# Maximum Power Point Tracking Biology Essay

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This part is a report in the MPPT Maximum Power Point Tracking methods that are used in order to increase the production of energy in PV systems. Lately, the needs for new methods of renewable energy have increased. One of the basic materials that used for the production of energy is the lignite. The reserves of this material have recorded important reduction in different countries.

With the quick development of society the alternative solution of a renewable energy resource is particularly important. Some of the renewable that have been developed the last years are the tidal and wind power. An important piece of renewable resources constitutes of the solar power.

The solar energy is more interesting in comparison with other renewable sources because it decreases the consumption of fuels for the production of energy, it is friendly for the environment and it has minimal cost for the construction and the maintenance. Also, an important element that renders the PV systems better than other methods is the minimal noise pollution that produces while operating.

The first PV arrays that were used for the production of energy presented some disorders at the duration of their operation. The most important problem was that in some cases the energy that produced the PV systems was not enough in order to cover the needs of the current that needed in one unit in order to function effectively (e.g. generator). This means that the PV systems need development thus the energy they produce to be satisfactory for the daily needs.

With the passage of time after different studies, various methods were developed in order to increase the production of energy in PV. Common objective of the different methods that was used, was to locate the maximum energy (MPP) that can produce the PV. At the duration of studies that have taken place in previous years the basic problem in PV systems is the non-linear relation between current - voltage (I-V).

The MPP in the PV systems depends from three important parameters. They are the solar radiation, solar illumination and the ambient temperature. Consequently the tracking control of the MPP in PV arrays is a complex situation. In order to face these problems that have been developed from different methods of tracking control for the MPP. Some of these methods are the neural network, fuzzy controller, shaded insulation and gradient method.

Some of these methods have some disadvantages such as high cost, difficulty, complexity and instability. The basic requirements in order to achieve the MPP in PV arrays are the simplicity, low cost, quick tracking under changing conditions, and small output power fluctuation.

Another important factor for the most optimal operation of PV systems is the tracking operation at the duration of operation of PV. From this process it is possible to check at any time the biggest energy that produced at the duration of operation.

## Characteristic of Photovoltaic Cell:

The PV cells are constituted by a connection of silicon P-N. When the silicon is exposed to light electrons exposed around by a closed circuit and in combination with the photons occurs an interaction between these particles. The result of these interactions is the production of energy in the PV cells. The next picture represents the basic circuit that is used for the production of energy in the most PV systems.

Figure : Photovoltaic cell equivalent circuit

The photo current Iph generated in the PV cell is proportional to the level of solar illumination. I is the output current of photovoltaic cell. The current (Id) through the bypass diode varies with the junction voltage Vj and the cell reverse saturation current I0.

V is the output of the photovoltaic cell.

Rsh and Rs are the parallel and series resistances, respectively. Parallel resistance Rsh is very large while the series resistance Rs is small.

When the number of cell in series is ns, and the number of cell in parallel is np.

The next mathematical equations are used in order to calculate the current that produced at the duration of PV systems operation.

From the above mathematical equations a basic output is concluded. The characteristics of the PV arrays change when solar illumination (S) and ambient temperature (T) change. In the next graphs represented the operation of PV systems proportionally with the solar illumination that drained in them and the ambient temperature.

## Figure : Simulate current versus voltage curves of PV array influenced by

solar illumination

## Figure : Simulated current versus voltage curves of PV array influenced

by temperature

In the first two graphs is observed the relation between the solar illumination and temperature that accepts the PV cells. The values of solar illumination that drained in the cells oscillate between 200 W/m2 and 1000 W/m2. The temperature in this phase remains constant in 40oC. The voltage that produced in this stage oscillate between 300 and 350 Volts. This means that when the solar illumination is altered and the temperature is constant the difference in the voltage is small. From the diagram shown that the voltage that created by this process oscillate between 300 and 350 Volts. On the other hand the solar illumination remains constant and changes only the temperature. Observing the production of voltage we can see that the distance in the voltage's values that produces are higher in comparison with the first graph. The voltage in the second plan oscillate between 250 and 400 Volts. This means that if the ambient temperature is increased then the voltage is increased as well.

Figure : Power versus voltage curves influence by the solar illumination

Figure : Power versus voltage curves influence by temperature

In these two graphs shown the relationship between Power - Voltage. The output power of a PV array is the product of current I and terminal voltage V.

From the above equation it becomes comprehensible that the output power is influenced by the change of solar illumination and the ambient temperature. As in the two first graphs while the solar illumination changes and the temperature remains constant the production of energy is almost same because it is oscillated between 300 and 350 Volts. When the solar illumination is constant and the temperature changes it is observed again that the voltage increased proportionally with the environmental temperature.

The aim of the above graphs and mathematical equations is to locate the MPP that the PV arrays produce. This is difficult because of the continuously changes of solar illumination and ambient temperature. The basic conclusion from the above graphs is that the MPP in PV systems depends immediately on the environmental conditions. Specifically when the solar illumination and the temperature change at the same time then the MPP is more difficult to be tracked according to the calculations that reported previously.

For this reason different methods have been developed in order to analyze better the MPP in the PV systems. Below, an analysis of the methods that have been developed for this aim is shown.

## MPPT methods:

The last years have been used a lot of methods in order to calculate the maximum power that can produce the PV systems proportionally with the environmental conditions. Many of them have been characterized complicated for their application and other particularly costly. The basic problem in order to locate the MPP is the non linear relationship of the characteristic I - V curve. In the following a description for some methods that have been used for the MPPT take place:

Fuzzy control method

Optimal gradient method

Grid connected Photovoltaic Using Neural method

Shaded insolation method

These four methods are some of those that have been used in order to locate the MPP in PV systems at the duration of their operation. The two first methods (fuzzy controller and gradient method) using the circuit that was analyzed in the second part for the production of energy. Neural method and shaded insolation following a different process for the localisation of MPP.

## Fuzzy controller method:

The last years fuzzy logic controllers have been used in different industrial processes owing to their heuristic nature which is connected with the simplicity and effectiveness for both linear and non linear systems. A MPP search based on fuzzy heuristic rules, which does not need any parameter information, consists of a stepwise adaptive search, leads to fast convergence and is sensorless with respect to sunlight and temperature measurements.

The main objective of fuzzy controller for the PV systems is to track and extract maximum energy from them, compared to the levels of solar illumination and ambient temperature. In the substance fuzzy controller is an algorithm which try to locate the biggest values that created at the duration PV systems operation. The fuzzy controller is constituted by three basic stages:

Fuzzification

Fuzzy rule algorithm

Defuzification

## Fuzzification:

As first step in fuzzification part created two variables the ΔP (k) and the ΔU (k). The small k represents the sampling prices which used for the recovery of maximum power value. P (k) and U (k) are the power and voltage of PV array. The output variable is ΔU (k+1). This symbol represents the voltage that produced according to the solar illumination that channelled in the PV cells and the ambient temperature. The next mathematical equations used in fuzzy method in order to calculate the MPP that produced from the PV systems.

ΔP(k)=P(k)-P(k-1)

ΔU(k)=U(k)-U(k-1)

This process is used in three different stages thus the results to have validity. These three stages are the following:

Figure : The membership function of input ΔP(k)

In the first stage becomes accidental sampling in order to locate the MPP. Via the samplings result five prices in the first stage placed by biggest to smallest place. Positive big (PB), positive small (PS), zero (ZE), negative small (NS), and negative big (NB). The program operation is denser in the middle of picture in order to provide more sensitivity against the variant in the PV array terminal voltage.

Figure : The membership function of input ΔU(k)

In the second plan were created only three samplings in order to locate biggest (P) negative (N) and zero (Z) PP.

Figure : The membership function of input ΔU(k+1)

The last part of this process is more complicated because it created more samplings in order to reflect completely the maximum and minimum point of PV operation. From the initial mathematical equations above seven new values came out for the maximum and minimum points of energy production, positive big (PB), positive middle (PM), positive small (PS), zero (ZE), negative small (NS), negative middle (NM), and negative big (NB).

The aim of this process is to investigate and compare the different values that created from the calculations and MATLAB simulations. This process is accurate in order to find the likely MPP .

Fuzzy rule algorithm:

In order to achieve this method certain regulations should be followed thus to emerge precise results. Some of the regulations that used in fuzzy algorithm are the following:

## in case that the last change in voltage ΔU(k) has caused the power to rise, then the next change in voltage ΔU(k+1)has to move at the same direction,or if it has caused the power to drop,then we can move it in the opposite direction.

## because the fact of the characteristic curves might change from the temperature of the sunlight level,at this point will leading to an overall shift of the optimum point.

## The optimum point start's to tends to satisfy the condition É™P/É™U=0, then might the system recognize a large plateau as a maximum power region and stop. also some rules have been identified to avoiding the stabilizing effect in a region that the true peak power is zero.also it will be necessary for the systemto provide a rule that stabilizes the point of the operation at a peak power point.

## Defuzzification:

After the evaluation of the rules, the last step was to calculate the crisp output of the fuzzy control with the process of defuzzification. in this paper we have used the center of gravity method for defuzzification . It computes the center of gravity from the final fuzzy space, and yields a result which is highly related to all of the elements in the same fuzzy set. The crisp value of control output ΔU(k+1) is computed by the following equation:

Where n is the maximum number of effective rules, wi is the weighting factor, and ΔUi is the value corresponding to the membership function of ΔU. after that, the final control voltage is obtained by adding this change to the previous value of the control voltage:

U(k+1)=U(k) + ΔU(k+1)

## Using the steps that we mentioned above, the fuzzy controller can be implemented in real time for MPPT.

## Gradient method:

## Optimal gradient method is a numerical calculation which bases on multi-dimension unconstraint and is originally an optimization method in applied mathematics. The basic idea of the optimal method is to choosing the negative gradient's direction of objective function as the direction of iteration step in order to close in minimize. P-V characteristic curves of PV cell can be seen as a nonlinear function, and the object of MPPT is to search the maximum in P-V characteristic curves. MPPT can be implemented by the optimal gradient. The optimal gradient method can be defined as follow:

Supposed n-dimensional function f (f: En) in Euclid space, and function f is successive and differentiable, so there is a n dimensional row vector ∇f (x) , ∇f (x) is defined as gradient and as follows:

Defined a n-dimensional column vector g(X) = ∇f (x)T , in order to expression's convenience, define gk = g(Xk) = ∇f (Xk) , the iteration algorithm of the optimal gradient can be defined as follow:

Where ak is a non-negative constant, searching maximum of P-V characteristic curve is towards to the direction of the positive gradient k g . From the characteristic of PV cell, if the series resistance is omitted, it can obtain the relationship between power and voltage as follow:

Where function P(V) is a nonlinear function, this function is successive and has one order differentiable, and V is an unique variant in function P(V). Now k g is as follow:

## Neural method:

Another method that has been used for the MPPT is the neural networks for grid-connected photovoltaic systems. Neural method is an algorithm that used in this case in order to check the maximum value of energy that produced from PV systems. Observing the picture the grid-connected photovoltaic system it is constituted by two basic parts, the boost converter and the single phase converter.

Figure : Grid-connected photovoltaic system considered in this paper.

## Boost Converter:

A boost converter can be used to increase the voltage magnitude of an inverter circuit and to control MPPT. Neural networks and pulse width modulation (PWM) method are used to generate a pulse for drive controllable switch (SB). The calculation of the output voltage of the boost converter can be seen from:

where Vn = input voltage (output voltage of PV array),

VO = output voltage,

Duty = duty ratio of controllable switch.

## Single phase inverter:

The inverter circuit is converting direct current to alternating current by using hysteresis current control. also provides current with sinusoidal waveform. this system is able to deliver energy with low harmonics and high power factor. The inverter circuit is composed of a DC source from a boost chopper circuit, four controllable switches (S1-S4), an inductance, and a transformer.

## Neural Networks:

Neural network has the potential to provide an improved method of deriving non-linear models which is complementary to conventional techniques. Neural networks have self-adapting capabilities which makes them well suited to handle non-linearities, uncertainnes and parameter variations which may occur in a controlled plant. In this method back propagation neural networks is utilized as pattern classifier. Back-propagation neural networks is an example of nonlinear layered feed-forward networks. It is a universal approximator.

## The development of the back-propagation algorithm represents a landmark in neural networks, in that case it provides a computationally efficient method for the training of the multilayer perceptrons. The back-propagation algorithm for the design may be viewed as an application of an optimization method knowning as stochastic approximation.

The above information is proposing the algorithm that is used for MPPT is portrayed in the next figure. That network has three layers, i.e. input layer, hidden layer and output layer. The input layer has 3 neurons for array voltage, array current and cell temperature. The output layer has one neuron for control boost converter. The hidden layer has 300 neurons. The network is fully connected, i.e. the output of each neuron is connected to all neurons in the hidden layer through a weight which is not shown in the figure. Also a bias signal is coupled to all the neurons through a weight.

Figure : Neural network structure for MPPT.

Algorithm is used for training and back propagation. The back-propagation training algorithm needs only inputs and the desired output to adapt the weight. Back-propagation training is referred as supervised training. Neural network was trained using MATLAB software. That network is trained with data 4,279 sets with various solar irradiations and temperatures until error function less than 0.065.

## Shaded insolation:

Shaded insolation is one of the simplest methods that have been used in order to locate the MPP in PV systems. The methods that reported above use algorithms in order to locate the MPP. These methods are particularly complicated and sometimes the operating point is likely to coverage on a local maximum power point which is not the true peak power point on the I - V curve of the PV arrays.

According to these information the shaded insolation method is simpler and the process that used is easy and comprehensible. As reported in the introduction part the MPP in the PV systems, depends on the environmental conditions (temperature, solar illumination). Another factor that influences the output of PV, is the uniform and non-uniform insolation. In non-uniform insolation observed different maximum points in the I-P curve. In uniform insolation is created one maximum. This is particularly complex because only one local maximum point is not always the true MPP in the I-V curve.

In the shaded insolation it is analyzed the non-uniform and uniform insolation conditions. With the comparison of those two it is easier to locate the precise maximum point. By observing the picture we can see two PV systems which are constructed from the same type. Each PV constituted from 930 sheets where 10 sheets connected in series and 93 sheets connected in parallel.

Figure : I-V and I-P characteristics when 114 sheets are shaded

Figure : I-V and I-P characteristics when 336 sheets are shaded

In the first case (fig. 11) the process realised under uniform conditions. This means that the solar illumination is constant in 1000 W/m2 and the ambient temperature is 25oC. From the total 930 sheets 114 are shaded. The second case realised under from non-uniform conditions. This means that the solar illumination is altered and oscillate between 100 W/m2 to 1000 W/m2 and the ambient temperature is the same as the previous PV 25oC. In this case the shaded sheets are 336.

The main objective of this process is located under the MPP comparing the results between uniform and non-uniform conditions under shaded insolation conditions. From the mathematical equations that will be used for the calculation of MPP , the results from local maximum points under non-uniform conditions will be compared and the local maximum point from uniform conditions.

It is important to notice that in this process the measurements are realised in real time. The types that used for the calculations are the following:

a is incremental value of Isc when surface temperature changes 1 degree C (Adegree C) (Under the standard condition),

β is incremental value of V, when surface temperature changes 1 degree C (A/degree C (Under the standard condition),

Rs is series resistance of a module (R)( Under the standard condition),

K is curve correction factor (Ω/degree C(Under the standard condition),

Isc is short circuit current (Under the standard condition),

V2 I 2E2 anrd T2 is voltage, current, insolation intensity and surface temperature of a module under the standard

condition,

V1, I1 E1 and T1 is measured values of voltage, current, insolation intensity and surface temperature of a module.

## Comparison of the above methods:

By completing this chapter we had some useful conclusions for the efficiency of the above methods and processes that used for the localisation of MPP in PV systems. After the analysis of the basic operation in each one of the above methods were observed some differences in the method that was applied in each method.

Each method has its own positive elements according to the studies that have been realised in order to achieve the MPP in the PV arrays. Fuzzy controller and Optimal gradient method using the same circuit for the production of energy as it was reported in part two of this chapter. The differences of those two methods are located in the process and the different algorithm that used for each process.

Fuzzy controller algorithm has the advantage that improves considerably the efficiency at the duration of tracking phase in comparison with a conventional algorithm for MPP in PV. Another advantage is that fuzzy algorithm is particularly suitable for the fast altered environmental conditions. Finally is simple for the installation and it can be used such as one simple digital signals processor. Also, Fuzzy logic controllers have the advantages of working with imprecise inputs, not needing an accurate mathematical model, and handling nonlinearity.

The advantages of Optimal gradient Method is that the particular algorithm it can follow any MPP fast and with precision. Another important advantage of this process is that it improves considerably the efficiency of PV at the duration a tracking phase against conventional algorithm.

The main disadvantage for those two methods is that are rather complicated, and sometimes the operating point is likely to converge on a local maximum power point which is not the true peak power point on the I-V curve of the PV array. Some extra disadvantages of the above two methods is that they have high cost, difficulty, complexity and instability.

Compared to the above methods the Grid-connected Photovoltaic system using neural network follows the same process and has roughly the same advantages and disadvantages with fuzzy controller method and to gradient method. The difference between these methods is that the Grid-connected PV using neural networks is simplicity and low cost, release quick tracking under changing conditions and has small output power fluctuation.

Finally, the shaded insolation process is very different in comparison with the above methods. The advantage of this process is that in shaded insolation did not use algorithm in order to make the process complicated as the other. The measurements for the localisation of MPP are realised in real time. Also in shaded insolation process can be realised different changes at the duration of tracking phase (less shaded sheets, more shaded sheets) in order to creates more safety results.

By Completing the analysis for the advantages and the disadvantages for each method the main conclusion is that each method is completed in 90 %. This means that there are some imperfections such as the effectiveness of operation and particularly for the methods that used algorithms for the localisation of MPP. This conclusion might be that MPP that locate the algorithms are not 100 % the right result but sure the divergence is minimal. According to these information the above methods and other similar should be improved more in order to create valid opinions for the MPP of PV arrays.