EDUCATIONAL EXAMPLE
The educational example is stated as follows: Carry out comparison and
make a ranking list of the optimization methods for solution of the OPF
problem on the on IEEE 30-bus test system in case minimization of fuel
cost.
This section presents the OPF results obtained by using theopfgui program. The program was run thirty times for each of
ten optimization methods. The parameter settings related to different
optimization methods are shown in Fig. 8. In order to fair comparisons,
the common parameters such as, population size (N), max iteration number
(tmax), and number of runs (Nru) are same for each algorithm. Other
parameter settings are adopted from the reference papers, as follows:
for PSO and GSA [2], for WDO [14], for FFA [15], for GWO
[17], for CS [18], for MSA [19], and for BSA [20].
Table 1 shows the best OPF results obtained over 30 runs of the program
for each of optimization methods in case minimization of fuel cost. The
statistical indicators, which are minimum, maximum, mean value and
standard deviation of the OPF results, obtained by different
optimization methods are shown in Table 2. Based on these indicators it
is can be make an evaluation of performances of optimization methods. It
can be seen from Table 2 that some methods have better some statistical
indicators than other methods, and contrary. For example, the TLBO has
best Min and Mean indicators, whereas the WDO algorithm has best Max and
Standard Deviation indicators. To the assessment of the methods should
be taken into account all statistical indicators. This can be achieved
by introducing the normalized values of statistical indicators. They are
calculated as ratio of the best value and corresponding value of the
statistical indicators. For example, normalized value of statistical
indicator Min for TLBO algorithm is 1, for PSO it calculated as
800.59/801.31=0.9991, etc. Table 3 shows the normalized values of
statistical indicators. Based on these values, the optimization methods
are ranked from best (WDO) to worst (GWO). This ranking applies only to
the given OPF case. In case other objective functions and/or test
systems, the ranking list of the optimization methods may be different.
This is in accordance with the “No Free Lunch” theorem [18] which
states that no single method is best in solving all optimization
problems.