energy procurement in the presence of intermittent sources jayakrishnan nair (cwi) sachin adlakha...
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Energy procurement in the presence of intermittent sources
Jayakrishnan Nair (CWI)Sachin Adlakha (Caltech)Adam Wierman (Caltech)
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generation
transmission
distribution
customers
utility
Small supply side uncertainty
Small demand side uncertainty
will change with high penetration of renewables
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How do we incorporate wind energy?
time
dayahead
realtime
longterm
Utility buys power to meet demand
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1. Allow wind producers to participate in real timeand/or day ahead markets
[CAISO PIRP program, Bitar et al. 2011, Cai et al. 2011]
time
dayahead
realtime
longterm
Utility buys power to meet demand
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2. Utilities form long term contracts with wind producers to buy all available wind for a fixed payment
[Meyn et al. 2009, Varaiya et al. 2010, Rajagopal et al. 2011]
time
dayahead
realtime
longterm
Utility buys power to meet demand
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time
dayahead
realtime
longterm
As renewable penetration increases: 1)Should markets be moved closer to real-time? 2)Should markets be added?
This talk: What is the impact of long term wind contracts?
![Page 7: Energy procurement in the presence of intermittent sources Jayakrishnan Nair (CWI) Sachin Adlakha (Caltech) Adam Wierman (Caltech)](https://reader030.vdocuments.site/reader030/viewer/2022032804/56649e495503460f94b3d5e8/html5/thumbnails/7.jpg)
timeint. real
timelongterm
price ↑
wind uncertainty ↓
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timeint. real
timelongterm
Assumption: wind forecasts evolve independently of the past [Martingale model of forecast evolution, Heath et al. ‘94]
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timeint. real
timelongterm
Objective: minimize average cost of procurement
subject to:
causality constraints.
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Theorem: The optimal procurement strategy is characterized by reserve levels rlt and rin such that
where
rlt uniquely solves
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time
dayahead
realtime
longterm
As renewable penetration increases: 1)Should markets be moved closer to real-time? 2)Should markets be added?
This talk: What is the impact of long term wind contracts?
![Page 12: Energy procurement in the presence of intermittent sources Jayakrishnan Nair (CWI) Sachin Adlakha (Caltech) Adam Wierman (Caltech)](https://reader030.vdocuments.site/reader030/viewer/2022032804/56649e495503460f94b3d5e8/html5/thumbnails/12.jpg)
time
dayahead
realtime
longterm
As renewable penetration increases: 1)Should markets be moved closer to real-time? 2)Should markets be added?
This talk: What is the impact of long term wind contracts?
![Page 13: Energy procurement in the presence of intermittent sources Jayakrishnan Nair (CWI) Sachin Adlakha (Caltech) Adam Wierman (Caltech)](https://reader030.vdocuments.site/reader030/viewer/2022032804/56649e495503460f94b3d5e8/html5/thumbnails/13.jpg)
Scaling regime
timeint. real
timelongterm
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Procurement with no wind uncertainty
extra procurementdue to wind uncertainty
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Depends on markets & prediction•Prices •Forecast accuracy
Depends on wind aggregation
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time
dayahead
realtime
longterm
As renewable penetration increases: 1)Should markets be moved closer to real-time? 2)Should markets be added?
This talk: What is the impact of long term wind contracts?
![Page 18: Energy procurement in the presence of intermittent sources Jayakrishnan Nair (CWI) Sachin Adlakha (Caltech) Adam Wierman (Caltech)](https://reader030.vdocuments.site/reader030/viewer/2022032804/56649e495503460f94b3d5e8/html5/thumbnails/18.jpg)
price ↑
wind uncertainty ↓
timeint. real
timelongterm
Q: Where should the intermediate market be placed to minimize procurement costs?
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price ↑
wind uncertainty ↓
timeint. real
timelongterm
Q: How does the optimal placement change as wind penetration grows?
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time
dayahead
realtime
longterm
As renewable penetration increases: 1)Should markets be moved closer to real-time? 2)Should markets be added?
This talk: What is the impact of long term wind contracts?
![Page 21: Energy procurement in the presence of intermittent sources Jayakrishnan Nair (CWI) Sachin Adlakha (Caltech) Adam Wierman (Caltech)](https://reader030.vdocuments.site/reader030/viewer/2022032804/56649e495503460f94b3d5e8/html5/thumbnails/21.jpg)
Q: What happens to E[Cost] if a market is added?
Obviously, E[Cost] ↓
Q: What happens to E[Procurement] if market is added?
E[Procurement]
realtime
longterm v/s int. real
timelongterm
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𝜀2 Gaussian
𝑝𝑙𝑡=6 6<𝑝𝑖𝑛<10 𝑝𝑟𝑡=10time
Int.realtime
longterm
6 6.5 7 7.5 8 8.5 9 9.5 10𝑝𝑖𝑛
]
2 markets
3 markets
Intermediate market disappears
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6 6.5 7 7.5 8 8.5 9 9.5 10𝑝𝑖𝑛
]
2 markets
3 markets
Higher procurement with 3 markets!
When can this happen?
𝜀2 Weibull
𝑝𝑙𝑡=6 6<𝑝𝑖𝑛<10 𝑝𝑟𝑡=10time
Int.realtime
longterm
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Forecast error is heavy-tailed to the left
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satisfied by the Gaussian dist.
When is an additional market beneficial?
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As renewable penetration increases: 1)Should markets be moved closer to real-time? 2)Should markets be added?
This talk: What is the impact of long term wind contracts?
Opt. placement insensitive to increasing penetration
Depends on forecast error distribution