【正文】 index used to measure the reactive power reserve margin of bus i after a contingency is defined as:: the lowest reactive power of QV curve when system is under the base condition.: the lowest reactive power of QV curve when system is under the contingency condition.The Mvar margin of the system can be defined as:KQ = max（KlQ, K2Q,… ,KiQ） i = 1, 2 ,…, nn : monitored bus number.To this index, the adopted criteria in our practical studies are less than 30% for single contingency, 70% for double contingencies and 100% for three or more contingencies.Uncertainty for different levels should be considered in online and offline studies, so the criteria for VSA can be different. The above methods and criteria are adopted for online VSA in this paper.It is difficult to distinguish which index is better between MW margin and Mvar margin, because power systems are described from different angle of view. Based on the suggestions proposed in [2], the MW margin is adopted as the main index to assess the voltage stability for a load center while the Mvar margin is taken as the secondary index to aid the assessment.IV. VOLTAGE STABILITY ASSESSMENT FOR LOAD CENTERA. Assessment for transmission interface contingenciesThe assessment for the transmission interface contingencies are indispensable for a load center, because great amount of demand has to be imported through the interface from the other systems. When an important interface line trips, power will transfer to other interface lines, which increase the transmission power of other elements and decrease the transmission capacity of the whole interface, consequently the MW margin of the load center system will be reduced. If the interface lines are under stress conditions before a contingency, the study deserves more attention.For a specified load center, generally the interface linked to outer systems consists of finite lines up to several decades。 therefore the calculation burden for detailed N1 even N2 contingencies is acceptable in the contingency screening to the interface. When what we are interested in are only the single or double interface contingency cases, more plicated algorithms for contingency selection and screening are needless.There are 20 transmission lines through the interface linking BPS to other systems. When the forecasted peak load equals to 9500 MW, as an example, the VSA results for the single interface line contingencies are listed in Table I.From Table I we can see that the system under all NI contingency cases doesn39。t violate the MW margin and Mvar margin criteria. The contingency ranks according to the MW margin. The first contingency, . the line L5, has the smallest MW margin.B. Assessment for local generator contingenciesFrom another point of view, voltage instability can be considered to be that the supply of power system cannot meet the demand of consumers (under static or dynamic conditions), especially the deficient reactive reserve may be vital to power system voltage instability [10]. For a load center, reactive power cannot be transmitted through the interface if the angle is very different at the sending and receiving terminals of the interface, even though the voltage magnitude is obviously different [11].Thus, as important reactive sources, the status of local generators will exert distinct effects on VSA for a load center.Just like the assessment for transmission interface contingencies, the assessment for the load center system can be pleted when only considering single local generator outage contingencies. When the forecasted peak load equals to 9500 MW, under single generator contingencies the VSA results for BPS are listed in Table II. Because the capacities for some generators are very small and can be neglected, only the ten severest contingency are presented here.From Table II we can see that the system under NI local generator contingency cases doesn39。t violate both the MW margin and Mvar margin criteria. The contingency ranks according to the MW margin. The first contingency, . the generator Ji GX, has the smallest MW margin.C. Assessment for contingency binationsLet n be the number of local generators plus transmission elements in a load center system. Each element i , is represented by a random variable ξ iI， i =1, 2, ..., n, and di is submitted to the distribution: (1)To a local generator or an interface line, 0 state means that it is out of service and 1 state means that it is in service with rated capacity.The system state x will be defined as x = (x1, x2,…,xn ) . The system state will have 24 distinct states in the state space S.Let Pr{X = x} be the probability associated with a state X. X is a random vector. Then (2)where element states are assumed independent.When the state space consists of more than 20 elements, the putation burden is huge, even impossible. For example, to the binations of 20 transmission lines and 20 generators, there are 240 states in the state space. The number is approximately , therefore it is impossible to pute.A state space truncation method used in [12][13] is adopted to reduce the scale of the state space. In this approach, system states are generated in an increasing order of overlapping outages. If the probability of generated states exceeds a specified level (usually 95%), the remaining states are neglected. In most cases, a level corresponding to three overlapping outages satisfies this constraint for power system.