A novel Data Envelopment Analysis model with complex numbers: measuring the efficiency of electric generators in steam power plants

• Authors: ESFANDIARI Mahmood , SAATI Saber , NAVABAKHSH Mehrzad , KHALILI-DAMGHANI Kaveh
• Languages of publication: EN

Abstracts

EN

The output of a generator in power plant is the electricity, and it consists of two parts, active and reactive power. These quantities are expressed as complex numbers in which the real part is the active power and the imaginary part is the reactive power. Reactive power plays an important role in an electricity network. Ignoring it will exclude a lot of information. With regard to the importance of the generators in power plants, surely, calculating the efficiency of these units is of great importance. Data Envelopment Analysis (DEA) is a nonparametric approach to measure the relative efficiency of Decision-Making Units (DMUs). Since the generators data are complex numbers, thus, if we the use classical DEA models in order to measure the efficiency of the generators in power plants, the reactive power cannot be considered, and the measurement is limited to the real number of electric power. In this paper, a new DEA model with complex numbers is developed in order to assess the performance of the power plant generators.

Keywords

EN

Data Envelopment Analysis; power plant; power plant efficiency; complex numbers

• Publisher: Politechnika Wrocławska. Oficyna Wydawnicza Politechniki Wrocławskiej
• Journal: Operations Research and Decisions
• Year: 2019
• Volume: 29
• Issue: 4
• Pages: 41-52

Contributors

author

ESFANDIARI Mahmood

• Department of Industrial Engineering, Faculty of Industrial Engineering, South Tehran Branch, Islamic Azad University, Tehran, Iran

author

SAATI Saber

• Department of Industrial Engineering, Faculty of Industrial Engineering, South Tehran Branch, Islamic Azad University, Tehran, Iran
• Department of Mathematics, North Tehran Branch, Islamic Azad University, Tehran

author

NAVABAKHSH Mehrzad

• Department of Industrial Engineering, Faculty of Industrial Engineering, South Tehran Branch, Islamic Azad University, Tehran, Iran

author

KHALILI-DAMGHANI Kaveh

• Department of Industrial Engineering, Faculty of Industrial Engineering, South Tehran Branch, Islamic Azad University, Tehran, Iran

References

• BANKER R.D., Maximum likelihood, consistency and data envelopment analysis. A statistical foundation, Manage. Sci., 1993, 39 (10), 1265–1273.
• BHOLA J.C., JYOTISHI P., Reactive power compensation in 132×33 kV grid of Narsinghpur Area, Int. J. Comp. Eng. Res., 2016, 6 (6), 6–15.
• CARLSON A., CRILLY P., RUTLEDGE J., Communication Systems, McGraw-Hill Series in Electrical and Computer Engineering, 2001.
• CHANDEL R., SINGH H., KUMAR R., Performance evaluation of state-owned thermal power plants in northern India using DEA, J. Global Energy Iss., 2017, 40 (6), 380–399.
• CHARNES A., COOPER W.W., RHODES E., Measuring the efficiency of decision-making units, Eur. J. Oper. Res., 1978, 2, 429–444.
• CHURCHILL R.V., BROWN J.W., VERHEY R.F., Complex Variables and Applications, McGraw-Hill, New York 1974.
• COOPER W.W., PARK K.S., YU G.I., Models for dealing with imprecise data in DEA, Manage. Sci., 1999, 45, 597–607 .
• FOWLES G., CASSIDAY G., Analytical Mechanics, Cengage Learning, Inc., CA. United States, 2004.
• KHALILI-DAMGHANI K., TAVANA M., HAJI-SAAMI E., A data envelopment analysis model with interval data and undesirable output for combined cycle power plant performance assessment, Exp. Syst. Appl., 2015, 42 (2), 760–773.
• LIU C.H., LIN S.J., LEWIS C., Evaluation of thermal power plant operational performance in Taiwan by data envelopment analysis, Energy Pol., 2010, 32 (2), 1049–1058.
• LYU X., SHI A., Research on the renewable energy industry financing efficiency assessment and mode selection, Sust., MDPI, Open Access J., 2018, 10 (1), 1–13.
• MILLER T.E., Reactive Power Control in Electric Systems, Wiley, New York 1983.
• MCCORMICK G.P., Computability of global solutions to factorable nonconvex programs. Part I. Convex underestimating problems, Math. Program., 1976, 10, 147–175.
• PARK S.U., LESOURD J.B., The efficiency of conventional fuel power plants in South Korea. A comparison of parametric and non-parametric approaches, Int. J. Prod. Econ., 2000, 63 (1), 59–65.
• PEARSON K., Mathematical contributions to the theory of evolution. Part III. Regression, heredity, and panmixia, Phil. Trans. R Soc. Lond., Series A, 1896, 187, 253–318.
• PORTELA M., THANASSOULIS E., SIMPSON G., Negative data in DEA. A directional distance approach applied to bank branches, J. Oper. Res. Soc., 2004, 55 (10), 1111–1121.
• SARIKA K., OR A., Efficiency assessment of Turkish power plants using data envelopment analysis, Energy, 2007, 32 (8), 1484–1499.
• SENGUPTA J.K., A fuzzy system approach in data envelopment analysis, Comp. Math. Appl., 1992, 24, 259–266.
• SENGUPTA J.K., Stochastic programming, Int. J. Syst. Sci., 1982, 7, 822–835.
• WEN M., GUO L., KANG R., YANG Y., Data envelopment analysis with uncertain inputs and outputs, Appl. Math., 2014, 2, 1–7.
• WU L., LI H., Analysis of the development of the wind power industry in China from the perspective of the financial support, Energy, Sust., Soc., 2017, 7 (37), 7–37.

Identifiers

DOI

10.37190/ord190403