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Although real power is the main traded commodity in electricity markets, reactive power plays a crucial role in power systems reliability and security. In competitive electricity markets, no market participant wants to subsidise others in any way. Market participants utilise the network in different ways to maximise their profits. It means that their effects on the system, such as losses, can also be different. The development of a fair and accurate loss allocation scheme for real and reactive power is significant in avoiding cross subsidies and to have the correct charge for each participant. A new method is introduced to allocate real and reactive power losses in bilateral markets. The basic idea of the method assumes that transactions have their own effects on the system as well as their interactive effects with each other. Each transaction share of losses is based on its contribution to the system current flows. The proposed method determines these currents contributions and adjusts them, due to system nonlinearity, using the introduced current adjustment factors (CAFs). Unlike other approaches, the proposed method can effectively and easily allocate both real and reactive power losses simultaneously, which saves time and effort. It also determines the contribution of each transaction to every branch on the system. In addition, a new index, voltage participation index (VPI), is proposed to measure reactive power supports participation. This index is based on modified Y-bus matrix method proposed previously. The CAF method and VPI are illustrated using a simple three-bus system. Then they are verified on many systems, but due to space limit, only the results of IEEE 14- and IEEE 300-bus systems are presented. Results illustrate consistency with expectation. Part 2 will address the issue of how to price reactive power based on the technique developed in Part 1.