Example 4: Combination parametric with linkage |  |  |  |

| This topic describes SAM 3.0 and has not been revised for SAM 2009 Beta. You may find useful information, especially if you are new to SAM, but some of the information may be inconsistent with the new version.

This example illustrates the use of both a combination parametric group and a linked group, which is useful when variables in a combination group that you want to appear in a single graph are also related to other variables. It is based on the fourth case in the sample file Parametrics Examples.sam.

What is the optimal array orientation for three different locations? In Example 3, we assigned the azimuth and tilt variables to a combination parametric group to plot system output versus tilt and azimuth on a contour graph. The graph showed that the optimal array tilt angle for the residential photovoltaic project in Boulder, Colorado was what we expected, 40 degrees north, close to Boulder's latitude. The optimal azimuth for Boulder, on the other hand, was about 10 degrees east of south, not the standard due south. Because the rule of thumb "array tilt equals latitude" was valid for Boulder, we assume in this exercise that it is also true for all three locations. In this example, we will use the same combination group of azimuth and tilt, and link the tilt variable to location, which will allow us to plot a graph of array output for a range of azimuth variables for each of the three locations on a single graph.

When you perform a parametric analysis with more than one variable, the number of calculations can become very large. In Example 3, Solar Advisor performed 49 simulations for each combination of 7 azimuth values and 7 tilt values. If we were to repeat that analysis for three locations instead of one, the number of calculations increases to 147 (49 combinations times three locations). Some analyses with larger numbers of variables and parametric values simulation run times can become impractically long. Linking related parametric variables can help minimize run times by avoiding unnecessary simulations. In this example, by linking the location variable to the latitude variable, Solar Advisor only simulates combinations of tilt and latitude values that make sense (assuming that we only want to simulate systems whose array tilt angle equals the location's latitude). For example, linking tilt to location will ensure that Solar Advisor does not run a simulation using Seattle's radiation data and Boulder's 40 degree latitude for the array tilt.

Define Location and Tilt as linked parametric variables:

1. | Open the file that you created in Example 3 and create a copy of the Example 3 - Combination case. To create a copy of the Example 3 - Combination case, right-click the tab and then click Duplicate on the shortcut menu.

If you did not follow the procedure in Example 3, you can start with the same case in the file Parametrics Examples.sam, which should be in the Solar Advisor folder (C:\SAM by default).

2. | Rename the new case to "Example 4 - Combination with Linkage." (Right-click the case's tab and click Rename on the shortcut menu.)

3. | On the Case menu, click Define Parametrics. The Define Parametric window should appear with the variables Azimuth and Tilt in the Combination Parametrics 1 box.

4. | Under Combination Parametrics, select Tilt and click Delete Variable.

5. | Under Combination Parametrics, click Add Variable and in the Add Variable window, click Location.

6. | Click OK to return to the Define Parametric window. Azimuth and Location appear in the Combination Parametrics 1 box.

7. | Under Linkages, click Add Variable.

8. | In the Add Variable Window, click Location and Tilt. (Scroll down to the Array section to find the Tilt variable).

9. | The Location and Tilt variable names should appear in the Linkage 1 box.

10. | Click Edit Linkage to open the Edit Linked Group window.

Notice that the Location variable values appear in the Edit Linked Group window in drop-down boxes because they are non-numeric values. Solar Advisor has assigned CO Boulder.tm2 to each of the Module Tilt values that we created in Example 3 because we have not yet assigned values to the Location variable.

11. | Assign the following values to the Location and Module Tilt variables: Boulder 40, Los Angeles 34, and Newark 41 and delete the remaining rows so that only three rows appear in the table. Set Boulder as the base value. Select location names from the drop-down lists, and use the Delete and Insert keys to delete and insert rows.

12. | Click OK to return to the Define Parametric window, and again to return to the main window.

Create a custom clustered bar graph to display the results:

1. | On the Results Summary page, click Add above the graph to open the Graph Info window.

2. | In the Graph Info window, type "Array Orientation vs Location" in the Name box, in Graph Type click Bar, in X Values click Location, in YValues click Annual Output, and in Parameter1 click Azimuth.

3. | Click OK to create the new graph.

Solar Advisor makes the calculations necessary to display the custom graph and then displays it on the main window.

The legend displays the Azimuth value for each bar color: the dark green bar is for -30 degrees, or 30 degrees east of south. The red bar is for 30 degrees west of south, and the light green bar is for zero degrees, or due south.

Tip. If the location labels do not appear on the graph, try resizing the main window to enlarge the graph. You can also clear the Legend check box below the graph to hide the legend and make more room for the graph.

The graph shows that the optimal array azimuth (in terms of total annual output) is different for each city. You can use the graph's advanced properties to change the y-axis scale to see the differences more clearly.

4. | Double-click the graph to display the chart editing window.

5. | In the navigation tree, under Axis, click Left Axis, and on the Scales tab, change the minimum value from 0 to 4000.

Tip. You can change other properties of the graph in the chart editing window. For example, to display the legend below the graph, in the navigation tree, click Legend and on the Position tab, click Bottom.

6. | Click OK to return to the chart editing window, and click Close to return to the Results Summary page.

7. | Save the file.

From the clustered bar graphs, you can tell which array azimuth provides the maximum annual output for each location. For Boulder, which is located just east of the Rocky Mountain foothills, where mountains and thunder clouds to the west often shade the city in the late afternoon, the optimal array orientation is away from the mountains: -10 degrees, or 10 degrees east of south, represented by the yellow bar. For Los Angeles, located on the Pacific coast and exposed to frequent morning fog, orienting the array to maximize exposure to the afternoon sun maximizes system output: the optimal orientation is 10 degrees west of south, represented by the orange bar. For Newark, the optimal array orientation is zero degrees, or due south, represented by the light green bar. The graphs also show that the difference in output for array orientations between ten degrees west of south and ten degrees east of south is relatively small.