1. Risk-Limiting Dispatch for Power Networks David Tse, Berkeley Ram Rajagopal (Stanford) Baosen Zhang (Berkeley)

2. Motivation Traditional power generators slow to ramp up and down. Have to be dispatched in advance based on predicted demand. Increased penetration of renewables comes increased uncertainty. Questions: How to do dispatch in face of uncertainty? How to quantify the impact of uncertainty? How to hedge against risks from randomness? 1/15

3. Add 25% wind, 20% error Total Error~2+5=7% Motivation 2/15 Forecasted load Error Reserve Forecasted net demand Error Reserve 1% is about $50 Million/yr (for CAISO) $1 Billion $300 Million

4. Notation Three types of devices in the power system: 3/15 Generators: Controllable Renewables: Random, High Uncertainty Loads: Random, Low Uncertainty Prediction Error Gaussian in this talk

5. Two-Stage Formulation Two-stage problem Dynamic programming problem: numerical solution possible but offers little qualitative insight. Make small ¾ assumption. 4/15 Stage 1 (day ahead) Stage 2 (real-time) Set fast generators

6. Nominal Problem 5/15 Stage 1 Stage 2 Nominal Problem Stage 1 Stage 2 optimal under small ¾ assumption

7. Impact of uncertainty 6/15

8. Nominally Uncongested Network Networks are lightly congested Result: 7/15 New England ISO Nominally Uncongested Single Bus Network Price of uncertainty

9. Single-bus network No congestion => single bus network Easy to get the optimal control 8/15 ~$100 Million/yr optimal

10. Price of Uncertainty 9/15 0 renewable>loadrenewable<load

11. Nominally Congested Network One nominally congested line 10/15 Midwest ISO ?

12. Dimensionality Reduction One congested line Single bus? Result: Reduction to an equivalent two- bus network always possible. 11/15 IEEE 13 Bus Network KVL x x

13. Two-bus network: Further reduction? Nominally congested line from 1 to 2 Congestion is nominal Errors still average 12/15 ? 1 2 x 1 2 Two isolated buses? x 1 2 Supply > expected Supply < expected Real-time Nominal x Back-flow

14. Nominal solution regions 13/15 x

15. Prices of uncertainty 14/15 x

16. Conclusion Management of risk in the presence of renewables Price of uncertainty –Intrinsic impact of uncertainties Dimension reduction for congested networks 15/15