Page 360 - Decision Making Applications in Modern Power Systems

322 Decision Making Applications in Modern Power Systems

At each time interval the amount of fuel supplied to each generator
F im must be within its lower limit, F min , and its upper limit, F max ; [59]
i i
such that
F min # F im # F i max ; iAN; mAM ð12:24Þ
i
where F im is the fuel supplied to the engine in the interval m, F min is the
i
minimum quantity of fuel supplied to the machine, F max is the maximum
i
quantity of fuel supplied to the machine.
An inequality constraint in terms of fuel storage limits
Each unit of fuel storage volume in each interval, V im ; should be within
its lower limit, V min , and the upper limit, V max , [59] so that

V min # V im # V max ð12:25Þ
2
Þ 1 F im 2 t m η 1 δ i P i 1 μ P iAN; mAM ð12:26Þ
V im 5 V m21ð i i i
where η ; δ i ; andμ are the fuel consumption coefficients for each generating
i
i
unit.
Although a strong review in the literature is made on the restrictions of
emissions comparing them with a ceiling which cannot be achieved, there
were no mathematical expressions of equal or unequal restriction emissions.

12.3.1.4 Objective functions
The objective function used to minimize the cost of fuel was expressed in
Eq. (12.9). It is important to note that to apply this equation; the coefficients
a i ; b i ; andc i of each engine were first calculated by putting all the engines of
power plants operating at different power values, which result in the power
curve versus the cost of each engine. Subsequently, regression equation
methods and their respective coefficients were obtained.
The function used to minimize the emission index is given by the follow-
ing equation:
n
I em P i 5 X d i 1 e i P i 1 f i P 3 mg=m 3 ð12:27Þ
ðÞ
i
i51
where d i ; e i ; andf are the coefficients of the characteristics of the emission
i
index for each unit.

12.3.2 Order environmental economic load: case studies
12.3.2.1 Problem formulation
Two plants to the case studies were chosen to examine the feasibility of the
proposed solution; we used a set of 10 thermal generating units of TPP in