j. mccalley wind, markets, and capacity. outline 1.basics of electricity markets 2.wind and markets...

J. McCalley

Wind, Markets, and Capacity

Outline1. Basics of electricity markets2. Wind and markets3. Dispatchable intermittent resources

(DIR)

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Summary of power balance control levelsNo. Control Name Time frame Control objectives Function

1 Inertial response 0-5 secsPower balance and

transient frequency dip minimization

Transient frequency control

2 Primary control, governor 1-20 secs

Power balance and transient frequency

recovery

Transient frequency control

3 Secondary control, AGC

4 secs to 3 mins

Power balance and steady-state frequency Regulation

4 Real-time market Every 5 mins Power balance and economic-dispatch

Load following and reserve provision

5 Day-ahead market Every day Power balance and

economic-unit commitmentUnit commitment and

reserve provision

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We are addressing inclusion of wind in real-time and day-ahead electricity markets

…

4

Basics of electricity markets

1. Locational marginal prices (LMPs)2. Markets compute the LMPs via an internet-

based double auction that maximizes participant benefits

3. There are 2 separate settlement processes.

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Locational marginal prices

1. One for each bus in the network.2. Three components – see above.3. If the network is lossless, and the

transmission capacity is infinite, then all buses have the same LMP.

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MISO and PJM balancing areas

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RT LMPs in the MISO and PJM balancing areas

7:20 am (CST) 9/8/2011MISO - PJM Interconnection Joint and Common Market Web site, located at www.miso-pjm.com/markets/contour-map.html.

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RT LMPs in the MISO and PJM balancing areas

7:40 am (CST) 9/8/2011MISO - PJM Interconnection Joint and Common Market Web site, located at www.miso-pjm.com/markets/contour-map.html.

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Average annual locational marginal prices

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Market clearing price

Computed as the price where the supply schedule intersects the demand schedule.

SUPPLY

DEMAND

Price ($/MWhr)

Quantity (MWhr)

L. Tesfatsion, “Auction Basics for Wholesale Power Markets: Objectives and Pricing Rules,” Proceedings of the 2009 IEEE Power and Energy Society General Meeting, July, 2009.

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Market clearing price

Computed as the price where the supply curve intersects the demand curve.

Price ($/MWhr)

Quantity (MWhr)

SUPPLY

DEMAND

L. Tesfatsion, “Auction Basics for Wholesale Power Markets: Objectives and Pricing Rules,” Proceedings of the 2009 IEEE Power and Energy Society General Meeting, July, 2009.

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Locational marginal prices

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CAISO market design

Schedules entire “next-day” 24hr period.

Schedules interchange for entire “next-day” 24hr period, starting at current hour, optimizing one hour at a time (1 value per hr)

Computes dispatch every 5 minutes.

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Electricity “two settlement” markets

Day-Ahead Market(every day)

Real-Time Market(every 5 minutes)

Energy & reserve offers from gens

Energy bids from loads

Internet system

Which gens get committed, at roughly what levels for next 24 hours, and settlement

Internet system

Energy offers from gens

Energy bids from loads

Generation levels for next 5 minutes and settlement for deviations from day-ahead market

Generates 100 mw; paid $100.

Generates 99 mw; pays $1.

Two markets and a process

Ref: M. Tackett, Experience with Implementing Simultaneous Co-optimization In The Midwest ISO Energy & Operating Reserve Markets, IEEE PES General Meeting, 2009.

The Day-Ahead Energy and Operating Reserve Market is a financially binding market that clears energy, reg reserve, spin reserve & supp reserve hourly.

SC-SCUC commits resources, schedules regulating reserves on committed resources and/or releases emergency operating ranges on resources.

The Real-Time Energy and Operating Reserve Market is a financially and physically binding market that clears energy, reg reserve, spin reserve and supp reserve every 5 minutes.

DAY-AHEAD MARKET (DAM)

Reliability Assessment Commitment Process (RAC)

REAL-TIME MARKET (RTM)

SC-SCED is used in Real-Time Energy/Operating Reserve Market to dispatch & price energy, regulating reserve, spinning reserve and supplemental reserve on a 5-minute basis.

SC-SCED is used to clear/price energy, regulating reserve, spinning reserve and supplemental reserve on hourly basis.

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Two markets - commentsNote the difference between use of SC-SCED for DAM and RTM.

SCUC gives a 24 hour solution

1 2 3 4 5 6 7 8 9 16 17 18 19 20 21 22 23 24

SCED gives one solution per hour

DAM

RTMReal-time

conditions (determined by SCUC and

RAC)

0 5 10 15 20 25 30 35 40 45 50 55 60 5 10 15 20 25 30…

SCED gives one solution every 5 minutes 16

Simplified versions of SCED and SCUC

CostsShutdown Costs StartupCosts ProductionCosts Fixed

min t i

ititt i

ititt i

ititt i

itit HxSyCgFz

busesgeneratorkgkk Ps

_

min

They are both tools to solve optimization problems. But different optimization problems. Here are some observations.

SCED Objective SCUC Objective

• Decision variables are Pgk

• Objective & constraints are linear• Pgk are continuous valued• It is a linear program (LP).• It is a convex programming problem.• It is solved by simplex, very efficient.• For a single time period (1 hr or 5 min).• It provides LMPs.

• Decision variables are zit, git, yit, xit

• Objective & constraints are linear• zit, yit, xit are discrete, git is continuous• It is a mixed integer linear program (MIP).• It is a non-convex programming problem.• It is solved by branch and bound.• For multiple time periods (2-24 hrs or more)• It does not provide LMPs.

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Day-ahead LMPs in ISO-NE balancing areas

For hour ending 11:00 am (EST) 9/8/2011New England ISO website, at http://www.iso-ne.com/portal/jsp/lmpmap/Index.jsp.

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RT LMPs in the ISO-NE balancing areas

10:25 am (EST) 9/8/2011New England ISO website, at http://www.iso-ne.com/portal/jsp/lmpmap/Index.jsp.

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RTAncillary service prices in ISO-NE bal areas

10:25 am (EST) 9/8/2011

Regulation clearing price is $5.11/MW.

Load Zones: Connecticut (CT), Southwest CT (SWCT), Northeast Massachusetts/Boston (NEMABSTN)

TMSR=10min spinning rsrvTMNSR=10min non-spinning rsrvTMOR=30min operating rsrv

New England ISO website, at http://www.iso-ne.com/portal/jsp/lmpmap/Index.jsp.

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How does wind participate in markets? Wind is price-taker.

Demand schedule without wind

Demand schedule with wind

Supply schedule

Quantity (MWhr)

Price ($/MWhr)

Point X

Point Y

“Old” approach #2.•Participates in day-ahead energy•Does not participate in AS or RT•Wind generates what it can•No deviation penalties•Paid based on computed LMP with wind, Point Y below•Marginal unit backed off•Assumes wind satisfies lowest “willing to pay” load

“Old” approach #1•Participates in day-ahead energy•Does not participate in AS or RT•Wind generates what it can•No deviation penalties•Paid based on computed LMP without wind, Point X below•Marginal unit backed off•Assumes wind satisfies highest “willing to pay” load.

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How does wind participate in markets?

“New” Midwest ISO approach: Dispatchable intermittent resource (DIR)

• Participates in day-ahead energy• Makes offer into RT market like any other

generator. But one unique DIR feature:• Instead of capacity max offered in by other generation

resources, the forecasted wind MW is used as the operation capacity maximum;

• Units are expected to follow the dispatch signal;• Units missing “schedule band” of 8% on either side

dispatch instruction for four consecutive 5-min periods are penalized.

•What are implications?Midwest ISO Market Subcom, “Dispatchable Intermittent Resource Implementation Guide,” March 1, 2011, at www.midwestiso.org/Library/Repository/Meeting%20Material/Stakeholder/MSC/2011/20110301/20110301%20MSC%20Item%2012a%20DIR%20Implementation%20Update.pdf.

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What are implications? Wind is dispatchable! Forecasting is key!•DIRs are expected to provide rolling forecast of 12 five-minute periods for the Forecast Maximum Limit.•If forecast not submitted in time, MISO forecast is used.•Each 5 minute dispatch optimization uses Forecast Maximum Limit based on the following order

1. Participant submitted Forecast for the interval•Must be less than or equal to the Feasibility Limit•Must have been submitted less than 30 minutes ago

2.MISO Forecast•Must be less than or equal to the Feasibility Limit•Must have been created less than 30 minutes ago

3.State Estimator

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Midwest ISO, “Dispatchable Intermittent Resource Design,” July 2010, available at https://www.midwestiso.org/Library/Repository/Meeting%20Material/Stakeholder/RSC/2010/20100726-27/20100726-27%20RSC%20Item%2019b%20Dispatchable%20Intermittent.pdf.

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Midwest ISO’s wind forecasting accuracy?

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Why is DIR beneficial?1. DIRs are more likely to reduce output when LMP is

negative because dispatch will instruct them to reduce; there are penalties for not following dispatch.

2. Inclusion of the DIRs in the RT dispatch will give SCED more flexibility to manage constraints. Therefore, there will be fewer manual curtailments:

• Benefits wind for increased MWhrs produced• Benefits to system because wind offers low and

therefore affects all time periods some (has very large effect during peak periods) – see next slide.

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Why is DIR beneficial?Difference in prices with (solid) and without (dashed) wind.Slanted lines are demand curves for night, day, and peak.Without wind, prices are slightly higher at night, significantly higher during the day, and much higher during the peak.

“Wind energy and Electricity Prices: Exploring the “merit order effect”,” a literature review by Poyry for the European Wind Energy Association, April , 2010., available at www.ewea.org/fileadmin/ewea_documents/documents/publications/reports/MeritOrder.pdf.

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Generation Expansion Planning

A simple statement of the GEP problem is as follows.

T

t

tOtMtFtStI1

)()()()()(minwhere•I(t) is total investment costs at year t•S(t) is total salvage value of retired plants at year t (and for all plants still in operation at year T). •F(t) is total fuel costs in year t. •M(t) is total maintenance costs in year t.•O(t) is the cost associated with outages.and the overbars in the objective function indicate values must be present-worth.

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Generation Expansion Planning

10

subject to

)()()()(min1

.LOLE(t)

tMtFtStIT

t

where•I(t) is total investment costs at year t•S(t) is total salvage value of retired plants at year t (and for all plants still in operation at year T). •F(t) is total fuel costs in year t. •M(t) is total maintenance costs in year t.•LOLE(t) is the expected duration of time, in number of days, the system would be in an interrupted state. A standard threshold for LOLE is 1 day/10yrs or 0.1 days/yr.and the overbars in the objective function indicate values must be present-worth.

An alternative formulation of the GEP problem removes outage costs from the objective function and then constrains an index reflecting reliability: loss-of-load probability, LOLP, loss of load expectation, LOLE, or expected unserved energy EUE)..

The EPRI program EGEAS is a well-known program that works like this.

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Capacity Value

The LOLE constraint is a function of three attributes:1.Capacity of each unit2.Availability of each unit (% of time it is available or 100-% of time it is forced out)3.Load

The capacity value of a generation resource is the contribution that it makes to generation system adequacy, i.e., to satisfying the LOLE constraint.

For standard generators, this value is NOT the unit’s capacity because the unit may be forced out of service. Forced outage rates (FORs) of conventional units range between 2 and 20% giving availability of 80-98%, whereas wind energy is available at varying levels that average between 30-45%.

For windfarms, this value is NOT the windfarms capacity because the windfarm may be forced out of service and because the wind resource is rarely sufficient for providing windfarm capacity.

Capacity credit is used to identify the percentage of a windfarm’s capacity which should be identified for reliability calculations at peak load. For example, MISO was using 12.9% capacity credit for wind. This indicates the reduced availability at peak load.

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Capacity Value

There is another issue why wind is considered to be less available than conventional generation.

For conventional generation, the outage of one plant is independent of the outage of another plant (except in certain cases related to cascading which we will not consider here).

On the other hand, if the wind speed decreases significantly at windfarm A, then it is also very likely to decrease significantly at a nearby windfarm B. In other words, wind capacity experiences correlation between plants; conventional capacity does not (and this “geodiversity” is one reason why larger boundaries for control areas can be more effective than smaller boundaries).

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Capacity Value

[*] “Capacity Value of Wind Power,” Task Force on the Capacity Value of Wind Power, IEEE Power and Energy Society, Andrew Keane, Member, IEEE, Michael Milligan, Member, IEEE, Chris J. Dent, Member, IEEE, Bernhard Hasche, Claudine D’Annunzio, Ken Dragoon, Hannele Holttinen, Nader Samaan, Lennart Söder, and Mark O’Malley, IEEE Trans on Power Systems, Vol. 26, Is 2, 2011, pp. 564-572.

An approach to account for low capacity factor and geodiversity is to set the capacity for variable generation equal to the amount of load that could be added without changing the risk of a shortage in generation capacity at peak load, as measured by loss of load expectation (LOLE) or loss of load probability (LOLP). This is referred to as the effective load carrying capability, or ELCC. This concept is illustrated below [*].

Horizontal line is LOLE=0.1. day is achieved for peak load less than or equal to 10000 MW.Addition of new gen moves LOLE function. If we required that the load remain the same, the LOLE would go down (get better) to about 0.09. Assume we want to maintain same LOLE value of 0.1we may grow load by 400 MW! This 400 MW load growth is called ELCC of new gen. ELCC of an additional gen will only be equal to capacity of that additional gen if additional gen is dispatchable & 100% reliable.

LOLE functions with & without new gen.

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Capacity Value


Ref [*] provides a three-step method for computing ELCC, which depends on development of the capacity outage probability table (COPT). The description is lifted verbatim as follows:1.“The COPT of the power system is used in conjunction with the hourly load time series to compute the hourly LOLPs without the presence of the wind plant. The annual LOLE is then calculated. The LOLE should meet the predetermined reliability target for that period. If it does not match, the loads can be adjusted, if desired, so that the target reliability level is achieved.2.The time series for the wind plant power output is treated as negative load and is combined with the load time series, resulting in a load time series net of wind power. In the same manner as step 1, the LOLE is calculated. It will now be lower (and therefore better) than the target LOLE in the first step.3.The load data is then increased by a constant across all hours using an iterative process, and the LOLE recalculated at each step until the target LOLE is reached. The increase in peak load (sum of) that achieves the reliability target is the ELCC or capacity value of the wind plant.”

1. What is a capacity outage probability table (COPT)?2. How to do the following: “The COPT of the power system is used in conjunction

with the hourly load time series to compute the hourly LOLPs” ?3. How to compute the COPT?

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What is a COPT?The capacity outage table is a table of generation outage states and their associated probabilities. A very simple COPT is provided below for a power system that has only one generation that may either be •up, generating C (with capacity outage 0) at probability A, or •down, generating 0 (with capacity outage C) at probability U.

Capacity Outage Probability0 AC U

If we had a power system comprised of 2 identical units, the COPT would be as below.

Capacity Outage Probability0 A2

C AUC UA

2C U2

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What is a COPT?Consider a system with two 3 MW units and one 5 MW unit, all of which have forced outage rates (FOR) of U=0.02. There is a procedure which will allow us to construct the COPT, and it results in the table below.

This table tells us that over a given time interval, the probability that the system will have a capacity outage:•of 0 MW is 0.941192;•of 3 MW is 0.038416;•of 5 MW is 0.019208;•of 6 MW is 0.000392;•of 8 MW is 0.000784;•of 11 MW is 0.000008.

Capacity outage state k

Capacity outage, Ck

Probability

1 0 0.9411922 3 0.0384163 5 0.0192084 6 0.0003925 8 0.0007846 11 0.000008

The procedure for obtaining the COPT is easily extended to consider any number of units with any forced outage rates, identical or not. But before considering that procedure, let’s answer the second question.

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COTP & hourly load time series for hourly LOLP

Question 2: How to do the following: “The COPT of the power system is used in conjunction with the hourly load time series to compute the hourly LOLPs” ?

Observe we will have loss of load if the load exceeds the generation capacity.

The generation capacity will be the installed capacity, call it IC, less the capacity that is outaged, call it Ck (corresponding to capacity outage state k). Thus, we see loss of load if

d>IC-Ck

So we would like to obtain Pr(d>IC-Ck).

We can view this another way, by observing the criterion for loss of load is

Ck>IC-dand so we desire

Pr(Ck>IC-d).

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Question 2: How to do the following: “The COPT of the power system is used in conjunction with the hourly load time series to compute the hourly LOLPs” ?

In our above example, we observe that our capacity is 11 MW. Let’s assume that the load is 5 MW. Then we may obtainPr(Ck>11-5)=Pr(Ck>6)= Pr(Ck=8)+Pr(Ck=11)= 0.000784+0.000008=0.000792.


Capacity outage, Ck

Probability

1 0 0.9411922 3 0.0384163 5 0.0192084 6 0.0003925 8 0.0007846 11 0.000008

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Denote the capacity outage as a random variable Y. Observe that the probabilities given by the COPT characterize a probability mass function (which is the discrete version of a probability density function); we will define it as fY(y), as indicated below.

Prob

abili

ty

12 9 6 3 0

0.019208

0.000784

Capacity outaged

0.000008

0.941192

0.038416

0.000392

fY(y)

We can then define a cumulative probability function FY(y) according to:

yy

jYyy

jYY

jj

yfyfyYPyF )(1)()()(

Cap outage state k

Capacity outage,

Ck

Probability

fY(y)

Cumulative probability

FY(y)1 0 0.941192 0.05882 3 0.038416 0.02043 5 0.019208 0.00124 6 0.000392 .00007925 8 0.000784 0.0000086 11 0.000008 0


Capacity outage, Ck

Probability

1 0 0.9411922 3 0.0384163 5 0.0192084 6 0.0003925 8 0.0007846 11 0.000008

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Cap outage state k

Capacity outage,

Ck

Probability

fY(y)

Cumulative probability

FY(y)1 0 0.941192 0.05882 3 0.038416 0.02043 5 0.019208 0.00124 6 0.000392 .00007925 8 0.000784 0.0000086 11 0.000008 0

Pro

babi

lity

12 9 6 3 0

0.0012

Capacity outaged

0.000008

0.0588

0.0204

0.0000792

FY(y) 1.0

0.0

Once we have this table, given a certain load d, we may compute the LOLP during the desired time interval, as the probability that the capacity outage exceeds IC-d, which is just FY(y=IC-d), that is, LOLP(d)=FY(y=IC-d).Recalling IC=11, with a load of 5 MW, we obtain LOLP(5)=FY(y=6)=0.000792.

Note that IC-d is reserve!So FY(y)=P(Y>y)=P(CapOutage>Reserve)=LOLP

At points of discontinuities, we should use the lower probability for the LOLP, i.e., LOLP(d=8)=Pr(Y>11-8)=Pr(Y>3)=0.0204

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Time d (MW)1 4.02 4.53 5.04 5.55 6.06 7.07 8.08 9.09 8.510 7.5… …

Pro

babi

lity

12 9 6 3 0

0.0012

Capacity outaged

0.000008

0.0588

0.0204

0.0000792

FY(y) 1.0

0.0

Load time series Time d (MW) y=IC-d

LOLP(d)=FY(y=IC-d)=Pr(Y>IC-d)

1 4.0 7.0 0.00007922 4.5 6.5 0.00007923 5.0 6.0 0.00007924 5.5 5.5 0.00125 6.0 5.0 0.00126 7.0 4.0 0.02047 8.0 3.0 0.02048 9.0 2.0 0.05889 8.5 2.5 0.058810 7.5 3.5 0.0204… …

To include the effect of wind, just use a net load time series instead of a load time series.

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Now we can obtain the LOLE as the expected amount of time during the year that load will be interrupted. This will be

Time d (MW) y=IC-d

LOLP(d)=FY(y=IC-d)=Pr(Y>IC-d)

1 4.0 7.0 0.00007922 4.5 6.5 0.00007923 5.0 6.0 0.00007924 5.5 5.5 0.00125 6.0 5.0 0.00126 7.0 4.0 0.02047 8.0 3.0 0.02048 9.0 2.0 0.05889 8.5 2.5 0.058810 7.5 3.5 0.0204… …

)())((8760

1

tTtdLOLPLOLEt

In this case, ∆T(t)=1hr, and so our LOLE expression is

8760

1

))((t

tdLOLPLOLE

For our 10 hour period given in Table 9, the contribution to LOLE is 0.1814 hrs, which is 10.884 minutes. If our 10 hours is representative of the rest of the year, then it means our annual LOLE would be

(8760/10)*10.884/60=158.91That is, our annual LOLE would be 159 hours, or 6.625 days. This would be significantly above our 0.1 day in 10 years!

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Capacity Value


We can then adjust loads and recompute, with and without wind, in order to obtain the below curves, and from them, the ELCC of wind.

LOLE functions with & without new gen.

j. mccalley wind, markets, and capacity. outline 1.basics of electricity markets 2.wind and markets...

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