# Performance Analysis of Fractional-Order PI-Based Controller for Variable Speed Hybrid Standalone WECS

Conference paper
Part of the Smart Innovation, Systems and Technologies book series (SIST, volume 161)

## Abstract

The presented work in the paper shows a comprehensive analysis of fractional-order PI (FOPI) controller based voltage and frequency (VF) control of variable speed hybrid-standalone wind-energy-conversion-system (WECS). The system comprises of two major components: (1) permanent-magnet-synchronous-generator (PMSG), (2) battery-energy-storage-system (BESS). For standalone operation, the frequency and magnitude of voltage need to be controlled at the load terminals. DSOGI-PLL (Dual-second-order-generalized-integral based phase-locked-loop) is designed to track the frequency of the system. Fractional-order (FO) controllers provide robustness to Voltage Source Converter (VSC) due to their fractional characteristic. FOPI (PIλ) controller has an extra degree-of-freedom λ (order of integral) with its proportional gain (Kp) and integral gain (Ki). Simulation analysis is carried out in MATLAB/Simulink for PMSG-BESS based WECS. Proposed controller’s performance is evaluated for varied conditions of operation. FOPI based controller is significantly minimizing the peak overshoot and settling time for the terminal voltage, also it improves the transient response of the system.

## Keywords

Standalone WECS PMSG BESS VSC Bi-directional converter PLL Fractional-order PI

## Nomenclature

$$v$$

Wind-velocity

$$\uprho$$

Air-density

$$A^{{\prime }}$$

$$\lambda^{{\prime }}$$

Tip-speed-ratio of wind turbine

$$C_{\text{p}}^{{\prime }}$$

Power-coefficient of wind turbine

$$\beta^{{\prime }}$$

$$P_{\text{turbine}}$$

Turbine power

$$\omega_{\text{r}}$$

Rotational-speed of rotor

$$r$$

$$\theta_{\text{e}}$$

Electrical angle

$$T_{\text{mech}}$$

Turbine torque

$$T_{\text{gen}}$$

Generator’s electromagnetic torque

$$P$$

Pole-pairs

$$\omega_{\text{m}}$$

Mechanical speed of rotor

$$\omega_{\text{e}}$$

Electrical speed of rotor

$$J$$

Moment of inertia

$$B$$

Viscous friction coefficient

$$R_{\text{s}}$$

Stator winding resistance

$$L_{d}$$

Direct axis stator inductance

$$L_{q}$$

$$\phi_{\text{m}}$$

$$V_{{{\text{s}}d}}$$

Direct-axis stator voltage

$$V_{{{\text{s}}q}}$$

$$I_{{{\text{s}}d}}$$

Direct-axis stator current

$$I_{{{\text{s}}q}}$$

$$\Gamma (x)$$

Gamma function

$$V_{\text{t}}$$

Terminal-voltage

$$I_{\text{Load}}$$

$$I_{\text{gen}}$$

Generator-current

$$I_{\text{converter}}$$

Converter-current

$$P_{\text{Load}}$$

$$P_{\text{gen}}$$

Generator-power

$$P_{\text{converter}}$$

Converter-power

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