2015.03.10, study, paper study notes-"study on the confidence degree of mixing amplitude of hydraulic turbine pressure pulsation"

Literature : Hu Jiang art. study on the confidence degree of mixing amplitude for hydraulic turbine pressure fluctuation . Water Conservancy Machinery Technology, 2014 (3). 17-22

abstract : According to the requirements of IEC test procedures, the common method for calculating the confidence degree of mixing amplitude of pressure fluctuation is analyzed in this paper. The distribution of random variables of pressure fluctuation is discussed with the results of model test. The practicability of the calculation method is analyzed, and the calculation method which meets the requirement is put forward.

keywords : Pressure fluctuation mixing amplitude confidence degree normal distribution

Notes :

The domestic pressure pulsation measurement adopts the relative amplitude of the mixed-frequency pressure pulsation, the peak-to-peak of the pressure fluctuation in the immediate domain and the amplitude of the water head H, in which the peak-to-peak value is calculated by the confidence method. The amplitude of the mixed-frequency pressure fluctuation defined by the IEC procedure is called the wideband amplitude , and the characteristic amplitude is suggested by the standard deviation of the pressure pulsation in the time domain.

Water head: The effective head for the function of the hydraulic turbine, the total water level difference of the inlet and outlet section of the turbine. It corresponds to the power station head, also known as Mao Head, that is, the elevation difference of the upstream and downstream water level.

In the technical guideline of the State on-line monitoring system ofGBT 28570 Hydro-Generator set: the definition of pressure pulsation is given: The pressure pulsation pressure the pulsation of the liquid pressure in the flow channel relative to the mean during the selected period.

The calculation method of peak-to-peak is given in the appendix.

Calculation method of peak-peak value of ⑵ pressure fluctuation

The pressure fluctuation Peak Peak value calculation should adopt the confidence degree method, that is, the data of the sampled points of the time domain waveform of the recorded pressure fluctuation is counted, the data in the non-trusted region is eliminated, the difference between the maximum and the minimum value of the residual data is the peak peak of the pressure fluctuation of the time domain waveform graph. The confidence degree of the State on-line monitoring system should be set, and the confidence of the reliability of the model test should be the same as 97%.

The peak-to-peak unit of pressure pulsation can be expressed in absolute ΔH (unit kpa) or relative value δh/h (unit%).

First, this paper uses the statistical method to carry on the peak-peak computation research. It sums up four ways.

1) Linear calculation method. The difference between the maximum and minimum values of the sample within the sampling time, multiplied by the confidence level. Here we use our own method, that is, the data from large to small sort, and then delete the two or 1.5% of the data, and then the (maximum-minimum value) to get the difference between the practice, we feel more reasonable.

2) Probability statistic method. The function relation between the characteristic amplitude ΔH and the confidence degree A is established, and then the difference fitting method is used to obtain the characteristic amplitude of the given confidence degree. The method of sampling this point falls in the number between the minimum and the current value, divided by the total number, to get the distribution function.

3) Probability distribution method. Assuming that the data obeys a normal distribution, go directly to the quantile U of the confidence level A, then the characteristic amplitude δh=2uδ. where u is the number of bits, δ is the variance.

4) Interval estimation. Assume that the data service is normally distributed, and the result is exactly the same as Method 3.

Secondly, the probability density function of pressure fluctuation under different operating conditions is given. for the pressure pulsation, according to the shape of the vortex belt in the tail water pipe, the operating range can be divided into: Yip Road Vortex region (including no-load zone), eccentric vortex zone, vortex-free region and straight vortex zone.

It is concluded that the bell-shaped curves of normal distribution are not obeyed.

Third, the use of MATLAB jbtest test, the conclusion of the hydraulic turbine pressure pulsation test, most of the operating conditions of the pressure fluctuation random variables do not conform to the normal distribution.

The results of linear calculation method and probability distribution and probability statistic method are different, and the latter two are close. But after the two in the second Vortex zone, that is, eccentric vortex zone tail water tube pressure fluctuation peak-to-peak difference, it is believed that the possible reason is that the data is approximate normal distribution under other conditions, but the eccentric vortex zone, the tail pipe pressure is mainly affected by eccentric vortex, the main component is approximate sinusoidal pressure waveform, is not a normal distribution.

Five, conclusion: pressure pulsation in various conditions, although the normal distribution of the density function diagram, shape, but the normal distribution test, at most can only be considered as approximate normal distribution. The probability statistic method does not consider the distribution, but directly adopts the basic concept of statistics, more in line with the requirements of IEC regulations.

So what do you learn from this article?

1) The process of reproducing the probability distribution method is realized by MATLAB.

2) Use your own data to verify compliance with normal distribution.

3) Why there is no problem involving fragmentation and calculation of the number of periods.

2015.03.10, study, paper study notes-"study on the confidence degree of mixing amplitude of hydraulic turbine pressure pulsation"