In power systems, there are many uncertainty factors such as power outputs of distributed generations and fluctuations of loads. It is very beneficial to power system analysis to acquire an explicit function describin...In power systems, there are many uncertainty factors such as power outputs of distributed generations and fluctuations of loads. It is very beneficial to power system analysis to acquire an explicit function describing the relationship between these factors(namely parameters) and power system states(or performances). This problem, termed as parametric problem(PP) in this paper, can be solved by Galerkin method,which is a powerful and mathematically rigorous method aiming to seek an accurate explicit approximate function by projection techniques. This paper provides a review of the applications of polynomial approximation based on Galerkin method in power system PPs as well as stochastic problems. First, the fundamentals of polynomial approximation and Galerkin method are introduced. Then, the process of solving three types of typical PPs by polynomial approximation based on Galerkin method is elaborated. Finally, some application examples as well as several potential applications of power system PPs solved by Galerkin method are presented, namely the probabilistic power flow, approximation of static voltage stability region boundary, and parametric time-domain dynamic simulation.展开更多
The influence of parameters on system states for parametric problems in power systems is to be evaluated.These parameters could be renewable generation outputs,load factor, etc. Polynomial approximation has been appli...The influence of parameters on system states for parametric problems in power systems is to be evaluated.These parameters could be renewable generation outputs,load factor, etc. Polynomial approximation has been applied to express the nonlinear relationship between system states and parameters, governed by the nonlinear and implicit equations. Usually, sampling-based methods are applied, e.g., data fitting methods and sensitivity methods,etc. However, the accuracy and stability of these methods are not guaranteed. This paper proposes an innovative method based on Galerkin method, providing global optimal approximation. Compared to traditional methods, this method enjoys high accuracy and stability. IEEE 9-bus system is used to illustrate its effectiveness, and two additional studies including a 1648-bus system are performed to show its applications to power system analysis.展开更多
Parametric Polynomial Method is used to analyze the three dimensional viscous flow through multistage turbomachines. Three high pressure stages in a 20MW steam turbine are calculated at design flow rate and small llow...Parametric Polynomial Method is used to analyze the three dimensional viscous flow through multistage turbomachines. Three high pressure stages in a 20MW steam turbine are calculated at design flow rate and small llow rate (G/G0 = 0.3). Large separated flow is predicted in the passage at small flow rate. The result shows that the upstream flow has a conspicuous effect on the downstream flow, so the multbetage fiow calculating is展开更多
The propagation of oscillating disturbances with various frequencies in multi stage turbine passages in a rocket is analyzed using the oscillating fluid mechanics theorem and the parametric polynomial method. The r...The propagation of oscillating disturbances with various frequencies in multi stage turbine passages in a rocket is analyzed using the oscillating fluid mechanics theorem and the parametric polynomial method. The results show that oscillating disturbances can be rapidly dissipated when the disturbance occurs at the inlet except for very high frequency oscillation such as 50 kHz. Dangerous low frequency oscillations occur at the outlet. The effects of the flow parameter variations on the oscillating disturbance propagation are also studied. The analysis will facilitate safe operation of the whole rocket system. 展开更多
The optimal condition and its geometrical characters of the least square adjustment were proposed. Then the relation between the transformed surface and least squares was discussed. Based on the above, a non iterative...The optimal condition and its geometrical characters of the least square adjustment were proposed. Then the relation between the transformed surface and least squares was discussed. Based on the above, a non iterative method, called the fitting method of pseudo polynomial, was derived in detail. The final least squares solution can be determined with sufficient accuracy in a single step and is not attained by moving the initial point in the view of iteration. The accuracy of the solution relys wholly on the frequency of Taylor’s series. The example verifies the correctness and validness of the method. [展开更多
基金supported by the National Natural Science Foundation of China (No. 51777184)。
文摘In power systems, there are many uncertainty factors such as power outputs of distributed generations and fluctuations of loads. It is very beneficial to power system analysis to acquire an explicit function describing the relationship between these factors(namely parameters) and power system states(or performances). This problem, termed as parametric problem(PP) in this paper, can be solved by Galerkin method,which is a powerful and mathematically rigorous method aiming to seek an accurate explicit approximate function by projection techniques. This paper provides a review of the applications of polynomial approximation based on Galerkin method in power system PPs as well as stochastic problems. First, the fundamentals of polynomial approximation and Galerkin method are introduced. Then, the process of solving three types of typical PPs by polynomial approximation based on Galerkin method is elaborated. Finally, some application examples as well as several potential applications of power system PPs solved by Galerkin method are presented, namely the probabilistic power flow, approximation of static voltage stability region boundary, and parametric time-domain dynamic simulation.
基金supported by National NaturalScience Foundation of China (No. 51777184)
文摘The influence of parameters on system states for parametric problems in power systems is to be evaluated.These parameters could be renewable generation outputs,load factor, etc. Polynomial approximation has been applied to express the nonlinear relationship between system states and parameters, governed by the nonlinear and implicit equations. Usually, sampling-based methods are applied, e.g., data fitting methods and sensitivity methods,etc. However, the accuracy and stability of these methods are not guaranteed. This paper proposes an innovative method based on Galerkin method, providing global optimal approximation. Compared to traditional methods, this method enjoys high accuracy and stability. IEEE 9-bus system is used to illustrate its effectiveness, and two additional studies including a 1648-bus system are performed to show its applications to power system analysis.
文摘Parametric Polynomial Method is used to analyze the three dimensional viscous flow through multistage turbomachines. Three high pressure stages in a 20MW steam turbine are calculated at design flow rate and small llow rate (G/G0 = 0.3). Large separated flow is predicted in the passage at small flow rate. The result shows that the upstream flow has a conspicuous effect on the downstream flow, so the multbetage fiow calculating is
基金Supported by the State Key Developments Plan Project of China( No.G19990 2 2 3 0 4 )
文摘The propagation of oscillating disturbances with various frequencies in multi stage turbine passages in a rocket is analyzed using the oscillating fluid mechanics theorem and the parametric polynomial method. The results show that oscillating disturbances can be rapidly dissipated when the disturbance occurs at the inlet except for very high frequency oscillation such as 50 kHz. Dangerous low frequency oscillations occur at the outlet. The effects of the flow parameter variations on the oscillating disturbance propagation are also studied. The analysis will facilitate safe operation of the whole rocket system.
文摘The optimal condition and its geometrical characters of the least square adjustment were proposed. Then the relation between the transformed surface and least squares was discussed. Based on the above, a non iterative method, called the fitting method of pseudo polynomial, was derived in detail. The final least squares solution can be determined with sufficient accuracy in a single step and is not attained by moving the initial point in the view of iteration. The accuracy of the solution relys wholly on the frequency of Taylor’s series. The example verifies the correctness and validness of the method. [
