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David leads the modeling and computational efforts that underlie Aurora’s PV performance simulation engine. He received his B.S., M.S., and Ph.D. degrees, all from Carnegie Mellon University.

## David Bromberg

David leads the modeling and computational efforts that underlie Aurora’s PV performance simulation engine. He received his B.S., M.S., and Ph.D. degrees, all from Carnegie Mellon University.

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When modeling how much energy a solar design will produce, there are many features of the components that must be taken into account to ensure an accurate estimate. One important factor that modeling software must account for in order to avoid over- or under-estimating the system’s energy production is whether or not the inverter(s) used are capable of “global maximum power point tracking.” In this post, we will examine what global maximum power point tracking means—and why accounting for it is so important.

#### Understanding Current-Voltage and Power-Voltage Curves

The datasheet of a solar panel includes a variety of data that allow one to understand the basic parameters of the device and to mathematically model its behavior within an electrical circuit. Typically, this will include graphs that illustrate the panel’s “current-voltage curve”—also known as an IV curve, for the standard abbreviations for current (I) and voltage (V) in mathematical equations—and “power-voltage curve.”

Looking at the power-voltage curve allows us to see the point (or points) at which the panel’s power output is maximized.

These graphs illustrate relationships between three electrical characteristics: current, voltage, and power. Power—which we intuitively understand as the energy produced by the panels—is defined as the rate, per unit time, at which electrical energy is transferred by an electric circuit. Current (I) is the rate at which charge is flowing through the circuit, while voltage (V) is the difference in electric potential energy between two points (e.g., the output wires of a solar panel) per unit electrical charge.

A common example used to explain these principles is to think of electricity like water in a tank; the pressure in the tank is analogous to the voltage, while current would be the flow of water out of the tank (Figure 1). The IV curve shows how the panel output current varies with panel output voltage. The power-voltage curve shows how panel output power (the product of the output current and output voltage) varies with panel output voltage.

Figure 1: The concepts of voltage and current as illustrated by the example of water in a tank.

Looking at the power-voltage curve allows us to determine the point (or points) at which the panel’s power output is maximized. On the IV curve, two values that are often indicated are “Vmp” and “Imp” — which indicate the levels of voltage and current at which the solar panel’s output power is maximized under standard test conditions (STC). Nothing about the panel itself dictates it must operate at maximum power, however; any point along the IV curve is a valid operating point. In designs using string inverters, it is the inverters that “choose” the operating point. The ability of the inverters to locate the operating point of a solar array at which output power is maximized is referred to as maximum power point tracking (MPPT).

If the solar array comprises identical solar panels operating under the same irradiance and at the same temperature—such that each constituent module has the same IV curve and maximum power point—the net IV curve of the entire array (which takes into account the IV curves of each individual module) will have a shape like the blue curve in the left half of Figure 2 below. The green curve shows the output power of the array as a function of output voltage; note that there is a single peak in power, occurring at the “knee” of the IV curve. The inverter will seek out this one point at which array power is maximized.

#### Accounting for Shade: The Role of Bypass Diodes

When parts of the array are shaded, however, the IV curve is much more complicated. The IV curves of the shaded modules are different than those of the unshaded modules, especially in regard to how much current the shaded modules can output. When the amount of irradiance on a module is low, the power of the entire string connected to the module can drop. This is due to the fact that the current through the string can only be as high as the current through the most shaded module.

Because bypass diodes allow the inverter to “skip over” shaded panels instead of operating at their lower current, the IV curve of an array that is partially shaded will look different than that of an unshaded array.

To help mitigate these effects, manufacturers integrate bypass diodes into their modules. A bypass diode can be thought of as an on/off switch, which conducts any amount of current when it is “on” and, conversely, cannot conduct current when it is “off.” When the diode is turned on, it effectively shorts out the shaded module by routing the string current through the diode (and around the module) rather than through the shaded solar cells.

Because bypass diodes allow the inverter to “skip over” shaded panels instead of operating at their lower current, the IV curve of an array that is partially shaded will look different than that of an unshaded array. The resulting IV curve may look like the blue curve on the right in Figure 2, with a corresponding power-voltage curve shown in green. As you can see, there are two distinct operating points at which power is “maximized” - a global maximum where the array operates at a higher current and lower voltage, and a local maximum where the array operates at a lower current and higher voltage. The global maximum occurs when the shaded modules are bypassed, and the local maximum occurs when the shaded modules are not bypassed.

Figure 2: (left) Current-voltage (blue) and power-voltage (green) curve of a solar array with no shading; (right) current-voltage (blue) and power-voltage (green) curve of a solar array with shading, where the activation of bypass diodes results in multiple possible maximum power points.

Global MPPT refers to the ability of an inverter to sweep the IV curve of the solar array (within the operating voltage limits of the inverter) and find the array voltage at which the global maximum power point occurs. How often the inverter sweeps the curve, and the resolution at which it does so, is generally manufacturer- and model-specific.

Importantly, not all inverters perform global MPPT. Some inverters are limited to only search for the maximum power point in a local region where it “usually” lies, a high voltage solution where no modules are bypassed. This can be beneficial for sites where there is no shading, because whenever the inverter is sweeping the IV curve searching for the maximum power point it is not actually operating at the maximum power point, and thus not producing as much energy as it could. If the maximum power point is not going to vary much because there is no shade and no reason to activate bypass diodes, then there is no reason to sweep the entire IV curve. Most modern residential inverters are capable of global maximum power point tracking because shading due to trees and obstructions is common and expected. Large commercial inverters and central inverters, however, may not have this functionality because it is generally assumed there will not be much shading.

Importantly, not all inverters perform global maximum power point tracking. Some inverters are limited to only search for the maximum power point in a local region where it “usually” lies, a high voltage solution where no modules are bypassed.

#### Modeling Global Maximum Power Point Tracking

If your design includes a string inverter with global MPPT functionality, it is critical that the simulation tool you use to model the system accurately represents that behavior. Consider the residential design in Figure 3, which includes two parallel strings connected to an input of an inverter and a third string connected to another input. The irradiance map (left) and 3D model (right) clearly show the effects of shade on this site. Of particular concern are the chimney on the southeast-facing roof plane and the large tree to the west of the house, both of which cast shade on several panels in the design at various times throughout the year. If we simulate this design without global MPPT, the annual production is 5.94 MWh. However, if the inverter actually does perform global MPPT, and we simulate it accordingly, the production estimate increases to 6.25 MWh (Table 1).

Figure 3: 2D view and irradiance map (left) and 3D view (right) of a residential design with shading from a chimney and tree, produced by Aurora Solar's software.

Annual Production Without Global MPPT Annual Production With Global MPPT Percent Difference
5.94 MWh 6.25 MWh 5.09%
Table 1: Annual energy production for a residential design with and without global maximum power point tracking.

Given the results shown in Table 1, it is clear that knowing when to model global MPPT is just as important as being able to model it at all. Assuming every inverter has this functionality is dangerous, because it could lead to severely underperforming systems post-install. Assuming no inverter has this functionality can be a costly mistake as well, because it may lead the designer to install a larger system size than necessary.

This is why Aurora has contacted leading inverter manufacturers to confirm exactly which inverter models perform global MPPT. If a design includes an inverter with this functionality, Aurora will automatically model it. Aurora will even model global MPPT and bypass diodes down to the cell string-level, including the power losses in the diodes themselves. If Aurora has not confirmed the inverter has global MPPT, or that the inverter only performs local tracking, this behavior will not be modeled. The performance simulation logs will indicate whether or not the simulation applied global MPPT. In this way, designers can be sure they are getting simulation results that are as accurate as possible given what is known about the equipment in their designs.

Takeaways

• Global MPPT allows an inverter to sweep the IV curve of a solar array to find the point at which output power is maximized, even under partial shading.
• We found a difference of over 5% in annual production when simulating a design with an inverter that has global MPPT versus one without it.
• Aurora has worked with leading inverter manufacturers to confirm which models apply global MPPT and automatically simulates this behavior for those inverters.

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Cover photo credit: NREL/DOE

As you likely know, solar cells produce direct current (DC) electricity, which is then converted to alternating current (AC) electricity by an inverter. Converting energy from DC to AC allows you to deliver it to the grid or use it to power buildings, both of which operate with AC electricity. When designing a solar installation, and selecting the inverter, we must consider how much DC power will be produced by the solar array and how much AC power the inverter is able to output (its power rating).

In this article, we’ll discuss some important considerations for solar projects to ensure that the inverters in your designs are appropriately sized. Specifically, we’ll examine the relationship between the amount of energy your solar array produces and the amount of power your inverter can output, and we’ll introduce the concept of inverter clipping.

## Understanding the DC-to-AC Ratio

The DC-to-AC ratio is defined as the ratio of installed DC capacity to the AC power rating of the inverter. It often makes sense to oversize a solar array, such that the DC-to-AC ratio is greater than 1. This allows for a greater energy harvest when production is below the inverter’s rating, which it typically is for most of the day.

Consider the graph of energy production as a function of time of day in Figure 1. The purple line shows a typical bell curve of AC output power peaking at noon, just below the rating of the inverter indicated by the dashed line. If we increase the size of the solar array by adding more panels, thereby increasing the DC-to-AC ratio of the system (as illustrated by the green curve), we can harvest more energy throughout the day. The area between the green and purple curves is the energy that is gained by increasing the DC-to-AC ratio.

Figure 1: Inverter AC output over the course of a day for a system with a low DC-to-AC ratio (purple curve) and high DC-to-AC ratio (green curve). The chart represents an idealized case; in practice, power output varies considerably based on weather conditions.

## Inverter Clipping

While oversizing the solar array relative to the inverter’s rating can help your system capture more energy throughout the day, this approach is not without costs. What Figure 1 also shows is an effect called inverter clipping, sometimes referred to as power limiting. When the DC maximum power point (MPP) of the solar array—or the point at which the solar array is generating the most amount of energy—is greater than the inverter’s power rating, the “extra” power generated by the array is “clipped” by the inverter to ensure it is operating within its capabilities. This leads to a flatline in the green curve, and thus lost energy production, during peak production hours. The inverter effectively prevents the system from reaching its MPP, capping the power at the inverter’s nameplate power rating.

It is crucial to model inverter clipping in order to properly design a system with a DC-to-AC ratio greater than 1, as well as in regions that frequently see an irradiance larger than the standard test conditions (STC) irradiance of 1000 W/m2 (because higher levels of irradiance lead to higher power output). Consider a south-facing, 20°-tilt ground mount system in North Carolina (35.37° latitude) with a 100 kW central inverter. If we design the system with a DC-to-AC ratio of 1, it will never clip; however, we will also not fully utilize the AC capacity of the inverter.

If we want a larger system size, we could place another 100 kW block (a section of solar panels connected to an inverter), or we can pack more DC power generation onto our first inverter. The latter allows us to save cost by not purchasing another inverter and, like we saw in Figure 1, we can still harvest more energy during off-peak hours. If we choose a high DC-to-AC ratio, we will also sacrifice some amount of energy to inverter clipping. The inherent design trade-off is between the cost of purchasing and installing a new inverter and the value of the energy lost due to inverter clipping.

Table 1 summarizes energy production results for three DC-to-AC ratios, as well as how much energy is clipped, for the aforementioned ground mount system. If a simulation tool does not properly model clipping, the designer may be led to believe that, for example, the 100 kW inverter can fully handle the DC-to-AC ratio of 1.5 and output 228.24 MWh, whereas in reality 11.0 MWh would be lost to clipping. This could lead to a system that underperforms relative to the expected result.

Knowing how much energy is clipped allows a designer to understand how effective the oversizing scheme is at increasing energy harvest and determine what system configuration is the most cost-effective, in order to make an informed decision about how much DC power to connect to the inverter.

DC-to-AC Ratio Annual AC Energy Production Energy Lost to Clipping
1.0 163.06 MWh 0.0 MWh
1.3 193.86 MWh 1.8 MWh (0.9%)
1.5 217.24 MWh 11.0 MWh (4.8%)

Table 1: Annual energy production out of a 100 kW inverter as a function of DC-to-AC ratio. As the DC-to-AC ratio increases, so does the AC output and clipped energy.

Aurora’s solar design and sales software automatically takes inverter clipping into account in its performance simulations. The amount of energy that is clipped throughout the year, and the percentage of total energy that amount represents, is presented to the user as a simulation warning and in our system loss diagram. Combined with Aurora’s NEC validation report, which ensures designs do not violate any electrical or mechanical constraints or rules of the National Electric Code (NEC), this feature allows users to be confident that the systems they design are appropriately-sized and code-compliant.

## Key Takeaways

• Oversizing a solar array relative to an inverter’s rating (DC-to-AC ratio greater than one) allows for increased energy harvest throughout most of the day, especially in the morning and late afternoon.
• When a DC array produces more energy than the inverter is rated to handle, the inverter clips the excess power and caps its output at its rated power (an effect known as inverter clipping).
• An alternate approach to increase energy production while avoiding inverter clipping would be to include another inverter. When deciding what approach to take, designers must consider the trade-off between the cost of purchasing and installing an additional inverter compared to the value of the energy that will be lost due to inverter clipping if they oversize the solar array.
• When estimating the energy production of a solar project design, it’s important that your performance simulations take inverter clipping into account (as Aurora does automatically), in order to ensure production results accurately reflect the system size of the design.

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Topics: solar design, solar engineering

Module datasheets often include current-voltage and power-voltage curves that show how the output power of the module decreases with decreasing irradiance. An example is shown in Figure 1, where we can see the peak of the power-voltage curves (thin lines) drop as the irradiance on the modules goes down from 1000 W/m2 to 600 W/m2. When the irradiance on the module is very low — as is the case when the module is fully-shaded — its power output is generally negligible. If this module is part of a string of panels connected to an inverter, it can cause the power of the entire string to drop. This is because the current through the string can only be as high as the current through the most shaded module, and as we can see from Figure 1, the current of a module (thick lines) decreases under shading.

Figure 1: Current-voltage (thick lines) and power-voltage (thin lines) curves for a solar panel with varying irradiance. Image source: Savana Solar

This is the reason why manufacturers integrate bypass diodes into their modules. As an example, consider the case where nine out of ten modules are capable of outputting 8 A of current at a voltage of 32.5 V, but one of the ten modules is shaded and can only produce 1 A at about the same voltage. If the weak module is not bypassed, then the total output power is roughly 10 ⨉ 32.5 V ⨉ 1 A = 325 W, because the entire string is forced to operate at the lowest current (note that this assumes the unshaded modules still operate at 32.5 V; in reality it will operate closer to its open circuit voltage). If, however, we can bypass the shaded module, then the total output power becomes 9 ⨉ 32.5 V ⨉ 8 A = 2,340 W, excluding the small power loss due to the diode voltage drop.

But what happens if only part of the module is shaded? Does the whole module have to be bypassed, or can we use the unshaded sections to generate energy? It turns out you can, and this is why manufacturers integrate more than one diode into a module, effectively dividing the module up into smaller sections, called cell strings, each with a parallel bypass diode. When there is shade on only one of these cell strings, it can be bypassed while the rest of the module operates at maximum power. For a module with three cell strings (and three bypass diodes), that means we only lose about ⅓ of the module’s power instead of the entire module’s power when only one cell string of the module receives shade.

This is why it is important to analyze where there is shade on a module down to the cell string-level. Modeling solar designs to this level of granularity can have an appreciable impact on energy production results, and therefore expected financial returns.

#### How Submodule Simulation Affects Projected Returns on Commercial Projects

Consider the commercial rooftop in Figure 2, located in California (latitude 37.47°). We will design systems with varying row spacing, at 20° tilt to see how much DC power can fit in the limited area of the roof. The total system size for different row spacings are shown in Table 1, as are the module-level and submodule-level simulation results. As the row spacing is reduced, we can fit more modules on the roof, leading to higher energy production; however, as the rows get closer they begin to cast shade on each other (Figure 3). This means that while the overall energy production is increasing, the system efficiency, or energy yield (kWh/kWp), is reducing.

When simulating system performance at the module-level, Aurora bypasses a module if any point on the module is shaded. However, this does not necessarily reflect what would happen in the real world, where if only one cell string in a module is shaded — such as those along the bottom of a row of modules when in the shadow of the next row — only that cell string needs to be bypassed. Modeling at the submodule-level becomes increasingly important as the row spacing is reduced because it captures this behavior exactly.

The lack of granularity in the module-level simulation leads to an overly pessimistic NPV.

As the results in Table 1 show, the differences can be on the order of a few percent. This may not seem significant, but for a commercial solar project a small change in energy production can translate to a significant dollar value. The net present value (NPV) of each system, given the energy production results of module-level and submodule-level simulation, is shown in Table 2. The 2% difference in the performance estimate for the design with 1.5 foot row spacing leads to a 5.4% change in the NPV of the system, assuming a cost of $4/watt, a utility rate escalation of 3%, NEM (TOU) rates, an energy offset of ~80%, and a project life of 25 years. Also worth noting is that the NPV of the project increases as we reduce the row spacing, until we run a module-level simulation with the tightest spacing. The lack of granularity in the module-level simulation leads to an overly pessimistic NPV. This is not observed for the submodule-level simulation, where the energy production results for the tightest row spacing are more realistic. Modeling at the submodule-level becomes increasingly important as the row spacing is reduced because it captures this behavior exactly. As the results in Table 1 show, the differences can be on the order of a few percent. Figure 2: Small commercial site with an example system design and irradiance map showing shade from obstructions and parapet walls. Table 1: System size and annual energy production results at the module-level (ML) and submodule-level (SL) for designs with decreasing row spacing. Row Sp. [ft] DC Size [kW] ML Prod. [MWh] ML Yield [kWh/kWp] SL Prod. [MWh] SL Yield [kWh/kWp] Diff. [%] 3 65.52 103.21 1575 104.26 1591 1.01 2.5 70.20 110.30 1571 111.51 1588 1.09 2 79.56 123.43 1551 125.20 1574 1.42 1.5 84.24 127.08 1509 129.75 1540 2.08 Figure 3: Aerial views of designs featuring 3 foot (top) and 1.5 foot (bottom) row spacing at noon in mid-December. Adjacent rows do not cast shade on each other in the design with larger row spacing, while there is significant inter-row shading in the design with narrower row spacing. Table 2: Row spacing and net present value (NPV) at the module-level (ML) and submodule-level (SL) for designs with decreasing row spacing. Row Sp. [ft] NPV, ML Simulation [$] NPV, SL Simulation [\$] Diff. [%]
3 62,689 64,092 2.21
2.5 66,388 67,933 2.30
2 72,933 74,769 2.49
1.5 72,209 76,218 5.40

#### Impacts of Submodule Simulation on Residential Designs

Accurately simulating a system at the submodule-level is important for the residential installer as well. Consider the design in Figure 4, which includes eight 255 W modules in series connected to a 3 kW string inverter. A module-level simulation gives an annual yield of 2.35 MWh, while a submodule-level simulation gives a result of 2.41 MWh — a difference of roughly 2.5%.

A module-level simulation gives an annual yield of 2.35 MWh, while a submodule-level simulation gives a result of 2.41 MWh — a difference of roughly 2.5%.

Of course, this is not a complete design for a house of this size. But it does serve to illustrate the importance of modeling at the submodule-level, especially under shaded conditions.

Figure 4: Design that includes a string of modules, with some modules experiencing concentrated shade from a chimney.

If the submodule simulation option is selected, Aurora’s performance simulation runs at the cell string level. The simulation algorithm takes into account exactly where on the module the shade falls and how the inverter bypasses shaded cell strings to maximize array power. Aurora makes no assumptions regarding the placement of bypass diodes inside the modules: we have contacted leading module manufacturers and confirmed exactly how they have configured their cell strings and bypass diodes, so our users can be confident that the simulation results accurately represent the systems they design.

We have contacted leading module manufacturers and confirmed exactly how they have configured their cell strings and bypass diodes, so our users can be confident that the simulation results accurately represent the systems they design.

To enable submodule simulation in Aurora, follow these instructions.

Takeaways:

• Bypass diodes inside modules are used to “skip over” shaded cell strings without bringing down the power output of the entire module (and string).
• Modeling the design down to the cell string level is necessary to accurately simulate the effects of bypass diodes, especially for commercial designs with inter-row shading.
• Submodule-level simulation can show production results 2% or greater (and closer to reality) than module-level simulation results.
• To enable submodule-level simulation in Aurora follow these instructions.

Want to see submodule simulation in action? Watch our webinar with Greentech Media: Improving Solar Energy Production Estimates with Submodule Simulation.