions defined with a nominal price function P (t)
22 / 48
[email protected] and Approaches
Dynamic Markets and their EquilibriaWho Commands the Wind?
Research Frontiers
Market AnalysisFirst Welfare Theorem
Efficient Equilibrium
max K(g, d) = E[∫
e−γt(WS(t) + WD(t)
)dt
]
.
subject to GS(t) = GD(t) for all t
Welfare functions defined with a nominal price function P (t)
Key component of equilibrium theory:
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).
22 / 48
[email protected] and Approaches
Dynamic Markets and their EquilibriaWho Commands the Wind?
Research Frontiers
Market AnalysisFirst Welfare Theorem
Efficient Equilibrium
max K(g, d) = E[∫
e−γt(WS(t) + WD(t)
)dt
]
.
subject to GS(t) = GD(t) for all t
Welfare functions defined with a nominal price function P (t)
Key component of equilibrium theory:
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”
22 / 48
[email protected] and Approaches
Dynamic Markets and their EquilibriaWho Commands the Wind?
Research Frontiers
Market AnalysisFirst Welfare Theorem
Efficient Equilibrium
max K(g, d) = E[∫
e−γt(WS(t) + WD(t)
)dt
]
.
subject to GS(t) = GD(t) for all t
Welfare functions defined with a nominal price function P (t)
Special case: Welfare functions are piecewise linear,
WS(t) := P (t)GS(t) − cG(t)
WD(t) := v min(D(t), GD(t))
− cbo max(0,−R(t)) − P (t)GD(t)
23 / 48
[email protected] and Approaches
Dynamic Markets and their EquilibriaWho Commands the Wind?
Research Frontiers
Market AnalysisFirst Welfare Theorem
Efficient Equilibrium
max K(g, d) = E[∫
e−γt(WS(t) + WD(t)
)dt
]
.
subject to GS(t) = GD(t) for all t
Welfare functions defined with a nominal price function P (t)
Special case: Welfare functions are piecewise linear,
WS(t) := P (t)GS(t) − cG(t)
WD(t) := v min(D(t), GD(t))
− cbo max(0,−R(t)) − P (t)GD(t)
Price function P (t) is irrelevant when GS(t) = GD(t)
23 / 48
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Dynamic Markets and their EquilibriaWho Commands the Wind?
Research Frontiers
Market AnalysisFirst Welfare Theorem
First Welfare Theorem ⇐⇒ Lagrangian Decomposition
max K(g, d) = E[∫
e−γt{(
WS(t) + WD(t))
+ λ(t)(GS(t) − GD(t)
)}
dt]
24 / 48
[email protected] and Approaches
Dynamic Markets and their EquilibriaWho Commands the Wind?
Research Frontiers
Market AnalysisFirst Welfare Theorem
First Welfare Theorem ⇐⇒ Lagrangian Decomposition
max K(g, d) = maxGS
E[∫
e−γt(WS(t) + λ(t)GS(t)
)dt
]
+ maxGD
E[∫
e−γt(WD(t) − λ(t)GD(t)
)dt
]
25 / 48
[email protected] and Approaches
Dynamic Markets and their EquilibriaWho Commands the Wind?
Research Frontiers
Market AnalysisFirst Welfare Theorem
First Welfare Theorem ⇐⇒ Lagrangian Decomposition
max K(g, d) = maxGS
E[∫
e−γt(WS(t) + λ(t)GS(t)
)dt
]
+ maxGD
E[∫
e−γt(WD(t) − λ(t)GD(t)
)dt
]
Assume: Social planner’s problem has a solution, and there is noduality gap.
25 / 48
[email protected] and Approaches
Dynamic Markets and their EquilibriaWho Commands the Wind?
Research Frontiers
Market AnalysisFirst Welfare Theorem
First Welfare Theorem ⇐⇒ Lagrangian Decomposition
max K(g, d) = maxGS
E[∫
e−γt(WS(t) + λ(t)GS(t)
)dt
]
+ maxGD
E[∫
e−γt(WD(t) − λ(t)GD(t)
)dt
]
Assume: Social planner’s problem has a solution, and there is noduality gap. Then P ∗(t) = P (t) + λ∗(t) provides an efficientequilibrium.
25 / 48
[email protected] and Approaches
Dynamic Markets and their EquilibriaWho Commands the Wind?
Research Frontiers
Market AnalysisFirst Welfare Theorem
First Welfare Theorem ⇐⇒ Lagrangian Decomposition
max K(g, d) = maxGS
E[∫
e−γt(WS(t) + λ(t)GS(t)
)dt
]
+ maxGD
E[∫
e−γt(WD(t) − λ(t)GD(t)
)dt
]
Assume: Social planner’s problem has a solution, and there is noduality gap. Then P ∗(t) = P (t) + λ∗(t) provides an efficientequilibrium.
What does an efficient equilibrium look like?
25 / 48
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Dynamic Markets and their EquilibriaWho Commands the Wind?
Research Frontiers
What does an efficient equilibrium look like?Market analysis assumptions
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.
26 / 48
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Dynamic Markets and their EquilibriaWho Commands the Wind?
Research Frontiers
What does an efficient equilibrium look like?Market analysis assumptions
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.
Cost
The production cost is a linear function of G(t),of the form cG(t) for some constant c > 0.
26 / 48
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Dynamic Markets and their EquilibriaWho Commands the Wind?
Research Frontiers
What does an efficient equilibrium look like?Market analysis assumptions
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.
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)).
26 / 48
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Dynamic Markets and their EquilibriaWho Commands the Wind?
Research Frontiers
What does an efficient equilibrium look like?Answer: Marginal value
Equilibrium price
The equilibrium price functional is a piecewise constant function ofthe equilibrium reserve process,
pe(re) = (v + cbo)I{re < 0}
27 / 48
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Dynamic Markets and their EquilibriaWho Commands the Wind?
Research Frontiers
What does an efficient equilibrium look like?Answer: Marginal value
Equilibrium price
The equilibrium price functional is a piecewise constant function ofthe equilibrium reserve process,
pe(re) = (v + cbo)I{re < 0}
P ∗(t) = pe(Re(t)) : marginal value of power to the consumer
27 / 48
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Dynamic Markets and their EquilibriaWho Commands the Wind?
Research Frontiers
Market EquilibriumPrice Dynamics
v + cbo
0
r∗
Prices
Reserves
Normalized demand
P ∗(t) = pe(Re(t)): The marginal value of power to the consumer
28 / 48
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Dynamic Markets and their EquilibriaWho Commands the Wind?
Research Frontiers
Market EquilibriumPrice Dynamics
v + cbo
0
r∗
Prices
Reserves
Normalized demand
P ∗(t) = pe(Re(t)): The marginal value of power to the consumer
Smoother prices obtained when cost/utility are strictly convex
28 / 48
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Dynamic Markets and their EquilibriaWho Commands the Wind?
Research Frontiers
Familiar, right?
Purchase Price $/MWh
Previous week
Spinning reserve prices PX prices $/MWh
100
150
0
50
200
250
10
20
30
40
50
60
70
APX Power NL, April 23, 2007
California, July 2000Illinois, July 1998
Ontario, November 2005
0
1000
2000
3000
4000
5000
Mon Tues Weds Thurs Fri Mon Tues WedsWeds Thurs Fri Sat Sun
Tues Weds ThursTime3 6 9 12 15 18 213 6 9 12 15 18 213 6 9 12 15 18 21
Demand in MW Last Updated 11:00 AM Predispatch 1975.11 Dispatch 19683.5
Hourly Ontario Energy Price $/MWh Last Updated 11:00 AM Predispatch 72.79 Dispatch 90.822000
21000
18000
15000
1500
1000
500
0Fore
cast
Pri
ces
Fore
cast
De
ma
nd
Pri
ce (E
uro
/MW
h)
Vo
lum
e (M
Wh
)
7000
6000
5000
4000
3000
2000
1000
0
400
300
200
100
0
Fri Sat Sun MonTues Wed Thus
Prev. Week Volume
Current Week Volume
Prev. Week Price
Current Week Price
29 / 48
[email protected] and Approaches
Dynamic Markets and their EquilibriaWho Commands the Wind?
Research Frontiers
Sustainable business?
Marginal value ofelectricity may bev + cbo =$200,000/MWh!
Purchase Price $/MWh
Previous week
Spinning reserve prices PX prices $/MWh
100
150
0
50
200
250
10
20
30
40
50
60
70
APX Power NL, April 23, 2007
California, July 2000Illinois, July 1998
Ontario, November 2005
0
1000
2000
3000
4000
5000
Mon Tues Weds Thurs Fri Mon Tues WedsWeds Thurs Fri Sat Sun
Tues Weds ThursTime3 6 9 12 15 18 213 6 9 12 15 18 213 6 9 12 15 18 21
Demand in MW Last Updated 11:00 AM Predispatch 1975.11 Dispatch 19683.5
Hourly Ontario Energy Price $/MWh Last Updated 11:00 AM Predispatch 72.79 Dispatch 90.822000
21000
18000
15000
1500
1000
500
0Fore
cast
Pri
ces
Fore
cast
De
ma
nd
Pri
ce (E
uro
/MW
h)
Vo
lum
e (M
Wh
)
7000
6000
5000
4000
3000
2000
1000
0
400
300
200
100
0
Fri Sat Sun MonTues Wed Thus
Prev. Week Volume
Current Week Volume
Prev. Week Price
Current Week Price
30 / 48
[email protected] and Approaches
Dynamic Markets and their EquilibriaWho Commands the Wind?
Research Frontiers
Sustainable business?
Marginal value ofelectricity may bev + cbo =$200,000/MWh!
Purchase Price $/MWh
Previous week
Spinning reserve prices PX prices $/MWh
100
150
0
50
200
250
10
20
30
40
50
60
70
APX Power NL, April 23, 2007
California, July 2000Illinois, July 1998
Ontario, November 2005
0
1000
2000
3000
4000
5000
Mon Tues Weds Thurs Fri Mon Tues WedsWeds Thurs Fri Sat Sun
Tues Weds ThursTime3 6 9 12 15 18 213 6 9 12 15 18 213 6 9 12 15 18 21
Demand in MW Last Updated 11:00 AM Predispatch 1975.11 Dispatch 19683.5
Hourly Ontario Energy Price $/MWh Last Updated 11:00 AM Predispatch 72.79 Dispatch 90.822000
21000
18000
15000
1500
1000
500
0Fore
cast
Pri
ces
Fore
cast
De
ma
nd
Pri
ce (E
uro
/MW
h)
Vo
lum
e (M
Wh
)
7000
6000
5000
4000
3000
2000
1000
0
400
300
200
100
0
Fri Sat Sun MonTues Wed Thus
Prev. Week Volume
Current Week Volume
Prev. Week Price
Current Week Price
Yet, in this equilibrium, expected price is preciselythe ‘marginal cost’ c.
30 / 48
[email protected] and Approaches
Dynamic Markets and their EquilibriaWho Commands the Wind?
Research Frontiers
Sustainable business?
Marginal value ofelectricity may bev + cbo =$200,000/MWh!
Purchase Price $/MWh
Previous week
Spinning reserve prices PX prices $/MWh
100
150
0
50
200
250
10
20
30
40
50
60
70
APX Power NL, April 23, 2007
California, July 2000Illinois, July 1998
Ontario, November 2005
0
1000
2000
3000
4000
5000
Mon Tues Weds Thurs Fri Mon Tues WedsWeds Thurs Fri Sat Sun
Tues Weds ThursTime3 6 9 12 15 18 213 6 9 12 15 18 213 6 9 12 15 18 21
Demand in MW Last Updated 11:00 AM Predispatch 1975.11 Dispatch 19683.5
Hourly Ontario Energy Price $/MWh Last Updated 11:00 AM Predispatch 72.79 Dispatch 90.822000
21000
18000
15000
1500
1000
500
0Fore
cast
Pri
ces
Fore
cast
De
ma
nd
Pri
ce (E
uro
/MW
h)
Vo
lum
e (M
Wh
)
7000
6000
5000
4000
3000
2000
1000
0
400
300
200
100
0
Fri Sat Sun MonTues Wed Thus
Prev. Week Volume
Current Week Volume
Prev. Week Price
Current Week Price
Yet, in this equilibrium, expected price is preciselythe ‘marginal cost’ c.
Is this a sustainable business?
30 / 48
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Dynamic Markets and their EquilibriaWho Commands the Wind?
Research Frontiers
Who Commands the Wind?
31 / 48
[email protected] and Approaches
Dynamic Markets and their EquilibriaWho Commands the Wind?
Research Frontiers
Extending the dynamic model
Goal
Extend the DA/RT market model to differentiate power generatedby wind and by conventional generation units
32 / 48
[email protected] and Approaches
Dynamic Markets and their EquilibriaWho Commands the Wind?
Research Frontiers
Extending the dynamic model
Goal
Extend the DA/RT market model to differentiate power generatedby wind and by conventional generation units
Assumption
All the wind power available is injected into the system
32 / 48
[email protected] and Approaches
Dynamic Markets and their EquilibriaWho Commands the Wind?
Research Frontiers
Extending the dynamic model
Goal
Extend the DA/RT market model to differentiate power generatedby wind and by conventional generation units
Assumption
All the wind power available is injected into the system
Key issue
Conventional generators serve residual demand.
32 / 48
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Dynamic Markets and their EquilibriaWho Commands the Wind?
Research Frontiers
Extending the dynamic model
Goal
Extend the DA/RT market model to differentiate power generatedby 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 inthe dynamic market equilibrium
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Dynamic Markets and their EquilibriaWho Commands the Wind?
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Emerging issues
Not only mean energy
The details depend on both volatility of wind and its proportion ofthe overall generation
What about now?
If the penetration of wind resources is low, then the increase inload volatility will be negligible, and hence there will be negligibleimpact on the market outcomes
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Dynamic Markets and their EquilibriaWho Commands the Wind?
Research Frontiers
Emerging issues
Not only mean energy
The details depend on both volatility of wind and its proportion ofthe overall generation
What about now?
If the penetration of wind resources is low, then the increase inload volatility will be negligible, and hence there will be negligibleimpact on the market outcomes
What about in 2020?
Potential negative market outcomes are possible with acombination of high wind generation penetration and highvolatility of wind
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Research Frontiers
Who Commands the Wind?Main findings
Volatility can have tremendous impact on the market outcome
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Dynamic Markets and their EquilibriaWho Commands the Wind?
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Who Commands the Wind?Main findings
Volatility can have tremendous impact on the market outcome
Asymmetric and surprising result
The supplier can achieve significant gains,even when the consumer commands the wind
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Dynamic Markets and their EquilibriaWho Commands the Wind?
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Who Commands the Wind?Main findings
Volatility can have tremendous impact on the market outcome
Asymmetric and surprising result
The supplier can achieve significant gains,even when the consumer commands the wind
Why?
1. Higher variance in forecasting =⇒ higher reserves in DAM fromtraditional sources such as coal.
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Dynamic Markets and their EquilibriaWho Commands the Wind?
Research Frontiers
Who Commands the Wind?Main findings
Volatility can have tremendous impact on the market outcome
Asymmetric and surprising result
The supplier can achieve significant gains,even when the consumer commands the wind
Why?
1. Higher variance in forecasting =⇒ higher reserves in DAM fromtraditional sources such as coal.2. Higher real-time volatility =⇒ greater reliance on ‘peakingunits’ such as gas-turbine generators.
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Consumers command the wind
Wind generating units are commanded by the demand side:
Consumers’ and suppliers’ welfare expressions
Wttl
D,W(t) = v min(Dttl(t), Gttl(t) + Gttl
W(t))
− cbo max(0,−R(t))
− P (t)G(t) − p(t)gda(t)
Wttl
S,W(t) =(P (t) − crt
)G(t) +
(p(t) − cda
)gda(t)
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Consumers command the wind
Welfare expressions: DAM/RTM decomposition
Wttl
D,W(t) = Wrt
D,W(t)
+{vdda(t) − p(t)(dda(t) − gda
W(t))
}
+{(P (t) − p(t))rda
0 + vGW(t)}
Wttl
S,W(t) = Wrt
S,W(t) +(p(t) − cda
)gda(t)
Wrt
D,W(t), Wrt
S,W(t): Welfare obtained in the RTMwith residual demand Dnet(t).
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Numerical Results: Parameters
Penetration and volatility
Coefficient of variation to capture the relative volatility of wind:
cv =σw
E[Gttl
W(t)]
Percentage of wind penetration:
k = 100 ∗ E[Gttl
W(t)]/Dttl
Remaining model/statistical details in 2010 preprint,The value of volatile resources in electricity markets.
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Numerical Results: Volatility ImpactsOptimal reserves rise with volatility
cv
k = 0
k = 5
k = 10
k = 15
k = 20
0.10 0.2 0.30
20
40
60
80Optimal Reserve Level
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Numerical Results: Consumers command the windConsumer welfare falls and supplier welfare rises with volatility
0 0.1 0.2 0.3 0.40 0.1 0.2 0.3 0.4
x 106
Supplier Welfare
k = 0
k = 5
k = 10
k = 15
k = 20
x 106
Consumer Welfare
10
0
5
15
k = 0
k = 5
k = 10
k = 15k = 20
3
4
5
cv
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Research Frontiers
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Dynamic Markets and their EquilibriaWho Commands the Wind?
Research Frontiers
Research FrontiersStrategic behavior
Q1
Building bridges
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Research Frontiers
Research FrontiersStrategic behavior
Q1
Building bridges between researchers in economics,systems/statistical sciences, and power engineers.
How could two smart people come to such different conclusions?
I had to get to the bottom of this. –MacKay 2009
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Research FrontiersStrategic behavior
Q1
Building bridges between researchers in economics,systems/statistical sciences, and power engineers.
How could two smart people come to such different conclusions?
I had to get to the bottom of this. –MacKay 2009
Q1a: Incorporate dynamics and uncertainty in a strategic setting?
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Dynamic Markets and their EquilibriaWho Commands the Wind?
Research Frontiers
Research FrontiersStrategic behavior
Q1
Building bridges between researchers in economics,systems/statistical sciences, and power engineers.
How could two smart people come to such different conclusions?
I had to get to the bottom of this. –MacKay 2009
Q1a: Incorporate dynamics and uncertainty in a strategic setting?
Approach: Follow the example of highway engineering:
Analysis of strategic behavior will be possible if agent behavior
is suitably constrained
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Dynamic Markets and their EquilibriaWho Commands the Wind?
Research Frontiers
Research FrontiersStrategic behavior
Q1
Building bridges between researchers in economics,systems/statistical sciences, and power engineers.
How could two smart people come to such different conclusions?
I had to get to the bottom of this. –MacKay 2009
Q1a: Incorporate dynamics and uncertainty in a strategic setting?
Approach: Follow the example of highway engineering:
Analysis of strategic behavior will be possible if agent behavior
is suitably constrained
Stalinist?
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Dynamic Markets and their EquilibriaWho Commands the Wind?
Research Frontiers
Research FrontiersStrategic behavior
Q1
Building bridges between researchers in economics,systems/statistical sciences, and power engineers.
How could two smart people come to such different conclusions?
I had to get to the bottom of this. –MacKay 2009
Q1a: Incorporate dynamics and uncertainty in a strategic setting?
Approach: Follow the example of highway engineering:
Analysis of strategic behavior will be possible if agent behavior
is suitably constrained
Stalinist? The economic security of the region is at stake! Expectationsto market participants must be made clear, and must be enforced!!
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Dynamic Markets and their EquilibriaWho Commands the Wind?
Research Frontiers
Research FrontiersStatistics
Q2
Learning
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Dynamic Markets and their EquilibriaWho Commands the Wind?
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Research FrontiersStatistics
Q2
Learning (a) Once a market framework is in place, agents willlearn over time to optimize their reward
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Research FrontiersStatistics
Q2
Learning (a) Once a market framework is in place, agents willlearn over time to optimize their reward Q-learning and
TD-learning are potential approaches
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Dynamic Markets and their EquilibriaWho Commands the Wind?
Research Frontiers
Research FrontiersStatistics
Q2
Learning (a) Once a market framework is in place, agents willlearn over time to optimize their reward Q-learning and
TD-learning are potential approaches
(b) Forecasting energy demand and supply with uncertain wind,tides, sun, and a ‘smart grid’.
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Dynamic Markets and their EquilibriaWho Commands the Wind?
Research Frontiers
Research FrontiersStatistics
Q2
Learning (a) Once a market framework is in place, agents willlearn over time to optimize their reward Q-learning and
TD-learning are potential approaches
(b) Forecasting energy demand and supply with uncertain wind,tides, sun, and a ‘smart grid’.
(c) Predicting blackout or cascading failures
(d), (e), ...
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Dynamic Markets and their EquilibriaWho Commands the Wind?
Research Frontiers
Research FrontiersControlling supply, storage, and demand
Q3
The impact of demand management and storage on the market
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Dynamic Markets and their EquilibriaWho Commands the Wind?
Research Frontiers
Research FrontiersControlling supply, storage, and demand
Q3
The impact of demand management and storage on the market
Q4
The impact of supply management and storage on the market.e.g., modern wind turbines allow pitch angle control.
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Dynamic Markets and their EquilibriaWho Commands the Wind?
Research Frontiers
Research FrontiersControlling supply, storage, and demand
Q3
The impact of demand management and storage on the market
Q4
The impact of supply management and storage on the market.e.g., modern wind turbines allow pitch angle control.
Beyond arithmetic:
What are the dynamical properties of the power grid in
LA county with dynamic pricing, hybrid cars, and
automated water pumping?
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Dynamic Markets and their EquilibriaWho Commands the Wind?
Research Frontiers
Research FrontiersFacing volatility
Q5
Not just “missing money” —
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Dynamic Markets and their EquilibriaWho Commands the Wind?
Research Frontiers
Research FrontiersFacing volatility
Q5
Not just “missing money” — Mechanisms to reduce consumersand suppliers exposure to volatility.
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Dynamic Markets and their EquilibriaWho Commands the Wind?
Research Frontiers
Research FrontiersFacing volatility
Q5
Not just “missing money” — Mechanisms to reduce consumersand suppliers exposure to volatility.
Especially supply-side volatility with introduction of renewableenergy, such as wind
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Dynamic Markets and their EquilibriaWho Commands the Wind?
Research Frontiers
Research FrontiersLong-term incentives
Q6
How to create policies to protect participants on both sides of themarket, while creating incentives for R&D on renewable energy?
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Dynamic Markets and their EquilibriaWho Commands the Wind?
Research Frontiers
Research FrontiersLong-term incentives
Q6
How to create policies to protect participants on both sides of themarket, while creating incentives for R&D on renewable energy?
The economic notion of efficiency disregards issues such asemissions, or public safety.
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Dynamic Markets and their EquilibriaWho Commands the Wind?
Research Frontiers
Research FrontiersLong-term incentives
Q6
How to create policies to protect participants on both sides of themarket, while creating incentives for R&D on renewable energy?
The economic notion of efficiency disregards issues such asemissions, or public safety.
We hope that the ideas described here will form a building blockfor constructing and analyzing far more intricate models, takinginto account a broader range of issues.
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Thanks!
Celebrating with Dutch Babies after finishing The value of volatile
resources...
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Complex Networks FOR
Sean Meyn
Control Techniques
References
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References
I.-K. Cho and S. P. Meyn. Efficiency and marginal cost pricing in dynamic
competitive markets. To appear in J. Theo. Economics, 2010.
M. Chen, I.-K. Cho, and S. Meyn. Reliability by design in a distributed power
transmission network. Automatica, 42:1267–1281, August 2006.
I.-K. Cho and S. P. Meyn. A dynamic newsboy model for optimal reserve
management in electricity markets. Submitted for publication, SIAM J. Control
and Optimization., 2009.
S. Meyn, M. Negrete-Pincetic, G. Wang, A. Kowli, and E. Shafieepoorfard.
The value of volatile resources in electricity markets. Submitted Proc. of the
49th Conf. on Dec. and Control, Atlanta, GA, 2010.
D. J. C. MacKay. Sustainable energy : without the hot air. UIT, Cambridge,
England, 2009.
L. M. Wein. Dynamic scheduling of a multiclass make-to-stock queue.
Operations Res., 40:724–735, 1992.
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