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Risk assessment of interruption times affecting domestic and non-domestic electricity customers
Electrical Power and Energy Systems 55 (2014) 59–65
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Electrical Power and Energy Systems journal homepage: www.elsevier.com/locate/ijepes
Risk assessment of interruption times affecting domestic and non-domestic electricity customers Irinel-Sorin Ilie ⇑, Ignacio Hernando-Gil, Sasa Z. Djokic Institute for Energy Systems, The University of Edinburgh, Mayfield Road, Edinburgh EH9 3JL, United Kingdom
a r t i c l e
i n f o
Article history: Received 27 February 2013 Received in revised form 28 August 2013 Accepted 30 August 2013
Keywords: Customer interruption Penalty target Reliability analysis Security of customer supply
a b s t r a c t Legislation defined to protect domestic and non-domestic customers from long durations of interruptions includes additional requirements to system’s reliability-related performance that distribution network operators (DNOs) must consider in planning the operation and maintenance process of power supply systems. DNOs are required to restore the supply to interrupted customers that fall into ‘‘unprotected’’ customer class within a given period of time, otherwise penalties are applied. In order to meet these requirements, comprehensive strategies must be defined based on upfront analyses. Accordingly, this paper proposes a deterministic algorithm for estimating DNOs’ risk of experiencing interruptions with durations above imposed targets. Besides the Regulator-defined legislation, security of supply requirements are engaged in the development of the proposed methodology. Failure analysis of network components is used to identify interrupted customers that are grouped into power demand classes such that the duration of interruptions can be addressed following the security of supply requirements. Moreover, the penalty times defined by the Energy Regulator are engaged in the analysis and used as thresholds to quantify the penalty risk that DNOs are exposed to. The proposed methodology is applied to a typical UK distribution system, whose average reliability performance is also considered in the analysis. 2013 Elsevier Ltd. All rights reserved.
1. Introduction Reliability performance of power supply systems is nowadays a major priority for distribution network operators (DNOs). Energy Regulators impose annual reliability and continuity of supply targets for the frequency and duration of customer interruptions and, accordingly, penalties or rewards are applied to each DNO based on the achieved performance. In the UK, DNOs’ annual reports submitted to Regulator (The Office of Gas and Electricity Markets, Ofgem) must contain a set of reliability indicators which reflect the network performance. Three system-related metrics [1], namely customer interruption (CI), customer minutes lost (CML) and short interruption (SI), are used to quantify the frequency and duration of long and short interruptions occurred within the supply system. Even though all three metrics are reported to Regulator, targets are only imposed for the CI and CML indices. In order to avoid penalties for poor reliability performance, DNOs must carefully plan the operation and maintenance process of the power supply systems they manage. However, statistics show that this is not an easy task as 14% of the UK DNOs have recently been penalised for not achieving the targets set up for ⇑ Corresponding author. Tel.: +44 131 650 5575. E-mail address: [email protected] (I.-S. Ilie). 0142-0615/$ - see front matter 2013 Elsevier Ltd. All rights reserved. http://dx.doi.org/10.1016/j.ijepes.2013.08.030
the CI index, while 50% of the DNOs exceeded the limits imposed for CML [2]. Besides the targets for CI and CML, DNOs must also obey additional requirements related to the duration of long interruptions for customers that are not protected by special contracts/agreements (i.e. residential). This means that for those customers that correspond to unprotected category, DNOs are obliged to restore the supply within a given period of time otherwise penalties are applied [3]. No rewards are however applied in this case and penalties are paid directly to affected customers and not to Regulator. An efficient planning strategy, which may lead to reported reliability indices below the targets and avoid unprotected customerrelated penalties, requires accurate upfront analyses of system’s reliability performance. Monte Carlo simulation (MCS) is an effective method that has widely been used in such surveys [4–22]. Detailed network modelling and statistics of failure rates and repair times for all network components are inputs for the MCS technique. The network model and failure rates are used to assess the frequency of the customers interrupted by failure/faults occurred within the system. Moreover, the duration of long interruptions is obtained based on the mean time to repair (MTTR) values of faulted network components, whereas the times corresponding to the protection settings are used to calculate the duration of short interruptions. Once the frequency and duration
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of interruptions are achieved, the reliability indices can further be calculated and different planning strategies can be adopted. This paper proposes a straightforward methodology for assessing the reliability performance response of power supply systems to targets which are imposed by Regulator to protect domestic and non-domestic customers from extremely long durations of interruptions. For that purpose, a comprehensive database with failure rates and repair times reported for network components operating in the UK, corresponding protection schemes, UK security of supply requirements and Regulator-related legislation are engaged in the reliability analysis. The risk of having interruptions above the targets is one of the main outputs of the proposed methodology.
residential and non-domestic customers from excessively long interruption events. These requirements are introduced to protect those categories of customers that have no special contracts or agreements with DNOs regarding the duration of interruptions. The Electricity Standard of Performance Regulations [3] is the main UK statutory instrument which indicates the maximum admissible durations of interruptions for up to 5000 customers and more than 5000 customers. Table 2 presents these interruption time limits together with the corresponding penalties DNOs will pay directly to the customers (not to the Regulator), if supply is not restored within the specified period of time.
3. Reliability analysis 2. Security of supply requirements and legislation for customer interruption process 2.1. Security of supply requirements Power supply systems are designed to meet security of supply requirements during events which lead to interruptions of customer supply. After an interruption, the supply to electricity customers has to be restored within a specified period of time. Therefore time limits are defined as maximum durations required by security of supply legislation to restore at least a minimum group of customers. Considering the design process, the network configuration, protection schemes and repair process of faulted network components are the main features which decide the duration of interruptions. Classes of supply are defined in [23] based on group demand ranges, for which the duration of interruptions is imposed so that the minimum demand can be met. An example of how customers’ supply is restored within different periods of time is presented in Table 1. Six classes of supply (A to F) are defined on group demand (GD) ranges for which the maximum durations of interruptions and minimum demand that has to be met are specified. For example, if a group of customers with the power demand between 1 MW and 12 MW is interrupted, the supply must be restored to most of the customers in three hours’ time. For the remaining interrupted customers within that group, the power supply can be restored in accordance with the duration necessary to repair the faulted component which affected the customers (i.e. in repair time/MTTR). 2.2. Legislation for DNOs supplying customers without interruptionsrelated contracts The UK Regulator specifies additional requirements for the duration of customer interruptions in order to protect domestic/ Table 1 UK security of supply requirements for interrupted customers [23]. Class of supply
Range of group demand (GD)
Minimum demands to be met after first circuit outage
A B
GD 6 1 MW 1 MW < GD 6 12 MW
C
12 MW < GD 6 60 MW
D
60 MW < GD 6 300 MW
E F
300 MW < GD 6 1500 MW GD > 1500 MW
In repair time: GD (a) Within 3 h: GD-1 MW (b) In repair time: GD (a) Within 15 min: min{GD-12 MW; 2/3 GD} (b) Within 3 h: GD (a) Immediately: GD-up to 20 MW (b) Within 3 h: GD Immediately: GD According to transmission license security standard
Analytical methods and simulation techniques can be employed to assess the reliability performance of power supply systems [9]. Analytical methods use mathematical models, which represent the analysed system in probability calculations of different states of the system and provide numerical solutions for reliability metrics. The outputs of the analytical methods are restricted to mean values and standard deviations, whereas the simulation procedures provide additional output results in the form of probability distributions of considered reliability parameters. Inverse Transform method, also known as Monte Carlo simulation [10,24–27], is adopted in this paper to address the interruption process of electricity customers. The first step of the MCS procedure is to identify physical parts of the analysed system and collect information on their electrical and mechanical parameters necessary for reliability analysis. Then, a comprehensive database with failure/fault rates and mean repair times for all network components within the system should be created as in Table 3. A random generator is used to assign random variables to an inverse distribution function in order to convert the failure rates and repair times into system states based on the operating and failure stages of individual network component. The operating and failure states of the system are determined from the corresponding component failure rates, whereas the repair times provide the duration of the failure states of the system. In this paper, the standard assumption that the initial conditions of component failure rates and repair times are exponentially distributed is considered, although other distributions such as Gamma, Weibull or Rayleigh can also be adopted [10]. The outputs of the reliability assessment procedure are expressed as frequency and duration of short and long interruptions, which can be further used to calculate the reliability indices that DNOs report to Regulator. The main steps of the MCS procedure are summarised in Fig. 1.
4. Deterministic algorithm for customer interruption risk assessment DNOs’ risk of being penalised due to durations of interruptions above the threshold of 18 h for up to 5000 customers and 24 h for more than 5000 customers has also consequences on the CML targets that DNOs must meet annually for the overall system reliability performance. This means that if the duration of interruptions is reduced for individual groups of customers in accordance with the thresholds given in Table 2, the system-related index CML will be decreased and thus the targets for the latter are more likely to be met. This paper proposes a deterministic algorithm for estimating DNOs’ risk of being penalised when the time requirements specified for domestic and non-domestic customers are considered as
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I.-S. Ilie et al. / Electrical Power and Energy Systems 55 (2014) 59–65 Table 2 Duration of interruption requirements for domestic and non-domestic customers [3].
*
No. of interrupted customers
Maximum duration to restore supply
Penalty paid to Domestic customers
Non-domestic customers
Less than 5000*
18 h After each succeeding 12 h
£54 £27
£108 £27
5000* or more
24 h After each succeeding 12 h
£54 £27
£108 £27
5000 Customers correspond to about 12 MW residential load.
Table 3 Reliability data for main network components [28].
Input data: Failure rates, repair times
Network component
Voltage level (kV)
Failure rate (failures/year)
Mean repair time (hours)
Overhead lines
0.4 11 33 132
0.168 0.091 0.034 0.0038
5.7 9.5 20.5 19.1
Cables
0.4 11 33 132
0.159 0.051 0.034 0.0277
6.9 56.2 201.6 222.7
11/0.4 33/0.4 33/11 132/11 132/33 400/132
0.002 0.01 0.01 0.0392 0.0392 0.0392
75 205.5 205.5 250.1 250.1 250.1
0.4 11 >11
0.005 0.005 0.08
24 120 140
0.4 11 33 132 275 400
0.005 0.0033 0.0041 0.0264 0.0264 0.0264
36 120.9 140 98.4 98.4 98.4
11
0.0004
35.3
Trans-formers
Buses
Circuit breakers
Switch fuses
Create a list with all power components k = 1,…, K
Set time step ΔT for reliability analysis
Assess probability of SI and LI interruptions
Select component k from list
Generate random variable (RVs)
Time to fail (TTF)
NO
Time to repair (TTR)
TTF<ΔT YES Count failures
Run power flow
NO
targets and included in the procedure that is used to assess the reliability performance of a supply system. Let us consider that N is the total number of group demand classes specified in the security of supply requirements and that customer group vector c = [c1, c2, . . ., cn] consists of n 6 N customer classes. For each group of customers ci, " i = 1, . . ., n, a time vector t = [t1, t2, . . ., tn] can be defined so as to contain the time classes ti which represent the durations required to restore the supply according to security of supply values. Each time class ti can take more than one value when the supply is restored on stages (i.e. classes B, C and D in Table 1). Furthermore, time thresholds sj, " j = 1, . . ., v as specified in Table 2 for domestic and non-domestic customers are used to define a time threshold vector s = [s1, s2, . . ., sv] " v 6 V, where V is the total number of imposed duration limits for restoring the supply. Both vectors t and s are incorporated in the MCS procedure to model the reconfiguration of the system after an event (i.e. restore the supply to interrupted customers within 15 min in the case of customer class C) and DNOs’ response to failures, which requires the replacement of faulted component, when the risk of being penalised is estimated in accordance with the time threshold targets sj instead of MTTR values. Thus, every time ‘‘In repair time’’ is given in the security of supply requirements (e.g. class A in Table 1), the value of ti (=MTTR) is replaced by the time thresholds sj.
Check loads interrupted YES
Count no. of interruptions
NO
SI
LI
YES Duration of SI given by protections
Duration of LI given by TTR
Centralise frequency and duration of SI and LI
Compute reliability indices
Fig. 1. Simplified block diagram of the MCS procedure.
The MCS procedure presented in Section 3 changes slightly during the risk assessment with the time thresholds sj. An initial stage is required to determine the network components whose failures lead to customer interruptions and for which the supply is not restored unless the faulted components are repaired within the time given by the MTTR values (e.g. there is no alternative supply which
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0.4kV 33kV
132kV
33kV
1MVA
11kV Grid Supply System
30MVA
L1
24MVA
L2
0.4kV
(33kV O/H Lines)
Zsys
30MVA
1MVA
24MVA
L3L4
0.4kV 33kV
1MVA
2.5MVA
2.5MVA
11kV
0.2MVA
0.4kV
1MVA
To adjacent MV Network
0.4kV 0.4kV
0.2MVA
1MVA
0.4kV 0.4kV
1MVA
0.2MVA
0.4kV To adjacent MV Network
* The whole system consists of about 15,000 customers
Fig. 2. UK distribution system with typical highly-urban and suburban configurations [29].
Table 4 Fault clearance time of typical UK protection systems [30,31]. Network component
Voltage level (kV)
Protection system
Fault clearance time (s)
Overhead lines
11
Circuit breaker with auto-reclosing Circuit breaker with auto-reclosing
10–120
33 Cables
11 33
Transformers
11/0.4 33/11 132/33
Busbars
0.4 11 33 132
Circuit breaker with auto-reclosing Circuit breaker with auto-reclosing
90 Up to 3 90
Fuse switches Circuit breaker with auto-reclosing Circuit breaker with auto-reclosing
Repair time 0.15–10
Fuse switches Circuit breaker Circuit breaker Circuit breaker
Repair time 0.15 0.15 0.15
0.15–10
allows for network reconfiguration). Firstly, two lists L1 and L2 are created: L1 = {1, . . ., k}, " k = 1, . . ., K with all network components K within the system and L2 = {1, . . ., m}, " m = 1, . . ., M with all customers M served by the system. Then, both lists are arranged in ascending order of their network components and customers’ identification number. The first network component is selected from L1 and a power-flow simulation is run to establish the group of customers affected by its failure. All interrupted customers are identified in L2 and assigned to their corresponding customer class ci. Once the class of interrupted customers is determined, its power
range is selected from the second column of Table 1. Moreover, the duration required to restore the supply to the interrupted customers is identified as the time corresponding to the customer class affected by the failure. The procedure is carried on with the selection of the second network component from L1, determination of the interrupted customers within L2 as a consequence of component’s failure, the class the interrupted customers fall into and the corresponding duration required to restore the supply to interrupted customers. The labelling process is repeated until all components are addressed, all customers are assigned to classes and the list L1 becomes empty. At this stage of the analysis it is known the duration corresponding to each network component within the analysed system that is necessary to reconfigure the system, find alternative supply or repair it in case it fails. The next step of the proposed deterministic algorithm is to replace the time values of those network components, which must be repaired within the time given by MTTR so as to restore the supply to interrupted customers, with the time thresholds sj and then run the MCS procedure. Thus, the reductions in the estimated penalty risk are quantified when the system’s reliability performance response to targets is addressed. A summary of the proposed methodology is provided in the following: (1) (2) (3) (4)
count the number N of group demand classes, define vector c with customer groups, define vector t with security of supply durations, define vector s with time thresholds for domestic and nondomestic customers, (5) create a list L1 with all network components, (6) create a list L2 with all customers served,
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I.-S. Ilie et al. / Electrical Power and Energy Systems 55 (2014) 59–65 MTTR
0.18 0.16
PDF
0.12 0.1 0.08 0.06 0.04
penalty threshold of 18 h
0.18 0.16 0.14 0.12 0.1 0.08 0.06 0.04 0.02 0
0.14
0
0.02
time threshold
5
10
15
Prob (duration > 18 h) = 36.8 % Prob (duration > 18 h) = 10.9 %
20
25
30
35
40
45
50
0 0
100
200
300
400
500
600
700
800
duration of interruptions (h)
(a) customer class c1 with interrupted power up to 1 MW. MTTR
0.6
time threshold
penalty threshold of 18 h
0.5
PDF
0.4 0.3 0.2 0.1
Prob (duration > 18 h) = 0.2 % Prob (duration > 18 h) = 0.1 %
0 0
5
10
15
20
25
30
35
40
duration of interruptions (h)
(b) customer class c2 with interrupted power between 1 MW and 12 MW. 1
MTTR
time threshold
0.8
PDF
0.6
0.4
Prob (duration > 18 h) = 0
0.2
0 0
0.2
0.4
0.6
0.8
1
1.2
duration of interruptions (h)
(c) customer class c3 with interrupted power between 12 MW and 60 MW. Fig. 3. Estimated durations of interruptions for the UK test distribution system.
(7) sort the contents of L1 and L2 in ascending order, (8) select first network component from L1 and check interrupted customers from L2 affected by its failure, (9) identify interrupted customers and assigned them to corresponding class ci (10) establish power range the interrupted customers fall into, (11) identify the duration to restore the supply to interrupted customers in security of supply requirements, (12) repeat process until list L1 becomes empty, (13) replace MTTR values with time thresholds sj, (14) run MCS procedure, (15) assess the risk associated with duration of interruptions. 5. Test system configuration and protection settings A typical UK distribution network consisting of two 11 kV highly-urban and suburban configurations with about 15,000 domestic and non-domestic customers is used in this paper for reliability simulations. Fig. 2 illustrates the test system with the
highly-urban configuration operated as a meshed network and the suburban system operated in a radial configuration. Moreover, all electricity customers are supplied through 11/0.4 kV transformers. The fault clearance times of the protection schemes in Fig. 2 are values used by the UK DNOs for their power supply systems. The protection settings adopted in this paper are shown in Table 4. These values correspond to the durations implemented in the
Table 5 Penalty risk estimated for durations of interruptions above Regulator-imposed time thresholds. Customer class
Class 1 Class 2 Class 3
Risk (%) results for MTTR inputs
Time thresholds inputs
36.8 0.2 0
10.9 0.1 0
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0.5
MTTR
time threshold
1000
1500
PDF
0.4
0.3
0.2
0.1
0 0
500
2000
2500
CML (minutes/customer/year)
(a) CML index. 0.6
MTTR
time threshold
0.5
PDF
0.4 0.3 0.2 0.1 0 0
50
100
150
200
250
300
CI (interruptions/100 customers/year)
(b) CI index.
PDF
0.6
MTTR
refers to the system’ reliability performance response to the time thresholds defined to protect customers from excessively long durations of interruptions. This means that instead of restoring the supply to interrupted customers within the time given by MTTR, the time thresholds sj are engaged into analysis. Employing the deterministic procedure proposed in this paper, it is found that all electricity customers supplied through the distribution system in Fig. 2 demand about 36 MW of power, which cover the first three customer classes c1, c2 and c3 defined in the security of supply requirements. Accordingly, the risk analysis for the duration of interruptions is carried out for each customer class. Fig. 3 presents the probability distribution functions (PDFs) of the duration of interruptions estimated for the three customer classes. The risk of having interruptions above the time threshold of 18 h decreases significantly with the increase of customer class power demand. This reduction is explained by the ability of the system to find alternative supply through system reconfiguration when faulted components disconnect large amounts of load. In case estimations are obtained based on MTTR, the penalty risk given by the probability of having interruptions above the threshold of 18 h is about 37% for customers within class c1, dropping to zero for customer classes c2 and c3, respectively. The duration of interruptions assessment against targets indicates a penalty risk of about 11% for class c1. This suggests that the penalty risk can be reduced sharply if average values of imposed targets are considered to restore the supply to interrupted customers instead of long repair times. Table 5 gathers all calculated risk values of having interruptions above the penalty threshold.
time threshold
0.5
6.2. Reliability indices reported to Regulator
0.4
The reliability performance of the test system is assessed through the calculation of the standard set of annual reliability indices CI, SI and CML [1] that the UK DNOs report to Ofgem. The calculation of these indices follows the relations (1)–(3) below.
0.3 0.2 0.1
CI ¼ 0 0
50
100
150
200
250
300
The sum of the total number of customers interrupted for all incidents 100 Total number of customers ð1Þ
SI (interruptions/100 customers/year)
(c) SI index. Fig. 4. Probabilistic estimations of reliability indices.
MCS procedure when the supply to interrupted customers is restored after short interruptions. 6. Simulation tests with the proposed methodology 6.1. Duration of interruptions assessment The risk of having interruptions with durations above the thresholds that protect domestic and non-domestic customers is addressed for the test system in Fig. 2. Firstly, the duration of customer interruptions are obtained from the actual system’s reliability performance computed with MTTR values, which are fed into the MCS procedure. This analysis would estimate the customer interruption process without any other planning decisions than simply restoring the supply to interrupted customers within the repair time. However, planning the customer interruption process should consider strategies that include the risk of facing penalties if supply is not restored within the time thresholds imposed by Regulator. For that reason, the second case analysed in this paper
SI ¼
The sum of the total number of customers interrupted by short interruptions 100 Total number of customers ð2Þ
CML ¼
The sum of the customer minutes lost for all restoration stages for all incidents Total number of customers ð3Þ
The system’s reliability performance response to the penalty targets, which protect domestic and non-domestic customers from long durations of interruptions, are compared in Fig. 4 against the results obtained for MTTR inputs. The proposed deterministic algorithm only has influence on the results of the duration-related index CML (Fig. 4a). An average value of 118 min per customer and year represents the performance of the system if supply is restored within the repair time (MTTR), whereas 50 min per customer and year is the performance response of the system at penalty time targets. A 58% reduction in the CML index could decide whether or not the system’s owner is rewarded for improved reliability performance. The frequency-related indices shown in Figs. 4b and c are not modified when the proposed deterministic procedure is implemented. The average values of CI and SI are for both analysed cases about 60 and 70 interruptions per 100 customers and year.
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7. Concluding remarks The time limits defined by the UK Energy Regulator to protect domestic and non-domestic electricity customers from excessively long durations of interruptions have been exploited in this paper to create a new deterministic algorithm that can be used in reliability analyses. The proposed methodology allows estimating the risk of interruption times above the Regulator-imposed limits when the reliability performance of the analysed system is tested to respond to those targets. Security of supply requirements have been employed in the proposed procedure to identify the network components whose failures lead to interruptions of the customer supply with durations equal to the repair times. Once those network components have been identified, the Regulator-imposed time limits are introduced in the analysis. The MTTR values are replaced by the time limits only for the identified components and the MCS procedure is applied. The outputs of the proposed procedure have firstly been expressed as risk values calculated for the durations of the customer interruption process, and then as system-related reliability indices. Reductions are significantly visible in all results that quantify the durations of interruptions after the repair times have been changed with the targets. Acknowledgements This work was supported by the UK Engineering and Physical Sciences Research Council (EPSRC) project EP/G052530/1. References [1] Quality of service regulatory instructions and guidance, RIGS version 5; March 2005. [2] Electricity distribution quality of service report, Ofgem, annual report; December 2009. [3] The electricity standard of performance regulations, Statutory Instruments, no. 698; March/April 2010. [4] Billinton R, Allan RN. Power system reliability in perspective. IEE Electron Power 1984:231–6. [5] Billinton R, Wojczynski E. Distributional variation of distribution system reliability indices. IEEE Trans Power Apparatus Syst 1985;11:3152–60. [6] Allan RN, Billinton R. Power system reliability and its assessment. Part 1: Background and generating capacity. Power Eng J 1992;6:191–6. [7] Allan RN, Billinton R. Power system reliability and its assessment. Part 2: Composite generation and transmission systems. Power Eng J 1992;6:291–7. [8] Allan RN, Billinton R. Power system reliability and its assessment. Part 3: Distribution systems and economic considerations. Power Eng J 1993;7:185–92.
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Electrical Power and Energy Systems journal homepage: www.elsevier.com/locate/ijepes
Risk assessment of interruption times affecting domestic and non-domestic electricity customers Irinel-Sorin Ilie ⇑, Ignacio Hernando-Gil, Sasa Z. Djokic Institute for Energy Systems, The University of Edinburgh, Mayfield Road, Edinburgh EH9 3JL, United Kingdom
a r t i c l e
i n f o
Article history: Received 27 February 2013 Received in revised form 28 August 2013 Accepted 30 August 2013
Keywords: Customer interruption Penalty target Reliability analysis Security of customer supply
a b s t r a c t Legislation defined to protect domestic and non-domestic customers from long durations of interruptions includes additional requirements to system’s reliability-related performance that distribution network operators (DNOs) must consider in planning the operation and maintenance process of power supply systems. DNOs are required to restore the supply to interrupted customers that fall into ‘‘unprotected’’ customer class within a given period of time, otherwise penalties are applied. In order to meet these requirements, comprehensive strategies must be defined based on upfront analyses. Accordingly, this paper proposes a deterministic algorithm for estimating DNOs’ risk of experiencing interruptions with durations above imposed targets. Besides the Regulator-defined legislation, security of supply requirements are engaged in the development of the proposed methodology. Failure analysis of network components is used to identify interrupted customers that are grouped into power demand classes such that the duration of interruptions can be addressed following the security of supply requirements. Moreover, the penalty times defined by the Energy Regulator are engaged in the analysis and used as thresholds to quantify the penalty risk that DNOs are exposed to. The proposed methodology is applied to a typical UK distribution system, whose average reliability performance is also considered in the analysis. 2013 Elsevier Ltd. All rights reserved.
1. Introduction Reliability performance of power supply systems is nowadays a major priority for distribution network operators (DNOs). Energy Regulators impose annual reliability and continuity of supply targets for the frequency and duration of customer interruptions and, accordingly, penalties or rewards are applied to each DNO based on the achieved performance. In the UK, DNOs’ annual reports submitted to Regulator (The Office of Gas and Electricity Markets, Ofgem) must contain a set of reliability indicators which reflect the network performance. Three system-related metrics [1], namely customer interruption (CI), customer minutes lost (CML) and short interruption (SI), are used to quantify the frequency and duration of long and short interruptions occurred within the supply system. Even though all three metrics are reported to Regulator, targets are only imposed for the CI and CML indices. In order to avoid penalties for poor reliability performance, DNOs must carefully plan the operation and maintenance process of the power supply systems they manage. However, statistics show that this is not an easy task as 14% of the UK DNOs have recently been penalised for not achieving the targets set up for ⇑ Corresponding author. Tel.: +44 131 650 5575. E-mail address: [email protected] (I.-S. Ilie). 0142-0615/$ - see front matter 2013 Elsevier Ltd. All rights reserved. http://dx.doi.org/10.1016/j.ijepes.2013.08.030
the CI index, while 50% of the DNOs exceeded the limits imposed for CML [2]. Besides the targets for CI and CML, DNOs must also obey additional requirements related to the duration of long interruptions for customers that are not protected by special contracts/agreements (i.e. residential). This means that for those customers that correspond to unprotected category, DNOs are obliged to restore the supply within a given period of time otherwise penalties are applied [3]. No rewards are however applied in this case and penalties are paid directly to affected customers and not to Regulator. An efficient planning strategy, which may lead to reported reliability indices below the targets and avoid unprotected customerrelated penalties, requires accurate upfront analyses of system’s reliability performance. Monte Carlo simulation (MCS) is an effective method that has widely been used in such surveys [4–22]. Detailed network modelling and statistics of failure rates and repair times for all network components are inputs for the MCS technique. The network model and failure rates are used to assess the frequency of the customers interrupted by failure/faults occurred within the system. Moreover, the duration of long interruptions is obtained based on the mean time to repair (MTTR) values of faulted network components, whereas the times corresponding to the protection settings are used to calculate the duration of short interruptions. Once the frequency and duration
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of interruptions are achieved, the reliability indices can further be calculated and different planning strategies can be adopted. This paper proposes a straightforward methodology for assessing the reliability performance response of power supply systems to targets which are imposed by Regulator to protect domestic and non-domestic customers from extremely long durations of interruptions. For that purpose, a comprehensive database with failure rates and repair times reported for network components operating in the UK, corresponding protection schemes, UK security of supply requirements and Regulator-related legislation are engaged in the reliability analysis. The risk of having interruptions above the targets is one of the main outputs of the proposed methodology.
residential and non-domestic customers from excessively long interruption events. These requirements are introduced to protect those categories of customers that have no special contracts or agreements with DNOs regarding the duration of interruptions. The Electricity Standard of Performance Regulations [3] is the main UK statutory instrument which indicates the maximum admissible durations of interruptions for up to 5000 customers and more than 5000 customers. Table 2 presents these interruption time limits together with the corresponding penalties DNOs will pay directly to the customers (not to the Regulator), if supply is not restored within the specified period of time.
3. Reliability analysis 2. Security of supply requirements and legislation for customer interruption process 2.1. Security of supply requirements Power supply systems are designed to meet security of supply requirements during events which lead to interruptions of customer supply. After an interruption, the supply to electricity customers has to be restored within a specified period of time. Therefore time limits are defined as maximum durations required by security of supply legislation to restore at least a minimum group of customers. Considering the design process, the network configuration, protection schemes and repair process of faulted network components are the main features which decide the duration of interruptions. Classes of supply are defined in [23] based on group demand ranges, for which the duration of interruptions is imposed so that the minimum demand can be met. An example of how customers’ supply is restored within different periods of time is presented in Table 1. Six classes of supply (A to F) are defined on group demand (GD) ranges for which the maximum durations of interruptions and minimum demand that has to be met are specified. For example, if a group of customers with the power demand between 1 MW and 12 MW is interrupted, the supply must be restored to most of the customers in three hours’ time. For the remaining interrupted customers within that group, the power supply can be restored in accordance with the duration necessary to repair the faulted component which affected the customers (i.e. in repair time/MTTR). 2.2. Legislation for DNOs supplying customers without interruptionsrelated contracts The UK Regulator specifies additional requirements for the duration of customer interruptions in order to protect domestic/ Table 1 UK security of supply requirements for interrupted customers [23]. Class of supply
Range of group demand (GD)
Minimum demands to be met after first circuit outage
A B
GD 6 1 MW 1 MW < GD 6 12 MW
C
12 MW < GD 6 60 MW
D
60 MW < GD 6 300 MW
E F
300 MW < GD 6 1500 MW GD > 1500 MW
In repair time: GD (a) Within 3 h: GD-1 MW (b) In repair time: GD (a) Within 15 min: min{GD-12 MW; 2/3 GD} (b) Within 3 h: GD (a) Immediately: GD-up to 20 MW (b) Within 3 h: GD Immediately: GD According to transmission license security standard
Analytical methods and simulation techniques can be employed to assess the reliability performance of power supply systems [9]. Analytical methods use mathematical models, which represent the analysed system in probability calculations of different states of the system and provide numerical solutions for reliability metrics. The outputs of the analytical methods are restricted to mean values and standard deviations, whereas the simulation procedures provide additional output results in the form of probability distributions of considered reliability parameters. Inverse Transform method, also known as Monte Carlo simulation [10,24–27], is adopted in this paper to address the interruption process of electricity customers. The first step of the MCS procedure is to identify physical parts of the analysed system and collect information on their electrical and mechanical parameters necessary for reliability analysis. Then, a comprehensive database with failure/fault rates and mean repair times for all network components within the system should be created as in Table 3. A random generator is used to assign random variables to an inverse distribution function in order to convert the failure rates and repair times into system states based on the operating and failure stages of individual network component. The operating and failure states of the system are determined from the corresponding component failure rates, whereas the repair times provide the duration of the failure states of the system. In this paper, the standard assumption that the initial conditions of component failure rates and repair times are exponentially distributed is considered, although other distributions such as Gamma, Weibull or Rayleigh can also be adopted [10]. The outputs of the reliability assessment procedure are expressed as frequency and duration of short and long interruptions, which can be further used to calculate the reliability indices that DNOs report to Regulator. The main steps of the MCS procedure are summarised in Fig. 1.
4. Deterministic algorithm for customer interruption risk assessment DNOs’ risk of being penalised due to durations of interruptions above the threshold of 18 h for up to 5000 customers and 24 h for more than 5000 customers has also consequences on the CML targets that DNOs must meet annually for the overall system reliability performance. This means that if the duration of interruptions is reduced for individual groups of customers in accordance with the thresholds given in Table 2, the system-related index CML will be decreased and thus the targets for the latter are more likely to be met. This paper proposes a deterministic algorithm for estimating DNOs’ risk of being penalised when the time requirements specified for domestic and non-domestic customers are considered as
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I.-S. Ilie et al. / Electrical Power and Energy Systems 55 (2014) 59–65 Table 2 Duration of interruption requirements for domestic and non-domestic customers [3].
*
No. of interrupted customers
Maximum duration to restore supply
Penalty paid to Domestic customers
Non-domestic customers
Less than 5000*
18 h After each succeeding 12 h
£54 £27
£108 £27
5000* or more
24 h After each succeeding 12 h
£54 £27
£108 £27
5000 Customers correspond to about 12 MW residential load.
Table 3 Reliability data for main network components [28].
Input data: Failure rates, repair times
Network component
Voltage level (kV)
Failure rate (failures/year)
Mean repair time (hours)
Overhead lines
0.4 11 33 132
0.168 0.091 0.034 0.0038
5.7 9.5 20.5 19.1
Cables
0.4 11 33 132
0.159 0.051 0.034 0.0277
6.9 56.2 201.6 222.7
11/0.4 33/0.4 33/11 132/11 132/33 400/132
0.002 0.01 0.01 0.0392 0.0392 0.0392
75 205.5 205.5 250.1 250.1 250.1
0.4 11 >11
0.005 0.005 0.08
24 120 140
0.4 11 33 132 275 400
0.005 0.0033 0.0041 0.0264 0.0264 0.0264
36 120.9 140 98.4 98.4 98.4
11
0.0004
35.3
Trans-formers
Buses
Circuit breakers
Switch fuses
Create a list with all power components k = 1,…, K
Set time step ΔT for reliability analysis
Assess probability of SI and LI interruptions
Select component k from list
Generate random variable (RVs)
Time to fail (TTF)
NO
Time to repair (TTR)
TTF<ΔT YES Count failures
Run power flow
NO
targets and included in the procedure that is used to assess the reliability performance of a supply system. Let us consider that N is the total number of group demand classes specified in the security of supply requirements and that customer group vector c = [c1, c2, . . ., cn] consists of n 6 N customer classes. For each group of customers ci, " i = 1, . . ., n, a time vector t = [t1, t2, . . ., tn] can be defined so as to contain the time classes ti which represent the durations required to restore the supply according to security of supply values. Each time class ti can take more than one value when the supply is restored on stages (i.e. classes B, C and D in Table 1). Furthermore, time thresholds sj, " j = 1, . . ., v as specified in Table 2 for domestic and non-domestic customers are used to define a time threshold vector s = [s1, s2, . . ., sv] " v 6 V, where V is the total number of imposed duration limits for restoring the supply. Both vectors t and s are incorporated in the MCS procedure to model the reconfiguration of the system after an event (i.e. restore the supply to interrupted customers within 15 min in the case of customer class C) and DNOs’ response to failures, which requires the replacement of faulted component, when the risk of being penalised is estimated in accordance with the time threshold targets sj instead of MTTR values. Thus, every time ‘‘In repair time’’ is given in the security of supply requirements (e.g. class A in Table 1), the value of ti (=MTTR) is replaced by the time thresholds sj.
Check loads interrupted YES
Count no. of interruptions
NO
SI
LI
YES Duration of SI given by protections
Duration of LI given by TTR
Centralise frequency and duration of SI and LI
Compute reliability indices
Fig. 1. Simplified block diagram of the MCS procedure.
The MCS procedure presented in Section 3 changes slightly during the risk assessment with the time thresholds sj. An initial stage is required to determine the network components whose failures lead to customer interruptions and for which the supply is not restored unless the faulted components are repaired within the time given by the MTTR values (e.g. there is no alternative supply which
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0.4kV 33kV
132kV
33kV
1MVA
11kV Grid Supply System
30MVA
L1
24MVA
L2
0.4kV
(33kV O/H Lines)
Zsys
30MVA
1MVA
24MVA
L3L4
0.4kV 33kV
1MVA
2.5MVA
2.5MVA
11kV
0.2MVA
0.4kV
1MVA
To adjacent MV Network
0.4kV 0.4kV
0.2MVA
1MVA
0.4kV 0.4kV
1MVA
0.2MVA
0.4kV To adjacent MV Network
* The whole system consists of about 15,000 customers
Fig. 2. UK distribution system with typical highly-urban and suburban configurations [29].
Table 4 Fault clearance time of typical UK protection systems [30,31]. Network component
Voltage level (kV)
Protection system
Fault clearance time (s)
Overhead lines
11
Circuit breaker with auto-reclosing Circuit breaker with auto-reclosing
10–120
33 Cables
11 33
Transformers
11/0.4 33/11 132/33
Busbars
0.4 11 33 132
Circuit breaker with auto-reclosing Circuit breaker with auto-reclosing
90 Up to 3 90
Fuse switches Circuit breaker with auto-reclosing Circuit breaker with auto-reclosing
Repair time 0.15–10
Fuse switches Circuit breaker Circuit breaker Circuit breaker
Repair time 0.15 0.15 0.15
0.15–10
allows for network reconfiguration). Firstly, two lists L1 and L2 are created: L1 = {1, . . ., k}, " k = 1, . . ., K with all network components K within the system and L2 = {1, . . ., m}, " m = 1, . . ., M with all customers M served by the system. Then, both lists are arranged in ascending order of their network components and customers’ identification number. The first network component is selected from L1 and a power-flow simulation is run to establish the group of customers affected by its failure. All interrupted customers are identified in L2 and assigned to their corresponding customer class ci. Once the class of interrupted customers is determined, its power
range is selected from the second column of Table 1. Moreover, the duration required to restore the supply to the interrupted customers is identified as the time corresponding to the customer class affected by the failure. The procedure is carried on with the selection of the second network component from L1, determination of the interrupted customers within L2 as a consequence of component’s failure, the class the interrupted customers fall into and the corresponding duration required to restore the supply to interrupted customers. The labelling process is repeated until all components are addressed, all customers are assigned to classes and the list L1 becomes empty. At this stage of the analysis it is known the duration corresponding to each network component within the analysed system that is necessary to reconfigure the system, find alternative supply or repair it in case it fails. The next step of the proposed deterministic algorithm is to replace the time values of those network components, which must be repaired within the time given by MTTR so as to restore the supply to interrupted customers, with the time thresholds sj and then run the MCS procedure. Thus, the reductions in the estimated penalty risk are quantified when the system’s reliability performance response to targets is addressed. A summary of the proposed methodology is provided in the following: (1) (2) (3) (4)
count the number N of group demand classes, define vector c with customer groups, define vector t with security of supply durations, define vector s with time thresholds for domestic and nondomestic customers, (5) create a list L1 with all network components, (6) create a list L2 with all customers served,
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I.-S. Ilie et al. / Electrical Power and Energy Systems 55 (2014) 59–65 MTTR
0.18 0.16
0.12 0.1 0.08 0.06 0.04
penalty threshold of 18 h
0.18 0.16 0.14 0.12 0.1 0.08 0.06 0.04 0.02 0
0.14
0
0.02
time threshold
5
10
15
Prob (duration > 18 h) = 36.8 % Prob (duration > 18 h) = 10.9 %
20
25
30
35
40
45
50
0 0
100
200
300
400
500
600
700
800
duration of interruptions (h)
(a) customer class c1 with interrupted power up to 1 MW. MTTR
0.6
time threshold
penalty threshold of 18 h
0.5
0.4 0.3 0.2 0.1
Prob (duration > 18 h) = 0.2 % Prob (duration > 18 h) = 0.1 %
0 0
5
10
15
20
25
30
35
40
duration of interruptions (h)
(b) customer class c2 with interrupted power between 1 MW and 12 MW. 1
MTTR
time threshold
0.8
0.6
0.4
Prob (duration > 18 h) = 0
0.2
0 0
0.2
0.4
0.6
0.8
1
1.2
duration of interruptions (h)
(c) customer class c3 with interrupted power between 12 MW and 60 MW. Fig. 3. Estimated durations of interruptions for the UK test distribution system.
(7) sort the contents of L1 and L2 in ascending order, (8) select first network component from L1 and check interrupted customers from L2 affected by its failure, (9) identify interrupted customers and assigned them to corresponding class ci (10) establish power range the interrupted customers fall into, (11) identify the duration to restore the supply to interrupted customers in security of supply requirements, (12) repeat process until list L1 becomes empty, (13) replace MTTR values with time thresholds sj, (14) run MCS procedure, (15) assess the risk associated with duration of interruptions. 5. Test system configuration and protection settings A typical UK distribution network consisting of two 11 kV highly-urban and suburban configurations with about 15,000 domestic and non-domestic customers is used in this paper for reliability simulations. Fig. 2 illustrates the test system with the
highly-urban configuration operated as a meshed network and the suburban system operated in a radial configuration. Moreover, all electricity customers are supplied through 11/0.4 kV transformers. The fault clearance times of the protection schemes in Fig. 2 are values used by the UK DNOs for their power supply systems. The protection settings adopted in this paper are shown in Table 4. These values correspond to the durations implemented in the
Table 5 Penalty risk estimated for durations of interruptions above Regulator-imposed time thresholds. Customer class
Class 1 Class 2 Class 3
Risk (%) results for MTTR inputs
Time thresholds inputs
36.8 0.2 0
10.9 0.1 0
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0.5
MTTR
time threshold
1000
1500
0.4
0.3
0.2
0.1
0 0
500
2000
2500
CML (minutes/customer/year)
(a) CML index. 0.6
MTTR
time threshold
0.5
0.4 0.3 0.2 0.1 0 0
50
100
150
200
250
300
CI (interruptions/100 customers/year)
(b) CI index.
0.6
MTTR
refers to the system’ reliability performance response to the time thresholds defined to protect customers from excessively long durations of interruptions. This means that instead of restoring the supply to interrupted customers within the time given by MTTR, the time thresholds sj are engaged into analysis. Employing the deterministic procedure proposed in this paper, it is found that all electricity customers supplied through the distribution system in Fig. 2 demand about 36 MW of power, which cover the first three customer classes c1, c2 and c3 defined in the security of supply requirements. Accordingly, the risk analysis for the duration of interruptions is carried out for each customer class. Fig. 3 presents the probability distribution functions (PDFs) of the duration of interruptions estimated for the three customer classes. The risk of having interruptions above the time threshold of 18 h decreases significantly with the increase of customer class power demand. This reduction is explained by the ability of the system to find alternative supply through system reconfiguration when faulted components disconnect large amounts of load. In case estimations are obtained based on MTTR, the penalty risk given by the probability of having interruptions above the threshold of 18 h is about 37% for customers within class c1, dropping to zero for customer classes c2 and c3, respectively. The duration of interruptions assessment against targets indicates a penalty risk of about 11% for class c1. This suggests that the penalty risk can be reduced sharply if average values of imposed targets are considered to restore the supply to interrupted customers instead of long repair times. Table 5 gathers all calculated risk values of having interruptions above the penalty threshold.
time threshold
0.5
6.2. Reliability indices reported to Regulator
0.4
The reliability performance of the test system is assessed through the calculation of the standard set of annual reliability indices CI, SI and CML [1] that the UK DNOs report to Ofgem. The calculation of these indices follows the relations (1)–(3) below.
0.3 0.2 0.1
CI ¼ 0 0
50
100
150
200
250
300
The sum of the total number of customers interrupted for all incidents 100 Total number of customers ð1Þ
SI (interruptions/100 customers/year)
(c) SI index. Fig. 4. Probabilistic estimations of reliability indices.
MCS procedure when the supply to interrupted customers is restored after short interruptions. 6. Simulation tests with the proposed methodology 6.1. Duration of interruptions assessment The risk of having interruptions with durations above the thresholds that protect domestic and non-domestic customers is addressed for the test system in Fig. 2. Firstly, the duration of customer interruptions are obtained from the actual system’s reliability performance computed with MTTR values, which are fed into the MCS procedure. This analysis would estimate the customer interruption process without any other planning decisions than simply restoring the supply to interrupted customers within the repair time. However, planning the customer interruption process should consider strategies that include the risk of facing penalties if supply is not restored within the time thresholds imposed by Regulator. For that reason, the second case analysed in this paper
SI ¼
The sum of the total number of customers interrupted by short interruptions 100 Total number of customers ð2Þ
CML ¼
The sum of the customer minutes lost for all restoration stages for all incidents Total number of customers ð3Þ
The system’s reliability performance response to the penalty targets, which protect domestic and non-domestic customers from long durations of interruptions, are compared in Fig. 4 against the results obtained for MTTR inputs. The proposed deterministic algorithm only has influence on the results of the duration-related index CML (Fig. 4a). An average value of 118 min per customer and year represents the performance of the system if supply is restored within the repair time (MTTR), whereas 50 min per customer and year is the performance response of the system at penalty time targets. A 58% reduction in the CML index could decide whether or not the system’s owner is rewarded for improved reliability performance. The frequency-related indices shown in Figs. 4b and c are not modified when the proposed deterministic procedure is implemented. The average values of CI and SI are for both analysed cases about 60 and 70 interruptions per 100 customers and year.
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7. Concluding remarks The time limits defined by the UK Energy Regulator to protect domestic and non-domestic electricity customers from excessively long durations of interruptions have been exploited in this paper to create a new deterministic algorithm that can be used in reliability analyses. The proposed methodology allows estimating the risk of interruption times above the Regulator-imposed limits when the reliability performance of the analysed system is tested to respond to those targets. Security of supply requirements have been employed in the proposed procedure to identify the network components whose failures lead to interruptions of the customer supply with durations equal to the repair times. Once those network components have been identified, the Regulator-imposed time limits are introduced in the analysis. The MTTR values are replaced by the time limits only for the identified components and the MCS procedure is applied. The outputs of the proposed procedure have firstly been expressed as risk values calculated for the durations of the customer interruption process, and then as system-related reliability indices. Reductions are significantly visible in all results that quantify the durations of interruptions after the repair times have been changed with the targets. Acknowledgements This work was supported by the UK Engineering and Physical Sciences Research Council (EPSRC) project EP/G052530/1. References [1] Quality of service regulatory instructions and guidance, RIGS version 5; March 2005. [2] Electricity distribution quality of service report, Ofgem, annual report; December 2009. [3] The electricity standard of performance regulations, Statutory Instruments, no. 698; March/April 2010. [4] Billinton R, Allan RN. Power system reliability in perspective. IEE Electron Power 1984:231–6. [5] Billinton R, Wojczynski E. Distributional variation of distribution system reliability indices. IEEE Trans Power Apparatus Syst 1985;11:3152–60. [6] Allan RN, Billinton R. Power system reliability and its assessment. Part 1: Background and generating capacity. Power Eng J 1992;6:191–6. [7] Allan RN, Billinton R. Power system reliability and its assessment. Part 2: Composite generation and transmission systems. Power Eng J 1992;6:291–7. [8] Allan RN, Billinton R. Power system reliability and its assessment. Part 3: Distribution systems and economic considerations. Power Eng J 1993;7:185–92.
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