Steady-state stability of the generator – comparison of load angle calculated using cotangent and sine function, and new instability proximity index

  • Suad Halilčević University of Tuzla
  • Izudinka Kapetanović Telekom of Bosnia and Herzegovina


This paper presents two ways of calculating the load angle of a non-salient pole synchronous generator. One of the goals of this paper is to determine which way of calculating the load angle gives more accurate results. The cotangent function used for calculation of the generator’s load angle is based on its active and reactive power and its external voltage. The sine function used for calculation of the load angle of the generator considers its internal voltage, which with variable synchronous reactance introduces a double error in the calculation of the load angle. Another goal of this paper is to present the steady-state stability of the generator with a new instability proximity index based on the cotangent function of load angle calculation. A new instability proximity index is the energy porosity defined as an approximate measure of how far the current operating state of the generator is from the state of instability. This dimensionless measure monitors the steady-state stability of a synchronous generator on a scale from zero to infinity (theoretically) giving an approximation of the distance of the operating state of the generator from its instability. The degree of danger of the generator entering an unstable state according to the relevant electrical quantities is especially emphasized by the sensitivity coefficients based on the new instability proximity index.

Electrical Engineering