Formula for Calculating Sending-end and Receiving-end Voltages of AC Two-bus System with Constant Power Load P+ jQ

For calculation of voltages of an AC two-bus system, there exist conventional methods such as Ohmic calculation, Equivalent resistance method and etc. This paper presents the formulas for calculating the sending-end voltage E and receiving-end voltage V for the AC two-bus system with a constant power load P+jQ connected via transmission line admittance $\dot{\mathrm{y}}$=G-jB. The V-P equation(voltage-power equation) composed of voltages E,V and load power P,Q has been presented in a recent publication, from which the formula for sending-end voltage E can be derived with ease when V is given. However, the receiving-end voltage V when solved by Ohmic calculation or $V-P$ equation, becomes a $4^{\mathrm{t}\mathrm{h}}$-order equation w.r.t. V. We have to solve the $4^{\mathrm{t}\mathrm{h}_{-}}$ order equation and must select one practical solution out of four mathematical roots. An explicit formula for calculating the receiving-end voltage V is proposed in this paper by converting the V-P equation into the $2^{\mathrm{n}\mathrm{d}}-$order equation w.r.t. $\mu$, under the assumption that the system is on voltage-stable operation. Every existing method has its own multi-steps of solving process for obtaining the solution for voltage E or V, however, the proposed formulas need no such process. A unique solution can be obtained by simply substituting the given data into the proposed formulas. Example systems are solved by existing methods Ohmic calculation and V-P equation - and by the proposed formulas to compare the solving processes and calculation results with each other.