A Two-Stage strategy to handle equality constraints in ABC-based power economic dispatch problems

  • Xiao-long Chen
  • Pei-hong WangEmail author
  • Qian Wang
  • Yi-hua Dong
Methodologies and Application


Power economic dispatch (ED) plays an important role in energy saving in power system operations. The penalty function method is widely used to handle equality constraints involved in ED problems. However, it is sometimes difficult to select the optimal penalty coefficients. To solve this problem, a Two-Stage strategy is proposed in this paper to handle equality constraints in artificial bee colony algorithm (ABC)-based ED problems, called as TSABC. Two groups of onlooker bees are employed in the first stage to search for feasible solutions satisfying all constraints. Then, in the second stage, a novel searching strategy with dynamic bounds for the elements of the solutions is introduced to keep the constraints always satisfied during the optimization process. The TSABC method does not require more control parameters and is easy to implement. Both based on basic ABC algorithm, the Two-Stage strategy is compared with the penalty function method (PFABC) for handling equality constraints in both static and dynamic economic dispatch problems. The comparative analysis reveals that the proposed TSABC method has merit in terms of effectiveness, reliability and solution quality.


Two-Stage strategy Power economic dispatch Equality constraints Artificial bee colony algorithm Dynamic bounds 



The authors would like to thank the editors and anonymous referees for their invaluable comments and suggestions. This work is supported by the National Natural Science Foundation of China (No. 51476028 and No. 51876035) and the scholarship from China Scholarship Council under the Grant CSC No. 201706090049.

Compliance with ethical standards

Conflict of interest

The authors declare that they have no conflict of interest.

Ethical standard

All procedures performed in studies involving human participants were in accordance with the ethical standards of the institutional and/or national research committee and with the 1964 Declaration of Helsinki and its later amendments or comparable ethical standards.

Human and animals rights

This article does not contain any studies with animals performed by any of the authors.

Informed consent

Informed consent was obtained from all individual participants included in the study.


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© Springer-Verlag GmbH Germany, part of Springer Nature 2019

Authors and Affiliations

  1. 1.Key Laboratory of Energy Thermal Conversion and Control of the Ministry of Education, School of Energy and EnvironmentSoutheast UniversityNanjingChina
  2. 2.School of Energy and PowerJiangsu University of Science and TechnologyZhenjiangChina
  3. 3.Zhejiang Energy Group Research Institute Co., Ltd.HangzhouChina

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