### abstract

- The electric power industry is in the midst of a fundamental restructuring, with the previous structure of vertically integrated utilities providing power at regulated rates giving way to a more competitive market place with equal access to the transmission system for all wholesale buyers and sellers. As the power industry is restructured, it will be vitally important for market participants to evaluate the effects of proposed transactions on the loadability of their systems, both so that they may account for these effects in setting prices and so that they may avoid proposals which place their system at risk. This will require the ability to quantify, and hence price, the capacity of the transmission system in near real-time. This paper focuses on estimating how quasistatic voltage stability considerations affect transmission system capacity. Specifically, it introduces a conveniently calculated measure of the proximity of a system to maximum loadability which, when used in conjunction with system reduction techniques to identify the most stressed areas of a system quickly, provides valuable information for making competitive decisions in setting and pricing power transactions. Many static voltage stability techniques have been presented in the literature. In particular, energy methods have provided a path-independent and easily calculated measure of the proximity of a system to maximum loadability. However, the energy measure is merely a number; without further computation it provides no physical information regarding the amount of additional load an area of the system can serve. For example, in the simple five-bus system shown in Figure 1, the use of energy measures alone suggests that the lower-voltage bus is far closer to maximum loadability than the higher-voltage. However, if load is increased uniformly at all buses as a function of a parameter X, it is seen that both sides of the system reach maximum loadability at the same value of X. The key to gauging relative loadability at a bus is not just its capacity to supply additional load, but rather this value (Figure Presented) Figure 1. Five-bus problem system (Figure Presented) Figure 2. Percent loading results, 5-bus system relative to some expected or designed capacity. Such a measure is obtained by calculating a quantity called percent loading: Percent Loading = (1 - v/v 0) 100 where v is the energy measure for the current load level, and v 0 is the corresponding energy measure for the system with all loads set to zero. Figure 2 correctly suggests that the two sides of the system are equally close to maximum loadability. The usefulness of the method is illustrated on the IEEE 118-bus and 300-bus systems and in an application assessing the effects of proposed transactions on the loadabilities of the areas involved. To hasten the identification of weak areas of large systems using percent loading estimates, a system reduction technique called the Fixed-Boundary-Bus-Voltage (FBBV) method may be employed. The sizes of FBBV subsystems are independent of the full system size, and the energy measures obtained from them approximate the full system energy measures fairly well. Thus, by calculating percent loading estimates for small FBBV subsystems, the weakest areas of the system can be quickly identified.