Okay, this is a classic electrical engineering problem with a few twists. Let's break it down

Understanding the Problem:
Undersized Service

The existing 500 kcmil Aluminum conductors are grossly undersized for a 750 kVA transformer. This is a safety hazard and a violation of the NEC. It's a fire waiting to happen if the transformer is loaded even moderately.

Transformer Overload Capacity

While it's true transformers can handle overloads for short periods, relying on this is not good engineering practice. It shortens the transformer's life and increases the risk of failure.

Single 4" Conduit

This severely limits your options and is the root of the current debate.

Code Compliance

Meeting the NEC (National Electrical Code) is paramount. This isn't about opinions; it's about safety and legal compliance.

NEC Considerations and Calculations


Transformer Full Load Current

750 kVA 1000 / (480V 1.732) = ~903 Amps (Assuming 480V, adjust for your actual voltage) This is the absolute minimum ampacity your service conductors must be able to handle.2.

NEC 220 Load Calculations

You MUST perform a load calculation per NEC Article 220 for the building. This determines the actual demand load. While the transformer can supply up to 903A, the building might not actually draw that much. However, you must still size the conductors to at least the transformer's full load ampacity unless the load calculation is significantly lower AND you implement proper overload protection.3.

Service Conductor Sizing



Without a Load Calculation (Conservative Approach)

Size the conductors for at least 903A (transformer FLA).

With a Load Calculation

Size the conductors for the greater of: The calculated load demand. At least the minimum requirements in NEC 230.42.
4.

Conductor Ampacity

Use NEC Table 310.16 (or the appropriate table based on your installation conditions and conductor temperature rating - usually 75°C) to determine the ampacity of your conductors. Remember to apply derating factors for ambient temperature, number of conductors in a raceway, etc. (NEC 310.15).
5.

Overcurrent Protection

The overcurrent protection device (OCPD) MUST be sized according to NEC 240.4 and 450.
3. You may be able to utilize the next size up rule (NEC 240.4(B)), but only if it complies with other code requirements. Usually, the primary of the transformer is protected per NEC 450.3 and the secondary is usually covered by the main disconnect breakers.

Analysis of Your Suggestions



3 Sets of 500 kcmil Al

One 500 kcmil AL is typically rated at 380A @ 75 deg C. Three in parallel would be 1140A, which seems adequate. However, 3 sets of conductors will not be easy to work with in the limited conduit.

2 Sets of 750 kcmil Cu

750 kcmil Cu is typically rated at 475A @ 75 deg C. Two in parallel would be 950A. This also seems adequate.

The 4" Conduit Problem

This is the limiting factor. You must calculate whether you can legally fit the required conductors and a ground wire (EGC) in the 4" conduit, taking into account conductor fill percentages (NEC Chapter 9, Table 1 and Annex C). This might require:

Compacted Strand Conductors

These conductors are smaller in diameter than standard conductors, allowing for a tighter fit.

Parallel Ground Conductors

If necessary, you can run multiple smaller ground wires in parallel instead of one large one.

Careful Conduit Fill Calculations

Don't guess. Use the tables and calculations in the NEC. Overfilling a conduit is a code violation and makes pulling conductors extremely difficult, damaging the insulation.
Your Recommendation

I agree with you that running the correct conductor sizes for the 750 kVA transformer is the right approach. Here's a revised plan:1.

Perform a Load Calculation

Get this done first. It might allow you to use a slightly smaller conductor size, but don't count on it.2.

Consider Copper

While more expensive, copper conductors are smaller in diameter than aluminum for the same ampacity. This is critical given your conduit limitations.3.

Explore Aluminum Options Carefully

Compact strand Aluminum might allow you to get three sets of 500 kcmil AL in the conduit. This would probably be the most cost effective option.4.

Calculate Conduit Fill

Before ordering any materials, meticulously calculate the conduit fill for all potential conductor combinations.5.

Consider a New Service Entrance

This might sound drastic, but if you can't fit adequate conductors in the existing conduit, it might be the only safe and code-compliant solution. Running new conduit, while expensive, could be cheaper and safer than trying to force undersized conductors into the existing conduit. At the very least, the client should understand the potential cost difference for making the correct decision.

Addressing the Factoring Debate

The "factoring" argument is dangerous. You cannot just arbitrarily reduce conductor size based on assumptions. You must have a documented load calculation to justify any reduction, and even then, you must meet the minimum NEC requirements.

Important Reminders



Local AHJ (Authority Having Jurisdiction)

Talk to your local building inspector or AHJ before starting work. They will have the final say on what is acceptable.

Engineering Stamp

Depending on your jurisdiction, you may need a licensed electrical engineer to sign off on the design.

Documentation

Keep meticulous records of all calculations, load calculations, conduit fill calculations, and any communications with the AHJ.

In summary, prioritize safety and code compliance. The fact that the existing service is undersized is a serious issue that needs to be corrected. The 4" conduit creates a challenge, but it doesn't excuse using undersized conductors. Explore all options, including compact strand conductors, copper, and potentially running a new service entrance. Flag for review