Page 356 - Decision Making Applications in Modern Power Systems

318 Decision Making Applications in Modern Power Systems

algorithms modified by NSGA-II [57] and NSGA-III [58] that are convenient
to solve the generation of EED optimization problems.
Therefore all previous models for EED only take into account the emis-
sions and the amount of emissions. This work presents the degree of influ-
ence of each type of emissions on the environment. In the coming sessions,
we develop a novel mathematical model that accurately classifies emissions
according to their impact on the environment and this will be one of the
functions to be optimized within the template.

12.3.1 Mathematical model for environmental economic dispatch

In the mathematical formulation of the multiobjective problem of EED, two
important goals in a thermal system of power generation have to be consid-
ered, which are economic and environmental impacts [52,59,60].

12.3.1.1 Minimizing costs
The fuel cost of a thermal unit is considered as an essential criterion for eco-
nomic viability. The fuel cost curve is assumed to be approximated by a qua-
dratic function of the output power of the generator P i [52,59,61,62]. The
function to be used to minimize the cost is
n
F 1 P i 5 X a i 1 b i P i 1 c i P 2 $=h ð12:9Þ
ðÞ
i
i51
where a i ; b i ; c i ; and P i are the fuel cost coefficients of the ith generating unit,
and n is the number of generators and the active power of each generator.
However, despite the great financial benefit of classical dispatch strategy
described by Eq. (12.9), whose fuel cost versus power generated curve is
shown in Fig. 12.5, it tends to produce high amount of SO 2 and NO x .
The fuel cost function of each thermal generating unit considering the
valve-point effect is expressed as the sum of a quadratic function and a sine
function [64,65]. The total cost of fuel in terms of active power can be
expressed as
M N S
X X 2 min
F 1 5 t m a s 1 b s P sm 1 c s P 1 d s sin e s ðP 2 P sm Þ ð12:10Þ

sm s
m51 s51
12.3.1.2 Minimizing the environmental impact
The generators with fossil fuels are the main source of emissions of nitrogen,
oxides, and other pollutants. Currently, there are strong constraints of
environmental protection agencies to reduce the emission of nitrogen oxides
(NO x ) being important from the point of view of environmental
conservation.