tutorial for energy systems week - cambridge 2010
DESCRIPTION
Energy Systems Week Isaac Newton Institute for Mathematical Sciences, May 24-28, 2010 Note: this is a 2010 tutorial. Much has changed in the past three years - you may find more recent tutorials on sideshare and at my website www.meyn.ece.ufl.edu/TRANSCRIPT
Issues and ApproachesReliability by Design
Dynamic Markets and their EquilibriaWho Commands the Wind?
Research FrontiersReferences
Dynamic Models and Dynamic Markets
for Electric Power Networks
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
May 25, 2010
1 / 66
Issues and ApproachesReliability by Design
Dynamic Markets and their EquilibriaWho Commands the Wind?
Research FrontiersReferences
Outline
1 Issues and Approaches
2 Reliability by Design
3 Dynamic Markets and their Equilibria
4 Who Commands the Wind?
5 Research Frontiers
6 References
2 / 66
Issues and ApproachesReliability by Design
Dynamic Markets and their EquilibriaWho Commands the Wind?
Research FrontiersReferences
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
Victoria
Tasmania
Issues and Approaches
3 / 66
Issues and ApproachesReliability by Design
Dynamic Markets and their EquilibriaWho Commands the Wind?
Research FrontiersReferences
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
4 / 66
Issues and ApproachesReliability by Design
Dynamic Markets and their EquilibriaWho Commands the Wind?
Research FrontiersReferences
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.
5 / 66
Issues and ApproachesReliability by Design
Dynamic Markets and their EquilibriaWho Commands the Wind?
Research FrontiersReferences
Issues: Complexity
Interconnected
network of
ENTSO-E
European Network of TransmissionSystem Operators for Electricity
6 / 66
Issues and ApproachesReliability by Design
Dynamic Markets and their EquilibriaWho Commands the Wind?
Research FrontiersReferences
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”
7 / 66
Issues and ApproachesReliability by Design
Dynamic Markets and their EquilibriaWho Commands the Wind?
Research FrontiersReferences
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?
8 / 66
Issues and ApproachesReliability by Design
Dynamic Markets and their EquilibriaWho Commands the Wind?
Research FrontiersReferences
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 ...
9 / 66
Issues and ApproachesReliability by Design
Dynamic Markets and their EquilibriaWho Commands the Wind?
Research FrontiersReferences
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, ...
9 / 66
Issues and ApproachesReliability by Design
Dynamic Markets and their EquilibriaWho Commands the Wind?
Research FrontiersReferences
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
9 / 66
Issues and ApproachesReliability by Design
Dynamic Markets and their EquilibriaWho Commands the Wind?
Research FrontiersReferences
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
CAISO Mission:
• Operate the grid reliably and efficiently• Provide fair and open transmission access• Promote environmental stewardship• Facilitate effective markets ...
10 / 66
Issues and ApproachesReliability by Design
Dynamic Markets and their EquilibriaWho Commands the Wind?
Research FrontiersReferences
Control solution: Model basedSimplest model that 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.
11 / 66
Issues and ApproachesReliability by Design
Dynamic Markets and their EquilibriaWho Commands the Wind?
Research FrontiersReferences
Control solution: Model basedSimplest model that 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+
11 / 66
Issues and ApproachesReliability by Design
Dynamic Markets and their EquilibriaWho Commands the Wind?
Research FrontiersReferences
Control solution: Model basedSimplest model that 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
11 / 66
Issues and ApproachesReliability by Design
Dynamic Markets and their EquilibriaWho Commands the Wind?
Research FrontiersReferences
Control solution: Model basedSimplest model that 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+}
11 / 66
Issues and ApproachesReliability by Design
Dynamic Markets and their EquilibriaWho Commands the Wind?
Research FrontiersReferences
Market Analysis: Perfect competition
A beautiful world...
In this lecture,Dynamic market equilibriaunder the most ideal circumstances:
12 / 66
Issues and ApproachesReliability by Design
Dynamic Markets and their EquilibriaWho Commands the Wind?
Research FrontiersReferences
Market Analysis: Perfect competition
A beautiful world...
In this lecture,Dynamic market equilibriaunder the most ideal circumstances:
Price manipulation is excluded
12 / 66
Issues and ApproachesReliability by Design
Dynamic Markets and their EquilibriaWho Commands the Wind?
Research FrontiersReferences
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”
12 / 66
Issues and ApproachesReliability by Design
Dynamic Markets and their EquilibriaWho Commands the Wind?
Research FrontiersReferences
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
12 / 66
Issues and ApproachesReliability by Design
Dynamic Markets and their EquilibriaWho Commands the Wind?
Research FrontiersReferences
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
12 / 66
Issues and ApproachesReliability by Design
Dynamic Markets and their EquilibriaWho Commands the Wind?
Research FrontiersReferences
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
Reliability by Design
13 / 66
Issues and ApproachesReliability by Design
Dynamic Markets and their EquilibriaWho Commands the Wind?
Research FrontiersReferences
Reliability: How to achieve the CAISO Mission?
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
Begin with,• Operate the grid reliably and efficiently
14 / 66
Issues and ApproachesReliability by Design
Dynamic Markets and their EquilibriaWho Commands the Wind?
Research FrontiersReferences
Reliability: How to achieve the CAISO Mission?
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
Begin with,• Operate the grid reliably and efficiently
These can wait:
• Provide fair and open transmission access• Promote environmental stewardship• Facilitate effective markets ...
14 / 66
Issues and ApproachesReliability by Design
Dynamic Markets and their EquilibriaWho Commands the Wind?
Research FrontiersReferences
A diffusion modelDynamic model for reserves
R(t) = Available power − Demand = G(t) − D(t)
15 / 66
Issues and ApproachesReliability by Design
Dynamic Markets and their EquilibriaWho Commands the Wind?
Research FrontiersReferences
A diffusion modelDynamic model for reserves
R(t) = Available power − Demand = G(t) − D(t)
D(t) = Actual demand − Forecast demand
G(t): Deviation in on-line capacity from day-ahead market
15 / 66
Issues and ApproachesReliability by Design
Dynamic Markets and their EquilibriaWho Commands the Wind?
Research FrontiersReferences
A diffusion modelDynamic model for reserves
R(t) = Available power − Demand = G(t) − D(t)
D(t) = Actual demand − Forecast demand
G(t): Deviation in on-line capacity from day-ahead market
Volatility
Deviation in demand D is modeled as a driftless Brownian motionwith instantaneous variance σ2 (imposed for computation)
15 / 66
Issues and ApproachesReliability by Design
Dynamic Markets and their EquilibriaWho Commands the Wind?
Research FrontiersReferences
A diffusion modelDynamic model for reserves
R(t) = Available power − Demand = G(t) − D(t)
D(t) = Actual demand − Forecast demand
G(t): Deviation in on-line capacity from day-ahead market
Volatility
Deviation in demand D is modeled as a driftless Brownian motionwith instantaneous variance σ2 (imposed for computation)
Friction
Generation cannot increase instantaneously:
G(t′) − G(t)
t′ − t≤ ζ , for all t ≥ 0, and t′ > t.
15 / 66
Issues and ApproachesReliability by Design
Dynamic Markets and their EquilibriaWho Commands the Wind?
Research FrontiersReferences
Social planner’s objective
Discounted welfare: For given initial generation and demand,
K(g, d) = E[
∫
e−γt(
WS(t) + WD(t) + WE(t))
dt]
.
Welfare functions:
Supplier, WS(t): payments - cost
16 / 66
Issues and ApproachesReliability by Design
Dynamic Markets and their EquilibriaWho Commands the Wind?
Research FrontiersReferences
Social planner’s objective
Discounted welfare: For given initial generation and demand,
K(g, d) = E[
∫
e−γt(
WS(t) + WD(t) + WE(t))
dt]
.
Welfare functions:
Supplier, WS(t): payments - cost
Consumer, WD(t): utility - payments - cost of b/o
16 / 66
Issues and ApproachesReliability by Design
Dynamic Markets and their EquilibriaWho Commands the Wind?
Research FrontiersReferences
Social planner’s objective
Discounted welfare: For given initial generation and demand,
K(g, d) = E[
∫
e−γt(
WS(t) + WD(t) + WE(t))
dt]
.
Welfare functions:
Supplier, WS(t): payments - cost
Consumer, WD(t): utility - payments - cost of b/o
External, WE(t): environmental, political
16 / 66
Issues and ApproachesReliability by Design
Dynamic Markets and their EquilibriaWho Commands the Wind?
Research FrontiersReferences
Social planner’s objective
Discounted welfare: For given initial generation and demand,
K(g, d) = E[
∫
e−γt(
WS(t) + WD(t) + WE(t))
dt]
.
Welfare functions:
Supplier, WS(t): payments - cost
Consumer, WD(t): utility - payments - cost of b/o
External, WE(t): environmental, political
Goal: Maximize the discounted social welfare
16 / 66
Issues and ApproachesReliability by Design
Dynamic Markets and their EquilibriaWho Commands the Wind?
Research FrontiersReferences
Social planner’s objectivePiecewise linear welfare
Linear costs and values
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)
17 / 66
Issues and ApproachesReliability by Design
Dynamic Markets and their EquilibriaWho Commands the Wind?
Research FrontiersReferences
Social planner’s objectivePiecewise linear welfare
Linear costs and values
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)
=⇒ discounted welfare is a function of reserves
K(g, d) = (v − c)d + E[
∫
e−γtw(R(t)) dt]
w(R(t)) = v min(0, R(t)) + cbo min(R(t), 0) − c(R(t))
17 / 66
Issues and ApproachesReliability by Design
Dynamic Markets and their EquilibriaWho Commands the Wind?
Research FrontiersReferences
Social planner’s objectivePiecewise linear welfare
Discounted welfare is a function of reserves
K(g, d) = (v − c)d + E[
∫
e−γtw(R(t)) dt]
w(R(t)) = v min(0, R(t)) + cbo min(R(t), 0) − c(R(t))
Threshold policy
Optimal threshold: r̄∗ =1
θ+log
(
cbo + v
c
)
where θ+ > 0 solves, 12σ2θ2 − ζθ − γ = 0
18 / 66
Issues and ApproachesReliability by Design
Dynamic Markets and their EquilibriaWho Commands the Wind?
Research FrontiersReferences
Social planner’s objectivePiecewise linear welfare
Threshold policy
Optimal threshold: r̄∗ =1
θ+log
(
cbo + v
c
)
where θ+ > 0 solves, 12σ2θ2 − ζθ − γ = 0
Average cost case:1
θ+→ 1
2
σ2
ζ, as γ ↓ 0.
19 / 66
Issues and ApproachesReliability by Design
Dynamic Markets and their EquilibriaWho Commands the Wind?
Research FrontiersReferences
Social planner’s objectiveReserve Dynamics
Optimal reserves = reflected Brownian motion:
0
r∗
Reserves
Normalized demand
Optimal threshold r̄∗ = 1θ+
log(
cbo+vc
)
,
where θ+ > 0 solves, 12σ2θ2 − ζθ − γ = 0
20 / 66
Issues and ApproachesReliability by Design
Dynamic Markets and their EquilibriaWho Commands the Wind?
Research FrontiersReferences
Primary and Ancillary ServiceMultiple thresholds
R(t) = Available power − Demand = Gp(t) + Ga(t) − D(t)
21 / 66
Issues and ApproachesReliability by Design
Dynamic Markets and their EquilibriaWho Commands the Wind?
Research FrontiersReferences
Primary and Ancillary ServiceMultiple thresholds
R(t) = Available power − Demand = Gp(t) + Ga(t) − D(t)
Social Planner’s Problem solved using an affine policy:
21 / 66
Issues and ApproachesReliability by Design
Dynamic Markets and their EquilibriaWho Commands the Wind?
Research FrontiersReferences
Primary and Ancillary ServiceMultiple thresholds
R(t) = Available power − Demand = Gp(t) + Ga(t) − D(t)
Social Planner’s Problem solved using an affine policy:
The cheaper resource Gp(t) ramps up when R(t) < r̄p
21 / 66
Issues and ApproachesReliability by Design
Dynamic Markets and their EquilibriaWho Commands the Wind?
Research FrontiersReferences
Primary and Ancillary ServiceMultiple thresholds
R(t) = Available power − Demand = Gp(t) + Ga(t) − D(t)
Social Planner’s Problem solved using an affine policy:
The cheaper resource Gp(t) ramps up when R(t) < r̄p
Ancillary service Ga(t) ramps up when R(t) < r̄a
21 / 66
Issues and ApproachesReliability by Design
Dynamic Markets and their EquilibriaWho Commands the Wind?
Research FrontiersReferences
Primary and Ancillary ServiceMultiple thresholds
R(t) = Available power − Demand = Gp(t) + Ga(t) − D(t)
Social Planner’s Problem solved using an affine policy:
The cheaper resource Gp(t) ramps up when R(t) < r̄p
Ancillary service Ga(t) ramps up when R(t) < r̄a
0
R
Ga
r∗a
r∗p
(R constrained
by affine policy
(t), Ga(t))
Trajectory of the two-dimensional model under an affine policy
21 / 66
Issues and ApproachesReliability by Design
Dynamic Markets and their EquilibriaWho Commands the Wind?
Research FrontiersReferences
Primary and Ancillary ServiceMultiple thresholds
R(t) = Available power − Demand = Gp(t) + Ga(t) − D(t)
Social Planner’s Problem solved using an affine policy:
The cheaper resource Gp(t) ramps up when R(t) < r̄p
Ancillary service Ga(t) ramps up when R(t) < r̄a
(R constrained
by affine policy
(t), Ga(t))Ga(t))
σ2
D = 6 σ2
D = 18 σ2
D = 24
qp∗qp
qaqa∗
CRW model CBM model
10- 10 0 20- 20 30
10
20
30
40
10- 10 0 20- 20 30
10
20
30
40
10- 10 0 20- 20 30
10
20
30
40
R
Ga
Solidarity between optimal policies for non-Brownian demand
22 / 66
Issues and ApproachesReliability by Design
Dynamic Markets and their EquilibriaWho Commands the Wind?
Research FrontiersReferences
Reliability by Design in NetworksThree-Node Example
Line 1 Line 2
Line 3
E1
E2 E3
Gp1
Ga2
Ga3
D Dallas1
D Houston3
D Austin2
F (t) = ∆Z(t)
23 / 66
Issues and ApproachesReliability by Design
Dynamic Markets and their EquilibriaWho Commands the Wind?
Research FrontiersReferences
Reliability by Design in NetworksThree-Node Example
Line 1 Line 2
Line 3
E1
E2 E3
Gp1
Ga2
Ga3
D Dallas1
D Houston3
D Austin2
F (t) = ∆Z(t)
Power flow on transmission lines F = (F1, F2, F3)T
Nodal power Z = (Gp1 − E1, G
a2 − E2, G
a3 − E3)
T
23 / 66
Issues and ApproachesReliability by Design
Dynamic Markets and their EquilibriaWho Commands the Wind?
Research FrontiersReferences
Reliability by Design in NetworksThree-Node Example
Power flow on transmission lines F = (F1, F2, F3)T
Nodal power Z = (Gp1 − E1, G
a2 − E2, G
a3 − E3)
T
Distribution factor matrix
∆ = 13
1 −1 02 1 0
−1 −2 0
24 / 66
Issues and ApproachesReliability by Design
Dynamic Markets and their EquilibriaWho Commands the Wind?
Research FrontiersReferences
Reliability by Design in NetworksThree-Node Example
Power flow on transmission lines F = (F1, F2, F3)T
Nodal power Z = (Gp1 − E1, G
a2 − E2, G
a3 − E3)
T
Distribution factor matrix
∆ = 13
1 −1 02 1 0
−1 −2 0
Constraints: F (t) ∈ F := {x ∈ Rℓt : −f+ ≤ x ≤ f+}
24 / 66
Issues and ApproachesReliability by Design
Dynamic Markets and their EquilibriaWho Commands the Wind?
Research FrontiersReferences
Reliability by Design in NetworksExtension to general topology
Primary and ancillary capacity processes at each node aresubject to ramp constraints
Deviation in demand is a multi-dimensional stochastic process– Brownian motion for computation.
Cost in social planner’s problem,
∑
i
(
cpi g
pi + ca
i gai + cbo
i (ei − di)−)
25 / 66
Issues and ApproachesReliability by Design
Dynamic Markets and their EquilibriaWho Commands the Wind?
Research FrontiersReferences
Reliability by Design in NetworksExtension to general topology
Primary and ancillary capacity processes at each node aresubject to ramp constraints
Deviation in demand is a multi-dimensional stochastic process– Brownian motion for computation.
Cost in social planner’s problem,
∑
i
(
cpi g
pi + ca
i gai + cbo
i (ei − di)−)
Optimization problem is now intractable!
25 / 66
Issues and ApproachesReliability by Design
Dynamic Markets and their EquilibriaWho Commands the Wind?
Research FrontiersReferences
Reliability by Design in NetworksRelaxations
Consider aggregate reserves and ancillary generalization:
RA(t) =∑
Ri(t) , GaA(t) =
∑
Gai (t).
26 / 66
Issues and ApproachesReliability by Design
Dynamic Markets and their EquilibriaWho Commands the Wind?
Research FrontiersReferences
Reliability by Design in NetworksRelaxations
Consider aggregate reserves and ancillary generalization:
RA(t) =∑
Ri(t) , GaA(t) =
∑
Gai (t).
For given
Aggregate state xA = (rA, gaA)T ∈ XA := R × R+
Demand vector d ∈ Rℓn
Effective cost: Cost of cheapest state vector consistent with xA:
26 / 66
Issues and ApproachesReliability by Design
Dynamic Markets and their EquilibriaWho Commands the Wind?
Research FrontiersReferences
Reliability by Design in NetworksRelaxations
Consider aggregate reserves and ancillary generalization:
RA(t) =∑
Ri(t) , GaA(t) =
∑
Gai (t).
For given
Aggregate state xA = (rA, gaA)T ∈ XA := R × R+
Demand vector d ∈ Rℓn
Effective cost: Cost of cheapest state vector consistent with xA:
min∑
i
(cpi g
pi + ca
i gai + cbo
i ri−)
subject torA =
∑
i(ei − di) gaA =
∑
i gai
0 =∑
i(gpi + ga
i − ei) 0 = e − d − q
f = ∆p ∈ F, e, q, gp ∈ Rℓn , ga ∈ R
ℓn
+
26 / 66
Issues and ApproachesReliability by Design
Dynamic Markets and their EquilibriaWho Commands the Wind?
Research FrontiersReferences
Reliability by Design in NetworksRelaxations and Effective Cost
- 50 - 40 - 30 - 20 - 10 0 10 20 30 40 500
10
20
30
40
A
AR
Ga
ra
rp
c(xA, d)
Level sets of
effective cost
27 / 66
Issues and ApproachesReliability by Design
Dynamic Markets and their EquilibriaWho Commands the Wind?
Research FrontiersReferences
Reliability by Design in NetworksAffine Policy for Relaxation
- 50 - 40 - 30 - 20 - 10 0 10 20 30 40 500
10
20
30
40
A
AR
Ga
ra
rp
c(xA, d)
Level sets of
effective cost
Monotone region
Constraint region
under affine policy
Affine policy is an affine enlargement of “monotone region” inwhich Ga
A ramps at maximum rate.
28 / 66
Issues and ApproachesReliability by Design
Dynamic Markets and their EquilibriaWho Commands the Wind?
Research FrontiersReferences
Reliability by Design in NetworksAffine Policy for Relaxation
- 50 - 40 - 30 - 20 - 10 0 10 20 30 40 500
10
20
30
40
A
A
1xA
2xA
3xA
4xA
R
Ga
ra
rp
c(xA, d)
Level sets of
effective cost
Monotone region
Constraint region
under affine policy
How does an affine policy respond in these four different scenarios?
29 / 66
Issues and ApproachesReliability by Design
Dynamic Markets and their EquilibriaWho Commands the Wind?
Research FrontiersReferences
Reliability by Design in NetworksEffective States in Relaxation
Effective state X ∗(xA):Minimizer in thecomputation of c̄(xA, d).
- 50 - 40 - 30 - 20 - 10 0 10 20 30 40 500
10
20
30
40
A
A
1xA
2xA
3xA
4xA
R
Ga
ra
rp
X ∗(x1A): Dallas is experiencing black-out!
30 / 66
Issues and ApproachesReliability by Design
Dynamic Markets and their EquilibriaWho Commands the Wind?
Research FrontiersReferences
Reliability by Design in NetworksEffective States in Relaxation
Effective state X ∗(xA):Minimizer in thecomputation of c̄(xA, d).
- 50 - 40 - 30 - 20 - 10 0 10 20 30 40 500
10
20
30
40
A
A
1xA
2xA
3xA
4xA
R
Ga
ra
rp
X ∗(x1A): Dallas is experiencing black-out!
Yet ancillary service is ramping down at maximum rate!
30 / 66
Issues and ApproachesReliability by Design
Dynamic Markets and their EquilibriaWho Commands the Wind?
Research FrontiersReferences
Reliability by Design in NetworksEffective States in Relaxation
Effective state X ∗(xA):Minimizer in thecomputation of c̄(xA, d).
- 50 - 40 - 30 - 20 - 10 0 10 20 30 40 500
10
20
30
40
A
A
1xA
2xA
3xA
4xA
R
Ga
ra
rp
X ∗(x1A): Dallas is experiencing black-out!
Yet ancillary service is ramping down at maximum rate!Each of the three transmission lines have reached theircapacity limits: Nodes 2 and 3 cannot transfer reserves tonode 1, and node 1 cannot extract more reserve to reduce theseverity of black-out.
30 / 66
Issues and ApproachesReliability by Design
Dynamic Markets and their EquilibriaWho Commands the Wind?
Research FrontiersReferences
Reliability by Design in NetworksEffective States in Relaxation
Effective state X ∗(xA):Minimizer in thecomputation of c̄(xA, d).
- 50 - 40 - 30 - 20 - 10 0 10 20 30 40 500
10
20
30
40
A
A
1xA
2xA
3xA
4xA
R
Ga
ra
rp
X ∗(x2A) and X ∗(x3
A): Black-out!
31 / 66
Issues and ApproachesReliability by Design
Dynamic Markets and their EquilibriaWho Commands the Wind?
Research FrontiersReferences
Reliability by Design in NetworksEffective States in Relaxation
Effective state X ∗(xA):Minimizer in thecomputation of c̄(xA, d).
- 50 - 40 - 30 - 20 - 10 0 10 20 30 40 500
10
20
30
40
A
A
1xA
2xA
3xA
4xA
R
Ga
ra
rp
X ∗(x2A) and X ∗(x3
A): Black-out!However, there is sufficient transmission capacity to provideincreased reserves to any node.
31 / 66
Issues and ApproachesReliability by Design
Dynamic Markets and their EquilibriaWho Commands the Wind?
Research FrontiersReferences
Reliability by Design in NetworksEffective States in Relaxation
Effective state X ∗(xA):Minimizer in thecomputation of c̄(xA, d).
- 50 - 40 - 30 - 20 - 10 0 10 20 30 40 500
10
20
30
40
A
A
1xA
2xA
3xA
4xA
R
Ga
ra
rp
X ∗(x2A) and X ∗(x3
A): Black-out!However, there is sufficient transmission capacity to provideincreased reserves to any node.Policy dictates that each generator ramp up at maximum rate.
31 / 66
Issues and ApproachesReliability by Design
Dynamic Markets and their EquilibriaWho Commands the Wind?
Research FrontiersReferences
Reliability by Design in NetworksEffective States in Relaxation
Effective state X ∗(xA):Minimizer in thecomputation of c̄(xA, d).
- 50 - 40 - 30 - 20 - 10 0 10 20 30 40 500
10
20
30
40
A
A
1xA
2xA
3xA
4xA
R
Ga
ra
rp
X ∗(x2A) and X ∗(x3
A): Black-out!However, there is sufficient transmission capacity to provideincreased reserves to any node.Policy dictates that each generator ramp up at maximum rate.
X ∗(x4A): High power reserves at each node, so that
generation ramps down.
31 / 66
Issues and ApproachesReliability by Design
Dynamic Markets and their EquilibriaWho Commands the Wind?
Research FrontiersReferences
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
32 / 66
Issues and ApproachesReliability by Design
Dynamic Markets and their EquilibriaWho Commands the Wind?
Research FrontiersReferences
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
33 / 66
Issues and ApproachesReliability by Design
Dynamic Markets and their EquilibriaWho Commands the Wind?
Research FrontiersReferences
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
33 / 66
Issues and ApproachesReliability by Design
Dynamic Markets and their EquilibriaWho Commands the Wind?
Research FrontiersReferences
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
34 / 66
Issues and ApproachesReliability by Design
Dynamic Markets and their EquilibriaWho Commands the Wind?
Research FrontiersReferences
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
34 / 66
Issues and ApproachesReliability by Design
Dynamic Markets and their EquilibriaWho Commands the Wind?
Research FrontiersReferences
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
35 / 66
Issues and ApproachesReliability by Design
Dynamic Markets and their EquilibriaWho Commands the Wind?
Research FrontiersReferences
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)
35 / 66
Issues and ApproachesReliability by Design
Dynamic Markets and their EquilibriaWho Commands the Wind?
Research FrontiersReferences
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).
35 / 66
Issues and ApproachesReliability by Design
Dynamic Markets and their EquilibriaWho Commands the Wind?
Research FrontiersReferences
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”35 / 66
Issues and ApproachesReliability by Design
Dynamic Markets and their EquilibriaWho Commands the Wind?
Research FrontiersReferences
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)
Price function P (t) is irrelevant when GS(t) = GD(t):
WS(t) := P (t)GS(t) − cGS(t)
WD(t) := v min(D(t), GD(t))
− cbo max(0,−R(t)) − P (t)GD(t)
36 / 66
Issues and ApproachesReliability by Design
Dynamic Markets and their EquilibriaWho Commands the Wind?
Research FrontiersReferences
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]
37 / 66
Issues and ApproachesReliability by Design
Dynamic Markets and their EquilibriaWho Commands the Wind?
Research FrontiersReferences
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]
38 / 66
Issues and ApproachesReliability by Design
Dynamic Markets and their EquilibriaWho Commands the Wind?
Research FrontiersReferences
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.
38 / 66
Issues and ApproachesReliability by Design
Dynamic Markets and their EquilibriaWho Commands the Wind?
Research FrontiersReferences
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.
38 / 66
Issues and ApproachesReliability by Design
Dynamic Markets and their EquilibriaWho Commands the Wind?
Research FrontiersReferences
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?
38 / 66
Issues and ApproachesReliability by Design
Dynamic Markets and their EquilibriaWho Commands the Wind?
Research FrontiersReferences
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.
39 / 66
Issues and ApproachesReliability by Design
Dynamic Markets and their EquilibriaWho Commands the Wind?
Research FrontiersReferences
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.
39 / 66
Issues and ApproachesReliability by Design
Dynamic Markets and their EquilibriaWho Commands the Wind?
Research FrontiersReferences
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)).
39 / 66
Issues and ApproachesReliability by Design
Dynamic Markets and their EquilibriaWho Commands the Wind?
Research FrontiersReferences
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}
40 / 66
Issues and ApproachesReliability by Design
Dynamic Markets and their EquilibriaWho Commands the Wind?
Research FrontiersReferences
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)) is the marginal value of power to the consumerat time t.
40 / 66
Issues and ApproachesReliability by Design
Dynamic Markets and their EquilibriaWho Commands the Wind?
Research FrontiersReferences
Market EquilibriumPrice Dynamics
v + cbo
0
r∗
Prices
Reserves
Normalized demand
P ∗(t) = pe(Re(t)): The marginal value of power to the consumer
41 / 66
Issues and ApproachesReliability by Design
Dynamic Markets and their EquilibriaWho Commands the Wind?
Research FrontiersReferences
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
41 / 66
Issues and ApproachesReliability by Design
Dynamic Markets and their EquilibriaWho Commands the Wind?
Research FrontiersReferences
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
42 / 66
Issues and ApproachesReliability by Design
Dynamic Markets and their EquilibriaWho Commands the Wind?
Research FrontiersReferences
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
43 / 66
Issues and ApproachesReliability by Design
Dynamic Markets and their EquilibriaWho Commands the Wind?
Research FrontiersReferences
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.
43 / 66
Issues and ApproachesReliability by Design
Dynamic Markets and their EquilibriaWho Commands the Wind?
Research FrontiersReferences
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?
43 / 66
Issues and ApproachesReliability by Design
Dynamic Markets and their EquilibriaWho Commands the Wind?
Research FrontiersReferences
Who Commands the Wind?
44 / 66
Issues and ApproachesReliability by Design
Dynamic Markets and their EquilibriaWho Commands the Wind?
Research FrontiersReferences
Extending the dynamic model
Goal
Extend the DA/RT market model to differentiate power generatedby wind and by conventional generation units
45 / 66
Issues and ApproachesReliability by Design
Dynamic Markets and their EquilibriaWho Commands the Wind?
Research FrontiersReferences
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
45 / 66
Issues and ApproachesReliability by Design
Dynamic Markets and their EquilibriaWho Commands the Wind?
Research FrontiersReferences
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.
45 / 66
Issues and ApproachesReliability by Design
Dynamic Markets and their EquilibriaWho Commands the Wind?
Research FrontiersReferences
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
45 / 66
Issues and ApproachesReliability by Design
Dynamic Markets and their EquilibriaWho Commands the Wind?
Research FrontiersReferences
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
46 / 66
Issues and ApproachesReliability by Design
Dynamic Markets and their EquilibriaWho Commands the Wind?
Research FrontiersReferences
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
46 / 66
Issues and ApproachesReliability by Design
Dynamic Markets and their EquilibriaWho Commands the Wind?
Research FrontiersReferences
Who Commands the Wind?Main findings
Volatility can have tremendous impact on the market outcome
47 / 66
Issues and ApproachesReliability by Design
Dynamic Markets and their EquilibriaWho Commands the Wind?
Research FrontiersReferences
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
47 / 66
Issues and ApproachesReliability by Design
Dynamic Markets and their EquilibriaWho Commands the Wind?
Research FrontiersReferences
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)
48 / 66
Issues and ApproachesReliability by Design
Dynamic Markets and their EquilibriaWho Commands the Wind?
Research FrontiersReferences
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).
49 / 66
Issues and ApproachesReliability by Design
Dynamic Markets and their EquilibriaWho Commands the Wind?
Research FrontiersReferences
Suppliers command the wind
The other alternative is to consider wind as part of the supply side,
Consumers’ welfare
Wttl
D,W(t) = v min(Dttl(t), Gttl(t) + Gttl
W(t))
− cbo max(0,−R(t))
− P (t)(G(t) + GW(t)) − p(t)(gda(t) + gda
W(t))
= Wrt
D,W(t)
+{
(v − p(t))dda + (P (t) − p(t))rda
0
}
+ (v − P (t))GW(t)
50 / 66
Issues and ApproachesReliability by Design
Dynamic Markets and their EquilibriaWho Commands the Wind?
Research FrontiersReferences
Suppliers command the wind
Suppliers’ welfare
Wttl
S,W(t) =(
P (t) − crt)
G(t) + P (t)GW(t)
+(
p(t) − cda)
gda(t) + p(t)gda
W(t)
= Wrt
S,W(t)
+(
p(t) − cda)
gda(t) + P (t)GW(t) + p(t)gda
W(t)
The welfare gain p(t)gda
W(t) is now taken by the suppliers
51 / 66
Issues and ApproachesReliability by Design
Dynamic Markets and their EquilibriaWho Commands the Wind?
Research FrontiersReferences
Numerical Results: Setting the stage I
Parameters used in all 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).
52 / 66
Issues and ApproachesReliability by Design
Dynamic Markets and their EquilibriaWho Commands the Wind?
Research FrontiersReferences
Numerical Results: Setting the stage II
Parameters (physical)
Ramp limit: ζ = 200 MW/min
Mean demand: D̄ = 50, 000 MW
Standard deviation: σ = 500 MW.
53 / 66
Issues and ApproachesReliability by Design
Dynamic Markets and their EquilibriaWho Commands the Wind?
Research FrontiersReferences
Numerical Results: Setting the stage III
Penetration and volatility
Coefficient of variation to capture the relative volatility of wind:
cv =σw
E[GttlW
(t)]
Percentage of wind penetration:
k = 100 ∗ E[Gttl
W(t)]/D̄
54 / 66
Issues and ApproachesReliability by Design
Dynamic Markets and their EquilibriaWho Commands the Wind?
Research FrontiersReferences
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
55 / 66
Issues and ApproachesReliability by Design
Dynamic Markets and their EquilibriaWho Commands the Wind?
Research FrontiersReferences
Numerical Results: Volatility ImpactsSocial planner’s welfare falls with volatility
x 106
0 1000200 400 600 80010
12
14
16
18
ζ = 200Total Welfare
σ
ζ =0.1
ζ = 500
56 / 66
Issues and ApproachesReliability by Design
Dynamic Markets and their EquilibriaWho Commands the Wind?
Research FrontiersReferences
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
57 / 66
Issues and ApproachesReliability by Design
Dynamic Markets and their EquilibriaWho Commands the Wind?
Research FrontiersReferences
Research Frontiers
58 / 66
Issues and ApproachesReliability by Design
Dynamic Markets and their EquilibriaWho Commands the Wind?
Research FrontiersReferences
Research FrontiersStrategic behavior
Q1
Building bridges
59 / 66
Issues and ApproachesReliability by Design
Dynamic Markets and their EquilibriaWho Commands the Wind?
Research FrontiersReferences
Research FrontiersStrategic behavior
Q1
Building bridges between this research and what was described byHobbs & Ralph — How to incorporate dynamics and uncertainty
in a strategic setting? How could two smart people come to such
different conclusions? I had to get to the
bottom of this. –MacKay 2009
59 / 66
Issues and ApproachesReliability by Design
Dynamic Markets and their EquilibriaWho Commands the Wind?
Research FrontiersReferences
Research FrontiersStrategic behavior
Q1
Building bridges between this research and what was described byHobbs & Ralph — How to incorporate dynamics and uncertainty
in a strategic setting? How could two smart people come to such
different conclusions? I had to get to the
bottom of this. –MacKay 2009
Approach: Follow the example of highway engineering:
Analysis of strategic behavior will be possible if agent
behavior is suitably constrained
59 / 66
Issues and ApproachesReliability by Design
Dynamic Markets and their EquilibriaWho Commands the Wind?
Research FrontiersReferences
Research FrontiersStrategic behavior
Q1
Building bridges between this research and what was described byHobbs & Ralph — How to incorporate dynamics and uncertainty
in a strategic setting? How could two smart people come to such
different conclusions? I had to get to the
bottom of this. –MacKay 2009
Approach: Follow the example of highway engineering:
Analysis of strategic behavior will be possible if agent
behavior is suitably constrained
Stalinist?
59 / 66
Issues and ApproachesReliability by Design
Dynamic Markets and their EquilibriaWho Commands the Wind?
Research FrontiersReferences
Research FrontiersStrategic behavior
Q1
Building bridges between this research and what was described byHobbs & Ralph — How to incorporate dynamics and uncertainty
in a strategic setting? How could two smart people come to such
different conclusions? I had to get to the
bottom of this. –MacKay 2009
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!!
59 / 66
Issues and ApproachesReliability by Design
Dynamic Markets and their EquilibriaWho Commands the Wind?
Research FrontiersReferences
Research FrontiersStrategic behavior
Q2
Learning
60 / 66
Issues and ApproachesReliability by Design
Dynamic Markets and their EquilibriaWho Commands the Wind?
Research FrontiersReferences
Research FrontiersStrategic behavior
Q2
Learning Once a market framework is in place, agents will learnover time to optimize their reward
60 / 66
Issues and ApproachesReliability by Design
Dynamic Markets and their EquilibriaWho Commands the Wind?
Research FrontiersReferences
Research FrontiersStrategic behavior
Q2
Learning Once a market framework is in place, agents will learnover time to optimize their reward Q-learning and TD-learning are
potential approaches
60 / 66
Issues and ApproachesReliability by Design
Dynamic Markets and their EquilibriaWho Commands the Wind?
Research FrontiersReferences
Research FrontiersControlling supply and demand
Q3
The impact of demand management and storage on the market
61 / 66
Issues and ApproachesReliability by Design
Dynamic Markets and their EquilibriaWho Commands the Wind?
Research FrontiersReferences
Research FrontiersControlling supply 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.
61 / 66
Issues and ApproachesReliability by Design
Dynamic Markets and their EquilibriaWho Commands the Wind?
Research FrontiersReferences
Research FrontiersControlling supply 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 thepower grid in LA county with dynamic pricing, hybrid cars, andautomated water pumping?
61 / 66
Issues and ApproachesReliability by Design
Dynamic Markets and their EquilibriaWho Commands the Wind?
Research FrontiersReferences
Research FrontiersFacing volatility
Q5
Not just “missing money” —
62 / 66
Issues and ApproachesReliability by Design
Dynamic Markets and their EquilibriaWho Commands the Wind?
Research FrontiersReferences
Research FrontiersFacing volatility
Q5
Not just “missing money” — Mechanisms to reduce consumersand suppliers exposure to volatility.
62 / 66
Issues and ApproachesReliability by Design
Dynamic Markets and their EquilibriaWho Commands the Wind?
Research FrontiersReferences
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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Issues and ApproachesReliability by Design
Dynamic Markets and their EquilibriaWho Commands the Wind?
Research FrontiersReferences
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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Issues and ApproachesReliability by Design
Dynamic Markets and their EquilibriaWho Commands the Wind?
Research FrontiersReferences
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.
63 / 66
Issues and ApproachesReliability by Design
Dynamic Markets and their EquilibriaWho Commands the Wind?
Research FrontiersReferences
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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Issues and ApproachesReliability by Design
Dynamic Markets and their EquilibriaWho Commands the Wind?
Research FrontiersReferences
Thanks!
Celebrating with Dutch Babies after finishing The value of volatile
resources...64 / 66
Issues and ApproachesReliability by Design
Dynamic Markets and their EquilibriaWho Commands the Wind?
Research FrontiersReferences
Complex Networks FOR
Sean Meyn
Control Techniques
References
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Issues and ApproachesReliability by Design
Dynamic Markets and their EquilibriaWho Commands the Wind?
Research FrontiersReferences
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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