PROBABILISTIC APPLICATIONS INPOWER SYSTEM PLANNING

Roy Billinton

University of SaskatchewanCANADA

2

Plan – “a proposed or intended course of action”

Planning – “the act of creating a plan or plans”Planning

Future Uncertainty

3

In order to consider “Uncertainty”

Planning criteria and processes can be designated as being:

“Deterministic” or “Probabilistic”

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“Deterministic”

To determine: to fixto resolveto settleto regulateto limitto define

- adjective

% Reserve( N-1 )Worst case condition

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“Probabilistic”

Probability – likelihood of an event, the expected relative frequency of occurrence of a specified eventin a very large collection of possible outcomes.

- adjective

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Probability a quantitative measure of the likelihood of an event.

a quantitative measure of the uncertainty associated with theevent occurring.

a quantitative indicator ofuncertainty.

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PROBABILISTIC APPLICATIONS IN POWER SYSTEM PLANNING

Quantitative incorporation of uncertainty in power system planning applications.

Task – to satisfy the future load requirement as economically as possible with a reasonable assurance of continuity and quality.

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HL I

HL III

HL II

Hierarchical Levels

9

Hierarchical Level I – HL-I

Classical generating capacity planning

Task – plan a generating system to meet the system loadrequirement as economically as possible with anacceptable level of reliability.

GR

GRemote Capacity

External CapacityLoad CharacteristicsUncertainty

Generation Alternatives• Fossil• Hydro• Nuclear• Gas• Renewables

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Risk Evaluation

Generation Load

RiskLoss of Load Expectation (LOLE)Loss of Energy Expectation (LOEE)Frequency & Duration (F&D)Other Indices

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Example Reliability Criterion – NERC Region XXX

“Sufficient megawatt generating capacity shall be installed to ensure that in each year for the XXX system the probability of occurrence of load exceeding the available generating capacity shall not be greater, on the average, than one day in ten years. Among the factors to be considered in the calculation of the probability are the characteristics of the loads, the probability of error in load forecast, the scheduled maintenance requirements for generating units, the forced outage rates of generating units, limited energy capacity, the effects of connections to the pools, and network transfer capabilities within the XXX systems.”

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Comparison of Alternatives Based on System Cost

• Implicit Cost Approach

Lowest overall cost (capital plus maintenance and operating costs) are compared using a fixed reliability criterion.

• Explicit Cost Approach

Lowest overall cost including the societal costs of unreliability.

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Implicit Cost Approach

LOLELOEE

Peak Load

Criterion

C1 C2

IPLCC

IPLCC – Incremental Peak Load Carrying Capability

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Explicit Cost Approach

Reliability

Cos

t

Optimum

Total cost

Utility costCustomer cost

Reserve Margin

xxxxxRopt

Overall Cost

Customer CostCustomer Outage Cost

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Renewable energy sources, such as wind and solar power, behave quite differently than conventional generation facilities.Consider wind as an example: Wind Energy Conversion System (WECS)

Wind Speed (km/h)Po

wer

Out

put (

MW

)

Pr

Vci Vr Vco

01020304050

1 25 49 73 97 121 145Time (hour)

Pow

er O

utpu

t (M

W)

Year 1 Year 2

0102030405060

1 25 49 73 97 121 145Hour

Win

d S

peed

(k

m/h

)

Year 1 Year 2

Wind speeds & power outputs from two consecutively simulated years (the first week of January)

Power Curve Parameters:Cut-in speed (Vci) = 14.4 km/hRated speed (Vr) = 36.0 km/hCut-out speed (Vco) = 80.0 km/h

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0

0.01

0.02

0.03

0.04

0.05

0 14 28 42 56Wind Speed (km/h)

Pro

babi

lity

0

0.2

0.4

0.6

0.8

1

1.2

Pow

er O

utpu

t (p.

u.)

ProbabilityPower Output

Avg.= 19.4 km/h, S.D.= 10.1 km/h

Year 1

0

0.01

0.02

0.03

0.04

0.05

0 14 28 42 56Wind Speed (km/h)

Pro

babi

lity

0

0.2

0.4

0.6

0.8

1

1.2

Pow

er O

utpu

t (p.

u.)

ProbabilityPower Output

Avg.= 19.6 km/h, S.D.= 10.8 km/h

Year 2

Probability distributions of annual wind speeds for two simulated years

0.000.050.100.150.200.250.300.35

0 4 8 12 16 20 24 28 32 36 40Power Output (MW)

Pro

babi

lity

Average = 9.56 MWCapacity credit = 0.24

Year 1

0.000.050.100.150.200.250.300.35

0 4 8 12 16 20 24 28 32 36 40Power Output (MW)

Pro

babi

lity

Year 2

Average = 10.10 MWCapacity credit = 0.25

Probability distributions of annual power outputs for two simulated years

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The power output of a WECS can be incorporated in a probability analysis.

0

1

2

3

4

5

6

7

8

0 50 100 150 200 250 300 350 400 500 700

WTG Total Capacity (MW)

LOLE

(Hou

r/ye

ar)

North Battleford Saskatoon ReginaSystem: IEEE-RTSIC = 3,405 MWPL = 2,850 MW

Sequential Monte Carlo Simulation approach:Auto-Regressive Moving Average (ARMA) time series model

Analytical or State Sampling Monte Carlo approaches:Multi-state WECS model

LOLE vs. WTG Capacity

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R

epla

cem

ent R

atio

Single Wind Site 2 Wind Sites 3 Wind Sites

Not Available (Single Wind Site) Not Available (2 Wind Sites)

0 2 4 6 8

10 12

12MW UnitRemoved

50MW UnitRemoved

100MW UnitRemoved

350MW UnitRemoved

Replacement ratio versus the capacity removed from the IEEE-RTS (single, two and three wind farms)

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Generating capacity planning has changed considerably due to DEREGULATION and OPEN TRANSMISSION ACCESS.

Greater system uncertainty now exists due to underlying uncertainties in business conditions and opportunities for independent power production.

This increased uncertainty also extends to HL-II and the planning of associated transmission facilities.

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There are many other areas of probabilistic application in HL-I. These include: Probabilistic production costing

Probabilistic unit commitmentProbabilistic assessment of hydroreservesProbabilistic assessment of spinning andoperating reservesProbabilistic assessment of renewableenergy reservesProbabilistic assessment of load servingentitiesProbabilistic of generation maintenance schedulingProbabilistic demand-side management

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Hierarchical Level II – HL-II (NH2)

Task – plan a bulk electric system (BES) to serve the load requirement at the BES delivery points as economically as possible with an acceptablelevel of reliability.

The system analysis is considerably more complicated at HL-II than at HL-I and the overall degree of uncertaintyis greater.

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Reliability

Adequacy Security

Existence of sufficient generation and transmis-sion facilities.

Ability to respond to system disturbances.

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IEEE-RTSBus 18 Bus

21Bus 22

Bus 17

Bus 16

Bus 19

Bus 20

Bus 23

Bus 13

Bus 12

Bus 11

Bus 24

Bus 3

Bus 9

Bus 10

Bus 6Bus 8

Bus 7

Bus 2

Bus 1

Bus 4

Bus 5

Bus 14Bus

15

30

31

32 33 38

363435 37

2928

242625 23

1918

21

20

16 17

15147

27

2

68

3

1

Cable1013

51211

9

4

22

Cable

230 kV

138 kV

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IEEE-RTS including Stations

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Composite System Reliability EvaluationAdequacy

Probability of Load Curtailment (PLC)Frequency of Load Curtailment (FLC)Expected Energy Not Supplied (EENS)Expected Customer Interruption Cost (ECOST)

Probability of Load Curtailment (SPLC)Frequency of Load Curtailment (SFLC)Expected Energy Not Supplied (SEENS)Expected Customer Interruption Cost (SECOST)Severity Index (SI)System Average Interruption Frequency Index (SAIFI)System Average Interruption Duration Index (SAIDI)

BES Load Point Indices:

BES Overall Indices:

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0

1000

2000

3000

4000

5000

6000

7000

8000

2850 MW 2907 MW 2964 MW 3021 MW

System Peak Load (MW)

EENS

(MW

h/ye

ar)

Bus 18Bus 19

02000400060008000

10000120001400016000

2850 MW 2907 MW 2964 MW 3021 MW

System Peak Load (MW)

EEN

S (M

Wh/

year

) System EENS

Load point EENS (Bus 18 & 19) for the IEEE-RTS at different system peak loads

System EENS for the IEEE-RTS at different system peak loads

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Composite system (HL-II) reliability assessment can be performed using:

Analytical methods:State enumeration

Monte Carlo techniques:State sampling (non-sequential)State duration sampling (sequential)

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0.00

0.10

0.20

0.30

0 1 2 3 4 5 6 7 8 9 10SAIFI (occ./yr.)

Prob

abili

ty

0%20%40%60%80%100%

FrequencyCumulative %Total (Priority)

Mean = 1.33S.D. =1.23

0.00

0.10

0.20

0.30

0 3 6 9 12 15 18 21 24 27SAIDI (hrs./yr.)

Prob

abili

ty

0%20%40%60%80%100%

FrequencyCumulative %Total (Priority)

Mean = 5.01S.D. = 5.97

The uncertainty associated with an annual BES index can be appreciated using index probability distributions

Probability distributions of SAIFI and SAIDI for the IEEE-RTS

Determined using state duration sampling (sequential) approach

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Performance Based Regulation (PBR)

0.5

1

Payment (p.u.)

Reliability Index

0

Reward zone

Penalty zone

2S.D.

2S.D.

2S.D.

2S.D.

Dead zone

Mean value

a b c d

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0

0.1

0 0.6 1.2 1.8 2.4 3 3.6 4.2 4.8SAIFI (occ./yr.)

Prob

abili

ty

0.0

1.0

PBR

(p.u

.)

Probability PBRMean = 1.33, S.D. = 1.23

ERP = + 0.0526 p.u.

Performance Based Regulation (PBR)

SAIFI distribution for the IEEE-RTS implemented in a PBR framework

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Security Based Adequacy Evaluation

Success

Healthy

Marginal

At Risk

System Well-Being Framework

Healthy state – all equipment and operating constraints are within limits and there is sufficient margin to serve the total load demand even with the loss of any element (i.e. N-1 deterministic criterion is satisfied.).

Marginal state – the system is still operating within limits, but there is no longer sufficient margin to satisfy the acceptable deterministic criterion.

At risk state – equipment or system constraints are violated and load may be curtailed.

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Security Based Adequacy Evaluation

Success

Healthy

Marginal

At Risk

System Well-Being Framework

System Well-Being Indices:

Prob{H} Freq{H}

Prob{M} Freq{M}

Prob{R} Freq{R}

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Security Based Adequacy Evaluation SuccessHealthy

Marginal

At RiskSystem Well-Being

Framework

Cliff

Healthy Marginal

At Risk

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Bulk system transmission planning in a deregulated open access environment introduces additional uncertainties including:

Market conditionsTransmission congestionPotential Co-Generation and IPPRenewable energy sources

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Consider the situation in which a wind farm is to be added to the IEEE-RTS.

What is the “best” transmission plan to accommodate this generation addition?

Bus 3

Bus 9

Bus 2Bus

1

Bus 4

Bus 5

16 15147

2

68

3

1

9

4

Cable

138 kV

Regina wind farm (x)

Swift Current wind farm (y)

Cross-correlation (Rxy) = 0.75

B.2 C.

2B.1

C.1

A

Alternative 1: Constructing Line AAlternative 2: Constructing Line B.1Alternative 3: Constructing Line C.1Alternative 4: Constructing Lines B.1 and B.2Alternative 5: Constructing Lines C.1 and C.2

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21.1919.8626.5021.5924.27DPUI (sys.mins)4.6094.3395.7404.7295.123ECOST (M$/yr)7.758.478.459.458.18EDLC (hrs/yr)2.883.533.054.012.77EFLC (occ/yr)

Alter. 5Alter. 4Alter. 3Alter. 2Alter. 1

Transmission Reinforcement AlternativeOverall SystemReliability

Indices

System reliability indices for the modified IEEE-RTS with the five transmission reinforcement alternatives

Probabilistic Reliability Evaluation

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There are many areas of probabilistic application in HL-II. These include: Probabilistic stability analysis

Probabilistic load flowProbabilistic fault analysisProbabilistic transfer capabilityProbabilistic assessment of voltagecollapseProbabilistic reactive and voltage controlsettingProbabilistic system expansion planningProbabilistic assessment in a powermarket (i.e. locational marginal price,bilateral transaction, etc.)

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Hierarchical Level III – HL-III

HL-III analysis is not usually conducted directly and HL-II values can be used as input parameters in a distribution system study.

Distribution system reliability evaluation is well established and relatively easily applied.

In a deregulated environment, customer supply can involve a number of entities and companies. It is important to be able to evaluate the contribution made by each entity to acceptable electric energy supply at the individual customer level.

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Probabilistic evaluation requires the consistent collection of relevant system and component data.

These data should be collected using comprehensive and consistent definitions thoroughly understood by the participating entities.

Planning involves looking into the future but it is important to appreciate that it is difficult if not impossible to determine where you want to go if you do not know where you have been.