CC BY
10
Power Stations, Grids and Systems
UDC 621.3 doi: 10.20998/2074-272X.2021.2.08
N. Benchouia, M. Saaidia
OPTIMIZATION AND RELIABILITY OF THE POWER SUPPLY SYSTEMS OF A COMPRESSOR STATION
As gas pipeline systems become larger and more complex, the importance of optimally operating and planning these facilities has increased. The capital costs and operating expenses of pipeline systems are so large that even small improvements in the use of the system can involve large sums of money. Purpose. This article proposes a method to improve the reliability and optimization of power supply systems for compressor stations. The novelty of the proposed work is the development of a new mathematical model that allows the choice of the most appropriate maintenance policies in the best way to significantly reduce costs as well as to optimize useful key performance indicators - failure rate, average time between breakdowns, the average repair time for equipment in compressor station electrical supply systems. Applying graph theory to represent this mathematical model from the schematic diagram of the different energy sources with respect to the five compressor stations is adequate. Methods. The problem that arises for the future operator or operator is, among others, how to balance two main aspects: a technical aspect and an economic aspect. The proposed methodology introduces a research algorithm to calculate the optimal values of the operating parameters of the power supply systems of compressor stations by combining technical and economic aspects in order to reduce costs and increase performance indicators. The proposed algorithm can be implemented in FORTRAN code. Results. The algorithm developed is an efficient tool for calculating maintenance costs and allows by means of programming to define the most appropriate maintenance policy. On the other hand, this technique could be used as an essential economic evaluation indicator for other equipment in order to choose among all the technically possible solutions the one which allow obtaining the best economic result. Practical value. The proposed algorithm has been examined in this third variant of the supply system with two turbogenerators. The result of the optimization shows a clear preference for selecting station C for the pipeline as this presents the minimum cost which is the definition of the algorithm optimizer. Then, it is important to adopt the most recommended maintenance policies and practices in order to ensure the availability of the power supply systems and to avoid unplanned outages with the resulting loss of production. References 12, table 2, figures 7.
Key words: power supply system, reliability, optimization, economic aspects, technical aspects, graph theory.
У Mipy того як газопровiднi системи стають dedani быьшими та складтшими, зростае значення оптимального функцюнування та планування цих об'eктiв. Каттальт витрати та експлуатацтт витрати трубопровiдних систем насттьки велию, що навть незначн вдосконалення у використанн систем можуть залучити велик суми грошей. Мета. У стaттi пропонуеться метод тдвищення нaдiйностi та оптимiзaцii систем електропостачання компресорних станцш. Новизна зaпропоновaноi роботи полягае у розробц новоi мaтeмaтично'i модeлi, яка дозволяе найкращим чином вибрати найбыьш вiдповiднi полтики техтчного обслуговування, щоб значно скоротити витрати, а також оптимiзувaти корисш ключовi показники eфeктивностi - рiвeнь вiдмов, середнш час мiж поломками, середнш час ремонту обладнання в системах електропостачання компрeсорноi станцп. Застосування теорп грaфiв для представлення ще% мaтeмaтичноi модeлi на принциповш схeмi рiзних джерел енергп щодо п 'яти компресорних станцш е достаттм. Методы. Задача, яка виникае у майбутнього або дючого оператора, полягае, серед тшого, у тому, як збалансувати два основш аспекти: техтчний аспект та eкономiчний аспект. Запропонована мeтодологiя вводить алгоритм до^дження для розрахунку оптимальних значень робочих пaрaмeтрiв систем електропостачання компресорних станцш шляхом поеднання техтчних та eкономiчних aспeктiв з метою зменшення витрат та збыьшення показниюв eфeктивностi. Запропонований алгоритм може бути рeaлiзовaний у прогрaмi на мовi програмування FORTRAN. Результаты. Розроблений алгоритм е ефективним тструментом для розрахунку витрат на техтчне обслуговування та дозволяе за допомогою програмування визначити найбыьш вiдповiдну полтику техтчного обслуговування. З тшого боку, цю методику можна використовувати як важливий показник eкономiчноi ощнки для тшого обладнання, щоб вибрати серед уЫх техтчно можливих рiшeнь те, яке дозволяе отримати найкращий eкономiчний результат. Практичне значення. Запропонований алгоритм був пeрeвiрeний у третьому вaрiaнтi системи живлення з двома турбогенераторами. Результат оптимiзaцii показуе чтку перевагу щодо вибору станцп С для трубопроводу, остльки це представляе мiнiмaльну варткть, яка е визначенням оптимiзaторa алгоритму. Тодi важливо прийняти найбыьш рекомендован полтики та практики техтчного обслуговування, щоб забезпечити доступтсть систем електропостачання тауникнути незапланованих вiдключeнь iз на^дком втрат виробництва. Бiбл. 12, табл. 2, рис. 7.
Ключовi слова: система електропостачання, надшшсть, оптимiзацiя, eKOHOMi4Hi аспекти, техшчш аспекти, теорiя графiв.
Introduction. Compressor station (CS) is an integral and an essential part of a gas pipeline, providing gas transportation by means of power equipment. It serves as a control element in the complex of buildings, belonging to the trunk gas pipeline. The pipeline operation mode is defined through the compressor station operation parameters.
Power supply system (PSS) is a combination of sources and systems of conversion, transmission and electric energy distribution. Power supply system does not usually include consumers (or electricity receivers).
The following requirements are to be met by power supply systems:
• reliability and continuity of power supply to consumers;
• quality of electric energy on consumer input;
• safety of PSS elements maintenance;
• unification (modularity, standardization);
• economic efficiency (includes such concepts as energy efficiency and energy conservation);
• ecological compatibility;
• ergonomics [1].
As natural gas pipeline systems have grown larger and more complex, the importance of optimal operation
© N. Benchouia, M. Saaidia
and planning of these facilities has increased. The investment costs and operating expenses of pipeline networks are so large that even small improvements in system utilization can involve substantial amounts of money saving [2].
For electric power supply systems, intended to provide the work of processing facilities with a continuous cycle (such systems include compressor stations of trunk gas pipelines) reliability and maintainability are considered to be the main properties. Problems of durability and safety of the system are not too much crucial. For modern electrical driven, equipped with powerful synchronous motors, problems of stability and vitality of the systems and their power supply are considered to be additional important properties [1].
In a gas transmission network, the overall operating cost of the system is highly dependent upon the operating cost of the compressor stations of the network. In fact, this compressor station's operating cost is generally measured by the quantity of the consumed fuel. According to [3], the operating cost of running the compressor stations represents between 25 % and 50 % of the total company's operating budget.
Recently, the issues of reliability improvement and configuration optimization of power supply systems of industrial facilities have been gaining significance [4]. Reliability is all that is required for a product to function without failure, or with a failure frequency low enough to be acceptable in its intended use. Its conservation concerns the Maintainability which takes care of what must be done so that a product is brought back under conditions as close as possible to those foreseen at the beginning of its operation.
Many researchers have presented and described proposed optimization and reliability methods for power supply systems of a compressor station. Literature reviews have been written to summarize the methods and the achievements. In [5] authors have illustrated the different influencing factors for the economic success of a gas compression station. Important criteria include first cost, operating cost (especially fuel cost), capacity, availability, life cycle cost, and emissions. Decisions about the layout of compressor stations such as the number of units, standby requirements, type of driver and type of compressors have an impact on cost, fuel consumption, operational flexibility, emissions, as well as availability of the station. An overview of important mathematical optimization and artificial intelligence (AI) techniques used in power optimization problems. Applications of hybrid (AI) techniques have also been discussed in [6]. The statistical data on the failures of the elements of the electrical power systems for the gas pumping compressor stations is studied in [7]. The distribution functions of operating time between failures, operating time between unplanned repairs, restoration time are chosen for power supply systems' elements. Parameters of Weibull distribution function are determined. The reliability of power supply system for gas pumping compressor station is simulated. Comparative analysis of the system reliability with hot and cold reserve is processed. The role of elements and their parameters for ensuring reliability are determined.
The rational boundaries for increasing reliability for the most important system elements are determined in [7]. In [8] authors solve the reliability design problem which is a very interesting problem often encountered in the energy industry. It is formulated as a sequence of redundancy optimization problems (ROP). The resolution of this problem uses a developing Ant Colony Optimization (ACO) method. This new algorithm for choosing an optimal series-parallel power structure configuration is proposed. It minimizes the total investment cost subject to availability constraints.
However, many of the algorithms currently used by the system operators and planners are based on heuristics and have severe limitations. Therefore, optimization algorithms used during operations need to be timely in detecting problems and suggesting corrective actions.
The goal of the paper is the proposal of a tool allowing to optimize the power supply systems of a real existing compressor station, taking into account the technical aspect and the economic aspect on the basis of a mathematical model which makes it possible to increase the reliability of the entire operation of the mechanism and to considerably ensure its availability in order to minimize the total expenditure of the electrical supply system of the BISKRA station, Algeria.
Subject of investigations. This paper carries out a comprehensive study of calculation and optimization of the power supply systems of compressor stations with the essential objective of choosing among all the technically possible solutions those which allows obtaining the best economic result.
In this article, a new flexible and efficient model and an optimization algorithm is proposed in order to solve the problem of reliability, maintainability and availability of operation in order to minimize the costs of the power supply systems of natural gas compression stations.
This paper is structured as follows: in Section 2, the description of the compressor station and the technological process used in the model formulation are presented; in Section 3, a development optimization criterion is introduced; the development of the power system optimization algorithm is presented in Section 4. The results showing the graphic presentation of the calculation and the performance of the proposed formulation are presented in Section 5. Finally, in Section 6, conclusion on the achieved results is presented.
Presentation of the compressor station. In [9] the gas pipeline GK1 (40'') GK2 (42'') is designed to ensure the connection between the departure terminal of HASSI R'MEL and the arrival terminal of SKIKDA, as well as the supply of the SONELGAZ (The Algerian Electricity production and distribution company) distribution centers in eastern Algeria.
Construction of the pipeline began in 1968 for it to be commissioned in its first phase in 1971.
In its first phase, the gas pipeline ensured a flow of 5.7*109 m3/year with no in-line compressor station (free flow).
In its second phase and with increasing energy requirements, two compressor stations were installed (stations B and D) to achieve a flow rate of 9.2*109 m3/year.
In its third phase, the gas pipeline is operated with five in-line compression stations thus ensuring maximum speed with a flow rate of 12.7*109 m3/year.
The natural gas pipe between HASSI R'MEL and SKIKDA has a length of 574.87 km. It is designed to service at an absolute pressure of 71.05±0.4 bars and a maximum temperature of 60 °C over its entire length.
The departure terminal controls the inlet pressure of 71.05±0.4 bars absolute of the pipe. The arrival terminal is able to maintain downstream pressure from 43 to 45 bars absolute. The annual flow from HASSI R'MEL is 12.7*109 m3/year (optimal conditions in summer and winter). Table 1 details the operating conditions of the five stations such as compressor suction pressure, compressor suction temperature, maximum power, etc.
Table 1
Service condition of stations
'—Station Condition A B C D E
Compressor (in service + reserve) 3+1 3+1 3+1 3+1 3+1
Gas flow per machine (kg/h) 455.93 449.96 442.46 439.80 432.30
Compressor suction pressure (bar) 50.49 48.15 48.30 48.41 50.14
Temperature compressor suction (°C) 38.06 44.86 43.94 44.60 40.93
Compressor cooling point (bar) 73 73 73 73 73
Compressor discharge temperature (°C) - - - - -
Maximum station output (bar) 71.5 71.5 71.5 71.5 71.5
Description of the technological process. The
station's gas compression system begins at the filter inlet manifold located in the northeast corner of the facility site (or refers to the north of the facility, not true north).
The gas passes through vertical filters that retain moisture and filings making the gas suitable for recompression in the station compressors to the turbocompressors (TC) suction manifold.
In [9] the «A», «B», «C» and «D» turbocompressors are individually connected to this manifold. The suction line of each compressor is 60.96 cm in diameter (see Fig. 1).
The gas is sucked into the compressor or its pressure is increased to 73 bars absolute. It is discharged into the discharge manifold through the 60.96 cm discharge line of each compressor. The discharge manifold directs gas to a calibrated orifice where the rate of flow is determined. The gas then passes into the after cooler where its temperature is reduced to a value not exceeding 60 °C.
From the coolers, the gas passes through the 101.6 cm mainline. The pressure losses in the gas refrigerants are 1.5 bars absolute; so at the exit of the station, we will have the extreme values of pressure and temperature which are 71.5 bars absolute and 60 °C.
For this technological process to be ensured, the turbocompressors must be in good working order. So the adopted power supply system plays a key role.
According to statistical calculations, failures of fuel systems have a direct influence on the reduction of the operating time of turbochargers (restarting, fuel and oil losses, etc.). This is why the analysis of adequate feeding systems for this type of process becomes an absolute necessity.
Figure 1 shows the technological process of the compressor station. We find that failures in the power supply system directly affect the decrease in uptime of turbocompressors.
REF
Raclure station
r*-
Cooler
Event
[y
I Valve by pass
CI+O+IAfl
station
Event Discharge manifold
ollec tor Aipirati
u
D
A
C
1
B
\J
J
1
ASP
Gas filters
Event
1
Event
skid gaz
Fig. 1. Technological process of a compressor station
Proposed optimization methodology. The
methodology of the proposed study is based on the calculation and optimization of the power supply systems of compressor stations on the basis of two main aspects: a technical aspect and an economic aspect.
Technical aspect. The technical aspect is the ability of the power supply system to provide the compressor station with the electrical energy of a required quality without interruption; which means to reduce the damage due to accidental failures (interruption in electrical energy) by increasing the reliability of the power supply system while maintaining the economic conditions surrounding the problem. The process of reliability evaluation may be done using two major groups of statistical indicators: X, MTBF (Mean Time Before Failure) and MTTR (Mean Time To Repair) are the two main indicators of reliability used industrially [10].
Failure rate X represents the failure rate or the damage rate. It characterizes the speed of variation of reliability over time for a given work period, total duration in active service
Total number of failures during service
A —-. (1)
Total operating time
In practice, the failure rate can be constant, but also increasing or decreasing over time, with gradual change and without discontinuity.
The failure rate is the probability that an entity will lose its ability to perform a function during the interval, knowing that it has not failed between [0, /]; we note it:
X(t) — ——. (2)
v' MTBF
MTBF is often translated as being the average of good functioning but represents the average of the times between two failures (TBF):
ZTBF
MTBF = -
N
(3)
where N is the number of failures.
n
MTTR is average time to repair which expresses the average time for repair spots. It is calculated by adding the active times maintenance as well as additional maintenance times, all divided by the number of interventions:
jLyrrrm S intervention time for N failures MUR =-, (4)
N
repair rate n is
1
(5)
MTTR
Economic aspect. In the economic study comparing the different variants of the power supply system, the factors directly influenced by reliability considerations are investments (installation expenditure), on one hand, and maintenance expenses, supervision expenses, expenses due to loss of electrical power and transformers and depreciation expenses on the other hand. These expenses are called operating expenses [11].
Therefore, the solution to be adopted must minimize the total expenditure on the power supply system in question, which is given by the following formula:
Ct = Pn .Cmst + Cop + D ^ min, (6)
where Pn is the normative coefficient of investment efficiency; Cinst is the installation (capital) expenses for power system components by line; Cop is the operating expenses; D is the damage due to accidental power system failures.
Pn depends on the period of depreciation of the invested capital as follow:
Pn = — = 0.12.
n t
Tri
where the period of depreciation as follows: Td=(8 +10) , year. Cinst is given by the following formula:
C,
inst-,
= Io ■ l .
(7)
(8)
(9)
where I0 is the kilometric price, (DA/km, DA - Algerian Dinar) and l is the length of line, km. For transformers:
C,
inst,
TR
= N ■ I
TR .
(10)
where N being the number of transformers to install and ITR is the price of a processor, DA. For turbogenerators:
Cin
1TG
= N ■ I
TG
(11)
where N is the number of turbogenerators; ITG is the price of a turbogenerator, DA.
Cop is given by the following formula:
Cnn = Co
' ^ dan ^ Cm
(12)
where Closses is the expenditure due to loss of electrical energy in the line and transformers, can be represented as follows:
Closses
= (Awi + Awtr )• Co, (13)
where Awl represents the losses of electrical energy in the line:
Awl =
Fn
r0 ■l ■ Tmax 10
(14)
where Smax is the maximum apparent power passing through the line (in MVA) depending on the parameters: Vn is the electrical power transmission rating, kV; r0 is the
specific resistance of the line, Q/km; l is the length of line, km; Tmax is the maximum time of loss of electrical energy during one year, h/year; AwTR is the losses of electrical energy in the transformer:
Awtr = Apo • Tf + APa • K.f • t
max '
(15)
where AP0 is the active power losses in the magnetic circuit (not depending on load), kW; Tf is the transformer operating time during one year (Tf = 8760 h); APa is the active power losses in windings created by Joule effect, kW; K is the transformer load factor (Kl = 0.7); C0 is the cost of one kilowatt hour of electrical energy, DA/kWh.
Annual depreciation expenses dan to offset expenses due to wear and tear of power system components is given by the following formula:
7 _ ^V J
an = 100
■ I.
(16)
where a is the depreciation rate; it varies from one element to another (for the line a = 2.4 %; for the transformer a = 6.4 %; for the turbogenerator a = 6.5); I is the clean investment; Cm is the maintenance, inspection and supervision expenses. These are directly related to the degree of reliability and safety level imposed on the power system:
Cm * 0.20 • dan . (17)
Damage due to accidental power system failures D: D = 1.08 • Awa • C0, (18)
where 1.08 is the reserve coefficient which takes into account the accidental downtime of less than 0.1 hours; Awa is the electrical energy not delivered for one year due to accidental failure of the power supply system, kW-h/year.
Awa = Pm • 8760 • Q • e • Pm • Pq, (19)
where PM is the maximum active power (calculated) of the compressor station, kW; Q is the total probability of accidental failure of two power system circuits.
Practice has shown that accidental failures follow an exponential law:
Q = t-11 - e
„- A
/8760 .
(20)
where t is the total repair time of the power supply system expressed in hours; X is the total failure rate of the power supply system expressed in 1/year; e is the coefficient of the carried power limitation in the damage regime:
p — p
e = pm Pa , (21)
PM
Pa = 1 .4 • SnTR cos^, (22)
where Pa is the allowable power of the transformer in the damage regime (in our study we considered the failure of two circuits of the power supply system, (Pa = 0 ^ s= 1); pm and Pq are respectively the filling coefficients of the monthly and daily load diagrams for a compression station: Pm = 0.97; Pq = 0.94.
Development of power system optimization algorithm. It is based on the graph theory which consists of developing a mathematical model based on the layout diagram of the different power sources compared to the five compressor stations. Figure 2 illustrates the graphic presentation of power supply system of compressor stations.
2
S
max
Y3 Y17
. .. .... . Compression Station
/4 \------1 21 I I I Electric Post
^^ Turbogenerator
_^^ --Existing Electric Line
¡f!) N-x ^ s --------New Electric Line
X17 X3 X
Fig. 2. Graphic presentation of power supply system of compressor stations
The power supply system is completely represented mathematically by a matrix A (N, M) which determines the connection between the compressor stations and the power sources (existing power line presents in Fig. 3).
This mathematical model allowed us to develop a calculation flowchart taking into account three essential conditions:
• substations (power sources) must have a reserve of electrical energy;
• a compressor station can only be powered from two power sources;
• the distance between the power source and a compressor station L must be less than the critical distance LCR which depends on the nominal voltage of electric power transmission and power:
L(i, j)< Lcr , (23)
where
L(, j) = - Xj ) + ( - yj ) , (24)
where (X,, yi) is the coordinates of the ith electrical post or compressor station; (Xj, yj) is the coordinates of jth the electrical post.
Power sources
Compression station N 6 7 8 9 - - - - M
1 0 1 0 0 0 1 0 0 0
2 1 0 0 1 0 0 0 0 0
3 0 0 1 0 1 0 0 0 0
4 0 0 0 0 0 0 1 1 0
5 0 0 0 0 1 1 0 0 0
Power sources 6 -1 0 0 -1 0 0 -1 0 0
7 0 -1 0 0 -1 0 0 0 0
8 0 0 -1 0 0 0 -1 0 0
l
l
N
Optimization criteria:
Ct = P n'Cfnst + C0p + D > min
Ct - total expenditure, DA; Pn - normative coefficient, Pn = 0.12; Cinst - installation expenses, DA; Cop - operating expenses, DA;
Cop Closses + dan + Cm
Ci0sses - expenses due to losses of electrical energy
in lines and transformers;
dan - annual depreciation expenses;
Cm - maintenance expenses, Cm = 0.20-dan;
D - damage due to accidental failures of PSS, DA.
Y
1-1 if (At, Aj) e E(G) - points connected by an existing line A(i, j) = 'S 0 if (Aj, Aj) t E(G) - no connections between points I 1 if (Aj, Aj) e E(G) - points connected by a new line
Fig. 3. The developed mathematical model of power supply system of compressor stations (where A(i, j) = -1 is connection between power sources (existing line); A(i, j) = 0 is no connection; A(i, j) = 1 is connection between power sources and compressor stations (new line)
Figure 4 shows the flow chart of the algorithm for optimization of «-electric power supply systems of compression stations. It allows, in its first part, to calculate the installation and operating expenses by different variants of the power supply system and in the second part, it allows us to calculate the damage due to accidental failures by different variants of the power supply system. This allows us to choose at the same time the most optimal variant of the power supply system which total expenses will be minimal.
Calculation of reliability parameters. The 100 % confidence in electrical equipment does not exist. So the concept of reliability only gives us the degree of confidence in this equipment. It leads to studies of failure rate (A), repair time (t), time of proper operation, etc. It becomes the link between the technological aspect and the economical aspect [11, 12]. For this reason, the reliability of an electrical power system is the probability
that it will perform its mission satisfactorily and under specified environmental conditions.
Considering reliability economically as high availability is expensive. It is certain that the cost price of the power supply system has to be increased if we want the failure rate of the system to be reduced.
Figure 5 shows the expenditure curves according to reliability. This approach attempts to determine the appropriate sums to invest in reliability is to compare the costs caused by failures (that is, the costs resulting from poor reliability) with the costs necessary to provide greater reliability. It is clear when increasing the reliability of the power system it means reducing the risk of its failure (reducing damage).
This power supply system is a set of electrical equipments belonging to the group of repairable elements. Therefore; reliability is characterized by the failure rate (A) and repair time (t).
Fig. 4.The proposed and developed optimization algorithm of the power supply system
k Expenses
Expenses + Damage
Expenses
Damage
-►
Optimal Reliability
Fig. 5. Expenditure curves according to reliability [11]
Then the proper functioning of the power supply system results from the proper functioning of the various
elements that compose it. In other words, the overall reliability requirement is reflected in the form of specific reliability requirements for each element.
These elements can be mounted in only two methods: in series or in parallel (or mixed). Three variants of the power supply system were considered for compressor stations:
a) from two electric lines;
b) from a single electric line and a turbogenerator (stand-alone power plant);
c) from two turbogenerators.
Our case study is based on this third variant of the supply system, i.e. from two turbogenerators.
Figure 6 shows the calculation of the reliability parameters X, t of the power supply system of compressor stations from two turbogenerators.
¿9 i Xts [-L,
5 Ale in □ -> T
o
nr
© ©
i
Fig. 6. Calculation of the reliability parameters X, t of the power supply system of compressor stations for the three variants
First variant of the power supply system - from two power lines.
First transformation.
X1,2 = X1 • X2 • (t1 +t2 ) = X9; (25)
_T\ ■ T2 _
T1,2 =-= T9 .
T1 ■ T2
(26)
where X1 and X2 are the failure rates of post 1 and post 2 respectively; ti and t2 are the repair times of post 1 and post 2 respectively;
(27)
(28)
X3,5 = X3 + X5 + X7 = X11; X4,6 = X4 + X6 + X8 = X12 ;
X3 ■ T 3 + X5 ■ T 5 + X7 ■ T 7
T 3,5 =
T 4,6 =
X3 + X5 + X7 X4 ■T4 + X6 ■ T6 + X8 ■ T8
(29)
(30)
X4 + X6 + X8
where X7 and X8 are the failure rates of the circuit breaker 0.4 kV; X3 and X4 are the failure rates of lines L1 and L2; X5 and X6 are the failure rates of transformers 1 and 2; t3 and t4 are the repair times of lines Li and L2; t5 and t6 are the repair times of transformers 1 and 2. Second transformation.
Xeq1 = X1,2 + K0(X3 + X4) = X13 ; _X1,2 • T1,2 + K0((3 + X4)t3.
T =-
eq1
X1,2 + K0 ■(X3 + X4 )
=T
13
Xeq2 = X3,5.X4,6(T3,5 T3,5 -r4,6
+T
=X
14
"eq2
" = T14,
(31)
(32)
(33)
(34)
r3,5 +r4,6
where K0 is the coefficient of the climatic conditions influence; K0(X3+X4) is the failure rate of the lines L1 and L2 simultaneously; t0 is the repair time of the two lines
T0 = T3 = T4.
Third transformation.
X15 = X13 + X14 ; (35)
. X13 • T13 + X14 • T14
T15 ="
(36)
X13 + X14
Finally, the expression of the probability of failure of the power supply system from two electric lines can be represented as follows:
Q = T15 ■Ii - e- X15
78760
(37)
Second variant of the power supply system -from a single electric line and a turbogenerator.
First transformation. X7 = X1 + X2 + X3 + X4 ; Xg = X5 + X6 (38)
A1 •T1 + A2 • ^2 + ^.3 • 73 + A4 • T4
T8 =
+ ^2 + + ^4 ^5 ■ ^5 +^5 ■T6
^5 +^6
(39)
(40)
Second transformation.
X7 = X7 • X8(t7 + T8); 79 =±Ll*-. (41)
t7 + t8
The expression of the probability of failure of the power supply system is:
Q = t9 • (1 — e ^^ ;/8760.
Third variant of the power supply system two turbogenerators.
First transformation.
X5 = X1 + X2; _ X1 • T1 + X2 • t 2 .
X6 = X3 + X4 , T = X3 ■ T3 + X4 ■ T 4
X1 + X2
X3 + X4
(42) from
(43)
(44)
where X1, X3 and X2, X4 are the failure rate turbogenerator and the circuit breaker 0.4 kV respectively; t1, t3 and t2, t4 are the repair times of the turbogenerator and the circuit breaker 0.4 kV respectively.
Second transformation.
X7 = X5 ■ X6 (t5 + T6 ); T7 =
T5 ■ T6
(45)
t5 + t 6
The expression of the probability of failure of the power supply system is:
Q = t 7
1 - e X I/8760.
(46)
The general formula of damage caused by accidental power system failures for all three variants is:
D = 1.08 • Pm • 8760 • Q • e • Pm • Pq • Q, DA. (47)
The Table 2 illustrates the reliability parameters of electrical equipment for different voltages.
Table 2
Reliability parameters of electrical equipment for different voltages
Electrical Failure rate X, MTBF, Repair time MTTR,
equipment 1/year h t, h h
Airline (100 km)
30 kV 2.2 0.454 5.6 0.178
60 kV 2.0 0.5 5.6 0.178
220 kV 1.4 0.714 6.5 0.153
Circuit breaker
(6 -10) kV 0.005 200 10 0.1
30 kV 0.005 200 10 0.1
60 kV 0.005 200 10 0.1
220 kV 0.02 50 24 0.041
Transformer
(6 -10) kV 0.023 43.478 70 0.014
30 kV 0.018 5.555 90 0.011
60 kV 0.02 50 100 0.01
220 kV 0.02 50 100 0.01
Turbogenerator
0.4 kV 5.80 0.172 70 0.014
where X1 - X4 are the failure rate of the electrical post, overhead line, transformer and the circuit breaker 0.4 kV respectively; t1 - t4 are the failure rate of the turbogenerator and the circuit breaker 0.4 kV respectively; X5 and X6 are the failure rate of turbogenerator and the circuit breaker 0.4 kV respectively; t5 and t6 are the repair times of the turbogenerator and the circuit breaker 0.4 kV respectively.
Graphical presentation of the calculation. The
operating procedure for the calculation of the optimization algorithm of the power supply systems of the five compressor stations has wide limits by combining the different variants of the power supply system that may exist.
In our case, as an explanation, we are limited to three variants of the electrical supply system for two compression
5
6
7
stations, knowing that each compression station has two independent power stations (turbogenerators).
Figure 7 clearly, shows the graphic presentation of the calculation of the three variants of the electrical supply system for two compression stations.
V
rn ¿fe
A ^
A \l
ÓO
V
A ^
A Nj
óo
ÉD ^ EL
A N
Fig. 7.Graphic presentation of the calculation
First variant. By keeping the local power supply system from two autonomous power plants of each compressor station, the calculation gave us the total expenses Cfl.
Second variant. By replacing a stand-alone power plant with a electric line, that is to say, power is supplied from a substation and a stand-alone power plant, the total expenditure which was found to be Ct2 is lower than the total expenditure Cfl (Cfl > Ct2).
Third variant. The power supply to a compressor station is provided by two independent electric lines, which allowed us to obtain the total expenses as Ct3 below the total expenses Ct2 (Cfl > Ct2 > Ct3), the variant of the most optimal power supply system with the minimum total expenditure (Ct ^ min).
Calculation procedure on the computer.
Initial data.
A. Expenditure calculation.
1. see if A(i, j) =1
2. calculation of L(i, j)
3. see if L(i, j) < Lcr
4. calculation of installation and operating expenditure for L(i, j) (post j ^ CS)
5. if L(i, j) =0
6. calculation of operating and installation expenses for turbogenerators (TAj ^ CSj).
7. if A(i, j) = -1
8. calculation of operating expenditure for the existing line (post i ^ post j)
« m
9. calculation: Cp(i, j)= 2 Z Cp(i, j). (48)
i=\}=1
B. Damage calculation.
1. if A(i, j) = 1
2. see if K = 2
3. calculation of damages for the two-line PSS.
4. see if K = 1
5. calculation of damage for the single-line PSS and a turbogenerator.
6. see if K = 0
7. calculation of the damage for the PSS with two turbogenerators
8. calculation: D(i) = 2 D(), (49)
i=i
9. sum total expenditure:
n m 5
D(i, j)=ZZ Cp(i,j)+2D(i), (50)
/=i;=i i=i
10. calculation of total expenditure for each variant according to the matrix (mathematical model of PSS chosen for the five (5) CS).
11. take the most optimal variant, the total expenditure of which will be minimal.
Conclusion.
This paper proposed a recent optimization technique based on the proposal of an algorithm combining two technical and economic aspects to help the operator to minimize the failures of the power supply systems directly influencing the reduction of the uptime of the turbocompressors (restart fuel and oil losses, etc.). In this study, we calculated the reliability parameters of three variants of the power supply system that were considered for compressor stations, from two electric lines, a single electric line, and a turbogenerator. Then, we calculated the damage. A graphical presentation by graph theory of this developed model is adequate.
From the calculation results, it can be concluded that currently taking into account the economic criterion and the initial data retained, the supply of electrical energy to the gas compression station «C» located at CHAIBA, is carried out from two autonomous sources, but from the point of view of reliability (technical criteria) or clearly sees that the power supply of the above-mentioned station, from two independent external lines is imposed.
From the results of the research, it can be said that the presented algorithm, developed in the FORTRAN programming language, greatly facilitates the calculation of the damage to the power system of any compressor station.
In the future, with the construction of new distribution stations near the gas compressor stations and the actual data, it can be seen that the variant of the supply system from two independent external lines is the most optimal. This allowed us to calculate the preventive power supply of two independent substations and impose the appropriate maintenance policies.
Conflict of interest. The authors declare that they have no conflicts of interest.
REFERENCES
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Received 20.12.2020 Accepted 25.01.2020 Published 05.04.2021
Nedjem-Eddine Benchouia ', Ph.D., HDR, Mohamed Saaidia 2, Ph.D.,
1 Department of Mechanical Engineering, Mohamed-Cherif Messaadia University,
Souk Ahras mailbox 1553, Souk-Ahras, 41000, Algeria, e-mail: [email protected]
2 Department of Electrical Engineering, Mohamed-Cherif Messaadia University,
Souk Ahras mailbox 1553, Souk-Ahras, 41000, Algeria, e-mail: [email protected]
Appendix 1 - Proposed program in FORTRAN code
! PSS SC Program
Dimension X(9),Y(9),W(11),V(11),pril(11,9),uam(11,9),
+upe(11 ,9),uen(11,9),d1(11,9),d(2),prixg(11,9),td30(9),
+tao30(9),tdl30(11,9),tdc30(11,9),taoc30(11,9),t30(2),
+s30(2),e30(2),d30(2),X30(2),h30(2),C30(2),
+prob(2)
Integer a(11,9)
Real l(11,9),lcr1
Data td30/0.,0., 0.,0., 0.5,0.5, 0.5,0.5,0.5/
+tao30/0.,0., 0.,0., 0.02,0.02,0. 02,0.02,0.02/
Data X/55.,55.,89.,89.,32.5,115.,118.,27.5,62.5/
+Y/62.5,62.5,97.5,97.5,82.5,82.,107.,161.5,152./
Data W/55.,89.,55.,55.,89.,89.,32.5,115.,118.,97.5,62.5/,
+V/62.5,97.5,62.5,62.5,97.5,97.5,82.5,82.,107.,161.5,152/
Data Pril1/20./,Pritr1/100./,Alp1/0.02/,ALP2/0.06/,
+ALP3/0.07/,prig/3500./,r01/0.77/,R02/0.64/,taom/5948./,
+delp/3. 1/,delpc/18./,ch/0.7/,betm/0.97/,betq/ 0.94/,
+tdtr1/0.02/,tddis/0.002/,tdg/5.8/,taol1/5.6/,
+taodis/1.75/,taog/70./,pm/2214.24/,epsi/1./,u1/30./,
+s/1232.5/,u2/60./,c0/0.00055/,taotr1/90./,tdl1/2.2/
Data a/1,0,-1,0,0,0,0,0,0,0,0,0,0,0,-1,0,0,0,0,0,0,0,0,0,
+0,0,-1,0,0,0,0,0,0,0,0,0,0,0,-1,0,0,0,0,0,1,0,0,0,0,
+0,-1,0,0,0,0,0,-1,0,0,0,0,0,-1,0,0,0,0,0,0,0,0,0,0,-1,
+-1,0,0,0,0,0,0,0,0,0,0,0,-1,-1,0,1,0,0,0,0,0,0,0,0,
+-1/
Data lcr1/50./
Open (unit=15,file='bou.d',status='unknown' ) J=1
6 do 4 i =1,2 If(a(ij).eq.0) goto 4
l(ij) = sqrt((x(j)-w(i))**2+(y(j)-v(i))**2)
if(l(ijj).eq.0.) goto 15
if(l(ij).gt.lcr1) goto 4
pril(ij)=pril1*l(i,j)+(pritr1)
uam(i,j)=(alp1*(pril1*l(i,j))+(alp2*pritr1))
uen(Ij)=0.2*uam(I,j)
upe(Ij)=(((s**2/u1**2)*r01*l(I,j)*taom)+
+((delp*8760)+(delpc*ch**2*taom)))*c0
d1(I,j)=0.12*pril(I,j)+uam(I,j)+uen(I,j)+upe(I,j)
write(15,12)i,j,d1(I,j)
goto 4
15 prixg(I,j)=prig
Uam(Ij) = alp3*prixg(I,j)
Uen(I,j)=0.2*uam(Ij)
d1(I,j)=0.12*prixg(I,j)+uam(I,j)+uen(I,j)
write(15,12)Ij,d1(I,j)
12 format(3x,»d1(«,i2,»,»,i2,»)= «,e11.4) 4 continue
J=j+1
If(j.le.9)goto 6 J=1
3 do 7 i=3,11 If(a(I,j) eq.0) goto 7
L(Ij)=sqrt((x(j)-w(i))**2+(y(j)-v(i))**2)
D1(I,J)=((s**2/60**2)*r02*l(Ij)*taom)*c0
Write(15,12)I,j,d1(I,j)
13 format(3X,»d1(«,i2,»,»,i2»,)=«e11.4)
7 continue J=j+1
If (j.le.9) goto 3 I=1 80 k=0 Do 10 j=1,9 If(a(Ij).ne.1) goto 10 K=k+1
If(L(I,j).ne.0) goto 10 K=K-1 10 continue If(k.eq.2.) goto 14 If(k.eq.1) goto 16 If(k.eq.0) goto 18
14 do 20 j=1,9 If(a(Ij).ne.1) goto 20 If(l(I,j).gt.lcr1) goto 20 If(l(I,j).eq.0) goto 20 tdl30(Ij)=tdl1*l(Ij)/100 tdc30(I,j)=tdl30(I,j)+tdtr1+tddis taoc30(Ij)=((tdl30(I,j)*taol1)+(tdtr1*taotr1)+ +(tddis*taodis))/tdc30(I,J)
20 continue
T30(i)=0
S30(i)=0
E30(i)=1
D30(i)=1
X30(i)=1
H30(i)=1
C30(i)=0
Do 30 J=1,9
If(a(I,j).ne.1) goto 30
If (l(I,j).gt.lcr1) goto 30
If (l(Ij).eq.0) goto 30
t30(i)=t30(i)+tdl30(I,j)
e30(i)=e30(i)*td30(j)
s30(i)=s30(i)+tao30(j)
d30(i)=d30(i)*tao30(j)
c30(i)=c30(i)+taoc30(Ij)
h30(i)=h30(i)*taoc30(Ij)
x30(i)=x30(i)*tdc30(Ij)
30 continue
Td9 =e30(i)*s30(i)/8760
Td34=0.2*t30(i)
Td12=td9+td34
Tao9=d30(i)/s30(i)
Tao12=((td9*tao9)+(td34*tao34))/td12 Td13=x30(i)*c30(i)/8760 Tao13=h30(i)/c30(i) Td14=td12+td13
Tao14=((td12*tao12)+(td13*tao13 ))/td14
Prob(i)=(tao14*(1-exp(-td14)))/8760
D(i)=1.08*pm*8760*prob(i)*epsi*betm*betq*c0
Write(15,26) I,d(i)
26 format(3x',d(',i1,')=',e11.4)
Goto 100
16 do 60 j=1,9
If(a(I,j).ne.1) goto 60
If(l(I,j).gt.lcr1) goto 60
If(l(I,j).eq.0) goto 60
Tdl30(Ij)=tdl1*l(Ij)/100
Tdc30(I,j)=tdl30(Ij)+td30((j)+tdtr1+tddis
Taoc30(Ij)=((tdl30(I,j)*taol1)+(td30(j)*tao30(j))+
+ (tdr1*taotr1 )+(tddis*taodis))/tdc30(I,j)
60 continue
Do 107 j=1,9
If(a(I,j).ne.1) goto 107
If(l(I,j).gt.lcr1) goto 107
If(l(I,j).eq.0) goto 107
Td8=tdg+tddis
Tao8=((tdg*taog)+(tddis*taodis))/td8 Td9=(tdc30(I,j)*td8)*(taoc30(Ij)+tao8)/8760 Tao9=taoc30(Ij)*tao8/(taoc30(Ij)+tao8) 107 continue
Prob(i)=(tao9*(1-exp(-td9)))/8760
D(i)=1.08*pm*8760*prob(i)*epsi*betm*betq*c0
Write(15,26)I,d(i)
Goto 100
18 td5=tdg+tddis
Tao5=(tdg*taog+tddis*taddis)/td5
Td7=(td5**2)*(tao5+tao5)/8760
Tao7=tao5/2
Prob(i)=(tao7*(1-exp(-td7)))/8760 D(i)=1.08*pm*8760*prob(i)*epsi*betm*betq*c0 Write(15,26) I,d(i) 100 i=i+1 If(i.le.2) goto 80 Close (unit =15) Stop End Result
d1( 1, 1)= 0.7140E+03 d1( 1, 5)= 0.1281E+06 d1( 2, 6)= 0.1288E+06 d1( 3, 1)= 0.0000E+00 d1( 4, 2)= 0.0000E+00 d1( 5, 3)= 0.0000E+00 d1( 6, 4)= 0.0000E+00 d1( 7, 5)= 0.0000E+00 d1( 8, 6)= 0.0000E+00 d1( 8, 7)= 0.2224E+05 d1( 9, 7)= 0.0000E+00 d1(10, 8)= 0.6184E+05 d1(11, 8)= 0.3204E+05 d1(11, 9)= 0.0000E+00 ,d(1)= 0.2011E+00 ,d(2)= 0.2011E+00
How to cite this article:
Benchouia N., Saaidia M. Optimization and reliability of the power supply systems of a compressor station. Electrical Engineering & Electromechanics, 2021, no. 2, pp. 54-63. doi: 10.20998/2074-272X.2021.2.08.
