Examining the benefits of load shedding strategies
using a stochastic mixed complementarity
equilibrium model
ESRI-UCC Energy Policy Seminar
Mel Devine, Valentin Bertsch
Economic and Social Research Institute.
3rd June 2016
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Overview
Introduction
Model
Data
Results
Summary & Conclusions
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Introduction
What is load shedding?
Way of making electricity system more flexible (demand-side)
Cost of load shedding highest in residential sector (Leahy and
Toll (2011))
Research questions:
Assuming that the required ICT is installed, what are the best
options for load shedding? What are the benefits?
Strategies for dispatching Auxliary Power Units (APUs)?
Work in progress
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Model
Electricity market model
Players
Conventional generation
Passive load shedding consumers
Active load shedding consumers
One generator is offline and it’s uncertain when it comes back
online. (short-term model)
Stochastic game theory model (multiple optimisations)
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Game theory optimisation model
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Players
Generators
Maximise profits subject to capacity constraints
5 Players: 4 price-takers and 1 price maker (peak generator)
One generator is offline and it’s uncertain when it comes back
online.
Passive load shedding consumers
Minimises cost of meeting their demand
Reduces load if cost of meeting is too much
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Players
Active load shedding consumers
Minimises cost of meeting their demand
Reduces load if cost of meeting is too much
Can supply auxiliary generation in order to meet demand
subject to storage (of diesel) constraint
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Data
Capacity (MW)
Marginal
(€/MW)
Generator 1
150
22
Generator 2
350
30
Generator 3
100
43
Generator 4
60
50
Generator 5
150
133
Passive load shedding
100
180 + 8x
Active load shedding
20
120 + 12x
100∗
186
Active auxiliary generation
∗ Constrained
over entire time period (MW h)
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cost
Scenarios for length of outage for generator 4
We consider horizons of T = 2, 6, 12, 24 and 48 hours.
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Assumed probability of length of outage
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Test cases
1
Base case: Passive and active load shedding & APU
generation (active demand only). Market power present.
2
Priority: Passive load shedding only. Market power present.
3
APU2Market Passive and active load shedding. APU
generation available to full market. Market power present.
4
NoMarketPower Passive and active load shedding & APU
generation (active demand only). No market power present.
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Results: expected total costs for consumers
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Results: expected total load shedding
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Results: expected total costs for consumers (base case)
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Results: active load shedding expected costs (base case)
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Results: active load shedding diesel in storage (base case)
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Results: expected prices (base case)
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Summary & conclusions
Introduced game theory model
Short-term model with uncertainty of length of outage
When market power is present, there is increased costs and
load shedding
Minimal benefit of allowing auxiliary generation to the full
market
Unclear what the “optimal” level of foresight is
Work in progress
Cost benefit analysis of load shedding versus investment in
new generation
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Thank you!
Questions?
[email protected]
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Appendix: generator’s problem
max
gi,t,s
X
s
prs
X
(γt,s − Fi )gi,t,s ,
t
subject to
gi,t,s ≤ Gimax ∀t, s.
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(1)
Appendix: passive load shedding consumer
min
P
∆gj,t,s
X
s
prs
X
P
P
P
P
γt,s · (Dj,t,s
− ∆gj,t,s
) + ∆gj,t,s
· Cj (∆gj,t,s
) ,
t
subject to
P
∆gj,t,s
≤ ∆gjP,max ∀t, s,
(2)
P
∆gj,t,s
≥ 0 ∀t, s.
(3)
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Appendix: active load shedding consumer
min
X
A
APU
∆gk,t,s
,gk,t,s
prs
s
T̂ X
A
A
APU
γt,s (Dk,t,s
− ∆gk,t,s
− gk,t,s
)
t=1
A
A
APU
APU
+ ∆gk,t,s
Ck (∆gk,t,s
) + gk,t,s
αk (gk,t,s
) ,
subject to
A
∆gk,t,s
≤ ∆gkA,max ∀t, s,
A
APU
A
∆gk,t,s
+ gk,t,s
≤ Dk,t,s
∀t, s,
X
(4)
(5)
APU
gk,t,s
≤ gkAPU,max ∀t, s,
(6)
APU
gk,t,s
≤ Vk ηk .
(7)
t
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