1. IEOR 180 Senior Project Toni Geralde Mona Gohil Nicolas Gomez Lily Surya Patrick Tam Optimizing Electricity Procurement for the City of Palo Alto

2. Outline City of Palo Alto Energy deregulation Tradeoffs Palo Alto’s current decision making tools Our linear optimization model Results

3. Founded: 1900 Area: 26 square miles Customers: 58,100 including residential homes small businesses corporate offices manufacturing facilities excluding Stanford University Campus Company Background

4. California Energy Deregulation Began January 1, 1998 Open buyer and seller market for electricity –Purchase Energy $X per Mega Watt Hour

5. California Energy Market Inflexible products: constant amount/ fixed prices Forwards High Load Load All Week Flexible products: variable amounts Spot market WAPA

6. Trade-Offs Futures contracts: –safeguard against price spikes versus cost of premium Spot Market –flexibility of amount versus exposure to risk

7. Meeting Demand Time of Day MWh Product II Spot Market/WAPA Demand Curve Product I Sell to spot 12am 11:59 pm pri Product III

8. Palo Alto Model: Challenges How much WAPA should be utilized –capacity charge based on maximum amount How much to purchase in advance via forwards

9. Optimize portfolio with two time periods: –Heavy load hours (HLH) –Light load hours (LLH) Purchase options: Forward contracts and WAPA City of Palo Alto: Current Solution LLHHLHLLH Demand curve MW Time of day 6 am10 pm

10. Problem Statement Optimize available energy sources with additional energy products and additional time periods to accommodate them: –WAPA –HLH forwards –LLH forwards –E3 blocks –All week forwards

11. Approach: Linear Program Based in Excel and What’s Best Solver WAPA E3 I E3 II Time LoadLoad 6am10am2pm6pm10pm

12. Available Data Forecasted Load –Hourly demand for one year Forecasted Market Prices Fixed Contract prices

13. Model features Flexible:Let the user input values for all parameters. Accurate: It follows the power demand closely by dividing the month into 150 periods. Handle risk: Control exposure to spot market for different demand loads. Automated

14. Subscripts b=Block index (1,…,5) d=Day index (1,…,31) K=Week index (1,…,5)

15. Decision variables Power from WAPA bd MAX Power from High Load Forward Power from Low Load Forward Power from All Week Forward Power from E3 bk

16. Parameters Upper and Lower limit for WAPA WAPA capacity cost Variable Cost of each product Demand Load bd, during each period

17. Objective function MIN  Cost of Product bdk * Product bdk + (WAPA Capacity Cost * MAX) -  (Load bdk - Product bdk )*Cost Forward bdk

18. Constraints WAPA Upper and Lower limit constraints MAX >= WAPA bd. Satisfy all demand All variables >= 0.

19. Model: Inputs

20. Quantifying Risk Risk Defined: –exposure to spot market Risk Implementation –% exposure to spot market during high load periods during normal load periods

21. Model: Quantifying Risk Risk is the exposure to the spot market

22. Model: Outputs for all product- decision variables

23. Model Outputs: the costs for different products Minimized

24. The Option to Sell Back Negative means unused capacity Unused capacity multiplied by the corresponding price Revenue from selling back

25. Chart Output: Percentage of different products

26. Quantifying Results Model Comparison Run models under various scenarios –Heavy load –Light load –Normal load Calculate cost reduction under new model

27. Model Comparison Based on same inputs –prices –forecasted demand Compare models against an actual load –Actual load = average load during time intervals utilized in UCB model

28. Model Comparison UCB Model is inherently better than Palo Alto’s current Model. Time LoadLoad 6am10am2pm6pm10pm

29. Monthly Savings

30. Annual Savings

31. Reduction in Variance

32. Summary of Results UCB Model Savings –$1.121 million for 1998 –4% cost reduction UCB with revenue Model –additional $180,762 for 1998 –additional 1% cost reduction Reduction in Variance

33. Benefits of UCB Model Utilizes all available procurement options Low Run-time Partitions day into finer time intervals –more closely follows demand curve –reduction in variance from actual load Reduction in risk

34. Recommendations Replace existing model with UCB model Negotiate with WAPA to reduce lower capacity limit –For June 1998, the max purchase quantity is ~ 40 mwh (no lower capacity limit) Incorporate spot market into decisions