Author:  Zhang, Jianfen 
Title:  Voltage stability analysis based on probability theory 
Degree:  Ph.D. 
Year:  2008 
Subject:  Hong Kong Polytechnic University  Dissertations Electric power system stability Probabilities 
Department:  Dept. of Electrical Engineering 
Pages:  v, 154 leaves : ill. ; 30 cm. 
InnoPac Record:  http://library.polyu.edu.hk/record=b2343023 
URI:  http://theses.lib.polyu.edu.hk/handle/200/5335 
Abstract:  In the last decades, several blackouts have occurred due to the voltage instability and led to huge economic losses. Voltage stability becomes an increasingly concerned problem. Many methods have been developed for voltage stability analysis. However, most of the computational tools developed so far are based on predetermined set of severe but credible situations. The essential weakness of such deterministic techniques is that they do not and cannot account for the probabilistic or stochastic nature of system behavior. However, there are uncertainties such as measurement errors, forecast inaccuracy and outages of system elements in power systems. To carry out deterministic voltage stability analysis for every possible or probable combination is impractical because of an extremely large computational requirement. Therefore, the present research attempts to apply probability theory to study voltage stability problem and to improve the voltage stability of power system considering uncertainties of load forecasts and load parameters. Similar to the prevailed deterministic approaches, voltage stability will be examined via 'static' and 'dynamic' system behaviors under probabilistic environment. The static voltage stability analysis based on power flow will regard the maximum load point as the critical point, where the Jacobian matrix of power flow equation is singular. The 'dynamic' voltage stability analysis based on small disturbance and using eigenvalue analyses will consider Hopf bifurcation or saddle node bifurcation as critical point, where system state matrix has one or a pair of eigenvalues with zero real part. In deterministic studies, the degree of voltage stability is often quantified in terms of stability margin, which is the distance between the normal operating point and the critical operating point. Static voltage stability analysis based on power flow is a common tool to assess stability margin index due to its simplicity and fast calculation. Under probabilistic studies, however, system loads are random variables such that the stability margin is also random variable. In the present study, probabilistic power flow technique combined with point of collapse method will be used to obtain probabilistic characteristics of stability margin and nodal voltages at the maximum load points. Maximum entropy will be employed to determine the probabilistic distribution of stability margin according to these probabilistic characteristics. After static study, voltage instability will be investigated using probabilistic eigenvalue approach by considering the dynamic behaviors of system components. With load assumed to be normal distribution, the characteristics of nodal voltages are obtained through probabilistic power flow. Probabilistic eigenvalues are used to determine probabilistic stability margin, taking into account the random load variations. The probabilistic studies will then be extended to examine the impact of the load parameter characteristics on voltage stability. With loads represented by exponential recovery load model, and with the assumption that the load parameters are normal distribution, the eigenvalues are also approximated by normal distribution. Expectation and standard deviation of eigenvalues that determine the distribution of eigenvalues are obtained from probabilistic characteristics of load parameters. The distribution of critical eigenvalue is used to determine the stability probability of power system. Effect of uncertainties of load parameters on probabilistic stability margin will be investigated. In all the above stability studies, probabilistic results will be compared by Monte Carlo approaches, using 10000 deterministic samples for each result, and effectiveness of the proposed techniques (static and eigenvalue) will be demonstrated. Finally, power system voltage stabilizer (PSVS) is adopted to improve voltage stability of power system considering the random variations of loads. Modal participation factor is used to locate power system voltage stabilizer; instability modal coefficient and probabilistic sensitivity index are employed to determine the input signal of PSVS. Then the QuasiNewton method will be used to adjust the parameters of PSVS. Subsequently, voltage stability of power system under wide range of operation can be enhanced by the present systematic PSVS design. 
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