STATIC STABILITY IN RELIABILITY PROBLEMS

Abstract

The possibility is considered of applying a mathematically correct criterion of zero transition of the Jacobian of sets of equations in post-emergency conditions in problems of reliability of estimation of static stability of energy systems in case of emergency shutdowns of main power transmission lines. With a common classical method of successive loading in a certain direction used, the problem of generation of estimated cross-sections for estimating the static stability has no unambiguous solution, and accordingly has no unambiguous result. In this case, it may turn out that for diff erent cross-sectional setups, the same disturbances (disconnections of power transmission lines, or blackouts of the circuit nodes) may or may not cause a disruption of static stability of the energy system. In this case, the chosen loading path will have a signifi cant impact on the zone of uncertainty of results. Therefore, to increase the stability of the results of calculations of static stability of an energy system, other principles are suggested for determining its static stability, which are characterized by unambiguity of solutions obtained. The analysis performed has enabled to draw two important conclusions that change the current principles of managing static stability: - with an increase in the power fl ow over a certain heterogeneous cross-section, the limit of static stability of the power system occurs when the power transmission angle reaches 90° in the line with the highest relative reactance (the «weakest link» model); - when the limit of static stability of the system is reached by the criterion of changing the sign of the Jacobian, at least one transmission line with a maximum transmission angle is necessarily found in the network, which must be included in the most dangerous section, regardless of its structure. Therefore, instead of identifying and monitoring the «dangerous cross-sections», it is proposed to calculate and control the power flow through the transmission lines with the largest transmission angle.