This paper presents two new non-iterative approximations of the power flow in a network. Real and reactive power are simultaneously modelled in complex equations. Also, resistances are not set to zero. This is a generalization of the DC approximation, where only real power is modelled with zero line resistance. Hence the proposed approximations are more accurate than the DC approximation. The voltage lag over a link in a short, low voltage, network link is ten times as accurate as with the DC approximation. In the Appendix a new mathematical constant is introduced.
 Ten Cate, A. (2012) The Socially Optimal Energy Transition in a Residential Neighbourhood in the Netherlands. http://www.cpb.nl
 Van Hertem, D., Verboomen, J., Purchala, K., Belmans, R. and Kling, W.L. (2006) Usefulness of DC Power Flow for Active Power Flow Analysis with Flow Controlling Devices. The 8th IEE International Conference on AC and DC Power Transmission, 28-31 March 2006, 58-62.
 Stott, B., Jardim, J. and Alsaç, O. (2009) DC Power Flow Revisited. IEEE Transactions on Power Systems, 24, 1290-1300. http://dx.doi.org/10.1109/TPWRS.2009.2021235
 Coffrin, C., Van Hentenryck, P. and Bent, R. (2012) Approximating Line Losses and Apparent Power in AC Power Flow Linearizations. IEEE Power and Energy Society General Meeting, San Diego, 22-26 July 2012, 1-8.