Small Signal Stability
The DIgSILENT PowerFactory modal analysis tool features small signal analysis of a dynamic multi-machine system. System representation is identical to the time domain model. It covers all network components such as generators, motors, loads, SVS, FACTS, or any other component used in the system representation, including controllers and power plant models.
Analysis of eigenvalues and eigenvectors is appropriate for applications such as low-frequency oscillatory stability studies, PSS tuning, determination of interconnection options and its basic characteritics, and is a natural complement to the time domain simulation environment. It also allows for the computation of modal sensitivities with respect to generator or power plant controllers, load characteristics, reactive compensation or any other dynamically-modelled equipment.
PowerFactory’s Eigenvalue Analysis is very user-friendly, requiring minimal configuration of the command. Its calculation steps are as follows:
- Based on a converged and adjusted power flow, the modal analysis starts with the calculation of the system initial conditions. Alternatively, any interrupted status of a time domain simulation could be used as the initial condition.
- The system A-matrix is constructed automatically for the complete system (including generators, general loads, predefined system plant and controller models as well as DSL devices).
- System and model linearization - including user-defined models - is performed by iterative procedures. Limiting devices are disabled automatically. The representation of the network model is equivalent to the simulation model, allowing a direct comparison/validation between time domain simulations and modal analysis results.
- Support of QR-algorithm as well as the Arnoldi-Lanczos method.
- Calculation of all eigenvalues based on QR algorithm
- Selective eigenvalue calculation:
- computation of a certain part of the eigenvalue spectrum: calculation of a user-definable number of (closest) eigenvalues around a complex reference point
- based on the Arnoldi-Lanczos method
- recommended as a fast approach for higher order systems for which calculation of all eigenvalues by QR algorithm is too time-consuming
- Calculation results include eigenvalues (together with oscillation information such as damped frequency, damping, damping ratio, damping time constant, etc) and left and right eigenvectors. From eigenvectors, the individual machines’ controllability, observability, and participation factors are derived with respect to each mode.
- Powerful post-processing tools for result visualization
- Tabular result representation of:
- Eigenvalues (including all oscillation information such as damped frequency, damping, damping ratio, damping time constant, etc)
- Eigenvectors (individual controllability, observability, participation of individual machines for any selected mode)
- Eigenvalue Plot
- Visualization of calculated eigenvalues in the Gaussian plane
- Various filter and scaling options
- Automatic determination of stability border, highlighting of stable/unstable eigenvalues
- Plot has interactive features that facilitate detailed analysis of individual modes; convenient creation of phasor plots/bar diagrams for each mode
- Mode Bar Plot
- Bar diagram visualization of controllability, observability and participation factors of individual machines for a given mode
- Various filter options (e.g. restriction to minimum participation, and/or individual generators)
- Mode Phasor Plot
- Phasor diagram visualization of controllability, observability and participation factors of individual machines for a given mode
- Various filter options
- Automatic detection and highlighting of clusters for convenient identification of inter-area modes
- Tabular result representation of:
