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This paper focuses on the use of advanced techniques in genetic algorithm for solving power system stabilization control problems. At the outset, the proposed hierarchical genetic algorithm (HGA) and parallel micro genetic algorithm (parallel microGA) are proposed and then they will be extended to solve two example problems. In the first example, these techniques are applied to simultaneously tune power system stabilizers (PSSs). The PSSs are optimally tuned to simultaneously shift the lightly damped and undamped oscillation modes to a stable zone in the s-plane and to self identify the appropriate PSS locations. In second example, parallel microGA is used to design the fuzzy logic controller (FLC) of STATCOM. The applied technique for designing a FLC helps us save time and does not require experts for designing. From these results, we can see that these advanced techniques provide enhanced versatility for solving problems in power system stabilization control.