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

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

September 7, 2006EPOC Winter Workshop, 2006Slide 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?

September 7, 2006EPOC Winter Workshop, 2006Slide 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?

September 7, 2006EPOC Winter Workshop, 2006Slide 4 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, 2006EPOC Winter Workshop, 2006Slide 5 Example Spring Washer ReactanceLossLimit A->B 0.010%1000 B->C 10%1000 A->C 0.0010%100 AB C

September 7, 2006EPOC Winter Workshop, 2006Slide 6 AB C

September 7, 2006EPOC Winter Workshop, 2006Slide 7 0.0989 * 0.01 + 0.0989 * 1 - 99.901 * 0.001 = 0 AB C 0.0989 99.901 0.0989 100 0 \$100 100

September 7, 2006EPOC Winter Workshop, 2006Slide 8 AB C 0 100.0 0.1 1000.1 \$100 \$200 \$10200 Increase Load at C to 100.1 MW Why? 100.1

September 7, 2006EPOC Winter Workshop, 2006Slide 9 AB C -10 100.0 0.2 9010.2 Increase Load at C to 100.2 MW -10* 0.01 + 0.2 * 1 - 100.0 * 0.001 = 0 100 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… 100.2

September 7, 2006EPOC Winter Workshop, 2006Slide 10 AB C -10 100.0 0.2 9010.2 \$100 \$200 \$10200 The difference in cost is… 0.1 more load at C gives.. 10.1 more generation at B 10 less generation at A 10.1 x \$200 - 10 x \$100 = \$1020 100.2

September 7, 2006EPOC Winter Workshop, 2006Slide 11 AB C -100 100.0 1.1 0.00 101.1 -\$998 \$200 \$100,000 Increase Load at C to 101.2 MW This problem has no feasible solution 0.1 \$100,000 101.2

September 7, 2006EPOC Winter Workshop, 2006Slide 12 When the demand at C is 100 + , and  ≥ 0.1 Also  must be no more than 1.1 for this basis to be feasible. Indeed the dispatch problem is infeasible if  >1.1. So the range of loads for which the \$10,200 price is valid is very small and close to infeasible.

September 7, 2006EPOC Winter Workshop, 2006Slide 13 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, 2006EPOC Winter Workshop, 2006Slide 14 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 60s reserve requirement. \$10,000 prices across the grid – significantly higher than highest offer and no binding transmission constraints.

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

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

September 7, 2006EPOC Winter Workshop, 2006Slide 17 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.

September 7, 2006EPOC Winter Workshop, 2006Slide 18 Illustration by example ReactanceLossLimit A->B 11%1000 AB B offers up to 500MW reserve at \$100 Total other reserve = 205 MW at \$0

September 7, 2006EPOC Winter Workshop, 2006Slide 19 Solution AB \$54,500\$55,000 205 500 495 7000 Generator A dispatched at 205MW - sets the risk = reserve (205) Generator B is fully dispatched (its reserve is not dispatched) Why the high prices? \$500 \$50

September 7, 2006EPOC Winter Workshop, 2006Slide 20 Increase load at B by 1 AB 304 400 401 396 7001 99 Generator A dispatched at 304MW - 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 \$500 \$50

September 7, 2006EPOC Winter Workshop, 2006Slide 21 Increase load at A AB 305400 396 7010 100 Change in cost = 100*500 – 100*50 + 100*100 = 55,000 Generator A dispatched at 305MW - sets the risk = reserve (205+100) Generator B is not fully dispatched, provides extra 100 reserve

September 7, 2006EPOC Winter Workshop, 2006Slide 22 Increase load at A some more AB 703-0.99xx x0.99x 7030 498-0.99x This problem has no feasible solution 703-0.99x x >= 202.05 498-0.99x+x x <= 200

September 7, 2006EPOC Winter Workshop, 2006Slide 23 Sensitivity depends on loss factor  =0.01 Basis matrix

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

September 7, 2006EPOC Winter Workshop, 2006Slide 25 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, 2006EPOC Winter Workshop, 2006Slide 26 Nodal reserve AB 305400 396 7010 205 For modelling convenience, reserve at B is allowed to cover risk at A. If called on the 100MW would lose 1% in transmission. 100

September 7, 2006EPOC Winter Workshop, 2006Slide 27 If reserve is nodal then AB 700+  -0.99x x x0.99x 700+  0 205 (495+  -0.99x)/0.99 This problem has no feasible solution for any  >0 (495 +  -0.99x)/0.99 +x 500+  /0.99 <= 500

September 7, 2006EPOC Winter Workshop, 2006Slide 28 Are there any other SPD surprises? 1010 200 0.0005 1 0.01 0.0005 0.002 100 \$100 \$500 AB CD 100

September 7, 2006EPOC Winter Workshop, 2006Slide 29

September 7, 2006EPOC Winter Workshop, 2006Slide 30 Line failure 100 1010 200 0.0005 1 0.01 0.0005 0.002 \$100 \$500 100.95 -0.05 0.05 101 AB CD 100

September 7, 2006EPOC Winter Workshop, 2006Slide 31 Add a security constraint 1010 200 0.0005 1 0.01 0.0005 0.002 \$100 \$500 AB DC 100

September 7, 2006EPOC Winter Workshop, 2006Slide 32

September 7, 2006EPOC Winter Workshop, 2006Slide 33 AB 205 500 495 8000 Renewables dispatched at 205MW Generator A is partially dispatched at 100MW Generator B is fully dispatched at 500MW \$500 \$50 100 Are there any other SPD surprises? Add a constraint that nonrenewables <= 600 MW \$495 \$500

September 7, 2006EPOC Winter Workshop, 2006Slide 34 AB 205 8010 \$500 \$50 What are the nodal prices? With constraint that nonrenewables <= 600 MW \$44550 \$45000 800 400 200 400396 Renewables dispatched at 205MW Generator A is partially dispatched at 200MW Generator B is partially dispatched at 400MW 500495 500 100 Change in cost = 100*500 – 100*50

September 7, 2006EPOC Winter Workshop, 2006Slide 35 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?

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