Optimized Type-2 Fuzzy Logic PSS Combined with H∞ Tracking Control for the Multi-machine Power System

Abstract

In this paper, an optimized type-2 fuzzy logic based on power system stabilizer combined with the optimal H∞ tracking control has been developed to design intelligent controllers for improving and enhancing the performance of stability for the multi-machine power system. The type-2 fuzzy logic based on interval value sets is capable for modeling the uncertainty and to overcome the drawbacks of the conventional power system stabilizer. The scaling factors of the type-2 fuzzy logic are optimized with the particle swarm optimization algorithm to obtain a robust controller. The optimal H∞ tracking control guarantees the convergence of the errors to the neighborhood of zero. The simulation results show the damping of the oscillations of the angle and angular speed with reduced overshoots and quick settling time.

Appendixes

The dynamical model of the ith machine is represented by the classical third-order model [17].

$$ \left\{ \begin{aligned} \dot{\delta }_{i} & = \omega_{i} - \omega_{s} \\ \dot{\omega }_{i} & = \frac{{\omega_{s} }}{{2H_{i} }}\left( {Pm_{i} - D_{i} \left( {\omega_{i} - \omega_{s} } \right) - E^{\prime}_{qi} I_{qi} } \right) \\ \dot{E^{\prime}}_{qi} & = \frac{1}{{T^{\prime}_{di} }}\left( {E_{fi} - E^{\prime}_{qi} - \left( {X_{di} - X^{\prime}_{di} } \right)I_{di} } \right) \\ \end{aligned} \right. $$

$$ \left\{ \begin{aligned} I_{qi} & = G_{ii} E^{\prime}_{qi} + \sum\limits_{j = 1,j \ne i}^{n} {E^{\prime}_{qi} \left\{ {G_{ij} \cos \left( {\delta_{j} - \delta_{i} } \right) - B_{ij} \sin \left( {\delta_{j} - \delta_{i} } \right)} \right\}} \\ I_{di} & = - B_{ii} E^{\prime}_{qi} - \sum\limits_{j = 1,j \ne i}^{n} {E^{\prime}_{qi} \left\{ {G_{ij} \sin \left( {\delta_{j} - \delta_{i} } \right) + B_{ij} \cos \left( {\delta_{j} - \delta_{i} } \right)} \right\}} \\ \end{aligned} \right. $$

The detailed parameters of the multi-machine power system:

$$ \begin{aligned} a_{i} & = \frac{{\omega_{s} }}{{2H_{i} }}Pm_{i} \quad ;\quad b_{i} = \frac{{\omega_{s} }}{{2H_{i} }}D_{i} \quad ;\quad c_{i} = \frac{{\omega_{s} }}{{2H_{i} }}G_{ii} \\ d_{i} & = \frac{{\omega_{s} }}{{2H_{i} }}\quad ;\quad e_{i} = \frac{{\left( {1 - \left( {X_{di} - X^{\prime}_{di} } \right)B_{ii} } \right)}}{{T^{\prime}_{di} }};\quad h_{i} = \frac{{X_{di} - X^{\prime}_{di} }}{{T^{\prime}_{di} }} \\ \end{aligned} $$