Let's break down this electrical calculation and address your questions

Understanding the Code and Table Selection
THWN/THHN

This indicates the insulation type of the conductors. Both THWN and THHN are common wire types used in residential wiring. The significance is that it tells you what table to use in the National Electrical Code (NEC) for ampacity.

Ampacity

The ampacity of a conductor is the maximum current, in amperes, that it can carry continuously under specified conditions of use without exceeding its temperature rating.

Temperature Ratings (75°C vs. 90°C)

Conductors are rated for the maximum temperature they can withstand. THWN and THHN have a 90°C rating, however the NEC often requires terminations (breakers, panels, etc.) to be rated for 75°C.

NEC 110.14(C)

This is a crucial section of the NEC that addresses termination temperature limitations. The general rule is this: For equipment rated 100 amps or less, and using conductors #14 AWG through #1 AWG, you must use the 60°C column for ampacity. For equipment rated over 100 amps, and/or using conductors #1/0 AWG and larger, you must use the 75°C column for ampacity.

Application to Your Problem

Since you have a 200-amp service, you MUST use the 75°C column for determining the minimum conductor size at the termination point.

Calculations and Answer Explanation1. Demand Load

You've correctly calculated the demand load as 200 amps 0.83 = 166 amps. (83% is for single family dwellings - table 310.12).
2.

Conductor Sizing (Based on 75°C)

You need to find an aluminum conductor that can carry at least 166 amps, using the 75°C ampacity column in the appropriate NEC table (usually Table 310.16, but pay attention to notes regarding ambient temperature correction and derating, although those aren't applicable in this simplified scenario).

4/0 AWG Aluminum

Has an ampacity of

180 amps in the 75°C column. This is the correct choice because it's the smallest conductor that meets or exceeds your 166-amp demand load. 3/0 AWG Aluminum

Has an ampacity of 155 amps in the 75°C column. This is too small.

Therefore, the minimum size THWN/THHN aluminum service-entrance conductors required is 4/0 AWG.Key Takeaways

Always consider the termination temperature limitations when sizing conductors. Most residential services will be limited to the 75°C column for larger conductors. Select the conductor based on the calculated demand load, and make sure the conductor's ampacity at the correct temperature rating meets or exceeds that demand. The fact that the conductor is also* rated for 90°C doesn't matter; you're bound by the termination temperature limitations.

Important Note: This explanation is simplified for the purpose of understanding the core concepts. A licensed electrician will consider all relevant NEC requirements and specific installation conditions (e.g., conduit fill, ambient temperature) to ensure a safe and code-compliant installation. Always consult with a qualified professional for electrical work. Flag for review