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The power flow is the fundamental tool for the study of power systems. The data for this problem are subject to uncertainty. This paper uses interval withmetic to solve the power flow problem. Interval arithmetic takes into consideration the uncertainty of the nodal information, and is able to provide strict bounds for the solutions to the problem: all possible solutions are included within the bounds given by interval arithmetic. Results are compared with those obtainable by Monte Carlo simulations and by the use of stochastic power flows. Object oriented programming techniques make it possible to use interval arithmetic with minimal modifications to existing software. However, to reduce the conservatism inherent in all interval arithmetic computations, the paper describes an iterative method used to obtain the "hull" of the solution set.

Hopf bifurcation of a power system leads to oscillatory instabilities and it is desirable to design system parameters to ensure a sufficiently large loading margin to Hopf bifurcation. We present formulas for the sensitivity of the Hopf loading margin with respect to any power system prameter. These first order sensitivities determine aa optimum direction in parameter space to change parameters to increase the loading margin. We compute the IIopf bifurcation sensitivities of a simple power system with a voltage regulator and a dynamic load model. Parameter sensitivities of the Hopf and saddle node bifurcations are compared. An idea for eliminating some Hopf bifurcations is presented.

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