In fact, different nodal power injections always exhibit correlation in a certain degree due to the impact of the consumer rest rules, geographical distribution, climate change and other factors. On the other hand, from the viewpoint of modeling, the existing PSSSA research considers the nodal power injections as independent random variables normally. Especially in a large-scale power system, this method tends to be unacceptable. In, the computation time of MCS-based PSSSA is studied and numerical results prove that a large amount of time is required to calculate the probability distribution function (PDF) of the system critical oscillation mode. Monte Carlo simulation (MCS) based numerical method is a generic way to deal with all kinds of uncertainties, but it requires a large number of repetitive simulations to obtain accurate solutions. In addition, these methods, based on the known probability distribution of random variables, have difficulty to handle the unknown empirical distribution situation. These methods usually need to approximately simplify the complex nonlinear functional relationship between the eigenvalues and input random variables, and the calculation error is inevitable. The analytical methods include point estimate method, cumulant method, and probabilistic collocation method (PCM). Up to now, the PSSSA methods of power system can be classified into analytical methods and numerical methods.
The system’s joint instability probability was evaluated by using the eigenvalue ensitivity to calculate the statistic characteristics of eigenvalue locations in the complex plane. Reference has introduced the probability concept into the power system dynamic stability analysis. Furthermore, with the rapid development of smart grid in recent years, to cope with the uncertainties, the PSSSA is a key issue. Therefore, probabilistic small signal stability analysis (PSSSA) considering various uncertainties attracts the interest of the researchers in the past few decades. These uncertainty factors, under the proper conditions, may gently push the system into an unstable operating mode and affect the power system small signal stability in a certain extent.
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In complex power system, uncertainties come from many aspects, such as volatility of load, uncertainty of line parameter, change of generator power, zero drift of controller parameter, model approximation, and so on. Uncertainty, however, is the inherent nature in a real world physical system. The main limitation of those methods is that the impact of various uncertainties on the stability of power system cannot be demonstrated comprehensively. Traditional small signal stability analysis (SSSA) methods focus on some special or the worst operating condition case.
Investigating the stability characteristics of dynamic systems under the action of small disturbance events, plays an important role in improving the overall security and reliability of the power grid. Power system always faces various small disturbances.
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