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Risk-Limiting Dispatch for Power Networks

Explore how to optimize power dispatch under uncertainty and quantify its impact in the presence of renewables. Learn about risk management strategies and dimensionality reduction in congested networks.

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Risk-Limiting Dispatch for Power Networks

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  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?

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

  4. Notation • Three types of devices in the power system: Renewables: Random, High Uncertainty Loads: Random, Low Uncertainty Generators: Controllable =net demand=Load-Renewable Gaussian in this talk Error Prediction

  5. Two-Stage Formulation • Two-stage problem • Dynamic programming problem: numerical solution possible but offers little qualitative insight. • Make small ¾ assumption. Actual net-demand: Predicted net-demand: Stage 2 (real-time) Stage 1 (day ahead) Set slow generators: Set fast generators Price ($/MW) Price ($/MW)

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

  7. Impact of uncertainty • We want to find (as a function of ) • Optimal cost • Optimal control • Also want • Intrinsic impact of uncertainty • Depend on Cost of uncertainty= Optimal Cost Clairvoyant Cost

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

  9. Single-bus network • No congestion => single bus network • Easy to get the optimal control 3 ~$100 Million/yr Reserve/ optimal

  10. Price of Uncertainty • Price of uncertainty is a function of • Small Error renewable>load renewable<load 0

  11. Nominally Congested Network • One nominally congested line ? Midwest ISO

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

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

  14. Nominal solution regions x

  15. Prices of uncertainty x

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

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