Nonlinear Power System Stabilizer Design for Small Signal Stability Enhancement

Abstract

The interconnected power system is exposed to a wide range of disturbances that may induce electromechanical oscillations of small magnitude and often persist for long periods. Such oscillations may sustain and grow, causing system separation if no adequate damping is provided. Conventional Power System Stabilizers (PSSs) are often used to provide the necessary damping torque to suppress the oscillation through the excitation system. The design of PSS in the previous work is either nonlinear or entirely linear based on a linearized model around an equilibrium point. Nonlinear controllers provide very robust performance. However, their complexity limits their deployment. On the other hand, linear-based PSSs are simple, but their performance degrades as the operating conditions move away from the region of attraction. Unlike previously published work, the design of the PSS in this paper explicitly uses the nonlinear model of the power system and linear control theory. This paper presents a nonlinear PSS based on feedback linearization. The Riccati equation is used to construct the new coordinate’s linear controller. The efficacy of the presented study is demonstrated through a comparison with nonlinear-based and linear-based PSSs. Performing an in-depth analysis of inertia’s impact on the system’s stability concludes the proposed study.

Appendices

Appendix

System Parameters

See Table

Table 2 System parameters used in the simulation

2.

Lie Derivative

$$Lf_{4} h = {\mathcal{L}}_{1} + {\mathcal{L}}_{2} + {\mathcal{L}}_{3} + {\mathcal{L}}_{4} + {\mathcal{L}}_{5}$$

where ${\mathcal{L}}_{{i^{\prime}s}}$ are defined as follows:

$$\begin{gathered} {\mathcal{L}}_{1} \triangleq \frac{{\frac{1}{2}\omega_{s} x_{3} V_{\infty } \sin \left( {x_{1} } \right)\left( {x_{2} - \omega_{o} } \right)}}{{Hx_{d}^{^{\prime}} }} + \frac{{\frac{1}{4}\omega_{s}^{2} x_{3} DV_{\infty } \cos \left( {x_{1} } \right)}}{{H^{2} }} \hfill \\ {\mathcal{L}}_{2} \triangleq - \frac{{\frac{1}{2}\omega_{s} V_{\infty } \cos \left( {x_{1} } \right)\left( {x_{4} - x_{3} - \frac{{\left( {x_{3} - V_{\infty } \cos \left( {x_{1} } \right)} \right)\left( {x_{d} - x_{d}^{^{\prime}} } \right)}}{{x_{d}^{^{\prime}} }}} \right)}}{{Hx_{d}^{^{\prime}} T_{do}^{^{\prime}} }} \hfill \\ \end{gathered}$$

$${\mathcal{L}}_{3} \triangleq \frac{{\frac{1}{2}\omega _{s} V_{\infty }^{2} \sin ^{2} \left( {x_{1} } \right)\left( {x_{d} - x_{d}^{'} } \right)}}{{Hx_{d}^{{'2}} T_{{do}}^{'} }}\left( {x_{2} - \omega _{o} } \right)$$

$$\begin{gathered} {\mathcal{L}}_{4} \triangleq \frac{1}{2H} \left[ {\frac{{\frac{1}{2}\omega_{s} V_{\infty } \cos \left( {x_{1} } \right)\left( {x_{2}-\omega_{o} } \right)}}{{Hx_{d}^{^{\prime}} }} \!+\! \frac{{\omega_{s}^{2} D^{2} }}{4}} \right]\left( {P_{m} \!-\! P_{e}\! -\! D\left( {x_{2}\! -\! \omega_{o} } \right)} \right) \hfill \\ - \frac{{\frac{1}{2}\omega_{s} V_{\infty } \cos \left( {x_{1} } \right)\left( {x_{2} - \omega_{o} } \right)}}{{Hx_{d}^{^{\prime}} }} + \frac{{\frac{1}{4}\omega_{s}^{2} DV_{\infty } \sin \left( {x_{1} } \right)}}{{H^{2} x_{d}^{^{\prime}} }} \hfill \\ - \frac{{\frac{1}{2}\omega_{s} V_{\infty } \sin \left( {x_{1} } \right)\left( { - 1 - \frac{{x_{d} - x_{d}^{^{\prime}} }}{{x_{d}^{^{\prime}} }}} \right)}}{{Hx_{d}^{^{\prime}} T_{do}^{^{\prime}} }} \hfill \\ \quad \quad \quad \quad \quad \times \frac{{x_{4} - x_{3} - \frac{{(x_{3} - V_{\infty } \cos \left( {x_{1} } \right)\left( {x_{d} - x_{d}^{^{\prime}} } \right)}}{{x_{d}^{^{\prime}} }}}}{{T_{do}^{^{\prime}} }} \hfill \\ \end{gathered}$$

$${\mathcal{L}}_{5} \!\triangleq\! - \frac{{\frac{1}{2}\omega_{s} V_{\infty } \sin \left( {x_{1} } \right)\left[ {K_{A} \left( {V_{ref} \!-\! V_{t} } \right) \!-\! x_{4} } \right]}}{{Hx_{d}^{^{\prime}} T_{do}^{^{\prime}} T_{A} }}$$