Equivalent Circuit Of Photovoltaic Cell Engineering Essay

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According to [1] DC-DC converters are widely used in regulated switch mode DC power supplies. The input of these converters is unregulated DC voltage, which is obtained by PV array and therefore will be fluctuated due to change in radiation and temperature. Renewable energy is growing rapidly and it is becoming significant in our world today and in the future to come. Photovoltaic (PV) is one of the most important area in the field of renewable energy and has attracted lots of research. In the past years, PV power generation systems have attracted attention due to the energy crisis and environment pollution. Photovoltaic power generation systems can mitigate effectively environmental issues such as the green house effect and pollution [2]. One major problem with photovoltaic module is that the electrical output power depends on the weather condition that is; the output is changing with a change in weather condition which makes photovoltaic module nonlinear power source. Due to the weather condition mention above and other factors listed below in (2.2.4), the maximum power point of the photovoltaic module as describe below in figure (4) and (5) will shift away from the maximum operating point of the module. Base on this result a maximum power point tracker (MPPT) employing DC-DC converter is develop and used to maintain the maximum power point (MPP) of the module.

Many MPPT methods have been develop over the years to achieve the maximum power point of the PV module in different papers; examples are the incremental conductance (IC) method [3], perturbation and observe (P&O) method [2], the fuzzy logic [2], microcontroller base method [4] [5] etc.

In this project it is intended to design an easy to use DC-DC converter (boost converter) with maximum power point tracker for photovoltaic module to control the photovoltaic interface so that the operating point of the load and photovoltaic module meet at the maximum power point no matter the electrical power output of the module. The converter will be connected between the photovoltaic module and the load (a led based light with nominal voltage of 24V) without a battery so as to supply the load with 24V at all time. The design will be used by both technical and non technical people, and will be both portable and practical in the field of engineering and renewable energy.

The method adopted in the project is a feedback microcontroller based MPPT control method with a boost converter operating in continuous conduction mode. This characteristic of continuous input current makes the boost converter suitable as photovoltaic interface. The block diagram of the adopted method is described below in figure 1. The component used in the propose control design is a pulse generator (555timer circuit) to change the duty cycle, a microcontroller and a Nand gate. In the project we will also design and implement the DC-DC converter (boost converter).

Figure 1. Block diagram of the proposed MPPT with DC-DC Boost converter.


2.1 Overview of DC-DC Converter

Before embarking on this project, let take a look at the different type of converters develop over the years and the idea behind it and also to know the function so as to enable us choice a suitable converter as photovoltaic interface for the photovoltaic module and the load.

DC-DC conversion technology is a major subject area in the field of power electronic, power engineering and drives. The conversion methods have application in industries such as telecommunications, automotive, renewable energy, research etc and have gone under series of developmental stages for more than sixty (60 years). This conversion technique is widely adopted in industrial application and computer hardware circuits. The ideas of DC-DC conversion technique and development have been on for over 80 years. The simplest DC-DC conversion technology is a voltage divider, potentiometer and so on. But the effect of these simple conversion techniques resulted in poor efficiency due to fact that transfer output voltage is lower than the input voltage. The second DC-DC conversion method used was the multiply quadrant chopper.

Before 1939 preliminary types DC-DC converters were adopted in industrial operations but during the period of the Second World War research and development of DC-DC converters were stopped but their applications were recognized in the course of the war. After the war, telecommunication technology grew rapidly and required low voltage DC power supplies. This paves the way for rapid and massive development of DC-DC conversion methods and techniques.

According to [6], there have been more than 500 prototypes of DC -DC converter developed for more than 60 years. All new topology and presently existing DC-DC converters were design to meet some sort of industrial or commercial applications. They are usually called by their function, for example, Buck converter, boost converter, buck-boost converter and zero-switching (ZCS) and zero voltage switching (ZVS) converters which are used to reduce, increase voltage ….respectively. The large number of DC-DC converters had not been evolutionary classified until 2001. These converters have been arranged systematically into six groups and these groups are called generations. The content of these generations are classified according to their characteristics and development sequence. This classification covers all existing DC-DC converter and categories including new prototypes. Since 2001, the DC-DC converter family tree has been built and this classification has been recognized worldwide. Now it easy to sort and allocate DC-DC converter and asses their technical features. See DC-DC converter family tree in figure 1, below.

DC-DC converters (e.g. boost, buck, buck boost, etc) are also implemented with other devices as maximum power point trackers (MPPT) for photovoltaic module due to changes in maximum power point (MPP) of the photovoltaic module which is as a result of changing radiation from the sun and other factors listed below in (2.2.4). Boost, buck and buck- boost converters are popularly used with maximum power point trackers as photovoltaic interface, for example in [7] a real time MPPT employing a DC-DC boost converter operating in conduction mode is used. It also includes a passive non dissipative turn on turn off snubber in order to achieve high efficiency and to reduce EMI level due to soft switching.

Figure 2: DC-DC converter family tree [6].

2.2. Overview of Photovoltaic array.

Photovoltaic cell also known as solar cell is used to convert energy from the sun directly into electrical energy without any form of rotational parts. Photovoltaic cells represent the basic fundamental power conversion unit of photovoltaic system. They are made from semiconductors and have such similar behavior with other solid-state electronic devices, such as diodes, transistors and integrated circuits. For practical operation, photovoltaic cells are usually arranged into modules and array [8]. The material presently used for the development of photovoltaic includes monocrystalline silicon, polycrystalline silicon, amorphous silicon, cadmium telluride, and copper indium selenide/sulfide [9].

There are different types of photovoltaic cells available on the market and yet different other types of cells are under development e.g. dye-sensitized Nand-crystalline cells. The reason for different types of photovoltaic cell, materials and structure is to extract maximum power from the cell and to maintain cost to a minimum. According to [9] efficiency above 30% have been achieved in laboratory and efficiency of practical application is usually less than half of this value. Crystalline silicon technology is well established and its cell is more expensive but still controls a major part of the photovoltaic market with efficiency approaching 18%. Other types of photovoltaic cells like amorphous thin films are less expensive but with disadvantage of poor efficiency. The use of photovoltaic array and maximum power point tracker (MPPT) is developing rapidly and to achieve our aim in this project, we must understand how photovoltaic cell works and its equivalent circuit.

2.2.1. How photovoltaic/solar cell works

Solar cell are made up of photosensitive materials known as semiconductor e.g. like silicon. When a piece of silicon is doped with phosphorous it becomes N-TYPE with one extra electron. Similarly, when doped with boron it becomes P-TYPE semiconductor. Solar cell consist of two layers known as the P-TYPE and N-TYPE semiconductors and these layers are connected or sandwiched together by some means, to create a pn junction. In fact, the pn junction creates an electric field across this junction and also a potential energy gap is form at the junction.

When photon of energy or particles of sunlight is allowed to strike the semiconductor as shown below in figure 3, it is absorbed by the electrons of semiconductor and these electrons starts moving randomly within the material. For each such negatively charge electron, a corresponding mobile positively charge called 'hole' are created. In solar cell, the electron and holes migrate in the opposite direction close to the junction by the action of the electric field and others diffuse towards the junction to replace them. This charge separation creates an electric field opposite to the electric field created by the diffusion of electron and holes in the opposite direction which result to electron flow. When the device is place to an external circuit, current will start following in the circuit which is known as electricity [10].

Figure 3.photovoltaic module under illumination [10]

2.2.2. Equivalent circuit of photovoltaic cell.

The equivalent circuit of the photovoltaic cell can be seen as a photodiode with a p-n junction. In the dark, the i-v characteristic of the cell has an exponential characteristic similar to that of a diode. When expose to sunlight, photons with energy greater than the boundary energy of the semiconductor are absorbed and create an electron hole pair. 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 incidence radiation. When the cell is short circuited, the current flows in the external circuit, when open circuited, this current is shorted internally by the intrinsic p-n junction diode. The characteristic of the diode therefore sets the open circuit voltage characteristic of the cell [11]. A simply equivalent circuit with one diode, series resistance and a photocurrent source is express in figure 4

Figure 4. A photovoltaic cell

2.2.3. I-V characteristic curve of photovoltaic module

The electrical output power of a photovoltaic module is determine by the product of the current and voltage (P=I*V). Due to the effect of changing irradiation, the module produces current at different level of voltage. However, the module performance can be analysis using a performance curve called the I- V characteristic curve, which demonstrate the relationship between the output current and voltages at different range of load using ohms law (V=I*R). The most important point on the I-V curve is the open circuit voltage Voc, short circuit current (Isc) and the maximum power point (MPP) as shown below in figure 5.

Figure 5. I-V curve

2.2.4 Factors that affect the electrical performance of photovoltaic module [12].

There are several factors that affect the electrical performance of a photovoltaic module from operating at optimal operating point. These factors are listed below as follows.

Sunlight intensity/irradiation

Cell temperature

Load resistance


Sunlight intensity/irradiation

The level of exposure of a photovoltaic module to sunlight/irradiation determines the module current. In fact, the irradiation is proportional to the module output current. The figure 6 below demonstrates this action. It can be seen that as the level of irradiation changes the area under i-v curve changes as well but its shape still maintained. Also the best operating point (MPP) of the photovoltaic module is affect by these changes.

Figure 6. Effect of Irradiation on photovoltaic module performance [12].

Cell temperature

Most photovoltaic modules are tested under standard test condition (STC) of 1000W/m2 and a cell temperature of 25 degrees. The temperature of the module plays a great role in its performance. Therefore, the changes in temperature above reference temperature of 25 degrees, affect the efficiency and output voltage of the module, as shown below in figure 7. The shape of the i-v curve remains the same but with a shift towards the left of the i-v curve as temperature increases. This change also affects the maximum operating point of the module as demonstrated below.

Figure 7. Effect of temperature on photovoltaic module performance [12]

Load resistance

Usually, the voltage at which the module operation is determine by the application of a load or battery. Therefore, to obtain a maximum power point or near maximum power, the load resistance must match the module I - v characteristic curve, which will result in the best realistic efficiency. When the load resistance increases there will simultaneous increase in voltage higher than the voltage at maximum power point resulting in decreasing output current and efficiency.


Shading is also one of the major factors that lead to poor module performance. Shading a module partially or fully will result to a poor electrical power output. In fact, one completely shaded module reduces output by much as 75%. That is why some manufacturer uses bypass diode to bypass shaded cell to prevent current from following into it.

2.3. Maximum power point tracker (MPPT)

A maximum power point tracker is a high-efficiency DC-DC converter, which functions as an optimal electrical load for photovoltaic cell, most commonly for a solar panel or array and converts the power to a voltage or current level which is more suitable to whatever load the system is design to drive. Photovoltaic cells have a single operating point where the values of current and voltage result in a maximum power output for the cell. Maximum power point tracker utilizes some type of control circuit or logic for this point and thus to allow the converter circuit to extract the maximum power available from the photovoltaic cell.

Maximum power point tracker (MPPT) is not a mechanical tracking system that physically moves the photovoltaic modules to face sunlight directly. It 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. The advantages of MPPT regulators are greatest during cloudy or hazy days, cold weather or when the battery is deeply discharged [13]. There are different types of maximum power point tracker developed over the years and they are listed below as follows

Perturb and observe method

Incremental conductance method

Artificial neutral network method

Fuzzy logic method

Peak power point method

Open circuit voltage method

Temperature method etc.

In this project the MPPT plays a very significant role because without the MPPT the desire output electrical power will not be achieve with changing weather conditions, and the factors listed above in (2.2.4).

3.0 Boost converter (Step up)

DC-DC boost converter (step up) plays a major part in this project. It is connected between the photovoltaic module and the load to enable the photovoltaic module operates at maximum power at all time. Boost converter is made of up four elements as shown below in figure 8, they include of inductance, diode, capacitor and Mosfet. As the name implies, the converter step up the input voltage which makes the output voltage greater than the input voltage. This converter is control through the mosfet which act as a switch. The on and off of this switch (Mosfet) controls the output voltage by changing the voltage of the inductance so as to enable the photovoltaic module power the load at maximum voltage.

Figure 8. Step up dc-dc converter [14].

The operation of this converter is analyzed in different operating condition when the switch (Mosfet) is turn on and off. The operating condition are called continuous, discontinuous conduction mode. Let's examine the conditions in these modes.

Continuous conduction mode.

As shown in figure 7 below, in continuous conduction mode the inductance current flows continuous [iL(t) >0] as describe with the steady state waveform below in figure 7.

Since in steady state the time integral of the inductor voltage over one time period must be zero,

Vdton + (Vd -Vo)toff = 0 …………………………………………………..(1)

When the switch (Mosfet) is on, the diode is reverse biased, thus isolating the output stage. The input supplies energy to the inductor. When the switch (Mosfet) is off, the output stage receives energy from the inductor as well from the input. In the steady state analysis presented here, the output filter capacitor is assumed to be very large to ensure a constant output voltage Vo (t) ~ Vo [10].

Figure 9. Equivalent circuit for boost converter in continuous conduction mode (CCM); (a) switch on; (b) switch off [1].

Dividing both sides by Ts and rearranging terms yield

…………………… (2)

And equation (2) confirms that the output voltage is greater than the input.

Assuming a losses circuit, Pd = Po,

Therefore VdId = VoIo

And …………………………………. (3) [14]

3.2. Discontinuous conduction mode (DCM)

Discontinuous conduction mode is completely avoided in this project because the current flowing through the inductor goes down to zero before the end switching time period. Also in discontinuous conduction mode the inductor discharges all its stored energy before the completion of the switching time period which can lead bad effect on the output voltage. The output voltage(Vo) of the discontinuous conduction mode does not depend only on the duty cycle but also on input voltage, inductor, switching time period and the output current which makes it more complex than the output voltage of the continuous conduction mode. See output voltage of discontinuous conduction mode in equation (4)

D = ………………………… (4)[14]

In actual practice D would be varied in other to keep Vo constant.

3.3. Reason for using boost converter in this project

There are over 500 prototypes DC-DC converters and these converters were design to meet some sort of industrial or commercial applications. They are usually called by their function e.g. buck and boost converters are used to reduce and to increase voltages respectively. In this project a photovoltaic module is used to power a load (led-base light, nominal voltage of 24V). But at different irradiation level the photovoltaic module output voltage was very low ranging from 11V to 15.98V and insufficient to meet the operating characteristic of the load. Due to this problem, a DC-DC boost converter is needed to step up the voltage from the photovoltaic module to the nominal voltage of the load. This is achieved by adjusting switch of the boost converter with the aid of MPPT, no matter the level of irradiation and other factors that affects the performance of the photovoltaic module. Figure 10, describe the use of the boost converter.

Figure 10. Boost converter used as a photovoltaic interface

3.4 Designed DC-DC boost converter analysis

As stated above that DC-DC boost converter is used as photovoltaic interface and is design to boost the output voltage to 24V to meet the requirement of the load. Base on this fact some specification of the boost converter was assume to meet the demand. The boost converter is design with an input voltage and input current are 15.98V and 0.1598A respectively which is the maximum power point of the photovoltaic module at 1000W/m2 and the output voltage is 24V (Led base light, nominal voltage) and current as 0.1064A . The assume specifications are listed below as;

Current ripple ΔI = 10%

Voltage ripple ΔV = 5%

Switching frequency = 20KHz

Continuous conduction

The equations used for the design are listed below as follows

……………………………………… (6) [7]

ΔI = ……………………………………… (7) [7]

ΔV = ………………………………………. (8) [7]

Pi = Po =Vi*Ii = Vo*Io (Assume 100% efficiency of converter) …… (9)

With these equations above, the Io, L, C and D were calculated as 0.1064, 16.5mH, 1.46μf, and 0.33 (33%) respectively.

L, inductance

C, capacitance

D, duty cycle

Io, output current.

Using the Ohms law (Vo= Io*RL), the load resistance is calculated as 225.6Ω. See implementation of design DC -DC converter with calculated values in figure 11 and it is also useful to adjust the values of each component including the duty circuit to achieve the required result.

Figure 11 Designed DC-DC boost converter.

Figure 12 simulation results for DC-DC boost converter.

Now we can observe the output voltage, current through inductance (input current. Ii) and output current, Io . It is also observe that the output voltage is 24V at 33% duty cycle which is the desired value for the load. It is also observe from the figure below that the inductance current is continuous. See figure 13.

Figure 13 inductance current for design boost converter.

From the results above it is concluded that the design DC-DC boost converter is suitable as photovoltaic interface for this project.

4.0 Part for MPPT design

From figure 1, the adopted configuration of the MPPT comprises of three components a Microcontroller, pulse generator and a Nand gate. Each component in the MPPT design plays a very important role to achieve the duty cycle for the control of the DC-DC boost converter. The function of each of this component will be analyzed based on its function in this project.

4.1 555timer (pulse generator)