- Email: [email protected]
distribution substation and its components
Electrical Power and Energy Systems 43 (2012) 992–995
Contents lists available at SciVerse ScienceDirect
Electrical Power and Energy Systems journal homepage: www.elsevier.com/locate/ijepes
New reliability coefficients of MV/LV transformer/distribution substation and its components Andrew Lukas Chojnacki ⇑ ´ stwa Polskiego 7, 25-314 Kielce, Poland Kielce University of Technology, Power Engineering Department, Al. Tysia˛clecia Pan
a r t i c l e
i n f o
Article history: Received 24 March 2011 Received in revised form 31 May 2012 Accepted 1 June 2012 Available online 15 July 2012 Keywords: Relay-distribution station Reliability Failure frequency Cost of unreliability
a b s t r a c t This paper introduces the possibility of application of u- and k-coefficient to operational reliability analysis of MV/LV transformer/distribution substations. The failure duration index was shown to have specific constraints in cost-related assessments of electric power system reliability. A direct correlation was assumed to exist between the failure duration and the actual emergency shutdown time, which can be shown with the u- and k-coefficients. The value of both indices has been determined on the basis of empirical data collected at two major power plants in Poland throughout the period of 10 years. Ó 2012 Elsevier Ltd. All rights reserved.
1. Introduction The contemporary demands on the quality and continuity of electricity supply have become very high. The unit rated power of MV substations and power lines has been steadily increasing, along with the risk of even more wide-ranging blackouts, and the resulting higher limitations in electricity supply to end-users, which brings about considerable financial losses or, in extreme circumstances, serious risks to human health and life. The costs arising from electric power system unreliability may be classified into three different groups [1,5,9,11,15]: costs – – – costs – – – – costs – –
borne by electric power distributors: loss of income arising from electric power outages; discounts and bonuses for electricity end-users; identification and removal costs of substation-originated failure. borne by industrial end-users: losses arising out of non-performance or delays in performance; losses attributed to process line re-starting downtime; costs resulting from the loss of raw materials and production materials; costs of staff remuneration during downtime. borne by private end-users: time lost during electric power outage; costs of perishable food products lost during electric power outage;
⇑ Tel.: +48 41 342 47 61; fax: +48 41 342 42 14. E-mail address: [email protected] 0142-0615/$ - see front matter Ó 2012 Elsevier Ltd. All rights reserved. http://dx.doi.org/10.1016/j.ijepes.2012.06.003
– costs attributed to sanitary and hygiene conditions deterioration; – losses to the economy when end-users stay at home during electrical power outage. Failure duration (time until recovery) ta is the basic parameter, which defines the extent of the power failure. Failure duration is the time elapsed from component failure until its repair/replacement and the successful restoration of electric power supply [15–17]. The failure duration parameter essentially reflects the quality of failure handling operations and the extent of the power failure in statistical terms. The duration of disruption in power supply to end users tp is another parameter used in assessing electric power system reliability. This is the time elapsed from the onset of power outage until successful restoration of electric power supply to end-users [17]. Failure-related substation downtime twa, is the time elapsed from emergency shutdown (automatically by control systems or manually by technical staff) until successful power restoration to the repaired substation. twa index and the failure duration index are by no means equivalent. The power can be supplied to the failed substation immediately after the major cause of the failure is eliminated and the substation functionality and operational safety is fully or partially restored, despite the fact that the failure status continues. The remaining repairs are performed under live line conditions. The failure cannot be considered to be completely eliminated, although the substation is no longer in the state of emergency shutdown. Moreover, failure is not always synonymous with emergency shutdown. A substation can continue to operate although despite the failure status.
A.L. Chojnacki / Electrical Power and Energy Systems 43 (2012) 992–995
The amount of losses suffered by distributors depends on failure duration and emergency shutdown time. The failure duration for the most part affects the costs of technical service and equipment. On the other hand, emergency shutdown time can influence the duration of power supply outage, and the resulting value of electric power shortage, as well as discounts and bonuses for end-users. The financial losses of electricity end-users depend predominantly on the duration of power supply outage, i.e. the actual substation shutdown time [2,9,17]. This is the actual time period during which end-users have no access to electricity. As a rule, there are no empirical data on emergency shutdown times in statistical data on the operational reliability of specific components of electric power systems. As a result, the extent of power failure and its technical and financial consequences are assessed on the basis of operational reliability indices: failure duration and the failure rare, which are typically easy to determine. This type of approach should be considered to be less accurate for a number of reasons, for example, the time of servicing operations under life line conditions cannot be properly accounted for. Electric power systems can be also repaired without being shutdown, or can be restarted before the failure is completely eliminated. In order to determine the actual costs of failure, all reliability parameters of the analysed components and the entire power systems need to be identified. Nevertheless, there have been no empirical data on electric power system reliability published in international literature within the past few years. This problem has not received all the attention it deserves. New analysis methods of operational reliability have been at the centre of attention. However, it is equally important to identify reliability indices of electric power substations and substation components. All traditional assessment methods of operational reliability should be based on the reliability indices of specific substation components, and reliability models are required to be developed to identify the reliability indices of the substation as a whole. It may be at times difficult to determine specific reliability models, and in particular, it may appear problematic to account for auxiliary systems and systems, which are not directly involved in electricity processing and supply (control and signalling systems, condenser batteries, lightning arresters, voltage transformers and current transformers). With reference to the foregoing, simulation methods have been recently introduced based on computational solutions, i.e. the Petri net [8,13,14], genetic algorithm methods [3–6], the Monte Carlo method [7,10,12] and many more. However, in order to be able to rely on the aforementioned reliability assessment methods, reliability parameters of all system components need to be determined. Irrespective of the reliability assessment method applied, the basic reliability data are required to be identified, including, but not limited to data on failure duration, emergency shutdown time, and the duration of power outage. Different aspects of reliability analyses (technical, economical, etc.) are required to be based on the applicable type of index. It has been attempted to identify mathematical correlations between reliability parameters referring to failure duration and emergency shut-down time in order to find the way to determine shutdown duration parameters based on failure duration parameters. Taking into account the most popular structural solutions of MV substations, servicing operations performed under live line conditions, and the characteristics of specific indices, the possible failure variants of MV transformer/distribution substations have been analysed in order to establish specific failure-related behaviours of substations.
2. Definition and determination of u- and k-index Failure duration, failure rate and failure-related unreliability indices are the most common reliability parameters of electric
993
power components and systems. The aforementioned parameters can be basically determined using data from the records of electricity distributing companies. A detailed analysis has been performed to determine whether the aforementioned parameters are sufficient to establish failure-related shutdown indices. It was also investigated whether any empirical correlations exist between failure duration and emergency shutdown time. Based on theoretical studies and comprehensive empirical examinations, the following new indices have been introduced:
kwa u¼ k
ð1Þ
and
k¼
qwa q
ð2Þ
where u is the share of emergency shut-down rate; k is the share of unreliability index of emergency shutdowns; k is the average total 1 failure rate yearde v ice; kwa is the average failure rate resulting in emer1 gency shutdown yearde v ice; q is the unreliability index (determined for all failure states); qwa is the unreliability index of emergency shutdowns. u-index has the following characteristics: u-index is in the range of u e h0; 1i; u = 0 where no emergency shut-down takes place after a component failure; u = 1 where emergency shut-down takes place after each failure; u-index is in the range of u e (0; 1) for all other types of components. k-index has the following characteristics: k P 0; k = 0 where no emergency shutdown takes place after a component failure, and where repairs are performed under live line conditions; k is the range of k e (0; 1) where failure can optionally, but not necessarily result in emergency shutdown, or if the time of emergency shutdown is shorter than the failure duration. In general, k-index values is in the range of k e (0; 1) if the following condition is fulfilled: kwa twa < k t a ; k = 1 where emergency shutdown takes place after each failure and where the failure duration equals the shutdown time. In general, k = 1 if the following condition is fulfilled: kwa twa ¼ k t a ; k > 1 if the emergency shutdown time is longer than the emergency duration, under the assumption that the component is shutdown whenever a failure takes place. In general, k > 1 if the following condition is fulfilled: kwa twa > k t a . This condition applies to systems with redundancy capability. It is possible to define specific average values of u and k indices for various structural solutions of substations. The indices would be then defined as the proportion of average failure rate causing substation shutdown to the total substation failure rate, and as the proportion of unreliability index defined for substation emergency shutdowns to unreliability index defined for all emergency conditions of the substation in question. Other indices related to emergency shut-downs, i.e. average emergency shut-down rate or emergency shut-down time can be defined on the basis of the share of emergency shut-down rate index kwa in the total failure rate k, the share of unreliability index of emergency shut-downs qwa in the total unreliability index q, failure duration and average failure rate. As a result, the operation of specific substation components and of substations in general can be determined in a more comprehensive manner.
994
A.L. Chojnacki / Electrical Power and Energy Systems 43 (2012) 992–995
Depending on the collected reliability data, and in consideration of the following empirical correlations [17]:
k ¼
2m ðnp þ nk Þ Dt
ð3Þ
where m is the number of conditions (failures, emergency shutdowns, etc.); np, nk is the sample size at the beginning and at the end of the period of observation; Dt is the period of observation, can be translated into a relationship (1) to be later used in determining u-index value: 2mwa
kwa ðn þn ÞDt mwa u ¼ ¼ p 2mk ¼ m k ðnp þnk ÞDt
ð4Þ
where mwa is the number of emergency shutdowns; m is the number of failures observed. Under the assumption that the emergency shutdowns and failures refer to the same sample and occur within the same period of observation. Based on the relationship [17]:
q¼
k t 1 þ k t
ð5Þ
where k is the rate of conditions in question (failures, emergency shutdowns, etc.); t is the duration of the conditions under analysis, can be also translated in to the following relationship (2):
k¼
k t wa kwa twa 1 þ k t a qwa 1þwa ¼ kkwat twa ¼ a q k ta 1 þ kwa twa t 1þk
ð6Þ
a
If the following relationships are met: k t a 1 kwa twa 1, the a/m relationship can be simplified into:
kwa t wa twa k¼ ¼u ta k ta
and
ð7Þ
If the values of u and k indices and failure durations are known for a specific substation component or the substation in general, the emergency shutdown time can be defined as:
t wa ¼ k t a u
ð8Þ
and the emergency shutdown rate can be determined as:
kwa ¼ u k
ð9Þ
3. Values of u and k indices for electric power components and substations operating in Poland Reliability indices for individual components and substations in general have been determined based on data collected in the course of a 10-year long reliability study of MV electric power substations at two major electricity distribution companies in Poland. 8500 substations in total were operating in the first year of the observation period. At the end of this period, the number of substations increased to 9638. The number of individual components at the beginning and at the end of the period of observation has been calculated on the basis of detailed analyses. The data are shown in Table 1. Within the 10-year period of observation, 3363 emergencies have taken place in MV substations. Table 1 presents also the number of failures per each group of components. u and k indices for MV electric power substations have been calculated on the basis of statistical sample referred to above. Table 2 presents the calculation results. The analysis clearly indicates that the highest u-index values have been obtained for cut-off switches (0.99), cable heads (0.97) as well as for transformers, lightning arresters and insulators (0.95). These components are nearly always shutdown in case of failure. Protection and control automation system elements (0.42), voltage transformers (0.65) or condenser batteries (0.75) represent a different group of components. Failure can optionally, but not necessarily trigger an emergency shutdown. Only 42 out of 100 failures of the protection and control automation systems cause an emergency shutdown of the component or the substation. In the remaining 58 cases, the substation continues to operate and the failure is removed without the substation being shutdown by the service staff. k-indices denoting the share of total emergency shutdown time in the total failure duration are relatively low, which confirms that reliability analyses relying exclusively on failure duration are insufficient to provide reliable data. k-index was the lowest for protection and control automation systems (0.30). The total emergency shutdown time for protection and control automation systems accounted for 30% of the total failure duration. The k-index for current transformers was estimated at 51%. Transformers were found to have the highest k-index (0.92). The total emergency shutdown time of transformers accounted for as much as 92% of the total failure duration. u- and k-indices were also determined for two typical structural solutions of substations operating in Poland: simple outdoor polemounted MV substations typical for rural areas, and urban-type
Table 1 Number of substation components and number of failures in MV substations. Component
– Condenser batteries Voltage transformers Current transformers Cut-off switches Bus-bars Circuit-breakers Isolating switches Insulators Cable heads Lightning arresters Protection and control automation systems Transformers
Number of substation components
Number of failures
Component failure rate vs. total failure rate
Failure rate vs. number of components
– 4959 289 289 4779 2982 1514 15250 88474 58983 17077 –
– 32 55 69 71 87 122 362 442 466 471 585
[%] 0.95 1.64 2.05 2.11 2.59 3.63 10.76 13.14 13.86 14.01 17.40
[%] 0.07 1.93 2.44 0.16 0.31 0.86 0.25 0.05 0.08 0.29 4.28
9883
601
17.87
0.65
At the beginning of the period of observation
At the end of the period of observation
– 4306 281 277 4146 2655 1325 13564 76815 51209 15103 – 8581
A.L. Chojnacki / Electrical Power and Energy Systems 43 (2012) 992–995 Table 2 u- and k-indices for selected MV substation components. Component
u-index
k-index
Condenser batteries Voltage transformers Current transformers Cut-off switches Bus-bars Circuit-breakers Isolating switches Insulators Cable heads Lightning arresters Protection and control automation systems Transformers
0.75 0.65 0.90 0.99 0.91 0.83 0.94 0.95 0.97 0.95 0.42 0.95
0.74 0.51 0.83 0.68 0.79 0.79 0.77 0.71 0.89 0.68 0.30 0.92
transformer/distribution substations with a more complicated structure. This type of substations is typically equipped with protection and control automation systems, remote control systems of connectors and monitoring systems of measurement instrumentation at the power dispatch centre. u- and k-indices of simple pole-mounted substations equalled 0.96 and 0.77, respectively. According to the u-index, simple pole-mounted substations are shutdown 96 times per 100 failures, and four out of 100 failures are repaired without being shutdown by the service staff. k = 0.77 means that the total emergency shutdown time of simple polemounted substations accounts for approximately 77% of the total failure time. u and k-indices for urban-type in-door substations have been calculated in the same manner to produce the following results: u = 0.52 and k = 0.34. u = 0.52 means that the complex in-door urban-type substations are shut-down 52 times per 100 failures, and 48 out of 100 failures are repaired without being shut-down by the service staff. k = 0.34 means that the total emergency shutdown time of urbantype in-door substations accounts for approximately 34% of the total failure time.
4. Summary Reliability analyses of electric power systems aimed at determining the extent of losses suffered by end users and electricity distributors are predominantly based on failure duration, failure rate and estimated average annual failure duration. This type of approach to reliability analysis appears to be insufficient due to the fact that parameters defining the failure duration are by no means equivalent to the parameters, which define the duration of power outages. In consideration of the foregoing, the analysis of financial losses should be based on reliability parameters referring to the duration of emergency shutdowns and power supply interruptions rather than the failure duration. Analyses carried out by the author showed that the use only of the duration of the failure causes an error of 10–30%. New reliability indices have been introduced which account for the failure type and failure sequence referring to individual substation components and the power substation in general. The new parameters are the attributes of a specific structural solution that a specific component or substation represents, and can be therefore classified as rated parameters. It is therefore possible to deter-
995
mine the value of component/substation shutdown time index only on the basis of its failure duration parameters. In traditional reliability assessment methods, reliability parameters of specific components are required to be determined along with reliability models for the substation in general. It can be at times difficult to determine specific reliability models, in particular, it may appear problematic to account for auxiliary systems and systems which are not directly involved in electricity processing and supply (control and signalling systems, condenser batteries, lightning arresters, voltage transformers, current transformers). When the u- and k-indices are used in the reliability analysis, the auxiliary systems are always accounted for in the reliability model, along with the actual impact of auxiliary systems on reliability parameters of the entire substation. The analysis performed showed the existence of an empiric relation between failure duration and emergency shut-down time of equipment operating in MV/LV transformer stations. This relation is determined by u- and k-indices defined in this paper. The values of the foregoing indices were determined for the key components of transformer station equipment on the basis of empirical data. These indices may be used for advanced economic reliability assessment of power engineering systems and equipment. References [1] Billinton R, Zhang W. Cost related reliability evaluation of bulk power systems. Int J Electr Power Energy Syst 2001;23(2):99–112. [2] Chojnacki AŁ. Analiza skutków gospodarczych niedostarczenia energii elektrycznej do odbiorców indywidualnych. Wiadomos´ci Elektrotechniczne Nr 2009;09:3–9. [3] Costa EO, Pozo A, Vergilio SR. A genetic programming approach for software reliability modeling. IEEE Trans Reliab 2010;59(1):222–30. [4] Costa EO, Vergilio SR, Pozo A, Souza G. Modeling software reliability growth with genetic programming. In: 16th IEEE international symposium on software reliability engineering, 2005, ISSRE; 2005. _ [5] Filipiak S. Strukturalna ocena niezawodnos´ci złozonych układów elektroenergetycznych sieci rozdzielczych z zastosowaniem zmodyfikowanego algorytmu genetycznego. Politechnika S´wie˛tokrzyska, Kielce: Praca Doktorska; 2003. [6] Fukuyama Y, Chiang HD, Nan Miu K. Parallel genetic algorithm for service restoration in electric power distribution systems. Int J Electr Power Energy Syst 1996;18(2):111–9. [7] Gonos IF, Ekonomou L, Topalis FV, Stathopulos IA. Probability of backflashover in transmission lines due to lightning strokes using Monte-Carlo simulation. Int J Electr Power Energy Syst 2003;25(2):107–11. [8] Tang Jianxin, Wang Fangming. Modeling of a transmission network protection system using Petri nets. Electr Power Syst Res 1998;44(3):175–81. [9] Kowalski Z. Niezawodnos´c´ zasilania odbiorców energii elektrycznej. Łódz´: Wydawnictwa Politechniki Łódzkiej; 1992. [10] Kumamoto H, Tanaka K, Inoue K. Efficient evaluation of system reliability by Monte-Carlo method. IEEE Trans Reliab 1977;R-26(5):311–5. [11] Leite da Silvaa AM, Rezendea LS, da Fonseca Mansob LA, de Resende LC. Reliability worth applied to transmission expansion planning based on ant colony system. Electr Power Energy Syst 2010;32(10):1077–84. [12] Lieber D, Nemirovskii A, Rubinstein RY. A fast Monte Carlo method for evaluating reliability indexes. IEEE Trans Reliab 1999;48(3):256–61. [13] Malhotra M, Trivedi KS. Dependability modeling using petri-nets. IEEE Trans Reliab 1995;44(3):428–40. [14] Salehfar H, Li T. Stochastic Petri nets for reliability assessment of power generating systems with operating considerations. In: Power engineering society 1999 winter meeting, IEEE, vol. 1; 31 January–4 February, 1999. p. 459–64. [15] Sozan´ski J. Niezawodnos´c´ i jakos´c´ pracy systemu elektroenergetycznego. Warszawa: WNT; 1990. [16] Sozan´ski J. Niezawodnos´c´ urza˛dzen´ i układów elektroenergetycznych. Warszawa: PWN; 1974. [17] Sozan´ski J. Niezawodnos´c´ zasilania energia˛ elektryczna˛. Warszawa: WNT; 1982.
Contents lists available at SciVerse ScienceDirect
Electrical Power and Energy Systems journal homepage: www.elsevier.com/locate/ijepes
New reliability coefficients of MV/LV transformer/distribution substation and its components Andrew Lukas Chojnacki ⇑ ´ stwa Polskiego 7, 25-314 Kielce, Poland Kielce University of Technology, Power Engineering Department, Al. Tysia˛clecia Pan
a r t i c l e
i n f o
Article history: Received 24 March 2011 Received in revised form 31 May 2012 Accepted 1 June 2012 Available online 15 July 2012 Keywords: Relay-distribution station Reliability Failure frequency Cost of unreliability
a b s t r a c t This paper introduces the possibility of application of u- and k-coefficient to operational reliability analysis of MV/LV transformer/distribution substations. The failure duration index was shown to have specific constraints in cost-related assessments of electric power system reliability. A direct correlation was assumed to exist between the failure duration and the actual emergency shutdown time, which can be shown with the u- and k-coefficients. The value of both indices has been determined on the basis of empirical data collected at two major power plants in Poland throughout the period of 10 years. Ó 2012 Elsevier Ltd. All rights reserved.
1. Introduction The contemporary demands on the quality and continuity of electricity supply have become very high. The unit rated power of MV substations and power lines has been steadily increasing, along with the risk of even more wide-ranging blackouts, and the resulting higher limitations in electricity supply to end-users, which brings about considerable financial losses or, in extreme circumstances, serious risks to human health and life. The costs arising from electric power system unreliability may be classified into three different groups [1,5,9,11,15]: costs – – – costs – – – – costs – –
borne by electric power distributors: loss of income arising from electric power outages; discounts and bonuses for electricity end-users; identification and removal costs of substation-originated failure. borne by industrial end-users: losses arising out of non-performance or delays in performance; losses attributed to process line re-starting downtime; costs resulting from the loss of raw materials and production materials; costs of staff remuneration during downtime. borne by private end-users: time lost during electric power outage; costs of perishable food products lost during electric power outage;
⇑ Tel.: +48 41 342 47 61; fax: +48 41 342 42 14. E-mail address: [email protected] 0142-0615/$ - see front matter Ó 2012 Elsevier Ltd. All rights reserved. http://dx.doi.org/10.1016/j.ijepes.2012.06.003
– costs attributed to sanitary and hygiene conditions deterioration; – losses to the economy when end-users stay at home during electrical power outage. Failure duration (time until recovery) ta is the basic parameter, which defines the extent of the power failure. Failure duration is the time elapsed from component failure until its repair/replacement and the successful restoration of electric power supply [15–17]. The failure duration parameter essentially reflects the quality of failure handling operations and the extent of the power failure in statistical terms. The duration of disruption in power supply to end users tp is another parameter used in assessing electric power system reliability. This is the time elapsed from the onset of power outage until successful restoration of electric power supply to end-users [17]. Failure-related substation downtime twa, is the time elapsed from emergency shutdown (automatically by control systems or manually by technical staff) until successful power restoration to the repaired substation. twa index and the failure duration index are by no means equivalent. The power can be supplied to the failed substation immediately after the major cause of the failure is eliminated and the substation functionality and operational safety is fully or partially restored, despite the fact that the failure status continues. The remaining repairs are performed under live line conditions. The failure cannot be considered to be completely eliminated, although the substation is no longer in the state of emergency shutdown. Moreover, failure is not always synonymous with emergency shutdown. A substation can continue to operate although despite the failure status.
A.L. Chojnacki / Electrical Power and Energy Systems 43 (2012) 992–995
The amount of losses suffered by distributors depends on failure duration and emergency shutdown time. The failure duration for the most part affects the costs of technical service and equipment. On the other hand, emergency shutdown time can influence the duration of power supply outage, and the resulting value of electric power shortage, as well as discounts and bonuses for end-users. The financial losses of electricity end-users depend predominantly on the duration of power supply outage, i.e. the actual substation shutdown time [2,9,17]. This is the actual time period during which end-users have no access to electricity. As a rule, there are no empirical data on emergency shutdown times in statistical data on the operational reliability of specific components of electric power systems. As a result, the extent of power failure and its technical and financial consequences are assessed on the basis of operational reliability indices: failure duration and the failure rare, which are typically easy to determine. This type of approach should be considered to be less accurate for a number of reasons, for example, the time of servicing operations under life line conditions cannot be properly accounted for. Electric power systems can be also repaired without being shutdown, or can be restarted before the failure is completely eliminated. In order to determine the actual costs of failure, all reliability parameters of the analysed components and the entire power systems need to be identified. Nevertheless, there have been no empirical data on electric power system reliability published in international literature within the past few years. This problem has not received all the attention it deserves. New analysis methods of operational reliability have been at the centre of attention. However, it is equally important to identify reliability indices of electric power substations and substation components. All traditional assessment methods of operational reliability should be based on the reliability indices of specific substation components, and reliability models are required to be developed to identify the reliability indices of the substation as a whole. It may be at times difficult to determine specific reliability models, and in particular, it may appear problematic to account for auxiliary systems and systems, which are not directly involved in electricity processing and supply (control and signalling systems, condenser batteries, lightning arresters, voltage transformers and current transformers). With reference to the foregoing, simulation methods have been recently introduced based on computational solutions, i.e. the Petri net [8,13,14], genetic algorithm methods [3–6], the Monte Carlo method [7,10,12] and many more. However, in order to be able to rely on the aforementioned reliability assessment methods, reliability parameters of all system components need to be determined. Irrespective of the reliability assessment method applied, the basic reliability data are required to be identified, including, but not limited to data on failure duration, emergency shutdown time, and the duration of power outage. Different aspects of reliability analyses (technical, economical, etc.) are required to be based on the applicable type of index. It has been attempted to identify mathematical correlations between reliability parameters referring to failure duration and emergency shut-down time in order to find the way to determine shutdown duration parameters based on failure duration parameters. Taking into account the most popular structural solutions of MV substations, servicing operations performed under live line conditions, and the characteristics of specific indices, the possible failure variants of MV transformer/distribution substations have been analysed in order to establish specific failure-related behaviours of substations.
2. Definition and determination of u- and k-index Failure duration, failure rate and failure-related unreliability indices are the most common reliability parameters of electric
993
power components and systems. The aforementioned parameters can be basically determined using data from the records of electricity distributing companies. A detailed analysis has been performed to determine whether the aforementioned parameters are sufficient to establish failure-related shutdown indices. It was also investigated whether any empirical correlations exist between failure duration and emergency shutdown time. Based on theoretical studies and comprehensive empirical examinations, the following new indices have been introduced:
kwa u¼ k
ð1Þ
and
k¼
qwa q
ð2Þ
where u is the share of emergency shut-down rate; k is the share of unreliability index of emergency shutdowns; k is the average total 1 failure rate yearde v ice; kwa is the average failure rate resulting in emer1 gency shutdown yearde v ice; q is the unreliability index (determined for all failure states); qwa is the unreliability index of emergency shutdowns. u-index has the following characteristics: u-index is in the range of u e h0; 1i; u = 0 where no emergency shut-down takes place after a component failure; u = 1 where emergency shut-down takes place after each failure; u-index is in the range of u e (0; 1) for all other types of components. k-index has the following characteristics: k P 0; k = 0 where no emergency shutdown takes place after a component failure, and where repairs are performed under live line conditions; k is the range of k e (0; 1) where failure can optionally, but not necessarily result in emergency shutdown, or if the time of emergency shutdown is shorter than the failure duration. In general, k-index values is in the range of k e (0; 1) if the following condition is fulfilled: kwa twa < k t a ; k = 1 where emergency shutdown takes place after each failure and where the failure duration equals the shutdown time. In general, k = 1 if the following condition is fulfilled: kwa twa ¼ k t a ; k > 1 if the emergency shutdown time is longer than the emergency duration, under the assumption that the component is shutdown whenever a failure takes place. In general, k > 1 if the following condition is fulfilled: kwa twa > k t a . This condition applies to systems with redundancy capability. It is possible to define specific average values of u and k indices for various structural solutions of substations. The indices would be then defined as the proportion of average failure rate causing substation shutdown to the total substation failure rate, and as the proportion of unreliability index defined for substation emergency shutdowns to unreliability index defined for all emergency conditions of the substation in question. Other indices related to emergency shut-downs, i.e. average emergency shut-down rate or emergency shut-down time can be defined on the basis of the share of emergency shut-down rate index kwa in the total failure rate k, the share of unreliability index of emergency shut-downs qwa in the total unreliability index q, failure duration and average failure rate. As a result, the operation of specific substation components and of substations in general can be determined in a more comprehensive manner.
994
A.L. Chojnacki / Electrical Power and Energy Systems 43 (2012) 992–995
Depending on the collected reliability data, and in consideration of the following empirical correlations [17]:
k ¼
2m ðnp þ nk Þ Dt
ð3Þ
where m is the number of conditions (failures, emergency shutdowns, etc.); np, nk is the sample size at the beginning and at the end of the period of observation; Dt is the period of observation, can be translated into a relationship (1) to be later used in determining u-index value: 2mwa
kwa ðn þn ÞDt mwa u ¼ ¼ p 2mk ¼ m k ðnp þnk ÞDt
ð4Þ
where mwa is the number of emergency shutdowns; m is the number of failures observed. Under the assumption that the emergency shutdowns and failures refer to the same sample and occur within the same period of observation. Based on the relationship [17]:
q¼
k t 1 þ k t
ð5Þ
where k is the rate of conditions in question (failures, emergency shutdowns, etc.); t is the duration of the conditions under analysis, can be also translated in to the following relationship (2):
k¼
k t wa kwa twa 1 þ k t a qwa 1þwa ¼ kkwat twa ¼ a q k ta 1 þ kwa twa t 1þk
ð6Þ
a
If the following relationships are met: k t a 1 kwa twa 1, the a/m relationship can be simplified into:
kwa t wa twa k¼ ¼u ta k ta
and
ð7Þ
If the values of u and k indices and failure durations are known for a specific substation component or the substation in general, the emergency shutdown time can be defined as:
t wa ¼ k t a u
ð8Þ
and the emergency shutdown rate can be determined as:
kwa ¼ u k
ð9Þ
3. Values of u and k indices for electric power components and substations operating in Poland Reliability indices for individual components and substations in general have been determined based on data collected in the course of a 10-year long reliability study of MV electric power substations at two major electricity distribution companies in Poland. 8500 substations in total were operating in the first year of the observation period. At the end of this period, the number of substations increased to 9638. The number of individual components at the beginning and at the end of the period of observation has been calculated on the basis of detailed analyses. The data are shown in Table 1. Within the 10-year period of observation, 3363 emergencies have taken place in MV substations. Table 1 presents also the number of failures per each group of components. u and k indices for MV electric power substations have been calculated on the basis of statistical sample referred to above. Table 2 presents the calculation results. The analysis clearly indicates that the highest u-index values have been obtained for cut-off switches (0.99), cable heads (0.97) as well as for transformers, lightning arresters and insulators (0.95). These components are nearly always shutdown in case of failure. Protection and control automation system elements (0.42), voltage transformers (0.65) or condenser batteries (0.75) represent a different group of components. Failure can optionally, but not necessarily trigger an emergency shutdown. Only 42 out of 100 failures of the protection and control automation systems cause an emergency shutdown of the component or the substation. In the remaining 58 cases, the substation continues to operate and the failure is removed without the substation being shutdown by the service staff. k-indices denoting the share of total emergency shutdown time in the total failure duration are relatively low, which confirms that reliability analyses relying exclusively on failure duration are insufficient to provide reliable data. k-index was the lowest for protection and control automation systems (0.30). The total emergency shutdown time for protection and control automation systems accounted for 30% of the total failure duration. The k-index for current transformers was estimated at 51%. Transformers were found to have the highest k-index (0.92). The total emergency shutdown time of transformers accounted for as much as 92% of the total failure duration. u- and k-indices were also determined for two typical structural solutions of substations operating in Poland: simple outdoor polemounted MV substations typical for rural areas, and urban-type
Table 1 Number of substation components and number of failures in MV substations. Component
– Condenser batteries Voltage transformers Current transformers Cut-off switches Bus-bars Circuit-breakers Isolating switches Insulators Cable heads Lightning arresters Protection and control automation systems Transformers
Number of substation components
Number of failures
Component failure rate vs. total failure rate
Failure rate vs. number of components
– 4959 289 289 4779 2982 1514 15250 88474 58983 17077 –
– 32 55 69 71 87 122 362 442 466 471 585
[%] 0.95 1.64 2.05 2.11 2.59 3.63 10.76 13.14 13.86 14.01 17.40
[%] 0.07 1.93 2.44 0.16 0.31 0.86 0.25 0.05 0.08 0.29 4.28
9883
601
17.87
0.65
At the beginning of the period of observation
At the end of the period of observation
– 4306 281 277 4146 2655 1325 13564 76815 51209 15103 – 8581
A.L. Chojnacki / Electrical Power and Energy Systems 43 (2012) 992–995 Table 2 u- and k-indices for selected MV substation components. Component
u-index
k-index
Condenser batteries Voltage transformers Current transformers Cut-off switches Bus-bars Circuit-breakers Isolating switches Insulators Cable heads Lightning arresters Protection and control automation systems Transformers
0.75 0.65 0.90 0.99 0.91 0.83 0.94 0.95 0.97 0.95 0.42 0.95
0.74 0.51 0.83 0.68 0.79 0.79 0.77 0.71 0.89 0.68 0.30 0.92
transformer/distribution substations with a more complicated structure. This type of substations is typically equipped with protection and control automation systems, remote control systems of connectors and monitoring systems of measurement instrumentation at the power dispatch centre. u- and k-indices of simple pole-mounted substations equalled 0.96 and 0.77, respectively. According to the u-index, simple pole-mounted substations are shutdown 96 times per 100 failures, and four out of 100 failures are repaired without being shutdown by the service staff. k = 0.77 means that the total emergency shutdown time of simple polemounted substations accounts for approximately 77% of the total failure time. u and k-indices for urban-type in-door substations have been calculated in the same manner to produce the following results: u = 0.52 and k = 0.34. u = 0.52 means that the complex in-door urban-type substations are shut-down 52 times per 100 failures, and 48 out of 100 failures are repaired without being shut-down by the service staff. k = 0.34 means that the total emergency shutdown time of urbantype in-door substations accounts for approximately 34% of the total failure time.
4. Summary Reliability analyses of electric power systems aimed at determining the extent of losses suffered by end users and electricity distributors are predominantly based on failure duration, failure rate and estimated average annual failure duration. This type of approach to reliability analysis appears to be insufficient due to the fact that parameters defining the failure duration are by no means equivalent to the parameters, which define the duration of power outages. In consideration of the foregoing, the analysis of financial losses should be based on reliability parameters referring to the duration of emergency shutdowns and power supply interruptions rather than the failure duration. Analyses carried out by the author showed that the use only of the duration of the failure causes an error of 10–30%. New reliability indices have been introduced which account for the failure type and failure sequence referring to individual substation components and the power substation in general. The new parameters are the attributes of a specific structural solution that a specific component or substation represents, and can be therefore classified as rated parameters. It is therefore possible to deter-
995
mine the value of component/substation shutdown time index only on the basis of its failure duration parameters. In traditional reliability assessment methods, reliability parameters of specific components are required to be determined along with reliability models for the substation in general. It can be at times difficult to determine specific reliability models, in particular, it may appear problematic to account for auxiliary systems and systems which are not directly involved in electricity processing and supply (control and signalling systems, condenser batteries, lightning arresters, voltage transformers, current transformers). When the u- and k-indices are used in the reliability analysis, the auxiliary systems are always accounted for in the reliability model, along with the actual impact of auxiliary systems on reliability parameters of the entire substation. The analysis performed showed the existence of an empiric relation between failure duration and emergency shut-down time of equipment operating in MV/LV transformer stations. This relation is determined by u- and k-indices defined in this paper. The values of the foregoing indices were determined for the key components of transformer station equipment on the basis of empirical data. These indices may be used for advanced economic reliability assessment of power engineering systems and equipment. References [1] Billinton R, Zhang W. Cost related reliability evaluation of bulk power systems. Int J Electr Power Energy Syst 2001;23(2):99–112. [2] Chojnacki AŁ. Analiza skutków gospodarczych niedostarczenia energii elektrycznej do odbiorców indywidualnych. Wiadomos´ci Elektrotechniczne Nr 2009;09:3–9. [3] Costa EO, Pozo A, Vergilio SR. A genetic programming approach for software reliability modeling. IEEE Trans Reliab 2010;59(1):222–30. [4] Costa EO, Vergilio SR, Pozo A, Souza G. Modeling software reliability growth with genetic programming. In: 16th IEEE international symposium on software reliability engineering, 2005, ISSRE; 2005. _ [5] Filipiak S. Strukturalna ocena niezawodnos´ci złozonych układów elektroenergetycznych sieci rozdzielczych z zastosowaniem zmodyfikowanego algorytmu genetycznego. Politechnika S´wie˛tokrzyska, Kielce: Praca Doktorska; 2003. [6] Fukuyama Y, Chiang HD, Nan Miu K. Parallel genetic algorithm for service restoration in electric power distribution systems. Int J Electr Power Energy Syst 1996;18(2):111–9. [7] Gonos IF, Ekonomou L, Topalis FV, Stathopulos IA. Probability of backflashover in transmission lines due to lightning strokes using Monte-Carlo simulation. Int J Electr Power Energy Syst 2003;25(2):107–11. [8] Tang Jianxin, Wang Fangming. Modeling of a transmission network protection system using Petri nets. Electr Power Syst Res 1998;44(3):175–81. [9] Kowalski Z. Niezawodnos´c´ zasilania odbiorców energii elektrycznej. Łódz´: Wydawnictwa Politechniki Łódzkiej; 1992. [10] Kumamoto H, Tanaka K, Inoue K. Efficient evaluation of system reliability by Monte-Carlo method. IEEE Trans Reliab 1977;R-26(5):311–5. [11] Leite da Silvaa AM, Rezendea LS, da Fonseca Mansob LA, de Resende LC. Reliability worth applied to transmission expansion planning based on ant colony system. Electr Power Energy Syst 2010;32(10):1077–84. [12] Lieber D, Nemirovskii A, Rubinstein RY. A fast Monte Carlo method for evaluating reliability indexes. IEEE Trans Reliab 1999;48(3):256–61. [13] Malhotra M, Trivedi KS. Dependability modeling using petri-nets. IEEE Trans Reliab 1995;44(3):428–40. [14] Salehfar H, Li T. Stochastic Petri nets for reliability assessment of power generating systems with operating considerations. In: Power engineering society 1999 winter meeting, IEEE, vol. 1; 31 January–4 February, 1999. p. 459–64. [15] Sozan´ski J. Niezawodnos´c´ i jakos´c´ pracy systemu elektroenergetycznego. Warszawa: WNT; 1990. [16] Sozan´ski J. Niezawodnos´c´ urza˛dzen´ i układów elektroenergetycznych. Warszawa: PWN; 1974. [17] Sozan´ski J. Niezawodnos´c´ zasilania energia˛ elektryczna˛. Warszawa: WNT; 1982.