Okay, Ken, you've got a complex problem with several layers of consideration. Let's break it down and offer some possible approaches

1. Extrapolating Annex B.2(2) to Aluminum:
The Challenge

Annex B's examples primarily use copper conductors. Aluminum has lower ampacity and different thermal characteristics.

Possible Approaches



Scaling Factor

The most common approach is to use a scaling factor based on the conductivity difference between copper and aluminum. For same-size aluminum vs. copper conductors, the aluminum ampacity is generally about 84% of the copper ampacity, due to its 61% IACS conductivity (compared to copper's 100%). Example: If Annex B.2(2) gives a copper ampacity of 375A for 500 kcmil, a reasonable starting point for aluminum would be 375A \ 0.84 = 315A.

However, this is a VERY rough approximation. Parallel Conductors

The 400KCMIL conductors from the utility should be rated ~335A each (Table 310.16). So the 12 in parallel are nominally rated 4020A total. But the termination lugs are rated 4000A, so it is probably the max.

Ampacity Tables and Adjustment Factors

Consult NEC Table 310.16 for the ampacity of 500 kcmil aluminum conductors in free air or direct buried, which will depend on the insulation type (e.g., THHN, XHHW-2). Then, apply the appropriate adjustment factors from NEC 310.15(B)(3) or 310.15(C)(1) for ambient temperature, number of conductors in a raceway, and soil thermal resistivity.

Software Simulation

Ampcalc (or similar software like ETAP, SKM Power Tools) is the most accurate way to model this. It considers the specific conductor types, spacing, soil characteristics, burial depth, etc. It provides a rigorous heat transfer analysis.

2. Load Factor (LF) and Inverter Current



Understanding Load Factor

Load factor represents the average load over a period compared to the peak load during that same period. For a typical commercial/industrial load, it might be a percentage of the maximum facility load based on billing history.

Solar-Specific Load Factor

With solar, the load factor is inherently tied to solar irradiance and inverter output.

Short-Term Peaks

While an inverter might hit its maximum for a short burst, the sustained output is what matters for thermal analysis.

Time Interval

The most appropriate time interval to calculate the load factor for solar installations used for ampacity calculations depends on the specific application and design considerations.

LF Calculation

Calculate: If the inverters can truly output at their max for only several minutes, to a few hours max, depending on DC/AC ratio, calculate the Average Current. Assume the "daylight hours" for simplicity. Example: Max Inverter = 500A; Inverter operates at Max for 2 Hours, then average 70% for 6 Hours, and then at 20% for the final 4 Hours. Average Output = ((500A \ 2) + (500A \ 0.7 \ 6) + (500A \ 0.2 \ 4)) / 12 Average Output = (1000A + 2100A + 400A) / 12 = 291.66A LF = Average Current / Max Current LF = 291.66A / 500A = 58.33% Then, compare that 58.33% to your 50% or 60% Load Factor tables.

NEC Guidelines

The NEC requires considering the continuous nature of the load. Inverter output is considered continuous, so a 125% factor is used on its rating to find the current used for conductor sizing.

Worst-Case Scenario

It's generally conservative (and safer) to base your calculations on the calculated continuous current (1.25 x Inverter max output). However, using the actual LF from the example above might be permissible.

3. Rho (Thermal Resistivity) and Annex Design Criteria



Understanding Rho

Rho (ρ) represents the thermal resistivity of the soil or surrounding materials. Lower Rho means heat dissipates more easily.

Rho Values

Concrete: Typically around 55-60 (kOhms-cm). Average Soil: Around 90 (kOhms-cm). Varies significantly with moisture content. Dry Sandy Soil: Can be much higher (150-200+).

"Rho Concrete = Rho Earth - 5"

This is a simplified assumption that the concrete encasement will have a slightly lower thermal resistivity than the surrounding earth. This is likely to facilitate heat dissipation. Don't treat this as a hard rule. It depends on the specific concrete mix.

Rho of PVC, Cable Insulation, and Jacket

These materials all impede heat transfer. Their Rho values contribute to the overall thermal resistance of the cable installation. Ampcalc (or similar software) uses these values, along with conductor dimensions and spacing, to calculate the temperature rise within the cable.

How to Use the Information


Soil Investigation

Crucially, conduct a soil thermal resistivity test at the site. This will provide the actual Rho value for your soil conditions. This is the most important factor.2.

Concrete Properties

If the duct bank will be encased in concrete, get the thermal conductivity (or Rho) from the concrete supplier.3.

Software Modeling

Input all these Rho values into the Ampcalc software to get accurate conductor ampacities.

4. Practical Approach Conservative Design

It's generally better to err on the side of over-sizing conductors, especially in high-current applications. Consider using larger conductors than the absolute minimum calculated.

Derating

Be VERY aggressive in derating for conduit fill and ambient temperature.

Spacing

Increase the spacing between conduits if possible. This improves heat dissipation.

Consider Direct Burial

Direct burial of the conductors (with proper burial depth and soil preparation) is often more thermally efficient than a duct bank.

For the 400KCMIL from CT Cab

It sounds like you are parallel 12 lines of 400KCMIL. At that point, you can replace with a bus bar, and solve any conductor ampacity issues.

5. General Comments Coordination with Utility

Communicate extensively with the utility company. Their requirements are paramount.

Engineering Expertise

Highly recommended to consult with a qualified electrical engineer experienced in medium-voltage system design and heat transfer analysis. This is a complex area, and a professional can help ensure safety and compliance.

NEC Compliance: Thoroughly review all relevant sections of the National Electrical Code (NEC) regarding conductor sizing, ampacity derating, and grounding.In summary, while Annex B provides a starting point, it's not a substitute for a detailed engineering analysis, especially with the high currents and long distances you're dealing with. A combination of conservative design, accurate Rho measurements, and software modeling (if possible) is essential. I highly recommend consulting with an experienced electrical engineer for this project. Flag for review