Is it necessary to light Shabbat candles according to the number of children?

Greetings, 

As a matter of strict halacha, it is sufficient to light one candle for Shabbat candles. In any case, it has become customary to light two candles, one corresponding to "Remember" and one corresponding to "Keep" (see Shulchan Aruch, Orach Chaim, siman 263, seif 1). Some have the custom to light seven candles, corresponding to the seven days of the week, and some light ten, corresponding to the Ten Commandments (Mishnah Berurah, seif katan 6). And there are women who have the custom to add another candle in honor of Shabbat for each child added to the family, and one who wishes may conduct herself in this manner, and before she begins it is recommended that she say that she is doing so "without a vow." 

Sources: Indeed, in She'eilat Ya'akov (by Rabbi Yehuda Tzvi Bluhm zt"l, siman 23) he wrote that there are women who say that a new Torah comes from them, and that when a baby is born they add candles, and that he has not seen even a hint of such a mitzvah anywhere. However, we find that some of the later authorities mentioned this custom, as written in the sefer Torat Chaim (siman 263, end of seif katan 4), that there are women who add one candle for each child born, and each place follows its own custom. Likewise, in Sefer Likkutei Maharich, part 2 (Order of Shabbat Eve practices), it is written that the custom of women is that when a son or daughter is born, they add one candle, and he brought support for this from the words of the Gemara in tractate Shabbat (23b), that in the reward for increasing the Shabbat lights one merits children and sons-in-law who are Torah scholars; therefore, each time a son or daughter is born, they increase the candles, so that through this they will merit children and sons-in-law who are Torah scholars. Also in Sefer Sha'arei Halacha uMinhag, part Orach Chaim, part 1 (page 262), it is written that there are women who light two candles corresponding to the woman and her husband, and when children are born they add one candle corresponding to each one, to illuminate the fortune of each one. See further what was written giving reasons for this custom in She'eilat Ya'akov, part 7 (siman 35), and in Teshuvot VeHanhagot, part 2 (page 123, beginning of the passage marked however). See also in Shemirat Shabbat keHilchata, part 2 (chapter 43, note 51), regarding what was written to comment on the words of the aforementioned She'eilat Ya'akov. 

With blessings, Hillel Meirs