Explicit loss formula, voltage formula and current flow formula for large-scale unbalanced distribution systems

Explicit formulas for determining system loss, current flows and voltages in terms of system and network data are developed for large-scale unbalanced distribution systems. The three-phase formulas consider multi-phase grounded or ungrounded loads and lines, cogenerators, multi-phase shunt elements and transformers of different connections all of which exist in large-scale unbalanced distribution systems. Test results on a number of distribution systems, including an actual 394-bus distribution network, are included to illustrate the accuracy and speed of the proposed formula for real-time analysis and control of distribution systems. It is shown numerically that the results given by these closed-form formulas are very close to those obtained by rigorous three-phase power flow methods. Applications of the explicit expressions to real-time control of distribution systems are also identified. Also, some features of the explicit formulas which are not possible with traditional power flow studies are discussed