Photovoltaic Array: Using Golden Section Search Algorithm

CHAPTER - 1
INTRODUCTION
1.1 STATE OF ART
Photovoltaic (PV) generation is becoming increasingly important as a renewable source since it offers many advantages such as incurring no fuel costs, not being polluting, requiring little maintenance and emitting no noise among others. But still, these modules have relatively low conversion efficiency due to their nonlinear and temperature-dependent voltage-current and voltage power characteristics. Power generated by PV generators and injected into the grid is gaining more and more visibility in the area of PV applications. This is mainly because the world’s power demand is steadily increasing.
PV is a solar power technology that uses solar cells or solar photovoltaic arrays to convert light from the sun directly into electricity. Photovoltaic is the direct conversion of light into electricity at the atomic level. Some materials exhibit a property known as the photoelectric effect that causes them to absorb photons of light and release electrons. When these free electrons are captured, electric current results that can be used as electricity. Solar cells produce direct current electricity from light, which can be used to power equipment or to recharge a battery. The PV arrays can be used either for standalone applications or grid connected. The first practical application of photovoltaic was to power orbiting satellites and other spacecraft and pocket calculators, but today the majority of photovoltaic modules are used for grid connected power generation. Grid connected photovoltaic energy conversion systems are composed of a dc-dc converter and an inverter. The dc-dc converter is controlled to track the maximum power point of the photovoltaic array and the inverter is controlled to produce voltage in such a way that the grid current has low total harmonic distortion (THD) and it is in phase with the grid voltage.
Not many PV systems have so far been put into the grid operation. This is due to a relatively high cost. The work in this context in this thesis work is to design an MATLAB/SIMULINK photovoltaic generation systems for connection in a three phase system so as to comply with the grid standards.
1.1.1 GRID-CONNECTED PV SYSTEM EQUIPMENT

Figure 1.1: Grid-connected PV system and equipment
1.The solar modules making up the solar array convert the sun’s energy to direct current (DC) electrical energy.
2. The mounting system supports the solar array at the desired angle to the sun.
3. The power center, custom-configured for the system, will include
a. A low-distortion inverter to transform DC into the alternating current (AC) used by most of our appliances and by the utilities;
b. An interconnect with incoming utility power; c. A connection to your breaker panel.
4. The system data monitor shows how much energy is flowing in from the energy sources and how much is flowing out to the loads.
5. The balance of system hardware consists of wiring, terminations, Ground Fault Interrupter, surge protections, DC and AC disconnects, etc

1.1.2 BENEFITS OF PHOTOVOLTAIC SYSTEMS
Solar electric systems offer many advantages including the fallowing
1. They are safe, clean and quiet to operate
2. They are highly reliable
3. They require virtually no maintenance
4. They operate with less cost – effectively in remote areas and many residential and
Commercial Applications.
5. They are flexible and can be expanded at any time to meet your electrical needs and give you increased autonomy – independence from the grid or backup during outages.

1.1.3 THESIS OBJECTIVE

This thesis aims to model photovoltaic system at steady state and study their transient responses to changing load. The PV System components which have been studied are the Photovoltaic Cell, DC to DC boost converter and grid connected inverter. It is intended that the work completed in this thesis will lay the ground work for further model development. The long term goal is to have of a highly sophisticated, complete model of a stand alone, grid connected PV system so as to allow for a full understanding of how PV System behave. The goal of this thesis is to build a complete model of a PV System including the PV array, MPPT, converters and their power electronics, a load and mains model in MATLAB/ SIMULINK.

1.2 LITERATURE REVIEW
L.A.C Lopes and Lienhardt -A simplified nonlinear power source for simulating PV panels [1].

This paper presents the development of power conditioning equipment for operation at the maximum power point and for utility interfacing usually requires Solar Array Simulators (SAS) that are relatively expensive and a simple nonlinear power source based on a PWM switched resistor that can be used for preliminary evaluations of power conditioning equipment for PV systems.

B. Kroposki, R. DeBlasio - Technologies for the New Millennium Photovoltaics as a Distributed Resource[2]. This recommended practice details power quality, safety, and protection requirements for connection to the utility grid. This paper describes what types of PV systems are available, what the benefits are for PV systems, and what the interconnection issues and solutions are for using PV as a distributed resource.
A. Hansen, P. Lars, H. Hansen and H. Bindner -Models for a Stand-Alone PV System[3].
This paper presents a number of models for modeling and simulation of a stand-alone photovoltaic (PV) system with a battery bank verified against a system installed at Riso National Laboratory. The study is carried out at Riso National Laboratory with the main purpose to establish a library of simple mathematical models for each individual element of a stand-alone PV system, namely solar cells, battery, controller, inverter and load.
Francisco M. González-Longatt -Model of Photovoltaic Module in MATLAB[4].
This paper define a circuit-based simulation model for a PV cell in order to allow estimate the electrical behavior of the cell with respect changes on environmental parameter of temperature and irradiance. An accurate PV module electrical model is presented based on the Shockley diode equation. The general model was implemented on MATLAB scrip file, and accepts irradiance and temperature as variable parameters and outputs the I-V characteristic.
Marcelo Gradella Villalva, Jonas Rafael Gazoli, and Ernesto Ruppert Filho-Comprehensive Approach to Modeling and Simulation of Photovoltaic Arrays [5].
The main objective of this paper is to find the parameters of the nonlinear I–V equation by adjusting the curve at three points: open circuit, maximum power, and short circuit. Given these three points, which are provided by all commercial array datasheets, the method finds the best I–V equation for the single-diode photovoltaic (PV) model including the effect of the series and parallel resistances, and warranties that the maximum power of the model matches with the maximum power of the real array.
D. P. Hohm, M. E. Ropp-Comparative Study of Maximum Power Point Tracking Algorithms Using an Experimental, Programmable, Maximum Power Point Tracking Test Bed[6].
The authors have compares all the different kinds of algorithm that are used for the maximum power point tracking. This helps in proper selection of the algorithm. Preliminary results indicate that perturb and observe compares favorably with incremental conductance and constant voltage. Although incremental conductance is able to provide marginally better performance in case of rapidly varying atmospheric conditions, the increased complexity of the algorithm will require more expensive hardware, and therefore may have an advantage over perturb and observe only in large PV arrays.
Riming Shao, Liuchen Chang - A New maximum power point tracking method for photovoltaic arrays using golden section search algorithm [7].
This paper introduces a new maximum power point tracking (MPPT) method with the golden section search (GSS) algorithm for photovoltaic (PV) systems. The basic principle and the implementation procedures of the GSS algorithm are elaborated in the paper; and the PV simulation model in Matlab/Simulink is also developed.
T. Esram, P. L. Chapman-Comparison of Photovoltaic Array Maximum Power Point Tracking Techniques[8].

A digital hill-climbing control strategy combined with a bidirectional current mode power cell is presented which allows to get a regulated bus voltage topology, suitable for space applications, by means of two converters. Theory, simulation and breadboard validation are successively detailed

W.J.A. Teulings, J.C. Marpinard, A. Capel, D.O’Sullivan-A new Maximum Power Point Tracking system[9]. A new MPPT system has been developed, consisting of a Buck-type dc/dc converter, which is controlled by a microcontroller-based unit.

Eftichios Koutroulis, Kostas Kalaitzakis-Development of a Microcontroller-Based,Photovoltaic Maximum Power Point Tracking Control System[10].

The many different techniques for maximum power point tracking of photovoltaic (PV) arrays are discussed. The techniques are taken from the literature dating back to the earliest methods. This paper should serve as a convenient reference for future work in PV power generation.

R.Kayalvizhi, S.P.Natarajan, D.Sivakumar, K.Elangovan - Design and Simulation of PI Control for Paralleled Positive Output Elementary Luo Converters for Distributed Power Supplies[11].

Luo converter is a recently developed DC-DC converter. Positive output Luo converter performs the voltage conversion from positive source voltage to positive load voltage. Parallel connection of Luo converters are used when available converters are of lower current rating but load requires higher current. The objectives of this work are to design and develop PI control for paralleled positive output Luo converters using MATLAB software.

Hyo-Sik Park, and Hee-Jun Kim-Simultaneous Control of DC-DC Converters by DSP Controller[12].
This paper presents a multi output converter system that controls, simultaneously and independently, the separate Buck converter and Boost converter with the different specification by one DSP digital controller. By setting the software switch state, PI controller can be applied as a controller for each converter without any change of hardware. Also, PI control characteristics of each DC-DC converter is validated by experimental results.
Z. Ye, R. Walling, L. Garces, R. Zhou, L. Li, and T. Wang- Study and Development of Anti-Islanding Control for Grid-Connected Inverters[13].
Control of inverters in distributed source environments such as in isolated ac systems, large and distributed uninterruptible power supply (UPS) systems are explained.
Zhihong Ye, L. Li, L. Garces, C. Wang, R. Zhang, M. Dame R. Walling, N. Miller-A New Family of Active Anti-Islanding Schemes Based on DQ Implementation For Grid-Connected Inverters[15].
Unintentional islanding protection of distributed generation is a key function for standards compliance. For those distributed generations that use an inverter as grid interface, the function can be implemented as part of the inverter control. Existing anti-islanding schemes used in inverters have power quality and non-detection zone issues. This paper proposes a new family of schemes that have negligible power quality degradation and no non-detection zone. Design guidelines based on frequency-domain analysis is also provided.
Nasrudin Abd Rahim, Jeyraj Selvaraj and Krismadinata-Hysteresis Current Control and Sensorless MPPT for Grid-Connected Photovoltaic Systems[16].
This paper describes a control method for single-phase transformerless grid-connected inverter system for photovoltaic (PV) application. The system consists of a DC-DC Boost Converter and a full-bridge inverter. The DC-DC Boost Converter implements a Sensorless Maximum Power Point Tracker (MPPT) algorithm with regulated DC bus voltage while the full-bridge inverter implements a Hysteresis Current Control as the control method.
N. Hamrouni and A.Chérif-Modelling and control of a grid connected photovoltaic system[17].
This paper presents a simulation model of the electric part of a grid connected photovoltaic generator. The model contains a detailed representation of the main components of the system that are the solar array, boost converter and the grid side inverter. A proper control of the DC/DC converter is developed in order to extract the maximum amount of from the photovoltaic generator.. The PQ control approach has been presented for the inverter.
J. M. A. Myrzik and M. Calais-String and Module Integrated Inverters for Single-Phase Grid Connected Photovoltaic Systems - A Review[18].

This paper presents an overview on recent developments and a summary of the state-of-the-art in inverter technology for single-phase grid connected photovoltaic (PV) systems. The information provided includes details on commercially available European string and module integrated PV inverters, their efficiency, price trends and market share. This review is given for inverters for a power level up to 6kW. Furthermore, the paper deals with the recent developments of new inverter topologies and PV system concepts and discusses possible future trends.

F. Blaabjerg, Z. Chen and S. Kjaer-Power Electronics as Efficient Interface in Dispersed Power Generation Systems[19].

This paper will first briefly discuss three different alternative/renewable energy sources. Next, various configurations of the wind turbine technology are presented, as this technology seems to be most developed and cost-effective. Finally, the developments and requirements from the grid are discussed.

S. B. Kjaer and F. Blaabjerg-Design optimization of a single phase inverter for photovoltaic applications[20].

This paper is to present a novel inverter topology for photovoltaic (PV) applications, in particular for the AC-Module. A modified version of the inverter proposed by Shimizu et al. solves a major problem within the original topology: regeneration of transformer leakage energy. Also presented is a decomposition of the currents and voltages inside the inverter.

CHAPTER-2
PHOTOVOLTIAC CELL
2.1 INTRODUCTION A solar cell or photovoltaic cell is a device that converts light directly into electricity by the photovoltaic effect. Sometimes the term solar cell is reserved for devices intended specifically to capture energy from sunlight, while the term photovoltaic cell is used when the light source is unspecified. Assemblies of cells are used to make solar panels, solar modules, or photovoltaic arrays. Photovoltaic’s is the field of technology and research related to the application of solar cells in producing electricity for practical use. The energy generated this way is an example of solar energy (also called solar power).

2.1.1 GENERATION OF PV CELL High efficiency solar cells are a class of solar cell that can generate more electricity per incident solar power unit (watt/watt). Much of the industry is focused on the most cost efficient technologies in terms of cost per generated power. The two main strategies to bring down the cost of photovoltaic electricity are increasing the efficiency (as many of the costs scale with the area occupied per unit of generated power), and decreasing the cost of the solar cells per generated unit of power. The latter approach might come at the expense of reduced efficiency, so the overall cost of the photovoltaic electricity does not necessarily decrease by decreasing the cost of the solar cells. The challenge of increasing the photovoltaic efficiency is thus of great interest, both from the academic and economic points of view. Solar cells are often electrically connected and encapsulated as a module. PV modules often have a sheet of glass on the front (sun up) side, allowing light to pass while protecting the semiconductor wafers from the elements (rain, hail, etc.). Solar cells are also usually connected in series in modules, creating an additive voltage. Connecting cells in parallel will yield a higher current. Modules are then interconnected, in series or parallel, or both, to create an array with the desired peak DC voltage and current. The power output of a solar array is measured in watts or kilowatts. In order to calculate the typical energy needs of the application, a measurement in watt-hours, kilowatt-hours or kilowatt-hours per day is often used. A common rule of thumb is that average power is equal to 20% of peak power, so that each peak kilowatt of solar array output power corresponds to energy production of 4.8 kWh per day (24 hours x 1kW x 20% = 4.8 kWh).To make practical use of the solar-generated energy, the electricity is most often fed into the electricity grid using inverters (grid-connected PV systems); in standalone systems, batteries are used to store the energy that is not needed immediately. Solar cells can also be applied to other electronics devices to make itself power sustainable in the sun. There are solar cell phone chargers, solar bike light and solar camping lanterns that people can adopt for daily use.
2.1.2 PV GENERATOR A photovoltaic PV generator is the whole assembly of solar cells, connections, protective parts, supports etc. In the present modeling, the focus is only on cell/ module/ array. Solar cells consist of a p-n junction fabricated in a thin wafer or layer of semiconductor (usually silicon). In the dark, the I-V output characteristic’s of a solar cell has an exponential characteristic similar to that of a diode [1]. When solar energy (photons) hits the solar cell, with energy greater than band gap energy of the semiconductor, electrons are knocked loose from the atoms in the material, creating electron-hole pairs [2]. These carriers are swept apart under the influence of the internal electric fields of the p-n junction and create a current proportional to the incident radiation. When the cell is short circuited, this current flows in the external circuit; when open circuited, this current is shunted internally by the intrinsic p-n junction diode. The characteristics of this diode therefore set the open circuit voltage characteristics of the cell [3].

2.2 MODELING THE SOLAR CELL

Thus the simplest equivalent circuit of a solar cell is a current source in parallel with a diode. The output of the current source is directly proportional to the light falling on the cell (photocurrent I ph). During darkness, the solar cell is not an active device; it works as a diode, i.e. a p-n junction. It produces neither a current nor a voltage. However, if it is connected to an external supply (large voltage) it generates a current Id, called diode (D) current or dark current. The diode determines the I-V characteristics of the cell.

Figure 2.1: Circuit diagram of the PV model

Increasing sophistication, accuracy and complexity can be introduced to the model by adding in turn [4]:
• Temperature dependence of the diode saturation current Io.
• Temperature dependence of the photo current IL.
• Series resistance Rs, which gives a more accurate shape between the maximum power point and the open circuit voltage. This represents the internal losses due to the current flow. • Shunt resistance Rsh, in parallel with the diode, this corresponds to the leakage current to the ground and it is commonly neglected.
• Either allowing the diode quality factor n to become a variable parameter (instead of being fixed at either 1 or 2) or introducing two parallel diodes with independently set saturation currents.
In an ideal cell Rs = Rsh = 0, which is a relatively common assumption [6]. For this paper, a model of moderate complexity was used. The net current of the cell is the difference of the photocurrent, IL and the normal diode current Io. ……………………………………………..(2.1) The model included temperature dependence of the photocurrent IL and the saturation current of the diode Io.

…………………………………………...(2.2)
…….……………………………………...(2.3)
……………….…………………………………..(2.4)
……………………………………….(2.5)
……………………………………………….(2.6)
A series resistance Rs was included; which represents the resistance inside each cell in the connection between cells.

…………………………………………………..(2.7)
……………………………………...(2.8)

The shunt resistance R sh is neglected. A single shunt diode was used with the diode quality factor set to achieve the best curve match. This model is a simplified version of the two diode model presented by Gow and Manning. The circuit diagram for the solar cell is shown in Figur1.

2.2.1 CURENT-VOLTAGE (I-V) CURVE FOR A PV CELL

A typical I-V characteristic of the solar cell for a certain ambient irradiation G and a certain fixed cell temperature (T), is shown in Fig (2.2). For a resistive load, the load characteristic is a straight line with scope I/V=1/R. It should be pointed out that the power delivered to the load depends on the value of the resistance only .

Figure 2.2: typical I-V characteristic of the solar module

However, if the load R is small, the cell operates in the region M-N of the curve (Fig 2.2), where the cell behave as a constant current source, almost equal to the short circuit current. On the other hand, if the load R is large, the cell operates on the regions P-S of the curve, the cell behaves more as a constant voltage source, almost equal to the open-circuit voltage [3]. A real solar cell can be characterized by the following fundamental parameters, which are also sketched in Fig. 2.2.
• Short circuit current: Ish = Iph. It is the greatest value of the current generated by a cell. It is produce by the short circuit conditions: V = 0.
• Open circuit voltage correspond to the voltage drop across the diode (pn junction), when it is transverse by the photocurrent Iph (namely IL = Iph), namely when the generated currents is I = 0. It reflects the voltage of the cell in the night and it can be mathematically expressed as:
……………………………………….(2.9)
Where V t = (m k T/ e) is known as thermal voltage and T is the absolute cell temperature.
• Maximum power point is the operating point A (V max, I max) in Fig 2.2, at which the power dissipated in the resistive load is maximum: P max =V max* I max.
\

• Maximum efficiency is the ratio between the maximum power and the incident light power as shown in equation 2.10.

…………………………..……………………(2.10)

Where ‘Ga’ is the ambient irradiation and ‘A’ is the cell area.
• Fill factor is the ratio of the maximum power that can be delivered to the load and he product of I sc and VOC

……………………………………………..(2.11)

The fill factor is a measure of the real I-V characteristic. Its valued is higher than 0.7 for good cells. The fill factor diminishes as the cell temperature is increased. The open circuit voltage increases logarithmically with the ambient irradiation, while the short circuit current is a linear function of the ambient irradiation. The dominant effect with increasing cell’s temperature is the linear decrease of the open circuit voltage, the cell being thus less efficient. The short circuit current slightly increases with the cell temperature.

2.2.2 THE MODEL OF ENVIRONMENT VARIABLES The influence of the ambient irradiation G and the cell temperature T on the cell characteristics, can be obtained from the model equations. The PV cell photocurrent I L (A) is directly proportional to solar irradiance G (W/m2). When the solar cell is short circuited, negligible current flows in to the diode. Hence the proportionally constant in (3) is set to the rated short circuit current ISC at is delivered under rated irradiation. Solar intensities are commonly normalized with respect to full solar radiation at sea level with average humidity and aerosol particulate concentration (1 Sun = 1000Watt/m2). Though somewhat contrary to intuition, PV cell performance does not degrade significantly between full sun and cloudy conditions. The power output decreases nearly lineally with incident solar energy, but efficiency is nearly flat over the region of concern. The relationship between the photo-current and temperature is linear (eqn.2.2) and is deduced by noting the change of photo-current with the change of temperature (eqn. 2.4). When the cell is not illuminated, the relationship between the cell’s terminal voltage and current is given by the Shockley equation. When the cell is open circuited and illuminated, the photo-current flows entirely in the diode. The I-V curve is offset from the origin by the photo generated current IL (eqn-2.1). The value of the saturation current Io at 25°C is calculated using the open circuit voltage and short circuit current at this temperature (eqn-2.6). An estimate must be made of the unknown “ideality factor”. Green[3] states that it takes a value between 1 and 2, being near one at high currents, rising towards two at low currents. A value of 1.3 is suggested as typical in normal operation, and may be used initially, until a more accurate value is estimated later through curve fitting. The relationship of I0 to temperature is complex, but fortunately contains no variables requiring evaluation (eqn-2.5) [4]. The series resistance of the panel has a large impact on the slope of the I-V curve at V = VOC. Equations 7 and 8 are found by differentiating equation 1, evaluating at V = VOC, and rearranging in terms of Rs [5].

2.2.3 MATLAB MODEL OF THE PV MODULE

The BP SX150 PV module was chosen for modeling, due is well-suited to traditional applications of photovoltaic. The BPSX 150 module provides 150 watt of nominal maximum power, and has 72 series connected polycrystalline silicon cells. The key specifications are shown in Table 6.1. The model of the PV module was implemented using a MATLAB program. The model parameters are evaluated during execution using the equations listed on the previous section. The program, calculate the current I, using typical electrical parameter of the module (ISC, VOC), and the variables Voltage, Irradiation (G), and Temperature (T).finally this MATLAB program is used to create the SIMULINK model of PV module.

CHAPTER-3
MAXIMUM POWER POINT TRACKER

3.1 INTRODUCTION Maximum Power Point Tracking, frequently referred to as MPPT, is an electronic system that operates the Photovoltaic (PV) modules in a manner that allows the modules to produce all the power they are capable of. MPPT is not a mechanical tracking system that “physically moves” the modules to make them point more directly at the sun. MPPT is a fully electronic system that varies the electrical operating point of the modules so that the modules are able to deliver maximum available power. Additional power harvested from the modules is then made available as increased battery charge current. MPPT can be used in conjunction with a mechanical tracking system, but the two systems are completely different.

3.1.1 NEED FOR MAXIMUM POWER POINT TRACKING
Power output of a Solar PV module changes with change in direction of sun, changes in solar insolation level and with varying temperature as shown in the fig. 3.1&3.2.

Figure 3.1: Changes in the characteristics of the solar PV module due to change in insolation level
As seen in the PV(power vs. voltage) curve of the module there is a single maxima of power. That is there exists a peak power corresponding to a particular voltage and current. We know that the efficiency of the solar PV module is low about 13%. Since the module efficiency is low it is desirable to operate the module at the peak power point so that the maximum power can be delivered to the load under varying temperature and insolation conditions. Hence maximization of power improves the utilization of the solar PV module. A maximum power point tracker (MPPT) is used for extracting the maximum power from the solar pv module and transferring that power to the load
.

Figure 3.2: Change in the module characteristics due to the change in temperature

3.1.2 THE I-V CURVE AND MAXIMUM POWER POINT

Figure 3.3 shows the I-V curve of the BP SX 150S PV module simulated with the MATLAB model. A PV module can produce the power at a point, called an operating point, anywhere on the I-V curve. The coordinates of the operating point are the operating voltage and current. There is a unique point near the knee of the I-V curvecalled a maximum power point (MPP), at which the module operates with the maximum efficiency and produces the maximum output power. It is possible to visualize the location of the by fitting the largest possible rectangle inside of the I-V curve, and its area equal to the output power which is a product of voltage and current. Figure 3.3: Simulated I-V curve of BP SX 150S PV module (1KW/m2, 25oC)

The power vs. voltage plot is overlaid on the I-V plot of the PV module, as shown in Figure (3.4). It reveals that the amount of power produced by the PV module varies greatly depending on its operating condition. It is important to operate the system at the MPP of PV module in order to exploit the maximum power from the module.

Figure 3.4: I-V and P-V relationships of BP SX 150S PV module Simulated with the MATLAB model (1KW/m2, 25oC)

3.2 METHODS OF PEAK POWER TRACKING

In fact, a lot of MPPT methods have been proposed such as hill-climbing, perturb and observe, incremental conductance method, and so on. References [6, 7, 8] compare different MPPT strategies and give some general reviews over them. It seems very difficult to determine which method among them is the best one. Nevertheless, the new MPPT method using golden section search (GSS) algorithm proposed in this chapter is another competitive one because of its advantages of fast response, robust performance, and guaranteed convergence [7].

3.2.1 GOLDEN SECTION SEARCH ALGORITHM

Under a specific environmental condition, the nonlinear voltage versus current characteristics of PV module can be represented by following function:

V a = f (I a, E, T)………………………………………………………(3.1)

where Va and Ia are the terminal voltage and current respectively of the PV, E is the irradiation level, T is the temperature, and f( ) is the assumed characteristic function. The approximate model which has been developed in [7] is employed to generate the above function. Then the PV output power Pout can be calculated through:

Pout = V a × I a = f (I a, E, T) × I a ……………………………………(3.2)

In Table 1, VOC and ISC are the open circuit voltage and the short circuit current of PV, VMPP and IMPP are the voltage and current at MPP, and MP is the output maximum power. The MPPT is supposed to be used to find those MPPs for different conditions.

3.2.1.1 GSS ALGORITHM IN MPPT

MPPT is typically a maxima-finding process. The procedures for finding a maximum with GSS technique is illustrated in Figure. 3.5. The goal is to find the maximum functional value of f(x) within the input interval (x1, x2). The searching steps can be described as below

Figure 3.5: Searching scheme for GSS
1. Initially, the values of f(x1), f(x2) and f(x3) are already known. Because f(x3) is greater than f(x1) and f(x2), the maximum must lie inside the section of (x1, x2).
2. The value of f(x4) at a new point x4 is being evaluated.
3. If f(x4) > f(x3) as shown on the solid line in Fig 2-5, the maximum point lies inside the section (x3, x2). The new point x4 is then inserted and x1 is discarded to create a new narrower search section (x3, x2) with still three known points x3, x4 and x2.
4. If f(x4) < f(x3) as shown on the dashed line in Fig. 3, the maximum point lies inside the section (x1, x4). The new point x4 is still inserted, but x2 is discarded to create another new narrower search section (x1, x4) with another set of three known points x1, x3 and x4.
5. Repeat the steps through 2 to 4 for a certain number of times, or until the search section is small enough to ensure that the new inserted point can be considered the maximum point. Obviously, for each iterating step there are two possible search sections like (x3, x2) and (x1, x4) in Fig. 3.5. Only one of them will be selected to be the next search section. It is required that the two possible sections are equally wide. Otherwise, the convergence speed would be slowed down when the wider sections being taken more frequently in some worse cases. Therefore, the selection of the new point x4 must satisfy the requirement: width of (x1, x4) = width of (x3, x2), that is (a + b) = (b + c) in Fig. 3.5.

As a result, it becomes possible that all the search sections of the iterations can have the same proportion of spacing between the three points such that the algorithm converges at a constant speed, i.e.

……………………………………………………..(3.3)

Solve (3.3) to yield:

…………………………………………..(3.4)

where ø is the golden ratio. That is the reason why this search strategy is called GSS. Where, irradiance E = 1 sun, temperature T = 25°c the short circuit current of PV is 4.75 A and the maximum of output power Pout is 150 W at Ia = 4.35 A, as mentioned before; and the terminal voltage of PV, Va, is taken here as the search variable. Then the initial search section (0, 43.5 V) is applied to guarantee a MPP within the section. According to the golden ratio, another point at Va= 26.8 V is selected as the third initialized point. It is seen that the GSS algorithm can reach the very close location to MPP after only 6 iterations. In fact, it can be analytically derived that it takes only 15 iteration steps for GSS to shrink the search interval to 0.1% of its original length. That means, for a digital control system with 0.1% resolution corresponding to a 10-bit analog-to-digital converter, no more than 15 iteration steps are needed for the GSS to get the best applicable solution. Hence, the GSS always converges very fast.
There is still another advantage of GSS which makes it appropriate for MPPT of PV. The GSS does not require any derivatives, so that it is of robust and noise-resistive capabilities considering the fact that the derivative calculation is easily disturbed by the sensor noises and the signal fluctuations which unfortunately can hardly avoided in a real practice, especially in a power converter with switching devices. Moreover, the GSS algorithm ensures that the evaluated points in an interval will not be close to each other during the iterations. Thus, the GSS algorithm can tolerate relatively big noises and disturbances. Knowing that most of the PV systems need switching mode converters to transfer power from PV array to grid, standalone loads, or batteries, while converters generally have the inherent big noises and power ripples, the GSS is a robust algorithm for the MPPT applications of PV arrays.

The model of the MPPT module was implemented using a MATLAB program. The model parameters are evaluated during execution using the algorithm listed on the previous section. The program, calculate the maximum current ‘Im’ and ‘Vm’, using typical electrical parameter of the module (ISC, VOC), and the variables Voltage, Irradiation (G), and Temperature (T).finally this MATLAB program is used to create the SIMULINK model of PVMPPT module, which includes PV cell and MPPT .

CHAPTER-4
POWER CONDITIONING UNIT
4.1 INTRODUCTION

The power conditioning system provides regulated dc or ac power appropriate for the application. It is the major component of a PV system. The output of the PV is an unregulated dc voltage and it needs to be conditioned in order to be of practical use. The power conditioner section converts the raw power into useable power for different applications. The power conditioning unit also controls electricity’s frequency and maintains harmonics to an acceptable level. The purpose of conditioners is to adapt the electrical current from PV to suit the electrical needs of the application.

The general configuration of the system will be the PV followed by a boost converter followed by an inverter. In general, the load for the boost stage is a filter and the inverter system. The boost converters for the PV will be operated in the voltage control mode. The boost converter is ideally suited for interfacing the inverter system with the PV.

Figure 4.1: Power conditioning system

Based on the load conditions, the boost stage can be commanded to draw a specific amount of current from the PV with a ripple well defined by the frequency, size of the inductor, and duty ratio. Similarly, the inverter is used for the interfacing of the PV system to the load to provide the load with voltage/current with proper frequency phase and magnitude where the input for the inverter comes from the boost converter stage and the inverter (with the filter) becomes the load for the boost converter.
The power conditioner is also used for the grid connection of the PV. An electrical power-generating system that uses PV as the primary source of electricity generation and is intended to operate synchronously, and in parallel with the electric utility network is a grid-connected PV system [16].

4.2 DC-DC CONVERTER CONTROL LOOPS

Figure 4.2: DC/DC converter control loop

The output voltage of PV at the series of the stacks is uncontrolled dc voltage which fluctuates with Temperature and Irradiance. This raw voltage, which is unregulated and uncontrolled, is regulated to an average value with help of dc/dc converter. The controlled voltage thus obtained is fed to the dc/ac inverter after it is filtered. The power obtained from this inverter is added to the grid. This system can be used as a standalone after the dc/dc converter stage if dc power is needed or after the dc/ac stage if ac power is needed.

This unregulated voltage has to be adjusted to a constant average value (regulated dc voltage) by adjusting the duty ratio to the required value. The voltage is boosted depending upon the duty ratio. The duty ratio of the boost converter is adjusted with the help of a PI controller. The duty ratio is set at a particular value for the converter to provide desired average value of voltage at the output, and any fluctuation in the PV. The PI controller changes the duty ratio properly to get the desired average value. The duty ratio of the converter is changed by changing the pulses fed to the switch in the dc/dc converter circuit by the PWM generator [11-12].

4.2.1 MODELLING OF DC/DC CONVERTER Figure 4.3: Circuit diagram of DC/DC Converter
………………………………………………………..(4.1)
……………………………………………………………...(4.2)
……………………………………....(4.3)
For continuous conduction the designed values of L, C is
…………………………………………………….....(4.4)
………………………………………………………...(4.5)
‘R’ is the load resistance
‘f ’ is the switching frequency

4.3 DC/AC CONVERTER (INVERTER) CONTROL LOOP

Figure 4.4: DC/AC converter control loop

Inverters are devices that change the dc electricity produced by PV into ac electricity. Utility interactive inverters are used in systems connected to a utility power line. The inverters produce ac electricity in synchronization with the power line, and of a quality acceptable to the utility company once the control strategy is implemented.

The inverter output voltage (i.e. load voltage) will be compared every time with the ref voltage. The change in the output (due to change in the load) and grid voltage is given as inputs to the PI controller, and the output of the PI controller is given to the PWM generator and this generator will generate 6 pulses.

These pulses will be given to the switches of the inverter which will change the duty ratio of the inverter. Due to this change in duty ratio the output voltage will be maintained constant during the loading conditions.

4.3.1 INVERTER SWITCHING MODEL WITH RL LOAD AND GRID

Figure 4.5 shows the inverter-, load- and grid-system diagram with the inverter being modeled as a switching model. The switching devices used for the inverter are insulated gate bipolar transistors (IGBTs).

Figure 4.5: Inverter Switching Model with RL Load and Grid

4.3.2 CONTROL STRATEGY FOR GRID CONNECTED INVERTERS

There are two basic control modes for the grid-connected inverters. One is constant current control and the other is constant-power control. It is still arguable whether an inverter should be allowed to regulate voltage during grid-connected operation. The current IEEE standard does not allow distributed generation (DG) to actively regulate voltage, but some people in the industry suggest that DG voltage regulation may have some positive impact on the grid [13].
In this study, only constant-current and power-controlled inverters are considered. In detailed analysis, constant-current controlled inverters are used as an example to demonstrate the concepts, which can be easily extended to constant-power controlled inverters.
The control design for a three-phase inverter can be realized either in ABC (stationary) or in DQ (rotating) frames [14]. The latter is more popular in modern digitally controlled inverters.

4.3.2.1 CONSTANT CURRENT CONTROL

Figure 4.6 shows the inverter with constant current control. The inverter output currents are regulated to the given current references. The controller is greatly simplified with a few key functional blocks like ABC/DQ transformation, DQ phase-lock loop, summing function, linear regulator (proportional-integral) and DQ/ABC transformation. Many functions to deal with practical issues are not modeled, e.g. negative sequence regulation, DQ decoupling, device protection, etc.

Figure 4.6: Block diagram of constant current-control inverter

4.3.2.2 CONSTANT POWER CONTROL

Figure 4.7 shows the inverter with constant power control. There are two key concepts in the DQ implementation. First, the active power is proportional to the D-axis components, and the reactive power is proportional to the Q-axis components. Therefore, the active and reactive power commands should feed into the D-axis and Q-axis, respectively. Second, since the overall vector (voltage or current) is the synthesis of the D and Q axes, changing one axis not only changes the magnitude of the vector, but also changes the angle between the D and Q axes. The angle change will result in frequency change, because frequency is the derivative of the angle.

Figure 4.7: Block diagram of constant-power-controlled inverter

Here the inverter output power is compared with the reference power and the error is given to the PI controller, the output of the PI controller represents direct axis current component (D-axis), similarly by comparing the reactive powers, quadrature axis current component (Q-axis) component is obtained. These current components is compared with the inverter output currents and the error is given to the PI controllers, the output of the PI controller is current signals which in turn given to the PWM generator and generate the pulses at switching frequency and then fed to the inverter switches.

CHAPTER-5
GRID CONNECTED SYSTEM
5.1 INTRODUCTION
Figure (5.1) shows the block diagram of distributed generation (DG) connected to load and grid. Although there are many types of DG, including traditional reciprocating engines, small gas turbines, as well as emerging technologies such as PV, micro turbines, sterling engines, fuel cell, wind turbines, etc., basically there are two interfaces for grid interconnection: One is rotating machines, including synchronous machines and induction machines and the other is inverters—as part of the overall power conditioning system, inverters convert variable frequency, variable voltage AC sources or DC sources to regulated frequency/voltage AC sources that can be interconnected to the grid. Figure 5.1: Block diagram of DG connected to Grid

The smallest possible grid connected PV system unit is a PV module with a module-integrated inverter. In this case, mismatching losses are minimized, since load matching for the individual PV module is achieved through its inverter. Additionally, DC wiring is minimized. However, there are drawbacks concerning efficiency due to the low power ratings involved and replacements in case of inverter faults may be difficult and expensive. Also, cost per watt remains high unless mass-production is possible. 5.2 TRANSFORMER LESS GRID CONNECTED INVERTER In the past few years the market share for transformer less inverters has steadily increased. Topologies without transformer generally have higher efficiencies and may be cheaper than comparable inverters with transformers. Both are crucial advantages to make PV systems more competitive with traditional generation. The main disadvantage, however, is the direct connection of the PV array to the grid without galvanic isolation. Depending on the inverter topology this may cause fluctuations of the potential between the PV array and ground.
These fluctuations may have sine or square wave behavior at grid frequency or even switching frequency. They generate two effects: 1. The surface of the PV array forms a capacitor, with respect to ground, which is energized by the fluctuating potential. A person, connected to ground and touching the PV array, may conduct the capacitive current to ground, causing an electrical hazard to the person involved. 2. The voltage fluctuations generate electric and magnetic fields around the PV array (electromagnetic interference)

The seriousness of these effects has been an area of concern and controversial discussion over the past years. Meanwhile different studies [17] show that the impact of PV systems with transformer less inverters on electromagnetic interference is usually negligible and does not pose a hazard. However, with respect to capacitive currents certain recommendations on inverter and PV system design should be followed to prevent dangerous current levels (above ~10 mA).

A recent paper from the Fraunhofer Institute for Solar Energy Systems in Germany [18] discusses the electrical hazard in case of a person touching the surface of a PV array. The capacitance between the point of contact and a single PV module has been calculated to range between 100 – 400 pF for the single PV module case and depending on the transformer less topology and the applied switching method, a current of max. 0.2 mA could flow through the human body. When considering larger PV arrays with ungrounded structures, the maximum possible current increases as the surface area of the PV array increases. The capacitance for larger ungrounded PV arrays has been found to be 50 – 150nF/kW for glass-faced modules and up to 1uF/kW for thin-film modules. Currents of several mA can then occur. However, it is important to note, that by grounding the PV array structure the respective parasitic capacitance is reduced and with this the associated hazardous current. Additionally, the type of transformer less topology and the applied switching scheme influence the magnitude and type of voltage fluctuation at the PV array with respect to ground. A detailed discussion of these is given in [17] and one example on recommended topologies and switching schemes are presented in the following. When following the recommendations on grounding the PV array structure, topology and switching scheme choice, Transformer less PV system do not present an increased hazard compared to PV systems with transformers.

Figure 5.2: Transformer less PV inverter with several conversion stages including boost stage.

CHAPTER-6
SIMULATION MODELS AND RESULTS
6.1 SIMULATION MODELS
6.1.1 PV ARRAY AND MPPT

A combination of PV array and the MPPT are modeled with the ‘PVMPPT’ block. This is a level 2 m-file s function block, which basically its MATLAB code represented as SIMULINK block. The input Irradiance (G) and Temperature (T) values are contained in the constant blocks G, T.

Figure 6.1: PV module and MPPT SIMULINK block

By arranging these PV modules in series (N s=14) and parallel (N p=24), the total PV system generates 50KW.The generated 50KW of solar power is applied to the dc/dc converter which is shown in figure 6.2.

6.1.2 SIMULATION MODEL OF DC/DC CONVERTER

The DC/DC converter boosts the low unregulated voltage to a desired regulated voltage. The input for the DC/DC converter is the PV cell voltage and output of the DC/DC converter is connected to the inverter circuit which was shown in Figure 6.4.

Figure 6.2: Simulation model of DC/DC converter

Figure 6.3: Simulation model of PI controller

6.1.3 SIMULATION MODEL OF DC/AC CONVERTER

The SIMULINK model of inverter, current regulator and power regulator for grid connected applications are presented below.

Figure 6.4: Simulation model of DC/AC converter

6.1.3.1 SIMULATION MODEL OF POWER REGULATOR Figure 6.5: Simulation model of Power regulator

6.1.3.2 SIMULATION MODEL OF CURRENT REGULATOR

Figure 6.6: Simulation model of Current regulator

6.1.4 SIMULATION MODEL PV SYSTEM CONNECTED TO THE GRID

Figure 6.7: Simulation model of PV system connected to the grid with load

6.2 SIMULATION RESULTS

6.2.1 SIMULATION RESULTS OF SINGLE BPSX 150 PV ARRAY AND MPPT

Figure 6.8: Simulated I-V characteristic of the BPSX 150solar module

Figure 6.9: Simulated P-V characteristic of the BPSX 150solar module

Figure 6.10: Simulated PV array and MPPT SIMULINK block
Maximum power (P max)
150W
Voltage at P max = (V mp)
34.5V
Current at P max = (Imp)
4.35A
Warranted maximum P max
140W
Short – circuit current (I sc)
4.75A
Open – circuit voltage (Voc)
43.5V
Temperature coefficient of I sc
(0.065±0.015)%/0C
Temperature coefficient of voltage
-(160±20)mV/0C

Temperature coefficient of power
-(0.5±0.05)%/ 0C

NOCT
47±20C

Maximum series fuse rating
20A (U Version)
15A (S,L Version)
Maximum system voltage
600V (U.S.NEC rating)
1000V (TUV Rheinland rating)

Table 1: Electrical characteristics of BPSX 150 solar cell at 25deg, 1000w/m2

RESULTS OBTAINED USING MATLAB PRORAM AND SIMULINK MODEL

MATLAB PROGRAM
SIMULINK MODEL VMAX 33.23 33.23 IMAX 4.482 4.482 PMAX 148.9 148.9 Table 2: comparing the results obtained using coding and SIMULINK
The result obtained from the MATLAB program which is shown in appendix is equal to results of above PVMPPT SIMULINK model.

6.2.2 SIMULATION RESULTS OF PV SYSTEM CONNECTED TO THE GRID WITHOUT LOAD (25°C, 1KW/m2)

Figure 6.11: Output voltage waveform of DC/DC Converter

Figure 6.12: Duty ratio of DC/DC Converter

Figure 6.13: Grid V, I at the time of NO load

Figure 6.14: Output power waveform of PV Generator

Figure 6.15: Grid P,Q at the time of no load

6.2.3 SIMULATION RESULTS OF PV SYSTEM CONNECTED TO THE GRID WITH LOAD (25°C, 1KW/m2)

a. 30KW, 1KVAR load

Figure 6.16: Output power waveform of PV Generator

Figure 6.17: Load P, Q at the time of 30KW,1KVAR load

Figure 6.18: Grid P, Q at the time of 30KW, 1KVAR load

b. 50KW, 1KVAR load

Figure 6.19: Grid P, Q at the time of 50KW, 1000VAR load

Figure 6.20: Load P, Q at the time of 50KW, 1000VAR load

b. 70KW, 1KVAR load

Figure 6.21: Load P, Q at the time of 70KW, 1000VAR load

Figure 6.22: grid P, Q at the time of 70KW, 1000VAR load

6.2.4 RESPONSE FOR STEP CHANGES IN LOAD (25°C, 1000 VAR)

At 25°C, 1000 VAR of input the generated power of PV is 50 KW. The following results are taken by putting input Temperature, irradiance at 25°C, 1000 VAR. When there is a sudden change in the load from NO LOAD to 30kW and to 50KW, the power taken by the grid and power given to the grid is possible. Up to 0.5 sec the load is zero so total power goes to the grid. After 0.5 sec the load is 30kW, so the grid will take remaining 20KW of power and then after 0.5 sec the load is 50kW, so no power goes to the grid.

Figure 6.23: Load voltage

Figure 6.24: Load current by varying the load from NO LOAD to 30KW AND TO 50KW

Figure 6.25: Grid V, I by varying the load from No load to 30KW AND TO 50KW (1-Ø)

Figure 6.26: Grid P, Q by varying the load from No load to 30KW AND TO 50KW

Figure 6.27: Grid P, Q by varying the load from No load to 30KW AND TO 50KW

CHAPTER-7
CONCLUSION AND FUTURE SCOPE

7.1 CONCLUSION The work provides an idea about the MATLAB/SIMULINK model of photovoltaic system and Implementation of new MPPT algorithm which is very fast. A DC-DC boost converter topology and its closed loop control feedback system have been built. A three phase inverter has been modeled and connected between the PV-DC-DC system on the one side and the utility grid on the other side.
A control strategy for the inverter switching signals has been discussed and modeled successfully. The inverter control scheme uses a constant power control strategy for grid connected Applications. The characteristics for the system have been obtained. The inverter voltage, current, power waveform have been plotted. The real power injection into the grid takes less than 30s to reach the commanded value of 50kW. The reactive power injection has been assumed to be zero and was evident from the simulation results. The system was then subjected to a step change in the reference real power from 0 to 70Kw. The DC link voltage was maintained at the reference value (700V) by the closed loop control system.
Step change in the reference power from 0 to 70kW has been considered in order to observe the sharing of power from inverter to grid and from grid to the load of the PV cell. The reactive power was zero until the step change and after the step change, oscillations were observed in the reactive power as well. Voltage, current, power characteristics of inverter, load and grid as been plotted for various conditions of load.

7.2 FUTURE SCOPE

The work can be further extended for simulating the hybrid, micro grid system i.e. wind, & PV cell, PV & fuel cell and it can further be extended for simulating the power train. Different placements of the PV cell unit can be studied and analyzed. The performance of multiple units at multiple locations can also be studied. The performance of the PV cell can also be tested by carrying out short circuit studies, islanding phenomena.
In future there is a need to develop a model that can perform very accurate system-wide simulations involving all the individual subsystems that constitute a photovoltaic system. Neural network models can be built based on a portion of measurements and validated using a different subset of measurements.

REFERENCES

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[2].B. Kroposki, R. DeBlasio, “Technologies for the New Millennium: Photovoltaics as a Distributed Resource”. Power Engineering Society Summer Meeting, 2000. IEEE, Vol. 3, p.p. 1798 – 1801,16-20 July 2000

[3].A. Hansen, P. Lars, H. Hansen and H. Bindner. “Models for a Stand-Alone PV System”. Risø National Laboratory, Roskilde, December 2000, ISBN 87-550-2776-8.

[4].Francisco M. González-Longatt. “Model of Photovoltaic Module in Matlab” 2do congreso iberoamericano de estudiantes de ingeniería eléctrica, electrónica y computación (ii cibelec 2005)

[5]. Marcelo Gradella Villalva, Jonas Rafael Gazoli, and Ernesto Ruppert Filho “Comprehensive Approach to Modeling and Simulation of Photovoltaic Arrays” 2009 IEEE Trans. on Energy System.

[6].D. P. Hohm and M. E. Ropp “Comparative Study of Maximum Power Point Tracking Algorithms,” Prog. Photovoltaics Res. Appl., Vol. 11, pp. 47-62, Jan. 2003. [7].Riming Shao Liuchen Changa “New Maximum Power Point Tracking Method For Photovoltaic Arrays Using Golden Section Search Algorithm” 2008 IEEE Trans. on Power System.

[8]. T. Esram, P. L. Chapman, “Comparison of Photovoltaic Array Maximum Power Point Tracking Techniques,” IEEE Trans. Energy Convers., vol. 22, pp. 439-449, June 2007.

[9].W.J.A. Teulings, J.C. Marpinard, A. Capel, D.O’Sullivan, “A new Maximum Power Point Tracking system” 1993 IEEE Transactions power system.

[10] .Eftichios Koutroulis, Kostas Kalaitzakis “Development of a Microcontroller-Based,Photovoltaic Maximum Power Point Tracking Control System”

[11]. R.Kayalvizhi, S.P.Natarajan, D.Sivakumar, K.Elangovan “Design and Simulation of PI Control for Paralleled Positive Output Elementary Luo Converters for Distributed Power Supplies” R.Kayalvizhi, S.P.Natarajan, D.Sivakumar, K.Elangovan 2006 IEEE transactions power electronics.

[12]. Hyo-Sik Park, and Hee-Jun Kim, Member, IEEE “Simultaneous Control of DC-DC Converters” by DSP Controller 2001 IEEE Trans. on Power Electronics.

[13].Z. Ye, R. Walling, L. Garces, R. Zhou, L. Li, and T. Wang, “Study and Development ofAnti-Islanding Control for Grid-Connected Inverters” General Electric Global Research Center Niskayuna, New York, May 2004.

[14].Zhihong Ye, L. Li, L. Garces, C. Wang, R. Zhang, M. Dame R. Walling, N. Miller. “A New Family of Active Anti-Islanding Schemes Based on DQ Implementation For Grid-Connected Inverters” .2004 I EEE Trans. Energy Converters.

[15]. Nasrudin Abd Rahim, Jeyraj Selvaraj and Krismadinata Department of Electrical EngineeringUniversity of Malaya Kuala Lumpur, Malaysia. “Hysteresis Current Control and Sensorless MPPT for Grid-Connected Photovoltaic Systems” 2007 IEEE Trans. Energy Converters.

[16]. N. Hamrouni* and A. Chérif .“Modelling and control of a grid connected photovoltaic system” Revue des Energies Renouvelables Vol. 10 N°3 (2007) 335 – 344.

[17] .J. M. A. Myrzik, and M. Calais, Member, IEEE“String and Module Integrated Inverters for Single-Phase Grid Connected Photovoltaic Systems - A Review”

[18] .F. Blaabjerg, Z. Chen and S. Kjaer, ‘Power Electronics as Efficient Interface in Dispersed Power Generation Systems’, IEEE Trans. on Power Electronics, Vol. 19, N°5, pp. 1184 - 1194, 2004.

[19].S. B. Kjaer and F. Blaabjerg, “Design optimization of a single phase inverter for photovoltaic applications,” in Proc. IEEE PESC’03, vol. 3, 2003, pp. 1183–1190.

[20] Muhammad h. Rashid “Power Electronics Circuits, Devices and Applications” 3rd edition, 2007.

APPENDIX

MATLAB CODE

PV ARRAY

The following is the MATLAB code for a PV array containing 1 bpsx150 panel

function Ia = bp_sx150(Va,G,TaC)
% function bp_sx150s.m models the BP SX !%)S PV module
% calculates module current under given voltage, irradiance and temperature
% Ia= bp_sx150s(Va,G,T)
% out: Ia= Module operating current (A), vector or scalar
% in: Va=module operating voltage (v) vector or scalar
% in:G (irradiance,kw/m2),Tac (temperature in deg C)
% define constants k=1.381e-23; %Boltzmann’s consatant q=1.602e-19; %electron charge
% the following constants are taken from the datasheet of PV module and
% curve fitting of i-v character n=1.62; %diode ideality factor
% 1(ideal diode) < n < 2
Eg=1.12; %band gap energy
Ns=72; % of series connected cells
TrK=298; %reference temperature
Voc_TrK=43.5/Ns; %open circuit voltage per cell
Isc_TrK=4.75; %short circuit current per cell a=0.65e-3; %temperature coefficient of Isc
% define variables
TaK=273+TaC; %module temperature in kelvin
% calculate short circuit current of Tak
Isc=Isc_TrK*(1+(a*(TaK-TrK)));
% calculate photan generated current @ given irradiance
Iph=G*Isc;
% define thermal potential(vt)at temp Trk
Vt_TrK=n*k*TrK/q;
% define b b=Eg*q/(n*k); % calulate reverse saturation current for given temp
Ir_TrK=Isc_TrK/(exp(Voc_TrK/Vt_TrK)-1);
Ir=Ir_TrK*(TaK/TrK)^(3/n)*exp(-b*(1/TaK-1/TrK));
% calculate series resistance per cell dVdI_Voc=-1.0/Ns; Xv=Ir_TrK/Vt_TrK*exp(Voc_TrK/Vt_TrK);
Rs=-dVdI_Voc-1/Xv;
Define thermal potential at Ta
Vt_Ta=n*k*TaK/q;
% solve for Ia by newton method
Vc=Va/Ns; %cell voltage
Ia=zeros(size(Vc));%intialize Ia with zeros for j=1:5
Ia=Ia-(Iph-Ia-Ir .*(exp((Vc+Ia .*Rs) ./Vt_Ta)-1))./(-1-Ir*(Rs ./Vt_Ta) .*exp((Vc+Ia .*Rs) ./Vt_Ta));
End

MPPT

The PV array connected to an MPPT, and this combination can be modeled by the following MATLAB code. the first half of this code is necessary to implement the code in to a SIMULINK block .there are several examples of m file SIMULINK block under the ‘user defined functions’ subheading in the SIMULINK library. function PVMPPT(block)

%find_PVMPPT: function to find the maximum power point of the PV module
%[Im,Vm]=find_PVMPPT(G,Tac)
%in: G (irradiance,kw/m2),Tac (temperature in deg C)
%out:I_max,V_max

setup(block); function setup(block)
% Register number of inputs and output ports block.NumInputPorts=2; block.NumOutputPorts=2;
% setup functional port properties to dynamically inherited. block.SetPreCompInpPortInfoToDynamic; block.SetPreCompOutPortInfoToDynamic;

block.InputPort(1).Complexity ='Real'; block.InputPort(1).DataTypeId =0; block.InputPort(1).SamplingMode ='Sample'; block.InputPort(1).Dimensions =1;

block.InputPort(2).Complexity ='Real'; block.InputPort(2).DataTypeId =0; block.InputPort(2).SamplingMode ='Sample'; block.InputPort(2).Dimensions =1; block.OutputPort(1).Complexity ='Real'; block.OutputPort(1).DataTypeId =0; block.OutputPort(1).SamplingMode ='Sample'; block.OutputPort(1).Dimensions =1; block.OutputPort(2).Complexity ='Real'; block.OutputPort(2).DataTypeId =0; block.OutputPort(2).SamplingMode ='Sample'; block.OutputPort(2).Dimensions =1;
% register methods block.RegBlockMethod('ProcessParameters', @ProcessPrms); block.RegBlockMethod('outputs', @Outputs); block.SetAccelRunOnTLC(true); % end function

function Outputs(block)
G=block.InputPort(1).Data;
TaC=block.InputPort(2).Data; tol=1; % take ‘0’, ‘Voc’ are the min,max values foe the search section
Vmin=0; %
Vmax=43.5; %open circuit voltage while (tol>0.0000001)
%Imin=solar1(Vmin,Suns,T);
%Imax=solar1(Vmax,Suns,T);
%Pmax=Imax*Vmax;
%Pmin=Imin*Vmin;
Vmax1=(Vmax-Vmin)/1.61803398+Vmin; % 1.61803398=Golden ratio
Vmax2=(Vmax-Vmax1)+Vmin;
Imax1=bp_sx150(Vmax1,G,TaC); % function calling of pv module program
Imax2=bp_sx150(Vmax2,G,TaC);
Pmax1=Imax1*Vmax1;
Pmax2=Imax2*Vmax2;
tol=Pmax1-Pmax2;
%if(tol Pmax2) Vmin=Vmax2; %Pmaxf=gsstmppt(Vmin,Vmax); else Vmax=Vmax1; %Pmaxf=gsstmppt(Vmin,Vmax); end end
Vmp=Vmax2;
Ia=Imax2; block.OutputPort(1).Data=Ia; block.OutputPort(2).Data=Vmp;

PARAMETERS IN BOOST DC-DC CONVERTER

L 0.0005 H C 7500µF RC 0.2 ohm
Switching frequency 8KHz Table 3: PARAMETERS IN BOOST DC-DC CONVERTER

KP 0.0005 KI 0.15 Table 4: KP & KI VALUES OF DC-DC CONVERTER

PARAMETERS IN DC-AC CONVERTER

POWER REGULATOR
CURRENT REGULATOR KP 0.4 1.5 KI 3000 4000 Table 5: KP & KI VALUES OF DC-AC CONVERTER FOR GRID

INVERTER

fS 8000
HZ
SWINCHING FREQUENCY
Vds
700
V
DC VOLTAGE
Lf
2.1E-3
H
FILTER INDUCTACE
V L-L 440
V
LINE-LINE VOLTAGE
VL-N
254
V
LINE-NUETRAL VOLTAGE
P
50000
W
RATED POWER
PF
1

POWER FACTER
P
50000
W
ACTIVE POWER OUTPUT
Q
0
VAR
REACTIVE POWER OUTPUT

Table 6: DATA FOR THE INVERTER