Final Presentation

MATLAB® Modelling of Capacity Outage

Probability Table for Transmission Systems

By:By:Abhishek Chakraborty (1MJ06EE001)Abhishek Chakraborty (1MJ06EE001)

Apurva Joshi (1MJ06EE005)Apurva Joshi (1MJ06EE005)Himanshu Mishra (1MJ06EE012)Himanshu Mishra (1MJ06EE012)

Prashobh Mohan P. (1MJ06EE026)Prashobh Mohan P. (1MJ06EE026)

Dept. of Electrical and Electronics Engineering

M.V.J. College of Engineering

External Guide:Shri V.V.S.K. ChakravarthiShri V.V.S.K. ChakravarthiEngg. Officer Gr. 2

Internal Guide:Dr. B.N. SarkarDr. B.N. SarkarProfessor

IntroductionIntroduction

• Power Systems designed to provide reliable and

economic supply of electrical energy to

customers.

• Redundancy: How much & at what cost?

• Power System Planning: To resolve the dilemma

between economic and reliability constraints.

Power System PlanningPower System Planning

Power SystemPlanning

DeterministicApproach

ProbabilisticApproach

Power System Planning:Power System Planning:Deterministic ApproachDeterministic Approach

• Generating Capacity: Installed capacity equals the expected maximum demand

• Operating Capacity: Spinning capacity equals expected load demand plus a reserve equal to one or more largest units

• Network Capacity: Construct a minimum number of circuits to a load group

Power System Planning:Power System Planning:Probabilistic ApproachProbabilistic Approach

• Forced Outage Rates (FOR) of generating units is a

function of unit size and type

• The failure rate of an overhead line is a function of

length, design, location, and environment

• Planning and operating decisions are based on load

forecasting techniques

Best Approach: ProbabilisticBest Approach: Probabilistic• Probabilistic Techniques deals with cases

which are stochastic in nature

• Instills more objective assessment in decision

making process

• Why was it not used before?

– Lack of data, limitations of computing resources, lack of

realistic reliability techniques, aversion to the use of

reliability and probability techniques.

Power System Nature: StochasticPower System Nature: Stochastic

• Failure of components, plants and systems occur randomly

• Frequency, duration, and impact of failures vary from year to year

• Following data are useful for Probabilistic Approach:– System Availability– Number of incidents and hours of interruption– Excursions beyond system voltage and frequency limits

These performance measures are These performance measures are valuable because they:valuable because they:

• Identify weak areas needing reinforcement or modifications.

• Establish chronological trends in reliability performance.

• Enable previous predictions to be compared with actual operating experience.

• Monitor the response to system design changes .

Basic Approach: Adequacy Evaluation

Generation Model Load Model

Risk Model

OBJECTIVE:

Basic System Representation

Total System Generation Total System Load

Transmission lines

Hierarchical Levels

Generation Facilities

Transmission Facilities

Distribution Facilities

Hierarchical Level I(HL I)

Hierarchical Level II(HL II)

Hierarchical Level III(HL III)

Capacity Outage Probability Table

• Simple array of capacity levels and the

associated probabilities of existence.

• Considers all the possible combinations of

generating units and transmission lines.

Component States

Unit Up(0)

Unit Down(1)

Failure

Repair

Example

• Consider a plant with 3 x 5 MW units.

• Each unit has a FOR of 0.02.

• Therefore,

Individual Availability = 1 – 0.02 = 0.98.

Single Line Diagram

5 MW

5 MW

5 MW

Load

Availability = 0.98

Availability = 0.98

Availability = 0.98

Capacity Outage Probability TableSr. No. Capacity Out

of service(MW)

Capacity in service(MW)

Individual Probability

Cumulative Probability

1. 0 15 0.941190 1.000000

2. 5 10 0.057624 0.058808

3. 10 5 0.001176 0.001184

4. 15 0 0.000008 0.000008

How was the COPT formulated?

Sr. No.

Capacity Out of service(MW)

Capacity in

service(MW)

Probability Cumulative Probability

1. 0 15 0.98 x 0.98 x 0.98 = 0.941190 1.000000

2. 5 10 3C1 x 0.98 x 0.98 x 0.02 = 0.057624

0.058808

3. 10 5 3C2 x 0.98 x 0.02 x 0.02 = 0.001176

0.001184

4. 15 0 0.02 x 0.02 x 0.02 = 0.000008 0.000008

Computation of COPT when generating units are not identical

15 MW

10 MW

5 MW

Load

Availability = 0.98

Availability = 0.97

Availability = 0.96

TRUTH TABLECase No: Unit1(15mw) Unit2(10mw) Unit3(5mw)

1. 0 0 0

2. 0 0 1

3. 0 1 0

4. 0 1 1

5. 1 0 0

6. 1 0 1

7. 1 1 0

8. 1 1 1

Unit available = 0 Unit unavailable = 1

Final COPTSL no Capacity in

Service, MWCapacity out of Service, MW

Individual Probability

Cumulative Probability

1. 30 0 0.912576 1.000000

2. 25 5 0.038024 0.087424

3. 20 10 0.028224 0.049400

4. 15 15 0.019800 0.021176

5. 10 20 0.000776 0.001376

6. 5 25 0.000576 0.000600

7. 0 30 0.000024 0.000024

Transmission line Network

Plant No. of Units Capacity

(MW)

Unavailabilit

y

1 4 20 0.01

2 2 30 0.05

Total 6 140

Generation Data:

Line Availability Unavailability

1 0.99636033 0.00363967

2 0.99545455 0.00454545

3 0.99658703 0.00341297

Transmission Line Statistics:

NETWORK CONFIGURATIONS

COPT for Transmission linesState Lines out Probability

1 0 0.98844633

2 1 0.00361076

3 2 0.00451345

4 3 0.00339509

5 1,2 0.00001649

6 1,3 0.00001237

7 2,3 0.00001546

8 1,2,3 0.00000006

Combined COPT(Generation and Transmission)

Total System Load

Transmission lines

Total System Generation

Data Required

Total Generation = 6 x 40 MW

Each having Availability of 0.98

Individual line carrying capacity of 160 MW

Generation COPTSTATE NO. OF

GENERATORS ON OUTAGE

CAPACITY AVAILABLE

PROBABLITY

1 0 240 0.88584238

2 1 200 0.10847049

3 2 160 0.00553421

4 3 120 0.00015059

5 4 80 0.00000230

6 5 40 0.00000002

7 6 0 0.00000000

State Probability of Transmission Lines

STATE NO. OF LNES ON OUTAGE

CAPACITY AVAILABLE

MW

PROBABLITY

1 0 320 0.999144

2 1 160 0.999574

3 2 0 0.000428

Combined COPTSTATE CONDITION CAPACITY

AVAILABLE MW

PROBABILITY

1 0G 0L 240 0.88508444

2 0G 1L 160 0.00075778

3 0G 2L 0 0.00000016

4 1G 0L 200 0.10837768

5 1G 1L 160 0.00009279

6 1G 2L 0 0.00000002

7 2G 0L 160 0.00552947

8 2G 1L 160 0.00000473

9 2G 2L 0 0.00000000

10 3G 0L 120 0.00015046

11 3G 1L 120 0.00000013

12 3G 2L 0 0.00000000

13 4G 0L 80 0.00000230

STATE CONDITION CAPACITY AVAILABLE MW

PROBABLITY

14 4G 1L 80 0.00000000

15 4G 2L 0 0.00000000

16 5G 0L 40 0.00000002

17 5G 1L 40 0.00000000

18 5G 2L 0 0.00000000

19 6G 0L 0 0.00000000

20 6G 1L 0 0.00000000

21 6G 2L 0 0.00000000

Single Line Diagram of the Roy Billinton Test System (RBTS)

Generating Unit Locations

Unit No. Bus Rating Type

1 1 40 Thermal

2 1 40 Thermal

3 1 10 Thermal

4 1 20 Thermal

5 2 5 Hydro

6 2 5 Hydro

7 2 40 Hydro

8 2 20 Hydro

9 2 20 Hydro

10 2 20 Hydro

11 2 20 Hydro

System Reliability Data

Unit Size Type No. of Units Forced Outage Rate

5 Hydro 2 0.010

10 Thermal 1 0.020

20 Hydro 4 0.015

20 Thermal 1 0.025

40 Hydro 1 0.020

40 Thermal 2 0.030

System Line Data

Line

Buses Impedance (p.u.)CurrentRating(p.u.)From To R X B/2

1,6 1 3 0.0342 0.180 0.0106 0.85

2,7 2 4 0.1140 0.600 0.0352 0.71

3 1 2 0.0912 0.480 0.0282 0.71

4 3 4 0.0228 0.120 0.0071 0.71

5 3 5 0.0228 0.120 0.0071 0.71

8 4 5 0.0228 0.120 0.0071 0.71

9 5 6 0.0228 0.120 0.0071 0.71

System Bus Data

BusLoad (p.u.)

ScheduledGeneration

(p.u.)Qmax Qmin Vint Vmax Vmin

P Q

1 0.00 0.00 1.0 0.50 -0.40 1.05 1.05 0.97

2 0.20 0.00 1.2 0.75 -0.40 1.05 1.05 0.97

3 0.85 0.00 0.0 0.00 0.00 1.00 1.05 0.97

4 0.40 0.00 0.0 0.00 0.00 1.00 1.05 0.97

5 0.20 0.00 0.0 0.00 0.00 1.00 1.05 0.97

6 0.20 0.00 0.0 0.00 0.00 1.00 1.05 0.97

The Algorithm – “Reliability.m”

• Step 1: Start

• Step 2: Input Line Data, Bus Data, Availability

Details for all components

• Step 3: Call “GeneratorCOPT.m”

The Algorithm – “GeneratorCOPT.m”

• Step 1: Retrieve No. of Units, Power Rating of each unit,

Availability of each unit

• Step 2: Form Truth Table to accommodate all states

• Step 3: Initialize matrix such that

– Column 1: Capacity in service

– Column 2: Capacity Out of service

– Column 3: State Probability

– Column 4: Cumulative Probability


• Step 4: Initialize counter i = 0

• Step 5: Check all elements of ith row

– If element is 0, add generator rating to column 1

and multiply availability to column 3

– If element is 1, add generator rating to column 2

and multiply unavailability to column 3


• Step 6: Add all similar capacities

• Step 7: Sort the table in descending order of

available capacities. Truncate the table.

• Step 8: Return table to main program

Reliability

Comparing Results

Input Data

Formation of Truth Table

0 – Unit Available1 – Unit Unavailable

Unit 1 Unit 2 Unit 3

Initialization of COPT matrix

Capacity Out of ServiceState ProbabilityCapacity In Service Cumulative Probability

Forming the Crude COPT

PR: Power Rating of the unitA: Availability of unit

Counter ‘i’

Unit 1: ‘Available’3 MW

Working of the loop

Working of the loop

Capacity In Service State Probability

Counter ‘i’


Working of the loop

Working of the loop


Counter ‘i’


Working of the loop

Working of the loop


Counter ‘i’



Unit 3: ‘Unavailable’5 MW

Working of the loop

Working of the loop

Capacity Out of Service State Probability

Counter ‘i’

Working of the loop

Counter ‘i’

Counter ‘i’

Counter ‘i’

Counter ‘i’

Counter ‘i’

Counter ‘i’

Counter ‘i’

Working of the loop

Adding the similar capacities

Working of the loop

Sorting the table

Truncating the table

Function PathFinder()PathFinder()

• 1 is the Start Node• 4 is the End Node

1 2

3 4

Function

PathFinder()

Finds all the possible

paths between the:

Start Node

and the

End Node

of a given Network

Step I: Adjacency Matrix

Adjacency Matrix:1 22 33 4

1 00 1 1 122 1 00 0 133 1 0 00 14 1 1 1 00

1 2

3 4

ith Node is Connected to jth Node; Adjacency (i,j) Adjacency (i,j) = 1

ith Node is Not Connected to jth Node; Adjacency (i,j)Adjacency (i,j) = 0

MATLAB® Code

Step II: Truth Table

• Start Node and End Node must be present

11 22 33 441 11 1 11 1 0 11 0 1 11 0 0 1

1 2

3 4

MATLAB® Code

Step III: Permutations for Each Case

• Case 1: 2: Present3: PresentBy Permutation:11 22 33 4411 33 22 44

1 2

3 4

11 22 33 44Refer Adjacency Matrix:

Adjacency (1,2)=1

Adjacency (2,3)=0

Adjacency (3,4)=1

11 33 22 44Refer Adjacency Matrix:

Adjacency (1,3)=1

Adjacency (3,2)=0

Adjacency (2,4)=1

• Case II:2: Present3: AbsentBy Permutation:11 22 44

1 2

3 4

1 2

3 4

• Case III:2: Absent3: PresentBy Permutation:11 33 44

11 22 44Refer Adjacency Matrix:

Adjacency (1,2)=1

Adjacency (2,4)=1

11 33 44Refer Adjacency Matrix:

Adjacency (1,3)=1

Adjacency (3,4)=1

• Case IV:2: Absent3: Absent

By Permutation:11 44Refer Adjacency Matrix:

Adjacency (1,4)=1

1 2

3 4

Possible Paths are:1 2 41 3 41 4

1 2

3 4

MATLAB® Code

Adds the name of the Node

Permutations

MATLAB® Code

Refers Adjacency Matrix for existence of path

Function CompositeCOPT()CompositeCOPT()

• Function CompositeCOPT() CompositeCOPT() finds Capacity Outage Probability Table for Hierarchical Level II System

• Calls function PathFinder()PathFinder() to find all the suitable transmission paths connecting to a particular load bus

• Calls function NewtonRaphsonLF()NewtonRaphsonLF() to perform AC load flow studies, to check line flow limit violations

Brief Description

• 11 Generator Bus

• 55 Load Bus

• 11224455:

Transmission Path in

Service.

1 2

43

5

• COPT of Bus 1 with Bus 2 are combined, considering transmission line availability in between

• Violation of line capabilities are checked

• This is then reduced to a Single Node, having a Single COPT

• This is repeated till the load bus is reached

1 2

43

5

1 2

4

5

COMBINECOMBINE

1122

4

5

AA

1122

4

5

AA

A4

5

BBCOMBINECOMBINE

A4

5

BB11224455

COPTCOPTCOMBINECOMBINE

MATLAB® Code

Formation of combined COPT

Loading COPT of Node 2

Loading COPT of Node 1Calling function PathFinder

MATLAB® Code

Bubble Sort

Combining Probabilities of Like States

MATLAB® Code

OUTPUT: LOAD FLOW

OUTPUT: COMPOSITE SYSTEM COPTFOR LOAD BUS 3:

STATE PROBABILITY FOR THE TRANSMISSION PATH: 1 3___________________________________________________________________CAPACITY AVAILABLE CAPACITY UNAVAILABLE PROBABILITY (MW) (MW) -------------------------------------------------------------------110 0 0.88104935100 10 0.0179806090 20 0.0225910180 30 0.0004610470 40 0.0544979060 50 0.0011122050 60 0.0013973840 70 0.0000285230 80 0.0008427520 90 0.0000172010 100 0.000021610 110 0.00000044

CONCLUSION

• It was desired to develop the Capacity Outage Probability Table for a composite Generation and Transmission System.

• The following studies have been made in that connection:– COPT for a power system has been formed taking

into consideration the generation and transmission facilities.

CONCLUSION

– The COPT so developed has been verified for several cases as available in the published literature

– MATLAB® Software has been used to execute the programme

– Using the designed programme, the COPT for any general system can be formulated

– However, the limitation for the programme is that the system should contain not more than 20 transmission lines.

FUNCTIONS APPROVED BYM/s. MathWorks

• COPT for Hierarchical Level I Studies:http://www.mathworks.com/matlabcentral/

fileexchange/27599-generator-capacity-outage-probability-table

• Function “PathFinder”:http://www.mathworks.com/matlabcentral/

fileexchange/27438-find-all-the-possiblepaths-between-a-start-and-an-end-node-of-a-graph

REFERENCE: TEXTBOOKS

• Billinton R., Allan R.N., ‘Reliability Evaluation of Power Systems’, Second Edition, Plenum Press, New York, 1996.

• Billinton R., Allan R.N., ‘Reliability Evaluation of Engineering Systems’, Second Edition, Plenum Press, New York, 1992.

• Billinton R., ‘Power System Reliability Evaluation’, Gordon and Breach Science Publishers, New York, 1970.

REFERENCE: PAPERS

• Billinton R., Karki B., Karki R., Gokaraju R., ‘Operating Reserve

Assessment of Wind Integrated Power Systems’, Power System Research

Group, University of Saskatchewan, Canada.

• R. Billinton, S. Kumar, N. Chowdhury, K. Chu, K. Debnath, L. Goel, E.

Khan, P. Kos, G. Nourbakhsh, J. Oteng-Adjei, ‘A Reliability Test System

For Educational Purposes – Basic Data’, IEEE Transactions On Power

Systems, Vol. 4, No. 3, August 1989

• R. Billinton, S. Kumar, N. Chowdhury, K. Chu, K. Debnath, L. Goel, E.

Khan, P. Kos, G. Nourbakhsh, J. Oteng-Adjei, ‘A Reliability Test System

For Educational Purposes – Basic Results’, IEEE Transactions On Power

Systems, Vol. 5, No. 1, February 1990

Thank You!!

MATLAB PROGRAMME

C:\MATLAB7\bin\win32\MATLAB.exe

Final Presentation

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