Reliability modeling and evaluation of sulaimani erbil electrical power system

1 Abstract-The work presented in this paper deals with the reliability evaluation of Sulaimani-Erbil electrical Power System by two different techniques, minimal cut set and disjoint technique. Computer program is written in Basic language in order to implement tie set and cut set algorithms for the evaluation of the unreliability index of the power network. Keywords-Reliability Modeling, Reliability indices, Graph Theory, Disjoint Technique. I. INTRODUCTION ower system is always consists of a large number of components which are interconnected in some purposeful way. The reliability of a power system depends on the reliability of its components as well as its configuration. In system reliability studies, the goal is to predict suitable reliability indices for the system based on the component failure data and system design [1]. A complete and accurate reliability model should be able to represent the variation characteristics of the system interested for all aspects of performance. Selection of the actual form and the type of the reliability model depends upon a large number of factors which should be carefully examined during the formulation process of the reliability analysts. The first factor which influences the selection of the reliability model is the system functional arrangement and the second factor arises from the types of variation which may take place in the performance aspects of the various elements of the system [2].In general, the system is of two types (depending on the structure of the system), a simple structure system and a complex structure system. The purpose of investigating the reliability for the area of Sulaimani-Erbil electrical power system is that: i) This system has been operated for more than 10 years as a split network due to the political and economical sanction against the last regime of Iraq in the Kurdistan region. ii) UN agencies were responsible to develop the network due to 986 UN resolution of oil for food program, and the agency UNDP was in charge of a large number of rehabilitation program and iii) It was necessary to identify the system maintenance requirements and to specify the weak points of the network and to list their priorities. II. DESCRIPTION OF SULAIMANI-ERBIL ELECTRICAL POWER SYSTEM Prior to about 1990, there were twelve 132 kV tie lines to the region from the other Governorates of Iraq. Now, there are only two 132 kV circuits which connect Dohuk Governorate to Mosul region. At present, there is no any connection to Erbil and Sulaimany Governorates from the national grid [3]. The energy supply to all three Governorates is restricted due to the shortages of power supply and even the available supply is not reliable due to the present network situation. The power network of Governorates Erbil and Sulaimani had been cut off from the national grid. The power supply of the two Governorates had to rely on the two hydropower stations at Derbandikhan and Dukan, located in the Sulaimani region with the only one 132 kV line connecting Dohuk with the original national grid. However, the electrical power supply of this line was also limited, infrequent and unreliable. The capacities of the power stations installed in Dokan and Derbandikhan are (5 x 80 MW) and (3 x 83 MW) respectively, which are insufficient to meet the power demand [4]. To improve the condition of power supply for these three governorates, a 29 MW Diesel power plant was installed in each governorate (Sulaimany, Erbil and Dohuk) [5]. The Sulaimani-Erbil 132 kV transmission system consists of 8 lines whose length varies between 25 and 99 km. III. TIE SET AND CUT SET METHOD A tie set of a network is a subset of edges (representing components) that constitutes a path from input to output. If all the components of the tie set operate, the overall system operates properly. If no node is passed through by more than one time when tracing the tie set, such a tie set is called the minimal tie set. In other words, if any one of the components of a given minimal tie set is removed, the remaining set is no longer a tie set. A cut set is a subset of system components which, when failed, causes failure of a system. In terms of a reliability network, the definition can be interpreted as a set of components which must fail in order to disrupt all paths between the input and output of the reliability network. The system reliability can be determined from the tie set and the cut set but the cut set method is more powerful than the tie set method in evaluating the reliability of a system for the following two reasons [6-7]: 1) It can be easily programmed with digital computer for the fast and efficient solution of any general network. 2) The cut set is directly related to the modes of system failure and therefore it is easy to identify the distinct and discrete ways in which a system may fail. The minimum subset of any given set of components which can cause system failure is known as a minimal cut set. A minimal cut set is a set of system components which, when failed, cause failure of the system but when none of the component of the set fails, the system will not be failure [7]. Asso R. Majeed, Ghamgeen Izat Rashed, S.J.Cheng, Senior Member, IEEE Reliability Modeling and Evaluation of Sulaimani – Erbil Electrical Power System P 1-4244-0493-2/06/$20.00 ©2006 IEEE. 2 Table 1 Networks information No. of cut sets No. Network No .of nodes No. of braches No .of Paths No .of minimal paths 1 st order 2 nd order 3 rd order Reliability Unreliability 1 Fig.2 6 9 13 13 0 2 17 0.999797 0.000203 2 Fig.3 8 12 26 26 0 3 35 0.999695 0.000305 3 Fig.4 12 20 164 150 0 2 39 0.999797 0.000203 The following definition of minimal cut set is also appropriate: If {A} is a cut set and no subset of {A} forms a cut set, then {A} is a minimal cut set [8]. IV. APPLICATION OF MINIMAL CUT SET The following example is used to illustrate the algorithm which can be used to obtain the minimal cut sets. Considering the bridge type network shown in Fig.(1-a)[7],the minimal tie set is made up of components: 3524514231 X and ,, XXXXXXXXX , as shown in Fig.(1-b), which means that the minimal tie set can be represented by Eqn.1: ) 1 .() .()()()( 3524514231 XXXXXXXXXXS ∩∩∪∩∩∪∩∪∩= Similarly, the minimal cut set is made up of components, 3524514321 X and ,, XXXXXXXXX , as shown in Fig.(1-C). Thus, it can be represented by Eqn.2 ) 2 () .()()()( 3524514321 XXXXXXXXXXS ′ ∩ ′ ∩ ′ ∪ ′ ∩ ′ ∩ ′ ∪ ′ ∩ ′ ∪ ′ ∩ ′ = Therefore, employing the minimum-cut-set method, the unreliability of the system is represented by Eqn,3: )()( )()()()()( 3121 43214321 EEPEEP EPEPEPEPEEEEPQ ∩−∩− +++=∪∪∪= )()()()( 43423241 EEPEEPEEPEEP ∩−∩−∩−∩− )()()( 431421321 EEEPEEEPEEEP ∩∩+∩∩+∩∩+ )3) (()( 4321432 EEEEPEEEP ∩∩∩−∩∩+ where 211 )( XXEP ′ ∩ ′ = 432 )( XXEP ′ ∩ ′ = 4513 )( XXXEP ′ ∩ ′ ∩ ′ = 3524 )( XXXEP ′ ∩ ′ ∩ ′ = 542143213524514321 XXXXXXXXXXXXXXXXXXQ ′′′′ − ′′′′ − ′′′ + ′′′ + ′′ + ′′ = )4 .( 2 54321435243515321 XXXXXXXXXXXXXXXXX ′′′′′ + ′′′′ − ′′′′ − ′′′′ − From this example, it is able to describe the algorithm used to form the minimal cut set as follows: 1) Deduce all minimal paths. 2) Construct an incidence matrix that identifies all component in each path. 3) If all elements of any column of the incidence matrix is non-zero, the component associated with that column forms a first order cut. 4) Combine two columns to form a second order cut. Elimination any cut containing first order cuts to give the second order minimal cuts. 5) Repeat step (4) with three columns at a time to give third order cuts and to eliminate any cuts containing first and second order cuts; and 6) Continue this procedure until maximum order of cut has been reached. Only the first, the second and the third order cut sets are considered in the current investigation. Two basic approximations are used to deal with the evaluation of power system reliability by the minimal cut set: 1) The first approximation is that Eqn.3 is a precise representation of the minimal cut set. However, as this is a very complicated equation, it is approximated by the following simplified form: )5) (()()()( 4321 EPEPEPEPQ +++≅ For this particular case the following representation can be obtained: )6 ( 3524514321 QQQQQQQQQQQ +++= If the terms in the right hand side of Eqn.6 are identical, the system unreliability becomes: )7( 22 32 QQQ sys += 2) The cut sets of high orders are neglected because the probability of their occurrence becomes relatively very small. Different networks shown in Fig.2-4 are solved using the above mentioned method. The results are given in table 1. 1 3 2 4 5 (a) 1 3 2 4 1 45 2 5 3 (b) 1 2 3 4 1 4 5 2 3 5 E1 E2 E3 E4 (c) Fig.(1) Reliability block diagrams showing bridge arrangement and its equivalents: a) bridge-type network; b) equivalent minimum-tie set diagram; c) equivalent minimum-cut set diagram 3 Read Input Data : 1-Number of Nodes 2 -Number o f Branches 3-Incidence an d Connectio n Ma trix Subroutine Pr ogram f or find ing all pa ths in th e system Subroutine Pr ogram f or finding minim al paths in the system Subroutine Pr ogram f or constructing incide nce matrix and from it minimal cutsets finding for the system Subroutine Pr ogram f or finding reliability of the system by using approxima tion metho d Printin g Resul ts Fig.5 Program Flowchart for Reliability Evaluation by using cut set method V. CONNECTION AND INCIDENCE MATRIX The connection matrix is defined as an analytic correspondence of the system configuration and has a size of kk × . The incidence matrix identifies all components between any two nodes. VI. SOFTWARE DEVELOPMENT For the purpose of reliability evaluation, a software package programmed in BASIC language is developed. The flowchart of the program is shown in Fig.5. The program consists of two parts. The first part makes the qualitative evaluation and second part makes the quantitative evaluation. In the first part the software package, the following steps are included: 1-Enter the number of nodes and the number of branches of the system. 2-Enter the connection matrix and the incidence matrix which can be used to identify each element between two nodes. 3-Establish the subprogram for finding all paths in the network. 4-Establish the subprogram for finding all minimal paths of the network from the paths obtained in step 3 by removing all paths that have a path sub set. 5-Construct the incidence matrix which can be used to identify all components in each path. 6-Form the minimal cut set from the incidence matrix obtained in step 5. In the second part of the software package, the quantitative steps are performed for reliability evaluation of the system from the minimal cut set by use of the approximation method mentioned above. VII. Disjoint Technique In a generalized network, the terminal pair reliability expression is usually derived from the logic diagram of the system by the following two steps [9]: 1) All minimal paths or cut sets are determined. 2) The system success / failure function is changed into reliability expression using probability theory, Boolean algebra and graph theory. VIII. EXCLUSIVE OPERATOR Exclusive operator E is a kind of operation of Boolean expression which is defined as follows: )8 .()( ii XXE ≡ ) 9 ) .(( )()() .( 12121121 mmm FEFFFFEFFEFFFE − ∪∪∪≡ )10) (() .()() ( 2121 mm FEFEFEFFFE ≡∪∪∪ For a particular case, if ii XF = , for all i , the above relationship can be simplified to the following form: )( .)()() ( 12121121 mmm XEXXXXEXXEXXXE − ∪∪∪= )11 ( 121211 mm XXXXXXX − ∪∪∪= )() .()() .( 2121 mm XEXEXEXXXE =∪∪∪ )12 .( 21 m XXX= It can be seen from Eqn.11 that all conjunctive terms are mutually disjoint. IX. Reliability Evaluation This method makes use of some of the elementary operators of Boolean algebra. The starting point can be either the system –success function or the system-failure function. The choice between of these two depends on the number of paths or cut set. The method consists in applying exclusive operator on )( functionsucesssystemS −− , which results in all its terms being mutually disjoint [9]. The following assumptions are used in this method [9]: 4n2 n3 n1 1 2 3 5 6 7 n5 n4 n6 8 9 4 Fig.2 Network No.1 n2 n5 n1 n3 n6 n4 n7 n8 1 2 68 12 11 97 3 510 4 Fig.3 Network No.2 n12 n9 n4 n11 n2 n1 n3 n7 n6 n5 n8 n10 20 12 11 2 1 3 5 6 7 8 16 15 14 13 19 17 10 9 Fig.4 Network No.3 4 n1 n2 n3 n4 n5 X4 X3X1 X2 X5 X7 X6 Fig.6 A general non series parallel network X1 x4 X3 x2 x5 Fig.7 bridge-type network 1- All nodes are perfectly reliable. 2- Each branch of the overall network takes either of the following two states: good or bad. 3-The network is free from self-loops and directed cycles. Steps used for the calculation of the terminal pair reliability are given below: 1) The system success function is written as: )13 .( . 21 m TTTS ∪∪∪= where i T represent the minimal paths of the network. Eq.13 is directly obtained by processing of determining paths. 2) For each i T , mi ≤< 1 , i F is defined to be the union of all predecessor terms 121 , .,, −i TTT in which any literal that is presented in both i T and any of the predecessor terms is deleted from those predecessor terms, i.e. 121 − ∪∪∪= ii TTTF for each literal of )14 (1 → i T In fact, the literals of i T are assigned the Boolean value of 1 and this value is substituted in any predecessor term in which they occur. The resulting function i F can be simplified by using standard Boolean reduction identities as shown in Appendix (A). 3) Using Exclusive operator E , to obtain: )15 () .(int)( 2 1 i m i i FETTdisjoS U = = 4) All logical variables are changed into their analogue probability variables to get the reliability expression (all terms are mutually exclusive). )16 (,int)( iiii qXpXdisjoSR → ′ →= If source –terminal cut set is used instead of the paths in a particular system, the system failure function is obtained and can be processed similarly to derive system unreliability expression. X. Application of Disjoint Technique Application One: Consider the general non series parallel network shown in Fig.6 [9]: 1- The cut set for the above network is 753265314326547621 ,,,,, XXXXXXXXXXXXXXXXXX ,thus the system unreliability function is give by Eqn. 17: ) 17 .( 753265314326547621 XXXXXXXXXXXXXXXXXXS ′′′′ ∪ ′′′′ ∪ ′′′ ∪ ′′′ ∪ ′′ ∪ ′′ = ′ By applying Eqn.14, the definition of exclusive operator and Eqn.15, i F , )( i FE and int)(disjoS can be calculated as follows: The representation of the unreliability is given as follows: ++++++= 61432127176542117621 ()()( ppqqqqppppqqqpqpqqqqQ )18) .(() 641753274265316751 pppqqqqpppqqqqqPPP ++ Application Two: To use system success function for finding the reliability expression of a system, consider the bridge shown in Fig.7: The minimal paths for this bridge are: 3525414231 ,,, XXXXXXXXXX and the system reliability can be expressed as: 3525414231 XXXXXXXXXXS ∪∪∪= By applying Eqn.14, the definition of exclusive operator and Eqn.15, i F , )( i FE and int)(disjoS are found as follows: The reliability expression is as follows: 41352235413113131 )()( qqpppqqpppqpqppppS ++++= If all components are assumed to be identical, the reliability expression is given by the followings: 2323322 qpqpqpqppS ++++= Assuming the component reliability 0.99 and applying the two methods mentioned above, the system reliability for the solved two examples is obtained and given in table 2. i F )( i FE )( ii FET 212 XXF ′′ = 211 XXX ′ ∪ )( 21176 XXXXX ′ ∪ ′′ 7213 XXXF ′ ∪ ′′ = )( 2117 XXXX ′ ∪ ))(( 2117654 XXXXXXX ′ ∪ ′′′ )( 57614 XXXXF ′ ∪ ′′ ∪ ′ = 675161 XXXXXX ′ ∪ )( 675161432 XXXXXXXXX ′ ∪ ′′′ 7425 XXXF ′ ∪ ′ ∪ ′ = 742 XXX )( 7426531 XXXXXXX ′′′′ 4616 XXXF ′ ∪ ′ ∪ ′ = 641 XXX )( 6417532 XXXXXXX ′′′′ i F )( i FE )( ii FET 312 XXF = 311 XXX ′ ∪ ′ )( 31131 XXXXX ′ ∪ ′ 233 XXF ∪= 23 XX ′′ )( 23541 XXXXX ′′ 414 XXF ∪= 41 XX ′′ )( 41352 XXXXX ′′ 5 It can be seen from table 2 that the approximation method gives the upper bound value of the reliability since the probability of the intersected events is ignored, while the disjointed reliability expression gives more accurate value. The error is included in the original starting set of cut set but not in the quantitative evaluation of the symbolic reliability expression. Table 2 System reliability for the two solved examples No. Network Approximation Method Disjoint Method 1 Fig.6 0.99979798 0.99979801 2 Fig.7 0.99879900 0.99979805 XI. Sulaimani-Erbil Electrical Power System Reliability Evaluation Fig.8 shows the single line diagram of the 132 kV systems for Sulaimani-Erbil electrical power system. For the purpose of reliability assessment, data were collected for each transmission line for the period of 6 years [10]. With the relevant data, the reliability indices were found and the reliability of each 132 kV transmission line is calculated for two cases: 1-Only forced outages of the line are taken into account 2-Both the forced and scheduled outages of the line are taken into account. The following assumptions are made: 1. Reliability values are assumed for those lines without available data. 2. The reliability of Dokan-Tasluja 132 kV transmission line during the period 1996 to 2001 is evaluated in two parts:  from 1996 to 1998 the line is operated with double circuit  and from 1999 to 2001 the line is operated with single circuit because one of the circuits is energized by 33 KV. 3. Reliability of Dokan and Derbandikhan H/P are considered to be 0.98 and 0.95 respectively [11]. 4. Reliability of the 29 MW Diesel power station is assumed to be 0.9. 5. Reliabilities of the 33 kV and 11 kV transmission lines are assumed to be 0.9. The reliability of each line is given in table 3 and table 4 for the period 1996-2001 XII. Reliability Modeling of the System A simplified reliability model for regional power system is shown in Fig.9, in which the following assumptions are made: 1. The line components are modeled as a single block also the sending and the receiving ends are assumed fully reliable. 2. The regional power stations are considered as a separate blocks. 3. All components are unidirectional except the components that construct ring in the system. The detail of the coding for the component numbers is given in table 5. XIII. Representation of nodes To represent nodes (branches) in the reliability network model, a general Terminal Numbering Convention (TNC) is used in this paper [12]. In this convention the numbering of nodes (branches) begins at the source and continues in such away that the output terminal of each branch (node) is assigned a number greater than the number assigned for its input terminal, taking further care that each node (branch) is assigned a specific number. Using TNC, the first vertex 1 n represents the source and the last vertex k n represents the sink where k is total number of the nodes. XIV. Case Study and Results From the reliability block diagram of regional power system fourteen case studies are investigated. The reliability of each case study is evaluated for the period of 1996-2001 for the following two states: In state one, only the forced outages of the line are take into account and in state two, both the scheduled and forced outages of the line are take into account. 1. Case 1 to case 8 reliability of regional power system evaluated by evaluating minimal paths and cuts of the system from the network modeling and by using the program that is established for this purpose. For each case study different S/S assumed to be the output of the system as: a. in case study no.1 Rizgary S/S is take as a sink node because this S/S is the main S/S in Sulaimani governorate and the main tie lines for Sulaimani region connected to this S/S. b. in case study no.3 Tasluja S/S is take as a sink node because this S/S supplying Tasluja cement factory and it is considered an important substation for reconnection of the regional system to the national grid. c. in case study no.5 Dokan S/S is take as a sink node because it supplies Dokan water pumping station. d. in case study no.6 Derbandikhan S/S is take as a sink node because it supplies some factories in this area. e. in case study no.7 and 8 Azadi and N.E. S/S are taken as a sink node respectively. These two S/S are the main substations in Erbil governorate and main tie lines for Erbil governorate connected with these two S/S. 2. Case study 9 and 10 reliability of the regional power system evaluated, with 29 MW Diesel power station are taken into account for both Sulaimani and Erbil governorate. 3. Case study 11 and 12 reliability of the regional power system evaluated by disjoint technique and compared with the previous case studies. 4. Case study 13 and 14 investigate the indices Annual Average Interruption Rate (AAIR), this indices indicated the expected number of days in a year that the specified outage for a given load point will happen and it’s evaluated from the following relation: AAIR = Q * 365 = (1-R) * 365 6 XV. Results of case Studies Table 6 shows the reliability for case 1 to 8 that is studied during the period of 1996-2001 with different types of outages taken into account. Table 7 shows the system reliability for cases 9 and 10 when the 29 MW Diesel power stations is take into account for both Sulaimani and Erbil region in the year 2001. Table 8 shows the unreliability for cases 11 and 12 obtained by deriving a symbolic equation using disjoint technique. Table 9 and table 10 show the results of AAIR evaluation for cases 13 and 14. XVI. Conclusions This paper investigates the reliability of power system. In the reliability evaluation, power system is modeled by the (RBD) and two techniques, cut sets and disjoint, are used. The investigation results show that both the cut sets and the disjoint techniques can be used to evaluate the reliability of power system. The disjoint technique gives more efficient and accurate solution. However, it is more complex and consequently more time consuming. As to the Sulaimani-Erbil power system, following conclusions are obtained: 1-It is found that the 132 kV transmission line power system that energized by 33 kV system reduces the reliability of the system. Therefore, in order to improve the reliability of the 132 kV power systems, these lines must be restored to 132 kV level. 2-The Reliability of the system will be increased if the 29 MW diesel power station is taken into account for Sulaimani-Erbil region. 3-As the outage of power plant greatly reduces the reliability of the power system, it must be carefully programmed 4-The T tied line greatly effects on the reliability of the overall power system. Table 4 regional 132 kV transmission line reliability data during the period 1996-2001 forced and scheduled outages are take into account Reliability Data (Forced and planning Outages Take into Account) Calculated Name of the line 1996 1997 1998 1999 Dokan-asluja 0.99853075 0.99993133 0.999996942 0.994440639 Tasluja-Rizgari ---- ---- ---- ---- Dokan-Azadi 0.918537492 0.965886606 0.976601979 0.965865677 Dokan-N.E. 0.917067016 0.912359209 0.962621766 0.944446347 Azadi-N.E. ---- ---- ---- ---- Tasluja-Azmer ---- ---- ---- ---- Azmer-Rizgari ---- ---- ---- ---- Derbandikhan-Rizgar i 0.970818154 0.968302892 0.976721842 0.945987443 Derbandikhan-Azmer 0.96340126 0.778076484 0.88245624 0.961244292 Table (4) Continue Reliability Data (Forced and planning Outages Take into Account) Calculated Name of the line 2000 2001 Assumed Dokan-asluja 0.999089253 0.997644597 ---- Tasluja-Rizgari ---- ---- 0.95 Dokan-Azadi 0.984105571 0.985761035 ---- Dokan-N.E. 0.971745978 0.913671994 ---- Azadi-N.E. ---- ---- 0.95 Tasluja-Azmer ---- ---- 0.95 Azmer-Rizgari ---- ---- 0.95 Derbandikhan-Rizgari 0.981360049 0.983837519 ---- Derbandikhan-Azmer 0.948315118 0.963759513 ---- Table (5) Component Coding of the system RBD Component Number Component Type 1 Dokan H/P 2 Dokan S/S 3 Dokan-Tasluja 132 KV Transmission line 4 Tasluja S/S 5 Tasluja-Rizgari 132 KV Transmission line 6 Rizgari S/S 7 Dokan-Azadi 132 KV Transmission line 8 Dokan-North Erbil 132 KV Transmission line 9 Tasluja-Azmar 132 KV Transmission line 10 Azmar-Rizgari 132 KV Transmission line 11 Azadi S/S 12 Azadi- North Erbil 132 KV Transmission line 13 North Erbil S/S 14 Azmar S/S 15 Derbandikhan-Azmar 132 KV Transmission line 16 Derbandikhan H/P 17 Derbandikhan S/S 18 Derbandikhan –Rizgari 132 KV Transmission line 19 29 MW Diesel Power Station 20 11 KV Transmission Line 21 29 MW Diesel Power Station 22 Industrial S/S 23 33 KV Transmission Line Table 3 regional 132 kV transmission line reliability data during the period 1996-2001 only forced outages are take into account Calculated Reliability index for all 132 kV Transmission lines Calculated Name of the line 1996 1997 1998 1999 Dokan-asluja 0.998776941 0.999999536 0.999999965 0.997707382 Tasluja-Rizgari ---- ---- ---- ---- Dokan-Azadi 0.959333257 0.98684551 0.993571157 0.99865106 5 Dokan-N.E. 0.955166591 0.995681126 0.996767504 0.99434551 Azadi-N.E. ---- ---- ---- ---- Tasluja-Azmer ---- ---- ---- ---- Azmer-Rizgari ---- ---- ---- ---- Derbandikhan-Rizgar i 0.976193458 0.982597032 0.992646499 0.999733638 Derbandikhan-Azmer 0.978348892 0.965863775 0.987840563 0.991093988 Table 3 Continue Calculated Reliability index for all 132 kV Transmission lines Calculated Name of the line 2000 2001 Assumed Dokan-asluja 0.999905131 0.999743151 ---- Tasluja-Rizgari ---- ---- 0.95 Dokan-Azadi 0.993825896 0.992802511 ---- Dokan-N.E. 0.995197708 0.979861111 ---- Azadi-N.E. ---- ---- 0.95 Tasluja-Azmer ---- ---- 0.95 Azmer-Rizgari ---- ---- 0.95 Derbandikhan-Rizgari 0.994573467 0.990711568 ---- Derbandikhan-Azmer 0.991442775 0.98391172 ---- 7 Table 6 reliability results for case study 1-8 during the period 1996-2001 Reliability Results for each case study obtained from the program ( Only Forced Outages Take into Account) Years Case Study Numbers 1996 1997 1998 1 0.99874341 0.99881959 0.99885482 2 0.99768347 0.99803263 0.99860013 3 0.99887484 0.99893808 0.99894822 4 0.99890494 0.99895394 0.99898607 5 0.94564784 0.94677657 0.94736171 6 0.97564787 0.97677660 0.97736174 7 0.99505866 0.99822354 0.99860597 8 0.99485034 0.99866533 0.99876583 Case Study Numbers Reliability Results for each case study obtained from the program ( Scheduled and Forced Outages Take into Account) 1 0.99870563 0.99865115 0.99876189 2 0.99735302 0.99671572 0.99748737 3 0.99884993 0.99880522 0.99889511 4 0.99886429 0.99863273 0.99882758 5 0.94479823 0.93976295 0.94440871 6 0.97479832 0.96976298 0.97440875 7 0.98807019 0.99411255 0.99685073 8 0.98799670 0.99143618 0.99615175 Table 8 Unreliability and Reliability Results for case study 11 and 12 Case Study Numbers Years Reliability results from disjoint method Reliability results from approximation method Only Forced Outages Taken into Account 1996 0.998748062 0.99874341 1997 0.998822864 0.99881959 1998 0.998857484 0.99885482 1999 0.998764729 0.99875963 2000 0.99885846 0.99885577 11 2001 0.998838939 0.99883592 1996 0.994950121 0.99485034 1997 0.998671602 0.99866533 1998 0.998769628 0.99876583 1999 0.998619351 0.99861377 2000 0.998681822 0.99867743 12 2001 0.997801362 0.99778998 Table 8 Continue Case Study Numbers Years Reliability results from disjoint method Reliability results from approximation method Scheduled and Forced Outages Taken into Account 1996 0.998711296 0.99870563 1997 0.998661428 0.99865115 1998 0.998767499 0.99876189 1999 0.998420777 0.99840850 2000 0.998767479 0.99876273 11 2001 0.998709733 0.99870372 1996 0.98835124 0.98799670 1997 0.991604149 0.99143618 1998 0.996203793 0.99615175 1999 0.994234003 0.99412298 2000 0.997079661 0.99705076 12 2001 0.993418684 0.99334556 Table ( 6)Continue Reliability Results for each case study obtained from the program ( Only Forced Outages Take into Account) Years Case Study Numbers 1999 2000 2001 1 0.99875963 0.99885577 0.99883592 2 0.99884975 0.99870163 0.99847949 3 0.9988296 0.99894410 0.99893349 4 0.99887538 0.99894452 0.9988609 5 0.94518203 0.94732368 0.94703025 6 0.97518206 0.97732371 0.97703028 7 0.99882901 0.99860883 0.99843705 8 0.99861377 0.99867743 0.99778998 Case Study Numbers Reliability Results for each case study obtained from the program ( Scheduled and Forced Outages Take into Account) 1 0.99840850 0.99876273 0.99870372 2 0.99587101 099787313 0.9979704 3 0.99860466 0.99888206 0.99881327 4 0.99861902 0.99888027 0.99882865 5 0.93961537 0.94545001 0.94442785 6 0.96961540 0.97545004 0.97442788 7 0.99519396 0.99766874 0.99695003 8 0.99412298 0.99705076 0.99334556 Table 7 Reliability Results For Case Study 9 and 10 Case Study Numbers Reliability Results (Only Forced Outage Taken into Account) 9 0.99979740 10 0.99935985 Case Study Numbers Reliability Results (Scheduled and Forced Outage Taken into Account) 9 0.99977642 10 0.99878043 8 Dokan H/P 5*8 0 M W 1 Dokan S/S 2 Tasluja S/S 34 Chamchamal S/S To Kirkuk Rizgary S/S 5 Azmar S/S 6 Old Kirkuk 7 8 Derbandikhan H/P 3*8 3 M W 9 10 Kifri S/S Hamrin H/P Azadi S/S 11 17 12 N.E S/S 13 18 19 Erbil Park S/S To Karkosh Salahadeen S/S 14 Khalifan S/S Soran S /S 15 Kalar S/S To Dibs G/P Fig.8 Single Line Diagram of 132 kV Power System For Sulaimani-Erbil Region Table 9 AAIR evaluation for case study 13 Q S AAIR (Days /Year) Years Only Forced Outages Taken into Account 1996 0.00125661 0.45866265 1997 0.00118041 0.43084965 1998 0.00114517 0.41798705 1999 0.00124035 0.45272775 2000 0.00114424 0.4176476 2001 0.00116409 0.42489285 Scheduled and Forced Outages Taken into Account 1996 0.00129435 0.47243775 1997 0.00134884 0.4923266 1998 0.00123808 0.4518992 1999 0.0015915 0.5808975 2000 0.00123728 0.4516072 2001 0.00129627 0.47313855 Table 10 AAIR evaluation for case study 14 Q S AAIR (Days /Year) Years Only Forced Outages Taken into Account 1996 0.00514967 1.87962955 1997 0.00133465 0.48714725 1998 0.00123419 0.45047935 1999 0.00138625 0.50598125 2000 0.00132259 0.48274535 2001 0.00221002 0.8066573 Scheduled and Forced Outages Taken into Account 1996 0.01200333 4.38121545 1997 0.00856382 3.1257943 1998 0.00384827 1.40461855 1999 0.00587702 2.1451123 2000 0.00294927 1.07648355 2001 0.00665445 2.42887425 21 22 23 12 3 4 6 7 8 11 12 13 19 20 16 17 15 14 9 10 18 5 Fig.9 Reliability Block Diagram for Sulaimani-Erbil Electrical Power System 9 Appendix A BOOLEAN ALGEBRA 1- Commutative Laws: a) abba +=+ b) abba ×=× 2-Distributive Laws: a) )()()( cabacba +×+=×+ b) )()()( cabacba ×+×=+× 3-Identity Laws: a) aa =+ 0 b) aa =×1 4-Complement Laws: a) 1= ′ + aa b) 0= ′ × aa 5-Idempotent Laws: a) aaa =+ b) aaa =× 6-Boundedness Laws: a) 11 =+a b) 00 =×a 7-Absorption Laws: a) abaa =×+ )( b) abaa =+× )( 8-Associative Laws: a) )()( cbacba ++=++ b) )()( cbacba ××=×× 9-Involution Law: aa = ′′ )( 10-DeMorgan’s Laws: a) baba ′ × ′ = ′ + )( b) baba ′ + ′ = ′ × )( 11-Disjoint set: baaba ′ +=+ REFERENCES [1] J. Endrenyi, “Reliability Modeling in Electrical Power Systems”, John Wiley and Sons, Newyork, Ny,1978 [2] A.E.Green and A.J.Bourne “ Reliability Technology”, John Wiley & Sons Ltd., 1972. [3] Feasibility study on the options for the addition of generation capacity in the northern governorates of Iraq. Final report, prepared by SMEC Nov. 1999 [4] Distribution Construction Manual, Revesion 2:February 2002, Distribution sector UNDP –ENRP. [5] Electricity Network Development plan Sulaimany governorate. Revesion 1: February 2002,UNDP-ENRP, Distribution sector. [6] T. Gönen “ Electric Power Transmission System Engineering Analysis and Design”, John Wiley and Sons, 1988. [7] R. Billinton and R. N.Allan “ Reliability Evaluation of Engineering Systems”, Pitman Advanced Publishing Program, 1983. [8] G.B.Jasmon and K.W. Foong “ A method for evaluating all the minimal cuts of a graph”, IEEE Transactions on Reliability, Vol.R-36, No.5, December 1987. [9] S. Rai and K.K. Aggarwal “ An efficient method for reliability evaluation of a general network”, IEEE Transactions on reliability, Vol.R-27, No.3, August 1978. [10] G.I.Rashed, A.R.Majeed and S. J.cheng “ Determination of Data for Reliability Analysis of a Transmission System in Sulaimani-Erbil Network”, Asian network for scientific information, Information Technologu Journal, Vol.(4), No.2, pp.106-113, Jan. 2005. [11] T.M.Tahir ”Load forecasting and power system reliability evaluation”, MSC.,Thesis, University of Technology, Electrical Engineering Dept., Nov. 1994. [12] S.S.Yau, Y.S. Tang “ An efficient algorithm for generating complete test sets for combinational logic circuit”, IEEE Trans. Computers, Vol.C-20, pp 1245-1251, Nov. 1971. Asso R. Majeed,(E-mail: drassomajeed@hotmail.com) received his Ph.D. in electrical engineering from Baghdad university, Iraq. Recently he is head of electrical engineering department in Sulaimani university. His area is power system reliability. Ghamgeen I. Rashed,(E-mail:gh197493@yahoo.com) received his bachelor degree in electrical engineering from Salahaadin University- Iraq, in 1995, and his M.sc. in University of Sulaimani-Iraq in 2003. Recently he is Ph.D student in Huazhong University of Science and Technology, China. Shijie Cheng, senior member IEEE,(E-mail:Sjcheng@hust.edu.cn). Got his ph.D. degree in Canada in 1988. He is a life professor of the Huazhong University of Science and Technology, China. In recent years he has been engaged in the areas of power line communication, intelligent control, stabilization control of power system and superconducting power technology. . 0.962621766 0.944446347 Azadi-N.E. -- -- -- - - -- -- -- - - Tasluja-Azmer -- -- -- - - -- -- -- - - Azmer-Rizgari -- -- -- - - -- -- -- - - Derbandikhan-Rizgar i 0.970818154 0.968302892. 0.996767504 0.99434551 Azadi-N.E. -- -- -- - - -- -- -- - - Tasluja-Azmer -- -- -- - - -- -- -- - - Azmer-Rizgari -- -- -- - - -- -- -- - - Derbandikhan-Rizgar i 0.976193458 0.982597032