Engineering and Technology Quarterly Reviews

ISSN 2622-9374

Published: 23 December 2020

Forced Outage Analysis of Brazilian Thermal Power Plants using the Kruskal-Wallis Test

Leonardo dos Santos e Santos

Itaqui Power Plant, Brazil

pdf download

Download Full-Text Pdf


Pages: 98-126

Keywords: Kruskal-Wallis Test, Forced Outage, Thermal Power Plant


In this paper, the forced outage data from the Brazilian National Interconnected System (SIN) is provided and the statistics from the thermal power plants are computed. The SIN is characterized by a marked seasonality in electricity supply. In addition, the expansion pattern of the Brazilian electric sector shows signs of exhaustion, and the demand for flexible thermal power plants, based on availability, requires outage management as a reliability-centered maintenance (RCM) strategy. In this work, the non-parametric Kruskal-Wallis test and Dunn’s pairwise-comparisons were chosen for evaluating the mean forced outage duration (MFOD) and the forced outage factor (FOF) using the data from the national electricity system operator (ONS) with R Software. The distribution fitting was provided using Weibull++ software from Reliasoft. Based on the MFOD and unit failure rate data, the FOF for Brazilian thermal power plants is 3.33% with a 90% probability and 95% confidence level. Finally, Brazilian thermal power plants were benchmarked against North American power plants.


  1. Alboukadel, K., 2020 a. ggpubr: “ggplot2” Based Publication Ready Plots. R package version 0.4.0. Available online: (accessed 12 August 2020).

  2. Alboukadel, K., 2020 b. rstatix: Pipe-Friendly Framework for Basic Statistical Tests. R package version 0.6.0. Available online: (accessed 12 August 2020).

  3. Andrew, C., 1998. Descriptive and inferential statistics, in: Leon. Alan, S.B., Michel, H. (Eds), Comprehensive Clinical Psychology. Pergamon, ISBN 9780080427072 3.12, 243–285.

  4. Balaji, G., Balamurugan, R., Lakshminarasimman, L., 2016. Fuzzy clustered multi objective differential evolution for thermal generator maintenance scheduling. Int. J. Intell. Eng. Syst. 9, 1–13.

  5. Camarillo, T., Mathur, V., Mitchell, Tyler, Ratra, B., 2017. Median statistics estimate of the distance to the galactic center. Publ. Astron. Soc. Pac. 130.

  6. Castro, N., Brandão, R., Rosental, R. Dorado, P., 2016. Background, current status and perspectives. Energy Procedia. Brazil and the Int. Electr. Integr. 106, 204–214. 10.1016/j.egypro.2016.12.116,

  7. Chan, Y., Walmsley, R.P., 1997. Learning and understanding the Kruskal-Wallis one-way analysis-of-variance-by-ranks test for differences among three or more independent groups (3), 322. Phys. Ther. 77, 1755–1762.

  8. De Comercialização de Energia Elétrica, C., 2020 d. Info Mercado Mensal, nº 155 – Contabilização de Maio de 2020. Available online: http:// (accessed 12 August 2020).

  9. Dinno, A., 2015. Nonparametric pairwise multiple comparisons in independent groups using Dunn’s test. STATA J. 15, 292–300.

  10. Dipak, K.S., 2015 a. Gas turbine and heat recovery steam generator, in: Dipak, K.S. (ed.), Thermal Power Plant. Elsevier, pp. 239–283.

  11. Dipak, K.S., 2015 b. Interlock and protection, in: Dipak, K.S. (ed.), Thermal Power Plant. Elsevier, pp. 387–405.

  12. Fagerland, M.W., Sandvik, L., 2009. The Wilcoxon-Mann-Whitney test under scrutiny. Stat. Med. 28, 1487–1497.

  13. Ferreira, J.C., Patino, C.M., 2015. What does the p value really mean? J. bras. pneumol. 41, 485–485. Available online: ISSN 1806-3756 (accessed 12 August 2020).

  14. Statistical tools for high-throughput data analysis (STHDA), 2017 b. Ggpubr: Publication Ready Plots. Available online: (accessed 12 August 2020).

  15. Geração termelétrica a gás natural: Comprovação de disponibilidade de combustível, 2017 a. Available online: (accessed 12 August 2020). Center for Regulatory and Infrastructure Studies Y3

  16. Hollander, M., Wolfe, D.A., Chicken, E., 2013. Nonparametric Statistical Methods, 3rd ed. John Wiley & Sons.

  17. IEEE-SA Standards Board, 2007. IEEE standard definitions for use in reporting electric generating Unit Reliability, Availability, and Productivity. IEEE std 762 2006 (Revision of IEEE Std 762-1987), C1–66.

  18. Laerd statistics. Kruskal-Wallis H test using SPSS statistics, 2020 Available online: (accessed 12 August 2020).

  19. Landeiro, V.L., 2011. Introdução ao uso do programa R. Instituto Nacional de Pesquisas Da Amazônia, Brazil.

  20. Lipár, M., 2012. Operational Safety of Nuclear Power Plants. 10.1533/9780857093776.3.773.

  21. Makarov, Y., Etingov, P., Ma, J., 2017. Incorporating Forecast Uncertainty in Utility Control Center. 10.1016/B978-0-12-809592-8.00011-1.

  22. Mangiafico, S.S., 2016. Summary and Analysis of Extension Program Evaluation in R 1. Available online: (accessed 12 August 2020). Rutgers, New Brunswick, NJ Cooperative Extension.

  23. Martins, A.S., 2013. Project finance aplicado ao setor de geração de energia elelétrica Brasileiro – Fontes alternativas: Análise dos riscos e mitigadores em projetos de energia eólica. 161 p. Available online: (accessed 12 August 2020). Departamento de Administração, Pontifícia Universidade Católica do Rio de Janeiro, Rio de Janeiro.

  24. McDonald, J.H., 2007. The handbook of biological statistics. Available online: (accessed 12 August 2020).

  25. Ministério de Minas e Energias, 2014. Portaria No 484, de 11 de setembro de. Available online: (accessed 12 August 2020).

  26. Minitab 19 Support. Interpret all statistics for Kruskal-Wallis test, 2020. Available online: (accessed 12 August 2020).

  27. Moreno, L., Morcillo, A., 2019. Comparação de três ou mais grupos independentes Teste de Kruskal-Wallis. 10.13140/RG.2.2.12990.43846.

  28. Nacional do Sistema, O., 2017. Boletim de Carga Mensal dezembro. Available online: (accessed 12 August 2020).

  29. Nacional do Sistema, O., 2018. Boletim de Carga Mensal dezembro. Available online: (accessed 12 August 2020).

  30. Nacional do Sistema, O., 2019 a.Boletim de Carga Mensal dezembro. Available online: (accessed 12 August 2020).

  31. Nacional do Sistema, O., 2019 b. Submódulo 14.2 Arranjos comerciais para os serviços ancillaries. Available online: (accessed 12 August 2020).

  32. Nacional do Sistema, O., 2019 c. DPL-REL-0099/2020 Relatório de Análise Estatística de Desligamentos Forçados de Equipamentos referente ao ano de 2019.

  33. Nacional do Sistema, O., 2019 d. Indicadores de desempenho de equipamentos e linhas de transmissão e das funções transmissão e geração. Available online: (accessed 12 August 2020).

  34. Nacional do Sistema, O., 2020 a. PEN sumário executivo plano da operação energética 2020/2024. Available online: (accessed 12 August 2020).

  35. Nacional do Sistema, O., 2020 b. Boletim de Carga Mensal junho. Available online: (accessed 12 August 2020).

  36. Nogueira, F.M.M., Alarcon, R., Arturo, D., 2019. Impacto das interrupções na geração hidrelétrica do Brasil. Available online: (accessed 12 August 2020). Inter-American Development Bank. 50p.

  37. North American Electric Reliability Corporation. 2020. About NERC. Available online: (accessed 12 August 2020).

  38. North American Electric Reliability Corporation, 2018. Generating Unit Statistical Brochure – Units reporting events. Available online: (accessed 12 August 2020).

  39. Agência Nacional de Energia Elétrica, 2020. Nota Tec.-SFG/ANEEL. Available online: (accessed 12 August 2020).

  40. DataNovia, 2020 Kruskal-Wallis test in R. Available online: (accessed 12 August 2020).

  41. Ostertagová, E., Ostertag, O., Kováč, J., 2014. Methodology and application of the Kruskal-Wallis test. Appl. Mech. Mater. 611, 115–120.

  42. Kassambara, A., 2020d. The comprehensive R Archive Network. Package ‘rstatix’. Available online: (accessed 12 August 2020).

  43. Patino, C.M., Ferreira, J.C., 2015. Confidence intervals: A useful statistical tool to estimate effect sizes in the real world. J. bras. pneumol. 41 (Cited 2020.8.11), 565–566. Available online: (accessed 12 August 2020). ISSN 1806-3756.

  44. Prajapati, B. Mark, D., Richard, A.A., 2010. Sample Size Estimation and Statistical Power Analyses.

  45. R Development Core Team, 2011. A:A language and environment for statistical computing. Available online: R Foundation for Statistical Computing, Vienna, Austria. ISBN 3-900051-07-0 (accessed 12 August 2020).

  46. Kassambara, A., 2020a. Rdocumentation. rstatix v0.6.0. Available online: (accessed 12 August 2020).

  47. Kassambara, A., 2020b. Rdocumentation. kruskal_test. Available online: (accessed 12 August 2020).

  48. Kassambara, A., 2020c. Rdocumentation. kruskal_effsize. Available online: (accessed 12 August 2020).

  49. Reliasoft, 2017. Weibull++/Alta. User’s Guide. Available online: 11 (accessed 12 August 2020).

  50. Ribeiro, H.F., 2019. Behavior analysis of thermal power stations in the national interconnected system. Available online: (accessed 12 August 2020). Universidade Federal do Rio de Janeiro, Escola Politécnica, Rio de Janeiro, RJ. 77p.

  51. Ronald, N., Forthofer, Eun, S.L., Mike, H., 2007. Nonparametric tests, in: Forthofer, R.N., Eun, S.L., Mike, H. (Eds), Biostatistics, 2nd ed. Academic Press, pp. 249–268.

  52. Sifonte, J.R., Reyes-Picknell, J.V., 2017. Reliability Centered Maintenance-Reengineered: Practical Optimization of the RCM Process with RCM-R.

  53. Sousa, J.R.F., 2009. A geração termelétrica: A contribuição das térmicas a gás natural liquefeito. Available online: (accessed 12 August 2020). Universidade Estadual de Campinas, Faculdade de Engenharia Mecânica, Campinas, SP. 131p.

  54. National Confederation of Industry, Brazil, 2018. Thermal Power Plants: The Inevitable Choice. Availableonline: (accessed 12 August 2020).

  55. Tomczak, Maciej, Tomczak, Ewa, 2014. The need to report effect size estimates revisited. An Overview Some Recommended Meas. Eff. Size 21, 19–25.

  56. Hecke, T.V., 2010. Power study of ANOVA versus Kruskal-Wallis test. J. Stat. Manag. Syst. 15.

  57. Wickham, H., Averick, M., Bryan, J., Chang, W., McGowan, L., François, R., Grolemund, G., Hayes, A., Henry, L., Hester, J., Kuhn, M., Pedersen, T., Miller, E., Bache, S., Müller, K., Ooms, J., Robinson, D., Seidel, D., Spinu, V., Takahashi, K., Vaughan, D., Wilke, C., Woo, K., Yutani, H., 2019. Welcome to the tidyverse. J. Open Source Softw. 4, 1686.

  58. Woo, S., 2017. Reliability Design of Mechanical Systems: A Guide for Mechanical and Civil Engineers.

About Us

The Asian Institute of Research is an online and open-access platform to publish recent research and articles of scholars worldwide. Founded in 2018 and based in Indonesia, the Institute serves as a platform for academics, educators, scholars, and students from Asia and around the world, to connect with one another. The Institute disseminates research that is proven or predicted to be of significant influence for the general public.

Contact Us

Please send all inquiries to the email:

Business Address:

5th Floor, Kavling 507, Fajar Graha Pena Tower, Jl. Urip Sumohardjo No.20, Makassar, Indonesia 90234

Copyright © 2018 The Asian Institute of Research. All rights reserved

Stay Connected

  • Instagram - Black Circle
  • Facebook - Black Circle
  • LinkedIn - Black Circle