Introducing FOPID-PSS to increase small-signal stability of multi-machine power system

Fractional-order proportional-integral-differential (FOPID) controller is a generalization of PID controller employing fractional calculus. In this paper, FOPID power system stabilizer (FOPID-PSS) called PI^λD^μ-PSS is introduced to improve damping of electromechanical (EM) low frequency oscillations (LFOs) in a multi-machine power system. FOPID-PSS design is formulated as a nonlinear optimization problem in which adjustable parameters are optimized simultaneously via an improved particle swarm optimization (IPSO) algorithm by minimizing integral of time multiplied squared error (ITSE) performance index. Dynamic stability of 3-machine 6-bus test system is evaluated by eigenvalue analysis and time domain simulations in MATLAB/SIMULINK environment considering FOPID-PSS. Results are compared with both classical integer-order PID-PSS (IOPID-PSS) and lead-lag conventional PSS (CPSS) from standpoints of dynamic response and system robustness with respect to different uncertainties. The investigations using various performance indices demonstrate that proposed FOPID-PSS achieves superior dynamic performance and more robustness against uncertainties in comparison with IOPID-PSS and CPSS.