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Risk-Limiting Dispatch for Power Networks

Risk-Limiting Dispatch for Power Networks. David Tse , Berkeley. Ram Rajagopal ( Stanford). Baosen Zhang (Berkeley). Motivation. Traditional power generators slow to ramp up and down. Have to be dispatched in advance based on predicted demand.

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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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