energy procurement in the presence of intermittent sources adam wierman (caltech) jk nair (caltech /...
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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 secondโฆThis talk is really about the role of uncertainty in newsvendor problems
Forget about energy for a secondโฆThis talk is really about the role of uncertainty in newsvendor problems
Estimate demand,
Purchase,
Demand is realized
lost revenue wasted inventory
uncertainty
โYou have to decide today how many newspapers you want to sell tomorrowโฆโ
Forget about energy for a secondโฆThis talk is really about the role of uncertainty in newsvendor problems
โYou have to decide today how many newspapers you want to sell tomorrowโฆโseasonal productsperishable goods
compute instancesenergy
โฆ
Key Constraint: Generation = Load(at all times)
low uncertainty
Generation Load
Now, back to energyโฆ
Generation Load
Key Constraint: Generation = Load(at all times)
low uncertaintycontrollablevia markets
Now, back to energyโฆ
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!
โฆbut incorporation into the grid isnโt easy
They are typically
Uncontrollable (not available โon demandโ)
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)
Tomorrowโs 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!
โON JUNE 16th something very peculiar
happened in Germanyโs electricity market. The
wholesale price of electricity fell to minus โฌ100
per megawatt hour (MWh). That is, generating
companies were having to pay the managers of
the grid to take their electricity.โ
โEnergiewende has so far
increased, not decreased,
emissions of greenhouse
gases.โ
What can be done?
Reduce the uncertainty
Design for the uncertainty
โขBetter predictionโข โAggregationโ โฆ in time (storage) โฆ in space (distributed generation) โฆ in generation (heterogeneous mix)
โขRedesign electricity marketsโข 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
priceโ
๐๐๐ก ๐๐๐ ๐๐๐ก
int. /day
ahead
realtime
longterm
price volatilityโ
๐๐๐ก ๐๐๐ ๐๐๐ก
๐๐๐ก ๐๐๐ ๐๐๐ก
๐ธ [๐๐๐ ]>๐๐๐ก ๐ธ [๐๐๐ก|๐๐๐ ]>๐๐๐
int. /day
ahead
realtime
longterm
priceโ
๐๐๐ก ๐๐๐ ๐๐๐ก
๐๐๐ก ๐๐๐ ๐๐๐ก
๏ฟฝฬ๏ฟฝ๐๐ก ๏ฟฝฬ๏ฟฝ๐๐ ๐ค
๐1=๏ฟฝฬ๏ฟฝ๐๐กโ ๏ฟฝฬ๏ฟฝ๐๐ ๐2=๏ฟฝฬ๏ฟฝ๐๐โ๐ค
Assumption: and are independent(A generalization of the martingale model of forecast evolution)
wind uncertainty โ
๐๐๐ก+๐๐๐+๐๐๐ก+๐คโฅ๐Key Constraint: Generation = Load
int. /day
ahead
realtime
longterm
priceโwind uncertainty โ
๐๐๐ก ๐๐๐ ๐๐๐ก
๐๐๐ก ๐๐๐ ๐๐๐ก
๏ฟฝฬ๏ฟฝ๐๐ก ๏ฟฝฬ๏ฟฝ๐๐ ๐ค
(we ignore network constraints)
int. /day
ahead
realtime
longterm
priceโwind uncertainty โ
๐๐๐ก ๐๐๐ ๐๐๐ก
๐๐๐ก ๐๐๐ ๐๐๐ก
๏ฟฝฬ๏ฟฝ๐๐ก ๏ฟฝฬ๏ฟฝ๐๐ ๐ค
Utility goal:min๐ธ [๐๐๐ก ๐๐๐ก+๐๐๐๐๐๐+๐๐๐ก๐๐๐ก ]Subject to causality constraints
int. /day
ahead
realtime
longterm
๐๐๐ก ๐๐๐ ๐๐๐ก
๐๐๐ก ๐๐๐ ๐๐๐ก
๏ฟฝฬ๏ฟฝ๐๐ก ๏ฟฝฬ๏ฟฝ๐๐ ๐ค
Utility goal:min๐ธ [๐๐๐ก ๐๐๐ก+๐๐๐๐๐๐+๐๐๐ก๐๐๐ก ]Subject to causality constraintsVariant of the newsvendor problem
[Arrow et. al. โ51], [Silver et. al. โ98], [Khouja โ99], [Porteus โ02], [Wang et. al. โ12].
Theorem:The optimal procurement strategy is characterized by reserve levels and such that
where
and uniquely solves
int. /day
ahead
realtime
longterm ๏ฟฝฬ๏ฟฝ๐๐ก ๏ฟฝฬ๏ฟฝ๐๐ ๐ค
๐1=๏ฟฝฬ๏ฟฝ๐๐กโ ๏ฟฝฬ๏ฟฝ๐๐ ๐2=๏ฟฝฬ๏ฟฝ๐๐โ๐ค
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
๐ ๐๐ (๐ธ )=๐ธ๐ถ ๐บ๐ (๐ธ )=๐ธ๐ฝ๐บ๐๐บ๐ (๐ธ )=๐ธ๐ฝ๐บ๐
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
๐2 Gaussian
๐๐๐ก=6 6<๐๐๐<10 ๐๐๐ก=10
๐๐๐
]
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
๐2 Weibull
๐๐๐ก=6 6<๐๐๐<10 ๐๐๐ก=10
6 6.5 7 7.5 8 8.5 9 9.5 10๐๐๐
]
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)