Optimal DC Cable Selection in PV Designs
Inside this Article
PV designers spend a good deal of time assessing the optimal size of dc conductors, such as those that run from combiner boxes in a large array field to the location of the inverter. If these conductors are specified too small, power losses erode a meaningful percentage of the potential solar energy harvest. If the conductors are specified too large, the cost of the conductors themselves becomes a meaningful proportion of overall system costs, driving up the levelized cost of energy. Neither situation is acceptable, yet there has been little quantitative analysis to determine optimal cable size.
In our engineering business designing large solar power plants, we frequently wrestle with this problem. We have modeled and analyzed it with the goal of optimizing the size, and therefore the cost, of these conductors for our customers. This article presents some of the surprising conclusions we have found through this analysis, which will help solar contractors determine optimal conductor sizing in terms of cost and transmission losses between the array and inverters.
Solar inverters are designed to operate within a wide range of dc input voltages to accommodate varying solar radiation levels. Determining voltage losses in the cables that deliver the solar power to inverters has traditionally been done via rules of thumb. For example, it is common practice in the electrical design industry to allow no more than a 5% voltage drop in cables. Such a limit is justified when designing commercial electrical systems for traditional industrial loads, such as motors, computer centers and lighting, which could be affected by voltages lower than nominal. Solar inverters, however, can operate flawlessly at lower dc input voltages—so long as they are within the operating voltage input window of the inverter. Therefore, if there were no other considerations, solar systems could be designed with greater voltage drops than 5% on the dc cables.
However, for economic reasons stemming from previously high module costs and high projected energy rates, designers have historically strived to minimize power losses on the dc conductors as much as possible by increasing the conductor size and cross-sectional area and, hence, the conductor cost. Many designers minimize losses on these conductors by designing for as little as 1.5% voltage drop as a standard for losses.
In this article, we suggest a method for optimally selecting the size of solar dc conductors considering only the solar irradiation at the site, cable cost, utility tariff rates and financial factors. If math is not your passion, we present our key findings here in the text and tell you where to skip ahead when we get to the equations.
Cable Cost Model
The cost model for installed dc conductors in a solar field consists of three separate elements:
- D = costs that are proportional to the conductor crosssectional area, such as the capital cost of the cable itself and the labor required to install it.
- E = costs that are inversely proportional to the conductor cross-sectional area, such as energy losses due to resistance.
- F = constant costs that are relatively unrelated to conductor cross-sectional area, such as the cost of trenching and conduits.
To simplify the model, we have assumed that a small variation in fixed costs, such as a slightly wider trench or a slightly larger conduit to accommodate larger conductors with respect to a reference conductor size, has a negligible impact on overall costs compared to the cost of the conductors themselves. In other words, conduit and trenching costs do not change much, even if the required conductors increase or decrease a wire size or two.
In addition, as a model simplification, we assume that conductor cost is roughly proportional to the conductor’s cross-sectional area since conductor material (copper or aluminum) is the dominant cost factor. This approximation is adequate if we assume that the optimal wire size is within a size or two of a wire size at a reference cross-sectional area for ampacity.
The lower limit for required dc conductor size is derived from ampacity considerations. This is the minimum acceptable conductor size when applying ampacity calculations required by the National Electrical Code. We use this as our lower limit since in the design of large solar arrays, the conductor size derived based on required NEC ampacity considerations alone usually results in excessive voltage drops due to resistance, and the conductors must be upsized.