Power System Small-Signal Stability Analysis

Power system small-signurbance stability analysis generally adopts the small-disturbance method, which introduces additional steps before calculating eigenvalues of the coefficient matrix from linear differential equations. In implementation, the algorithm first requires determination of the system's initial state parameters including power, voltage, and reactance values. Using these parameters, the coefficient matrix for the linear differential equations is constructed programmatically. The eigenvalue calculation module then computes the characteristic roots through numerical methods like QR decomposition. Specifically, the implementation requires these input parameters: initial complex power S0 (in a+bi format), infinite bus voltage V0, direct-axis equivalent reactance Xd, synchronous angular speed, inertia time constant Tj, and comprehensive damping coefficient D. The code validates these inputs before assembling the state matrix A for eigenvalue analysis. The stability assessment algorithm evaluates eigenvalue positions in the complex plane - systems are stable when all eigenvalues have negative real parts. Based on the stability margin calculated from eigenvalue distributions, control logic can automatically suggest parameter adjustments for power, voltage, and reactance to enhance system stability. This enhanced computational framework enables more accurate small-signal stability assessment and facilitates proactive stabilization measures for secure power system operation.