Distributed Maximum Power Point Tracking of Photovoltaic Arrays
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Access provided by: anon Sign Out. However, this curve changes as a function of the sun irradiation and the solar cells temperature, as previously stated. These variations of the characteristic points are approximately linear in relation to the temperature, T :. As aforementioned, sun irradiation variations also modify the I - V curve.
However, manufacturers normally do not include any information regarding these variations in the solar panel datasheets. Commonly, the shape of the I-V curve is considered essentially invariant with irradiation levels within ranges around one solar constant, so this leads to the following equation, considering, respectively, linear and exponential variations of the short-circuit current, I sc , and the open-circuit voltage, V oc , with temperature, whereas R s remains unaffected for temperature variations [ 44 ].
Those conditions lead to the following equation [ 39 ]:. Taking all the above statements into account, a simple but accurate i. Establish the temperature range in which the solar panel behavior should be modeled and calculate the I - V curve characteristic points in that range by making use of 8. Obtain from expressions 7 the equivalent circuit parameters within the selected temperature range.
Fit a polynomial expression to the variations of the equivalent circuit parameters as a function of temperature. Introduce the effect of the irradiance in the parameter I pv by using expression 9. Data regarding the characteristic points of the I - V curve from the manufacturer's datasheet are included in Table 1. With regard to the ideality factor some additional considerations have been made. After choosing the value for the ideality factor, the other parameters have been calculated using 7 ; see Figure 4. The polynomial fittings to the data have also been included in the graphs of the figure, the irradiance level, G , being considered in the case of the photocurrent, I pv ; see the following:.
Then, the efficiency of the method can be estimated with the following expression [ 45 ]:.
Calculated values of the equivalent circuit parameters R s , R sh , I pv , and I 0 , for YLCb monocrystalline panel as a function of the temperature, T. Calculated points are indicated with symbols whereas the polynomial approximations fitted to those data 10 have been included in each case as solid lines. As these expressions are implicit and coupled, their resolution needs to be done by using numerical calculation or through simplifications in order to reduce the complexity of the calculations [ 46 ].
To the authors' knowledge, no method to uncouple variables I mp and V mp from 5 and 6 has been proposed in the available literature. Nevertheless, this possibility does indeed exist by making the following changes of variable:. Then, from 5 and 6 , it is possible to obtain uncoupled equations as a function of the above new variables:.
Then, unmaking the change of variables, I mp and V mp , can be derived after only one implicit equation resolution:. This procedure gives the values of current and voltage at the MPP in a very easy way, avoiding voltage sampling or simplifications that could reduce the accuracy of the results. Two different ambient conditions sun irradiance and temperature levels have been considered for the simulations carried out. The first one is a cloudy day, with low but very unstable irradiance level, and the second one is a sunny day; see graphs in Figure 5. Temperature and wind speed conditions corresponding to those days have been obtained from the measurements done at Washington, DC, this city being quite close to GSFC [ 48 ].
Ambient conditions on May 13, a , b , and May 14, c , d. Solar irradiance is represented in left side, and temperature and wind velocity are in right side. With the data of Figure 5 regarding sun irradiance and ambient temperature it is possible to calculate temperature of the solar panel with the equation.
This last parameter is normally included in the manufacturers' datasheet. These graphs were calculated according to ambient conditions for those days; see Figure 5 and Following the procedure described in the previous section and taking into account the aforementioned sun irradiance Figure 5 and panel temperature Figure 6 data, it is possible to calculate the I - V curve of the selected solar panel YLCb in each instant of the specified cloudy and sunny days. On the surface plotted in the figures, a thick line has been drawn to indicate the maximum power point MPP which, as can be observed, indicates variations regarding the current and voltage at the aforementioned MPP during the chosen days.
These current and voltage levels at MPP have been separately plotted in Figures 7 b , 7 c , 8 b , and 8 c. These values of the maximum power available from the solar panel are used in the following section as a reference to compare the studied MPPT methods. Evolution of current b and voltage c at maximum power point MPP. As mentioned in Section 1 , the aim of the present work is to describe a simple methodology to model a solar panel operating within a wide range of ambient conditions and to analyze different MPPT options for photovoltaic systems see in Figure 9 the block-diagram corresponding to a photovoltaic system equipped with a MPPT.
In the following subsections four MPPT methods are studied as an example of the proposed method:.
In this comparison example the ideal Boost-converter has been selected due to its simplicity see Figure However, it should be underlined that other more sophisticated DC-DC converter possibilities could also be included in the simulation with the proposed methodology, this possibility being out of the scope of the present work, which is focused on the solar panel accurate modeling for MPPT analysis.
The principle of the Boost-converter consists of two operational modes, depending on the position of the switch, T sc. When the switch is closed on-state the inductor L stores the energy of the source while the capacitor feeds the load.
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Otherwise, when the switch is opened off-state the only path available for the current is through the diode D and the source feeds the load and charges the capacitor. For an ideal Boost-converter, the relationship between the input and output variables current and voltage is defined by. Therefore, bearing in mind 17 and 18 , the effect of the Boost-converter can be considered as an equivalent resistor, whose value depends on the duty cycle:. Therefore, the task of an MPPT method would be to find the particular value of the duty cycle which maximizes the output power from the solar panel.
As previously mentioned, in the following subsections four MPPT methods are analyzed using the proposed solar panel method, the corresponding algorithms being adapted from the work by Dolara [ 31 ]. Effect of Boost-converter duty cycle i. This is the simplest MPPT method among the four considered methods. It is based on maintaining the operating voltage of the panel, V , as close as possible to a reference value, V ref.
This reference value can be based on the data supplied by the manufacturer. Although this method represents an improvement in terms of energy efficiency when compared to the case of no MPPT method, it is also true that it can be only optimized for one ambient condition. Therefore, the operational point will not be coincident with the maximum power point of the I - V curve for other sun irradiance and temperature conditions. This method is based on the principle that the MPP voltage is always a constant fraction of the open-circuit voltage i.
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This consideration closely matches reality, although the value of the relationship depends on the solar panel being studied and, as previously suggested, is not entirely constant in the face of sun irradiance and temperature variations. A major drawback of this method is the need to know the open-circuit voltage for given conditions. This voltage level is normally measured by opening the circuit. Logically, this operation stops the flow of energy.
Therefore, the number of measurements per unit of time should be adjusted to reduce the loss of energy, bearing in mind that too many measurements will capture variations of the ambient conditions but reduce the solar panel output power. The control principle of the Boost-converter is the same as the previously explained method. This method is based on a similar principle to the previous one. In this case the current at MPP is considered to be a fraction of the short-circuit current i.
This fraction is supposed to remain constant in every ambient condition. As with the previous case, this closely matches reality, although there are slight variations depending on sun irradiance and temperature changes.
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In this case part of the power is lost during the short-circuit current measurements. This algorithm is based on continuous modifications of the solar panel operational voltage, checking after each perturbation if the generated power has increased or decreased. If the power increases the next voltage perturbation will go in the same direction and is changed if the power decreases. This process is indicated in the corresponding block-diagram in Figure The solar panels were modeled following indications from Section 2.
The ambient conditions considered are those described in Section 3 , the temperature of the solar panels being calculated with Regarding the short-current pulse method and the open voltage method a measurement of I sc and V oc was taken every 3 seconds time steps. The control parameters corresponding to the studied methods were optimized, for the solar panel considered in the present work, following these criteria. Results are included in Table 2 and Figure 13 , together with the maximum extractable power from the solar panel obtained with expressions 13 and The high efficiency obtained for all MPPT methods can be explained as in every case an ideal DC-DC converter without energy losses has been considered.
The best performance of MPPT method for the studied conditions seems to be the perturb and observe method, the reason being the noninterrupted power extraction from the solar panel. The worst performance of MPPT method is the constant voltage method, as it shows the larger influence from the ambient conditions. The open voltage and short-current pulse methods show a quite good performance, the grey zone below the plots being produced by the switching that disconnect the solar panel to perform the measurements of V oc and I sc.
Maximum extractable power ideal has been also included. Logically, the efficiency of the studied MPPT methods is worse in case of cloudy days than in case of sunny days. This is clear due to the faster variations on the ambient conditions. In order to check the proposed methodology, a real photovoltaic facility, whose behavior was measured, together with the ambient conditions, by Houssamo et al. This photovoltaic facility is formed by eight QPI solar panels manufactured by Conergy, organized in four two-panel series connected in parallel.
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The characteristics of the panels are included in Table 3 , whereas the sun radiation and the panel temperature during the measurements are included in Figure Ambient conditions irradiance and solar panels temperature during operation of the photovoltaic facility studied from [ 50 ]. The procedure described in Section 4 was followed in order to model the studied photovoltaic facility.
The results from the simulation show a higher extracted power when compared to the behavior measured directly on the facility, this discrepancy between results being explained as no power losses wiring, connections, dirt over the panels, degradation, losses at the Boost-converter, etc. Bearing in mind that no information regarding these losses was included in [ 50 ], the results were scaled down by multiplying by a constant 0. Also, an equivalent resistor can be then considered in order to take into account the power losses. The results corresponding to the simulation carried out with a 1.
A quite good correlation between the results obtained with the present methodology and the ones measured by Houssamo et al.