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A Closed Form Approach

RER Renewable Energy Research

Presentation

Link to SESCI (conference)

Ross, Michael M. D. "Optimal Wire Size for Photovoltaic Systems Operating at Maximum Power Point: A Closed Form Approach". *Proceedings of the 30th Annual Conference of the Solar Energy Society of Canada*, Burnaby, B.C., August 20 to 24, 2005.

While the purchase of cable represents an admittedly minor part of the cost of installing a photovoltaic system, it is a cost nonetheless, and one that should be examined with rigor by a maturing photovoltaic industry. Using larger cables between array and point of connection to the battery or grid-tied inverter reduces array power losses, but increases the costs of the cables. In the past, little attention has been paid to the optimization of the sizing of the cables; the effort of doing a simulation study did not appear to justify the potential gains.

This study shows that, in fact, a very simple relation can be used to determine the financially optimum cable size. This simple relation is derived from basic considerations of the costs associated with wiring losses and the wiring itself. The challenge is to determine average level of losses, since these will depend on the varying level of sunshine over the course of a year. This study uses a simple exponential expression for the frequency distribution of array power output; this distribution is characterized by three parameters: the number of daylight hours in the year, the annual output of the array, and the maximum power output of the array. This simple distribution has the advantage of giving rise to an integrable expression for the frequency distribution of power losses in the cables. The result can be incorporated into an expression for the total cost of the cables (costs associated with purchase and losses), which can then be minimized, yielding a simple expression for the optimum cable size.

This closed form solution demonstrates that the length of the cable run is irrelevant to the optimal cable size. This somewhat counterintuitive result is explained in the development of the closed form solution itself.

The predictions of this closed form solution are compared to simulations to establish its validity. The application of the close-form relation to the problem of cable selection is then illustrated with an example. The method is also used to comment on the Canadian Electrical Code stipulations for wiring.

Created 2005/07/18 Updated 2005/10/04 ©2005 RER Renewable Energy Research