## 1 Introduction  
Electrical transmission systems are continuously evolving and growing larger. Moreover, the systems are now being operated closer to their limits more frequently and as a result power systems today are more vulnerable to disturbances than ever before. In order to enhance the reliability and security of bulk power transmission, protections are commonly utilized in modern high voltage transmission networks for fault detection/location. Conventionally, _current differential protection_ is one of the commonly used techniques in the protection of transmission lines [1; 2; 3; 4]. In principle, differential protection is heavily dependent on the quality of the communication system. It uses the signals from both ends of the protected component, which need to be transmitted through communication channels, to locate faults. Thus, when differential protection is used to protect transmission lines, a number of communication problems due to the impact of the external environment, equipment operating conditions or other factors, could cause performance degradation. At 50 Hz an uncompensated communication delay of 1 ms will translate into an error of approximately 13 degrees in the phase angle computation [5]. Any protection performance degradation may threaten the security of and cause stability problems in the power system. For instance, in June 2003, when a fault happened to a 500 kV transmission line in the China Southern grid, one differential protection unit failed to trip this line because of a long _communication delay_. Therefore, with considering communication problems, it seems clear that there is a need to evaluate the reliability of differential protection so that the high security inherent in protection systems can be maintained. Recently, data driven/model free solutions for reliability, control and monitoring issues of complicated systems have been developed in the research literature [6; 7; 8; 9]. Existing references have been mainly focusing on three communication issues: _inconsistent communication delays_, _consistent communication delays_, and _bit errors_[10]. To study the effects of communication delays and bit errors on differential current protection, the presently used methods are mainly qualitative or experimental methods. A simulation method applied in [11] to study the effects of delays showed that any significant inconsistent communication delays may cause errors in data synchronization, which may result in a _false trip_ of the relay protection. It has been proved that long consistent communication delays may cause _refuse-operation_ errors in relay protection [12]. In fact, protection systems are time delay systems which have been an active research area for the last few decades. There have been a great number of research results concerning time delay systems scattered in the literature due to the ever-increasing expectations of dynamic performance [13]. In [14], several tests results are provided which showed that a large number of communication bit errors could cause refuse-operation relay protection faults. Generally, the effects of communication issues on differential protection can be summed up as: inconsistent communication delay causes data synchronization problems, which may result in false trips; consistent communication delays lead to the loss of speed, which may result in refuse-operation faults; and communication bit errors cause incorrect current signals and cause synchronization problems, which may result in refuse-operation faults. However, in all previous references no reliability analysis models for differential protection have been introduced. This paper studies the impact of communication delays and bit errors on current differential protection. First, the mechanism of how the communication delays and bit errors impact the differential protection is revealed.