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 Billions of dollars in stimulus plan ( 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

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 (1generator &1storage, SP, no analytical result)  Economic Dispatch of Intermittent Resources Xie et al (Do not consider storage.)  Electricity storage evaluation Walawalkar & et al (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  Electricity is a special type of perishable inventory  Bridge OM & electricity Dynamic programming Linear/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 GenerationTransmissionDistribution

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 events 1 14 t bid Energy forecast price t+1 Price 1 Sell in Day-ahead Sell in Real-time Buy from Real-time Price 2 Avail Energy Stage 1: BiddingStage 2: Operational Info. Decisions Price 1: For tomorrow’s day-ahead Tomorrow afternoon Morning Afternoon noon 11 22 33 44 Source 1: 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 time Construct a Dynamic Programming model and solved analytically

 1 battery and 1 generator  Theorem 1: closed form solutions  Sell t day-ahead = bid t -1 (Intuition)  Optimal inventory policy Expected real-time price VS Discounted future value of inventory  Optimal bidding t Day-ahead VS real-time Bid capacity/ zero Results: Closed-form Recursive solutions 16 t t+1 Sell All Fill 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 policyN/A Without battery Bid zero, and sell in real-time % Bid forecast, and make up in real-time, sell extra % Other rules* With battery Bid forecast, and store, sell extra, make up % Many rules possible* * From literature and practice

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

 1 battery, no generator  Sell t day-ahead = bid t -1  Optimal inventory decision Appendix- Results: Dual Imbalance Prices 21 O* I Initial Inventory Ending Inventory Buy up to Sell down to Keep Inventory Do nothing Same Intuition may hold for a more general case A B C III IIIIV