N4SID and MOESP Algorithms to Highlight the Ill-conditioning into Subspace Identification

In this paper,an analysis for ill conditioning problem in subspace identifcation method is provided.The subspace identifcation technique presents a satisfactory robustness in the parameter estimation of process model which performs control.As a frst step,the main geometric and mathematical tools used in subspace identifcation are briefly presented.In the second step,the problem of analyzing ill-conditioning matrices in the subspace identifcation method is considered.To illustrate this situation,a simulation study of an example is introduced to show the ill-conditioning in subspace identifcation.Algorithms numerical subspace state space system identifcation(N4SID)and multivariable output error state space model identifcation(MOESP)are considered to study,the parameters estimation while using the induction motor model,in simulation(Matlab environment).Finally,we show the inadequacy of the oblique projection and validate the efectiveness of the orthogonal projection approach which is needed in ill-conditioning;a real application dealing with induction motor parameters estimation has been experimented.The obtained results proved that the algorithm based on orthogonal projection MOESP,overcomes the situation of ill-conditioning in the Hankel s block,and thereby improving the estimation of parameters.

A Hybrid Coordinated Design Method for Power System Stabilizer and FACTS Device Based on Synchrosqueezed Wavelet Transform and Stochastic Subspace Identification

The occurrence of low-frequency electromechanical oscillations is a major problem in the effective operation of power systems. The scrutiny of these oscillations provides substantial information about power system stability and security. In this paper, a new method is introduced based on a combination of synchrosqueezed wavelet transform and the stochastic subspace identification (SSI) algorithm to investigate the low-frequency electromechanical oscillations of large-scale power systems. Then, the estimated modes of the power system are used for the design of the power system stabilizer and the flexible alternating current transmission system (FACTS) device. In this optimization problem, the control parameters are set using a hybrid approach composed of the Prony and residual methods and the modified fruit fly optimization algorithm. The proposed mode estimation method and the controller design are simulated in MATLAB using two test case systems, namely IEEE 2-area 4-generator and New England-New York 68-bus 16-generator systems. The simulation results demonstrate the high performance of the proposed method in estimation of local and inter-area modes, and indicate the improvements in oscillation damping and power system stability.