risk-limiting dispatch for power networks
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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. - PowerPoint PPT PresentationTRANSCRIPT
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Risk-Limiting Dispatch for Power Networks
David Tse, Berkeley
Ram Rajagopal (Stanford)
Baosen Zhang(Berkeley)
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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
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• Add 25% wind, 20% error• Total Error~2+5=7%
Motivation
• Currently: 3 rule• Error~2%
3/15
Forecasted load
ErrorReserve𝜎
Forecasted net demand
Error
Reserve
1% is about $50 Million/yr (for CAISO)
$1 Billion$300 Million
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Notation
• Three types of devices in the power system:
4/15
=net demand=Load-Renewable
Generators:Controllable
Renewables:Random,
High Uncertainty
Loads:Random,
Low Uncertainty
Prediction Error Gaussian in this talk
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Two-Stage Formulation
• Two-stage problem
• Dynamic programming problem: numerical solution possible but offers little qualitative insight.
• Make small ¾ assumption.5/15
Stage 1 (day ahead)
Predicted net-demand:
Set slow generators:
Stage 2 (real-time)
Actual net-demand:
Set fast generators
Price ($/MW) Price ($/MW)¿
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Nominal Problem
6/15
Stage 1 Stage 2
�̂� 𝑑𝑔𝛼 𝛽
Nominal Problem
�̂�𝛼
Stage 1 Stage 2
optimal undersmall ¾ assumption
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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
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Nominally Uncongested Network
• Networks are lightly congested
Result:
8/15
New England ISO
Nominally Uncongested
Single Bus Network
Price of uncertainty
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Single-bus network
• No congestion => single bus network• Easy to get the optimal control
9/150 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
/
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Price of Uncertainty
• Price of uncertainty is a function of • Small Error
10/15
0
renewable>load renewable<load
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Nominally Congested Network
• One nominally congested line
11/15
Midwest ISO
?
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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
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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
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Nominal solution regions
14/15
𝑐
𝐶
−𝐶
−𝐶
𝐶
x
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Prices of uncertainty
15/15
𝑐𝐶
−𝐶
−𝐶
𝐶
x
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Conclusion
• Management of risk in the presence of renewables• Price of uncertainty
– Intrinsic impact of uncertainties• Dimension reduction for congested networks
16/15