Answer: The Mishna Berura (263:28) writes that when a married man is not home for Shabbos, he needs to light where he is staying as he can’t rely on his wife’s lighting elsewhere.
R’ Moshe Stern (Baer Moshe, Kuntres Electric 6:58:5) and R’ Shraga Feivish Schneebalg (Shraga Hameir 5:11:3) write that while one transgresses Shabbos by switching on an electric light, it isn’t the same as regular candles and one cannot say a beracha when switching them on for Shabbos. R’ Schneebalg stresses, too, that it is important that it is apparent that these lights were lit specially for Shabbos (See Teshuvos Vehanhagos 2:157:4).
The consensus among poskim, however, is that one can use electric lights when necessary. R’ Ovadia Yosef (Yabia Omer OC 2:17) explains why flicking a light switch on is akin to lighting a candle. R’ Zvi Pesach Frank (Har Zvi OC 143), R’ Eliezer Waldenberg (Tzitz Eliezer 1:20:11) and R’ Ephraim Greenblatt (Rivevos Ephraim 6:128) write that the light itself matters more than how the light came on. R’ Yehoshua Neuwirth (Shemiras Shabbos Kehilchasa 43:4; n22) quotes various poskim who maintain that one can recite a beracha upon lighting with electric lights.
R’ Benzion Abba Shaul (Ohr Letzion 2:18:13; 3:18:3) and R’ Shlomo Zalman Auerbach (quoted in Shemiras Shabbos Kehilchasa 43:n22) maintained that one can only fulfil ones obligation with a battery powered lamp. As regular electric lights are powered by an electric current that is continually being fed into the wiring, it is akin to lighting a lamp that doesn’t contain sufficient fuel when it’s lit.
While it is ideal to have special lights for Shabbos, the Rema (OC 263:4) writes that if necessary one can (extinguish or) switch off one’s lights and switch them on again.
In conclusion, when one cannot light regular candles, one can use electric lights, ideally ones powered by batteries that one lights specially for Shabbos.