Top Banner
Risk-Limiting Dispatch for Power Networks David Tse, Berkeley Ram Rajagopal (Stanford) Baosen Zhang (Berkeley)
16

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

Dec 21, 2015

Download

Documents

Marjory Rogers
Welcome message from author
This document is posted to help you gain knowledge. Please leave a comment to let me know what you think about it! Share it to your friends and learn new things together.
Transcript
Page 1: Risk-Limiting Dispatch for Power Networks David Tse, Berkeley Ram Rajagopal (Stanford) Baosen Zhang (Berkeley)

Risk-Limiting Dispatch for Power Networks

David Tse, Berkeley

Ram Rajagopal

(Stanford)Baosen Zhang

(Berkeley)

Page 2: 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.

• 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?

2/15

Page 3: Risk-Limiting Dispatch for Power Networks David Tse, Berkeley Ram Rajagopal (Stanford) Baosen Zhang (Berkeley)

• Add 25% wind, 20% error• Total Error~2+5=7%

Motivation

• Currently: 3 rule• Error~2%

3/15

Forecasted load

ErrorReserve

𝜎

Forecasted net demand

Error

Reserve

1% is about $50 Million/yr (for CAISO)

$1 Billion$300 Million

Page 4: Risk-Limiting Dispatch for Power Networks David Tse, Berkeley Ram Rajagopal (Stanford) Baosen Zhang (Berkeley)

Notation

• Three types of devices in the power system:

4/15

=net demand=Load-Renewable

Generators:

Controllable

Renewables:

Random,

High Uncertainty

Loads:

Random,

Low Uncertainty

Prediction Error Gaussian in this talk

Page 5: Risk-Limiting Dispatch for Power Networks David Tse, Berkeley Ram Rajagopal (Stanford) Baosen Zhang (Berkeley)

Two-Stage Formulation

• Two-stage problem

• Dynamic programming problem: numerical solution possible but offers little qualitative insight.

• Make small ¾ assumption.

5/15

Stage 1 (day ahead)

Predicted net-demand:

Set slow generators:

Stage 2 (real-time)

Actual net-demand:

Set fast generators

Price ($/MW) Price ($/MW)¿

Page 6: Risk-Limiting Dispatch for Power Networks David Tse, Berkeley Ram Rajagopal (Stanford) Baosen Zhang (Berkeley)

Nominal Problem

6/15

Stage 1 Stage 2

�̂� 𝑑𝑔𝛼 𝛽

Nominal Problem

�̂�𝛼

Stage 1 Stage 2

optimal under

small ¾ assumption

Page 7: Risk-Limiting Dispatch for Power Networks David Tse, Berkeley Ram Rajagopal (Stanford) Baosen Zhang (Berkeley)

Impact of uncertainty

• We want to find (as a function of )– Optimal cost– Optimal control

• Also want

• Intrinsic impact of uncertainty– Depend on

7/15

Cost of uncertainty= Optimal Cost Clairvoyant Cost

Page 8: Risk-Limiting Dispatch for Power Networks David Tse, Berkeley Ram Rajagopal (Stanford) Baosen Zhang (Berkeley)

Nominally Uncongested Network

• Networks are lightly congested

Result:

8/15

New England ISO

Nominally

Uncongested

Single Bus Network

Price of uncertainty

Page 9: Risk-Limiting Dispatch for Power Networks David Tse, Berkeley Ram Rajagopal (Stanford) Baosen Zhang (Berkeley)

Single-bus network

• No congestion => single bus network• Easy to get the optimal control

9/15

0 5 10 15 20 25 30-0.5

0

0.5

1

1.5

2

2.5

3

3.5

/

Q-1

(

/) ~$100 Million/yr

3

optimal

Res

erve

/

Page 10: Risk-Limiting Dispatch for Power Networks David Tse, Berkeley Ram Rajagopal (Stanford) Baosen Zhang (Berkeley)

Price of Uncertainty

• Price of uncertainty is a function of • Small Error

10/15

0

renewable>load renewable<load

Page 11: Risk-Limiting Dispatch for Power Networks David Tse, Berkeley Ram Rajagopal (Stanford) Baosen Zhang (Berkeley)

Nominally Congested Network

• One nominally congested line

11/15

Midwest ISO

?

Page 12: Risk-Limiting Dispatch for Power Networks David Tse, Berkeley Ram Rajagopal (Stanford) Baosen Zhang (Berkeley)

Dimensionality Reduction

• One congested line• Single bus?

Result:

Reduction to an equivalent two-bus network always possible.

12/15IEEE 13 Bus Network

KVL

x

x

Page 13: Risk-Limiting Dispatch for Power Networks David Tse, Berkeley Ram Rajagopal (Stanford) Baosen Zhang (Berkeley)

Two-bus network: Further reduction?

• Nominally congested line from 1 to 2

• Congestion is nominal

• Errors still average

13/15

?

1

2

x1

2Two isolated

buses?

x1

2 Supply > expected

Supply < expected

Real-timeNominal x Back-flow

Page 14: Risk-Limiting Dispatch for Power Networks David Tse, Berkeley Ram Rajagopal (Stanford) Baosen Zhang (Berkeley)

Nominal solution regions

14/15

𝑐

𝐶

−𝐶

−𝐶

𝐶

x

Page 15: Risk-Limiting Dispatch for Power Networks David Tse, Berkeley Ram Rajagopal (Stanford) Baosen Zhang (Berkeley)

Prices of uncertainty

15/15

𝑐

𝐶

−𝐶

−𝐶

𝐶

x

Page 16: Risk-Limiting Dispatch for Power Networks David Tse, Berkeley Ram Rajagopal (Stanford) Baosen Zhang (Berkeley)

Conclusion

• Management of risk in the presence of renewables• Price of uncertainty

– Intrinsic impact of uncertainties

• Dimension reduction for congested networks

16/15