Harmony Search Applications in Mechanical, Chemical and Electrical Engineering - Music-Inspired Harmony Search Algorithm: Theory and Applications - page 78

⎧

min l

P ≤ P ≤ P

i i i ,

⎪
⎨

u k l k

(7)

P ∈ P ≤ P ≤ P , k = 2 , , z

…

i i , − 1 i i , i

⎪
⎩

u max

P ≤ P ≤ P

i , z i i i

l / u

, is the lower/upper bound of the k th prohibited zone of unit i and z i is the
i th prohibited zone.

where

P k

Fig. 5. Prohibited operating zones

(iv) Line flow constraint
Line flow constraints can be expressed as follows:

max

Lf ≤ Lf , i = 1 .. N (8)

i i L

max

where Lf is the allowable maximum flow of transmis-

sion line i (line capacity), and N L is the number of transmission lines subject to line
capacity constraints.

Lf is the MW line flow.

i i

(v) Ramp-rate limits constraint
To avoid excessive thermal stresses on the boiler and combustion equipments, the rate
of change in the output power of each thermal unit must not exceed a certain rate dur-
ing increasing or decreasing the power output of each unit. This constraint can be
formulated as follows:

min o max o

max( P , P − DR ) ≤ P ≤ min( P , P + UR ) (9)

i i i i i i i

o

P is the previous output power. UR i is the upramp limit of the i th generato-
rand and DR i is the downramp limit of the i th generator.

where