Criteria for the existence of established modes of power systems
Аннотация
Abstract This article considers the criteria for the existence of established modes of power systems. Nonlinear nodal equations of steady-state modes are presented, which have many solutions or do not have any physically realizable solutions. Criteria for the existence of solutions are given based on derivatives of power losses depending on the parameters of the power system modes. Equivalent circuit of the electrical system was performed using the South-Western MEN (MAIN ELECTRIC NETWORKS). The paper highlights the results of calculations of steady-state modes of the electrical system at weighted values of node 12. The maximum normal modes of electrical systems for the power of nodes was determined by the criteria are set <?CDATA $\frac{\partial \Delta P_{c}}{\partial \varPi_{i}}=\infty$?> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mrow> <mml:mfrac> <mml:mrow> <mml:mi mathvariant="normal">∂</mml:mi> <mml:mi mathvariant="normal">Δ</mml:mi> <mml:msub> <mml:mrow> <mml:mi>P</mml:mi> </mml:mrow> <mml:mrow> <mml:mi>c</mml:mi> </mml:mrow> </mml:msub> </mml:mrow> <mml:mrow> <mml:mi mathvariant="normal">∂</mml:mi> <mml:msub> <mml:mrow> <mml:mi mathvariant="italic">Π</mml:mi> </mml:mrow> <mml:mrow> <mml:mi>i</mml:mi> </mml:mrow> </mml:msub> </mml:mrow> </mml:mfrac> <mml:mo>=</mml:mo> <mml:mi mathvariant="normal">∞</mml:mi> </mml:mrow> </mml:math> .