*3.1.2. Analysis for constant voltage load-type*

and boost converters are not indicate for this proposal, since their tracking area is only a part of the whole I-V plan. In order to validate the proposed theory, buck, boost and buck-

boost converters were designed and assembled in laboratory, according to Figure 15.

102 Sustainable Energy - Recent Studies

**Figure 15.** a) buck, (b) boost and (c) buck-boost power stage converters.

curve was traced, and the found results are shown at Figure 16.

theoretically defined for each converter, validating the analysis.

ployed in battery charges, or even, delivering power to a regulated dc bus.

For achieving the experimental tests, the converters duty cycle was linearly varied from 0 to 1, while PV voltage and current were measured. By the use of a scope on XY mode, the I-V

Notice that I-V curve is partially plotted on the I-V plan when buck and boost converters are regarded, and on the whole I-V plan, when buck-boost converter is considered. Additional‐ ly, the area in which the I-V curves were traced is in accordance with the tracking region,

On the next subsection, the resistive load will be replaced by a constant voltage load-type. This analysis is relevant and mandatory, since in many applications, PV systems are em‐ The analysis concerning to dc-dc converters operating as MPPT when a constant voltage load-type is considered follows the same procedures presented for resistive loads. For be‐ ginning, consider the MPPT system shown in Figure 17, in which a dc voltage source is sup‐ plied by a PV module through a literal dc-dc converter.

**Figure 16.** Experimental results for (a) buck, (b) boost and (c) buck-boost converters.

**Figure 17.** MPPT supplying a constant voltage load-type.

In this case, the output converter voltage is imposed by the load, permitting to write (15) and to model both, dc-dc converter and voltage load, as a controlled voltage source, as is shown in Figure 18.

*VPV* <sup>|</sup> *<sup>D</sup>*=*D*min

**terminals**

*VPV* <sup>|</sup> *<sup>D</sup>*=1

**Table 6.** Minimum and maximum voltage values across the PV module terminals.

Buck *VPV <sup>|</sup> D=1 <sup>=</sup> Vbus VPV <sup>|</sup> D=Dmin*

**Figure 19.** Tracking and non tracking regions for: (a) buck converter; (b) boost converter and (c) buck-boost, Cuk, SEP‐

=0 <sup>V</sup> *VPV* <sup>|</sup> *<sup>D</sup>*=0

=0 <sup>V</sup> *VPV* <sup>|</sup> *<sup>D</sup>*=*D*min

Extending the analysis for further converters, Table 6 is obtained.

**Power dc-dc converter Minimum voltage across the PV module**

Boost *VPV* <sup>|</sup> *<sup>D</sup>*=1

track it.

Buck-boost, Cuk, SEPIC and zeta

IC and zeta converters.

<sup>=</sup> *Vbus*

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

The graphical representation allows understanding how the dc-dc converter feature impacts on the tracking quality when constant voltage loads are employed, as depicts Figure 19. When the maximum power point is located inside the tracking region, the dc-dc converter may apply on the PV output terminals a voltage value for ensuring its operation on the MPP. Otherwise, even when the better tracking algorithm is used, there is no possible to

*<sup>D</sup>*min =*Voc* (18)

**Maximum voltage across the PV module terminals**

*= Voc*

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

105

=*Vbus*

=*Voc*

**Figure 18.** Equivalent MPPT system obtained from the PV module terminals.

Taking into account the static gain *G* presented at Table 2, it is possible to define the equiva‐ lent voltage source for each dc-dc converter as a function of the duty cycle *D*, resulting on Table 5. Due to the duty cycle range restriction, 0*<D<*1, the voltage imposed by the equiva‐ lent controlled voltage source across the PV module terminals is also limited. For example, when buck converter is regarded, equations (16) and (17) are obtained from the first line of Table 5, describing the system behavior for *D=*0 and *D=*1, respectively.


**Table 5.** Minimum and maximum effective load inclination for some dc-dc converters.

$$\left.V\_{PV}\right|\_{D=0} = \frac{V\_{hw}}{0} \to \infty \tag{16}$$

$$\left.V\_{PV}\right|\_{D=1} = V\_{bus}\tag{17}$$

It is important to emphasize that the maximum voltage across the PV module terminals is its open circuit voltage, thus, the minimum duty cycle value must be defined in order to satisfy this condition. From the exposed, (16) is replaced by (18).

An Optimized Maximum Power Point Tracking Method Based on PV Surface Temperature Measurement http://dx.doi.org/10.5772/51020 105

$$\left.V\_{PV}\right|\_{D=D\_{\min}} = \frac{V\_{bus}}{D\_{\min}} = V\_{oc} \tag{18}$$

Extending the analysis for further converters, Table 6 is obtained.

In this case, the output converter voltage is imposed by the load, permitting to write (15) and to model both, dc-dc converter and voltage load, as a controlled voltage source, as is

Taking into account the static gain *G* presented at Table 2, it is possible to define the equiva‐ lent voltage source for each dc-dc converter as a function of the duty cycle *D*, resulting on Table 5. Due to the duty cycle range restriction, 0*<D<*1, the voltage imposed by the equiva‐ lent controlled voltage source across the PV module terminals is also limited. For example, when buck converter is regarded, equations (16) and (17) are obtained from the first line of

**Power dc-dc converter Equivalent voltage source value**

Boost *VPV* =(1−*D*)*Vbus*

Buck *VPV <sup>=</sup> Vbus*

Buck-boost, Cuk, SEPIC and Zeta *VPV* <sup>=</sup> (1 <sup>−</sup> *<sup>D</sup>*)

<sup>=</sup> *Vbus*

It is important to emphasize that the maximum voltage across the PV module terminals is its open circuit voltage, thus, the minimum duty cycle value must be defined in order to satisfy

*<sup>G</sup>* (15)

*D*

*<sup>D</sup> Vbus*

<sup>0</sup> →*∞* (16)

=*Vbus* (17)

*VPV* <sup>=</sup> *Vbus*

**Figure 18.** Equivalent MPPT system obtained from the PV module terminals.

Table 5, describing the system behavior for *D=*0 and *D=*1, respectively.

**Table 5.** Minimum and maximum effective load inclination for some dc-dc converters.

this condition. From the exposed, (16) is replaced by (18).

*VPV* <sup>|</sup> *<sup>D</sup>*=0

*VPV* <sup>|</sup> *<sup>D</sup>*=1

shown in Figure 18.

104 Sustainable Energy - Recent Studies

The graphical representation allows understanding how the dc-dc converter feature impacts on the tracking quality when constant voltage loads are employed, as depicts Figure 19. When the maximum power point is located inside the tracking region, the dc-dc converter may apply on the PV output terminals a voltage value for ensuring its operation on the MPP. Otherwise, even when the better tracking algorithm is used, there is no possible to track it.


**Table 6.** Minimum and maximum voltage values across the PV module terminals.

**Figure 19.** Tracking and non tracking regions for: (a) buck converter; (b) boost converter and (c) buck-boost, Cuk, SEP‐ IC and zeta converters.

In addition, notice that temperature changes may directly affect the tracking quality: com‐ monly, PV systems are designed considering its operation on the SCT, i.e., *T* =25° , howev‐ er, when PV modules are exposed to the solar radiation, its real temperature of operation encreases and, as consequence, the voltage associated to MPP is moved to the left. This be‐ havior is critical for buck converter, as per Figure 19 (a), since its non tracking region is also on left of *V bus*.

Before presenting this proposal, a review of the most commonly employed MPPT algo‐ rithms is presented, where Constant Voltage, Perturb and Observe (P&O) and Incremental

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

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107

This method is achieved in or to impose the voltage across the PV terminals clamped at a fixed value, normally specified to ensure the maximum power transfer on the STC [4]. Once a single voltage sensor is needed, it is featured by simplicy of implementation and low cost,

Perturb and Observe (P&O) is one of the most diffused MPPT algorithms, whose tracking response is independent on the environmental conditions, however, its implementation re‐

When in operation, the P&O algorithm calculates the PV output power and perturbs the converter duty cycle (increasing or decreasing it). After perturbation, the PV output power is recalculated and, if it was increased, the perturbation is repeated on the same direction,

The main drawbacks associated to this method are the oscillation in steady-state, due to the constant perturbations, the slow tracking dynamic and the inability to proper operate dur‐

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‐

**a.** if *dPPV* / *dVPV* 0 (left of MPP), the duty cycle is changed for elevating the PV mod‐

**b.** if *dPPV* / *dVPV* 0 (right of MPP), the duty cycle is alterated for decreasing the out‐

*IPV* (*n* −1)− *IPV* (*n*)

*VPV* (*<sup>n</sup>* <sup>−</sup>1)−*VPV* (*n*) (19)

but for any temperature change, the PV operating point is set out of the MPP.

quires a voltage and a current sensor, increasing the cost and complexity [11].

Conductance (IncCond are briefly discussed.

*3.2.1. Constant Voltage*

*3.2.2. Perturb and Observe*

otherwise, it is inverted.

ing fast changes of solar radiation.

*dPPV dVPV*

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

= *IPV* (*n*) + *VPV* (*n*)

*3.2.3. Incremental Conductance*

ing to (19).

ule voltage;

put voltage;

Although boost converter also presents a non tracking region, in this case it presents a prop‐ er tracking behavior, once temperature increasing replaces the MPP to left, toward to the tracking region, in according to Figure 19 (b).

Finally, buck-boost converter (and similars) can track the MPP independent on its position on the I-V pan, as is shown on Figure 19 (c). Furthemore, these converters are also indicated for tracking applications, when constant voltage loads are employed.
