Optimizing Array-to-Inverter Power Ratio

Developers and PV system designers are challenged to stay competitive in the constantly evolving solar marketplace. With the steep decline of solar module prices, designers are exploring the economic benefits of increasing the array-to-inverter power ratio. Here I discuss dc loading in general, then focus on array-to-inverter sizing design approaches. I describe some scenarios supporting the trend for higher dc load ratios and present some relevant production modeling results. I also discuss typical inverter operational limits related to dc loading.

DC Loading

The array-to-inverter power ratio is defined as the relationship between array capacity in dc watts and inverter capacity in ac watts. Array capacity is determined by the array nameplate power rating under standard test conditions (STC), meaning at 1,000 W/m2, 25°C cell temperature and a reference solar spectral irradiance of air mass 1.5. The total inverter maximum output power rating determines the inverter capacity. For example, if you connect a solar array with an STC rating of 575 kWdc to one or several inverters with a total maximum rated output power of 500 kWac, then the resulting array-to-inverter power ratio is 1.15, or 115% (575 kWdc ÷ 500 kWac). Other terms for array-to-inverter power ratio include dc load ratio, dc-to-ac ratio, oversizing ratio and overloading ratio.

Evolving Design Practices

System design approaches to dc loading have evolved over the past 5 years and are closely tied to module price trends. The traditional design approach to dc loading is conservative, as it was a direct response to high module prices. Newer design approaches use higher loading ratios, in large part because module prices are an increasingly smaller percentage of total project costs.

Traditional approach. When module prices were high, the system designer’s main goal was to define a dc load ratio that ensured none or very little of the power produced by the expensive PV array was wasted. Designers specifically wanted to avoid inverter power limiting, which occurs whenever the array is capable of producing more power than the inverter can process. They would typically determine a project’s optimal dc-to-ac sizing ratio by analyzing the annual energy production per kilowatt of PV energy at different loading ratios. This kWh/kW metric is known as specific yield and is a measure of production efficiency.

The traditional design approach generally results in dc load ratios within a 1.1–1.2 range, depending on the project location and design details. These conservative overloading ratios allow the designer to offset a variety of environmental and system-level loss factors—such as cell temperature, irradiance, tilt angle, soiling, module mismatch, array degradation, conductor resistance and so forth—without exceeding the inverter capacity under typical real-world conditions.

Higher dc loading approach. As module prices have fallen, PV system design philosophy has shifted. Rather than focusing on production efficiency and maximizing the output of each individual module, designers have begun designing for maximum financial efficiency at the system level. In many cases, the incremental cost to increase PV array capacity is small compared to the value of the associated energy production gains. This allows system designers to capitalize on higher dc load ratios—up to 1.5 and in some cases even higher—despite the potential for PV power generation to exceed inverter capacity during peak hours.

Rationale for High-DC Loading

Project developers and system designers might opt to increase dc loading beyond 1.2 for several reasons. Higher dc load ratios allow designers to get more value from fixed development costs. They also allow designers to capitalize on high-value energy rates, or time-of-delivery or time-of-day (TOD) rate structures that incentivize summer production. Increasing the dc load ratio is a compelling design approach when there is a limit on ac system size but no corresponding limit on dc system size. It also allows designers to increase production in response to suboptimal conditions such as cloudy climates or long-term array degradation.

Fixed development costs. When system designers increase the dc-to-ac load ratio beyond 1.2, the total system cost does not increase in direct proportion to the increase in array capacity since many of the project costs remain the same. These fixed costs include permitting, interconnection fees, legal fees, and inverter and ac interconnection hardware costs. Therefore, the cost to add array capacity is limited to the material and labor costs associated with adding more modules and dc balance of system components. By increasing the dc loading ratio, designers may be able to take full advantage of these fixed development and structural costs.

In their article “Designing for Value in Large-Scale PV Systems(SolarPro magazine, June/July 2013), Graham Evarts and Matt LeDucq explain how getting the most value for the development costs applies within the context of a ground-mounted PV power plant: “Developers have invested a lot of money in land, interconnection fees, lawyers and personnel to create the project opportunity. They have also built a substantial ac system infrastructure—one that includes inverters, transformers, switchgear and a substation—and they want to push as much energy as possible through that fixed investment over the life of the PPA [power purchase agreement], even if that means sacrificing production efficiency.”

High-value rate structures. System designers have more incentive to increase dc load ratios when the value for the produced energy is high, as is the case with Ontario’s feed-in tariff program, or when energy generated on summer afternoons is subject to preferential on-peak pricing, as is the case with some utilities serving the desert Southwest. Increasing dc load ratios allows designers to deliver more high-value electricity.

Evarts and LeDucq explain how TOD multipliers for on-peak energy can influence system design decisions: “To capitalize on energy values that are two to three times the baseline rate, designers oversize the dc-to-ac ratio so that inverters run at full power when energy is the most valuable. The general idea is that you are willing to give away (via clipping) 2 MWh of energy at $100/MWh to get 1 MWh of energy at $250/MWh, because this nets you $50.” Figure 1 illustrates how designers can use a high dc-to-ac load ratio in response to on-peak pricing to generate more high-value energy.

AC capacity limits. Since the NEC 2011 edition, Section 705.12(A) specifically limits the capacity of supply-side interconnected electric power production sources: “The sum of the ratings of all overcurrent devices connected to power production sources shall not exceed the rating of the service.” Furthermore, Section 690.8 requires that the overcurrent device rating for an inverter output circuit be no less than 125% of the inverter continuous output-current rating. Taken together, these requirements effectively limit the inverter capacity rating for a supply-side connection to no more than 80% of the service transformer kVA rating. For a site served by a 500 kVA transformer, the maximum interconnected inverter capacity is 400 kW.

In this scenario and others pertaining to load-side interconnections, the NEC places a hard limit on inverter capacity. However, manufacturer product specifications and available array area are the only hard limits to dc system capacity. Therefore, as long as system designers use the inverter according to the manufacturer’s installation instructions, they can increase the PV array capacity until the available array area is fully utilized or there is no economic justification for installing additional modules.

There are also scenarios where a designer might choose to limit the ac system capacity and use a high dc load ratio to avoid high capital costs associated with purchasing specialized equipment or upgrading a service. For example, the utility may have special requirements—such as redundant relaying or direct transfer trip—above a certain capacity threshold, or the existing electrical infrastructure or building service may limit the ac system size. A designer might also opt to limit inverter capacity in response to break points in a feed-in tariff program.

Suboptimal conditions. In the desert Southwest, PV modules are routinely exposed to irradiance values approaching and even exceeding 1,000 W/m2. These high-irradiance conditions are less common in other parts of North America. For example, in Ontario or New England the plane-of-array irradiance on a typical clear day might reach 800 W/m2. In locations like these, it makes sense for designers to increase the dc load ratio.

PV system designers can also use a high dc load ratio to offset the inevitable impacts of array degradation. As PV arrays age, module performance degrades. Ideally, this degradation is linear and the annual power loss does not exceed 0.5% annually. If designers want to ensure that a PV array’s power output fully loads an inverter under certain conditions in the summer of year 10 or year 20, then they must specify a higher dc-to-ac ratio than is required to accomplish this same loading in year 1.

Modeling Performance

The best way for system designers to optimize the array-to-inverter power ratio for a specific project is to use a PV system modeling program such as HelioScope, PVsyst, PV*SOL or System Advisor Model (SAM). By keeping the inverter capacity constant and varying the array capacity, designers can model the financial and production efficiencies resulting from different dc loading options. They can then select the optimal design based on typical meteorological year weather data and other project-specific variables. When choosing the PV system model, designers must select a simulation program that can model the effects of inverter power limiting and changes in inverter efficiency based on different voltage and power levels.

The basis of comparison when optimizing dc loading ratio is typically a financial metric like cost per kilowatt-hour, levelized cost of energy, net present value or internal rate of return. Several project-specific factors determine the optimal level of dc loading, including location, system design and inverter topology. The project’s cost structure and financial goals also drive design decisions. On average, designers and developers reach a point of diminishing economic returns at array-to-inverter ratios of about 1.5. Beyond that, they eventually reach a tipping point above which the incremental cost to increase array capacity outweighs financial gains from the additional energy production. This tipping point is unique for every project. To ensure that a project meets energy production and financial performance goals, it is important for designers to optimize dc-to-ac power ratios on a project-by-project basis.

For example, Figure 2 shows the modeled internal rate of return (IRR) at three different load ratios for a project in Ontario, where the available solar resource is modest but the value of PV-generated energy is relatively high. The model inputs assume that installed system costs are relatively low, as might be the case with aggressive module pricing, and that the system is deployed using high-efficiency transformerless string inverters. The results confirm that higher dc load ratios can increase a project’s IRR, even though initial installation costs are greater. Of course, the optimal dc load ratio is very different in Ontario than in New Mexico. Similarly, the dc load ratio sweet spot might be different for a project that uses central inverters rather than distributed string inverters.

Inverter Operational Limits

To deploy PV systems with high dc load ratios, designers and developers need to account for the effects of array oversizing and observe any operational limits that the inverter manufacturer imposes.

Common-sense limits. When the available dc power from a PV array exceeds the inverter maximum power rating, the control logic in the inverter responds by moving the PV array off its maximum power point. Limiting power in this manner ensures that excess power is not dissipated as waste heat in the inverter. In effect, the inverter components are not exposed to this excess power under normal operating conditions. However, an inverter with a high dc load ratio is still exposed to higher internal operating temperatures compared to an inverter with a low dc load ratio, simply because an overloaded inverter operates at its maximum rated power more often and for longer periods of time. Further, the inverter may operate less efficiently when limiting array power, with an increase in internal waste heat.

Designers can account for this effect by designing the system to promote optimal inverter cooling. Additionally, system owners and O&M providers should ensure that inverter cooling system components—like fans and filters—are maintained properly.

Hard design limits. Designers must use inverters in accordance with the manufacturer’s installation instructions. As part of UL 1741, the product safety standard for “Inverters, Converters, Controllers and Interconnection System Equipment for Use with Distributed Energy Resources,” inverters are subjected to a series of abnormal-condition tests. During the output-overload test, a technician applies twice the rated input current to the inverter, which must maintain its rated output power. While this test proves that a listed inverter can limit power under normal operating conditions, it is only one of several factors that determine the maximum equipment rating.

Another critical factor is the amount of short-circuit current that internal components such as busbars and disconnect switches can withstand during a fault on the dc side of the inverter. In the unlikely event that the inverter’s firmware fails to limit the input current from the PV array, the inverter components must be able to withstand the full short-circuit current of the dc source for the duration of the fault without breaking or compromising safety. For this reason, designers should follow inverter manufacturers’ recommendations for maximum allowable array-to-inverter ratios. Most importantly, designers must ensure that the available PV array short-circuit current never exceeds the manufacturer’s published maximum dc input short-circuit current value.

Verena Sheldon / AE Solar Energy / Sacramento, CA / solarenergy.advanced-energy.com

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