{'fraction_non_alphanumeric': 0.02072141212586339, 'fraction_numerical': 0.004604758250191865, 'mean_word_length': 5.20952380952381, 'pattern_counts': {'":': 0, '<': 0, '<?xml version=': 0, '>': 0, 'https://': 0, 'lorem ipsum': 0, 'www.': 0, 'xml': 0}, 'pii_count': 0, 'substrings_counts': 0, 'word_list_counts': {'cursed_substrings.json': 0, 'profanity_word_list.json': 0, 'sexual_word_list.json': 0, 'zh_pornsignals.json': 0}}
Parallel Flow Problem in Electromagnetic Loop Networks

An electromagnetic loop network (EMLN) is the loop configuration that consists of different voltage lines in the power network. The power flows in the higher voltage lines and the lower voltage lines interact each other and possibly make the EMLN weak. Such problem is designated as the parallel flow problem. Generally, there are two extreme attitudes toward EMLNs: 1) rejecting the EMLN despite the resulting waste of resources; and 2) misusing the EMLN despite the latent danger. These misunderstandings arise from the deficiency of a persuasive argument on the parallel flow problem. For this reason, this paper establishes an analytical model for the EMLNs. Then the flow decomposition function and the parallel flow function are derived from the network equations. These functions formulate the parallel flow problem in four aspects: 1) extracting the parallel flow; 2) formulating the interaction between the power flows in the higher voltage lines and the lower voltage lines in the EMLN; 3) identifying the pivotal branches in the EMLN; and 4) visualizing the parallel flow distribution. Accordingly, whether an EMLN can maintain an appropriate operating condition is assessable, which can result in a reasonable attitude toward the EMLN.