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)
generation
transmission
distribution
customers
utility
Small supply side uncertainty
Small demand side uncertainty
will change with high penetration of renewables
How do we incorporate wind energy?
time
dayahead
realtime
longterm
Utility buys power to meet demand
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
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
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?
timeint. real
timelongterm
price ↑
wind uncertainty ↓
timeint. real
timelongterm
Assumption: wind forecasts evolve independently of the past [Martingale model of forecast evolution, Heath et al. ‘94]
timeint. real
timelongterm
Objective: minimize average cost of procurement
subject to:
causality constraints.
Theorem: The optimal procurement strategy is characterized by reserve levels rlt and rin such that
where
rlt uniquely solves
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?
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?
Scaling regime
timeint. real
timelongterm
Procurement with no wind uncertainty
extra procurementdue to wind uncertainty
Depends on markets & prediction•Prices •Forecast accuracy
Depends on wind aggregation
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?
price ↑
wind uncertainty ↓
timeint. real
timelongterm
Q: Where should the intermediate market be placed to minimize procurement costs?
price ↑
wind uncertainty ↓
timeint. real
timelongterm
Q: How does the optimal placement change as wind penetration grows?
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?
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
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
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
Forecast error is heavy-tailed to the left
satisfied by the Gaussian dist.
When is an additional market beneficial?
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