On Spring Washers, Constrained Dispatch, and Dispatch Model Sensitivity

1
On Spring Washers, Constrained Dispatch, and
Dispatch Model Sensitivity

• Andy Philpott
• Duncan Ashwell
• Graeme Everett

2
Motivation

• Electricity Commission May 19, 2006 Discussion
  Document and submissions
• TP 36, June 19, 2006 gave a surprising result.
• Transmission constraints are likely to become
  binding more often.
• Are extremely high price spikes a sensible
  signal?
• What, if anything, should be done?

3
Summary

• What is a spring washer effect?
• What happened on June 19, 2006?
• Are there any other SPD surprises?
• What, if anything, should be done?

4
Spring washer effects

• Well documented see Grant Reads talk in last
  years EPOC workshop.
• Occur in loop transmission systems with a
  constrained link.
• Highest nodal price observed at the constrained
  end, and decrease around loop to lowest price at
  unconstrained end.
• Examples

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Example Spring Washer
Reactance
Loss
Limit
A-gtB
0.01
0
1000
B-gtC
1
0
1000
A-gtC
0.001
0
100
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0
100
0.0989
100
100
99.901
0.0989
100
100
0.0989 0.01 0.0989 1 - 99.901 0.001 0
8
Increase Load at C to 100.1 MW
100
0.1
0
200
100
0.1
100.0
10200
100.1
Why?
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Increase Load at C to 100.2 MW
90
10.2
-10
0.2
100.0
100.2
100 flows from A to C 0.2 must flow from B to C
to supply demand at C Therefore 10 must flow back
from B to A because
-10 0.01 0.2 1 - 100.0 0.001 0
10
The difference in cost is
90
10.2
-10
200
100
0.2
100.0
10200
0.1 more load at C gives.. 10.1 more generation
at B 10 less generation at A
100.2
10.1 x 200 - 10 x 100 1020
11
Increase Load at C to 101.2 MW
0.00
101.1
-100
A
B
1.1
100.0
C
101.2
This problem has no feasible solution
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When the demand at C is 100 a, and a 0.1
Also a must be no more than 1.1 for this basis to
be feasible.
Indeed the dispatch problem is infeasible if
agt1.1. So the range of loads for which the
10,200 price is valid is very small and close
to infeasible.
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Observations

• Prices are higher than the highest offer price.
• High prices caused by constraint binding, meaning
  perturbation in load involves more than one
  marginal station.
• Solution is close to infeasibility.
• Prices are all nonnegative here (but may be
  negative in some examples).

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What happened at 1730 on June 19 (TP 36)?

• Dispatch prices were high (300-400) but without
  binding transmission constraints.
• In final pricing run, market infeasible as
  insufficient generation and reserve offers to
  meet demand.
• Provisional prices with infeasibilities were very
  high.
• Solution feasible after relaxation of RHS of a
  security constraint, and 60s reserve requirement.
• 10,000 prices across the grid significantly
  higher than highest offer and no binding
  transmission constraints.

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June 19 provisional prices with infeasibilities
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June 19 final price solution
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Explanation of final prices

• All 60s reserve is fully dispatched.
• OTA is not fully dispatched for energy but is
  fully dispatched for energy and reserve together.
• HLY is fully dispatched and is sending power
  North.
• HLY reduces dispatch and thus provides reserve.
• OTA increases dispatch and decreases reserve
  which exceeds HLY reduction because of line
  losses.
• The difference gives extra supply at OTA, at some
  cost.

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Illustration by example
A
B
Reactance
Loss
Limit
A-gtB
1
1
1000
B offers up to 500MW reserve at 100 Total other
reserve 205 MW at 0
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Solution
500
50
205
500
500
495
A
B
700
0
Generator A dispatched at 205MW - sets the risk
reserve (205) Generator B is fully dispatched
(its reserve is not dispatched)
Why the high prices?
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Increase load at B by 1
401
50
304
500
99
400
396
A
B
700
1
Generator A dispatched at 304MW - sets the risk
reserve (20599) Generator B is not fully
dispatched, provides extra 99 reserve
Change in cost 99500 10050 99100
54,400
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Increase load at A
305
400
A
B
701
0
Generator A dispatched at 305MW - sets the risk
reserve (205100) Generator B is not fully
dispatched, provides extra 100 reserve
Change in cost 100500 10050 100100
55,000
22
Increase load at A some more
703-0.99x
x
A
B
498-0.99x
703
0
703-0.99x lt 500 gt x gt 202.05
498-0.99xx lt 500 gt x lt 200
This problem has no feasible solution
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Sensitivity depends on loss factor a0.01
Basis matrix
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Inverse basis matrix is large
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Remarks

• Basis matrix at optimality is close to singular.
• Small changes in RHS can lead to big changes in
  dispatch.
• This makes the range of loads giving high prices
  small.
• So accuracy in measurements is important
  otherwise the effect is an artifact of noisy
  measurement and not a real effect.
• Effect in this case depends on an artifact of
  modelling reserve at a single NI node.

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Nodal reserve
305
400
205
100
A
B
701
0
For modelling convenience, reserve at B is
allowed to cover risk at A. If called on the
100MW would lose 1 in transmission.
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If reserve is nodal then
700d-0.99x
x
205
A
B
(495d-0.99x)/0.99
700d
0
(495d-0.99x)/0.99 x lt 500 gt 500d/0.99 lt
500
This problem has no feasible solution for any dgt0
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Are there any other SPD surprises?
200
200
100
500
0.01
A
B
0.0005
0.002
1
100
100
C
D
0.0005
101
0
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Line failure
200
200
100
500
0.01
-0.05
A
B
0.0005
0.05
0.002
100.95
1
100
100
101
C
D
0.0005
101
0
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Add a security constraint
200
200
100
500
0.01
A
B
0.0005
0.002
1
100
100
D
C
0.0005
101
0
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Are there any other SPD surprises?
500
50
100
500
205
500
495
A
B
495
500
800
0
Renewables dispatched at 205MW Generator A is
partially dispatched at 100MW Generator B is
fully dispatched at 500MW
Add a constraint that nonrenewables lt 600 MW
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What are the nodal prices?
50
500
205
A
B
44550
45000
800
801
0
With constraint that nonrenewables lt 600 MW
Renewables dispatched at 205MW Generator A is
partially dispatched at 200MW Generator B is
partially dispatched at 400MW
Change in cost 100500 10050
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Conclusions

• Changing the primal changes the dual.
• Basis matrix is nearly singular, so its inverse
  is large, giving large shadow prices.
• Sensitivity of outcomes to data.
• Perturbing data to lower the price is not the
  answer.
• Is the infeasibility check sensible?
• Why do Transpower use 100,000?
• What happens when we cannot relax security?
• How should we ration an infeasible solution?
• Is there a case for some demand-side bidding?