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Energy procurement in the presence of intermittent sourcesAdam Wierman (Caltech)
JK Nair (Caltech / CWI)Sachin Adlakha (Caltech)
Forget about energy for a second…This talk is really about the role of uncertainty in newsvendor problems
Forget about energy for a second…This talk is really about the role of uncertainty in newsvendor problems
Estimate demand,
Purchase,
Demand is realized
lost revenue wasted inventory
uncertainty
“You have to decide today how many newspapers you want to sell tomorrow…”
Forget about energy for a second…This talk is really about the role of uncertainty in newsvendor problems
“You have to decide today how many newspapers you want to sell tomorrow…”seasonal productsperishable goods
compute instancesenergy
…
Key Constraint: Generation = Load(at all times)
low uncertainty
Generation Load
Now, back to energy…
Generation Load
Key Constraint: Generation = Load(at all times)
low uncertaintycontrollablevia markets
Now, back to energy…
timeint. /day
ahead
realtime
longterm
Utility buys power to
meet demand
Electricity markets
markets
MW
WorldwideWind:
MW
Europe
AmericasChina
Solar PV:
Renewable energy is coming!
…but incorporation into the grid isn’t easy
They are typically
Uncontrollable (not available “on demand”)
Intermittent (large fluctuations)
Uncertain (difficult to forecast)
Each line is wind generation over 1 day
Renewable energy is coming!
Key Constraint: Generation = Load
less controllable
high uncertaintylow uncertainty
(at all times)
Tomorrow’s grid
Key Constraint: Generation = Load
less controllable
high uncertaintylow uncertainty
(at all times)
1) Huge price variability, leading to generators opting out of markets!2) More conventional reserves needed, countering sustainability gains!
“ON JUNE 16th something very peculiar
happened in Germany’s electricity market. The
wholesale price of electricity fell to minus €100
per megawatt hour (MWh). That is, generating
companies were having to pay the managers of
the grid to take their electricity.”
“Energiewende has so far
increased, not decreased,
emissions of greenhouse
gases.”
What can be done?
Reduce the uncertainty
Design for the uncertainty
•Better prediction• “Aggregation” … in time (storage) … in space (distributed generation) … in generation (heterogeneous mix)
•Redesign electricity markets• Increase amount of demand response
this session
timeint. /day
ahead
realtime
longterm
markets
PIRP
timeint. /day
ahead
realtime
longterm
markets
This talk: What is the impact of long term wind contracts?
As renewable penetration increases: 1)Should markets be moved closer to real-
time? 2)Should markets be added?
4 hr market
How should utilities procure electricity in the presence of renewable energy?First step:
This talk: What is the impact of long term wind contracts?
As renewable penetration increases: 1)Should markets be moved closer to real-
time? 2)Should markets be added?
int. /day
ahead
realtime
longterm
price↑
𝑝𝑙𝑡 𝑝𝑖𝑛 𝑝𝑟𝑡
int. /day
ahead
realtime
longterm
price volatility↑
𝑝𝑙𝑡 𝑝𝑖𝑛 𝑝𝑟𝑡
𝑞𝑙𝑡 𝑞𝑖𝑛 𝑞𝑟𝑡
𝐸 [𝑝𝑖𝑛 ]>𝑝𝑙𝑡 𝐸 [𝑝𝑟𝑡|𝑝𝑖𝑛 ]>𝑝𝑖𝑛
int. /day
ahead
realtime
longterm
price↑
𝑝𝑙𝑡 𝑝𝑖𝑛 𝑝𝑟𝑡
𝑞𝑙𝑡 𝑞𝑖𝑛 𝑞𝑟𝑡
�̂�𝑙𝑡 �̂�𝑖𝑛 𝑤
𝜀1=�̂�𝑙𝑡− �̂�𝑖𝑛 𝜀2=�̂�𝑖𝑛−𝑤
Assumption: and are independent(A generalization of the martingale model of forecast evolution)
wind uncertainty ↓
𝑞𝑙𝑡+𝑞𝑖𝑛+𝑞𝑟𝑡+𝑤≥𝑑Key Constraint: Generation = Load
int. /day
ahead
realtime
longterm
price↑wind uncertainty ↓
𝑝𝑙𝑡 𝑝𝑖𝑛 𝑝𝑟𝑡
𝑞𝑙𝑡 𝑞𝑖𝑛 𝑞𝑟𝑡
�̂�𝑙𝑡 �̂�𝑖𝑛 𝑤
(we ignore network constraints)
int. /day
ahead
realtime
longterm
price↑wind uncertainty ↓
𝑝𝑙𝑡 𝑝𝑖𝑛 𝑝𝑟𝑡
𝑞𝑙𝑡 𝑞𝑖𝑛 𝑞𝑟𝑡
�̂�𝑙𝑡 �̂�𝑖𝑛 𝑤
Utility goal:min𝐸 [𝑝𝑙𝑡 𝑞𝑙𝑡+𝑝𝑖𝑛𝑞𝑖𝑛+𝑝𝑟𝑡𝑞𝑟𝑡 ]Subject to causality constraints
int. /day
ahead
realtime
longterm
𝑝𝑙𝑡 𝑝𝑖𝑛 𝑝𝑟𝑡
𝑞𝑙𝑡 𝑞𝑖𝑛 𝑞𝑟𝑡
�̂�𝑙𝑡 �̂�𝑖𝑛 𝑤
Utility goal:min𝐸 [𝑝𝑙𝑡 𝑞𝑙𝑡+𝑝𝑖𝑛𝑞𝑖𝑛+𝑝𝑟𝑡𝑞𝑟𝑡 ]Subject to causality constraintsVariant of the newsvendor problem
[Arrow et. al. ’51], [Silver et. al. ’98], [Khouja ’99], [Porteus ’02], [Wang et. al. ’12].
Theorem:The optimal procurement strategy is characterized by reserve levels and such that
where
and uniquely solves
int. /day
ahead
realtime
longterm �̂�𝑙𝑡 �̂�𝑖𝑛 𝑤
𝜀1=�̂�𝑙𝑡− �̂�𝑖𝑛 𝜀2=�̂�𝑖𝑛−𝑤
baseline, e.g., average output of a wind farm scale, e.g., number of wind farms
Scaling regime
aggregation, e.g., degree of correlation between wind farms
𝒘 𝒍𝒕 (𝜸 )=𝜸𝜶 𝜺𝟐 (𝜸 )=𝜸𝜽𝜺𝟐𝜺𝟏 (𝜸 )=𝜸𝜽𝜺𝟏
baseline, e.g., average output of a wind farm scale, e.g., number of wind farms
Scaling regime
aggregation, e.g., degree of correlation between wind farms
Theorem:
Procurement with zero uncertainty
Extra procurementdue to uncertainty
baseline, e.g., average output of a wind farm scale, e.g., number of wind farms
Scaling regime
aggregation, e.g., degree of correlation between wind farms
Theorem:
Depends on markets & predictions - prices - forecasts
Depends on wind aggregation - =1/2 (independent) - =1 (correlated)
baseline, e.g., average output of a wind farm scale, e.g., number of wind farms
Scaling regime
aggregation, e.g., degree of correlation between wind farms
Theorem:
This form holds more generally than the model studied here:
-- more than three markets: [Bitar et al., 2012]-- when prices are endogenous: [Cai & Wierman, 2014]-- when small-scale storage is included: [Hayden, Nair, & Wierman, Working paper]
timeint. /day
ahead
realtime
longterm
markets
Electricity markets
This talk: What is the impact of long term wind contracts?
As renewable penetration increases: 1)Should markets be moved closer to real-
time? 2)Should markets be added?
No! (See paper)
timeint. /day
ahead
realtime
longterm
markets
Electricity markets
This talk: What is the impact of long term wind contracts?
As renewable penetration increases: 1)Should markets be moved closer to real-
time? 2)Should markets be added?
4 hr ahead marke
t?
realtime
longterm v/s int.
realtime
longterm
What happens to if a market is added?
What happens to if a market is added?
6 6.5 7 7.5 8 8.5 9 9.5 10
int. /day
ahead
realtime
longterm
𝜀2 Gaussian
𝑝𝑙𝑡=6 6<𝑝𝑖𝑛<10 𝑝𝑟𝑡=10
𝑝𝑖𝑛
]
2 markets
3 markets
3 markets are always better!
When does this happen?
Theorem:If is increasing for , decreasing for , and satisfies:
is decreasing for is decreasing for
then the expected procurement is lower with 3 markets than with 2 markets.
Satisfied by the Gaussian distribution
int. /day
ahead
realtime
longterm
𝜀2 Weibull
𝑝𝑙𝑡=6 6<𝑝𝑖𝑛<10 𝑝𝑟𝑡=10
6 6.5 7 7.5 8 8.5 9 9.5 10𝑝𝑖𝑛
]
2 markets
3 markets
3 markets can be worse!
When does this happen?
Theorem:If satisfies the condition:
=0 , then there exist prices such that the expected procurement is higher with 3 markets than with 2 markets.
Estimation errors are heavy-tailed(specifically, long-tailed)
timeint. /day
ahead
realtime
longterm
markets
This talk: What is the impact of long term wind contracts?
As renewable penetration increases: 1)Should markets be moved closer to real-
time? 2)Should markets be added?
No! (See paper) It depends, Gaussian or heavy-tailed?
4 hr market
timeint. /day
ahead
realtime
longterm
markets
This talk: What is the impact of long term wind contracts?
markets
PIRP
Big question: How should wind be incorporated into the markets?
Energy procurement in the presence of intermittent sourcesAdam Wierman (Caltech)
JK Nair (Caltech / CWI)Sachin Adlakha (Caltech)