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

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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

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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)