Simulating NEC Voltage and Current Values: Page 3 of 3

Model inputs. To input project data, I started a new detailed PV project without the optional financial model. The inputs to the model are organized by input page and include location and resource, module, inverter, system design, shading and snow, and losses. 

Location and resource: I specified the weather data by selecting the TMY3 dataset for RDU. In most cases, you will choose a location at or near your site from the solar resource library. If you have a custom weather file, you can upload these data via this input page.

Module: I selected “CEC performance model with user-entered specification” from the menu. This selection allows users to manually enter specific PV module data. The CEC performance model is an extension of the original De Soto five-parameter model, which uses a database of module parameters that the CEC maintains. As such, the CEC performance model meets the Code requirement for an industry-standard calculation method. I entered the module specification from the manufacturer’s datasheet. To simulate the ground-mounted array, I selected “ground or rack mounted” and “one story building height or lower.”

Inverter: I selected “inverter datasheet” from the menu. This allows users to manually enter inverter-specific data. While inverter data are not as important to the results as module data, I recommend using a model that is as accurate as possible. I entered inverter specifications from the manufacturer’s datasheet, and I left the inverter losses at the default settings.

System design: I specified an array design with 19 modules per string, 20 strings and four inverters. I modeled the system as a single dc array (subarray 1) with a fixed tilt of 25° and a 180° azimuth. I left the ground-coverage ratio at the default value.

Shading and snow: Since the intent of this exercise is to model the worst-case (maximum) voltage and current, the results should not take any shading or snow effects into account, so I turned all shading and snow input off. With self-shading turned off, factors such as row pitch and ground-coverage ratio are irrelevant to the results.

Losses: The same logic applies to system losses. I set all the loss values to 0%. Ignoring electrical losses and soiling losses ensures that the calculations will return the worst-case design values.

Having set all of the inputs, I saved the project settings, ran the simulation and collected the following data for each hour of the model year: weather file ambient temperature (°C), subarray 1 cell temperature (°C), subarray 1 POA total irradiance nominal (W/m2) and subarray 1 open-circuit voltage (V). In Figure 1, these are the values in the third row of the flowchart (boxed in green) derived by entering project specifications into a no-loss system design model. Additional data processing is required to arrive at the maximum voltage and current values.

Maximum voltage calculation. To calculate the maximum open-circuit voltage for each hour of operation, I used Equation 1 (see “Post-Processing Equations”), where Voc0 is the calculated open-circuit voltage at that hour, Vocm0 is the open-circuit voltage from the model for that hour, βVoc is the PV module temperature coefficient of Voc (in this case, 0.32%/C), Tamb0 is the weather file ambient temperature for that hour, and Tc0 is the PV module cell temperature from the model for that hour.

Equation 1 corrects modeled Voc values, which are based on module cell temperature, to a Voc based on ambient temperature, the worst-case condition for that hour. After processing the modeled Voc values, I sorted the data to identify the maximum open-circuit voltage for any hour of the year. In this case, the calculated maximum PV system voltage based on simulation program results is 967.5 V. By comparison, the maximum voltage based on the voltage correction factors in Table 690.7(A) is 981.9 V, assuming an extreme minimum temperature of -10.3 °C.

Maximum current calculation. To calculate the maximum short-circuit current for each hour of operation, I used Equation 2 (see “Post-Processing Equations”), where Isc0 is the calculated short-circuit current for that hour, Isc is the PV module nameplate short-circuit current at STC (in this case, 9.29 A), Ee0 is the POA total irradiance nominal from the model for that hour, ESTC is the STC irradiance (1,000 W/m2), αIsc is the PV module temperature coefficient of Isc (in this case, 0.05%/C), Tc0 is the PV module cell temperature from the model for that hour and TSTC is the STC cell temperature (25°C).

Equation 2 calculates the short-circuit value for a given hour based on the POA total irradiance and module cell temperature, which is the worst-case condition for that time. I then calculated 3-hour average short-circuit current values and found the maximum of those 3-hour averages. In this example, the maximum 3-hour current average is 9.95 A. By comparison, the traditional Isc value according to 690.8(A)(1)(1) is 11.61 A (9.29 A × 125%). It is important to remember that the 690.8(A)(1)(2) current value may not be less than 70% of the value calculated in 690.8(A)(1)(1). In this example, 9.95 A fulfills that criterion as it is greater than 8.12 A (11.61 A × 70%).

Validation. I used three basic techniques to validate the output of these maximum voltage and current calculations. First, I verified at each step that the results were reasonable. Second, I changed variables in both the performance model and the post-processing spreadsheet to verify that the outputs changed as expected. This is how I discovered that a no-loss system design model produces the worst-case maximum voltage and current values. Lastly, I used graphical techniques, such as the plots in Figure 2, to verify that the outputs were statistically significant.

Potential Benefits

The engineering analysis in the previous example lowered both the maximum voltage and current values compared to traditional methods. Does this provide any real benefit to the client or project developer? Do the potential benefits outweigh the additional engineering costs? Perhaps not in this simple string inverter–based example, but consider the implications in large-scale PV power systems deployed using central inverters.

In the case study, the new current calculation method reduced the maximum PV source-circuit current from 11.61 A to 9.95 A, which is a 14.3% reduction or a percentage difference or improvement of 15.4%. In a central inverter–based system, this lower current value could result in a design that requires fewer combiner boxes. In some scenarios, these reduced string-current values could produce cost savings for parallel circuit array harnesses and custom homerun harnesses. As systems scale, these balance of system cost savings add up and offset additional engineering costs.

There may be instances where the ability to add a module to a PV source circuit results in a design that improves overall system economics. However, from a financial performance perspective, improvements in source-circuit current values are likely a more interesting avenue of exploration and optimization. The maximum current comparison sidebar above illustrates how these improvements will vary predictably based on project location, weather data source and mounting details. These data will help project stakeholders identify opportunities for design optimization based on PV source-circuit current improvements.

Charles Ladd, PE / Ecoplexus / Durham, NC / ecoplexus.com

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