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Mathematical Problems in Engineering
Volume 2018 (2018), Article ID 8192710, 8 pages
Research Article

Sufficient Condition for the Parallel Flow Problem of Electromagnetic Loop Networks

1Department of Electrical Engineering and Automation, Harbin Institute of Technology, Harbin 150001, China
2Harbin Institute of Technology at Zhangjiakou, Hebei 075421, China

Correspondence should be addressed to Yi Yang

Received 20 August 2017; Revised 18 November 2017; Accepted 23 November 2017; Published 27 February 2018

Academic Editor: Konstantinos Karamanos

Copyright © 2018 Yi Yang and Zhizhong Guo. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


Electromagnetic loop networks (EMLNs) are pervasive in power networks. Their major characteristic is parallel flow. EMLNs with substantial parallel flow are considered to have a parallel flow problem. There is currently a serious disagreement about whether EMLNs have a parallel flow problem, which has resulted in different configurations of national grids. Therefore, this paper proposes a general model of EMLNs and derives the parallel current function, which formulates parallel flow, from the network equations of both the high and low voltage sides of an EMLN. Accordingly, the high and low voltage sides of an EMLN are equivalent to two sets of parallel identical multi-transmission lines. Finally, this paper considers operating margins and derives the sufficient condition under which parallel flow can be ignored. The sufficient condition not only determines whether an EMLN has a parallel flow problem but also reveals simple approaches to visually diminishing parallel flow. If the EMLN satisfies the sufficient condition, parallel flow can be ignored; otherwise, the EMLN needs to operate in a restricted way or to adopt open loop planning.