Okay, this is a common point of confusion, especially with large generators and their connections to switchgear. Let's break down the NEC articles and figure out the appropriate grounding conductor sizing.

Understanding the Key Articles NEC 250.66 - Sizing Grounding Electrode Conductors (GEC)

This article covers the conductor that connects the grounding electrode system (e.g., ground rods, building steel, etc.) to the system neutral (typically at the service equipment or, in this case, potentially at the generator). Its primary purpose is to provide a path for fault current to return to the source and clear the overcurrent protective device (OCPD) on a ground fault. This is related to grounding for earth.

NEC 250.122 - Sizing Equipment Grounding Conductors (EGC)

This article deals with the conductors that connect the non-current-carrying metal parts of electrical equipment (e.g., enclosures, raceways, equipment frames) back to the source of power (the generator neutral in your case). Its primary purpose is also to provide a low-impedance path for fault current to return to the source, but it focuses on clearing faults on equipment.

NEC 250.30 Grounding Separately Derived AC Systems

This section talks about the grounding requirements for generators and other separately derived systems.

Which Code Applies to Your Situation?

In your specific case, NEC 250.122(F)(1) is the applicable code for the equipment grounding conductor (EGC).

Here's why:1. Generator as Separately Derived System

Your generator is considered a separately derived system (SDS). This means it's a power source that is electrically isolated from the utility grid (or other power sources). As a SDS, the generator requires its own grounding system.2.

Equipment Grounding (EGC) Function

The ground conductors you are running between the generator enclosure (and any other non-current carrying metal parts of the generator system) and the switchgear enclosure are primarily functioning as

equipment grounding conductors (EGCs). Their purpose is to: Provide a low-impedance fault current path back to the generator neutral. Bond the metal enclosures together to minimize voltage differences and touch potential during a fault. Ensure that a fault to ground will quickly trip the 4000A breaker.3. 250.122(F)(1) Specifics

Because the overcurrent protection is greater than 1000 amps, 250.122(F)(1) states: "Where the overcurrent device is rated or set at more than 1000 amperes, the equipment grounding conductor shall be sized not smaller than 12.5 percent of the area of the largest phase conductor. Where the phase conductors are paralleled, the equipment grounding conductor shall be based on the total area of the paralleled phase conductors."4.

NEC 250.30(A)(3) - Equipment Grounding Connection Specifically requires bonding the generator frame to the grounding electrode for the separately derived system.

Calculations and Requirements based on 250.122(F)(1)1. Total Phase Conductor Area

You have (10) 444 KCMIL conductors per phase. So, total conductor area per phase is 10 444,000 circular mils = 4,440,000 circular mils.2.

Minimum EGC Area

The minimum EGC area is 12.5% of the total phase conductor area: 0.125 4,440,000 circular mils = 555,000 circular mils.3.

Number of 444 KCMIL Conductors

Each 444 KCMIL conductor has an area of 444,000 circular mils. You need a minimum of 555,000 circular mils / 444,000 circular mils/conductor = 1.25 conductors.
4.

Minimum Ground Conductors Required

You will need a minimum of 2 - 444 KCMIL ground cables.

Grounding Electrode Conductor (GEC) and its role You still need a GEC from the generator's neutral (or bonded frame) to a suitable grounding electrode system (ground rod, building steel, etc.). This is covered in NEC 250.30 and 250.
66. This conductor is related to grounding the system to earth. This provides a reference to earth in the case of voltage transients or imbalances.

Important Considerations and Recommendations Inspector is likely correct

Your inspector is very likely correct in requiring compliance with 250.122(F)(1).

Documentation

Document your calculations and clearly indicate the reasoning for your grounding conductor sizing to the inspector.

NEC 250.4(A)(5) and (B)(4)

Pay close attention to these sections, which discuss effective ground-fault current paths and minimizing impedance. Proper bonding and conductor routing are crucial.*

Manufacturer Recommendations

Consult the generator and switchgear manufacturer's documentation. They may have specific grounding requirements or recommendations that exceed the NEC minimums.

In Summary

While you do need a grounding electrode conductor (GEC) per 250.66, the ground conductors running between the generator enclosure/frame and the switchgear are primarily equipment grounding conductors (EGCs) and must be sized per 250.122(F)(1). Make sure you also have a separate GEC connecting to the generator's neutral. Always follow the latest version of the NEC and consult with a qualified electrical engineer if you have any doubts. I hope this information is helpful. Flag for review