**6. Applications: Power quality problem analysis**

72 Electrical Generation and Distribution Systems and Power Quality Disturbances

Time (msec)

zv; measured model; fit: 97.03%

zv; measured model; fit: 91.7%

5.5 6 6.5 7 7.5 8 8.5 9 9.5

Time (ms)

5.5 6 6.5 7 7.5 8 8.5 9 9.5

Fig. 21. Comparison of AC voltage and current output waveforms of a steady state FVMC

In Table 3 *nbi* , *nfi* and *nki* are poles, zeros and delays of a linear model. The subscript (1, 2, 3 and 4) stands for relations between DC voltage-AC voltage, DC current-AC voltage, DC voltage-AC current and DC current-AC current respectively. Therefore, the linear

The first value of percentages of fit in each type, shown in the Table 3, is the accuracy of the voltage output, the second the current output from the model. From the results, nonlinear estimators can describe the photovoltaic grid connected system. The estimators are good in terms of accuracy, with a low order model or a low FPE and AIC. Under most of testing conditions, high accuracy of more than 85% is achieved, except the case of FVLC. This is because of under such an operating condition, the inverter has very small current, and it is operating under highly nonlinear behavior. Then complex of nonlinear function and parameter adjusted is need for achieve the high accuracy and low order of model. After obtaining the appropriate model, the PVGCS system can be analyzed by nonlinear and linear analyses. Nonlinear parts are analyzed from the properties of nonlinear function such as dead-zone interval, saturation interval, piecewise range, Sigmoid and Wavelet properties. Nonlinear properties are also considered, e.g. stability and irreversibility In order to use linear analysis, Linearization of a nonlinear model is required for linear control design and analysis, with acceptable representation of the input/output behaviors. After linearizing the model, we can use control system theory to design a controller and perform linear analysis. The linearized command for computing a first-order Taylor series approximation for a system requires specification of an operating point. Subsequently, mathematical representation can be obtained, for example, a discrete time invariant state space model, a

parameters of the model are 1234 [,,,] *nnnn bbbb* , 1234 [,,,] *nnnn ffff* , 1234 [,,,] *nnnn kkkk* .



MIMO model

transfer function and graphical tools.

A C C urrent (A )

0

5

A C v oltage (V )

0

200

A power quality analysis from the model follows the Standard IEEE 1159 Recommend Practice for Monitoring Electric Power Quality [59]. In this Standard, the definition of power quality problem is defined. In summary, a procedure of this Standard when applied to operating systems can be divided into 3 stages (i) Measurement Transducer, (ii) Measurement Unit and (iii) Evaluation Unit. In comparing operating systems and modeling, modeling is more advantageous because of its predictive power, requiring no actual monitoring. Based on proposed modeling, the measurement part is replaced by model prediction outputs, electrical values such as RMS and peak values, frequency and power are calculated, rather than measured. The actual evaluation is replaced by power quality analysis. The concept representation is shown in Fig.22.

Fig. 22. Diagram of power quality analysis from IEEE 1159 and application to modeling
