The problem of voltage instability has been a major concern of electric utilities for a long time. This problem has drawn great interest as voltage instability-related outage events occur around the world and result in blackouts. Although considerable efforts have been devoted to voltage stability assessment methods, most are only usable in off-line applications.
The most popular method of assessing voltage stability is the use of continuation power flow to identify the collapse point where the system power flow diverges, as disclosed in “Assessment of Voltage Security Methods and Tools”, EPRI report TR-105214, 1995; and Taylor C W, “Power system voltage stability [M],” McGraw-Hill, Inc., New York, America, 1994. This method is widely employed in the industry, and serves as a reference to new methods. Disadvantages of the continuation power flow method include:                Considerable system-wide power flow calculations making the method difficult to implement in a real time application;        Impossible to accurately handle actual time-dependent load characteristics (voltage- and frequency-related loads);        Possible premature divergence in system continuation power flows;        Inaccurate line parameters (resistance and reactance of lines), which are assumed to be constant in any environment or weather condition;        Inconsistency between off-line model and real life situation; and        Incapability to identify weak lines and buses that cause system collapse.        
Various voltage stability indices have been proposed for voltage instability. The indices may be divided into two types: system-wide indices and localized indices. The system-wide indices are based on system power flow calculations (as disclosed in Young Huei Hong, Ching Tsai Pan, and Wen Wei Lin, “Fast calculation of a voltage stability index of power systems [J],” IEEE Trans. on Power Syst., vol. 12, no. 4, pp. 1555-1560, November 1997; and P Kessel, H Glavitsch, “Estimating the voltage stability of a power system [J],” IEEE Trans on Power Delivery, vol. PWRD-1, no. 3, pp. 346-354, July 1986) and thus have the same disadvantages as the continuation power flow method. The localized indices focus on individual buses (as disclosed in Ivan {hacek over (S)}mon, Gregor Verbi{hacek over (c)}, and Ferdinand Gubina, “Local voltage-stability index using Tellegen's theorem [J],” IEEE Trans. on Power Syst., vol. 21, no. 3, pp. 1267-1275, August 2006; and K. Vu, M. M. Begovic, D. Novosel and M. M. Saha, “Use of local measurements to estimate voltage stability margin,” IEEE Trans. Power Systems, Vol. 14, No. 3, pp. 1029-1035, August 1999) or lines (as disclosed in M. Moghavvemi and M. O. Faruque, “Power system security and voltage collapse: a line outage based indicator for prediction [J],” Electrical Power and Energy Systems, Vol. 21, pp. 455-461, 1999; B. Venkatesh, R. Ranjan, and H. B. Gooi, “Optimal reconfiguration of radial distribution systems to maximize loadability [J],” IEEE Trans. on Power Syst., vol. 19, no. 1, pp. 260-266, February 2004; and M. Moghavvemi “New method for indicating voltage stability condition in power system [C],” Proceeding of IEE International Power Engineering Conference, IPEC 97, Singapore, pp. 223-227), and generally do not require continuation power flow calculations and are relatively easy for use in the on-line environment. However, problems of prior art localized indices include inaccuracy in theoretical derivation and calculations; and incapability to filter invalid measurements. The indices Lp and Lq, given in the Moghavvemi references above, cannot reach the expected value at the system collapse point even in the results of the authors' example. In fact, studies found that these two indices are based on an implied assumption of the line impedance factor being equal to the power factor, which is not true in most cases. The index presented in the Venkatesh reference targets a radial distribution line with an assumption of constant voltage at the sending bus, which is not true in looped transmission systems. Also, its denominator can be mathematically zero in which case the index becomes meaningless. Particularly, all the existing line indices do not consider impacts of the whole system beyond the line so they do not provide accurate and correct information in actual applications.
The localized index disclosed in the {hacek over (S)}mon and Vu references, and in the U.S. Pat. No. 6,219,591 and U.S. Pat. No. 6,690,175 is based on the Thevenin theorem and conceptually can be used in real time applications. Unfortunately, such index and method have the following concerns and disadvantages:                The calculation of the index requires measurements of voltages and currents in at least two system states and is based on the assumption that the equivalent Thevenin voltage and impedance are constant in the two system states. If the two system states are far apart, this assumption is invalid whereas if they are too close, it may result in a large calculation error for the estimate of equivalent Thevenin impedance. This assumption therefore, causes inaccuracy and difficulties in the actual implementation.        The method has no way to identify any wrong or invalid measurement. If any measurement of voltages or currents is incorrect or has a relatively large error, which can happen in any real measurement system, the index becomes useless.        The index cannot identify the weak lines that cause system collapse.        The method cannot be implemented using the existing SCADA (Supervisory Control And Data Acquisition) measurements and EMS (Energy Management Systems), which are available at utility control centers.        
U.S. Pat. No. 6,232,167 discloses a method to identify weak lines (branches) only. U.S. Pat. No. 6,904,372 disclose a method to identify weak buses only. Neither of these methods is designed for identification of system instability. U.S. Pat. No. 5,610,834 discloses a method to improve voltage stability using a P-V curve approach, and U.S. Pat. No. 5,745,368 discloses a method to reduce computing efforts in calculating the voltage collapse point on a P-V or Q-V curve. Such methods are based on off-line system power flow calculations and cannot be used in a real time environment. U.S. Pat. No. 7,096,175 discloses a technique to predict system stability by using phasor measurements and conducting a fast system power flow calculation after a contingency. However, the time-varying characteristics of line parameters (resistance and reactance) are not considered. Also, the method cannot be used to identify weakest lines or buses that cause system instability as its criterion is based on the divergence of power flow calculations of whole system.