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

THIS paper presents two ways of calculating the load angle of a non-salient pole synchronous generator. 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. The cotangent function used for calculation of the generator’s load angle is based on its active and reactive power and its external voltage. 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. 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. The key findings from this research are found in the more accurate calculation of the load angle of the synchronous generator and in connection with that the accurate estimation of the distance of the generator from the point of instability. As the more accurate load angle is that calculated via the cotangent function and which is smaller than the load angle calculated via the sine function, it is possible to load the generator more with the same degree of stability compared to the load based on the load angle calculated via the sine function. This results not only in a better safety aspect of the generator operation, but also economically, because this approach in calculating the stability of the generator enables greaterutilization of the generator capacity.