**2. PV grid connected system (PVGCS) operation**

In this section, PV grid connected structures and components are introduced. Structures of PBGCS consist of solar array, power conditioners, control systems, filtering, synchronization, protection units, and loads, shown in Fig. 1.

Fig. 1. Block diagram of a PV grid connected system

## **2.1 Solar array**

54 Electrical Generation and Distribution Systems and Power Quality Disturbances

conditioner of a PV system consists of power electronic switching components, complex control systems [16]. In addition, their operations depends on several factors such as input weather condition, switching algorithm and maximum power point tracking (MPPT) algorithm implemented in grid-connected inverters, giving rise to a variety of nonlinear behaviors and uncertainties [17]. Operating conditions of PV based inverters can be considered as steady state condition [18], transient condition [19-20], and fault condition such islanding [21-22]. In practical operations, inverters constantly change their operating conditions due to variation of irradiances, temperatures, load or grid impedance variations. In most cases, behavior of inverters is mainly considered in a steady state condition with slowly changing grid, load and weather conditions. However, in many instances conditions suddenly change, e.g. sudden changes of input weather, cloud or shading effects, loads and grid changes from faults occurring in near PV sites [23]. In these conditions, PV based inverters operate in transient conditions. Their average power increases or decreases upon the disturbances to PV systems [24]. In order to understand the behavior of PV based inverters, modeling and simulation of PV based inverter systems is the one of essential tools

There are two major approaches for modeling power electronics based systems, i.e. analytical and experimental approaches. The analytical methods to study steady state, transient models and islanding conditions of PV based inverter systems, such as state space averaging method [26], graphical techniques [27-28] and computation programming [29]. In using these analytic methods, one needs to know information of system. However, PV based inverters are usually commercial products having proprietary information; system operators do not know the necessary information of products to parameterize the models. In order to build models for nonlinear devices without prior information, system identification methods are exposed [33-34]. In the method reported in this paper, specific information of inverter is not required in modeling. Instead, it uses only measured input and output

Many recent research focuses on identification modeling and control for nonlinear systems [35-37]. One of the effective identification methods is block oriented nonlinear system identification. In the block oriented models, a system consists of numbers of linear and nonlinear blocks. The blocks are connected in various cascading and parallel combinations representing the systems. Many identification methods of well known nonlinear block oriented models have been reported in the literature [38-39]. They are, for example, a NARX model [40], a Hammerstein model [41], a Wiener model [42], a Wiener-Hammerstein model and a Hammerstein-Wiener model [43]. Advantages of a Hammerstein model and a Wiener model enables combination of both models to represent a system, sensors and actuators in to one model. The Hammerstein-Wiener model is recognized as being the most effective for

In this paper, real operating conditions weather input variation, i.e. load variations and grid variations, of PV- based inverters are considered. Then two different experiments, steady state and transient condition, are designed and carried out. Input-output data such as currents and voltages on both dc and ac sides of a PV grid-connected systems are recorded. The measured data are used to determine the model parameters by a Hammerstein-Wiener nonlinear model system identification process. In the Section II, PV system characteristics are introduced. The I-V characteristic, an equivalent model, effects of radiation and temperature on voltage and current of PV are described. In the Section III, system identification methods, particularly a Hammerstein-Wiener Model is explained. In the

for analysis, operation and impacts of inverters on the power systems [25].

modeling complex nonlinear systems such PV based inverters [44].

waveforms.

Environmental inputs affecting solar array/cell outputs are temperature (T) and irradiance (G), fluctuating with weather conditions. When the ambient temperature increases, the array short circuit current slight increases with a significant voltage decrease. Temperature and I-V characteristics are related, characterized by array/cell temperature coefficients. Effects of irradiance, radiant solar energy flux density in W/m2, apart from solar radiation at sea level, are determined by incident angles and array/cell envelops. Typical characteristics of relationship between environmental inputs (irradiance and temperature) and electrical parameters (current and voltage of array/cells) are shown in Fig. 2 [45]. In our experimental designs, operating conditions of PV systems under test is designed and based on typical operating conditions.

#### **2.2 Operating conditions of a PV grid connected system**

A PV system, generating power and transmitting it into the utility, can be categorized in three cases, i.e. a steady state condition, a transient condition and a fault condition like islanding. Three factors affecting the operation of inverters are input weather conditions, local loads and utility grid variations.

Modeling of Photovoltaic Grid Connected Inverters

stability and reliability of power systems.

**2.3 Power converter** 

Fig. 4(b) [54].

**PV Array**

illustrated.

**DC-DC with**

**Isolation DC-AC AC Filter**

Fig. 4. Control techniques for an inverter

**3. System Identification** 

/ δ

**V**

**Controller**

**V/0**

Based on Nonlinear System Identification for Power Quality Analysis 57

AM - 14:OO PM). Loads fluctuate upon activities of customer groups, for example, a peak load for industrial zones occurs in afternoon (13:00 - 17:00 PM) and a peak load for residential zones occurs in evening(18:00 - 21:00 PM). Variations from steady state conditions impact power quality such as overvoltage, over-current, harmonics, and so on. In case of transients, there are variations in inputs, loads and utility. Weather variations such solar irradiance and temperature exhibit significant changes. Unexpected accidents happen. Local loads may sudden change due to activities of customers in each time. A utility has some faults in nearby locations which impact utility parameters such grid impedance. These conditions lead to short duration power quality problems with such spikes, voltage sag, voltage swell. In some extreme cases, abnormal conditions, such as very low solar irradiance or abnormal conditions such islanding, the gird-connected PV systems may collapse. The PV systems are black out and cut out of the utility grid. Such can affect power quality,

There are several topologies for converting a DC to DC voltage with desired values, for example, Push-Pull, Flyback, Forward, Half Bridge and Full Bridge [49]. The choice for a specific application is often based on many considerations such as size, weight of switching converter, generation interference and economic evaluation [50-51]. Inverters can be classified into two types, i.e. voltage source inverter (VSI) if an input voltage remains constant and a current source inverter (CSI) if input current remains constant [52-53]. The CSI is mostly used in large motor applications, whereas the VSI is adopted for and alone systems. The CSI is a dual of a VSI. A control technique for voltage source inverters consists of two types, a voltage control inverter, shown in Fig. 4(a) and a current control inverter,

**L**

**PV Array**

**DC-DC with**

**Isolation DC-AC AC Filter**

**Controller**

**I-ref**

**Iac**

**L**

**N**

**N**

(a) Voltage Control Inverter (b) Current Control Inverter

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

Fig. 2. Temperature and irradiance effects on I-V characteristics of PV arrays/cells [46]

Fig. 3. Variations of solar irradiance and temperature throughout a day conditioning PVGCS operation

Firstly, under a steady state condition, input, load and utility under consideration are treated as being constant with slightly change weather condition. Installed capacities of PV systems in a steady state are low, medium and high capacity. According to the weather conditions throughout a day as shown in Fig. 3 [47-48], a low radiation about 0-400 W/m2 is common in an early morning (6:00 AM-9:00 AM) and early evening (16:00 PM-19:00 PM), medium radiation of 400-800 W/m2 in late morning (9:00 AM-11:00 PM) and early afternoon (14:00 PM-16:00 PM) and high radiation of 800-1000 W/m2 around noon (11.00 AM - 14:OO PM). Loads fluctuate upon activities of customer groups, for example, a peak load for industrial zones occurs in afternoon (13:00 - 17:00 PM) and a peak load for residential zones occurs in evening(18:00 - 21:00 PM). Variations from steady state conditions impact power quality such as overvoltage, over-current, harmonics, and so on. In case of transients, there are variations in inputs, loads and utility. Weather variations such solar irradiance and temperature exhibit significant changes. Unexpected accidents happen. Local loads may sudden change due to activities of customers in each time. A utility has some faults in nearby locations which impact utility parameters such grid impedance. These conditions lead to short duration power quality problems with such spikes, voltage sag, voltage swell. In some extreme cases, abnormal conditions, such as very low solar irradiance or abnormal conditions such islanding, the gird-connected PV systems may collapse. The PV systems are black out and cut out of the utility grid. Such can affect power quality, stability and reliability of power systems.
