Научная статья на тему 'PERFORMABILITY ANALYSIS OF MULTISTATE ASH HANDLING SYSTEM OF THERMAL POWER PLANT WITH HOT REDUNDANCY USING STOCHASTIC PETRINETS'

PERFORMABILITY ANALYSIS OF MULTISTATE ASH HANDLING SYSTEM OF THERMAL POWER PLANT WITH HOT REDUNDANCY USING STOCHASTIC PETRINETS Текст научной статьи по специальности «Медицинские технологии»

CC BY
113
35
i Надоели баннеры? Вы всегда можете отключить рекламу.
Ключевые слова
Availability / Performability / Petri Nets / Ash Handling System

Аннотация научной статьи по медицинским технологиям, автор научной работы — Er. Sudhir Kumar, Dr. P.C. Tewari

This work seeks to propose a Petri nets-based technique for evaluating the performability features of ash handling system of a coal-based thermal power plant. The impact of failure and repair parameters on system performance has been determined. For the modelling of the system Stochastic Petri Nets (SPN) an extended version of Petri nets is applied. The recommended methodology used in this study allows for a better understanding of the system's performance behavior under various operating situations. The study provides Decision Support System which will assist managers in making informed decisions about inventory and spare parts for plant operations.

i Надоели баннеры? Вы всегда можете отключить рекламу.
iНе можете найти то, что вам нужно? Попробуйте сервис подбора литературы.
i Надоели баннеры? Вы всегда можете отключить рекламу.

Текст научной работы на тему «PERFORMABILITY ANALYSIS OF MULTISTATE ASH HANDLING SYSTEM OF THERMAL POWER PLANT WITH HOT REDUNDANCY USING STOCHASTIC PETRINETS»

PERFORMABILITY ANALYSIS OF MULTISTATE ASH HANDLING SYSTEM OF THERMAL POWER PLANT WITH HOT REDUNDANCY USING STOCHASTIC

PETRINETS

Er. Sudhir Kumar *

Research Scholar, Department of Production & Industrial Engg., National Institute of Technology, Kurukshetra, Haryana, India sudhirtamak@gmail.com

Dr. P.C. Tewari

Professor & Head, Department of Mechanical Engineering, National Institute of Technology, Kurukshetra, Haryana, India pctewari1@gmail.com

Abstract

This work seeks to propose a Petri nets-based technique for evaluating the performability features of ash handling system of a coal-based thermal power plant. The impact of failure and repair parameters on system performance has been determined. For the modelling of the system Stochastic Petri Nets (SPN) an extended version of Petri nets is applied. The recommended methodology used in this study allows for a better understanding of the system's performance behavior under various operating situations. The study provides Decision Support System which will assist managers in making informed decisions about inventory and spare parts for plant operations.

Keywords: Availability, Performability, Petri Nets, Ash Handling System

I. Introduction

In the present era, integrated automation in the industries has evolved a tendency to design and construct the systems with higher flexibility, complexity, and production capacity as a result of rapid technological breakthroughs. Power generation units are also facing a number of obstacles in meeting the rising demand for electricity in both industrial and domestic applications. High productivity, as well as high payback ratios, have become critical for these units' survival. The desire for improved availability has arisen as a result of the dynamic behavior of industrial equipment and systems. As a result, such industrial systems are expected to operate for as long as feasible in order to meet the appropriate level of output requirements. Performability practitioners' jobs have become more difficult as a result of having to investigate, characterize, measure, and analyse system behavior. Industrial systems, on the other hand, are practically impossible to operate without failure. Output losses, on the other hand, could be reduced by using enough redundant parts or expanding the system's production capacity [1].

II. Literature Review

A large number of research papers have sought to use reliability principles to examine the performance of real-world industrial systems. These are largely concerned with the modelling and analysis of multi-component complex systems. Cherry et al. [2] evaluated the plant's long-run availability assuming constant failure rate and repair for its various subsystems in a chemical industry. Dhillon and Rayapati [3] discussed the application of reliability engineering principles to chemical associated industries, as the risk associated with these industries is extremely significant. Singh [4] discussed the use of reliability approaches in a biogas plant was considered. Kumar et al. [5-8] In his research work for studying and evaluating the performance of paper, sugar, and fertilizer industries, Markov approach modelling was applied. Arora and Kumar [9] offered a stochastic study of a thermal power plant's ash handling system to aid plant personnel's in predicting the behavior of running units. Michelson [10] discussed the current state of reliability technology in the process industry and offered recommendations for the future. Singh and Mahajan [11] studied the reliability behavior of a utensil manufacturing plant. Sarkar and Sarkar [12] have addressed strategies for determining the availability and restricting the average availability of a system that is inspected on a regular basis, has a spare unit, and is well-maintained. Dai et al. [13] analyzed the service reliability and availability for a distribution system. Madu [14] in order to achieve competitiveness and customer happiness, the strategic importance of reliability and maintainability management was investigated. Singh and Garg [15] under the premise of constant failure and repair rates did an availability analysis of the core veneer manufacturing system in a plywood manufacturing system. Gupta et al. [16] used exponentially distributed failure rates of various components while evaluating the reliability metrics of a butter producing system in a dairy factory. Singh et al. [17] analyzed the reliability of ash-handling system with ash water pumps in which two units are operational at the same time and the third is a cold standby. More recently, Kumar et al [18, 19, and 20] for modeling and analysis of performability of various complex industrial systems, Petri nets were used.

III. System Description

After coal is burned, ash is continuously produced in the plant, necessitating an efficient ash handling system to dispose of this waste material. Figure 1 depicts the flow diagram of a thermal power plant's coal ash handling system. The following subsystems are arranged in a sequence in this system:

i) Furnace (F): A boiler furnace is used to produce high-temperature heating by combusting coal

with the least amount of smoke possible. The outside half of these furnaces is made of cast iron, while the interior is made of a brick shell and glass wool. There is no hot redundancy available for furnace, hence the failure of furnace will shift the whole system into completely down state.

ii) Electrostatic Preceptor (Ei): It is a device that is extensively used to remove fly ash from flowing gas (boiler emissions) with the help of an electric charge. There are two Electrostatic Preceptor provides hot redundancy to the system. Failure of any one of these will brings the system into the state of working in reduced capacity.

iii) Vessel (V): These Vessels are positioned just below the ESP hoppers with the dome valve arrangement. These are supposed to hold the fly ash for a period of time before being transported to the fly ash silos. There is no hot redundancy available for vessel also, hence the failure this will shift the whole system into completely down state.

iv) Compressor Transportation Line (C): In the plant, there is a compressed air station. The

Sudhir Kumar, P.C. Tewari RT&A, No 3 (69)

PA OF MSAHS OF TPPL WITH HR USING SPN_Volume 17, September 2022

compressed air station supplies air to the pneumatic conveying system and the fabric filter purging system. Similarly, there is no redundant unit available for Compressor Transportation Line. The failure of this will cause complete failure of system. v) Ash Silo (Ai): It keeps the fly ash generated by the boiler at the highest possible level of continuous operation. There are three number of Ash Silo connected parallelly available in the system.

Furnace ( F1 )

ESP ( E1 ) ESP ( E 2)

Vessel ( V1)

CTL (C1)

Ash Silo Ash Silo Ash Silo

AS1 AS2 AS3

Figure 1: Flow Diagram of Ash Handling System

IV. Performance Modeling

The Petri Nets approach was used to create the performance model. It depicts the interactions between the many subsystems of system. When a number of repair facilities aren't up to snuff, all of the failures can't be handled at once, and the failed units have to wait in line to be repaired. In Fig.2, the PN model of the plant's ash handling system is illustrated as follows:

Figure: 2 Petri Nets Modelling of Ash Handling System

V. Performance Analysis

The system's dynamic behavior was analyzed utilizing a set of variables to determine the performability parameters. In consultation with the plant's maintenance engineers, the permissible value pair of failure and repair rates for the subsystems (Table 1) was determined. The impact of repairman availability on these factors is also explored. The results are shown in the tables below (Tables 2 to 11) and discussed further below.

Table 1: Failure and Repair Rated of various subsystems of Ash Handling System

Name of Subsystem Failure Rate (per hour) Repair Rate (per hour)

Furnace 0.0045 0.20

Electrostatic Preceptor 0.014 0.20

Vessel 0.0025 0.125

Compressor Transportation Line 0.014 0.065

Ash Silo 0.00006 0.015

Table 2: Performability Matrix for Furnace of Ash Handling System in Full Capacity

pl 0.10 0.15 0.20 0.25 0.30

|1 Constant Parameters

0.0025 0.7437 0.7690 0.7710 0.7793 0.7810

0.0035 0.7389 0.7650 0.7700 0.7714 0.7790 l2= = 0.014 p 2= 0.20

0.0045 0.7353 0.7614 0.7680 0.7700 |3= 0.7757 l4= = 0.0025 p 3=0.125 = 0.014 p 4=0.065

0.0055 0.7344 0.7564 0.7610 0.7681 0.7750 |a5= = 0.00006 p 5=0.015

0.0065 0.7278 0.7530 0.7592 0.7633 0.7677

Table 3: Performability Matrix for Furnace of Ash Handling System in Reduced Capacity

pl 0.10 0.15 0.20 0.25 0.30

|1 Constant Parameters

0.0025 8700.42 8731.13 8745.91 8749.65 8757.19

0.0035 8666.48 8713.40 8732.40 8744.18 8748.26 |2= 0.014 p 2= 0.20

0.0045 8647.71 8702.28 8726.70 8737.67 8746.96 |3= 0.0025 p 3=0.125 |4= 0.014 p 4=0.065

0.0055 8627.91 8689.00 8714.44 8731.01 8740.47 |5= 0.00006 p 5=0.015

0.0065 8599.39 8678.57 8705.44 8720.97 8735.03

Furnace

Repair Rate Failure Rate

Figure: 3 Impact of Variation in FRR of Furnace on the Performability of Ash Handling System

Figure: 4 Impact of Variation in FRR of Furnace on the Performability of Ash Handling System (Reduced Capacity)

The change in the failure and repair rates has a moderate impact on the system's availability, as shown in Fig. 3. The system availability is reduced by 5.32 percent due to an increase in furnace failure rates from 0.0025 to 0.0065 and a fall in repair rates from 0.3 to 0.1. However, changes in furnace failure and repair rates have a substantial impact on the system's ability in reduced capacity; variation up to 15.78 percent is observed. Figure 4 depicts the situation.

Table 4: Performability Matrix for Crusher of ESP Handling System in Full Capacity

p2 0.10

0.15

0.20

0.25

0.30

|2

0.012 0.7624 0.7941 0.8043 0.8291 0.8421

0.013 0.7310 0.7628 0.7871 0.8055 0.8145

0.014 0.7121 0.7417 0.7680 0.7776 0.8043

0.015 0.6790 0.7126 0.7528 0.7660 0.7821

0.016 0.6541 0.6990 0.7208 0.7504 0.7638

Constant Parameters

|1=0.0045 p 1=0.20

|a3= 0.0025 p 3=0.125

|4= 0.014 p 4=0.065

|5= 0.00006 p 5=0.015

Table 5: Performability Matrix for Crusher of ESP Handling System in Reduced Capacity

p2 0.10 0.15 0.20 0.25 0.30

|2 Constant Parameters

0.012 0.013 0.014 8621.50 8520.06 8434.72 8756.70 8682.05 8610.48 8846.73 8782.05 8726.70 8909.32 8856.89 8810.61 8954.51 8907.44 8869.15 |1=0.0045 |3= 0.0025 |4= 0.014 p 1=0.20 p 3=0.125 p 4=0.065

0.015 8347.87 8544.23 8661.92 8758.54 8829.18 |5= 0.00006 p 5=0.015

0.016 8278.33 8477.67 8626.18 8722.35 8789.41

Electrostatic Preceptor (ESP)

Repair Rate Failure Rate

Figure: 5 Impact of Variation in FRR of ESP on the Performability of Ash Handling System

The variance in the ESP's failure and repair rates has a major impact on the system's availability, as shown in Figure 5. An increase in ESP failure rate from 0.012 to 0.016, as well as a fall in repair rates from 0.3 to 0.1, reduces system availability by up to 18.80%. The same changes in ESP failure and repair rates, on the other hand, have a moderate impact on the system's performability at reduced capacity varies up to 6.76 percent. Figure 6 depicts the situation.

Electrostatic Preceptor (ESP)

9000 ____. ------

-n 8500 -

u 8000 ■ V, 0.3

T3

и 0£

0.25

0.2

0.15

0.0135 °-014 00,45

0.015 0 0155 0 016

iНе можете найти то, что вам нужно? Попробуйте сервис подбора литературы.

0.1 *o"oi2 00125 (>'()l3

Repair Rate Failure Rate

Figure: 6 Impact of Variation in FRR of ESP on the Performability of Ash Handling System (Reduced Capacity)

Table 6: Performability Matrix for Vessel of Ash Handling System in Full Capacity

p3 0.025

0.075

0.125

0.175

0.225

^3

0.0021 0.7618 0.7736 0.7742 0.7772 0.7814

0.0023 0.7550 0.7603 0.7723 0.7760 0.7809

0.0025 0.7430 0.7617 0.7680 0.7752 0.7765

0.0027 0.7354 0.7562 0.7592 0.7616 0.7700

0.0029 0.7275 0.7451 0.7544 0.7609 0.7690

Constant Parameters

|д1=0.0045 p 1=0.20

|д2= 0.014 p 2= 0.20

|д4= 0.014 p 4=0.065

|д5= 0.00006 p 5=0.015

Table 7: Performability Matrix for Vessel of Ash Handling System in Reduced Capacity

p3 0.025 0.075 0.125 0.175 0.225

^3

0.0021 8196.63 8644.88 8877.38 9022.68 9118.56

0.0023 8061.35 8551.31 8804.98 8962.56 9067.80

0.0025 7946.32 8454.31 8726.70 8890.41 9005.73

0.0027 7796.23 8359.00 8648.22 8824.13 8943.50

0.0029 7691.22 8264.24 8566.09 8756.02 8884.35

Constant Parameters

^1=0.0045 |д2= 0.014 |д4= 0.014 |д5= 0.00006

p 1=0.20 p 2= 0.20 p 4=0.065 p 5=0.015

Vessel

0.8

Repair Rate Failure Rate

Figure : 7 Impact of Variation in FRR of Vessel on the Performability of Ash Handling System

The change in the Vessel's failure and repair rates has a lesser impact on the system's availability, as shown in Fig. 7. The system availability is reduced by 5.39 percent due to an increase in Vessel failure rates from 0.0021 to 0.0029 and a fall in repair rates from 0.225 to 0.025.

Figure : 8 Impact of Variation in FRR of Vessel on the Performability of Ash Handling System (Reduced Capacity)

However, the same fluctuations in the Vessel's failure and repair rates have a significant impact on the system's performability at reduced capacity, up to 14.27 percent change observed. Figure 8 depicts the situation.

Table 8: Performability Matrix for CTL of Ash Handling System in Full Capacity

И

p4 0.045 0.055 0.065 0.075 0.085

0.010 0.7166 0.7597 0.7742 0.7781 0.7793

0.012 0.7012 0.7568 0.7692 0.7713 0.7763

0.014 0.6930 0.7552 0.7680 0.7687 0.7754

0.016 0.6894 0.7483 0.7655 0.7685 0.7733

0.018 0.6849 0.7422 0.7586 0.7658 0.7656

Constant Parameters

1^1=0.0045 p 1=0.20

|д2= 0.014 p 2= 0.20

|д3= 0.0025 p 3=0.125

|д5= 0.00006 p 5=0.015

Table 9: Performability Matrix for CTL of Ash Handling System in Reduced capacity

p4 0.045

0.055

0.065

0.075

0.085

И4

0.010 8401.68 8690.45 8738.07 8750.19 8762.42

0.012 8364.56 8682.63 8735.64 8748.93 8756.41

0.014 8318.63 8671.83 8726.70 8746.05 8751.93

0.016 8291.45 8665.80 8719.08 8744.20 8747.90

0.018 8271.02 8655.22 8718.37 8735.35 8745.78

Constant Parameters

^1=0.0045 |д2= 0.014 |д3= 0.0025 |д5= 0.00006

p 1=0.20 p 2= 0.20 p 3=0.125 p 5=0.015

Failure 1

Figure : 9 Impact of Variation in FRR of CTL on the Performability of Ash Handling System

Failure I

Figure : 10 Impact of Variation in FRR of CTL on the Performability of Ash Handling System ( Reduced Capacity)

Table 10: Performability Matrix for Ash Silo of Ash Handling System in Full Capacity

p5 0.005 0.010 0.015 0.020 0.025

Constant Parameters

0.00004 0.00005 0.7679 0.7599 0.7674 0.7634 0.7698 0.7685 0.7707 0.7701 0.7740 0.7730 ^1=0.0045 |д2= 0.014 p 1=0.20 p 2= 0.20

0.00006 0.7576 0.7630 0.7680 0.7661 0.7712 |a3= 0.0025 p 3=0.125

0.00007 0.7571 0.7621 0.7646 0.7660 0.7703 |д4= 0.014 p 4=0.065

0.00008 0.7555 0.7576 0.7574 0.7607 0.7616

Table 11: Performability Matrix for Ash Silo of Ash Handling System in reduced Capacity

p5 0.005

0.010

0.015

0.020

0.025

^5

0.00004 8694.94 8729.57 8742.85 8750.96 8753.96

0.00005 8674.05 8717.78 8736.01 8743.07 8749.00

0.00006 8653.00 8707.61 8726.70 8736.81 8744.16

0.00007 8635.81 8700.05 8721.50 8732.69 8740.76

0.00008 8615.26 8687.43 8713.46 8727.31 8736.70

Constant Parameters

^1=0.0045 |д2= 0.014 |a3= 0.0025 |д4= 0.014

p1=0.20 p 2= 0.20 p 3=0.125 p 4=0.065

The change in failure and repair rates of the CTL has a significant impact on the system's availability, as shown in Fig. 9. The system availability is reduced by 9.44 percent due to an increase in CTL failure rates from 0.010 to 0.018 and a fall in repair rates from 0.085 to 0.045. The same changes in CTL failure and repair rates, on the other hand, have the least impact on the system's ability to operate at a reduced capacity of up to 4.91 percent. Figure 10 depicts it.

Failure ]

Figure : 11 Impact of Variation in FRR of Ash Silo on the Performability of Ash Handling System

Failure J

Figure : 12 Impact of Variation in FRR of Ash Silo on the Performability of Ash Handling System ( Reduced Capacity)

The variance in failure and repair rates of the Ash Silo has a small impact on the system's availability, as shown in Fig. 11. The system availability is reduced by 1.85 percent due to an increase in Ash Silo failure rates from 0.010 to 0.018 and a fall in repair rates from 0.085 to 0.045. However, the same changes in the Ash Silo's failure and repair rates have had the least impact on the system's ability to perform in decreased capacity by up to 1.38 percent. Figure 12 depicts it.

Table 12: Impact of Variation in the Repair Facilities on Performability of Ash Handling System

No. of Repair Facilities 1 2 3 4 5

iНе можете найти то, что вам нужно? Попробуйте сервис подбора литературы.

Availability 0.7680 0.7872 0.7877 0.7883 0.7882

Reduced Capacity 8726.70 8918.72 8922.80 8922.86 8922.80

8950,00

8900,00

>. 8850,00

^ 8800,00 £

£ 8750,00

QJ

8700,00 8650,00 8600,00

Figure : 13 Impact of Variation in Repair Facilities on the Performability of Ash Handling System

The influence of the number of repair facilities on system performance is depicted in Figure 13. When there are two or more repairmen in the system, the performance metrics stabilize. It leads to the conclusion that two separate repair facilities are required to obtain the best system performance.

VI. Conclusions

The Electrostatic Precipitator is the most vital part of the Ash Handling System, and it requires the most meticulous maintenance, according to the results of the current case study. The management will be aided in choosing the product mix by an examination of systems operating at decreased capacity and with degraded quality. The impact of repairmen availability on system performance will aid in resource allocation decisions. This will assist in lowering operation and maintenance expenses while also increasing output volume. It will also assist in raising the product's quality requirements.

Petri Nets can aid in the reduction of the time-consuming computational efforts required by Markov and other similar modelling methods. Choosing an appropriate technique, in fact, has a direct impact on operational and maintenance costs.

Decision Support System was developed based on the analysis as illustrated in Table 13. This will assist managers in making informed decisions about inventory and spare parts for plant operations.

Performability

2 3 4

No. of Repair Facilities

Table 13 : Decision Support System

Name of Subsystem Impact of Variations in FRR on Performability at full capacity ( percent ) Impact of Variations in FRR on Performability with reduced capacity(%) Maintenance Priorities Suggestions

Furnace 5.32 15.78 IV

Electrostatic Preceptor 18.80 6.76 I

Vessel 5.39 14.27 III

Compressor Transportation Line 9.44 4.91 II

Ash Silo 1.85 1.38 V

References

[1] Galikowsky C, Sivazlian BD, Chaovalitwongse P (1996) optimal redundancies for reliability and availability of series systems. Microelectron Reliab 36(10):1537-1546.

[2] Cherry, D.H., Grogan, J.C., Holmes, W.A. and Perris, F.A. (1978) 'Availability analysis for chemical plants', Chem. Eng. Prog., Vol. 74, No. 1, pp.55-60.

[3] Dhillon, B. and Rayapati, S. (1988) 'Chemical system reliability: a review', IEEE Trans. Reliab., Vol. 37, No. 2, pp.21-26.

[4] Singh J (1989) Reliability analysis of a biogas plant having two dissimilar units. Microelectron Reliab 29:779-781. doi:10.1016/ 0026-2714(89)90178-9.

[5] Kumar D, Singh IP, Singh J (1988) Reliability analysis of feeding system in the paper industry. Microelectron Reliab 28:213-215. doi:10.1016/0026-2714(88)90353-8.

[6] Kumar D, Singh J, Pandey PC (1989) Maintenance planning for pulping system in the paper industry. Reliab Eng Syst Saf 25 (4):293-302. doi:10.1016/0951-8320(89)90059-8.

[7] Kumar D, Pandey PC, Singh J (1991) Process design for a crystallization system in the urea fertilizer industry. Microelectron Reliab 31:855-859. doi:10.1016/0026-2714(91)90024-2.

[8] Kumar D, Singh J, Pandey PC (1992) Availability analysis of crystallisation system in the sugar industry under common cause failure. IEEE Trans Reliab 41(1):85-91. doi:10.1109/ 24.126677.

[9] Arora N, Kumar D (1997) Availability analysis of steam and power generation systems in the thermal power plant. Microelectron Reliab 37(5):795-799. doi:10.1016/0026-2714(95 001158.

[10] Michelson Q (1998) Use of reliability technology in the process industry. Reliab Eng Syst Saf 60:179-181.

[11] Singh J, Mahajan P (2000) Reliability of utensils manufacturing plant—a case study. Opsearch 36(3):178-185.

[12] Sarkar J, Sarkar S (2001) Availability of a periodically inspected system supported by a spare unit, under perfect repair and perfect upgrade. Stat Probab Lett 53:207-217. doi:10.1016/S0167-7152 (01)00087-6.

[13] Dai YS, Xie M, Poh K, Liu GO (2003) A study of service reliability and availability for distribution system. Reliab Eng Syst Saf 79:103-112. doi:10.1016/S0951-8320(02)00200-4.

[14] Madu CN (2005) Strategic value of reliability and maintainability management. Int J Qual Reliab Manage 22(3):317-328. doi:10.1108/02656710510582516.

[15] Singh J, Garg S (2005) "Availability Analysis of Core Veneer Manufacturing system in Plywood Industry." International Conference on Reliability and Safety Engineering, Indian Institute of Technology, Kharagpur, 497-508.

[16] Gupta P, Lal A, Sharma R, Singh J (2005) Numerical analysis of reliability and availability of the series processes in butter oil processing plant. Int J Qual Reliab Manage 22(3):303-316. doi:10.1108/02656710510582507.

[17] Singh DV, Tuteja R, Taneja G, Minocha A (2005) "Analysis of Reliability Model for an Ash Handling Plant Consisting of Three Pumps." International Conference on Reliability and Safety Engineering, Indian Institute of Technology, Kharagpur, 465-472.

[18] Kumar N, Tewari PC, Sachdeva A (2021), "Stochastic modelling and availability analysis of repairable system of a milk processing plant" Int. J. Simulation and Process Modelling, Vol. 16, No. 4, 2021.

[19] N. Kumar, P.C. Tewari, A. Sachdeva (2020) "Petri Nets Modelling and Analysis of the Veneer Layup System of Plywood Manufacturing Plant" Engineering Modelling 33 (2020) 1-2, 95-107.

[20] Kumar N, Tewari PC, Sachdeva A (2021), "Performance Modeling and Analysis of Refrigeration System of a Milk Processing Plant using Petri Nets" International Journal of Performability Engineering Volume 15, Number 7, July 2019, pp. 1751-1759 DOI: 10.23940/ijpe.19.07. p1.175117.

i Надоели баннеры? Вы всегда можете отключить рекламу.