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This paper investigates the smoothness of the transfer limit surface, or the loadability surface, of power systems. The reactive power output constraints of generators are taken into consideration. A new methodology employed for the investigation is based on characterizing each maximum loading point by the state of the generators (PV or PQ). Then the transfer limit surface is investigated through careful observation of nose curves. In those special cases with only one constraint, the transfer limit surface is smooth. However, in the more general case of multiple constraints, the transfer limit surface is nonsmooth. These properties have been confirmed in a numerical example using a system with two constraints and three load parameters.Index Terms-Bifurcation set, electric power system, generator reactive power limits, inequality constraints, static model, transfer limit surface, voltage stability.

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SUMMARYIn the transport section, it is necessary to reduce the amount of CO 2 emissions and oil dependence. Bio fuels and fuel cell vehicle (FCV), electric vehicle (EV) and plug-in hybrid electric vehicle (PHEV) are expected to reduce CO 2 emissions and oil dependence. We focus on PHEV. PHEV can reduce total energy consumption because of its high efficiency and can run with both oil and electricity. Introduction of PHEV reduces oil consumption, but it also increases electricity demands. Therefore, we must evaluate PHEV's CO 2 reduction potential, not only in the transport section but also in the power grid section. To take into account the distribution of the daily travel distance is also very important. All energy charged in the PHEV's battery cannot always be used. That influences the evaluation.We formulate the total model that combines passenger car model and power utility grid model, and we also consider the distribution of the daily travel distance. With this model, we show the battery cost per kWh at which PHEV begins to be introduced and oil dependence in the passenger car section is to be reduced to 80%. We also show PHEV's CO 2 reduction potentials and effects on the power supply system.

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