Small Signal Stability in Electric Power Systems
Small signal rotor angle stability analysis in power systems is associated with insufficient damping of oscillations under small disturbances. Rotor angle oscillations due to insufficient damping have been observed in many power systems around the world. This entry overviews the predominant approach to examine small signal rotor angle stability in large power systems using eigenvalue analysis.
KeywordsSmall signal rotor angle stability Oscillatory modes Low-frequency oscillations Eigenvalues Eigenvectors Mode shape Participation factors
Small Signal Rotor Angle Stability in Power Systems
As power system interconnections grew in number and size, automatic controls such as voltage regulators played critical roles in enhancing reliability by increasing the synchronizing capability between the interconnected systems. As technology evolved the capabilities of voltage regulators to provide synchronizing torque following disturbances were significantly enhanced. It was, however, observed that voltage regulators tended to reduce damping torque, as a result of which the system was susceptible to rotor angle oscillatory instability. An excellent exposition of the mechanism and the underlying analysis is provided in the textbooks (Anderson and Fouad 2003; Sauer and Pai 1998; Kundur 1993), and a number of practical aspects of the analysis are detailed in Eigenanalysis and Frequency Domain Methods for System Dynamic Performance (1989) and Rogers (2000). Two types of rotor angle oscillations are commonly observed. Low-frequency oscillations involving synchronous machines in different operating areas are commonly referred to as inter-area oscillations. These oscillations are typically in the 0.1–2 Hz frequency range. Oscillations between local machines or a group of machines at a power plant are referred to as plant mode oscillations. These oscillations are typically above the 2 Hz frequency range. The modes associated with rotor angle oscillations are also termed inertial modes of oscillation. Other modes of oscillations associated with the various controls also exist. With the integration of significant new wind and photovoltaic generation which are interconnected to the grid using converters, new modes of oscillation involving the converter controls and conventional synchronous generator states are being observed.
The basis for small signal rotor angle stability analysis is that the disturbances considered are small enough to justify the use of linear analysis to examine stability (Kundur et al. 2004). As a result, Lyapunov’s first method Vidyasagar (1993) provides the analytical underpinning to analyze small signal stability. Eigenvalue analysis is the predominant approach to analyze small signal rotor angle stability in power systems. Commercial software packages that utilize sophisticated algorithms to analyze large-scale power systems with the ability to handle detailed models of power system components exist.
Small Signal Stability Analysis Tools for Large Power Systems
Calculation of a specific eigenvalue at a specified frequency or with a specified damping ratio
Simultaneous calculation of a group of relevant eigenvalues in a specified frequency range or in specified damping ratio range
Frequency response plots
Transfer functions, residues, controllability, and observability factors
Linear time response to step changes
Eigenvalue sensitivities to changes in specified parameters
Applications of Small Signal Stability Analysis in Power Systems
Small signal stability analysis tools are used for a range of applications in power systems. These applications include:
Power system stabilizer design
Automatic voltage regulator tuning
DC link current control
Small signal stability analysis for subsynchronous resonance
Load modeling effects on small signal stability
References Eigenanalysis and Frequency Domain Methods for System Dynamic Performance (1989) and Rogers (2000) provide comprehensive examples of the analysis conducted for each of the problems listed above.
Power system stabilizer design
HVDC link modulation
Static VAr compensator controls
References Eigenanalysis and Frequency Domain Methods for System Dynamic Performance (1989); Rogers (2000) again provide details of the analysis conducted for each of the problems listed under this category.
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