Background. Enhancing transmission line capacity is a critical challenge in modern power engineering. One of the promising approaches in this field involves the implementation of series compensation devices, which significantly impact power system static stability. The small-signal stability analysis method is widely employed for assessing power system stability. This technique formulates system motion differential equations under minor disturbances of the initial state and examining the resulting free oscillation patterns. A crucial step of this method is deriving the characteristic equation, which roots determine system stability. However, for complex multi-machine systems, particularly with automatic control of excitation of generators and series compensation devices, the characteristic equation becomes high-order, complicating direct analysis. Consequently, studying the characteristic equation's constant term gains particular importance, as its sign is critically significant to determine static aperiodic stability.
Materials and methods. Methods of mathematical modeling of the electric power system, the theory of long-distance power lines and electromechanical transients, automatic control theory for power systems, as well as methods of analyzing the stability of electric power systems have been used. The original software in C ++ programming language has been used as a modeling tool.
Results. A system of differential equations describing electromagnetic transients in the studied power system has been developed. Based on the initial nonlinear model, a first-approximation linearized system of equations has been obtained using the small-signal method, accounting for the mutual influence of generators as well as parameters of automatic excitation regulators and series compensation devices. To analyze the stability of the system, a characteristic determinant has been formulated and a corresponding characteristic equation of the eighth order has been obtained. The dependence of the constant term values on the angle d between the EMFs of the two generators has been established.
Conclusions. It has been proven analytically using numerical methods that the final expression for a constant term does not directly contain the tuning parameters of the automatic excitation controllers. The obtained result has significant practical value. Since, on the one hand, it reduces the required symbolic computations and simplifies mathematical models and on the other hand, it completely maintains accuracy and validity in the system's stability assessment. The co-use of automatic excitation controllers and series compensation devices also requires coordinated tuning.