Net work PassIve Component Neutral FIGURE 63.4 Positive sequence network for the system of Fig 63.3 II=YV+Yv2+Yv3+ Yv (63.2) 2=Y21V1+Y2y2+Y23V3+Y24V4 (63.3) YV+Yv+Y. L4=Y4V+Y2v2+Yv,+Y4V4 (63.5) The admittances in Eqs. (63. 2)through(63.5), Yi> are the ijth entries of the bus admittance matrix for the ower system. The unknown voltages could be found using linear algebra if the four currents I.I were known. However, these currents are not known. Rather, something is known about the complex power and voltage at each bus. The complex power injected into bus k of the power system is defined by the relationship between complex power, voltage, and current given by Eq (63.6 S, =VI Therefore (63.7) By substituting this result into the nodal equations and rearranging, the basic power flow equations for the four-bus system are given as Eqs. (63. 8)through(63. 11) SGI-SDI=VY,V,+Y12 V2+Y,,+Y, (63.8) e 2000 by CRC Press LLC© 2000 by CRC Press LLC (63.2) (63.3) (63.4) (63.5) The admittances in Eqs. (63.2) through (63.5), – Yij, are the ijth entries of the bus admittance matrix for the power system. The unknown voltages could be found using linear algebra if the four currents – I1… – I4 were known. However, these currents are not known. Rather, something is known about the complex power and voltage at each bus. The complex power injected into bus k of the power system is defined by the relationship between complex power, voltage, and current given by Eq. (63.6). (63.6) Therefore, (63.7) By substituting this result into the nodal equations and rearranging, the basic power flow equations for the four-bus system are given as Eqs. (63.8) through (63.11) (63.8) FIGURE 63.4 Positive sequence network for the system of Fig. 63.3. I YV YV YV YV 1 11 1 12 2 13 3 14 4 =+++ I YV YV YV YV 2 21 1 22 2 23 3 24 4 =+++ I YV YV YV YV 3 31 1 32 2 33 3 34 4 =+++ I YV YV YV YV 4 41 1 42 2 43 3 44 4 =+++ S VI k kk * = I S V S S V k k * k * Gk * Dk * k * = = − SG1 – S V YV YV YV YV * D1 * 1 * 11 1 12 2 13 3 14 4 = +++ [ ]