**Modeling of Photovoltaic Grid Connected Inverters Based on Nonlinear System Identification for Power Quality Analysis**

Nopporn Patcharaprakiti1,2, Krissanapong Kirtikara1,2, Khanchai Tunlasakun1, Juttrit Thongpron1,2, Dheerayut Chenvidhya1, Anawach Sangswang1, Veerapol Monyakul1 and Ballang Muenpinij1 *1King Mongkut's University of Technology Thonburi, Bangkok, 2Rajamangala University of Technology Lanna, Chiang Mai Thailand* 

#### **1. Introduction**

52 Electrical Generation and Distribution Systems and Power Quality Disturbances

Munteau, I., AI. Bratcu, N-A. Cutululis, E. Ceaga , Optimal control of wind energy, towards

Nikman,T., (2010) A new fuzzy adaptive hybrid particle swarm optimization algorithm for

Pothiya, S., I. Nagamroo, and W. Kongprawechnon, Application of multiple tabu search

Price, K., R. Storn, and J. Lampinen, Differential Evolution: A Practical Approach to Global

Simon, D., Biogeography-based optimization, *IEEE Trans. Evol.Comput*., vol. 12, no. 6, pp.

Storn, R. and K. Price, Differential Evolution-A Simple and Efficient Adaptive Scheme for

Sttot, B., and J. L. Marinho, Linear programming for power system network security

Wood, J. , and B. F. Wollenberg, Power Generation, Operation, and Control, 2nd ed. New

Wood, J., and B. F. Wollenberg, Power Generation, Operation, and Control, 2nd ed. New

Yankui, Z., Z. Yan, B. Wu, J. Zhou, Power injection model of STATCOM with control and

Zhang, X.P., Energy loss minimization of electricity networks with large wind generation

non-linear, non-smooth and non-convex economic dispatch, *Journal of Applied* 

algorithm to solve dynamic economic dispatch considering generator constraints, *International Journal of Energy Conversion and Management*, vol. 49, pp. 506-516, 2008.

Global Optimization Over Continuous Spaces, International Computer Science

applications, *IEEE Trans. Power Apparat. Syst*., vol. PAS-98, pp. 837-848, May/June

operating limit for power flow and voltage stability analysis, *Electic Power Systems* 

using FACTS, *IEEE Power and Energy Society General Meeting-Conversion and Delivery* 

a global approach, London: Springer-Verlag: 2008.

Optimization. Berlin, Germany: Springer- Verlag, 2005.

Institute, Berkeley, CA, 1995, Tech. Rep. TR-95–012.

*of Electrical Energy in the 21st Century*, 2008.

*Energy*, vol. 87, pp. 327-339.

702–713, Dec. 2008.

York: Wiley, 1984.

York: Wiley, 1984.

*Researchs*, 2006.

1979.

Photovoltaic systems are attractive renewable energy sources for Thailand because of high daily solar irradiation, about 18 MJ/m2/day. Furthermore, renewable energy is boosted by the government incentive on adders on electricity from renewable energy like solar PV, wind and biomass, introduced in the second half of 2000s. For PV systems, domestic rooftop PV units, commercial rooftop PV units and ground-based PV plants are appealing. Applications of electricity supply from PV plants that have been filed total more than 1000 MW. With the adder incentive, more households will be attracted to produce electricity with a small generating capacity of less than 10 kW, termed a very small power producer (VSPP). A possibility of expanding domestic roof-top grid-connected units draw our attention to study single phase PV-grid connected systems. Increased PV penetration can have significant [1-2] and detrimental impacts on the power quality (PQ) of the distribution networks [3-5]. Fluctuation of weather condition, variations of loads and grids, connecting PV-based inverters to the power system, requires power quality control to meet standards of electrical utilities. PV can reduce or improve power quality levels [6-9]. Different aspects should be taken into account. In particular, large current variations during PV connection or disconnection can lead to significant voltage transients [10]. Cyclic variations of PV power output can cause voltage fluctuations [11]. Changes of PV active and reactive power and the presence of large numbers of single phase domestic generators can lead to long-duration voltage variations and unbalances [12]. The increasing values of fault currents modify the voltage sag characteristics. Finally, the waveform distortion levels are influenced in different ways according to types of PV connections to the grid, i.e. direct connection or by power electronic interfaces. PV can improve power quality levels, mainly as a consequence of increase of short circuit power and of advanced controls of PWM converters and custom devices. [13]

Grid-connected inverter technology is one of the key technologies for reliable and safety grid interconnection operation of PV systems [14-15]. An inverter being a power

Modeling of Photovoltaic Grid Connected Inverters

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

synchronization, protection units, and loads, shown in Fig. 1.

**Power Converter**

**Control Unit**

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

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

operating situations.

**Solar Array**

**2.1 Solar array** 

operating conditions.

local loads and utility grid variations.

Based on Nonlinear System Identification for Power Quality Analysis 55

following section, the experimental design and implementation to model the system is illustrated. After that, the obtained model from prior sections is analyzed in terms of control theories. In the last section, the power quality analysis is discussed. The output prediction is performed to obtain electrical outputs of the model and its electrical power. The power quality nature is analyzed for comparison with outputs of model. Subsequently, voltage and current outputs from model are analyzed by mathematical tools such the Fast Fourier Transform-FFT, the Wavelet method in order to investigate the power quality in any

In this section, PV grid connected structures and components are introduced. Structures of PBGCS consist of solar array, power conditioners, control systems, filtering,

**Filtering**

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

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,

**PCC**

**Utility**

**Load**

**Synchronization & Protection**

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

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 waveforms.

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

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 following section, the experimental design and implementation to model the system is illustrated. After that, the obtained model from prior sections is analyzed in terms of control theories. In the last section, the power quality analysis is discussed. The output prediction is performed to obtain electrical outputs of the model and its electrical power. The power quality nature is analyzed for comparison with outputs of model. Subsequently, voltage and current outputs from model are analyzed by mathematical tools such the Fast Fourier Transform-FFT, the Wavelet method in order to investigate the power quality in any operating situations.
