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

2.1.1. Standard Test Condition

The Standard Test Conditions (STC) refers to the conditions under which PV modules are tested in laboratory. STC defines the values of irradiance, temperature and air mass index, in which the manufactures feature the PV devices, permitting to compare their performance and efficiency conversion.

2.1.2. Irradiance

The Sun energy reaches to the Earth through electromagnetic waves, resulting in an irradiance (or solar radiation) of about 1366 W/m² on its outer atmosphere. However, due to atmospheric effects – scattering, absorption and reflection -, the incoming irradiance is modified before reaching the Earth’s surface [20].

The process of scattering occurs when small particles and gas molecules diffuse the radiation in random directions, while absorption is defined as a process in which the solar radiation is retained by atmosphere substances and converted into heat. In addition, part of the total solar radiation is redirected back to the space by reflection and part, termed by direct solar radiation, reaches the Earth's surface unmodified by any of the above atmospheric processes, as depicts Figure 2.

Since the direct radiation on a clear day, at noon, is typically 1000 W/m², this value is adopted as reference at STC.

2.1.3. Air Mass

The Air Mass (AM) index quantify the solar radiation path (L) across the atmosphere, normalized by the shorter path (L ₀), measured from the zenith angle, as is depicted in Figure 3 and mathematically described by (1) [19]. The index AM0 is used to describe the radiation path out of the atmosphere, where the irradiance is constant and equal to 1366 W/m².

On industry, PV modules are standardized considering an air mass index of AM=1.5. This value comes from a angle of aproximatly 48^°, proper representing the PV instalitions around the most populed centres across Europe, China, Japan and United States of America, located in mid-latitudes. This value is also adopted as reference at STC.

2.1.4. Temperature

The third parameter used to characterize a PV module is its surface temperature. The STC temperature value adopted for PV modules characterization is T=25 ^°C.

3.1.1. Analysis for resistive load-type

When a resistive load is connected to the dc-dc converter, Figure 11 may be redrawn as per Figure 12 and equation (7) can be derived.

Taking into account a literal dc-dc converters static gain G, the input system variables (V _PV and I _PV ) can strictly be associated to the output ones (V _R and I _R ), through (8) and (9).

Isolating V _R in (8) and I _R in (9) and substituting the found results into (7), it is possible to obtain (10).

The term V _PV /I _PV describes the effective resistance R _eff obtained from the PV module terminals. In other words, the dc-dc converter emulates a variable resistance, whose value can be modulated in function of the converter static gain G. This conclusion allows redesigning Figure 12 as Figure 13 and writes (11).

When plotted on the I-V plan, equation (11) results in a straight line whose inclination angle θ, given by 12, is modified according to the converter static gain G.

Table 2 presents static gain, as a function of the duty cycle D, for the dc-dc converter cregarded in this chapter, for operation in continuous conduction mode (CCM). Applying the results from Table 2 in (12), it is possible to describe the effective inclination angle θ, for each converter, as a variable dependent on the duty cycle D, as consequence, Table 3 is obtained.

Theoretically, since the duty cycle is limited between 0 and 1, the effective inclination angle becomes restricted into a range whose extremes are dependent on the considered dc-dc converter. For instance, when buck converter is taken into account, for null duty cycle, D=0, (13) is found.

Thereby, if the duty cycle is set on its high value, D=1, (14) may be written.

In other to extend the presented analysis for further converters, a similar procedure may be applied, resulting at Table 4 and Figure 14.

From Table 4 it is noticed that effective load inclination angle defines an area on the I-V plan where the maximum power can be tracked. For a better understanding, Table 4 is graphically explained through Figure 14, from where two distinct regions are identified: tracking and non tracking regions.

The tracking region refers to the area on the I-V plan in which the dc-dc converter is able to emulate a proper effective load curve in order to intercept the I-V curve exactly on the MPP, ensuring the maximum power transfer. Note, when solar radiation or temperature change, the maximum power point is relocated on the I-V plan, thus, the effective load inclination angle must also be modified in order to reestablish the maximum power transfer. However, this condition is only suitable if the MPP is located inside the tracking region, otherwise, the system operating point will be set out of the MPP.

Comparing the graphical results, it is verified that buck-boost, Cuk, SEPIC and zeta are the most appropriated converters for maximum power point tracking applications, once they may track the MPP independently on its position on the I-V plan. On the other hand, buck 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.

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

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. Additionally, the area in which the I-V curves were traced is in accordance with the tracking region, theoretically defined for each converter, validating the analysis.

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

3.1.2. Analysis for constant voltage load-type

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 beginning, consider the MPPT system shown in Figure 17, in which a dc voltage source is supplied by a PV module through a literal dc-dc converter.

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.

Taking into account the static gain G presented at Table 2, it is possible to define the equivalent 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 equivalent 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.

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).

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

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.

In addition, notice that temperature changes may directly affect the tracking quality: commonly, PV systems are designed considering its operation on the SCT, i.e., T=25°, however, 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 behavior is critical for buck converter, as per Figure 19 (a), since its non tracking region is also on left of V _bus .

Although boost converter also presents a non tracking region, in this case it presents a proper 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.

3.2.1. Constant Voltage

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

3.2.2. Perturb and Observe

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

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, otherwise, it is inverted.

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 during fast changes of solar radiation.

3.2.3. Incremental Conductance

The Incremental Conductance (IncCond) method is featured for combining both, tracking speed and accuracy [13]. From the voltage V_PV and current I_PV measurements, the algorithm calculates the photovoltaic output power P_PV and its derivative in function of the voltage dP_PV/dV_PV , 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 according to (19).

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

1. if dPPV/dVPV0(left of MPP), the duty cycle is changed for elevating the PV module voltage;

2. if dPPV/dVPV0(right of MPP), the duty cycle is alterated for decreasing the output voltage;

3. 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 calculated 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], consists 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 temperature. 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 configuration needed for implementation of this new method is depicted at Figure 21.

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

1. The PV module surface temperature T and the load volatge V _Load are measured by a temperature sensor and a volatge sensor, respectivelly;

2. Both sinals are applyed as input data for the tracking algorithm, whose output is the dc-dc converter static gain G _mpp , in acordance with (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 acomplished when (21) is rewritten as (22).

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

Table 7 evidences the simplicity of the proposed method: from the temperature measurement 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 requirements, recursive procedures and, due to the slow dynamic associated to the temperature 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 previously studied at last section, may imply in a poor tracking quality, even when the MPPT-temp 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 buck-boost converter was chosen for composing the hardware, because of its proper tracking behavior. Consequently, the equation to define the duty cycle is given by (23).

For measuring the PV module surface temperature, a precision centigrade temperature sensor (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 refers to the PV output current, was employed.

In order to prove that the obtained experimental trajectory coincides with the MPP, the values 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 27^o.

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 Figure 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.