Enhanced multi-objective crisscross optimization for dynamic economic emission dispatch considering demand response and wind power uncertainty

  • C L. ChinnadurraiEmail author
  • T. Aruldoss Albert Victoire
Methodologies and Application


In this paper, the dynamic economic emission dispatch problem in electric power system is formulated as a multi-objective optimization problem in a smart grid perspective. Accordingly, two additional subproblems are included in the dynamic economic emission dispatch formulation. Firstly, the wind power generation is penetrated into the system such that the uncertain power varies between a predicted upper and lower bounds. Secondly, a demand response program is implemented at the customer end, to modify the consumption pattern of electricity according to different electricity prices at valley, peak and off-peak periods. A two-level optimization is proposed to determine the optimal schedule of generating units such that the upper level solves for the minimization of cost and emission, whereas the lower level minimizes the wind power output interval reduction. An enhanced multi-objective crisscross optimization using non-dominated sorting approach is proposed as main optimizer to solve upper-level problem, and a linear programming is adopted to solve the lower-level problem. A 10-unit system is taken as a case study for demonstration, and the result shows the effectiveness of proposed formulation in terms of minimizing cost and emission.


Dynamic economic emission dispatch Demand response Wind power Crisscross optimization Smart grid 

List of symbols

ai, bi, ci, ei, fi

Cost coefficients of generating unit i

αi, βi, γi, ηi, δi

Emission coefficients of generating unit i

Pi,min, Pi,max

Minimum and maximum power generating capacity of unit i

Bij, Bio, B00

Transmission loss coefficients

DRi, URi

Down/up ramp rate limit of unit i

Pi, t

Power output of unit i at time t

Pl, t

Transmission line loss at time t

Pd, t

Power demand at time t

\( \underline{w}_{t} ,\overline{w}_{t} \)

Lower and upper bounds of predicted wind power

\( \tilde{w}_{t} \)

Actual wind power at time t

\( \tilde{P}_{t,i} \)

Actual power output of generating unit i at time t


Wind power curtailment at time t


Scaling factor

ρA, ρP, ρOP, ρV

Initial average, peak, off-peak, valley electricity price




Net profit


Profit of customer


Population size


Number of variables


Random population


Horizontal moderation solutions


Dominant horizontal solutions


Vertical moderation solutions


Dominant vertical solutions


Load factor


Peak valley factor


Peak compensation



This study was not funded by any individual/organization.

Compliance with ethical standards

Conflict of interest

The authors declare that they have no conflict of interest.

Ethical approval

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


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Copyright information

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

Authors and Affiliations

  1. 1.Department of Electrical and Electronics EngineeringAnna University Regional CampusCoimbatoreIndia

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