# Design Optimization in Constrained Applications: Page 2 of 4

## Understanding the Major Constraints

A number of common constraints apply when designing solar arrays, including physical area, budget, energy demand and power injection back to the grid.

Area. An area constraint is most common in commercial arrays, as those systems often have ample energy demand and a sufficient financial budget relative to their roof space. This constraint can also come up in residential arrays, especially if you restrict designs to south-facing roofs only, as well as in ground-mount designs.

The ultimate objective for this design constraint is to maximize energy yield per unit of area, which generally results in an economically optimal array. Specifically, this means maximizing the module fill within the available area, meaning that you want to maximize power density (kWp per unit of area) rather than specific yield (kWh per kWp). Since power density typically increases faster than specific yield decreases, maximizing this value tends to maximize energy density (kWh per unit of area). In a world of relatively inexpensive hardware, this approach produces a clear economic win.

The variables that move the needle on power density are the tilt and spacing of the modules. Specifically, optimizing area-constrained applications tends to result in systems with lower tilt angles and tighter spacing between modules, especially with low-cost modules. This is why the industry has seen a huge push toward commercial mounting systems with 5° tilt angles or dual-tilt orientations.

Budget. A budget constraint can happen in systems of all sizes. Assuming the project is a cash deal where the off-taker is the purchaser, available cash can be a determining factor in the size and design of an array. This constraint also applies if an incentive is capped in total dollars or based on system capacity. For example, a local jurisdiction might offer a dollar-per-watt incentive up to a certain system size. For optimization purposes, this acts as a budget constraint because the marginal economics of a system larger than what is incentivized become much less appealing.

Financing options such as power purchase agreements and loans are popular across the industry because they mitigate budget constraints. As long as the economic returns are adequate, many customers are able to access up-front financing. Property assessed clean energy (PACE) financing is a possible exception, as PACE funds are often capped at 20% of the property value in commercial applications, which sometimes acts as a budgetary constraint for large commercial rooftops.

With a constrained cost, the financial return (revenue minus costs) for a system tracks closely with the total revenue. The costs are tied to the system's dc nameplate value because the module costs, racking costs, electrical costs and installation labor are all directly related to the dc capacity rating. As a result, the objective that tends to matter most is maximizing the array’s specific yield: the revenue is tied to the energy (kWh) generated, while the costs, and therefore the capacity (kWp), are fixed.

The design goals are similar in a capacity-constrained market. If a developer can only obtain a certain quantity of modules per quarter, that developer will want to deploy them in a way that derives as much financial value as possible. This optimization exercise would mimic that for a budget-constrained application.

Energy demand. This constraint is most common in residential arrays, where the homeowner uses only so much energy. It becomes particularly acute with net metering, since the designer must not only design to an annual energy budget, but also align the energy production by month or even hour of the day. This type of optimization exercise is all about system capacity. When there is only so much demand for energy, the size of the array is critical, especially since overproduction can waste energy.

Two metrics matter here: energy usage and specific yield. First, the engineer must understand the usage demands, typically based on the off-taker’s energy bills. This can be complex based on when the customer’s bills are trued up, whether it is monthly, annually or every 15 minutes (for demand charges). Next, the designer focuses on delivering that energy most efficiently by maximizing specific yield. In residential applications, designers tend to have fewer tools at their disposal, as the roof area is often relatively constrained and the roof itself determines the tilt angle.

In residential applications with energy-demand constraints, designers generally base their decisions on which roof surfaces to use and how close to get to shading obstructions. In commercial or ground-mount applications, optimizing a system with energy-demand constraints often leads to wider row spacing and a higher tilt angle, as these options improve system yield and profitability.

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