A frequency domain design of UPFC-based damping controller through direct synthesis approach

Abstract

This paper proposes the design of damping controllers using a frequency response matching approach to enhance the small-signal stability in a unified power flow controller (UPFC) based single-machine infinite-bus (SMIB) power system. The design methodology follows the direct synthesis approach that works on the construction of a reference model, which is synthesized based on the proposed design criteria and the system dynamics. Five alternative schemes have been proposed for the investigation of the applicability of the method using two UPFC control signals (boosting amplitude modulation ratio, $m_{b}$ and boosting phase angle, $\delta_{e}$ independently or simultaneously. The eigenvalue analysis, time-domain simulations, Bode plots, and various performance indices reveal that the proposed controllers provide effective results for an unstable system with non-minimum phase characteristics that may be subjected to model perturbation and measurement noise.

Appendix

$C_{dc}$ :

Capacitance of DC link

$D$ :

Damping coefficient

$E^{\prime}$ :

Voltage behind the transient reactance

$E_{q}^{\prime }$ :

Q-axis generator internal voltage

$E_{fd}$ :

Field voltage

$m_{b}$ :

Boosting amplitude modulation ratio

$m_{e}$ :

Excitation amplitude modulation ratio

$P_{m}$ :

Prime mover power

$\delta_{e}$ :

Excitation phase angle

$\xi$ :

Damping factor

$\omega$ :

Rotor angular speed

$C_{mb} \left( s \right)$ :

$m_{b}$ Based UPFC damping controller

$C_{\delta e} \left( s \right)$ :

$\delta_{e}$ Based UPFC damping controller

$\tau_{r}$ :

Time constant of non-minimum phase real pole

$P_{e}$ :

Air-gap power

$V_{b}$ :

Infinite-bus voltage

$V_{dc}$ :

Voltage of dc link

$V_{Et}$ :

Voltage at UPFC bus

$X_{d}$ :

Direct axis synchronous reactance

$X_{d}^{^{\prime}}$ :

Direct axis transient reactance

$X_{e}$ :

Transmission line reactance

$\delta_{b}$ :

Boosting phase angle

$\Delta \omega$ :

Speed deviation

$\omega_{b}$ :

Base speed

$\omega_{n}$ :

Undamped natural frequency

$X_{B}$ :

UPFC boosting transformer reactance

$X_{E}$ :

UPFC excitation transformer reactance

$\tau_{n}$ :

Time constant of non-minimum phase zero