Cross differential protection of double lines based on supper-imposed current

The double circuit or parallel transmission lines are more and more widely used in modern power system to improve transmission capability and reliability. Many types of relaying protection techniques can be used to protect parallel double transmission lines, such as over-current relay, distance relay and pilot relay^[1]. Current and distance relays do not need communication channel but can not operate at all points on the line without time-delay. Pilot relay is able to offer fast operation without time-delay but need communication channel^[2]. The cross differential protection has been more and more widely used to protect parallel double transmission lines in power systems since it can operate without time-delay and does not need communication link.