Eigenanalysis

The RAMSES Eigenanalysis tool is a MATLAB-based tool for computing eigenvalues and eigenvectors of power system models in descriptor form, extracted from RAMSES simulations.

Overview

The tool analyzes small-signal stability by computing eigenvalues of the system Jacobian matrix. It supports both differential-algebraic equation (DAE) systems and provides multiple computational methods.

Features

• Multiple analysis methods: QZ (standard), ARPACK (sparse), Arnoldi (iterative), JDQR (targeted)
• Interactive analysis: dominant eigenvalue identification, mode shape analysis, participation factors, damping ratios
• Automatic Jacobian extraction from RAMSES simulation data

Prerequisites

• MATLAB R2016a or later
• PyRAMSES for Jacobian matrix extraction

Installation

addpath('path/to/RAMSES-Eigenanalysis')
addpath('path/to/RAMSES-Eigenanalysis/scripts')

Workflow

1. Extract Jacobian from RAMSES

Use PyRAMSES to run a simulation and export the Jacobian:

import pyramses

ram = pyramses.sim()
case = pyramses.cfg('cmd.txt')
ram.execSim(case)

Ensure the disturbance file includes the Jacobian export command:

time(s) JAC 'jac'

And the solver settings include:

$OMEGA_REF SYN ;
$SCHEME IN ;

2. Run Eigenanalysis in MATLAB

ssa('jac_val.dat', 'jac_eqs.dat', 'jac_var.dat', 'jac_struc.dat')

With custom parameters:

ssa('jac_val.dat', 'jac_eqs.dat', 'jac_var.dat', 'jac_struc.dat', ...
    real_limit, damp_ratio, method)

Parameters

Parameter	Description	Default
jac_val.dat	Matrix values in coordinate format	—
jac_eqs.dat	Equation descriptions (differential/algebraic)	—
jac_var.dat	Variable descriptions (differential/algebraic)	—
jac_struc.dat	Decomposed power system structure (optional)	—
real_limit	Real part threshold for dominant eigenvalues	$-\infty$
damp_ratio	Damping ratio threshold	1.0
method	Analysis method: 'QZ' or 'ARP'	'QZ'

Analysis Methods

QZ Method (Default)

• Uses MATLAB’s eig() function with algebraic variable elimination
• Suitable for small to medium systems (< 50,000 states)
• Provides the complete eigenvalue spectrum
• Supports mode shape and participation factor analysis

ARPACK Method

• Sparse descriptor approach using Krylov-Schur algorithm via MATLAB’s eigs()
• Suitable for large systems
• Computes a subset of eigenvalues near a specified target

JDQR Method

• Jacobi-Davidson QR method for targeted eigenvalue computation
• Useful for finding specific eigenvalues (e.g., poorly damped modes)

Interactive Analysis

After computing eigenvalues, the tool provides an interactive menu to:

1. View dominant eigenvalues
2. Analyze mode shapes
3. Calculate participation factors
4. Examine damping ratios
5. Explore system structure

Repository

Source code: SPS-L/RAMSES-Eigenanalysis