*3.2.3. Incremental Conductance*

The Incremental Conductance (IncCond) method is featured for combining both, tracking speed and accuracy [13]. From the voltage *VPV*and current *IPV* measurements, the algo‐ rithm calculates the photovoltaic output power *PPV* and its derivative in function of the volt‐ age *dPPV/dVPV*, using both results to define if the duty cycle must be increased or decreased, in order to impose the system operating point on the MPP. Usually the IncCond method is implemented digitally, and the derivative is calculated by the microcontroller accord‐ ing to (19).

$$\frac{d\,P\_{PV}}{dV\_{PV}} = I\_{PV}(n) + V\_{PV}(n)\frac{I\_{PV}(n-1) - I\_{PV}(n)}{V\_{PV}(n-1) - V\_{PV}(n)}\tag{19}$$

From (19), the following decision logic is achieved:


**c.** if *dPPV* / *dVPV* =0 (at MPP), the duty cycle is maintened unchangeable.

This tecnique is characterized for presenting high tracking speed (variabe step) and accuracy (no oscillation), however, it is more complexy than P&O, once the derivative must be calcu‐ lated in real time and also require a voltage and a current sensor.

### *3.2.4. A MPPT algorithm based on temperature measurement*

The MPPT algorithm based on temperature measurement, named by MPPT-temp [22], con‐ sists on the unification of simplicity related to Constant Voltage method with the velocity and accuracy tracking related to the Incremental Conductance technique.

The development of this method comes from (3), rewritten in (20). Note that the voltage in which the maximum power is established depends exclusively on the PV surface tempera‐ ture. Thereby, accomplishing the temperature measurement, the maximum power voltage *V mpp* may be determined and actively imposed across the PV terminals in real time. The con‐ figuration needed for implementation of this new method is depicted at Figure 21.

$$V\_{mpp} = V\_{mpp}^{STC} + \left(T - T^{STC}\right)\mu\_V \tag{20}$$

3.Defining the dc-dc converter, an expression for determine the duty cycle may be derived. For example, considering a buck converter, i.e. *G=D*, the maximum power point is acom‐

An Optimized Maximum Power Point Tracking Method Based on PV Surface Temperature Measurement

*STC* <sup>+</sup> (*<sup>T</sup>* <sup>−</sup> *<sup>T</sup> STC*)*μV*

For extending the analisys, Table 7 present the equitions employed by the tracking algo‐

**Power dc-dc converter Duty cycle for operation on the MPP**

*V mpp*

*V mpp*

*V Load* + *V mpp*

*STC <sup>+</sup> (T* <sup>−</sup> *<sup>T</sup> STC)*μ*<sup>V</sup>*

*STC* <sup>+</sup> (*<sup>T</sup>* <sup>−</sup> *<sup>T</sup> STC*)μ*<sup>V</sup>*

*STC* <sup>+</sup> (*<sup>T</sup>* <sup>−</sup> *<sup>T</sup> STC*)μ*<sup>V</sup>*

*<sup>V</sup> Load* <sup>+</sup> 29.8 <sup>−</sup> 0.14*<sup>T</sup>* (23)

Buck *Dmpp <sup>=</sup> <sup>V</sup> Load*

Boost *Dmpp* =1<sup>−</sup> *<sup>V</sup> Load*

Table 7 evidences the simplicity of the proposed method: from the temperature measure‐ ment it is possible directly set the duty cycle, ensuring the maximum power transfer from the PV module to the load. Additionally, there is no need computational require‐ ments, recursive procedures and, due to the slow dynamic associated to the tempera‐ ture changes, the tracking is smooth, stable and occurs in real time, for any combination

It is important to emphasize the restrictions associated to the dc-dc converter, as it was pre‐ viously studied at last section, may imply in a poor tracking quality, even when the MPPTtemp method is employed. In order to finalize the chapter, the results obtained from an

The prototype was implemented for processing the power generated by a KC200GT PV module, from Kyocera, whose electrical specifications are listed at Table 1. A dc-dc buckboost converter was chosen for composing the hardware, because of its proper tracking be‐

For measuring the PV module surface temperature, a precision centigrade temperature sen‐ sor (LM35) was used. This device presents a linear gain of 10 mV/°C. Furthermore, in order to execute the tracking algorithm, a simple PIC 18F1320 microcontroller was employed.

<sup>=</sup> *<sup>V</sup> Load*

havior. Consequently, the equation to define the duty cycle is given by (23).

*STC* <sup>+</sup> (*<sup>T</sup>* <sup>−</sup> *<sup>T</sup> STC*)*μV*

*Dmpp* <sup>=</sup> *<sup>V</sup> Load V Load* + *V mpp*

(22)

109

http://dx.doi.org/10.5772/51020

*Dmpp* <sup>=</sup> *<sup>V</sup> Load V mpp*

rithm to calculate the duty cycle that imposes the PV operating point on the MPP.

Buck-boost, Cuk, SEPIC and zeta *Dmpp* <sup>=</sup> *<sup>V</sup> Load*

plished when (21) is rewritten as (22).

**Table 7.** Duty cycle for maximum power point operation.

of solar radiation and temperature.

experimental prototype are presented.

**Figure 21.** Configuration of the new tracking method.

The following steps describe how the maximum power point is achieved by the proposed method:


$$\mathbf{G}\_{mpp} = \frac{V\_{Load}}{V\_{mpp} + \{T - T^{\circ}C\}\_{\mu\_V}} \tag{21}$$

3.Defining the dc-dc converter, an expression for determine the duty cycle may be derived. For example, considering a buck converter, i.e. *G=D*, the maximum power point is acom‐ plished when (21) is rewritten as (22).

$$D\_{mppp} = \frac{V\_{Load}}{V\_{mpp}^{STC} + \{T - T^{STC}\}\mu\_V} \tag{22}$$

For extending the analisys, Table 7 present the equitions employed by the tracking algo‐ rithm to calculate the duty cycle that imposes the PV operating point on the MPP.


**Table 7.** Duty cycle for maximum power point operation.

**c.** if *dPPV* / *dVPV* =0 (at MPP), the duty cycle is maintened unchangeable.

and accuracy tracking related to the Incremental Conductance technique.

*Vmpp* =*Vmpp*

temperature sensor and a volatge sensor, respectivelly;

dc converter static gain *G mpp*, in acordance with (21);

**Figure 21.** Configuration of the new tracking method.

method:

lated in real time and also require a voltage and a current sensor.

*3.2.4. A MPPT algorithm based on temperature measurement*

108 Sustainable Energy - Recent Studies

This tecnique is characterized for presenting high tracking speed (variabe step) and accuracy (no oscillation), however, it is more complexy than P&O, once the derivative must be calcu‐

The MPPT algorithm based on temperature measurement, named by MPPT-temp [22], con‐ sists on the unification of simplicity related to Constant Voltage method with the velocity

The development of this method comes from (3), rewritten in (20). Note that the voltage in which the maximum power is established depends exclusively on the PV surface tempera‐ ture. Thereby, accomplishing the temperature measurement, the maximum power voltage *V mpp* may be determined and actively imposed across the PV terminals in real time. The con‐

The following steps describe how the maximum power point is achieved by the proposed

**1.** The PV module surface temperature *T* and the load volatge *V Load* are measured by a

**2.** Both sinals are applyed as input data for the tracking algorithm, whose output is the dc-

*STC* <sup>+</sup> (*<sup>T</sup>* <sup>−</sup> *<sup>T</sup> STC*)*μV*

*Gmpp* <sup>=</sup> *<sup>V</sup> Load V mpp*

*STC* <sup>+</sup> (*<sup>T</sup>* <sup>−</sup>*<sup>T</sup> STC*)*μV* (20)

(21)

figuration needed for implementation of this new method is depicted at Figure 21.

Table 7 evidences the simplicity of the proposed method: from the temperature measure‐ ment it is possible directly set the duty cycle, ensuring the maximum power transfer from the PV module to the load. Additionally, there is no need computational require‐ ments, recursive procedures and, due to the slow dynamic associated to the tempera‐ ture changes, the tracking is smooth, stable and occurs in real time, for any combination of solar radiation and temperature.

It is important to emphasize the restrictions associated to the dc-dc converter, as it was pre‐ viously studied at last section, may imply in a poor tracking quality, even when the MPPTtemp method is employed. In order to finalize the chapter, the results obtained from an experimental prototype are presented.

The prototype was implemented for processing the power generated by a KC200GT PV module, from Kyocera, whose electrical specifications are listed at Table 1. A dc-dc buckboost converter was chosen for composing the hardware, because of its proper tracking be‐ havior. Consequently, the equation to define the duty cycle is given by (23).

$$D\_{mppp} = \frac{V\_{Load}}{V\_{Load} + V\_{mpp}^{STC} + \left\{T - T^{-STC}\right\}\_{\mu\_V}} = \frac{V\_{Load}}{V\_{Load} + 29.8 - 0.14T} \tag{23}$$

For measuring the PV module surface temperature, a precision centigrade temperature sen‐ sor (LM35) was used. This device presents a linear gain of 10 mV/°C. Furthermore, in order to execute the tracking algorithm, a simple PIC 18F1320 microcontroller was employed.

The tracking method validation was achieved plotting the PV operating point on the I-V plan during temperature and solar radiation changes, as is illustrated in Figure 22. For reaching this result a scope on XY mode, where X refers to the PV output voltage and Y re‐ fers to the PV output current, was employed.

**Solar radiation Temperature** 900 W/m<sup>2</sup> 51°C 850W/m<sup>2</sup> 50°C 830W/m<sup>2</sup> 49°C 802W/m<sup>2</sup> 41°C 787W/m<sup>2</sup> 34°C 770W/m<sup>2</sup> 26°C 700W/m<sup>2</sup> 51°C 600W/m<sup>2</sup> 51°C 500W/m<sup>2</sup> 51°C 400W/m<sup>2</sup> 51°C 300W/m<sup>2</sup> 52°C 200W/m<sup>2</sup> 52°C 100W/m<sup>2</sup> 53°C 50W/m<sup>2</sup> 53°C

An Optimized Maximum Power Point Tracking Method Based on PV Surface Temperature Measurement

http://dx.doi.org/10.5772/51020

111

**Table 8.** Solar radiation and temperature values obtained from data logger during experimental tests.

is equivalent to the trajectory described by the maximum power point.

**4. Conclusion**

From Table 8, and employing (3) and (4), the theoretical voltage and current values for the system operating on the MPP were determined and plotted on the I-V plan, resulting at Fig‐ ure 23, from where it is possible to conclude that the trajectory obtained by experimentation

Currently the most common employed PV tracking algorithm are Perturb and Observe and Incremental Conductance. Perturb and observe is simple, however it failures to track the MPP under abrupt changes on solar radiation and presents oscillations around the MPP on steady-state. Incremental conductance is accurate, however, it implementation is more com‐ plex. In these both algorithms, it is necessary to measure the PV output voltage and current.

The proposed algorithm is simpler than perturb and observe and more accurate than the in‐ cremental conductance. Furthermore, the current sensor is substituted by a temperature sen‐ sor, implying in cost reduction. Eliminating the current sensor means avoid the output power high frequency variation associated to the PV current (directly proportional to solar radiation), thus, there is no oscillation around the MPP. Since the tracking is based on the

temperature, its low dynamic ensures a soft tracking, but accurate and fast.

**Figure 22.** Experimental PV operating point on I-V plan during temperature and solar radiation changes. Scope on XY mode (X-voltage, Y-current)

**Figure 23.** Theoretical MPP trajectory for solar radiation and temperature measured during experimental evaluation.

In order to prove that the obtained experimental trajectory coincides with the MPP, the val‐ ues of solar radiation and temperature were also collected by a data logger and summarized by Table 8. The measurements were achieved on middle of April in the Florianopolis Island – south of Brazil – located at latitude 27o .


An Optimized Maximum Power Point Tracking Method Based on PV Surface Temperature Measurement http://dx.doi.org/10.5772/51020 111

**Table 8.** Solar radiation and temperature values obtained from data logger during experimental tests.

From Table 8, and employing (3) and (4), the theoretical voltage and current values for the system operating on the MPP were determined and plotted on the I-V plan, resulting at Fig‐ ure 23, from where it is possible to conclude that the trajectory obtained by experimentation is equivalent to the trajectory described by the maximum power point.
