Fractional Order PID Controller Analysis

Abstract— This paper presents the application of Fractional Order PID controller as a supplementary controller to improve the dynamics of Load Frequency Control in an interconnected system. FOPID is a PID controller whose derivative and integral orders are of fractional rather than integer. The extension of derivative and integration order from integer to fractional order provides more flexibility in the design of the controller there by improving the dynamics of the system. Using integral square error as performance criteria to be optimized, the FOPID controller parameters are optimized using Cat Swarm Optimization (CSO). The performance obtained with CSO is compared with PSO. The simulation results demonstrate that CSO has much better performance
Introduction Load frequency control is a very important issue in power system operation and control for supplying sufficient and reliable electric power with good quality. The main goal of the LFC is to maintain zero steady state error for frequency deviation and tie line power deviations in a multi-area interconnected system [1-3]. The classical PID controller is the most widely used controller for industrial applications due to its simplicity in realization and tuning [4-6]. In recent years, the extension of derivative and integration order from integer to fractional order provides more flexibility in the design of the controller, there by controlling the wide range of dynamics of a system. Fractional calculus is a mathematical analysis which studies the ability of taking real number power of the differential operator and integration operator. It is an extension of the concept dny(t)/dtn where n is an integer number to the concept dαy(t)/dtα where α is non-integer number with possibility to be complex [7]. The classical IOPID controllers are particular cases of FOPID controllers. As the FOPID has two more extra tuning knobs than the classical IOPID controller, it gives more flexibility for the design of a control system and gives better opportunity to adjust the system dynamics
Apart from that another undesired effect has to be compensated by secondary control. Active power imbalances and primary control actions cause changes in the power flows in the tie lines to other areas, i.e. power exchanges not according to the scheduled transfers. The secondary control ensures by a special mechanism that this is remedied after a short period of time. Hence the control task is to minimize the system frequency and tie-line power deviations in the three areas in case of any load disturbance in any area. This is achieved conventionally with the help of a suitable integral control action. The supplementary control of the ith area with integral gain Ki is therefore made to act on ACEi given by (1) which is an input signal to the controller