Chemical and Petroleum Engineering, Vol. 43, Nos. 9–10, 2007

METHODS OF DETECTING ROTATING SURGE AND STALL BASED ON GROUP STATISTICAL TREATMENT OF CENTRIFUGAL COMPRESSOR REGIME PARAMETERS Ya. Z. Guzel’baev and A. L. Khavkin

It is noted that one of the most promising trends in the field of detecting turbocompressor stall and revelation of the signs that characterize different forms of the development of gas dynamic instability (stall and rotating surge) is the use of statistical processing methods and signals. A procedure is presented for using statistical functions for analyzing the nonstationary nature of compression in turbocompressors and revelation of signs of stall based on calculating covariation of signals of regime parameters. Results are provided for studies based on analyzing covariation of the signals of regime parameters for centrifugal compressors of different construction that demonstrate the suitability of this parameter for detecting the phenomenon of compression gas dynamic instability. The procedure proposed is used successfully in practice in the form of special software for stall signalers used in centrifugal compressor automation systems.

Devices for detecting gas dynamic instability of compression are an important part of contemporary systems providing safe operation of turbocompressors. Currently, there is extensive use of electronic devices (stall indicators) that react to the start of stall. They continuously analyze transducer signals of turbocompressor regime parameters with the aim of revealing signs of the start of gas dynamic instability (stall) and they send a signal to the control system in order to take extreme measures for withdrawing the compressor from dangerous regimes. One of the most promising trends in the field of improving methods for detecting turbocompressor stall and revelation of the distinguishing signs that characterize different forms of the development of gas dynamic instability (stall and rotating surge) is the use of statistical methods for processing transducer signals of compressor regime parameters [1]. In information science, the achievements of statistical detection methods are well known, distinguished by high efficiency and resistance to interference. In view of this, it is necessary to note work in [3] in which observation of rotating surge is carried out by analyzing the signs of transience, preceding stall, on the basis of calculating the self-correlation function of the signal from the pressure transducer. However, this method has not been used widely. A method of detecting stall is proposed based on calculation on a real time scale of the average value x and disper2 sion σ x of the signal [2]: 1 x= N −1

σ 2x =

1 N −1

N

∑ xi ; i =1

N

∑ ( xi − x ) 2 ,

(1)

i =1

where xi is signal of the ith reading; N is a number determining the averaging time aperture. V. B. Shnepp NIIturbocompressor ZAO, Kazan. Translated from Khimicheskoe i Neftegazovoe Mashinostroenie, No. 9, pp. 27–29, September, 2007. 0009-2355/07/0910-0543 ©2007 Springer Science+Business Media, Inc.

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Fig. 1. Stall of an air centrifugal compressor Aerokom 250/9.4: 1) discharge pressure pd; 2) current strength of the main electric drive I; 3) relative covariance covre; 4) discrete signal for the start of stall x.

A criterion for the start of stall is considered to be exceeding the relative dispersion of the transducer signal for some threshold dispersion σ2re ≤ σ2thr. The relative dispersion (variation coefficient) of the signal is calculated by the equation σ2re = σx2 /x 2. As sources of signals it is possible to use pressure drop transducers in a flowmeter device or the discharge pressure. This criterion was realized in the form of applied software for stall indicators and it showed good results during operation. Development of a procedure for using statistical functions in order to analyze compression transience in turbocompressors is the study of signs of stall and development of methods based on calculating the covariation of regime parameter signals. During analysis, there was use of different turbocompressor regime parameters written in digital form during stall tests. From two parameters (x, y), having correlation tendencies in the prestall and stall periods, there was calculation of the following: the average value x by Eq. (1), y by a similar equation y=

1 N −1

N

∑ yi , i =1

and covariation cov{x, y} by the equation 1 cov{x , y} = N −1

N

∑ ( xi − x ) 2 ( yi − y ) 2 . i =1

As a parameter that characterizes the level of transience, a dimensionless parameter of relative covariation was formulated: cov re =

cov{x , y} . xy

(2)

The studies performed, based on analyzing covariation data, obtained in stall tests for centrifugal compressors of different construction, operating on different compression media, demonstrated the suitability of this parameter for detecting compression transience. The following condition was used as a criterion for the start of stall: covre ≥ covthr, where covthr is some threshold covariation. Analysis showed that for detection of stall it is possible to use effectively covariation of pressure drop signals in the flowmeter device and compressor discharge pressure, signals of the pressure drop in the flowmeter device and current strength of the main electric drive, signals of the pressure drop in the flowmeter device and rotor axial shear, signals of the pressure drop in the flowmeter device and rotor rotation frequency (with use of a turbine as the compressor drive). 544

Fig. 2. Stall indicators based on microprocessor controllers CompactLogix from Allen-Bradley (USA) (a) and POMPC1 produced by Émikon ZAO (Russia) (b).

The efficiency of the stall detection method based on covariation is shown in Fig. 1. This method has a number of advantages over single-parameter methods based on self-correlation and dispersion analysis. Advantages are connected with the fact that the group behavior as a minimum of two centrifugal compressor parameters is analyzed. This makes it possible to increase the resistance of the algorithm for detecting stall to false responses without a reduction in sensitivity to the development of compression gas dynamic transience. In a number of cases when stall is implicit in nature or when gas dynamic instability is limited to the development of rotating surge, the method proposed gives positive results for detection whereas other methods are inoperative. This feature is important for centrifugal compressors with a gas turbine drive having magnetic supports (bearings). In these cases, the phenomenon of gas dynamic instability is not accompanied by stall self-vibrations and inherent to them marked discharge pressure and flow rate pulsations, that makes stall testing and determination of the stall limit very difficult. Use of diagnosis methods for gas dynamic instability, based on calculating covariation, in these cases are almost without an alternative and they make it possible to determine the stall limit correctly. The informativeness of the covariation parameter, calculated by Eq. (2), has been confirmed on the example of data obtained with stall tests of a booster NTs-12/56-1.44 (GPA-12 Ural) at KS Permskaya. These studies demonstrated that with correct selection of signal sources, the sampling period (discretization frequency) for the transducer and the number of points for reading covariation, determining the time aperture, detects stall effectively by the method proposed. The universal nature of detection algorithms based on the proposed method is confirmed by the stability of work on all test examples of compressors of different types with a change in the frequency of stall vibrations over wide limits and the use of different types of transducers as signal sources. As a result of the work carried out, optimum frequencies for signal discretization and the number of points for reading dispersion and covariance were determined. Studies showed that a reduction in time aperture for reading the relative optimum value reduces the efficiency of stall detection algorithms and increases the probability of false operation caused by noise and interference. In turn, an increase in the aperture leads to worsening of the rapid action of algorithms and reduces sensitivity. It should be noted that for reliable operation of algorithms it is necessary to calculate covariance parameters over the whole aperture at each step of transducer signal sampling, i.e., to accomplish continuous signal processing on a real time scale. The algorithm makes it possible to introduce into a centrifugal compressor automation system a warning indicator for the “prestall” condition (start of rotating surge) in the for of additional “settings” that are lower than the threshold value for working out the preventative control signal in an open bypass armature. The main virtues of algorithms for detecting stall in centrifugal compressors based on calculating covariance are as follows: • the high reliability and efficiency of stall detection; 545

• resistance to noise and interference; • the possibility of practical implementation on a real time scale in contemporary commercial programmable controllers for automation systems. In order to introduce methods for stall detection [4] in centrifugal compressor control systems, special software was developed making it possible to optimize calculation of statistical functions on a real time scale required for detecting stall. This made it possible to create applied software for practical implementation of these methods on the basis of commercial microprocessor controllers of both domestic and overseas production. A stall indicator is shown in Fig. 2 used in compressor automation systems. Currently almost all centrifugal compressor automation systems produced by Kazan’kompressormash are fitted with stall indicators. These indicators are either integrated into the master PLC-controller in the form of a special programmed unit in an applied program and a high-speed module for the input of analog signals, or a separate microprocessor controller specially developed for this purpose. The indicators make it possible to detect stall simultaneously by four algorithms (three covariant and one dispersion). Introduction of stall indicators on the basis of probability methods for detecting stall phenomena have made it possible to increase the efficiency and reliability of centrifugal compressor stall protection systems.

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Ya. Z. Guzel’baev and A. L. Khavkin, “Statistical methods for detecting rotating surge and stall of centrifugal compressors,” Trudy ZAO NIIturbokompressor, I. G. Khisameev (ed.), No. 5, 58–73. Ya. Z. Guzel’baev and A. L. Khavkin, “Features of the practical implementation of a method for calculating signal dispersion in order to detect rotating surge and stall in centrifugal compressors,” Trudy ZAO NIIturbokompressor, I. G. Khisameev (ed.), No. 5, 44–57, Kazan (2004). R. A. Izmailov et al., “Design and study of compressor machines,” Trudy ZAO NIIturbokompressor, I. G. Khisameev (ed.), No. 4, 93–99, Kazan (1999). Ya. Z. Guzel’baev and A. L. Khavkin, RF Patent 2247869, “Turbocompressor stall diagnostic method and system for its implementation,” Publ. 03.10.2005, Byull. No. 7.