Photovoltaic system in northern climes to 5.61 kWh/m²/day in the sunniest regions. For large systems, the energy gained by using tracking systems can outweigh the added complexity (trackers can increase efficiency by 30% or more). For very large systems, the added maintenance of tracking is a substantial detriment. Tracking is not required for flat panel and low-concentration photovoltaic systems. For high-concentration photovoltaic systems, dual axis tracking is a necessity. Pricing trends affect the balance between adding more stationary solar panels versus having fewer panels that track. When solar panel prices drop, trackers become a less attractive option. Systems designed to deliver alternating
Length of a module precisely the simple modules. For every finite-dimensional vector space (viewed as a module over the base field), the length and the dimension coincide. The length of the cyclic group Z/"n"Z (viewed as a module over the integers Z) is equal to the number of prime factors of "n", with multiple prime factors counted multiple times. A module "M" has finite length if and only if it is both Artinian and Noetherian. (cf. Hopkins' theorem) If "M" has finite length and "N" is a submodule of "M", then "N" has finite length as well, and we have length("N") ≤ length("M"). Furthermore,