Transportation is of major concern nowadays for city and country development. Rapid growth in transportation demand leads to a worldwide trend of developing high-speed railway. Co-phase traction power supply structure eliminates neutral sections and locomotive speed limitations. It thus has high potential for application in high-speed railway. However, in order to relieve power quality problems, power quality compensators are installed in railway power. The newly developed capacitive-coupled railway hybrid power quality conditioner (Railway HPQC) requires less operation voltage and is more beneficial than the inductive-coupled railway power quality conditioner (RPC). The co-phase traction power supply system with Railway HPQC thus has multiple advantages of (a) elimination of neutral section quantities and locomotive limitations; (b) higher transformer utilization ratio and reliability; and (c) lower power quality compensator operation voltage. In this chapter, the overall background of railway traction power, including its structure and worldwide development, is introduced. The power quality problems in railway power supply and existing solution methods are discussed, especially on flexible alternating current transmission system (FACTS) compensation devices. There are also discussions on recent research on railway power compensation.