The Sun (Tai Yang, 太阳) in the Self palace (Ming Gong, 命宫)

What the classic says, Zi Wei Dou Shu Quan Shu (紫微斗数全书), volume two

Well placed, an imposing figure and a full, square face; born by day it is strong, born by night it is weak. Kind-hearted and open-handed. In the seat of the self, blessing and long life, more so with the Power transformation (化权) and the Fortune transformation (化禄) both, and with the two Patrons, the Scholar and the Artist and the two Aides (魁钺昌曲左右) gathered, rank and wealth. Badly placed, guard against harsh malefics: brooding, advancing and retreating, a life held together by hard work. Turned away from its light, a busy mind and ordinary means.

太阳火，南北斗化贵，为官禄主。太阳入庙形貌堂堂，雄壮面方圆满，夜生陷日生庙旺，心慈面紫色，好济施。太阳入男命吉凶诀：命里逢阳福寿浓，更兼权禄两相逢，魁昌左右来相凑，富贵双全比石崇。太阳入女命吉凶诀：太阳正照妇人身，姿貌殊常性格贞，更得吉星同主照，金冠封赠作夫人。太阳安命有奇能，陷地须防恶杀凌，作事沈吟多进退，辛勤度日免家倾。太阳反照主心忙，衣禄平常寿不长，克过良人还克子，只宜荫下作偏房。太阳入限吉凶诀：二限偏宜见太阳，添财进业福非常，婚姻和合添嗣续，仕者高迁坐庙堂。太阳守限有多般，陷地须防恶杀侵，加忌逢凶多阻滞，横事破财家伶仃。

“Well placed” and “badly placed” refer to the star’s brightness in the branch the palace falls on: the same star in the same palace reads differently bright and dim, and the clause says how.

Source

How this placement actually turns up

• Well placed (exalted or strong) in 43% of those charts, badly placed (fallen) in 25%, in between the rest.
• Alone in the palace in 51%; sharing it with The Moon (太阴) 17%, The Voice (巨门) 16%, The Elder (天梁) 15%.
• Carries a birth-year transformation in 30%: Fortune (化禄) 11%, Power (化权) 9%, Trouble (化忌) 10%.
• How often the conditions the classic’s line names actually occur — one of the four difficult stars (擎羊陀罗火星铃星) in the palace with it: 30%; one of the six helper stars (左辅右弼文昌文曲天魁天钺) with it: 40%; Lu Cun (禄存) with it: 8%.

Counted by casting every day from 1950 to 2009 at each of the twelve hours — 262,980 charts, 8.3% of which have The Sun here (every main star sits in every palace in about one chart in twelve). A count, not a reading.