Optimal DC Cable Selection in PV Designs: Page 5 of 7
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where Tc was calculated as above, as the tariff at which S = SA . Rearranging Equation 13 to solve for S, the optimal conductor cross-sectional area, we get:
Equation 14 demonstrates our interesting result number three: An optimally sized conductor for a particular run in a solar power plant depends only on the local utility’s tariff paid for delivered solar energy as a function of the critical tariff rate at which S = SA. In other words, the cross-sectional area S of the optimally sized conductor to be used is expressed as a function of only SA, the conductor size required for ampacity; the local utility tariff T; and the critical utility tariff to Tc , which we can calculate.
It is also clear from Equation 14 that a special case is when T > Tc , as this corresponds to situations in which the optimally sized conductor S > SA , the conductor size for ampacity. In the case when T < Tc , S cannot be less than SA since the minimum acceptable conductor size must be SA, as determined by ampacity requirements.
Bringing It All Together
Although the derivation was complex, the result is simple: Using a few well-known or easily determined parameters, you can follow a simple procedure to find the critical tariff Tc and from that derive the optimal conductor size. To calculate Tc , you need the following inputs:
- Minimum conductor size SAas derived from ampacity calculations,
- Unit cost U for the cable selected and the labor cost W associated with its installation,
- Solar insolation at the particular site, to determine K factor,
- Solar module selected, to determine Imp,
- Conductor material (copper or aluminum), to determine Ρ, and
- Expected inflation and discount rates for the next 25 years, to determine γ25.
Once you have calculated Tc and SA, you need to know only the local utility’s tariff, T, paid for delivered solar energy to calculate the optimal cross-sectional conductor size, S, using Equation 14. The metric result of that calculation should then be converted to a conductor size in kcmil for US installations.
A real-world example can make all of this tangible. First, we calculate the critical utility tariff, which allows us to determine the optimal conductor size, and then we examine the relevance of voltage drop.
McCalmont Engineering designed a large ground-mounted solar field for a customer near San Jose, California. The nearest location for TMY3 insolation data was the San Jose International Airport.
The modules are configured in 12-module strings with 12 source circuits per combiner box. Combiner box to inverter conductor runs are located underground in PVC conduit and subject to an ambient temperature less than 30°C. In addition, each homerun to the inverter was independent (meaning each conduit contained only two conductors plus ground, which avoided additional conductor ampacity derating). The modules have an Impof 8.23 A, and hence the Imp of the PV output circuit is 98.76 A. Module Isc is 8.91 A and the Isc of the PV output circuit is 106.92 A. Working voltages are a module Vmp of 29.8 V and a string Vmp of 357.6 V.
THE CRITICAL UTILITY TARIFF
First, we solve for Tc . The procedure below guides us through the steps:
1. Calculate required cable ampacity: The minimum required ampacity of the cable (the circuit Isc and a 1.56 multiplier per the NEC) is: