Renewable integration to power systems.pptx

Impact of Increasing Renewable Energy
Developments on the Reliability of Power
Generating Systems
1

Introduction
 Renewable energy share is gradually increasing in many
power systems [1].
2
[1] World energy council, “World energy perspectives: renewable integrations 2016”, 2016.
Source- IRENA

3
Introduction
Source -http://www.ceb.lk/do-business-with-us/#tab-1439815407733-3-3

Introduction
 The intermittency of wind and solar power generation derogates power system
stability and reliability.
 The calculation of system reliability indices is complex with renewable energy
addition.
 The chronological characteristics of the renewable source and its effects on the
renewable power output should be taken in to the account.
 Intermittent and variable generation sources may not be best suited as base-
load plant, but contributing more to ancillary services, peak demand and
seasonal variations.[2]
4
[2] S. Butler, “The nature of UK electricity transmission and distribution networks in an intermittent renewable and embedded electricity generation future”. Imperial College of
Science, Technology and Medicine, Centre for Environmental Technology in collaboration with Parliamentary Office of Science and Technology, September 2001.[Online]. Available:
www.parliament.uk/post/e5.pdf. [Accessed May. 18, 2018].

Literature review- Overview of system reliability
5
Generation
systems reliability
Systems adequacy
assessment
Deterministic
approach
Reserve margin
Loss of largest unit
Probabilistic
approach
Monte Carlo
simulation
Sequential MCS
Non sequential
MCS
Analytical methods
Population based
models
Swarm
optimization
Genetic algorithms
Evolutionary
algorithms
Artificial immune
system
Ant colony system
Systems security
assessment
[3] L. Wang and C. Singh, "Population-Based Intelligent Search in Reliability Evaluation of Generation Systems With Wind Power Penetration," in IEEE Transactions on Power
Systems, vol. 23, no. 3, pp. 1336-1345, Aug. 2008.

System adequacy assessment
6
Generation
model
Load model
Risk of
Generation < Load
Reliability Indices
[4] R. N. Allan and R. Billinton, Reliability Evaluation of Power Systems, vol. 11. Springer Science & Business Media, 2013.[online] Available:
https://link.springer.com/book/10.1007%2F978-1-4899-1860-4#about.

Generation model
 2 state or multi state Markov model [1]
7
2 state model λ=failure rate μ=Repair rate
3 state model

 Capacity credit
The capacity value of wind power indicates the extent to which wind power
contributes to the generation system adequacy of a power system[5].
Capacity credit =
capacity of thermal plant displaced
rated output of wind plant
8
[5] B. Hasche, A. Keane and M. O'Malley, "Capacity Value of Wind Power, Calculation, and Data Requirements: the Irish Power System Case," in IEEE Transactions on Power Systems,
vol. 26, no. 1, pp. 420-430, Feb. 2011.

Evaluation of capacity credit
1. Retrospective analysis
 Wind plants are modelled as load modifiers, where the hourly wind generation
capacity is deducted from the expected demand [6]
1. Firm capacity method / Effective Load Carrying Capability (ELCC) method
2. Equivalent capacity method
9
[6] M. Milligan and K. Porter, “Determining the Capacity Value of Wind : An Updated Survey of Methods and Implementation Preprint,” Natl. Renew. Energy Lab. U.S. Dep. Energy.,
2005.

Evaluation of capacity credit- Retrospective analysis
Firm capacity method / Effective Load Carrying Capability (ELCC) method
 The firm capacity/ELCC method is based on the LOLP measure of system reliability.
 It incorporates LOLP calculations in such a way that adding a new generator (for example a
wind plant) is benchmarked against an ideal, perfectly reliable unit with 100% availability[6].
 Research has been carried out to estimate capacity credit of concentrated solar farms[7].
10
[6] M. Milligan and K. Porter, “Determining the Capacity Value of Wind : An Updated Survey of Methods and Implementation Preprint,” Natl. Renew. Energy Lab. U.S. Dep. Energy.,
2005.
[7] A. Alferidi and R. Karki, "Adequacy considerations in concentrated solar thermal integrated electric power system," 2017 IEEE Conference on Technologies for Sustainability
(SusTech), Phoenix, AZ, 2017, pp. 1-6.

Equivalent capacity method
 Substitutes an alternative unit (for example a natural gas unit) instead of the ideal unit
 This method provides a more practical value of capacity credit than using the ideal, perfectly
reliable unit in the firm capacity/ELCC method
11

Retrospective analysis
 Contributions
• It takes into account the detailed chronological variation of the wind plant output.
 Limitations
• It does not allow the variance of the wind plant output to be captured and quantified into
the LOLP calculation.[8]
12
[8] M. Milligan, Measuring Wind Plant Capacity Value, National Renewable Energy Laboratory, U.S. Department of Energy, 1996. [Online] Available :
https://www.nrel.gov/docs/legosti/fy96/20493.pdf.

Evaluation of capacity credit-
2. Prospective analysis
 The approach modelled wind plants with a capacity level and effective FOR that takes into
accounts both mechanical and wind availability[6].
13
[6] M. Milligan and K. Porter, “Determining the Capacity Value of Wind : An Updated Survey of Methods and Implementation Preprint,” Natl. Renew. Energy Lab. U.S. Dep.
Energy., 2005.

Evaluation of capacity credit- prospective analysis
Prospective analysis
 Contributions
• The chronological characteristics of wind is partially integrated in LOLP calculations.[9]
 Limitations
• Larger number of output states should be considered to get highly accurate LOLP
calculation which is complex and large processing powers is required.
14
[9] C. D'Annunzio, S. Huang and S. Santoso, "Generation adequacy assessment of power systems with wind generation: A system operations perspective," 2009 IEEE Power &
Energy Society General Meeting, Calgary, AB, 2009, pp. 1-7.

3. Reliability curves
 Wind plant is modelled as load modifier.
 different reliability indices (LOLE) can be obtained by varying the annual peak load.
 The LOLE can be plotted against the system load for two cases; without wind generation and
with wind generation.
15

Reliability curves
16
[6] M. Milligan and K. Porter, “Determining the Capacity Value of Wind : An Updated Survey of Methods and Implementation Preprint,” Natl. Renew. Energy Lab. U.S. Dep.
Energy., 2005.
Evaluation of capacity credit- Reliability curves

 Wind generator can be modeled using multi state Markov model [10,11,12,13,14,15]
 Limitations
 Computational over-head during reliability evaluation with large amount of wind
generators.
17
[10] A. S. Dobakhshari and M. Fotuhi-Firuzabad, "A Reliability Model of Large Wind Farms for Power System Adequacy Studies," in IEEE Transactions on Energy Conversion, vol. 24,
no. 3, pp. 792-801, Sept. 2009.
[11] R. Billinton and Y. Gao, "Multistate Wind Energy Conversion System Models for Adequacy Assessment of Generating Systems Incorporating Wind Energy," in IEEE Transactions
on Energy Conversion, vol. 23, no. 1, pp. 163-170, March 2008.
[12] R. Billinton, R. Karki, Y. Gao, D. Huang, P. Hu and W. Wangdee, "Adequacy Assessment Considerations in Wind Integrated Power Systems," in IEEE Transactions on Power
Systems, vol. 27, no. 4, pp. 2297-2305, Nov. 2012.
[13] Y. Ding, C. Singh, L. Goel, J. Østergaard and P. Wang, "Short-Term and Medium-Term Reliability Evaluation for Power Systems With High Penetration of Wind Power," in IEEE
Transactions on Sustainable Energy, vol. 5, no. 3, pp. 896-906, July 2014.
[14] M. Aien, A. Biglari and M. Rashidinejad, "Probabilistic reliability evaluation of hybrid wind-photovoltaic power systems," 2013 21st Iranian Conference on Electrical Engineering
(ICEE), Mashhad, 2013, pp. 1-6.
[15] L. Wu, J. Park, J. Choi, A. A. El-Keib, M. Shahidehpour and R. Billinton, "Probabilistic reliability evaluation of power systems including wind turbine generators using a simplified
multi-state model: A case study," 2009 IEEE Power & Energy Society General Meeting, Calgary, AB, 2009, pp. 1-6.
Model Wind power generation

 Wind power can be modelled using simulation models such as auto regressive method[16,17,40].
 ARMA model is more suitable for the reliability assessment of large power systems than the Markov
model[16]
 Limitations
 Heavy computation overhead.
 Relying on large amount of data for training ARMA parameters.
18
[16] J. Lin, L. Cheng, Y. Chang, K. Zhang, B. Shu, and G. Liu, “Reliability based power systems planning and operation with wind power integration: A review to models, algorithms and
applications,” Renew. Sustain. Energy Rev., 2014.
[17 R. Karki, Po Hu and R. Billinton, "A simplified wind power generation model for reliability evaluation," in IEEE Transactions on Energy Conversion, vol. 21, no. 2, pp. 533-540, June
2006.
[18] R. Billinton and L. Gan, "Wind power modelling and application in generating adequacy assessment," IEEE WESCANEX 93 Communications, Computers and Power in the Modern
Environment - Conference Proceedings, Saskatoon, Saskatchewan, Canada, 1993, pp. 100-106.
[40] P. Chen, T. Pedersen, B. Bak-Jensen and Z. Chen, "ARIMA-Based Time Series Model of Stochastic Wind Power Generation," in IEEE Transactions on Power Systems, vol. 25, no. 2,
pp. 667-676, May 2010.

Load model
 Fixed load
 Consider the peak demand as a fixed load level for the entire period of the study.
 Chronological load
 This model shows the hourly variations of the system demand and can also be used to
determine the annual peak demand or the minimum load level.
 Load duration curve (LDC)
 LDC model is the hourly load curve rearranged from chronological order into an order
based on magnitude.
19

Load model
 Clustered model
 The clustering technique can be used to create a multistep model of the annual load
duration curve.
K-means[18]
Fuzzy C means[19]
20
[19] X. Li and M. Ding, "Load Model Based on Integrative K-means Clustering For Reliability Evaluation in Operational Planning," 2010 Asia-Pacific Power and Energy Engineering
Conference, Chengdu, 2010, pp. 1-4.
[20] J. C. Bezdek, R. Ehrlich, and W. Full, “FCM: The Fuzzy C-Means Clustering Algorithm,” Comput. Geosci., vol. 10, no. 2–3, pp. 191–203, 1984.

Evaluation of LOLP, LOLE and other reliability
indices with renewable integration
21
Probabilistic approach
1. Analytical methods
2. Monte Carlo simulation

Evaluation of LOLP, LOLE and other reliability indices with renewable integration
› Analytical methods (Enumeration method)
– capacity outage probability table (COPT)[11,12]
1. Develop COPT using load model, renewable power as load modifier, conventional
generator model.
2. Develop COPT using load model+ Markov model for renewable power, conventional
generator model.
3. 2 COPTs are constructed: (1) the outage due the unavailability of the input, and (2) the
outage due to failure of system components.
These two COPTs are then combined to produce a single COPT that can be
viewed as a single source with multi-de-rated states.[20]
[12] R. Billinton, R. Karki, Y. Gao, D. Huang, P. Hu and W. Wangdee, "Adequacy Assessment Considerations in Wind Integrated Power Systems," in IEEE Transactions on Power Systems,
vol. 27, no. 4, pp. 2297-2305, Nov. 2012.
[11] R. Billinton and Y. Gao, "Multistate Wind Energy Conversion System Models for Adequacy Assessment of Generating Systems Incorporating Wind Energy," in IEEE Transactions on
Energy Conversion, vol. 23, no. 1, pp. 163-170, March 2008.
[9] C. D'Annunzio, S. Huang and S. Santoso, "Generation adequacy assessment of power systems with wind generation: A system operations perspective," 2009 IEEE Power & Energy
Society General Meeting, Calgary, AB, 2009, pp. 1-7.
[21] S. Sulaeman, M. Benidris and J. Mitra, "Modeling the output power of PV farms for power system adequacy assessment," 2015 North American Power Symposium (NAPS),
Charlotte, NC, 2015, pp. 1-6.
22

Limitations
 Analytical methods do not incorporate the chronological variation(both diurnal and seasonal)
of power output of renewable sources.
 Time consuming process when having large number of renewable plants.
23
Evaluation of LOLP, LOLE and other reliability indices with renewable integration-Analytical methods

 Non sequential Monte Carlo
 Randomly select power system states and evaluate[25,26].
 concentrated on improving computation efficiency[16].
 Sequential Monte Carlo
Simulate power generation over many years chronologically. [22,23,24,28,25].
concentrated on improving computation accuracy[16].
Evaluate the system states where Generation < Load
24
[22] R. Billinton and R. Karki, “Application of Monte Carlo Simulation to Generating System Well-Being Analysis,” IEEE Trans. Power Syst., vol. 14, no. 3, pp. 1172–1177, 1999.
[23] R. Ghajar and R. Billinton, “A Monte Carlo simulation model for the adequacy evaluation of generating systems,” Reliability Engineering & System Safety, vol. 20, no. 3, pp. 173–
186, 1988.
[24] Ruimin Zheng and Jin Zhong, "Generation adequacy assessment for power systems with wind turbine and energy storage," 2010 Innovative Smart Grid Technologies (ISGT),
Gothenburg, 2010, pp. 1-6.
[18] R. Billinton and L. Gan, "Wind power modelling and application in generating adequacy assessment," IEEE WESCANEX 93 Communications, Computers and Power in the Modern
Environment - Conference Proceedings, Saskatoon, Saskatchewan, Canada, 1993, pp. 100-106.
[25] C. Borges and J. Dias, "A model to represent correlated time series in reliability evaluation by nonsequential Monte Carlo simulation," 2017 IEEE Power & Energy Society General
Meeting, Chicago, IL, 2017, pp. 1-1.
[26] M. Mosadeghy, R. Yan and T. K. Saha, "A Time-Dependent Approach to Evaluate Capacity Value of Wind and Solar PV Generation," in IEEE Transactions on Sustainable Energy,
vol. 7, no. 1, pp. 129-138, Jan. 2016.
Monte Carlo method

 In the presence of large scale wind penetration, sequential MCS provides accurate
results[27].
 Monte Carlo simulation can be combined with regression techniques such as ARIMA to
integrate renewables[29].
 Monte Carlo(MC) simulations can be incorporated with Neural networks to model system
reliability indices[28].But large number of MC simulations are needed for training the ANN.
 Several methods speed up MC convergence are explained in [30,31,39,41]
25
[27] Y. Zhou, P. Mancarella and J. Mutale, "Generation adequacy in wind rich power systems: Comparison of analytical and simulation approaches," 2014 International Conference on
Probabilistic Methods Applied to Power Systems (PMAPS), Durham, 2014, pp. 1-6.
[28] M. S. Miranda and R. W. Dunn, "Fast Adequacy Determination for Systems with Wind Power Generation," 2005 IEEE/PES Transmission & Distribution Conference & Exposition: Asia
and Pacific, Dalian, 2005, pp. 1-5.
[29] R. Billinton and Guang Bai, "Generating capacity adequacy associated with wind energy," in IEEE Transactions on Energy Conversion, vol. 19, no. 3, pp. 641-646, Sept. 2004.
[30] D. Frenkel, “Speed-up of Monte Carlo simulations by sampling of rejected states,” Proc. Natl. Acad. Sci., 2004.
[31] R. Billinton and W. Li, "Reliability Assessment of Electric Power Systems Using Monte Carlo Methods". New York: Plenum Press, New York, 1994.
[39] Z. Shu and P. Jirutitijaroen, "Latin Hypercube Sampling Techniques for Power Systems Reliability Analysis With Renewable Energy Sources," in IEEE Transactions on Power Systems,
vol. 26, no. 4, pp. 2066-2073, Nov. 2011.
[41] A. M. Leite da Silva, R. A. G. Fernandez and C. Singh, "Generating Capacity Reliability Evaluation Based on Monte Carlo Simulation and Cross-Entropy Methods," in IEEE
Transactions on Power Systems, vol. 25, no. 1, pp. 129-137, Feb. 2010.
Evaluation of LOLP, LOLE and other reliability indices with renewable integration-MCS

26
Population based methods
1. Swarm intelligence
2. Genetic algorithms
3. Evolutionary algorithms
4. Artificial immune system
5. Ant colony system
Evaluation of LOLP, LOLE and other reliability indices with renewable integration-Analytical
[3] L. Wang and C. Singh, "Population-Based Intelligent Search in Reliability Evaluation of Generation Systems With Wind Power Penetration," in IEEE Transactions on Power
Systems, vol. 23, no. 3, pp. 1336-1345, Aug. 2008.

 Swarm intelligence
 Binary particle swarm optimization (BPSO) can be used to derive a set of meaningful
system states.[32,33]
 BPSO can search for system failure states and then power system reliability indices can
be calculated.
 BPSO can be combined with evolutionary algorithms.[34]
27
[32] Lingfeng Wang, Chanan Singh and Kay Chen Tan, "Reliability evaluation of power-generating systems including time-dependent sources based on binary particle swarm
optimization," 2007 IEEE Congress on Evolutionary Computation, Singapore, 2007, pp. 3346-3352.
[33] J. Kennedy and R. C. Eberhart, "A discrete binary version of the particle swarm algorithm," 1997 IEEE International Conference on Systems, Man, and Cybernetics. Computational
Cybernetics and Simulation, Orlando, FL, USA, 1997, pp. 4104-4108 vol.5.
[34] V. Miranda, L. de Magalhaes Carvalho, M. A. da Rosa, A. M. L. da Silva and C. Singh, "Improving Power System Reliability Calculation Efficiency With EPSO Variants," in IEEE
Transactions on Power Systems, vol. 24, no. 4, pp. 1772-1779, Nov. 2009.

 Genetic algorithms
 Similar to the BPSO,GA is used to find out a set of most probable failure states which
contributes considerably to system reliability indices.[35,36,37]
28
[35] L. Wang and C. Singh, "Genetic Algorithm Based Adequacy Evaluation of Hybrid Power Generation System Including Wind Turbine Generators," 2007 International Conference
on Intelligent Systems Applications to Power Systems, Toki Messe, Niigata, 2007, pp. 1-5.
[36] S. Sulaeman, F. T. Alharbi, M. Benidris and J. Mitra, "A new method to evaluate the optimal penetration level of wind power," 2017 North American Power Symposium (NAPS),
Morgantown, WV, 2017, pp. 1-6.
[37] N. Samaan and C. Singh, "Adequacy assessment of power system generation using a modified simple genetic algorithm," in IEEE Transactions on Power Systems, vol. 17, no. 4,
pp. 974-981, Nov. 2002.

 Contributions of population based methods
 Computation time is considerably lower than MCS[3,35].
 Limitations of population based methods
 Lack of mechanisms preventing the revisiting of states: repeated visits to the same state may well
happen if the method does not perform satisfactorily.
 Some sort of memory must be organized to keep track of visited states and recognize new ones.
Searching through such memory will become a increasingly time-consuming task towards the end
of the process, when many states have already been visited[16].
 The larger the power system the greater the computation cost.
29
[35] L. Wang and C. Singh, "Genetic Algorithm Based Adequacy Evaluation of Hybrid Power Generation System Including Wind Turbine Generators," 2007 International Conference on
Intelligent Systems Applications to Power Systems, Toki Messe, Niigata, 2007, pp. 1-5.
[3] L. Wang and C. Singh, "Population-Based Intelligent Search in Reliability Evaluation of Generation Systems With Wind Power Penetration," in IEEE Transactions on Power Systems,
vol. 23, no. 3, pp. 1336-1345, Aug. 2008.

For planning stage,
 For planning stage, computational accuracy is important than the computational efficiency.
 Computational accuracy of reliability indices is mainly depend on the renewable power generation
models.
 Main emphasis will be given to develop renewable power generation models which captures both
diurnal and seasonal variations.
30

Non sequential Monte Carlo Model
 Algorithm to evaluate LOLP without renewables
 Start loop until LOLP converges
 Step 1: Randomly select system generation value(gen)
loop until all the generators are considered
u= random(0,1)
If (gen I FOR > u) then gen I is available, else Gen I is not available
loop end
 Step 2: Randomly select load value(load)
 Step 3: Evaluate the state
 If (gen<load) then system failure
 Step 4: Calculate LOLP
 LOLP=number of failure states/All states
 End
 R studio is used to develop this algorithm.
31

1. World energy council, “World energy perspectives: renewable integrations 2016”, 2016.
2. S. Butler, “The nature of UK electricity transmission and distribution networks in an intermittent renewable and embedded electricity
generation future”. Imperial College of Science, Technology and Medicine, Centre for Environmental Technology in collaboration with
Parliamentary Office of Science and Technology, September 2001.[Online]. Available: www.parliament.uk/post/e5.pdf. [Accessed May. 18,
2018].
3. L. Wang and C. Singh, "Population-Based Intelligent Search in Reliability Evaluation of Generation Systems With Wind Power
Penetration," in IEEE Transactions on Power Systems, vol. 23, no. 3, pp. 1336-1345, Aug. 2008.
4. R. N. Allan and R. Billinton, Reliability Evaluation of Power Systems, vol. 11. Springer Science & Business Media, 2013.[online] Available:
5. B. Hasche, A. Keane and M. O'Malley, "Capacity Value of Wind Power, Calculation, and Data Requirements: the Irish Power System Case,"
in IEEE Transactions on Power Systems, vol. 26, no. 1, pp. 420-430, Feb. 2011.
6. M. Milligan and K. Porter, “Determining the Capacity Value of Wind : An Updated Survey of Methods and Implementation Preprint,” Natl.
Renew. Energy Lab. U.S. Dep. Energy., 2005.
7. A. Alferidi and R. Karki, "Adequacy considerations in concentrated solar thermal integrated electric power system," 2017 IEEE Conference
on Technologies for Sustainability (SusTech), Phoenix, AZ, 2017, pp. 1-6.
8. M. Milligan, Measuring Wind Plant Capacity Value, National Renewable Energy Laboratory, U.S. Department of Energy, 1996. [Online]
Available : https://www.nrel.gov/docs/legosti/fy96/20493.pdf.
9. C. D'Annunzio, S. Huang and S. Santoso, "Generation adequacy assessment of power systems with wind generation: A system operations
perspective," 2009 IEEE Power & Energy Society General Meeting, Calgary, AB, 2009, pp. 1-7.
10. A. S. Dobakhshari and M. Fotuhi-Firuzabad, "A Reliability Model of Large Wind Farms for Power System Adequacy Studies," in IEEE
Transactions on Energy Conversion, vol. 24, no. 3, pp. 792-801, Sept. 2009.
11. R. Billinton and Y. Gao, "Multistate Wind Energy Conversion System Models for Adequacy Assessment of Generating Systems
Incorporating Wind Energy," in IEEE Transactions on Energy Conversion, vol. 23, no. 1, pp. 163-170, March 2008.
33
References

12. R. Billinton, R. Karki, Y. Gao, D. Huang, P. Hu and W. Wangdee, "Adequacy Assessment Considerations in Wind Integrated Power
Systems," in IEEE Transactions on Power Systems, vol. 27, no. 4, pp. 2297-2305, Nov. 2012.
13. Y. Ding, C. Singh, L. Goel, J. Østergaard and P. Wang, "Short-Term and Medium-Term Reliability Evaluation for Power Systems With High
Penetration of Wind Power," in IEEE Transactions on Sustainable Energy, vol. 5, no. 3, pp. 896-906, July 2014.
14. M. Aien, A. Biglari and M. Rashidinejad, "Probabilistic reliability evaluation of hybrid wind-photovoltaic power systems," 2013 21st Iranian
Conference on Electrical Engineering (ICEE), Mashhad, 2013, pp. 1-6.
15. L. Wu, J. Park, J. Choi, A. A. El-Keib, M. Shahidehpour and R. Billinton, "Probabilistic reliability evaluation of power systems including wind
turbine generators using a simplified multi-state model: A case study," 2009 IEEE Power & Energy Society General Meeting, Calgary, AB,
2009, pp. 1-6.
16. J. Lin, L. Cheng, Y. Chang, K. Zhang, B. Shu, and G. Liu, “Reliability based power systems planning and operation with wind power
integration: A review to models, algorithms and applications,” Renew. Sustain. Energy Rev., 2014.
17. R. Karki, Po Hu and R. Billinton, "A simplified wind power generation model for reliability evaluation," in IEEE Transactions on Energy
Conversion, vol. 21, no. 2, pp. 533-540, June 2006.
18. R. Billinton and L. Gan, "Wind power modelling and application in generating adequacy assessment," IEEE WESCANEX 93
Communications, Computers and Power in the Modern Environment - Conference Proceedings, Saskatoon, Saskatchewan, Canada,
1993, pp. 100-106.
19. X. Li and M. Ding, "Load Model Based on Integrative K-means Clustering For Reliability Evaluation in Operational Planning," 2010 Asia-
Pacific Power and Energy Engineering Conference, Chengdu, 2010, pp. 1-4.
20. J. C. Bezdek, R. Ehrlich, and W. Full, “FCM: The Fuzzy C-Means Clustering Algorithm,” Comput. Geosci., vol. 10, no. 2–3, pp. 191–203,
1984.
21. S. Sulaeman, M. Benidris and J. Mitra, "Modeling the output power of PV farms for power system adequacy assessment," 2015 North
American Power Symposium (NAPS), Charlotte, NC, 2015, pp. 1-6.
22. R. Billinton and R. Karki, “Application of Monte Carlo Simulation to Generating System Well-Being Analysis,” IEEE Trans. Power Syst., vol.
14, no. 3, pp. 1172–1177, 1999.
34

23. R. Ghajar and R. Billinton, “A Monte Carlo simulation model for the adequacy evaluation of generating systems,” Reliability Engineering
& System Safety, vol. 20, no. 3, pp. 173–186, 1988.
24. Ruimin Zheng and Jin Zhong, "Generation adequacy assessment for power systems with wind turbine and energy storage," 2010
Innovative Smart Grid Technologies (ISGT), Gothenburg, 2010, pp. 1-6.
25. C. Borges and J. Dias, "A model to represent correlated time series in reliability evaluation by nonsequential Monte Carlo simulation,"
2017 IEEE Power & Energy Society General Meeting, Chicago, IL, 2017, pp. 1-1.
26. M. Mosadeghy, R. Yan and T. K. Saha, "A Time-Dependent Approach to Evaluate Capacity Value of Wind and Solar PV Generation," in
IEEE Transactions on Sustainable Energy, vol. 7, no. 1, pp. 129-138, Jan. 2016.
27. Y. Zhou, P. Mancarella and J. Mutale, "Generation adequacy in wind rich power systems: Comparison of analytical and simulation
approaches," 2014 International Conference on Probabilistic Methods Applied to Power Systems (PMAPS), Durham, 2014, pp. 1-6.
28. M. S. Miranda and R. W. Dunn, "Fast Adequacy Determination for Systems with Wind Power Generation," 2005 IEEE/PES Transmission
& Distribution Conference & Exposition: Asia and Pacific, Dalian, 2005, pp. 1-5.
29. R. Billinton and Guang Bai, "Generating capacity adequacy associated with wind energy," in IEEE Transactions on Energy Conversion,
vol. 19, no. 3, pp. 641-646, Sept. 2004.
30. D. Frenkel, “Speed-up of Monte Carlo simulations by sampling of rejected states,” Proc. Natl. Acad. Sci., 2004.
31. R. Billinton and W. Li, "Reliability Assessment of Electric Power Systems Using Monte Carlo Methods". New York: Plenum Press, New
York, 1994.
32. Lingfeng Wang, Chanan Singh and Kay Chen Tan, "Reliability evaluation of power-generating systems including time-dependent
sources based on binary particle swarm optimization," 2007 IEEE Congress on Evolutionary Computation, Singapore, 2007, pp. 3346-
3352.
33. J. Kennedy and R. C. Eberhart, "A discrete binary version of the particle swarm algorithm," 1997 IEEE International Conference on
Systems, Man, and Cybernetics. Computational Cybernetics and Simulation, Orlando, FL, USA, 1997, pp. 4104-4108 vol.5.
35

34. V. Miranda, L. de Magalhaes Carvalho, M. A. da Rosa, A. M. L. da Silva and C. Singh, "Improving Power System Reliability Calculation
Efficiency With EPSO Variants," in IEEE Transactions on Power Systems, vol. 24, no. 4, pp. 1772-1779, Nov. 2009.
35. L. Wang and C. Singh, "Genetic Algorithm Based Adequacy Evaluation of Hybrid Power Generation System Including Wind Turbine
Generators," 2007 International Conference on Intelligent Systems Applications to Power Systems, Toki Messe, Niigata, 2007, pp. 1-5.
36. S. Sulaeman, F. T. Alharbi, M. Benidris and J. Mitra, "A new method to evaluate the optimal penetration level of wind power," 2017 North
American Power Symposium (NAPS), Morgantown, WV, 2017, pp. 1-6.
37. N. Samaan and C. Singh, "Adequacy assessment of power system generation using a modified simple genetic algorithm," in IEEE
Transactions on Power Systems, vol. 17, no. 4, pp. 974-981, Nov. 2002.
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