CC BY
63
Customer Orientated Indices and Reliability Evaluation of Meshed Power Distribution System
Aditya Tiwary
Dept. of Fire Technology & Safety Engineering, IPS Academy, Institute of Engineering and science,
Rajendra Nagar, Indore (M.P), India [email protected]
Abstract
Reliability evaluation of a system or component or element is very important in order to predict its availability and other relevant indices. Reliability is the parameter, which tells about the availability of the system under proper working conditions for a given period of time. The study of different reliability indices are very important considering the complex and uncertain nature of the power system. In this paper reliability, evaluation of the meshed distribution system is presented. This paper also evaluates basic indices such as average failure rate, average outage time and average annual outage time. Along with basic indices, customer orientated indices such as system average interruption frequency index, system average interruption duration index and customer average interruption duration index of an electrical power distribution system is also evaluated. The electrical power distribution system taken for study is meshed distribution system in nature. Keywords: Reliability; Availability; Meshed distribution system; average interruption frequency index; system average interruption duration index.
I. Introduction
Reliability evaluation of a system or component or element is very important in order to predict its availability and other relevant indices. Reliability is the parameter which tells about the availability of the system under proper working conditions for a given period of time. A Markov cut-set composite approach to the reliability evaluation of transmission and distribution systems involving dependent failures was proposed by Singh et al. [1]. The reliability indices have been determined at any point of composite system by conditional probability approach by Billinton et al. [2]. Wojczynski et al. [3] discussed distribution system simulation studies which investigate the effect of interruption duration distributions and cost curve shapes on interruption cost estimates. New indices to reflect the integration of probabilistic models and fuzzy concepts was proposed by Verma et al. [4].
Zheng et al. [5] developed a model for a single unit and derived expression for availability of a component accounting tolerable repair time. Distributions of reliability indices resulting from two sampling techniques are presented and analyzed along with those from MCS by Jirutitijaroen and Singh [6]. Dzobe et al. [7] investigated the use of probability distribution function in reliability worth analysis of electric power system. Bae and Kim [8] presented an analytical technique to evaluate the reliability of customers in a microgrid including distribution generations. Reliability network equivalent approach to distribution system reliability assessment is proposed by Billinton and Wang [9].
Evaluation of Reliability indices accounting omission of random repair time for distribution
systems using Monte Carlo simulation [10]. Determination of Optimum period between Inspections for Distribution system based on Availability Accounting Uncertainties in Inspection Time and Repair Time, Tiwary et al. [11]. Jirutitijaroen et al. [12] developed a comparison of simulation methods for power system reliability indexes and their distribution. Determination of reliability indices for distribution system using a state transition sampling technique accounting random down time omission Tiwary et al. [13]. Tiwary et al. [14] proposed a methodology based on inspection repair based availability optimization of distribution systems using Teaching Learning based Optimization. Bootstrapping based technique for evaluating reliability indices of RBTS distribution system neglecting random down time was evaluated [15].
Volkanavski et al. [16] proposed application of fault tree analysis for assessment of the power system reliability. Li et al. [17] studies the impact of covered overhead conductors on distribution reliability and safety. Reliability enhancement of distribution system using Teaching Learning based optimization considering customer and energy based indices was obtained in Tiwary et al. [18]. Self-Adaptive Multi-Population Jaya Algorithm based Reactive Power Reserve Optimization Considering Voltage Stability Margin Constraints was obtained in Tiwary et al. [19]. A smooth bootstrapping based technique for evaluating distribution system reliability indices neglecting random interruption duration is developed [20]. The impact of covered overhead conductors on distribution reliability and safety is discussed [21]. Sarantakos et al. [22] introduced a method to include component condition and substation reliability into distribution system reconfiguration. Battu et al. [23] discussed a method for reliability compliant distribution system planning using Monte Carlo simulation. Tiwary et al. [24] has discussed a methodology for reliability evaluation of an electrical power distribution system, which is radial in nature. Uspensky et al. [25] has developed a method for reliability assessment of the digital relay protection system. Sharma et al. [26] deals with the reliability analysis of a two identical unit system model with safe and unsafe failures, switching device and rebooting.
Physically a system configuration will be a series reliability network if system fails even if a single component fails or system survives if all the components are working successfully.
The system is having a constant failure rate and therefore the reliability of the system having constant failure rate is evaluated by using the following relation.
Where R(t) represents the reliability of each distribution section. A represents the failure rate per year and t represents time period which is taken as one year.
If one assumes reliability of each component as r1,r2...rn, then reliability of series system (Rs) is given as
Where ri represents the reliability of components from i=1....n.
A system configuration will be a parallel reliability network, the system fails, if all components fail. System performs its function even if a single component is working.
The reliability of parallel system (Rp) is given as
II. Reliability evaluation of electrical distribution system
R(t)=eA(-At)
(1)
Rs=nri
(2)
(3)
Where ri represents the reliability of components from i=1....n.
III. Basic reliability indices evaluation of series and parallel system
When reliability studies are concerns, three basic reliability parameters are average failure rate, average outage time and average annual outage time, which are mentioned as follows for series system.
As=£Ai Us=£ [Ai.ri]
(4)
(5)
rs=(£Airi)/(£Ai)
(6)
For parallel system the three basic reliability indices can be evaluated as follows . _ r'ri
ri + Tj
Upara — ¿para 4 ' para
(7)
(8) (9)
Where Aj is failure rate per year
ri , rj is average repair time, hours
IV. Evaluation of customer orientated indices
Customer orientated indices related to reliability studies are system average interruption frequency index, system average interruption duration index and customer average interruption duration index, which are mentioned as follows.
System average interruption frequency index (SAIFI)
„ . total number of customer interruptions Hft,
SAIFl —--(1U)
total number of customers served
System average interruption duration index (SAIDI)
c . m j _ sum of customer interruption durations /11 \
SnlMl — (11)
total number of customers
Customer average interruption duration index (CAIDI)
nAJr.T _ sum of customer interruption durations /1
LnlMl — (12)
total number of customer interruptions
V. Results and Discussions
Meshed distribution system consists of 18 distributor segments and 4 load points from LP-1 to LP-4 Fig. 1, [10].
Figure 1 Sample Meshed Distribution System
Table I [10] provides the initial data for the meshed distribution system. Table I consists of failure rate per year and repair time in hours of each distribution section from 1 to 18 of the meshed distribution system. Table II consists of number of customers at each load point LP-1 to LP-4. Evaluated Reliability at each distribution section is provided in Table III. The reliability at each distribution section is evaluated by using equation 1. Fig.2 provides magnitude of reliability at different distribution sections. Table IV gives the calculated value of the reliability at each and every load point of the meshed distribution system. The reliability at each and every load point is obtained by using the equation 2 and 3. Fig.3 provides magnitude of reliability at different load points of the distribution system.
Basic reliability indices at each load point i.e average failure rate, average outage time and average annual outage time are evaluated are presented in Table V. Fig.4 provides magnitude of average failure rate at different load points of the distribution system. Fig.5 and Fig.6 provides magnitude of average outage time and average annual outage time at different load points of the meshed distribution system.
Customer orientated indices such as system average interruption frequency index (SAIFI) is evaluated as 0.3965, system average interruption duration index (SAIDI) is obtained as 4.1057 and customer average interruption duration index (CAIDI) is evaluated as 10.3556 for the meshed distribution system.
Table 1 [10]
System data for sample meshed distribution system
Distribution section 4', failure/year Average repair time rf, h
#1 0.310400 10.280412
#:2 0.127600 5.0 1 06 58
#3 0.070000 33.985714
#4 0.013520 14.335503
#5 0.084600 10.557447
#6 0.017640 13.555102
#7 0.008460 10.557447
#8 0.078000 11.023077
#9 0.008460 15.800000
#10 0.063000 27.565217
#1 1 0.155200 6.865979
#12 0.155200 6.865979
#13 0.070000 33.985714
#14 0.013520 14.335503
#15 0.156600 10.714943
#16 0.017640 13.555100
#17 0.078000 11.023077
#18 0.084600 10.557447
Table 2 Initial data for the load points
Load Point 1 2 3 4
Number of customers 1000 800 600 700
Table 3 Evaluated Reliability at each distribution section
Distribution Section Reliability
1 0.7331
2 0.8802
3 0.9324
4 0.9866
5 0.9189
6 0.9825
7 0.9916
8 0.9250
9 0.9916
10 0.9333
11 0.8562
12 0.8562
13 0.9324
14 0.9866
15 0.8550
16 0.9825
17 0.9250
18 0.9189
Figure 2 Magnitude of Reliability for distribution sections 1 to 18.
Table 4 Evaluated Reliability at each load points
Load point Reliability
1 0.6421
2 0.5973
3 0.6504
4 0.6958
Figure3 Magnitude of Reliability at different Load Points 1 to 4.
Table 5 Evaluated Basic Reliability indices at each load points
Load point 1 2 3 4
average failure rate 0.3951 0.4671 0.3951 0.3189
average outage time 10.3384 10.4247 10.3381 10.2875
average annual outage time 4.0847 4.8697 4.0846 3.2807
0.5 0.45 0.4 0.35 0.3 0.25 0.2 0.15 0.1 0.05 0
12 3 4
Figure 4 Magnitude of average failure rate at different Load Points 1 to 4.
10.45
10.4
10.35
10.3
10.25
10.2
12 3 4
Figure 5 Magnitude of average outage time at different Load Points 1 to 4.
Figure 6 Magnitude of average annual outage time at different Load Points 1 to 4.
VI. Conclusion
Evaluation of reliability for a power distribution system is very essential. In this paper a meshed distribution system is taken in consideration. Reliability of each and every distribution section is calculated. Load point reliability is also obtained for the meshed distribution system for each and every load point. The three basic reliability parameters of importance average failure rate, average outage time and average annual outage time are also obtained for the load points considered. Important customer orientated indices such as system average interruption frequency index, system average interruption duration index and customer average interruption duration index are also evaluated for the meshed distribution system.
References
[1] C. Singh. (1981). Markov cut-set approach for the reliability evaluation of transmission and distribution systems. IEEE Trans. on Power Apparatus and Systems, 100: 2719-2725.
[2] R. Billinton. (1969). Composite system reliability evaluation. IEEE Trans. on Power Apparatus and Systems, 88:276-281.
[3] E. Wojczynski, R. Billinton. (1985). Effects of distribution system reliability index distributions upon interruption cost/reliability worth estimates. IEEE Trans. on Power Apparatus and Systems, 11:3229-3235.
[4] A. K. Verma, A. Srividya, H. M. R. Kumar. (2002). A framework using uncertainties in the composite power system reliability evaluation. Electric Power Components and Systems, 30:679-691.
[5] Z. Zheng, L. Cui, Alan G. Hawkes. (2006). A study on a single-unit Markov repairable system with repair time omission. IEEE Trans. on Reliability, 55:182-188.
[6] P. Jirutitijaroen, C. singh. (2008). Comparison of simulation methods for power system
Aditya Tiwary
CUSTOMER ORIENTATED INDICES AND RELIABILITY EVALUATION , ^^ N°, 1„(/56)
OF MESHED POWER DISTRIBUTION SYSTEM_Volume I5, M 2020
reliability indexes and their distributions. IEEE Trans. on Power Systems, 23:486-493.
[7] O. Dzobe, C. T. Gaunt, R. Herman. (2012). Investigating the use of probability distribution functions in reliability-worth analysis of electric power systems. Int. J. of Electrical Power and Energy Systems, 37:110-116.
[8] I. S. Bae, J. O. Kim. (2008). Reliability evaluation of customers in a microgrid. IEEE Trans. on Power Systems, 23:1416-1422.
[9] R. Billinton, P. Wang. (1998). Reliability-network-equivalent approach to distribution-system-reliability evaluation. IEE Proc. generation, transmission and distribution, 145:149153.
[10] L. D. Arya, S. C. Choube, R. Arya and Aditya Tiwary. (2012). Evaluation of Reliability indices accounting omission of random repair time for distribution systems using Monte Carlo simulation. Int. J. of Electrical Power and Energy System, (ELSEVIER), 42:533-541.
[11] Aditya Tiwary, R. Arya, S. C. Choube and L. D. Arya. (2012). Determination of Optimum period between Inspections for Distribution system based on Availability Accounting Uncertainties in Inspection Time and Repair Time. Journal of The Institution of Engineers (India): series B (Springer), 93:67-72.
[12] Jirutitijaroen P, singh C. (2008). Comparison of simulation methods for power system reliability indexes and their distribution. IEEE Trans Power Syst, 23:486-92.
[13] Aditya Tiwary, R. Arya, S. C. Choube and L. D. Arya. (2013). Determination of reliability indices for distribution system using a state transition sampling technique accounting random down time omission. Journal of The Institution of Engineers (India): series B (Springer), 94:71-83.
[14] Aditya Tiwary, L. D. Arya, R. Arya and S. C. Choube. (2016). Inspection repair based availability optimization of distribution systems using Teaching Learning based Optimization. Journal of The Institution of Engineers (India): series B (Springer), 97:355-365.
[15] Aditya Tiwary, R. Arya, L. D. Arya and S. C. Choube. (2017). Bootstrapping based technique for evaluating reliability indices of RBTS distribution system neglecting random down time. The IUP Journal of Electrical and Electronics Engineering, X:48-57.
[16] Volkanavski, Cepin M, Mavko B. (2009). Application of fault tree analysis for assessment of the power system reliability. Reliab Eng Syst Safety, 94:1116-27.
[17] Li BM, Su CT, Shen CL. (2010). The impact of covered overhead conductors on distribution reliability and safety. Int J Electr Power Energy Syst, 32:281-9.
[18] Aditya Tiwary. (2017). Reliability enhancement of distribution system using Teaching Learning based optimization considering customer and energy based indices. International Journal on Future Revolution in Computer Science & Communication Engineering, 3:58-62.
[19] Aditya Tiwary. (2018). Self-Adaptive Multi-Population Jaya Algorithm based Reactive Power Reserve Optimization Considering Voltage Stability Margin Constraints. International Journal on Future Revolution in Computer Science & Communication Engineering, 4:341-345.
[20] R. Arya , Aditya Tiwary , S. C. Choube and L. D. Arya. (2013). A smooth bootstrapping based technique for evaluating distribution system reliability indices neglecting random interruption duration. Int. J. of Electrical Power and Energy System, (ELSEVIER), 51:307-310.
[21] M. BinLi, C. TzongSu, C. LungShen. (2010). The impact of covered overhead conductors on distribution reliability and safety. Int. J. of Electrical Power and Energy System, (ELSEVIER), 32:281-289.
[22] I. Sarantakos, D. M.Greenwood, J.Yi, S. R. Blake, P. C. Taylor. (2019). A method to include component condition and substation reliability into distribution system reconfiguration. Int. J. of Electrical Power and Energy System, (ELSEVIER), 109:122-138.
[23] N. R. Battu, A. R. Abhyankar, N. Senroy. (2019). Reliability Compliant Distribution System Planning Using Monte Carlo Simulation. Electric power components and systems, 47:985-997.
[24] Aditya Tiwary. (2019). Reliability evaluation of radial distribution system - A case study. Int. J. of Reliability: Theory and Applications, 14,4(55):9-13.
Aditya Tiwary
CUSTOMER ORIENTATED INDICES AND RELIABILITY EVALUATION , ^^ N° V,56 OF MESHED POWER DISTRIBUTION SYSTEM_V°lume 15, M 2020
[25] Michael Uspensky. (2019). Reliability assessment of the digital relay protection system. Int. J. of Reliability: Theory and Applications, 14:10-17.
[26] Akshita Sharma, Pawan Kumar. (2019). Analysis of reliability measures of two identical unit system with on switching device and imperfect coverage. Int. J. of Reliability: Theory and Applications, 14:44-52.
