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