Partial Shading
BP380 PV modules [23] form the basis for the simulation model used in this chapter. Eight modules are connected in series and experience non-uniform environmental conditions due to moving shadows from obstacles in the environ- ment representing static PSC and cell degradation modelled as constant PSC. Real irradiance data is used to model transient PSC which is assumed to affect all modules simultaneously due to the size of the system. Each obstacle in the environment is defined based on its own coordinate system where the PV modules are located to the South-East of the obstacle. The obstacle is located at the origin of its coordinate system. The obstacle data file also contains the height and width of the obstacle. The system is simulated to be located in Tasmania at the site of the Cape Grim weather monitoring station at latitude -40.6817 and longitude 144.6892. At this site, one minute solar irradiance data is recorded throughout the year. The analysis is focussed on the performance under PSC, so only the minutes of data throughout the year when the modules experience shading due to the obstacles, are considered. The global irradiance is used to provide a simplified analysis of the shading conditions to reduce the
computational burden associated with executing a more detailed shading model based on suggestions given later in this chapter.
Each module has a shading factor which is assessed by considering the number of cells in the module that may be shaded. A cell is considered to be shaded if its mid-point is within half of the shadow width from the central shadow projection. The shadow projection is calculated using the shadow geometry based on the position of the object and the position of the sun at the time of interest. The end point of the shadow is evaluated using the equations for the shadow geometry and the central shadow projection is considered to be a straight line joining the object’s origin to the shadow tip. The width of the shadow is assumed to be equal to the object width and uniform at all distances away from the object origin. The shading factor represents the percentage of cells shaded in the module and how this limits the irradiance available to that module. For instance, if no cells are shaded, the shading factor is 1 as all cells receive the global horizontal irradiance. However, if all the cells are shaded in the module, the shading factor becomes 0. The shading factor is defined in (3.13).
sf = 1−(shaded cells/36) (3.13)
The irradiance on each module is determined by multiplying the shading factor by the one-minute irradiance data obtained from the Australian Bureau of Meteorology [81]. This irradiance is then also multiplied by the constant PSC shading factor representing the effect of cell degradation on the irradiance received by the module. The combination of the object shading and cell degradation modelled by shading factors and the real irradiance data creates an authentic indication of the irradiance experienced by the modules when shading occurs in the environment.
An object in the environment is oriented at position (0,0) where the y-axis points in the direction of north, and the x-axis points east. The PV system considered in case 1 is located 10 meters south of the obstacle and 5 meters east. This is shown in Fig. 3.1. The dimensions of each PV module are 0.537 m x 1.209 m. The width of the shadow is assumed equal to the width of the obstacle and the (x,y) co- ordinates of the tip of the shadow are assumed to lie along the centre of the width.
Figure 3.1: XY representation of the obstacle and PV modules in the environment for case 1.
The execution process in the model involves using the real irradiance data as the base amount of irradiance that each module experiences. The time of day data is combined with the obstacle location and the equations presented in Section 3.3. This gives a shadow vector in terms of an x and y coordinate corresponding to the tip of the shadow. Each module then considers this shadow vector and whether or not it will pass through any of the cells in the module. This is determined by looking at the angle and length of the vector. Each module has an angle range defined for each obstacle which indicates when shading might occur. If the shadow vector is within this range, it is evaluated if the shadow vector will cause shading on any of the cells in the module. Cells may be shaded by multiple obstacles at any one time. The shadow vector gives the centrepoint of the shadow and the width is incorporated to see if the centrepoint of each cell is within the tolerance/width of the centreline of the obstacle’s shadow. Once the shaded cells for each module have been determined, the factor of the 36 cells which are shaded gives the shading factor for the module. This process is completed for each module and gives the relative irradiance on each module.
At each minute the shading factors are determined and the real irradiance from the Bureau of Meteorology one-minute data is applied in the system. Using this data the I-V and P-V characteristics are obtained by sweeping the voltage across the range 0 to 157 V. This is repeated for each minute of data in the irradiance file.
The process outputs a number of data files which are detailed below. Sample output files are given in Appendix B.
• year month day x.xlsx - This file contains information on the I-V and P-V curves obtained for the particular day of study. The data columns corre- spond to reference time, time, voltage, current, power.
• year month mpps.xlsx - This file contains information on the GMPP loca- tions for each test irradiance. The data columns correspond to reference time, irradiance, MPP power, MPP voltage, MPP current.
• year month shaded patterns 1.xlsx - This file contains information on which cells in the module experience shading at each point in time. If a cell is shaded it is indicated as 1, if it is unshaded it is 0. There is a correspond- ing file for each module. The data columns correspond to reference time, irradiance, cell1....cell36.
• year month shadow location.xlsx - This file records the (x,y) coordinates of the shadow tip for each object considered for each sample irradiance. The data columns correspond to reference time, x and y coordinates of each obstacle.
• year month irradiance on all modules.xlsx - This data file gives the shading factors and irradiance on each module and combines the information from the shading patterns file for each module. The data columns correspond to reference time, module1...module8 irradiance.
Of these files, theyear month mpps.xlsx file is used in the analysis in this chapter to show how the MPP location varies with changing irradiance and the movement of shadow in the environment. The MPP power will continually jump due to the changing irradiance in the environment which is unavoidable. The MPP voltage however should undergo a much smaller jump as the irradiance changes. The analysis is interested in how far the MPP voltage moves under PSC and how frequently it moves between successive MPPs. In particular in [90], it is identified that the MPPs lie with separation of approximately 0.8Voc, so this analysis looks
to see how frequently the GMPP jumps to another peak under real irradiance conditions and with a variety of obstacles in the environment. The purpose of this analysis is to identify how frequently GMPPT should be initiated and to deter- mine whether an intelligently tuned conventional MPPT technique could provide superior performance by remaining around the location of the most likely GMPP.
The inputs to the simulation are an irradiance file and an obstacles file. A sample few lines from an irradiance file is shown in Fig. 3.2, where the columns are:
• A - year • B - month • C - day • D - hour • E - minute • F - simulation time
• G - input for lookup table for voltage sweep, alternates between 0 and 157 so that the simulation model varies the voltage across this range
• H - irradiance
A sample obstacles file for two obstacles in the environment is shown in Fig. 3.3, where the columns are:
• A - height
• B - width
• C - obstacle x coordinate relative to PV system
• D - obstacle y coordinate relative to PV system
The proposed flowchart of this PSC assessment is shown in Fig. 3.4 for a PV system consisting of eight modules. It is possible to change the number of modules by changing the constant in the decision block If module ref <= 8 of Fig. 3.4. The eight module simulation model is shown in Fig. 3.5 to Fig. 3.8.
Figure 3.3: Obstacles input file sample for two obstacles.
Figure 3.4: Proposed partial shading study flowchart for PV system with eight modules and any number of obstacles.