On Spring Washers Constrained Dispatch and Dispatch Model

On Spring Washers, Constrained Dispatch, and Dispatch Model Sensitivity Andy Philpott Duncan Ashwell Graeme Everett September 7, 2006 EPOC Winter Workshop, 2006 1

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? September 7, 2006 EPOC Winter Workshop, 2006 2

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? September 7, 2006 EPOC Winter Workshop, 2006 3

Spring washer effects • Well documented – see Grant Read’s talk in last year’s 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 September 7, 2006 EPOC Winter Workshop, 2006 4

Example Spring Washer A B C A->B B->C A->C September 7, 2006 Reactance 0. 01 1 0. 001 Loss 0% 0% 0% EPOC Winter Workshop, 2006 Limit 1000 100 5

A B C September 7, 2006 EPOC Winter Workshop, 2006 6

100 0 0. 0989 A B $100 99. 901 $100 0. 0989 C $100 0. 0989 * 0. 01 + 0. 0989 * 1 - 99. 901 * 0. 001 = 0 September 7, 2006 EPOC Winter Workshop, 2006 7

Increase Load at C to 100. 1 MW 100 0. 1 0 A B $100 $200 0. 1 100. 0 C $10200 100. 1 Why? September 7, 2006 EPOC Winter Workshop, 2006 8

Increase Load at C to 100. 2 MW 90 A 10. 2 -10 B 0. 2 100. 0 C 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 September 7, 2006 EPOC Winter Workshop, 2006 9

The difference in cost is… 90 10. 2 -10 A B $100 0. 2 100. 0 0. 1 more load at C gives. . $200 C $10200 10. 1 more generation at B 100. 2 10 less generation at A 10. 1 x $200 - 10 x $100 = $1020 September 7, 2006 EPOC Winter Workshop, 2006 10

Increase Load at C to 101. 2 MW 0. 00 101. 1 -100 A B $200 -$998 1. 1 100. 0 C $100, 000 0. 1 $100, 000 101. 2 This problem has no feasible solution September 7, 2006 EPOC Winter Workshop, 2006 11

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 a>1. 1. So the range of loads for which the $10, 200 price is valid is very small and close to infeasible. September 7, 2006 EPOC Winter Workshop, 2006 12

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). September 7, 2006 EPOC Winter Workshop, 2006 13

What happened at 17: 30 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 60 s reserve requirement. • $10, 000 prices across the grid – significantly higher than highest offer and no binding transmission constraints. September 7, 2006 EPOC Winter Workshop, 2006 14

June 19 provisional prices with infeasibilities September 7, 2006 EPOC Winter Workshop, 2006 15

June 19 final price solution September 7, 2006 EPOC Winter Workshop, 2006 16

Explanation of final prices • All 60 s 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. September 7, 2006 EPOC Winter Workshop, 2006 17

Illustration by example A A->B Reactance 1 B Loss 1% Limit 1000 B offers up to 500 MW reserve at $100 Total other reserve = 205 MW at $0 September 7, 2006 EPOC Winter Workshop, 2006 18

Solution 205 495 $55, 000 500 $500 500 A 700 B $54, 500 0 Generator A dispatched at 205 MW - sets the risk = reserve (205) Generator B is fully dispatched (its reserve is not dispatched) Why the high prices? September 7, 2006 EPOC Winter Workshop, 2006 19

Increase load at B by 1 304 401 $500 396 99 400 A 700 B 1 Generator A dispatched at 304 MW - sets the risk = reserve (205+99) Generator B is not fully dispatched, provides extra 99 reserve Change in cost = 99*500 – 100*50 + 99*100 = 54, 400 September 7, 2006 EPOC Winter Workshop, 2006 20

Increase load at A 305 400 396 A 701 100 400 B 0 Generator A dispatched at 305 MW - sets the risk = reserve (205+100) Generator B is not fully dispatched, provides extra 100 reserve Change in cost = 100*500 – 100*50 + 100*100 = 55, 000 September 7, 2006 EPOC Winter Workshop, 2006 21

Increase load at A some more 703 -0. 99 x x 0. 99 x A x B 498 -0. 99 x 703 0 703 -0. 99 x <= 500 => x >= 202. 05 498 -0. 99 x+x <= 500 => x <= 200 This problem has no feasible solution September 7, 2006 EPOC Winter Workshop, 2006 22

Sensitivity depends on loss factor a=0. 01 Basis matrix September 7, 2006 EPOC Winter Workshop, 2006 23

Inverse basis matrix is large September 7, 2006 EPOC Winter Workshop, 2006 24

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. September 7, 2006 EPOC Winter Workshop, 2006 25

Nodal reserve 305 400 205 396 A 701 100 400 B 0 For modelling convenience, reserve at B is allowed to cover risk at A. If called on the 100 MW would lose 1% in transmission. September 7, 2006 EPOC Winter Workshop, 2006 26

If reserve is nodal then 700+d-0. 99 x 205 x 0. 99 x A x B (495+d-0. 99 x)/0. 99 700+d 0 (495+d-0. 99 x)/0. 99 +x <= 500 => 500+d/0. 99 <= 500 This problem has no feasible solution for any d>0 September 7, 2006 EPOC Winter Workshop, 2006 27

Are there any other SPD surprises? 200 $100 $500 0. 01 A 0. 0005 0. 002 1 100 D 100 0. 0005 101 September 7, 2006 B EPOC Winter Workshop, 2006 C 0 28

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Line failure 200 $100 A 0. 002 100 $500 0. 01 -0. 05 B 0. 0005 0. 05 100. 95 100 101 D 1 C 0. 0005 101 September 7, 2006 EPOC Winter Workshop, 2006 0 30

Add a security constraint 200 $100 $500 0. 01 A 0. 002 100 0. 0005 1 100 D 0. 0005 101 September 7, 2006 B C 0 EPOC Winter Workshop, 2006 31

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Are there any other SPD surprises? 100 500 $500 205 495 A 500 B $495 $500 800 0 Renewables dispatched at 205 MW Generator A is partially dispatched at 100 MW Generator B is fully dispatched at 500 MW Add a constraint that nonrenewables <= 600 MW September 7, 2006 EPOC Winter Workshop, 2006 33

What are the nodal prices? 200 100 400 500 $500 205 A 396 495 400 500 B $44550 $45000 801 0 With constraint that nonrenewables <= 600 MW Renewables dispatched at 205 MW Generator A is partially dispatched at 200 MW Generator B is partially dispatched at 400 MW Change in cost = 100*500 – 100*50 September 7, 2006 EPOC Winter Workshop, 2006 34

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? September 7, 2006 EPOC Winter Workshop, 2006 35