Convex Hull Pricing Extended LMP (“ELMP”)

Stakeholder WorkshopMay 3, 2010

2

Topics for Today’s Workshop

• Introduction• Energy Prices and Uplift• ELMP Methodology • Simple Examples of Determination of LMP and

ELMP• Impacts of ELMP• Benefits of ELMP

Introduction

4

Convex Hull Pricing• Convex hull pricing (CHP) is a system under

development in the Midwest ISO to enhance the calculation of LMPs so as to have prices reflect costs of commitment decisions as well as dispatch decisions.

– The method would include gas turbines and demand response in the price determination.

– The enhancements also would provide other improvements, such as minimizing uplifts.

• A previous Webinar explained the economic foundations of CHP (October 30, 2009).

• The purpose of the present discussion is to provide additional insight into the CHP pricing method.

5

New Name for CHP: ELMP

• The name, “Convex Hull Pricing” (CHP), refers to a mathematical technique used to determine LMPs that incorporate costs of commitment decisions.

• This presentation introduces a new name to emphasize the central tie to LMP:

ELMP: Extended LMP

6

Most Market Elements Would Not Change

• ELMP would not change the most fundamental elements of electricity markets in the Midwest ISO, including :

– Bid-based day-ahead market using security constrained unit commitment and economic dispatch (SCUC and SCED),

– SCUC-based reliability commitment process to ensure that sufficient capacity will be on-line to meet forecast real-time requirements,

– Bid-based real-time security constrained economic dispatch,– Locational prices for day-ahead and real-time settlements,– Co-optimization of day-ahead and real-time markets for energy and

ancillary services,– Bidding rules, schedules and portals for generation, load, ancillary

services and transmission service,– ARR and FTR rules and markets.

7

ELMP Modifies Calculation of Prices

• ELMP would modify the methodology used to calculate the settlement prices for energy (LMP) and ancillary services.– ELMPs would be calculated after dispatch, taking as

given the least-cost security-constrained dispatch determined by the Midwest ISO and all of the bids and offers provided into the dispatch.

– ELMPs would be calculated using a methodology that takes into account costs of commitment decisions, while also maintaining differences in energy prices between locations that reflect congestion differences between locations in that dispatch.

– Equivalently, we can view ELMPs as being calculated so as to minimize the uplift paid for the dispatch.

8

• ELMP would be an improvement in the way energy and ancillary services prices are calculated, while staying very close to the fundamental principles guiding the way the Midwest ISO Market operates today. – For a given set of bids and offers, the unit

commitment and dispatch would be exactly the same under ELMP as under today’s LMP rules.

– Locational differences in prices would be similar to those under LMP.

ELMP Modifies Calculation of Prices

9

Why Consider ELMP?• ELMP would provide an analytically grounded and

internally consistent methodology for achieving a number of objectives:

– Minimizing uplift, – Allowing gas turbines and other units operating at their

economic minimum or maximum to affect the energy price when appropriate,

– Allowing interruptible load, demand resources and emergency demand response to affect prices when appropriate,

– Reducing the impact of deviations from an unit optimal commitment on day-ahead prices,

– Ameliorating real-time price spikes that result from forecasting errors and commitment errors.

• These and other benefits of ELMP will be discussed following explanation of the ELMP methodology.

Energy Prices and Uplift

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• ELMP is a further step in enhancing energy and ancillary services pricing to reflect the physical reality of how costs are incurred in generating electricity.

• Electricity markets will function most efficiently, and with the least ad hoc intervention, when structured to provide prices that are consistent with the underlying cost structure.

– In order to address this physical reality, generators in the Midwest ISO are permitted to make offers for start-up costs, minimum generation (no load) costs, ramp rates (up and down), and minimum and maximum run times, among other things.

– LMP itself originated in order to reflect the physical reality that congestion costs cause locational differences in prices.

• LMP incorporates the costs of dispatch in the prices. • ELMP incorporates the costs of commitment as well as dispatch in the prices.

(This explanation of ELMP adopts a generation perspective for simplicity, but generalizes to load.)

Pricing to Reflect Engineering and Economics

12

• The motivation for ELMP begins with the physical reality that bid-based cost curves for individual generators, and for the RTO as a whole, generally have steps, and marginal cost curves may slope down over some ranges of output.– These stepped cost curves, which are downward

sloping over some range of output, are called “non-convex”.

Bid-Cost Curves Not Upward-Sloping

13

Bid-Cost Curves Not Upward-Sloping

• Suppose that a generator with a 40 MW minimum generation level has the following costs:– $300 in no-load costs– Marginal costs as follows:

• $50/MWh to operate at up to 100 MW• $55/MWh to operate between 100 MW and 120 MW• $65/MWh to operate between 120 MW and 140 MW

• The following slide shows the marginal and average costs for this generator.

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Bid-Cost Curves Not Upward-Sloping

$48

$50

$52

$54

$56

$58

$60

$62

$64

$66

0 20 40 60 80 100 120 140

Generator Output (MW)

Cos

t ($/

MW

h)

Minimum Average Cost = $53/MWh

Average Cost at Minimum Output

= $57.50/MWhAverage Cost at

Maximum Output = $55/MWh

Average Cost

Marginal Cost

$48

$50

$52

$54

$56

$58

$60

$62

$64

$66

0 20 40 60 80 100 120 140

Generator Output (MW)

Cos

t ($/

MW

h)

Minimum Average Cost = $53/MWh

Average Cost at Minimum Output

= $57.50/MWhAverage Cost at

Maximum Output = $55/MWh

Average Cost

Marginal Cost

15

• Because of the non-convex shape of the bid-based generator cost curves, all electricity markets, including those using LMP, today require:– Rules, in addition to the fundamental principle of

marginal cost, to determine energy market prices.– Uplift to compensate generators if market prices do

not cover their bid/offer costs for their scheduled level of production. These are also called make-whole payments.

Implications for Energy Prices and Uplift

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• Rules are needed to determine energy market prices because with non-convex cost curves:– Marginal costs are not defined at all levels of output.– Even when marginal costs are defined and used to

set market prices, they may not fully compensate generators for their scheduled level of output.

• The situation in electricity markets is different than in textbook economics, where market clearing prices are equal to marginal costs when cost curves are steadily upward-sloping.

Marginal Costs and Energy Market Prices

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• In the previous example of the non-convex bid-based cost curve for a generator:

Marginal Costs and Energy Market Prices

$48

$50

$52

$54

$56

$58

$60

$62

$64

$66

40 50 60 70 80 90 100 110 120 130 140

Generator Output (MW)

Cos

t ($/

MW

h)

Marginal CostAverage Cost

Minimum Average Cost = $53/MWh

Average Cost at Minimum Output

= $57.50/MWh Average Cost at Maximum

Output = $55/MWh

$48

$50

$52

$54

$56

$58

$60

$62

$64

$66

40 50 60 70 80 90 100 110 120 130 140

Generator Output (MW)

Cos

t ($/

MW

h)

Marginal CostAverage Cost

Minimum Average Cost = $53/MWh

Average Cost at Minimum Output

= $57.50/MWh Average Cost at Maximum

Output = $55/MWh

• The marginal cost is not defined at 100 or 120 MWh.• If the energy price were set equal to the marginal cost from 40 MWh to 100 MWh, generators would be paid less than their average cost, so that they would not be covering their total offer costs for their scheduled levels of output.

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• A variety of decision rules are used by the different RTOs to determine energy market prices, given the necessity of supplementing the principle of pure marginal cost pricing.– In the Midwest ISO, LMP is defined as the

incremental offer cost in the dispatch of delivering the next unit of energy at each location.

– In the NYISO, the pricing algorithm assumes (among other things) that block-loaded GTs can be flexibly dispatched between 0 MW and EconMax.

Rules to Determine Energy Market Prices

19

• The rules for setting the market price are a key factor in driving the amount of uplift in an electricity market.

– Uplift is required to compensate generators for the gap between the market price and the average cost of energy for the generator’s scheduled level of output.

– Uplift is paid to ensure that generators produce the schedule determined in the least bid-cost dispatch.

• ELMP would take into consideration this interaction between market prices and uplift in the determination of market prices.

Uplift Required to Supplement Market Price

20

Uplift Payments if LMP is $50/MWh

$48

$50

$52

$54

$56

$58

$60

$62

$64

$66

0 20 40 60 80 100 120 140

Generator Output (MW)

Cos

t ($/

MW

h)

Uplift Payment Required at 99 MW of Output

Uplift Payment Required at 40 MW of Output

Average Cost

Marginal Cost

$48

$50

$52

$54

$56

$58

$60

$62

$64

$66

0 20 40 60 80 100 120 140

Generator Output (MW)

Cos

t ($/

MW

h)

Uplift Payment Required at 99 MW of Output

Uplift Payment Required at 40 MW of Output

Average Cost

Marginal Cost

21

Uplift Payments if LMP > $50/MWh for 100 MWh of Output

$48

$50

$52

$54

$56

$58

$60

$62

$64

$66

0 20 40 60 80 100 120 140

Generator Output (MW)

Cos

t ($/

MW

h)

Uplift Payment Required

$52.50/MWh is Midpoint of Step in Supply Curve

Average Cost

Marginal Cost

$48

$50

$52

$54

$56

$58

$60

$62

$64

$66

0 20 40 60 80 100 120 140

Generator Output (MW)

Cos

t ($/

MW

h)

Uplift Payment Required

$52.50/MWh is Midpoint of Step in Supply Curve

Average Cost

Marginal Cost

22

• If generators were not paid at least their average bid cost for their scheduled level of output they would:– Not produce as scheduled or,– Modify their offers, to ensure that they are fully

compensated. – Either of these actions would lead to something

other than the least bid-cost levels of production.

Uplift Provides Incentive to Follow Dispatch

23

LMPs and Uplift Today

• The calculation of LMPs today does not take into account uplift; uplift is a residual that is determined from the LMPs.– In the Midwest ISO, the LMPs are taken directly from the

dispatch, where they are known as “shadow prices”.– Because the pricing model is based only on committed

units and does not take into account the effects of startup costs, no-load costs, and costs of operating any resources dispatched at minimum, LMPs today do not reflect the full bid-based cost of producing power to serve load.

24

Summary: Energy Prices and Uplift

• ELMP is a principled methodology to extend LMPs in order to include the effects of startup costs, no-load costs and costs of operating any resources dispatched at minimum, thereby minimizing uplift.

– LMPs today are called “the” market prices of electricity, but even when LMPs can be set equal to marginal costs, they are not “market clearing” for energy markets, i.e., they will not lead generators to produce the least bid cost dispatch unless they are also paid uplift.

– Because of the non-convexity of bid-based cost curves for electricity, in many dispatches there is no set of internally consistent set of locational prices that are also market clearing prices.

ELMP Methodology

26

ELMPs are Locational• ELMPs would be calculated after the dispatch

period, taking as given the least-cost security-constrained dispatch so as to:– Minimize the uplift paid for the dispatch, and also– Maintain differences in energy prices between

locations that reflect congestion differences between locations in the dispatch.

• The ELMP cannot be adjusted to reduce uplift at one location without changing the ELMPs at all electrically similar locations, i.e., locations that impact the same dispatch constraints.

27

ELMPs Are Based on All Bids and Offers

• The ELMP determination takes into account all bids and offers made into the unit commitment and dispatch, including those of generators or loads that are not committed or dispatched.

• There are several reasons for this approach:– Provides prices that reflect costs if resources must be committed to

manage a constraint but the constraint is no longer binding in the dispatch after the resources have been committed.

– Provides prices that take into account the dispatch of units, such as gas turbines, that are operating at their economic minimum or maximum, and also interruptible load, demand resources and emergency demand response.

– Eliminates the impact of sub-optimal unit commitment, whether due to forecast error, operator error or software limitations, on the ELMPs.

28

Several Types of Uplift Minimized• The ELMP determination takes into account the

uplift required to give generators and loads incentives to follow the Midwest ISO’s schedule.– Uplifts cover operating costs of following the dispatch schedule

that are not covered by the price paid.• Uplift would be paid to compensate generators for the gap between the

ELMP and the average offer cost of energy for the generator’s scheduled level of output, just as under LMP.

• Price-sensitive loads would be paid for ELMP charges in excess of their bids for their dispatch schedules.

– Uplifts also cover opportunity costs if a schedule is below the optimal level given the price.

• Generators would receive “constrained down” payments if the ELMP exceeds their offer to provide output that is not scheduled in the least-cost dispatch.

• Price-sensitive loads would be paid for load that is not scheduled, although it has a bid that exceeds the ELMP.

29

Several Types of Uplift Minimized

• In addition, under ELMP uplift payments may be needed to maintain the revenue adequacy of FTRs.– This uplift could be assigned to owners of FTRs as is

currently done when FTRs are not revenue adequate.• All sources of uplift are included in the uplift

minimization under ELMP.

30

Constrained Down Payments Under ELMP

• Constrained down payments are similar to the constrained up payments in today’s market; they ensure that generators produce the schedule determined in the least-cost dispatch.

• If generators were not paid their opportunity costs when the ELMP exceeded their offer for unscheduled output, they would:– Produce more than scheduled, i.e., “follow the price”, or– Modify their offers in order to be scheduled.– Either of these actions would lead to something other than the

least bid-cost levels of production.

31

Constrained Down Payments Under ELMP

• One way to understand the need for constrained down payments under ELMP is to follow the logic of what happens when units with fixed minimum generation levels affect the prices.– When units with fixed minimum generation levels are part of the least

cost dispatch, the pricing calculation will attempt to minimize the uplift associated with these units, as well as all other uplift.

– When a GT is committed with a fixed minimum generation level, it may require a reduction in the dispatch of a more flexible unit, with a lower incremental offer cost.

– Under ELMP, the price at this lower-cost unit’s location may be higher than the incremental offer of the lower cost unit.

– The lower cost unit must be paid constrained down payments for its unscheduled output; the alternative is a system of penalties to enforce the least cost dispatch.

32

Uplift for FTRs Under ELMP• Uplift also may occur under ELMP if congestion revenues are

inadequate to fund FTRs.– This can occur even if the FTRs satisfy the simultaneous feasibility test under current

conditions (loopflows, topology and limits).

• The result may occur when resources must be committed to manage transmission constraints.

– Resources may be committed to avoid violation of transmission constraints, but once the resources are committed, the dispatch flows over these constraints may be less than the constraint limits.

– ELMPs, unlike LMPs, reflect the locational costs of committing the resources and will place non-zero shadow prices on the constraints even though they are not binding in the actual dispatch after the resources are committed.

– Revenue inadequacy can occur in the FTRs because the ELMPs do not take the unit commitment as given, so that the dispatch that is consistent with the ELMPs may not be physically feasible. The dispatch that would occur based on the ELMPs might violate one of the lumpy constraints that the ELMPs smooth over.

• There are alternative ways to handle this uplift:– It could be collected from market participants like other uplifts.– Alternatively, this portion of uplift could be treated as FTR underfunding and collected from

those owning FTRs.

33

Simple Three-Bus Example of ELMP

• A simple three bus example illustrates:– The formula used to calculate ELMPs is the same as for LMP. In

a given hour, the formula (leaving out losses) is:

– Under ELMP, the reference bus price and constraint shadow prices are calculated after the dispatch.

– ELMP minimizes uplift while preserving locational differences between prices that stem from differences in shift factors for generation or load across transmission constraints.

jELMP (bus i) = Ref Price -

(shift factor bus i on constraint j) * (shadow price

of constraint j){ }Σ

34

Simple Three-Bus Example of ELMP

A

CB

Gen C1Gen C2

Gen A1Gen A2

Gen B1

All Lines 200 MW0 ResistanceEqual Reactance

550 MW Load

• In the example, the binding constraint will occur on line A-C in the three-bus model shown below.

• The reference bus is at bus C.– Generation at bus A to load at the reference bus has a shift factor of

0.67 on line A-C.– Generation at bus B to load at the reference bus has a shift factor of

0.33 on line A-C.

35

Simple Three-Bus Example of ELMP • Generators A1, A2, C1 and C2 are committed and dispatched to

serve a 550 MW load at bus C.• The 200 MW constraint on line A-C is binding because relatively

cheap generation is available at bus A.

A

CBGen C1Gen C2

Gen A1Gen A2

Gen B1

All Lines 200 MW0 ResistanceEqual Reactance

550 MW Load

100 MWh

Generator

No-Load Offer($/hr.)

Incremental Offer

($/MWh)Capacity

(MW)

Least-Cost Commitment and Dispatch

(MW)A1 320 35 160 160A2 320 37 160 140B1 640 39 160 0C1 640 43 160 160C2 640 45 160 90Total 550

36

Simple Three-Bus Example of ELMP • The ELMPs for the dispatch can be calculated from the ELMP price

at the reference bus and the ELMP shadow prices for the binding constraint occurring on line A-C.

• The ELMP reference bus price and shadow prices are determined from application of the ELMP software to the unit commitment and dispatch solution.

jELMP (bus i) = Ref Price -

(shift factor bus i on constraint j) * (shadow price

of constraint j){ }Σ

Bus

Shift Factor on

A-C Constraint

ELMP Shadow Price for A-C Constraint($/MWh)

ELMP Reference Bus Price($/MWh)

ELMP($/MWh)

A 0.67 15 49 39B 0.33 15 49 44C (ref.) 0.00 15 49 49

37

Simple Three-Bus Example of ELMP • With these ELMPs, the uplift for 550 MW of load is $480.

– Generators A2 and C2 receive uplift to cover their total offer cost for their scheduled output.

– Generator B1 receives $160, which is its lost margin on unscheduled capacity.

Generator

No-Load Offer($/hr.)

Incremental Offer

($/MWh)Capacity

(MW)

Least-Cost Commitment and Dispatch

(MW)ELMP

($/MWh)

ELMP Revenue

($/hr.)Total Cost

($/hr.)

Uplift for Scheduled

Output($/hr.)

Uplift for Unscheduled

Capacity($/hr.)

Total Uplift($/hr.)

A1 320 35 160 160 39 6,240 5,920 0 0 0A2 320 37 160 140 39 5,460 5,500 40 0 40B1 640 39 160 0 44 0 0 0 160 160C1 640 43 160 160 49 7,840 7,520 0 0 0C2 640 45 160 90 49 4,410 4,690 280 0 280Total 550 480

38

Simple Three-Bus Example of ELMP • In order to illustrate the interaction between uplift minimization and

the determination of ELMPs, suppose that in order to reduce the uplift paid to generator B1 the ELMP at bus B were decreased from $44/MWh to $43/MWh.

• The price at bus B cannot be changed without also changing prices at other buses that impact the same constraints as generation or load at bus B.

• Holding constant the reference bus price, a price of $43/MWh at bus B implies a shadow price of $18/MWh on the A-C line and a price of $37 at bus A.

Bus

Shift Factor on

A-C Constraint

ELMP Shadow Price for A-C Constraint($/MWh)

ELMP Reference Bus Price($/MWh)

ELMP($/MWh)

A 0.67 18 49 37B 0.33 18 49 43C (ref.) 0.00 18 49 49

39

Simple Three-Bus Example of ELMP • The overall effect of changing the ELMP at bus B to $43 is to

increase uplift to $600.• Reducing the ELMP to $43 at bus B reduces the uplift paid to

generator B1, but the related decrease in the price at bus A increases the uplift paid to generator A2.

Generator

No-Load Offer($/hr.)

Incremental Offer

($/MWh)Capacity

(MW)

Least-Cost Commitment and Dispatch

(MW)ELMP

($/MWh)

ELMP Revenue

($/hr.)Total Cost

($/hr.)

Uplift for Scheduled

Output($/hr.)

Uplift for Unscheduled

Capacity($/hr.)

Total Uplift($/hr.)

A1 320 35 160 160 37 5,920 5,920 0 0 0A2 320 37 160 140 37 5,180 5,500 320 0 320B1 640 39 160 0 43 0 0 0 0 0C1 640 43 160 160 49 7,840 7,520 0 0 0C2 640 45 160 90 49 4,410 4,690 280 0 280Total 550 600

40

Solution Methodologies for ELMPs• Elements of the ELMP methodology have been developed

under a number of names: – Brendan Ring (University of Canterbury, 1995): best-compromise

pricing,– Bill Hogan (Harvard University, 2003): uplift-minimizing pricing,– Paul Gribik (Midwest ISO, 2007): convex hull pricing.

• Recent work has shown that uplift minimizing prices are the same as those that result from a solution methodology called the convex hull approximation. (See “Market Clearing Electricity Prices and Energy Uplift”, Gribik, Hogan and Pope, December 31, 2007).– This means that we can think of the method intuitively as uplift

minimization, although the convex hull approximation is used for the current software implementation.

– The work has shown that uplift is an indication of how close the resulting prices come to having profit (or benefit) maximizing participants clear the market.

41

Calculating the ELMP• ELMPs are determined from a cost function that

approximates the actual, non-convex cost function as closely as possible, while:– Removing all of the non-convexities, i.e., steps or places where

the marginal cost is non-increasing.– Remaining below, but as close as possible to the actual cost

function at all levels of output.

• This approximated cost function is called the “convex hull” of the minimum cost supply curve as a function of demand. F(x)

Fc(·)

Simple Examples of Determination of LMP and ELMP

43

Example of ELMP vs. LMP• A simple example helps to explain the calculation of ELMPs and

some of the differences between ELMPs and LMPs. In the example: – There is one hour and a single node.– The market operator will commit generators based on their offers:

• Start-up/no-load costs,• Incremental energy costs,• Min and max output if committed.

– Demand is fixed and is not price sensitive.• This simplifies the example because we only need to minimize production

cost to find the efficient (socially optimal) outcome.– Locational marginal cost (LMP) is defined as the marginal cost of

serving demand at the node.• The cost of serving an infinitesimal increment (or decrement) of demand at

the node using the generation offers submitted.• Commitment cannot change in response to an infinitesimal change in

demand.

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Unit Offers• Three units offer into the market.

• Generators A and B can be flexibly dispatched after reaching their minimum dispatch level of 40 MW. (Generator B corresponds to the first 100 MW of the generator used in the examples in the preceding section.)

• Generator C must be block-loaded at 40 MW.

At Minimum Output

At Maximum Output

A 40 100 49 100 51.50 50.00 B 40 100 50 300 57.50 53.00 C 40 40 60 0 60.00 60.00

Generator

Average Cost ($/MWh)Minimum Output if Committed

(MW)

Maximum Output if Committed

(MW)

Energy Cost

($/MWh)

No-Load Cost($/hr)

45

Minimum Cost Increases with Demand• The minimum cost of meeting demand (i.e., bid-cost supply curve) is non-

convex; steps occur because of dispatch minimums and no-load costs.

$0

$2,000

$4,000

$6,000

$8,000

$10,000

$12,000

$14,000

40 60 80 100 120 140 160 180 200 220 240

Load (MW)

Tota

l Cos

t ($/

hr)

Generator B Dispatched

Generator C Dispatched

Generator A Dispatched

$0

$2,000

$4,000

$6,000

$8,000

$10,000

$12,000

$14,000

40 60 80 100 120 140 160 180 200 220 240

Load (MW)

Tota

l Cos

t ($/

hr)

Generator B Dispatched

Generator C Dispatched

Generator A Dispatched

46

LMP as Function of Demand• The LMP in this market is $49/MWh when load is less than 140 MW, since Generator A on the

margin, and $50/MWh when load exceeds 140 MW, since Generator B is on the margin.• LMP is not well defined at all levels of output (e.g., 140 MWh), and is only computable under the

assumption that the commitment is fixed.

$0

$10

$20

$30

$40

$50

$60

$70

40 60 80 100 120 140 160 180 200 220 240

Load (MW)

LMP

($/M

Wh)

Generator A Committed and Dispatched to Meet

Additional Load

Generators A and B

Committed; Gen. A

Dispatched to Meet Add’l

Load

Gens. A-C Committed;

Gen. B Dispatched

to Meet Add’l Load

Generators A and B Committed; Gen.

B Dispatched to Meet Additional

Load

$0

$10

$20

$30

$40

$50

$60

$70

40 60 80 100 120 140 160 180 200 220 240

Load (MW)

LMP

($/M

Wh)

Generator A Committed and Dispatched to Meet

Additional Load

Generators A and B

Committed; Gen. A

Dispatched to Meet Add’l

Load

Gens. A-C Committed;

Gen. B Dispatched

to Meet Add’l Load

Generators A and B Committed; Gen.

B Dispatched to Meet Additional

Load

47

Least-Cost Dispatch for 220 MW

• If demand is 220 MW, Generator B is the marginal unit and it sets LMP at $50/MWh.

• The least-cost commitment and dispatch is:– Generator A committed and dispatched at 100 MW,– Generator B committed and dispatched at 80 MW,– Generator C committed and dispatched at 40 MW.

48

Uplift and LMP for 250 MW• If price were set using LMP, the total uplift that must be

paid to suppliers is $700.– Generator B requires uplift to cover its no-load costs.– Generator C requires uplift to cover its energy costs, which are

not reflected in LMP because it is block-loaded.

GeneratorOutput(MWh)

Energy Cost

($/MWh)

No-Load Cost($/hr)

Total Cost($/hr)

LMP Revenue

($/hr)Uplift($/hr)

Net Margin($/hr)

A 100 49 100 5,000 5,000 - - B 80 50 300 4,300 4,000 300 - C 40 60 0 2,400 2,000 400 - Total 220 11,700 11,000 700 -

49

No Market Clearing Price• LMP is not a market clearing price.

– At a price of $50/MWh, profit maximizing Generator A would produce as much as 100 MW and Generators B and C would produce 0 MW.

– No more than 100 MW would be produced, falling 120 MW short of demand.

• There is no market clearing price.– At any price below $60/MWh, Generator C would be unwilling to

commit. This causes a shortfall of at least 20 MW.– At any price above $60/MWh, all three generators would commit and

operate at maximum output, causing an excess of at least 20 MW.

• Because market clearing prices do not exist, uplift provide incentives for participants to follow the least-cost dispatch.

50

Uplift when LMP is the Market Price• For load between 40 and140 MW, uplift covers Gen. A’s no-load costs.• For load between 100 and 140 MW uplift also covers Gen. B’s no-load costs and the difference

between the LMP and its energy costs to operate at its minimum.• For load above 140 MW uplift covers Gen. B’s no-load costs.• For load above 200 MW uplift also covers the difference between the LMP and Gen. C’s energy

costs.

$0

$100

$200

$300

$400

$500

$600

$700

$800

40 60 80 100 120 140 160 180 200 220 240

Load (MW)

Upl

ift P

aym

ents

($/h

r)

51

Calculating the ELMP• ELMPs are determined from an approximated cost function, called the

“convex hull” of the minimum bid-cost supply curve as a function of demand.• The convex hull function smoothes out the steps in this curve.

$0

$2,000

$4,000

$6,000

$8,000

$10,000

$12,000

$14,000

40 60 80 100 120 140 160 180 200 220 240

Load (MW)

Tota

l Cos

t ($/

hr)

CostConvex Hull

52

ELMP as a Function of Demand• ELMPs are the slope of the convex hull function at each level of demand, i.e., they

are the marginal cost of the next unit of energy, determined from the convex hull function.

• In the example, ELMPs rise as successively more expensive units are committed to meet demand.

$0

$10

$20

$30

$40

$50

$60

$70

40 60 80 100 120 140 160 180 200 220 240

Load (MW)

Pric

e ($

/MW

h)

LMPELMP

53

ELMP as a Function of Demand• The simplified example shows that ELMPs exceed LMPs

at some levels of demand.– There is truth to this result; ELMPs may exceed LMPs in some locations

and in some dispatches. – At the same time, the example greatly exaggerates what would be

expected to occur in an average hour. • Relevant examples necessarily address hours with non-trivial uplift. • Moreover, the small numbers in the example likely exaggerate the price

movement that would occur under ELMP; i.e., the non-convexities have greater steps in price than are likely in practice.

– ELMPs can also be below LMPs at some locations and times.• One possible reason is that ELMP would be based on all bids and offers, not

just those made by generators and loads that are scheduled in the dispatch.

• The example is intended as an illustration of ELMP, not as a prediction of the magnitude of price changes in the Midwest ISO under ELMP.

54

ELMPs for 220 MW

• In this example with a single location, ELMPs would be calculated so as to minimize the uplift paid for the dispatch.

• When demand is 220 MW, a price of $60/MWh comes as close to clearing the market as possible, i.e., would require the least uplift.

• At $60/MWh, profit maximizing generators would respond as follows:– 100 MW from Generator A;– 100 MW from Generator B;– Either 0 MW or 40 MW from Generator C.– The supply would differ from demand by ±20 MW.

• The ELMP price is closer to clearing the market than LMP.

55

ELMP and Uplift for 220 MW

• If the ELMP were $60/MWh, total uplift payments would be $200 for 220 MW. – Generator B would receive uplift payments to compensate it for

the $200 it loses because it was not dispatched to its maximum generation level.

GeneratorOutput(MWh)

Energy Cost

($/MWh)

No-Load Cost($/hr)

Total Cost($/hr)

ELMP Revenue

($/hr)Uplift($/hr)

Net Margin($/hr)

A 100 49 100 5,000 6,000 - 1,000 B 80 50 300 4,300 4,800 200 700 C 40 60 0 2,400 2,400 - - Total 220 11,700 13,200 200 1,700

ELMP Minimizes Uplift• If the ELMP were instead set at $61/MWh, uplift

payments would increase to $220.– Payments to Gen. B to compensate it for being dispatched

below its maximum generation level would rise.

GeneratorOutput(MWh)

Energy Cost

($/MWh)

No-Load Cost($/hr)

Total Cost($/hr)

ELMP Revenue

($/hr)Uplift($/hr)

Net Margin($/hr)

A 100 49 100 5,000 6,100 - 1,100 B 80 50 300 4,300 4,880 220 800 C 40 60 0 2,400 2,440 - 40 Total 220 11,700 13,420 220 1,940

56

ELMP Minimizes Uplift• Likewise, if the ELMP were set at $59/MWh, uplift

payments would increase to $220.– Payments to Gen. B to compensate it for being dispatched

below its maximum generation level would fall.– This reduction would be more than offset by payments to Gen.

C, to compensate it for the difference between ELMP and its energy costs.

GeneratorOutput(MWh)

Energy Cost

($/MWh)

No-Load Cost($/hr)

Total Cost($/hr)

ELMP Revenue

($/hr)Uplift($/hr)

Net Margin($/hr)

A 100 49 100 5,000 5,900 - 900 B 80 50 300 4,300 4,720 180 600 C 40 60 0 2,400 2,360 40 - Total 220 11,700 12,980 220 1,500

57

58

ELMP Uplift as Function of Demand• In the example, uplift rises each time a new unit is committed, but does not

rise dramatically at high levels of demand, because ELMPs are also increasing.

$0

$100

$200

$300

$400

$500

$600

$700

$800

40 60 80 100 120 140 160 180 200 220 240

Load (MW)

Upl

ift P

aym

ents

($/h

r)

Uplift Under LMPUplift Under ELMP

59

ELMP and LMP as a Function of Demand• Under ELMP, relatively more of the energy compensation paid by

load occurs through the energy market price than under LMP, and relatively less occurs through uplift.

0.0%

1.0%

2.0%

3.0%

4.0%

5.0%

6.0%

7.0%

8.0%

9.0%

40 60 80 100 120 140 160 180 200 220 240

Load (MW)

Upl

ift P

aym

ents

as

a Pe

rcen

tage

of T

otal

Pay

men

ts b

y Lo

ad

Under LMPUnder ELMP

60

ELMP and LMP as Function of Demand

$0

$2,000

$4,000

$6,000

$8,000

$10,000

$12,000

$14,000

$16,000

40 60 80 100 120 140 160 180 200 220 240

Load (MW)

Tota

l Cos

t ($/

hr)

Total Payment by Load Under LMPTotal Payment by Load Under ELMPNet Generator Margin Under LMPNet Generator Margin Under ELMP

61

ELMP and LMP as Function of Demand

• The results for this simplified example show that payments by load under ELMP exceed those under LMP.– It is also possible that payments by load may be lower under

ELMP; see example starting on slide 73.

• While this example shows a significant difference between LMP and ELMP, the Midwest ISO’s limited testing to date indicates that the differences are unlikely to be this large, especially in the day-ahead market.

• The differences shown here are due in part to the small scale of the example.

62

Applying to Midwest ISO Markets• In order to apply the ELMP methodology to the Midwest

ISO market, it has been extended (or is in the process of being extended) to address a variety of issues not discussed in the simple example:– Multiple time periods,– Losses,– Transmission constraints,– Ancillary services,– Resource characteristics and operating constraints.

• The losses and transmission constraints must be priced as well as energy and AS in each time period.

Impacts of ELMP

64

LMP Comparison• Stakeholders are naturally interested in comparing

ELMPs to the prices that would occur under LMP in the Midwest ISO for the same dispatch.– Comparison of ELMP and LMP has not yet been completed for a

system the size of the Midwest ISO in models that include transmission constraints.

• There are differences in the detail with which aspects of the system such as transmission are modeled in the unit commitment software and in the economic dispatch software. This can have an impact on LMPs, affecting the comparison to ELMPs.

– Testing of systems without transmission constraints shows that the LMP and ELMP for energy are likely to be close in the day-ahead market.

– Differences are expected to become greater in real-time as more gas turbines are committed and there are no virtual bids.

65

LMP Comparison Caveat• A full comparison of LMP and ELMP prices – if and when they are

available – presumes that LMPs, as they are currently calculated, are an appropriate benchmark.– LMPs are not defined in many circumstances and are not always

market-clearing prices.– Uplift is required to incent generators and loads to follow the dispatch

because LMPs understate the actual bid-based cost of the dispatch.– The Midwest ISO methodology tends to yield lower LMPs than those

that would be determined with the pricing methodologies of some other RTOs.

• Even if ELMP is not implemented, changes are likely to occur in the Midwest ISO pricing methodology.

66

Limitations of Midwest ISO Pricing Today

• Loads in the DA market (and deviations from DA schedules in RT) in some areas of the Midwest ISO have benefited from the current LMP pricing rules because the uplift paid to low marginal cost generation with high start-up and no-load costs at their location has been recovered from all load in the Midwest ISO in the DA market and all deviations from DA schedules in the RT market.

– The LMPs paid by these loads have been kept low by the low incremental cost offers of generators at their location.

– These low LMPs often do not cover the start-up costs, no-load costs, or incremental energy costs of units operating at minimum at that location.

• Similarly, some loads (deviations) have paid higher LMPs set by generators with higher incremental costs, and have also paid a share of the uplift for the start-up and no load costs of generators in other locations.

• ELMP would address these issues more comprehensively than current proposals to introduce a locational component into the uplift allocation.

Benefits of ELMP

68

Economic Properties of ELMPs• ELMPs come close to providing participants with

sufficient incentives to follow efficient and market clearing schedules when efficient and market-clearing prices do not exist.– If efficient and market clearing prices exist, they will be equal to

ELMPs.– When market clearing prices do not exist, ELMPs minimize uplift.

• ELMPs increase as demand increases which is how one expects prices to behave; LMPs may not.– LMPs can go down with increasing demand when optimal

commitment changes in response to increasing demand. (See example in Gribik, Hogan, Pope white paper “Market-Clearing Electricity Prices and Energy Uplift”).

69

Improvements in the Price Signal• ELMPs incorporate the costs of commitment

decisions as well as dispatch decisions, improving the price signal and providing the opportunity for increased efficiency. – Block loaded gas turbines, price-responsive demand

and other resources operating at their economic minimum or maximum affect the energy price.

– Start-up and no-load costs of all units are able to participate in setting price, not just block-loaded gas turbines and EDR.

– Prices will reflect congestion on constraints that bind in the unit commitment but not in the dispatch.

70

Decouples Unit Commitment and Pricing

• The ELMP methodology decouples pursuit of the least cost unit commitment from concern for possible impacts on energy market price levels and volatility.

• Today’s LMPs and uplift are both affected by the unit commitment decisions of the RTOs.

• LMPs will tend to be lower and uplift will tend to be higher if an extra unit is committed for reliability, and vice versa.

71

Reduction in Price Volatility

• By including uplift and the offer/bid costs of non-committed resources in the pricing determination, ELMP will tend to make day-ahead and real-time prices less volatile. – ELMP will address the pricing impacts of sub-optimal unit commitment.

This includes price spikes and swings that could occur if the load forecast differs from the actual load, or operator judgment leads to constraint violations and, consequently, high LMPs.

– Real-time prices will be less vulnerable to forecast errors.– The ELMP methodology determines prices taking into account all

resources that could have been used to better manage actual constraints.

72

Example of Reduction in Price Volatility• The following example shows how ELMP may alleviate

price spikes in situations where the RTO is not capacity short but has not committed available units either due to forecast errors or economics.

• In either case, a LMP price spike can occur because there is a shortage of capacity at the time of the dispatch.

• The ELMP pricing step would take into account available quick start resources and use them in pricing even if the RTO failed to commit them due to economics or forecast error.

73

Example of Reduction in Price Volatility• In the example there are four units and 12 fifteen minute

periods.– The shortage cost is $500/MWh.– Demand rises until period 11, when it peaks at 2,045 MW.

Quarter-Hour 1 2 3 4 5 6 7 8 9 10 11 12Demand (MW) 1,900 1,920 1,930 1,990 2,001 2,002 2,005 2,015 2,035 2,040 2,045 2,040

Generator

Minimum Output if Committed

(MW)

Maximum Output if Committed

(MW)

Start-Up Offer ($/hr.)

Incremental Offer

($/MWh)A 200 1,000 0 20B 200 1,000 0 25C 50 100 1,000 50D 50 100 1,000 55

74

Example of Reduction in Price Volatility• In the least cost commitment and dispatch, it is lower cost to delay the

commitment of Unit C until period 7, incurring a shortage charge in periods 5 and 6.

• In period 7 demand increases to the point where it is more cost effective to commit Unit C and back down Unit B to accommodate Unit C’s minimum production level.

• The increased incremental energy cost of committing Unit C early and backing down Unit B to accommodate Unit C in periods 5 and 6 would be $643.75 while the cost of not committing Unit C and incurring the resulting shortage in those two periods would be $375.

1 2 3 4 5 6 7 8 9 10 11 12A 1,000 1,000 1,000 1,000 1,000 1,000 1,000 1,000 1,000 1,000 1,000 1,000B 900 920 930 990 1,000 1,000 955 965 985 990 995 990C 0 0 0 0 0 0 50 50 50 50 50 50D 0 0 0 0 0 0 0 0 0 0 0 0Shortage 0 0 0 0 1 2 0 0 0 0 0 0

Output Level in Quarter-Hour (MW)Generator

75

Example of Reduction in Price Volatility• In the example, LMPs spike in periods 5 and 6, but

ELMPs do not.• ELMP takes into account that Unit C is available to be

committed in periods 5 and 6 and would be if demand were higher.

• Both generator profit and uplift are lower under ELMP in this example.– LMP profit: $487,125; ELMP profit: $133,362.50. – LMP uplift: $2,875; ELMP uplift: $1,637.50.

Quarter-Hour 1 2 3 4 5 6 7 8 9 10 11 12LMP ($/MWh) 25 25 25 25 500 500 25 25 25 25 25 25ELMP ($/MWh) 25 25 25 25 50 50 50 50 50 50 90 50

76

Example of Reduction in Price Volatility• Similar effects occur in real-time if the RTO

under-forecasts load or over-forecasts imports. • The RTO may not commit an available quick

start unit which would have been optimal to commit at the actual level of load, causing a shortage in the dispatch engine and a price spike.

• ELMP would take into account the available quick start resources and use them in pricing even if the RTO failed to commit them due to forecast error.

77

Example of Reduction in Price Volatility

• In the previous example, suppose that forecast demand differs from actual demand in periods 5 and 6.

• The RTO uses forecast demand to commit resources and actual demand to dispatch resources in real-time.

Quarter-Hour 1 2 3 4 5 6 7 8 9 10 11 12Forecast Demand (MW) 1,900 1,920 1,930 1,990 1,999 1,999 2,005 2,015 2,035 2,040 2,045 2,040Actual Demand (MW) 1,900 1,920 1,930 1,990 2,003 2,003 2,005 2,015 2,035 2,040 2,045 2,040

78

Example of Reduction in Price Volatility• In the optimal unit commitment based on the

forecast demand Unit C is off line in hours 5 and 6.

1 2 3 4 5 6 7 8 9 10 11 12

A On Line

On Line

On Line

On Line

On Line

On Line

On Line

On Line

On Line

On Line

On Line

On Line

B On Line

On Line

On Line

On Line

On Line

On Line

On Line

On Line

On Line

On Line

On Line

On Line

C Off Line

Off Line

Off Line

Off Line

Off Line

Off Line

On Line

On Line

On Line

On Line

On Line

On Line

D Off Line

Off Line

Off Line

Off Line

Off Line

Off Line

Off Line

Off Line

Off Line

Off Line

Off Line

Off Line

Status in Quarter-HourGenerator

79

Example of Reduction in Price Volatility• In the dispatch to serve actual load, there is a

shortage because actual load exceeds forecast load in periods 5 and 6.

1 2 3 4 5 6 7 8 9 10 11 12A 1,000 1,000 1,000 1,000 1,000 1,000 1,000 1,000 1,000 1,000 1,000 1,000B 900 920 930 990 1,000 1,000 955 965 985 990 995 990C 0 0 0 0 0 0 50 50 50 50 50 50D 0 0 0 0 0 0 0 0 0 0 0 0Shortage 0 0 0 0 3 3 0 0 0 0 0 0

Output Level in Quarter-Hour (MW)Generator

80

Example of Reduction in Price Volatility• The 0.2% error in the demand forecast at the

time of the unit commitment results in a price spike when there is actually sufficient capacity available.

• ELMP takes the availability of that capacity into account when setting prices, alleviating the price spike.

Quarter-Hour 1 2 3 4 5 6 7 8 9 10 11 12LMP ($/MWh) 25 25 25 25 500 500 25 25 25 25 25 25ELMP ($/MWh) 25 25 25 25 50 50 50 50 50 50 90 50

81

Reduction in Price Volatility• Results similar to those in the previous example

can also occur due to the impact of constraints other than the demand requirement. – Reserve requirements, zonal reserve requirements

and transmission constraints all can cause price spikes either because it is more cost effective to violate the requirement than commit a resource at the time or because of forecast errors.

– ELMP will take into account the availability of such resources and alleviate the price spike.

82

Long-Run Improvements in Unit Commitment

• The Midwest ISO expects that the application of ELMP pricing over time will reveal opportunities to improve the least cost unit commitment.

• Under ELMP it will be clear where and when the cost-minimizing solution to the convex hull differs from the SCUC solution.– Identify when and why forecast error is significant.– Explore reasons for operator error.– Investigate other data or modeling issues resulting in

deviations from the cost-minimizing solution.

83

FTRs Hedge a Greater Percentage of the Energy Costs of Load

• Because uplift is minimized, LSEs can use FTRs to hedge a greater proportion of the total cost of their load under ELMP.

0.0%

1.0%

2.0%

3.0%

4.0%

5.0%

6.0%

7.0%

8.0%

9.0%

40 60 80 100 120 140 160 180 200 220 240

Load (MW)

Upl

ift P

aym

ents

as

a Pe

rcen

tage

of T

otal

Pay

men

ts b

y Lo

ad

Under LMPUnder ELMP

84

Reduced “Pay-as-bid” Incentives• “Pay-as-bid” incentives are reduced for infra-marginal

resources and, as a result, there is increased incentive for generators and loads to provide bids and offers that reflect real resource costs.– LMPs can be below the average cost of meeting load.– Uplift closes this gap, but means that infra-marginal generators will earn

no margin on energy. In the previous example:

GeneratorOutput(MWh)

Energy Cost

($/MWh)

No-Load Cost($/hr)

Total Cost($/hr)

LMP Revenue

($/hr)Uplift($/hr)

Net Margin($/hr)

A 100 49 100 5,000 5,000 - - B 80 50 300 4,300 4,000 300 - C 40 60 0 2,400 2,000 400 - Total 220 11,700 11,000 700 -

85

Reduced “Pay-as-bid” Incentives

• Under LMP, infra-marginal generators (and loads) that receive uplift have an incentive to increase their offers and their uplift payments; this incentive is reduced under ELMP.– When the market operator uses LMP, generating units A and B

receive uplift, so they are paid only their offer cost. – Infra-marginal generators, knowing that this is the case under

LMP, have an incentive to increase their offers as much as possible without losing their place in the dispatch.

– Infra-marginal generators would increase their offers so that their full output would be paid something close to the ELMP price.

86

Reduced “Pay-as-bid” Incentives• In the example, generating units A and B would

raise their total offer costs to around $60/MWh each whenever they expect generating unit C to be dispatched, and would be better off.– In the end, load could expect to pay around $13,200,

rather than $11,700 for 220 MW; this is close to what load would pay under ELMP pricing.

– Moreover, under LMP, dispatch and pricing could be more volatile as generators adjust their offers to maximize their revenues given how they expect other generators and loads to offer.

– Incentives for generators to raise their offers can lead to a less efficient dispatch.

87

Summary

• Additional workshops are planned at the end of May and June.– Workshop 3 is scheduled for May 26.– Details will be posted at www.midwestiso.org

• Click Here for documents and presentations are available