Power Systems Engineering Research Center (PSERC ) An NSF Industry / University Cooperative Research Center. Mission

Transcription

1 Power Systems Engineering Research Center ( ) An NSF Industry / University Cooperative Research Center 1 Mission Universities working with industry and government to find innovative solutions to challenges facing a restructured electric power industry. Multi-disciplinary (engineering, economics, operations research, etc.) Multi-university Collaborative Research and education activities 2 1

2 Universities Cornell University (lead university) Arizona State University University of California at Berkeley Carnegie Mellon University Colorado School of Mines Georgia Institute of Technology The University Of Illinois at Urbana Iowa State University Texas A&M University Washington State University University of Wisconsin-Madison 3 Research Program Three research stems Markets Transmission and distribution technologies Systems Leveraged research (such as Consortium for Electric Reliability Technology Solutions) Public documents: 4 2

3 Electric Service Reliability Fernando L. Alvarado Professor, University of Wisconsin Invited Presentation 43 rd NARUC Program East Lansing, Michigan, August 15, Outline Traditional reliability concepts LOLP n-1 security Reserve margins Reliability in a market context The Value Of Lost Load (VOLL) Some market power issues 6 3

4 Traditional reliability concepts Loss of load probability (LOLP) Expected Demand Not Served (EDNS) n-1 security Reserve margins Electric service reliability End-user perspective: Any involuntary loss of power is a reliability event Bulk system perspective: Any system condition leading to loss of load is a reliability event Only those leading to widespread or extended outages are considered true reliability events The outage of a component is not an event 8 4

5 Reliability Time Frames The planning time frame The operations time frame Reliability in this timeframe is sometimes called security In this talk we will emphasize the operations time frame 9 Loss of load probability A planning concept Based on random outage of generators, what is the probability that the available generators will be insufficient to meet the anticipated load Measured in frequency of expected outages EDNS extends the concept to consider energy not served 10 5

6 The n-1 security criterion The outage of any single piece of equipment shall not result in an uncontrolled loss of load A pretty universal and fundamental way of operating the system Cost in not in the equation Sometimes n-2 and n-3 criteria are used 11 Applying the n-1 criterion Outage of any generator does not cause overloads or other problems n-1 criterion used to establish reserve requirements Outage of any line or transformer should not cause any other overloads If a potential problem exists, system is redispatched for security reasons (either via CED, via TLR, or via prices) 12 6

7 Why do systems fail? Cascading overloads A simple line or transformer outage is not enough except in radial situations Most distribution systems are radial Loss of system stability Transient or dynamic Voltage collapse Insufficiency of generation 13 Reserves The loss of any generator shall not cause an uncontrolled loss of load The area control error (ACE) must be brought under control NERC has well-defined rules for this At present the rules are voluntary 14 7

8 What is the ACE? To facilitate control, the power system is divided into control areas All exports and imports are monitored Every area balances its energy to attain the desired exports or imports It also contributes to frequency control The ACE is the deviation between the intended frequency+exports and the actual values 15 More on reserves Reserves may have to be locational They must consider time of response Reserves are often classified this way Sustainability attribute of reserves has been underconsidered to date The cost of procuring reserves can be quite important Reactive reserves are important 16 8

9 Reserve margins How far are we from a failure under normal conditions And how about under contingency conditions A contingency is the loss of a component You must also ask in what direction How far is the nearest gas station is different from how far is the next gas station Often the direction is total system load 17 Choosing reserve margins Depends on largest credible event Sometimes the probability of a triggered event is factored in Play it more conservative during bad weather Margins often expressed in terms of size of largest generator or loss of biggest import 18 9

10 Temporal classification Spinning reserves Fast-responding, usually instantaneously Supplemental reserves You can bring resources on-line quickly Backup reserves They can be brought on line after some time 19 Reliability in a market context Reliability event occurs when demand exceeds supply The supply and demand curves do not intersect! 10

11 What is reliability anyway? The CAISO just disconnected you as a result of insufficient reserves This is an example of a reliability event You had vountarily signed up for an interruptible program and got cut off This is not a reliability event 21 Economics 101 Consumer surplus Demand function (value of electricity to customers) Total consumer surplus (area) Equilibrium Quantity 11

12 Economics 101 Production function (cost of electricity to producers) Producer surplus Equilibrium Total producer surplus (area) Quantity Economics 102 Total consumer surplus (area) Total producer surplus (area) Equilibrium Quantity 12

13 Some realities Demand function is closer to vertical Supply function tends to have steps Supply function does not extend to infinity 25 A market problem No Equilibrium? Quantity 13

14 A market failure Inelastic demand No Equilibrium Quantity Reliability & market failure Market failure Reliability event Reliability event Market failure? Certain reliability events are not the result of market failure There must have been a market in the first place 28 14

15 Assumptions Exactly two technologies Each technology has a known price No market power Inelastic demand 29 Deterministic Demand and Supply, low demand case Security Margin Available supply Demand (inelastic) Maximum available power Quantity (power) Clearing price 15

16 Deterministic Demand and Supply, high demand case Clearing price Available supply Demand (inelastic) Maximum available power Quantity (power) Unfeasible case, no demand elasticity No intersection 16

17 The effect of demand elasticity Demand elasticity makes case feasible Greater elasticity does not help much more (price is still high) Interruptible demand Interruptible demand also helps 17

18 Probabilistic Demand, high demand case Probability of low prices Outage probability The piece-wise nature of the supply curve Generator 1 Generator 2 Generator 3 Generator 4 Generator 5 Generator 6 18

19 The effect of a generator outage Outaged generator Old supply limit New supply limit Effect of demand uncertainty and generator outage Probability p2 Probability p1 n-1 secure insecure Outage probability is p1*p2 19

20 System A Low price Secure System B High price n-1 insecure Generator 1A Generator 2A Generator 3A Generator 4A Generator 5A Generator 6A Generator 1B Generator 2B Generator 3B Generator 4B Generator 5B System A Low price n-1 secure System B High price n-1 secure 20

21 System A Low price n-1 secure Flow System B Low price n-1 secure Temptation: construct a composite supply curve unnecessary Low price n-1 secure + 21

22 Situation with line transmission limits System A Low price n-1 secure Max flow Flow Outaged generator System B Low price n-1 insecure Normal conditions Unable to clear Max flow Use of distributed reserves System A Low price n-1 secure Max flow Flow System B Low price n-1 secure 22

23 Reality Many flowgates Networked sysyem Demand can be elastic Time delays important Generators have fixed (investment) costs and restrictions Load is uncertain Transmission outages exacerbate problems If one firm dominates a technology, market power occurs (next) If one firm dominates a location, market power results 45 The effect of congestion Total consumer surplus (area) Equilibrium point Equilibrium region Total producer surplus (area) Congestion level Surplus net loss Quantity 23

24 Who gets what Producer surplus loss Producer surplus gain Congestion level Quantity Who gets what, part II Only under monopsony or regulated conditions Consumer surplus gain Congestion level Quantity 24

25 The incentive to congest Producer surplus gain Gain: p*c Loss: C*p Producer surplus loss p C Congestion level Quantity Equilibrium with congestion Gain: p*c Loss: C*p p C Equilibrium when: p*c = C*p, or p/ C=p/C Quantity 25

26 The effect of congestion Congestion creates gaming opportunities Producers have an incentive to congest (Up to a point) The only unambiguous way to characterize the effect of congestion is to look at net surplus loss Translated: when we compute congestion costs, we do not care who incurs them Additional remarks Two-technology suppliers can lead to higher than marginal prices as the knee of the supply curve is approached Larger number of suppliers reduces this effect Market power studies should consider investment recovery issues Transmission congestion makes matters worse!! 52 26

27 Features of the example Only two areas (one flowgate) Radial Demand is inelastic Time delays are not an issue Generators have no startup/shutdown costs or restrictions or minimum power levels 53 Observations Demand elasticity is important Locational aspects of reserves matter LMP for reserves Ramping rates matter In deregulated markets only units explicitly committed to reserves are available In regulated markets and in PJM all units are Reliability requires that we increase supply Standby charges tend to reduce supply (Tim Mount) 54 27

28 Reliability and price spikes* What has happened in California? caps have come down Average prices have increased volatility has decreased There have been involuntary curtailments (*) Some of this material comes from Tim Mount at Cornell 55 $/MWh PJM daily average on-peak spot price and max load MW Maxload /97 6/97 8/97 10/97 12/97 2/98 4/98 6/98 8/98 10/98 12/98 2/99 4/99 6/99 8/99 10/99 12/99 2/00 4/00 date

29 Assorted PJM offer curves PJM Offer Curves at 5pm from April to August (last Tuesday) 1200 Offer April (4/27/99) : $29.4/MWh 28.2GW/h Offer May (5/25/99) : $25.9/MWh 30.3GW/h Offer June (6/29/99) : $59.5/MWh 48.1GW Offer July (7/27/99) : $935.0/MWh 49.2GW Offer August (8/24/99) : $33.7/MWh 38.5GW

30 Observations spikes have developed not so much under high load conditions as under tight reserve conditions For suppliers that own more than one technology, there are strong incentives to withhold capacity There is a strong connection between reserves and reliability (and market power) 59 Market Power? The ability to raise prices significantly above the efficient economic equilibrium Disclaimer: the slides that follow are not really a market power study but rather they represent a simplified illustration of how higher prices could result as a result of market concentration. 30

31 Market Power: Assumptions There are exactly two technologies Each technology has a fixed marginal price availability of the expensive technology Limited availability of the cheap technology Cheap technology has fixed costs (investments) to recover Demand is inelastic All suppliers but a schedule all their cheap power a owns P MW in n 1 equal-sized generators Supplier a can withhold one or more generators Bidding above marginal cost is not allowed, withholding is The piece-wise nature of the supply curve revisited Other suppliers Supplier a generator 2 Demand Supplier a generator 1 If generators bid marginal price, the generators surplus is zero Clearing price 31

32 Red generator decides to withhold one generator Clearing price Surplus for blue supplier Surplus for red supplier Withheld generator Red supplier now has large surplus Of course blue supplier has even LARGER surplus! If margins are increased Question: and how are the expensive technology units supposed to recover their investment if they always clear at their marginal cost? Answer: you may end up with less capacity than you thought Raising prices would require collusion Now it is not possible for red supplier to withhold and gain Clearing price 32

33 If demand is uncertain Probability p that withholding will result in surplus π 2 P 1 price π 1 Quantity (power) The expected surplus gain is: p*(π 2 -π 1 )*P 1 Since π 1 is cheap unit s marginal cost, there is no expected surplus loss Additional observations If the margin to the knee is P m, any supplier with a total ownership above P m may profit from withholding If more than one supplier meets this conditions, chances are that someone will withhold 66 33

34 Effect of granularity Surplus is P*(π 2 -π 1 ) for demand above this level With only one generator, it is impossible to withhold and benefit P For two generators, surplus is P*(π 2 -π 1 )/2 for demand above this level Effect of granularity, three generator case Surplus is P*(π 2 -π 1 )/3 for demand above this level Surplus is 2P*(π 2 -π 1 )/3 for demand above this level 34

35 Effect of granularity With n=1, there is no surplus Surplus Surplus with n=2 Surplus with n=3 Surplus with n=4 Demand level Surplus with n Observations and assumptions For worst case effect, assume n= Assume withholding will occur Withholding softens the supply curve High cost periods needed for investment recovery Demand is probabilistic Suggestion: market power occurs if expected surplus far exceeds investment recovery This is also a signal for system expansion 35

36 Effect of number of suppliers on supply curve One supplier 2 suppliers 3 suppliers 10 suppliers Demand Effect of demand uncertainty on investment recovery Period during which investment recovery can take place Withholding increases the period during which surplus accrues but reduces the amount that accrues Demand 36

37 The effect of demand uncertainty on investment recovery Period during which investment recovery can take place Demand Numerical studies Demand is 60/70/80/90/95% of knee σ for demand varies from 0 to 20% Demand probability function is normal Supplier has equal size units available There are 3/6/10/15/ suppliers We illustrate the investments that can be recovered for each of the case combinations above according to our earlier withholding assumptions 74 37

38 Investment recovery without market power ( suppliers) 250 Thousands per year per MW % Demand level as a percentage of available capacity 95% 90% 80% Variance of demand (per unit) Investment recovery (thousands per MW-year) % 70% 80% 90% 95% suppliers, demand level as a parameter Even for high demand levels, some demand variance is essential for cost recovery Demand Variance (percent) 38

39 suppliers, demand level as a parameter Investment recovery (thousands per MW-year) For high enough demand levels cost recovery is possible even without demand variance 60% 70% 80% 90% 95% Demand Variance (percent) suppliers, demand level as a parameter Investment recovery (thousands per MW-year) For high demand levels demand variance can become irrelevant 60% 70% 80% 90% 95% Demand Variance (percent) 39

40 400 6 suppliers, demand level as a parameter Investment recovery (thousands per MW-year) For low demand levels it is very difficult to recover investments 60% 70% 80% 90% 95% Demand Variance (percent) suppliers, demand level as a parameter Investment recovery (thousands per MW-year) % 70% 80% 90% 95% For high demand levels, high variance can even be slightly detrimental to profits Demand Variance (percent) 40

41 450 3 suppliers, demand level as a parameter Investment recovery (thousands per MW-year) % 70% 80% 90% 95% With three or less suppliers, it becomes feasible at high variances to recover investments by withholding at low demand Demand Variance (percent) Investment recovery (thousands per MW-year) Demand level 60%, number of suppliers as a parameter suppliers 15 suppliers 10 suppliers 6 suppliers 4 suppliers 3 suppliers At low demand and low variance it is impossible to recover investments Demand Variance (percent) 41

42 Fixed cost recovery (thousands per MW-year) Demand level 70%, number of suppliers as a parameter suppliers 15 suppliers 10 suppliers 6 suppliers 4 suppliers 3 suppliers At higher demand with 3 suppliers it is possible to recover costs at low variance Demand Variance (percent) 400 Demand level 90%, number of suppliers as a parameter Fixed cost recovery (thousands per MW-year) As demand increases, withholding becomes profitable even when there are many suppliers suppliers 15 suppliers 10 suppliers 6 suppliers 4 suppliers 3 suppliers Demand Variance (percent) 42

43 450 Demand level 95%, number of suppliers as a parameter Fixed cost recovery (thousands per MW-year) Only in the case of infinite suppliers is it suppliers 15 suppliers 10 suppliers 50 6 suppliers 4 suppliers 3 suppliers impossible to recover costs Demand Variance (percent) Comments on numerical results The number of suppliers has a strong influence on investment recovery Below a certain number of suppliers, investment recovery by withholding becomes easier There are demand thresholds beyond which there is a jump in the ability to recover investments All studies have assumed that supplier adjusts withholding after learning the demand Demand variance affects reliability It also influences the ability to recover investments 43

44 Final remarks Reliability not decoupled from economics Tight reliability precursor to price spikes The structure of two-technology suppliers can lead to higher prices as the knee of the supply curve is approached More suppliers reduce this effect Market power studies should consider investment recovery, locational effects Congestion, loop flows, voltage, frequency are also important 87 Reliability spikes Reserves 44