Basic Resource Adequacy Study Concepts

DRAFT

Basic Resource Adequacy Study Concepts

Wayne CostePrincipal Engineer, Resource Adequacy

RC MeetingMay 14, 2009

Basic Resource Adequacy Study ConceptsMay 14, 2009

© 2009 ISO New England Inc. DRAFT

Resource Adequacy Metrics/Calculations

• Resource Adequacy assessments are studies– That attempt to answer the question

– May be framed in simple or complex terms– Resource Adequacy frameworks have evolved over time

• Simple deterministic analyses• More complex deterministic analyses• Probabilistic analyses

– Local area– Local area plus neighbors– Local area plus neighbors plus their neighbors and their neighbors

• “Resource Adequacy” will be used instead of “Reliability”– “Reliability” is a concept of “will the system fail”

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“Do I have enough resources to serve the loads under all reasonably foreseeable circumstances”



Resource Adequacy Metrics

• In “ancient days” when systems were small and the next resource to be added would be the largest unit on the system, some “Rules-Of-Thumbs” were developed – “Largest Unit Rule”

– “Largest Unit and a Half Rule”– Percent Reserve Margin

• As unit size began to stabilize and systems became strongly interconnected– “Largest units” became small part of the total system

– Different approaches were used to answer the question, “when do I need more resources?”

– Probabilistic approaches were developed in the 1950s

– Use of these techniques became widespread in the 1960s

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Probabilistic Resource Adequacy

• Resource Adequacy now based on probabilistic analysis– Probabilistic assessments are translated into adequacy metrics

• Percent reserve margins

• Percent capacity margins

• Amount of resources needed (total MW)

• Maximum peak load that can be served

– Probabilistic assessments assume• Some factors are correlated

– All areas / regions see the same heat wave at the same time– A resource outage can be correlated to an interface rating change– Seasonal derating

• Many resource adequacy risks are random and independent– One resource outage does not affect the “state” of another resource– “Independent” is a key assumption

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Risk and Probabilities

• For every hour, of every day, the probability of insufficient resources to serve load can be quantified– For most hours, this probability is (virtually) zero– For some hours, the probability is non-zero and has a contribution– Basic metric is “Loss of Load Probability” or “LOLP”

• Given a load distribution and a supply distribution – LOLP is the probability of insufficient resources to serve load– There are no “measurement units” associated with a probability– “Measurement units” are “per period,” “per event” or “per coin flip,” etc.

• Summation of LOLP over time gives an “expectation”

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“Expectation” in Adequacy Studies

• Adequacy index is “Loss of Load Expectation” or “LOLE”– LOLP is calculated for each time period

• Peak load of the day, or

• Each hour (including the peak hour)

– Time period used depends on desired adequacy index• Every hour

• Every contiguous event (i.e., possibly more than one per day)

• Every daily peak (i.e., a day is limited to one Loss of Load event)

– Summation of the LOLPs over a specified period of time• 5-day-week, 7-day-week, month, season, year or ten-years

– If absolutely unreliable … maximum 260 days per year (week days) – If absolutely unreliable … maximum 365 days per year (all days)

• Gives an “expectation” of how many occurrences could be experienced over a period of time

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Other Probabilistic Indices

• Loss of Load Hours (LOLH)– The expected number of hours when shortages would occur– LOLH (hours/year) is not LOLE (days/year) times 24

• 0.1 days / year * 24 hours / day = 2.4 hours per year – Would happen only if peak occurred in each of the 24 hours of the day

– New England’s LOLH would be about 0.3 to 0.5 hours per year

• Loss of Energy Expectation (LOEE)– Measure of how many MWhs would be lost in each hour times the

probability of shortage (typically used for comparing load shape changes)

– Also called Expected Un-served Energy (EUE)

• Frequency & Duration (F&D)– Indication of how frequently outages would occur and how long they

might last (typically used for comparing load shape changes)

• Loss of Reserve Expectation (LORE)– Indication of how often emergency operations would be required

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Interchangeability of Indices

• Expressing adequacy with different measurement units does not provide additional information about the adequacy of the system– “Measurement units” may not describe “different aspects” of adequacy

– Indices expressed using “different terms” may highlight secondary effects

• A parallel for “measurement units” can be made to a person’s height– The height of the presenter can be stated in different ways

• 6 feet tall• 72 inches tall• 182 centimeters tall• 18 hands tall (as used in measuring horses)• 0.001136 miles tall

• Indices can reflect “different aspects” for more information– Total height

– Total height and weight

– Total height, weight and shoe size

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LOLE Criterion for Resource Adequacy

• This development of the LOLE index considers– Possible levels of peak loads due to weather variations – Impact of assumed generating unit performance– Load and capacity relief obtainable (Through the use of ISO NE Operating

Procedure No. 4 - Action During a Capacity Deficiency)

• LOLE index used in New England– A day with any loss-of-load counts only once

• Does not describe how many hours load is interrupted

• Two possible events in a single day – i.e., an outage at noon, then recovery, then an evening outage– Counts as only one day with loss-of-load

– Does not quantify how many MW are interrupted– Does not quantify the number of MWhs interrupted

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Resource Adequacy Tools

• Westinghouse/ABB Capacity model program– It is a “Single Area” program

• Single area refers to the assumption that there is adequate transmission to deliver energy where and when it is needed

• All loads and generators assumed to be connected to a single bus• Maintenance scheduled to minimize LOLE throughout the year

– Uses mathematical (i.e., “closed form”) technique for solution– Probabilistic calculations to capture the random nature of loads

and resource availability• Determines the probabilities of different amounts of unavailable

capacity on the system as a result of resource forced outages• Mathematics gets very complex if any transmission is included

– A two-area Westinghouse/ABB model does exist, but has not been used in nearly 20 years

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Resource Adequacy Tools (cont.)

• GE Multi-Area Reliability Simulation (MARS) model– MARS is a “Multi-Area” program

• Multi-area refers to the assumption that transmission constraints may impede delivery of energy to where and when it is needed

• Loads and generators can be assumed to be connected to different parts of the system

• Provides a locational dimension for resource adequacy studies

– MARS model uses different technique to “do the math”• Uses “Monte-Carlo” sampling instead of “closed form” solutions

• Exactly the same inputs would produce exactly the same results– Load distributions– Resource distributions

• “Monte-Carlo” models can include more constraints than analytical “closed form” models

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Resource Adequacy Tools (cont.)

• Other types of resource adequacy models have been developed– Attempt to be more detailed– Potentially at a bus level resolution– Uncertainty whether

• Useful input assumptions are available at a detailed level

• Whether those assumptions are meaningfully robust

• What the meaning of a failure state actually means – Add more New England wide capacity, or– Add static capacitors at a specific location

– Uncertain how this more detailed information could / should be used in resource adequacy analysis

• Models more granular than MARS will not be discussed

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Resource Adequacy – Excluded Factors

• Major factors not considered in adequacy calculations– Common mode failures of resources

– Catastrophic long-term resource outages

– Delays in resource additions or retirements

– Energy / fuel limited resources• Energy / fuel supply• Fuel delivery issues

– Uncertainty in assumptions for forced outage rate statistics

– Intra-hour load excursions

– Internal transmission constraints or transmission forced outages

– Effects of ambient air temperatures above 90oF on combustion turbine technologies

– Effect of air and water environmental restrictions

– Number of loss-of-load days that will actually incur a loss of load

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Resource Adequacy – Excluded Risks

• Not all risks are considered– Perfect foresight is assumed in operations

• All resources are assumed to be available if they are not “broken”

• All resources are assumed to be committed in a timely manner so that all resources are ready when needed

• All resources are committed if higher than expected loads materialize

– Non-peak seasons contribute miniscule amounts to LOLE• No transmission outages are considered

• Generation maintenance, while modeled, is not a problem – For New England which is strongly summer peaking– Because we neglect transmission outages and additional constraints

• Non-peak season LOLE risk – LOLE risk in the “non-peak season” is a non-trivial operational issue– This is a question of “outage management” and not “resource adequacy” – Not part of the question “do we have sufficient resources” for peak loads

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Resource Adequacy – Included Risks

• The most significant factors to be considered are– Customer load distributions

– Random resource outages• Generating resources

• Demand Resources

• Intermittent resources

– Static transmission interface limits• Based on specific system configurations

• Actual conditions may change interface limits significantly

– Operating Procedure No. 4, “Actions During a Capacity Deficiency” (OP-4)

• Voltage reductions

• Erosion of required operating reserve

• Emergency assistance from neighboring systems

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Customer Load Distributions

• Uses distributions of daily peak loads for each week, explicitly taking into account weather uncertainty– Westinghouse load model is developed for

• Non-holiday weekday peaks

• Excludes weekend peaks

– Assumes weekend peak contribution to system risk is negligible• Weekend peaks are much lower that weekday peaks

• Risk of not having enough installed capacity is “much” lower

• Weekend operational issues may reduce flexibility of the system– Resource maintenance– Transmission maintenance– More units on reserve shutdown (i.e., not needed)

• MARS load model developed to mimic Westinghouse loads (to be discussed later)

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Loads Model Development

• Loads represented by distributions of weekday peak loads– Represents daily peak loads only, not all hours– 52 weekly distributions for each year– Based on historical weather distributions from the last 3 decades

• These distributions are the key inputs in adequacy studies– Projected monthly and seasonal peak loads

• Are specific points on these load distribution curves

• Specific points are useful as guideposts– 50/50 summer peak load is one point on composite distribution– 90/10 summer peak load is another point on composite distribution

– Shape of load distributions affect the adequacy calculations– Statistical parameters for the distributions are used to characterize

the load levels with the probability of their occurrence

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Peak Load Distribution Development

• For each of the 52 weeks of the forecast year– A distribution of 1,000 possible peak load points are developed

• Weather uncertainty is the primary uncertainty considered• Seasonal trends in composition of load (heating / cooling / other)

– Distribution of raw peak load data– Raw peak load points approximated by a continuous distribution

• Parameters estimated for three moments of the distribution– Mean– Standard deviation– Skewness (fat / skinny tails)

• Skewness is needed to capture the frequency of highest daily peak loads accurately as shown in next few slides

• The following distributions are illustrative and not for a specific year

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Distribution of Raw Data for One Week

1000 Peak Load Points For Week 30 (2001)Cumulative Probability Distribution

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Normal Approximation is “Generally Good”

1000 Peak Load Points For Week 30 (2001)Cumulative Probability Distributions

0.000.100.200.300.400.500.600.700.800.901.00

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1000 Points Per Week Normal Approx

High loads dominate risk calculations


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“Generally Good” Neglects the Upper Tail

1000 Peak Load Points For Week 30 (2001)Cumulative Probability Distributions

0.900.910.920.930.940.950.960.970.980.991.00

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1000 Points Per Week Normal Approx

Normal Approximation does not represent the probability of higher peak loads. Skewness (fat / skinny tail) corrects for much of this. [Note: At the 97th percentile, the approximated load is 800 MW lower than the distribution.]


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Cumulative Daily Peak Distribution for Highest Summer Week

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Daily Peak Density Distribution for Highest Summer Week

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Distributions of Daily Peak LoadsDensity Distribution For Highest Summer Week

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Daily Peak Density Distribution for Highest Seven Summer Weeks

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Load Level (MW)

Distributions of Daily Peak LoadsDensity Distribution For Highest Seven Summer Weeks

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Note: Each distribution represents 5 weekdays

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Cumulative Daily Peak Distribution for Highest Seven Summer Weeks

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Peak Load (MW)

Distribution of Weekday Peak Loads - Highest Seven WeeksIndivudual Week Distributions

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Note: Each distribution represents 5 weekdays

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Cumulative Daily Peak Distribution for Highest Seven Summer Weeks

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Distributions of Daily Peak LoadsCumulative Distribution of Daily Peak Loads

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Summer Peak Week

Note: This load distribution represents 35 weekdays

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Effect of Including all 52 Weeks

Note: Seven week distribution represents 35 weekdays 52 week distribution represents 260 weekdays

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Distributions of Daily Peak LoadsCumulatve Distribution For all 52 Weeks

and 31,000 MW of Resources

Composite 52 Week Loads Seven Week Composite

52 week composite reflects lower loads

7 week composite reflects peak loads

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Illustrating LOLP

• LOLP is the cornerstone of probabilistic adequacy studies• Adequacy studies compare differences between

– Loads to be served, and – Available resources (e.g., not on forced or scheduled outages)

• If resources were perfectly available when needed– Whenever loads are less than installed resources

• Then: no “Loss Of Load” (i.e., no contribution to LOLP)

– Whenever loads are more than installed resources• Then: a “Loss of Load” occurs (i.e., contribution to LOLP)

• Following examples– Assumes 31,000 MW of perfectly reliable resources– Resource uncertainty will be incorporated in later slides

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Illustrating LOLP (cont.)

• Approach shown here is applicable to both– New England-wide Installed Capacity Requirements (ICR), and– Minimum and maximum locational capacity requirements

• Loads – Total New England loads are developed as shown– Loads for sub-areas are

• Approximately a percentage of the total load

• Percentage changes by month

• Calculations are identical– Question addressed by the calculation is

• What is the MINIMUM of capacity that is required IN THE AREA UNDER STUDY to satisfy the reliability criterion, GIVEN the risks and constraints that have been modeled

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Load Level (MW)

Distributions of Daily Peak LoadsDensity Distribution For Highest Summer Week


Summer Peak Week Available Resources

LOLP With 31,000 MW of Resources

Loss of Load Probability: when loads greater than available resources

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LOLP and LOLE Calculations

• Probability of loads exceeding available capacity– Probability of loads in excess of 31,000 MW– 0.01293 probability (area under the curve above 31,000 MW)

• If the load distribution represents 1 day then– The “expectation” that load would exceed available resources

would be 0.01293 for that one day• Restating this would be 0.01293 “expected outage events per day”• Identical days have the same probability value

• If the load distribution represented five weekdays– The “expectation” would be the same for each of the five days– The “expectation” would be five times or 0.06463 expected

outage events per week– Risk in other weeks to be evaluated separately and then summed

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Load Level (MW)

Distributions of Daily Peak LoadsDensity Distribution For Seven Highest Summer Weeks


Week 28 Week 29 Week 30 Week 31

Week 32 Week 33 Week 34 Available Resources

Seven Critical Weeks of Peak Loads

LOLP changes for each week’s peak load distribution

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LOLE adequacy Index for Seven Weeks

• Loss of Load Probabilities vary for each week depending on the level of the loads– Each week represents five weekdays– Loss of load expectation equals LOLP times number of days

– With 31,000 MW of resources and the seven peak load weeks • We have a LOLE of 0.26831 outage events per summer• If these were the only weeks with significant LOLP, then adequacy

index would be 0.26831 expected outage events per year (or LOLE)

Loss of Load Probability (LOLP)Loss of Load Expectation (LOLE)

Expected outage events per weekWeek 28 0.00783 0.03913Week 29 0.01028 0.05139Week 30 0.01293 0.06463Week 31 0.01174 0.05870Week 32 0.00687 0.03433Week 33 0.00403 0.02014Week 34 0.00263 0.01316Total 0.26831

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Load Level (MW)

Distributions of Daily Peak LoadsComposite Density Distribution For Highest Seven Summer Weeks



Single Distribution Can Represent the 35 Days

LOLP for seven week composite distribution is 0.00804Note: 0.00804 x 35 days/ period = 0.2814 days/period

Note: This distribution represents 35 weekdays

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Equivalent LOLE When Adjusted for Days

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Distributions of Daily Peak LoadsCumulatve Distribution For all 52 Weeks


Composite 52 Week Loads Seven Week Composite Available Resources

Note: Seven week distribution represents 35 weekdays 52 week distribution represents 260 weekdays

LOLP times 260 days per distribution

LOLP times 35 days per distribution

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0.00110 x 260 days/ year = 0.2860 days/ year

Note: 0.00804 x 35 days/ period = 0.2814 days/period



Effect of Resource Unavailability

• Previous examples assumed that– There were 31,000 MW available– Perfectly reliable capacity– LOLE was only the area to the right of 31,000 MW

• However, real capacity is not perfectly reliable– In a large system

• All of the resources are never 100% available

• All of the resources are never completely broken

• Amount of resources available can be described as a distribution

– The LOLP calculation becomes more complicated• No longer a vertical line

• Now a cumulative distribution

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Resource Unavailability Distribution

• Following slides show how resource unavailability is represented in a probabilistic analysis– Each resource has a probability of outage– Whenever any unit is unavailable, total available resources are

reduced

• When the risk of discrete units possibly being on outage are considered, a stair-step distribution will result– This example assumes the 31,000 MW is comprised of

• Thirty one 1000 MW units• Unavailability rate is 5 percent

• Normal approximation is shown for these outages– Not a good representation for only 31 large resources – Used here for illustrative purposes only

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Perfect Capacity vs. One Resource with Uncertainty (1000 MW out of 31000 MW)

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Cumulative Distribution For Discrete OutagesAssumed 31 1000 MW resources with 5% Unavailability

No Resource Uncertainty With One 1000 MW Unit Uncertain



Normal Approximation of Capacity Outages

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No Resource Uncertain ty With 31 1000 MW Units Uncertain Normal Approximation o f Resource Outages

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Density Distribution of Capacity Outages

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Cumulative and Density Distribution For Discrete OutagesAssumed 31 1000 MW Resources with 5% Unavailability

No Resource Uncertain ty With 31 1000 MW Units Uncertain

Normal Approximation o f Resource Outages

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Availability Capacity Density Distribution

Distributions of Daily Peak LoadsCombined Density Distribution For

Seven Summer Weeks

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With uncertainty, more resources than 31,000 MW are neededNote: This load distribution represents 35 weekdays

Available Resource Distributions

With no resource uncertainty only 31,000 MW needed

Loss of Load> 0.1 days/year

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Effect of Resources with Different EFOR

• Equivalent Forced Outage Rate (EFOR) is a statistic that describes the probability of finding a resource in a state – Available or – Unavailable

• With 100 percent available resources (EFOR = 0%)– “Fewer” resources needed to meet peak loads with a given LOLE

• With 70 percent available resources (EFOR = 30%)– “More” resources needed to meet peak loads with a given LOLE

• With a variety of resources with different EFOR statistics– Each resource’s contribution to meeting peaks can be quantified

• Removing any resource will mean that the peak load that could be served, at a given LOLE, must decrease

• Can be expressed in terms of the MW effect of the reserve margin

42



Available Capacity Cumulative Distribution


Seven Summer Weeks

0.0000

0.0000

0.0000

0.0001

0.0001

0.0001

0.0001

0.0001

0.0002

0.0002

0.0002

1500

0

1600

0

1700

0

1800

0

1900

0

2000

0

2100

0

2200

0

2300

0

2400

0

2500

0

2600

0

2700

0

2800

0

2900

0

3000

0

3100

0

3200

0

3300

0

3400

0

Load Level (MW)

Pro

bab

ilit

y D

ensi

ty f

or

Lo

ad

0.00000

0.20000

0.40000

0.60000

0.80000

1.00000

1.20000

Cu

mu

lati

ve P

rob

abil

ity

fo

r A

vail

able

Cap

acit

y


Note: This load distribution represents 35 weekdays LOLP for seven week composite distribution and cumulative capacity

35,000 MW Minimum Installed Resources

Loss of Load = 0.1 days/year

43



0.00000

0.20000

0.40000

0.60000

0.80000

1.00000

1.20000

0.0000

0.0000

0.0000

0.0001

0.0001

0.0001

0.0001

0.0001

0.0002

0.0002

0.0002

1500

0

1600

0

1700

0

1800

0

1900

0

2000

0

2100

0

2200

0

2300

0

2400

0

2500

0

2600

0

2700

0

2800

0

2900

0

3000

0

3100

0

3200

0

3300

0

3400

0

Cu

mu

lati

ve P

rob

abil

ity

fo

r A

vail

able

Cap

acit

y

Pro

bab

ilit

y D

ensi

ty f

or

Lo

ad

Load Level (MW)


Seven Summer Weeks

Sum m er Peak Week Available Resources

Effect of Base Resources with High EFOR

LOLP for seven week composite distribution and cumulative capacityNote: This load distribution represents 35 weekdays

Installed Resources

Loss of LoadIncreases

44



0.00000

0.10000

0.20000

0.30000

0.40000

0.50000

0.60000

0.70000

0.80000

0.90000

0.0000

0.0000

0.0000

0.0001

0.0001

0.0001

0.0001

0.0001

0.0002

0.0002

0.0002

1500

0

1600

0

1700

0

1800

0

1900

0

2000

0

2100

0

2200

0

2300

0

2400

0

2500

0

2600

0

2700

0

2800

0

2900

0

3000

0

3100

0

3200

0

3300

0

3400

0

Cu

mu

lati

ve P

rob

abil

ity

fo

r A

vail

able

Cap

acit

y

Pro

bab

ilit

y D

ensi

ty f

or

Lo

ad

Load Level (MW)


Seven Summer Weeks


Adding Resources Returns Risk to TargetAdjusted Minimum Installed Resources

Loss of Loadreturned to 0.1 days/year


45



Effect of Base Resources with Low EFOR

0.00000

0.20000

0.40000

0.60000

0.80000

1.00000

1.20000

0.0000

0.0000

0.0000

0.0001

0.0001

0.0001

0.0001

0.0001

0.0002

0.0002

0.0002

1500

0

1600

0

1700

0

1800

0

1900

0

2000

0

2100

0

2200

0

2300

0

2400

0

2500

0

2600

0

2700

0

2800

0

2900

0

3000

0

3100

0

3200

0

3300

0

3400

0

Cu

mu

lati

ve P

rob

abil

ity

fo

r A

vail

able

Cap

acit

y

Pro

bab

ilit

y D

ensi

ty f

or

Lo

ad

Load Level (MW)


Seven Summer Weeks


Minimum Installed Resources


Loss of Loaddecreased

46



0.00000

0.20000

0.40000

0.60000

0.80000

1.00000

1.20000

0.0000

0.0000

0.0000

0.0001

0.0001

0.0001

0.0001

0.0001

0.0002

0.0002

0.0002

1500

0

1600

0

1700

0

1800

0

1900

0

2000

0

2100

0

2200

0

2300

0

2400

0

2500

0

2600

0

2700

0

2800

0

2900

0

3000

0

3100

0

3200

0

3300

0

3400

0

Cu

mu

lati

ve P

rob

abil

ity

fo

r A

vail

able

Cap

acit

y

Pro

bab

ilit

y D

ensi

ty f

or

Lo

ad

Load Level (MW)


Seven Summer Weeks


Removing Resources Returns Risk to TargetAdjusted Minimum Installed Resources


Loss of Loadreturned to 0.1 days/year

47



Calculation Techniques

• Preceding illustration suggests an analytical solution– Numerical solution to intersection of distributions– Adjustment to loads or resources done first then LOLP calculated

• Illustration could be done with a Monte Carlo simulation– Monte Carlo representation would require many “draws” or

“replications” to represent the distributions– Easier to reflect conditionality (explicit correlation) with a state

specific representation– Interface constraints can be easily represented

• Interface constraint modeling can quantify when an interface limit causes a loss of load that would not otherwise occur

• Subdividing an area into several sub-area now requires monitoring and understanding relationships between multiple indices

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Load Model Development for MARS

• Load Models– Loads in the Westinghouse / ABB model are input as continuous

mathematical functions• Includes low probability, higher loads

• Includes all loads (i.e., 30/70 … 50/50 … 60/40 … 90/10 … 95/05 …)

– Loads in MARS are input as discrete 8760 hourly loads• When representing a future year, highest load is 50/50

• Need to reflect larger range of possible loads

• This is done using Load Forecast Multipliers (LFU)– Seven pairs of “scaling factor” and “associated probability”– These pairs are optimized to replicate the high loads in the load model– Each replication year is now seven cases with different load levels that,

probabilistically, are summed to represent one year

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Discrete Load Model Before Load Forecast Uncertainty Multipliers

50

Cumulative Daily Peak Load Distribution for Month

Based on Discrete Loads

0.500.550.600.650.700.750.800.850.900.951.00

15000 16000 17000 18000 19000 20000 21000 22000 23000

Load (MW)

Pro

bab

ility

Load Distribution



Load Model After Load Forecast Uncertainty Multipliers

51

Peak Load Distribution for Week

Probability of Load or Higher

0.0000.1000.2000.3000.4000.5000.6000.7000.8000.9001.000

15000 17000 19000 21000 23000 25000 27000 29000

Load (MW)

Pro

bab

ility

Load Distribution

DRAFT

Sub-Area / Multi-Area LOLE Indices



Multi-Area LOLE Index Characteristics

• Understanding LOLE index characteristics is important– “Control area” level LOLE indices to be used

• “Control area” indices based on individual sub-area LOLE indices

• Union of LOLE events across all sub-areas of a control area

– A “high” sub-area LOLE index may, or may not be indicative of a sub-area resource adequacy problem

• Initial resource and load balance in a sub-area– Will influence where an LOLE ‘hit’ will be assigned– Could be a sub-area problem or a control-area wide shortage

• Comparison of “Control Area” LOLE and “Sub-Area” LOLE with Venn diagrams can provide insight

53

Total area LOLE of 0.1 days per year

Total area LOLE Sub-area LOLE



Multi-Area LOLE Index Characteristics (cont.)

• Adding capacity in one area (or sub-area) – Will improve the LOLE index of that area the most– Will improve the LOLE of other areas

• Amount of improvements will depend on number of joint shortages

• Any intervening transmission constraints

• Sharing and priority rules can affect where benefits are “steered”

54

Total area LOLE becomes less than 0.100 days per year

Capacity added to “yellow” area

Total area LOLE of 0.1 days per year



Sub-Area LOLE Index Characteristics

• Generation only sub-area (no load) always has zero LOLE

• For a sub-area that has only load and no generation

– LOLE ‘hit’ will occur whenever there is a control area wide shortage

– LOLE ‘hit’ will NOT occur if another part of the control area is short and this sub-area is “export” constrained to the “short” area

• For a sub-area with BOTH load and resources

– LOLE ‘hit’ will occur whenever there is a control area wide shortage and the sub-area is deficient in that shortage hour

– LOLE ‘hit’ will NOT occur if the area is initially not in shortage

• Control area to control area considerations

– If control area has sufficient resources

• It will satisfy its own loads first

• Before providing assistance to other control areas

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Understanding a Sub-Area Index

• Four sub-areas with no constraints– One sub-area has only generation– One sub-area has only load– Two sub-areas have balance of both

MARS Index Example

Little GenSome Load

More GenSome Load

All GenNo Load

No GenAll Load

Sub Area Iter 1 Iter 2 Iter 3 Iter 4 Iter 5 Iter 6 AverageResource

Q 1100 1100 900 1100 700 900R 0 0 0 0 0 0S 350 450 510 450 510 490T 549 355 549 450 549 549

LoadQ 0 0 0 0 0 0R 1000 1000 1000 1000 1000 1000S 500 500 500 500 500 500T 500 500 500 500 500 500

Surplus MW -1 -95 -41 0 -241 -61Pool LOLE Yes Yes Yes No Yes Yes

Pool LOLE 'Hit' 1 1 1 0 1 1 0.83Q LOLE 'Hit' 0 0 0 0 0 0 0.00R LOLE 'Hit' 1 1 1 0 1 1 0.83S LOLE 'Hit' 1 1 0 0 0 1 0.50T LOLE 'Hit' 0 1 0 0 0 0 0.17

56

T

Q R

S

R = 0.83S = 0.50T = 0.17Q = 0.00

Venn Diagram for this example



Multiple Control Area LOLE Indices

• Indices for multiple control areas calculated identically– LOLE for each control areas could be brought to 0.100 days/year

• Sometimes Area ‘X’ is deficient and sometimes Area ‘Y’ is deficient

• Sometimes both are deficient simultaneously

• Union of all events for combined XY area may be 0.162 days per year– Adding more capacity to combined area XY

• Could bring the LOLE of XY area to 0.100 days per year

• Individual area LOLE would then be less than 0.10 days per year

• Capacity could be added in either area X or area Y if there is no area criterion

– An area specific criterion may require some capacity to be added in each– No transmission constraints are even considered at this stage

57

X YEach area LOLE is 0.100 days per year

X YUnion of LOLE forBoth is 0.162 days per year



Multiple Control Area and Tie Benefits

• Other areas, say area “Z,” can provide tie benefits to– Area “X” (preference) or – Area “Y” (preference)– Both areas “X” and “Y” (no preference)

• Transmission interface from “Y” to “X” could affect the sharing of tie benefits from “Z”– If areas “X” and “Y” are deficient at the same time,– Some of the tie benefits that would have been shared with “X” can’t get

there and “Y” get a disproportionate share of the benefits

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X Y Z



Contract Modeling

• Multi-Area models can represent contracts between control areas– Define originating sub-area– Define destination sub-area– Designate a transmission interface link as the contract path

• Removal / Transfer reduction of contract path– Contract flow has priority rights on contract path link– Uses as much transmission capacity as necessary

• Contracting allows for improving reliability in one area vis-à-vis another area– Contracted capacity treated as the exporter’s native load– Contracted capacity treated as the importer’s native capacity

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Monte Carlo Indices

• Monte Carlo simulations are the result of many replications– Some replications have un-resolvable shortages– Shortages require loss of customer loads– Shortages are the basis of a Loss of Load event

• With 10,000 years replicated (365 days per year at risk)– If 1,000 days result in shortages

LOLE = (1000 days with Loss of Load) / (10,000 years)

LOLE = 0.100 days per year

• Convergence criterion for a Monte Carlo– Tells the model that enough replications have been done– Resulting index is “stable” (as defined by the criterion)

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Monte Carlo: Year-to-Year Variability

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Distribution of Loss of-Load Days in 10,000 Simulated Years

(1000 Loss-of-Load-Days => Expectation of 0.100 Days/Year)

0

20

40

60

80

100

120

1 6 11 16 21 26 31 36 41 46

Number of Loss-of-Load-Days Lost in Simulated Year

Occ

ura

nce

s o

f T

his

Man

y D

ays

0.100 days per year (expected value)

Goes out to10,000 years



Bringing an Area to Criterion: Resources

• Add or remove generation– Specific resources would need to be added or removed– Each resource has its own characteristics

• Size

• EFOR

– Depending upon resource characteristics, the effect of one MW may not be equal to a different MW

• If future, unspecified, resource additions are needed– A proxy units is used– Characteristics are “typical” of the rest of the system– Neutral impact on an area’s reserve metric (i.e., reserve margin)

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Bringing an Area to Criterion: Loads

63



Deliverability

• All resources are assumed to be fully deliverable within a sub-area– Resources are assumed able to put capacity up on the grid– Deliverability between sub-areas are assumed to be limited only

by pre-specified transmission interface limits– Load within a sub-area is assumed able to receive and distribute

energy / capacity from the grid to customers

• Real world conditions may affect the validity of these assumptions depending on the actual system configuration

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Basic Resource Adequacy Study Concepts

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