A nonlinear fractional programming approach for environmental–economic power dispatch

• A nonlinear fractional programming approach for EEPD problems is proposed.
• Total fuel cost and total emissions are minimized by two simultaneous models.
• The first model is to minimize a quotient of [total emission]/[total fuel cost].
• The second model is to minimize the total fuel cost being a quadratic function.
• The first model is solved by Dinkelbach’s algorithm.

A nonlinear fractional programming approach is provided for addressing the environmental–economic power dispatch problems in the thermal power dispatch systems. The objective of this study is to simultaneously minimize the total fuel cost and total emissions of the power dispatch systems, which is realized by two simultaneous models with nonlinear constraints. The first model is to minimize the quotient of two competing and conflicting functions (i.e. [total emission function]/[total fuel cost function]), and the second one is to minimize the total fuel cost expressed by a quadratic objective function. In particular, the process of solving the first model uses Dinkelbach’s algorithm to convert the minimization problem with the nonlinear fractional objective function into a sequence of non-fractional minimization problems. The effectiveness of this approach is demonstrated through applying to the standard IEEE 30-bus test system. Comparison between the present approach and other existing approaches shows that the proposed approach can generate superior decision alternatives from the view point of realizing a more environmentally friendly and cost-effective scheme and/or considering the power transmission loss rate in the power dispatch systems.