Page 358 - Decision Making Applications in Modern Power Systems

320 Decision Making Applications in Modern Power Systems

the weights are not 0, minimizing both the cost of fuel and emissions at the
same time becomes the problem.
For [67], the amount of emission of each generator is given as a function
of its output, which is the sum of a quadratic function and an exponential
function. The total emission system can be expressed as
M N S
X X
2
F 2 5 t m α s 1 β P sm 1 γ P 1 η expðδ s P sm Þ ð12:14Þ
s
s
s sm
m51 s51
where α s ; β ; γ ; η ; andδ s are the coefficients of the emission characteristics
s
s
s
of each generator, and P sm is the power of each generator.
According [68], the multiobjective problem of dispatch emissions and
combined economic can be converted into an optimization problem of a sin-
gle goal by introducing a factor h penalty price as follows:
Minimize F 5 F C 1 h i 3 EC ð12:15Þ
where F C is the fuel cost function and EC is the total amount of emissions.
Expression (12.15) is subject to the equations and power flow restrictions.
The price of the penalty factor h combines the issue with the cost of fuel and
F is the total operating cost in $/h. The price penalty factor is the ratio of the
maximum cost of fuel and the emission maximum of the corresponding gen-
erator h i [68]:

F C P max
g i
h i 5 ð12:16Þ
EC P max
g i
where F C is the fuel cost function, EC is the total amount of emissions and
g i is the power in generator ith.
The emissions that are considered most important in the power generation
industry due to their effects on the environment are sulfur dioxide (SO 2 ) and
nitrogen oxides (NO x ) [13,69]. These emissions can be modeled by associat-
ing functions with emission power production for each unit. One approach to
represent the emissions of SO 2 and NO x is to use a combination of polyno-
mial terms [68,70]:
X
2
EC P g 5 α i P 1 β P g i 1 γ 1 ε i exp λ i P g i ð12:17Þ
g i i i
where α i ; β ; γ ; ε i ; andλ i are the emission characteristics of the coefficients
i
i
of the total power generated, P g , which is the power of each generator.
Second [71], the total emission F 2 (P i ) of air pollutants such as sulfur
dioxide, SO 2 , and nitrogen oxides, NO x , caused by the combustion of fuel in
thermal units may be expressed as
n
3
F 2 P i 5 X d i 1 e i P i 1 f i P 3 m =h ð12:18Þ
ðÞ
i
i51