**3. System Identification**

System identification is the process for modeling dynamical systems by measuring the input/output from system**.** In this section, the principle of system identification is described. The classification is introduced and particularly a Hammerstein-Wiener model is explained. Finally, a MIMO (multi input multi output model with equation and characteristic is illustrated.

Modeling of Photovoltaic Grid Connected Inverters

power system.

response.

**3.1.2 Physical modeling** 

Covariance function Correlation analysis

Impulse response Spectral analysis

Empirical Transfer Function Estimate and Periodogram

Step response

are done by complex digital controls.

**System Identification**

**Nonparametric Model Parametric Model**

Auto regressive (AR)

Auto regressive with exogenous (ARX) Box-jenkin (BJ)

Auto regressive moving averaging with exogenous

Output Error (OE)

Linear state space model (LSS) Laplace Transfer function (LTF)

(ARMAX)

Fig. 7. Classification of system identification

**3.1.3 Model structure selection** 

Based on Nonlinear System Identification for Power Quality Analysis 59

mathematical and physical characteristics and details of systems for the purposes of controlling, maintenance and trouble shooting of systems, and planning of managing the

Photovoltaic inverters, particularly commercial products, compose of two parts, i.e. a power circuit and a control circuit. Power electronic components convert, transfer and control power from input to output. The control system, switching topologies of power electronics

Model structure selection is the stage to classify the system and choose the method of system identification. The system identification can be classified to yield a nonparametric model and a parametric model, shown in Fig 7. A nonparametric model can be obtained from various methods, e.g. Covariance function, Correlation analysis. Empirical Transfer Function Estimate and Periodogram, Impulse response, Spectral analysis, and Step

**Linear Model Nonlinear Model**

Parametric models can be divided to two groups: linear parametric models and nonlinear parametric models. Examples of linear parametric models are Auto Regressive (AR), Auto Regressive Moving Average (ARMA), and Auto Regressive with Exogenous (ARX), Box-Jenkins, Output Error, Finite Impulse Response (FIR), Finite Step Response (FSR), Laplace Transfer Function (LTF) and Linear State Space (LSS). Examples of nonlinear parametric models are Nonlinear Finite Impulse Response (NFIR), Nonlinear Auto-Regressive with Exogenous (NARX), Nonlinear Output Error (NOE), and Nonlinear Auto-Regressive with

Nonlinear State space model (NSS)

Nonlinear Autoregressive with moving average exogenous

(NARMAX)

Hammerstein

Wiener

Nonlinear Box-Jenkins (NBJ)

Nonlinear Autoregressive with exogenous (NARX)

Hammerstein - Wiener

Wiener - Hammerstein

Nonlinear Output Error Model (NOE)
