Harmony Search Applications in Mechanical, Chemical and Electrical Engineering - Music-Inspired Harmony Search Algorithm: Theory and Applications - page 77

⎧

2 min

a + b P + c P fuel 1 P ≤ P ≤ P

i 1 i 1 i i 1 i i i i 1

⎪ ⎪
⎨

2

a + b P + c P fuel 2 P < P ≤ P

i 2 i 2 i i 2 i i 1 i i 2

(4)

C =

Ti

#

⎪
⎩

⎪

2

a + b P + c P fuel k P < P ≤ P

ik ik i ik i ik − 1 i ik

where C Ti is the fuel cost function of the i th unit. The coefficients a ik , b ik and c ik are
cost coefficients of the i th unit using fuel type k.

Fig. 4. Valve-point effects

Generally, the ED problem is subjected to the following constraints:

(i) Power balance constraint

n

∑
=

P = P + P

(5)

i D L

i 1

where P D is the total demand and P L is the total transmission network loss.
(ii) Generation limit constraint
Generation power of each generator is assumed between maximum and minimum
limits:

min max

P ≤ P ≤ P (6)

i i i

(iii) Prohibited zones constraint
A unit with prohibited operating zones has a discontinuous input-output power gen-
eration characteristic (Fig. 5), and as a result, there are additional constraints on the
unit operating range: