**5.2 GA-P15 Folly\_secondSS**

The following GA parameters have been used during the design


308 Bio-Inspired Computational Algorithms and Their Applications

The fitness function is used to provide the measure of how individuals performed. In this instance, the problem domain was that the PSS parameters should stabilize the system simultaneously over a certain range of specified operating conditions. The PSS which parameters are to be optimized has a structure similar to the conventional PSS (CPSS) as shown in Fig. A. 3. of Appendix 8.2.3. There are three parameters *KS*, *T*1 and *T*<sup>2</sup> that are to be optimized, where *Ks* is the PSS gain and *T*1 and *T*2 are lead-lag time constants. *Tw* is the washout time constant which is not critical and therefore has not

The fitness function that was used is to maximize the lowest damping ratio. Mathematically

ς

2 2 *ij*

σ

σ ω

*<sup>i</sup>* j is the damping ratio of the ݅th eigenvalue of the jth operating conditions. The number of

*ij* and *ωij* are the real part and the imaginary part (frequency) of the eigenvalue,

0 < Ks ≤ 20

0.001 ≤ Ti ≤ 5

The following parameter domain constraints were considered when designing the PSS.

where *Ks* and T*i* denote the controller gain and the lead lag time constants, respectively .


The parameters of the BGA-PSS are given in *Table A.*1 of Appendix 8.2.3.

<sup>−</sup> <sup>=</sup>

*ij ij*

+

*ij*

ς

the eigenvalues is *n*, and *m* is the number of operating conditions.

The following BGA parameters have been used during the design

(4)

**4. Fitness function** 

been optimized.

*i* = 1,2, … n , *j* =1, 2, ….m

where

ζ

σ

respectively.

**5. PSS design** 

**5.1 BGA-PSS** 



the objective function is formulated as follows:

max(min( )) *<sup>i</sup> <sup>j</sup> val* =


More information on the selection, crossover and mutation can be found in (Michalewicz, 1996), (Sheetekela & Folly, 2010).

The parameters of the GA-PSS are given in *Table A.*1 of Appendix 8.2.3.
