## 1 Introduction  
Transparency is one of the most important measures of the open access network in the deregulated environment. Besides metering, a more transparent load with known power distribution is valuable to draft energy strategies. The network company or ISO needs to allocate the total cost of transmission among all electrical users in an equitable and non-discriminatory manner, which also provides a correct, market-based economical signal to all participants timely, especially when the volatile green power is gaining its position in the climate changing environment. There are many studies dealing with related subjects [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41]. Three basic categories can be used to classify the power distributions: (i) the real power distribution, (ii) the reactive power distribution, and (iii) the loss allocation. Refs. [3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 14] traced the contributions of generators and line flows based on a solved power flow and proportional sharing assumption. As pointed out in [42], the proportional assumption with contribution factors lacks the theoretical proof for correctness and physical justification. In [18, 19, 20, 21, 22], the authors used the state graph concept to represent the network structure according to line flow directions, based on the topological analysis with the sink/source concept, where the power was presumed to flow in one direction only. In [20, 23], currents were used to determine the active and reactive power contributions and the loss was also allocated. Many studies focused on the loss issue [1; 24; 25; 26], with simplifications used such as the Taylor series, quadratic loss formula, postage stamps, and B-coefficients. Simplifying by omitting other factors usually leads to errors. Optimization methods, game theory, and artificial intelligence, such as neural networks, were also used in loss allocation [27; 28; 29; 30; 31; 32], where we can see that the inherited problems of combinatorial optimization, increasing of problem size, overfitting, and the complicated training data preparations will be involved. Reactive power also plays an important role. With the reactive power being usually highly restrained than the active power, the contributions were approximated on the basis of active flows or very often neglected [2; 15; 18; 19]. Refs. [1; 16; 17] discussed the reactive flow tracing by using the same concept as the active power. Contribution factors with proportional sharing were used in [3; 4; 5; 6; 7; 8; 9; 10; 11; 12; 14], with inherited problems as indicated in [43]. OPF based methods with marginal cost were also adopted in [33; 34; 35; 36; 37; 38; 39]. Regardless of the number of the many studies published, studying only the reactive power itself means lacking of active power considerations, further accompanied by omission of mutual couplings. Counter flow is another issue where the flow component goes in the opposite direction of the net flow. Some theorems discussed this issue from a cost viewpoint, which insisted that counter flows pay for the cost and the toll even if the network congestion is involved. In tracing methods using the direct current (DC) flow model, the counter flows were not even considered. However, examining the contributions in relieving the congestion and postponing the system reinforcement, counter flows should be properly rewarded [40; 41]. As discussed above, every method tried to cover the problem from a particular angle, while a good method should cover the whole story. The real power, reactive power, mutual coupling terms, the loss, and the counter flows are all interrelated electrical components, and are mutually bundled and non-separable. Any separation by focusing on one issue will create error. A good method should consider these components altogether, and satisfy all electrical theories.