Spatiotemporal Monitoring of Electricity Consumption by Using Residual-based Control Charts

Document Type : Original Article


1 Department of Industrial Engineering, Faculty of Engineering, University of Kurdistan, Sanandaj, Iran

2 Department of Industrial Engineering, K. N. Toosi University of Technology, Tehran, Iran



The optimum use of energy carriers is one of the important factors affecting the sustainable growth and development of countries. Therefore, monitoring energy consumption is of considerable importance. Energy monitoring with Statistical Process Control (SPC) methods provides a breakdown of energy usage and makes it easier to perceive trends to reduce consumption. A review of the literature shows that previous research has addressed detecting change’s time in consumption. Developing these methods in spatial and temporal aspects of changes in energy consumption, which means detecting the time and location of changes simultaneously, would be able to provide more accurate diagnostic information. In this paper, a novel spatiotemporal framework based on the extension of the generalized likelihood ratio (GLR) and T2 control charts are used for monitoring the electricity consumption of eight-time series related to eight western cities in Mazandaran province, North of Iran, from March 21, 2019, to August 21, 2019. Due to the presence of autocorrelation in electricity consumption data, a model-based approach is proposed to reduce the autocorrelation’s effect on chart performance. The performance of the proposed charts in identifying significant deviations in electricity consumption was evaluated, which indicates the greater diagnostic power of the GLR chart in detecting the time and location of changes. Application of the recently-established spatiotemporal surveillance mechanisms for energy consumption monitoring is the main contribution of this study it would enable practitioners to analyze discrepancies of usage patterns better and make policies for continual improvement of the regional management of electricity distribution.


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1. E. Rizzo, F. Cousin, R. Lucca, and S. Lautenschlager, “Autonomous metering system for monitoring water consumption,” AQUA—Water Infrastructure, Ecosystems and Society, vol. 70, no. 6, pp. 797–810, 2021.
2. K. L. Hameed and N. H. Barnouti, “Electricity monitoring and controlling iot smart system,” in 2019 International Engineering Conference (IEC), pp. 182–187, IEEE, 2019.
3. M. Zini and C. Carcasci, “Machine learning-based monitoring method for the electricity consumption of a healthcare facility in italy,” Energy, vol. 262, p. 125576, 2023.
4. J. Melendez, L. Burgas, F. Gamero, J. Colomer, and S. Herraiz, “Fault detection and diagnosis web service module for energy monitoring in buildings,” IFAC-PapersOnLine, vol. 51, no. 10, pp. 15–19, 2018.
5. G. Stuart, P. Fleming, V. Ferreira, and P. Harris, “Rapid analysis of time series data to identify changes in electricity consumption patterns in uk secondary schools,” Building and Environment, vol. 42, no. 4, pp. 1568–1580, 2007.
6. V. S. Puranik, “Cusum quality control chart for monitoring energy use performance,” in 2007 IEEE International Conference on Industrial Engineering and Engineering Management, pp. 1231–1235, IEEE, 2007.
7. L. Braga, A. Braga, and C. Braga, “On the characterization and monitoring of building energy demand using statistical process control methodologies,” Energy and Buildings, vol. 65, pp. 205–219, 2013.
8. M. Shamsuzzaman, S. Haridy, I. Alsyouf, and A. Rahim, “Design of economic x chart for monitoring electric power loss through transmission and distribution system,” Total Quality Management & Business Excellence, vol. 31, no. 5-6, pp. 503–523, 2020.
9. M. Shamsuzzaman, A. Shamsuzzoha, A. Maged, S. Haridy, H. Bashir, and A. Karim, “Effective monitoring of carbon emissions from industrial sector using statistical process control,” Applied Energy, vol. 300, p. 117352, 2021.
10. S. Houidi, F. Auger, H. B. A. Sethom, D. Fourer, and L. Miègeville, “Multivariate event detection methods for non-intrusive load monitoring in smart homes and residential buildings,” Energy and Buildings, vol. 208, p. 109624, 2020.
11. M. Faisal, R. F. Zafar, N. Abbas, M. Riaz, and T. Mahmood, “A modified cusum control chart for monitoring industrial processes,” Quality and Reliability Engineering International, vol. 34, no. 6, pp. 1045–1058, 2018.
12. A.-M. Golmohammadi and S. K. Golestan, “Statistical process control for energy consumption monitoring in a cement factory iranian cement factory,” International Journal of Applied Optimization Studies, vol. 1, no. 01, pp. 59–70, 2018.
13. D. C. Montgomery, Introduction to statistical quality control. John wiley & sons, 2019.
14. W. Jiang, S. W. Han, K.-L. Tsui, and W. H. Woodall, “Spatiotemporal surveillance methods in the presence of spatial correlation,” Statistics in Medicine, vol. 30, no. 5, pp. 569–583, 2011.
15. D. Wang, F. Li, and K. Liu, “Modeling and monitoring of a multivariate spatio-temporal network system,” IISE Transactions, vol. 55, no. 4, pp. 331–347, 2023.
16. J. Derenski, E. Porse, H. Gustafson, D. Cheng, and S. Pincetl, “Spatial and temporal analysis of energy use data in los angeles public schools,” Energy Efficiency, vol. 11, pp. 485–497, 2018.
17. F. M. Megahed, L. J. Wells, J. A. Camelio, and W. H. Woodall, “A spatiotemporal method for the monitoring of image data,” Quality and Reliability Engineering International, vol. 28, no. 8, pp. 967–980, 2012.
18. Z. He, L. Zuo, M. Zhang, and F. M. Megahed, “An image-based multi-variate generalized likelihood ratio control chart for detecting and diagnosing multiple faults in manufactured products,” International Journal of Production Research, vol. 54, no. 6, pp. 1771–1784, 2016.
19. M. Koosha, R. Noorossana, and F. Megahed, “Statistical process monitoring via image data using wavelets,” Quality and Reliability Engineering International, vol. 33, no. 8, pp. 2059–2073, 2017.
20. L. Zuo, Z. He, and M. Zhang, “An ewma and region growing based control chart for monitoring image data,” Quality Technology & Quantitative Management, vol. 17, no. 4, pp. 470–485, 2020.
21. B. M. Colosimo and M. Grasso, “Spatially weighted pca for monitoring video image data with application to additive manufacturing,” Journal of Quality Technology, vol. 50, no. 4, pp. 391–417, 2018.
22. R. Noorossana and S. J. M. Vaghefi, “Effect of autocorrelation on performance of the mcusum control chart,” Quality and Reliability Engineering International, vol. 22, no. 2, pp. 191–197, 2006.
23. S.-H. Sheu and S.-L. Lu, “Monitoring autocorrelated process mean and variance using a gwma chart based on residuals,” Asia-Pacific Journal of Operational Research, vol. 25, no. 06, pp. 781–792, 2008.
24. H. Khusna, M. Mashuri, Suhartono, D. D. Prastyo, M. H. Lee, and M. Ahsan, “Residual-based maximum mcusum control chart for joint monitoring the mean and variability of multivariate autocorrelated processes,” Production & Manufacturing Research, vol. 7, no. 1, pp. 364–394, 2019.
25. B. Žmuk, “Capabilities of statistical residual-based control charts in short-and long-term stock trading.,” Our Economy (Nase Gospo-darstvo), vol. 62, no. 1, 2016.
26. G. C. Runger and T. R. Willemain, “Model-based and model-free control of autocorrelated processes,” Journal of Quality Technology, vol. 27, no. 4, pp. 283–292, 1995.
27. G. E. Box, G. M. Jenkins, G. C. Reinsel, and G. M. Ljung, Time series analysis: forecasting and control. John Wiley & Sons, 2015.
28. R. Noorossana, M. Eyvazian, A. Amiri, and M. A. Mahmoud, “Statistical monitoring of multivariate multiple linear regression profiles in phase i with calibration application,” Quality and Reliability Engineering International, vol. 26, no. 3, pp. 291–303, 2010.
29. W. R. Tobler, “A computer movie simulating urban growth in the detroit region,” Economic geography, vol. 46, no. sup1, pp. 234–240, 1970.
30. P. A. Moran, “Notes on continuous stochastic phenomena,” Biometrika, vol. 37, no. 1/2, pp. 17–23, 1950.
31. H. Hotelling, “Multivariate quality control-illustrated by the air testing of sample bombsights,” Techniques of statistical analysis, 1947.
32. D. S. Holmes and A. E. Mergen, “Improving the performance of the t2 control chart,” Quality Engineering, vol. 5, no. 4, pp. 619–625, 1993.
33. R. L. Mason, N. D. Tracy, and J. C. Young, “Decomposition of t 2 for multivariate control chart interpretation,” Journal of quality technology, vol. 27, no. 2, pp. 99–108, 1995.
34. E. Page, “Cumulative sum charts,” Technometrics, vol. 3, no. 1, pp. 1–9, 1961.
35. S. Wang and M. R. Reynolds Jr, “A glr control chart for monitoring the mean vector of a multivariate normal process,” Journal of Quality Technology, vol. 45, no. 1, pp. 18–33, 2013.