Intermittent Resource in Deregulated Electricity Market
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.
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
Eric wanted to be part of the solution to save his Victorian house.
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?
Intermittent Resources with Storage in a Deregulated Electricity Market
Yangfang Zhou, Stephen Smith, Alan Scheller-Wolf, Nicola Secomandi
Contents
9
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 Review
10
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 Management
11
What does operations Management do?
Create and use operations research techniques
Optimize business operations : inventory
Dynamic programming
Linear/Integer programming
Stochastic programming
Constraint programming
…...
When to order , how much to order
Electricity is a special type of perishable inventory
Bridge OM & electricity
Where is Eric’s firm?
Generator A
Generator B
Generator C
Utility A
ISO
Utility B
Utility C
Wholesale Market
Generation Transmission
Retail Market
Distribution
Model (1/3)
Solar and wind energy
Energy forecast
Energy output
Historical prices
How to bid and trade
Information flow
Decision flow
Maximize profits over a finite horizon
Model (2/3)-Sequences of events
1
14
Assumption 1:
One bid a day bid
Buy from
Real-time
Assumption 2:
Price is exogenous, price-taker
Sell in
Real-time
Decisions
Sell in
Day-ahead
Info.
Energy forecast price
Price 1
Morning
Stage 1: Bidding
Avail Energy
3
4 t+1
Price 2
Tomorrow afternoon
Afternoon Price 1: For tomorrow’s day-ahead
Stage 2: Operational
Source 1: www.nyiso.com
, www.caiso.com
, www.ercot.com
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 time
Construct a Dynamic Programming model and solved analytically
Results: Closed-form Recursive solutions
16
1 battery and 1 generator
Theorem 1: closed form solutions
Sell t day-ahead = bid t -1
(Intuition)
Expected real-time price VS
Discounted future value of inventory
Fill
Battery
Keep inventory level
Optimal bidding t
Day-ahead VS real-time
Bid capacity/ zero
RT Price
Charging price: Function of state variable, computed recursively.
Sell All
Discharging price
17
Preliminary comparison with practice
Policy
Without battery
With battery
Optimal policy
Bid zero, and sell in real-time
Bid forecast, and make up in real-time, sell extra
Other rules*
Bid forecast, and store, sell extra, make up
Many rules possible*
* From literature and practice
Improvement of our policy over heuristics
N/A
20.6442%
23.0758%
11.4315%
Future work
18
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
Appendix- Results: Dual Imbalance
Prices
21
1 battery, no generator
Sell t day-ahead = bid t -1
Same Intuition
Optimal inventory decision
Ending
Inventory
O* may hold for a more general case
Sell down to
C Keep
Inventory
B
Do nothing
A
Buy up to
Buy up to
I II III IV
I
Initial
Inventory
