The Fable of Eric

Eric was born in Alaska in 1970s . He lived happily in a beautiful Victorian house facing the sea…

Thirty years later, global warming made the coastline erode. Eric’s childhood house was about to collapse.

Eric wanted to be part of the solution to save his Victorian house.

To save millions of Eric’s houses, government demanded 25% of the electricity come from

renewable energy by 2025. • Billions of dollars in stimulus plan (www.usnews.com)

• 31 states: Renewable Energy Portfolio Standards (RPS)• NYISO: 30% by 2013

He hired a few people to set up a wind farm and put together some solar panels.

He sells the electricity to an ISO and finds out he can barely make a living: • Price and wind generation negatively

correlated: • The wind tends to blow the strongest at night

when the price is the lowest, sometimes even negative.

• Penalty fee/ imbalance cost• Bidding: Advanced contracting• Forecast error 30%~50% • Entering into a long-term contract

Someone advises him to buy a big battery:• Store when price is low/ or there is

excess• Sell when the price is high.

• The catch is that battery is expensive.• 1MW NaS costs $1M? Is it worth it?

• Can I get my investment back?• When? How?

Yangfang Zhou, Stephen Smith, Alan Scheller-Wolf, Nicola Secomandi

Intermittent Resources with Storage in a Deregulated

Electricity Market

Contents9

Literature Review Who we are and what we do

OM perspective Our model

High level model, Sequence of events, Research questions

Results: optimal policy, value of the storage Compare (preliminary)

Future work

Literature Review10

Electricity Generation and Storage Joint optimization of wind-hydro plant

Gonzalez et al. 2008 (1generator &1storage, SP, no analytical result)

Economic Dispatch of Intermittent Resources Xie et al. 2008 (Do not consider storage.)

Electricity storage evaluation Walawalkar & et al. 2008 (data: arbitrage in different

markets)

… many others Inventory Theory and Commodity Storage

Trace back 50 years Secomandi 2009 : Commodity trading

Optimal inventory policy for batteries coupled with intermittent generators in an electricity market & value of storage is still open.

Operations Management11

What does operations Management do? Create and use operations research

techniques Optimize business operations

Electricity is a special type of perishable inventory

Bridge OM & electricity

Dynamic programmingLinear/

Integer programming

Stochastic programming

…...

When to order, how much to order When to store, how much to store

Constraint programming

: inventory

Where is Eric’s firm?

Utility A

Utility C

ISO

Utility B

Retail MarketWholesale Market

Generator A

Generator B

Generator C

Generation Transmission Distribution

Model (1/3)

Solar and wind energy

Information flow

Energy output

Energy forecast

Historical prices

How to bid and trade

Decision flow

Maximize profits over a finite horizon

Model (2/3)-Sequences of events1

14

t

bid

Energy forecastprice

t+1

Price 1

Sell inDay-ahead

Sell inReal-time

Buy from Real-time

Price 2Avail Energy

Stage 1: Bidding

Stage 2: Operational

Info.

Decisions

Price 1: For tomorrow’s day-ahead

Tomorrow afternoon

Morning Afternoon

noon

1 2 3 4

Source 1: www.nyiso.com, www.caiso.com, www.ercot.com

Assumption 1: One bid a day

Assumption 2: Price is exogenous, price-taker

Model (3/3)-Research Questions

15

Optimal bidding strategy (stage 1 every morning)?

Optimal storing strategy (stage 2 every afternoon)? Sell/Buy/Store?

Value of storage Help bidding Arbitrage across timeConstruct a Dynamic Programming model

and solved analytically

1 battery and 1 generator Theorem 1: closed form

solutions Selltday-ahead = bidt -1

(Intuition) Optimal inventory policy

Expected real-time price VS Discounted future value of inventory

Optimal biddingt Day-ahead VS real-time Bid capacity/ zero

Results: Closed-form Recursive solutions

16

t

t+1

Sell AllFill

Battery

Keep inventory level

All-Or-Nothing

Charging price: Function of state variable,

computed recursively.

Discharging price

RT Price

Preliminary comparison with practice

17

Policy

Improvement of our policy

over heuristics

Optimal policy N/A

Without battery

Bid zero, and sell in real-time

20.6442%

Bid forecast, and make up in real-time, sell extra

23.0758%

Other rules*

With battery

Bid forecast, and store, sell extra, make up

11.4315%

Many rules possible** From literature and practice

Future work18

Calibrate price models with more data Use financial models Waiting for more data from CME…

Benchmark literature and practice How good is our policy over heuristics and

practice? Value of storage

R.O.I. Storage value to balance network

For the whole grid, how much battery is needed for security and economic concerns

19

Thank you. Questions?

20

Appendix

1 battery, no generator Selltday-ahead = bidt -1

Optimal inventory decision

Appendix- Results: Dual Imbalance Prices

21

O*

IInitial

Inventory

Ending Inventor

y

Buy up to

Buy up to

Sell down to

Keep Invento

ryDo

nothing

Same Intuition

may hold for a more general

case

A

B

C

I II III IV