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Reliability improvement of distribution systems using SSVR
ISA Transactions 48 (2009) 98–106
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Reliability improvement of distribution systems using SSVR Mehdi Hosseini a,∗ , Heidar Ali Shayanfar a , Mahmoud Fotuhi-Firuzabad b a
Center of Excellence for Power System Automation and Operation, Department of Electrical Engineering, Iran University of Science & Technology, Tehran, Iran
b
Department of Electrical Engineering, Faculty of Electrical Engineering, Sharif University of Technology, Tehran, Iran
article
info
Article history: Received 6 July 2008 Received in revised form 21 September 2008 Accepted 3 October 2008 Available online 11 November 2008 Keywords: Distribution system SSVR Reliability improvement
a b s t r a c t This paper presents a reliability assessment algorithm for distribution systems using a Static Series Voltage Regulator (SSVR). Furthermore, this algorithm considers the effects of Distributed Generation (DG) units, alternative sources, system reconfiguration, load shedding and load adding on distribution system reliability indices. In this algorithm, load points are classified into 8 types and separated restoration times are considered for each class. Comparative studies are conducted to investigate the impacts of DG and alternative source unavailability on the distribution system reliability. For reliability assessment, the customer-oriented reliability indices such as SAIFI, SAIDI, CAIDI ASUI and also load- and energy-oriented indices such as ENS and AENS are evaluated. The effectiveness of the proposed algorithm is examined on the two standard distribution systems consisting of 33 and 69 nodes. The best location of the SSVR in distribution systems is determined based on different reliability indices, separately. Results show that the proposed algorithm is efficient for large-scale radial distribution systems and can accommodate the effects of fault isolation and load restoration. © 2008 ISA. Published by Elsevier Ltd. All rights reserved.
1. Introduction The basic function of a distribution system is to provide customers demand to the entire load with an acceptable level of reliability and voltage constraint. Over the past few decades, power system reliability evaluation has been mainly concentrated on generation and transmission. The basic reason for this is that generation and transmission systems are capital intensive, and their inadequacy can cause widespread catastrophic consequences for both society and its environment [1]. However, analysis of the customer failure statistics of most utilities shows that the distribution system makes the greatest individual contribution to the unavailability of supply to a customer and the electrical distribution network failures account for approximately 80% of the average customer interruptions [2,3]. Therefore, distribution systems have begun to receive more attention for reliability assessment. During different contingencies in the distribution systems, loads may be interrupted; lines may be over-loaded or disconnected due to internal or external influences. These anomalies lead to a loss of revenue (especially in a competitive environment) and utility integrity. To overcome these problems, power engineers
∗
Corresponding author. Fax: +98 77240490. E-mail addresses: [email protected] (M. Hosseini), [email protected] (H.A. Shayanfar), [email protected] (M. Fotuhi-Firuzabad).
have proposed several methods such as feeder reconfiguration, capacitor switching for VAR control, series voltage regulator and dispersed generation installation [4]. Feeder reconfiguration is an important measure to improve the operational performance [4–6]. In restoring a process by feeder reconfiguration, the path connecting the loads and the topological structure of the distribution system are changed. In the new configuration, load voltages and line currents may be violated and therefore, the operator is forced to shed some load from the distribution system. Dispersed generations are used for the improvement of reliability of the distribution systems [7–9]. After experiencing an interruption, when the fault is isolated, distributed generators in the part of the feeder not affected by the fault may be allowed to reconnect and operate in a stand-alone or an island mode. Furthermore, most dispersed generators are operated between 0.85 lagging and 1.0 power factor [8] and reactive power compensation (leading current) is provided by other devices. In order to operate in the island mode, DG(s) should be able to meet the required load of the island and therefore, keep the voltage within an acceptable range. Accordingly, additional devices are needed for voltage improvement and reactive power compensation in the distribution systems. The development of electronics-based equipment for distribution systems leads to appearance of new devices for power quality improvement [10–15]. Since the topology of these devices is similar to those implemented for FACTS (Flexible AC Transmission systems) devices, they are also called Distribution FACTS (DFACTS).
0019-0578/$ – see front matter © 2008 ISA. Published by Elsevier Ltd. All rights reserved. doi:10.1016/j.isatra.2008.10.006
M. Hosseini et al. / ISA Transactions 48 (2009) 98–106
Despite the conventional devices such as series voltage regulators and shunt capacitors, D-FATCS have quick response and continuous operation to changes in the network [10,11]. Static Series Voltage Regulator (SSVR) is a series D-FATCS device used in distribution systems for power quality improvement such as voltage sag [14], and under-voltage [15]. Modeling of SSVR in distribution systems load flow is presented in [15]. In that work, it is shown that SSVR is an effective device for the steady-state voltage improvement and also active and reactive power loss reduction. This model is also used for reliability improvement in this paper. Several methods for assessing the distribution system reliability have been developed [1–3,16–20]. Ref. [18] presents an approach to search for the shortest paths between any two nodes of a distribution system. The classification of nodes has been made by considering the sections controlled by protection devices based on the shortest path. The algorithm is suitable for the large-scale distribution system with multiple sub feeders and is used in this paper. In [18], nodes have been classified into four types, whereas in our paper, load points in a distribution system are divided into eight classes. Also, the effect of DG and alternative source unavailability is expressed in restoration time of load points and used in the reliability algorithm. The rest of this paper is organized as follows: Section 2 presents effect of SSVR in voltage improvement in distribution systems, briefly. In Section 3, the effect of DG in reliability improvement, and also load shedding and load adding, and reconfiguration techniques used in this paper are briefly described. The reliability modeling of the distribution systems is explained in Section 4. Details of the proposed algorithm for the reliability assessment are illustrated in Section 5. In Section 6, the proposed algorithm is examined on 33-bus and 69-bus standard distribution using SSVR. Finally, Section 7 summarizes the main points and results of this paper. 2. Static Series Voltage Regulator (SSVR) Fig. 1 shows a typical model of a SSVR installed in a line connected between busses i and j of network. SSVR consists of DC capacitor, voltage source converter and series injection transformer. It can exchange reactive power with the system for voltage regulation and therefore the injected voltage by SSVR should be kept in quadrate with its current flow (Fig. 2). SSVR is used to compensate voltage of bus j, changing it from Vj to Vjnew by injecting a series voltage (VSSVR ) as shown in Fig. 2. The method for calculation of injected series voltage and reactive power by SSVR and also the modeling of SSVR in distribution systems load flow is presented in [15]. 3. Distributed generation; load shedding, and reconfiguration, and load adding techniques 3.1. Distributed generation The utilities evaluate different approaches to provide competitive rates and acceptable reliability levels to customers. DG consists of small generators typically ranging in capacity from several kilowatts to 10 MW connected to distribution systems [8]. The high cost associated with the power interruptions and considering that the costs of transmission and distribution systems are taking an increasingly large portion of the utility capital investment, use of DG in power industry could be a cost effective solution to enhance system reliability. When a fault occurs in the distribution system, by opening switches in the upstream and down stream side of DGs, an isolated area can be supplied. In other words, DGs can improve reliability through islanding operation. Furthermore, DGs can operate as on-site or backup units. In this paper both of these situations are considered.
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Fig. 1. Single line diagram of two busses of a distribution system with SSVR consideration.
Fig. 2. Phasor diagram of voltages and current of the system shown in Fig. 1.
3.2. Load shedding For a distribution system consisting of M sections, the total number of sections sets is 2M − 1. A section is defined as group of loads which is connected to a protection device; consequently, M is the number of protection devices in local area for load shedding action. To select the best section for shedding, a Priority Weighting Factor (PWF) has been used based on the Sector Customer Damage Functions (SCDF) and feeder load [21] and is used in this paper. SCDF provides the customer interruption cost models for different customers consisting of large user, industrial, commercial, agriculture, residential, government and institutions and office and buildings categories. PWF for section j in the distribution system for the failure duration ri , is determined using the following equation [21]: PWFij =
N X
Lk ck (ri )
(1)
k=1
where, k represents load point k, N is the number of loads connected to section j, Lk is the load connected to load point k, and ck (ri ) is the per unit customer cost for duration ri . The load shedding procedure for determining which section or sections of load points should not be restored consists of the following steps: 1. The Priority Weighting factor (PWF) for each section is calculated and then the sections are sorted in ascending manner. 2. The first section from the sorted list is selected and the total load to be cut for this section is determined. 3. If load shedding action is used in an isolated area with some dispersed generators, the total load of the section must be smaller than or equal to the sum of generator capacities. Otherwise, this state is omitted from the sorted list. 4. The selected section is shed from the determined area and load flow is run. The voltage and current constraints must be checked after shedding this section from the system. If the constraints are satisfied, load shedding is stopped. Otherwise, the next section from the sorted list is selected and the process goes to step 2.
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The above procedure is repeated until the voltage and current constraints are reached by optimum load shedding with the minimum value of PWF index. 3.3. Reconfiguration and load adding Distribution systems are normally operated as radial systems; however, configuration of the system can be changed (reconfigured) by changing the state of some normally-closed switches placed on the line sections of the system. Different feeders are connected through normally-open tie switches, allowing certain interrupted customers to be temporarily transferred to adjacent feeders during maintenance and repair [6]. In this paper feeder reconfiguration is used to improve voltage regulation and reliability. The interrupted sections with maximum total interruption cost are firstly selected to be restored by normally-open switches. Also, load adding to the safe area is considered for reliability improvement. For this purpose, the section sets including at least one normally-open switches connected to the energized part of system, are selected and PWF index is calculated for them. If there is more than one normally open switch in the section, there are different options to add this section to the safe area. In this situation, the best option is obviously the section with the greatest interruption cost. It should be noted that load shedding, reconfiguration and load adding are applied in the distribution system while voltage constraints, capacity constraints of lines and radial structure constraint of the distribution system are satisfied. 4. Distribution reliability modeling 4.1. Reliability indexes The basic distribution system reliability indexes are the three Load Point (LP) indexes: (1) Average failure rate λs ; (2) average outage duration rs ; (3) annual outage duration Us . A radial distribution system consists of a set of series components, including lines, breakers, fuses, disconnected switches, and etc. A customer connected to a load point of such a system requires all components between himself and the supply point to be operating. Consequently, the principle of series systems can be applied directly to these systems is as below [3,17]:
λs =
X
λi
(2)
Us =
λi ri
(3)
i
rs =
Us
λs
.
5. Solution algorithm 5.1. Overall algorithm The overall algorithm is the determination of three areas of system, i.e. safe, interrupted and isolated. Then, the reliability indexes for each load point in these areas are calculated. For this purpose, at first, during system failure, the distribution system is divided into different classes by protective devices (will be described in 5.2). Then, the interrupted area is identified and load points that are fed with the main source, alternative source and distributed generators, are recognized after power flow, load shedding, reconfiguration and load adding techniques. These techniques are used to improve the reliability of the distribution system. The load shedding, reconfiguration and load shedding priority among sections of the distribution system are determined to minimize the total system interruption cost. It should be noted that this algorithm is based on the assumption that the distribution system has a radial structure. After a fault has been cleared, two kinds of switching operations may be done. The first action is isolating the failure point from the system. The second one is determination of the affected areas which are disconnected from the source and may be resupplied from the available sources (the source, the alternative source or DGs). The restoration procedure includes the process of decision making, and various switching and repairing actions using the switches. In this paper it is assumed that at first, the load points are re-supplied from the main source as far as possible by reconfiguration. In the next priority step, loads are however resupplied from an alternative source and finally, the interrupted loads are fed by DGs (island operation). Based on this assumption, different classifications for the load points are considered and described in the following section. 5.2. Load point classification
i
X
3. Only an overcurrent protection device such as breaker or fuse can interrupt fault currents. Also protective devices such as breakers, fuses, disconnectors, normally open and closed switches have the function of fault isolation. 4. A fault in a radial subsystem is interrupted by the nearest overcurrent protection device (fuse/breaker) on its source side and is isolated by the nearest protective devices. 5. Protection devices are 100% reliable. 6. The location of switches, alternative and DGs on the distribution system are known.
(4)
The customer-oriented reliability indices such as SAIFI, SAIDI, CAIDI ASUI and load- and energy-oriented indices such as, ENS and AENS can be calculated from the three basic LP indexes [3, 17]. In this paper, these indices are considered for the reliability evaluation of the test systems. 4.2. Basic assumption In this paper the following assumptions are considered in the proposed algorithm: 1. A two-state up/down representation for the operation/repair cycle of an element is used. 2. All failures in the distribution systems are independent.
The distribution system is divided into sections by the protection and isolation components. A section is a group of components whose entry component is a switch or a protection device. Therefore, each section has only one switch or protection device. When a failure occurs in the network, it must be isolated by the nearest upstream breaker or fuse. Then, the sections that are affected by this failure must be isolated from the system. When the faults are on the lines with switches, they are isolated by those switches and faults on lines without switches are isolated by opening proper downstream and upstream switches. Distribution system is divided into different areas in terms of the location of sectionalizers, normally open switch, alternative source location(s), and DG location(s). The restoration times of load points in each area will not be the same due to restoration switching sequence. In this paper, load in a distribution system is divided into eight classes as follows: Class A: Load points that are not affected by a fault (restoration time is equal to zero).
M. Hosseini et al. / ISA Transactions 48 (2009) 98–106
Class B: The upstream load points of faulted component whose outage duration is equal to the time of isolating the fault plus the reclosing time of the breaker. The load points in this class are restored through the main supply. Class C: The load points whose outage duration is equal to the time of isolating the fault plus the reconnection time of the breaker plus the switching time of a tie switch or normally open switch. The load points in this class are connected to the nodes in class A or B by normally open switching. Therefore, they are energized through the main supply. Class D: The load points whose outage duration is equal to the isolating time of the fault plus the breaker reclosing time of an alternative source. Class E: The load points whose outage duration is equal to the time of isolating the fault plus the breaker connection time of an alternative source plus the switching time of a tie switch or normally open. The load points in this class are connected to the nodes in class D by normally open and therefore, are energized through the alternative source. Class F: The load points whose outage duration is equal to the time of isolating the fault plus the starting time of DG. Class G: The load points whose outage duration is equal to the isolating time of the fault plus the starting time of DG plus the switching time of a tie switch or normally open. The load points in this class are connected to the nodes in class F by normally open and are energized through a DG. Class H: The load points whose outage durations are equal to the time of isolating the fault and repair the failed components. Furthermore, before the classification of nodes, a load flow calculation is performed. If the load flow is converged and the nodes voltages and line currents are in the acceptable limit then the classification is done. Otherwise, after reconfiguration and load shedding and finally load adding, the parts of the subsystem with voltage and current in the acceptable ranges are classified and the other nodes are considered as new subsystems which are candidate to be categorized to other classes. It should be mentioned that if the load flow calculation is performed for a part of system that include SSVR, its model [15] is considered in the load flow calculations. It should be noted that in classes A, B, C, D or E, if there are several distributed generators, the distribution system is first converted to an equivalent single source network with radial configuration [22] and then the load flow problem is solved. Similarly, in the isolated areas (class G or H) if there are several distributed generators, the DG unit with the highest capacity is modeled as a voltage source taking into account its capacity limit. Accordingly, using the method proposed in [22], the subsystem with several DGs can be converted to a radial structure. 5.3. Effect of alternative source and DG unavailability on restoration time As mentioned in Section 5.2., the restoration time of different classes is not the same and it increases from class A to class H. It is not always feasible that the alternative source and DG be available when they are required. Therefore, restoration of classes D, E (supplied by alternative source), F, G (supplied by DG) should be modified. In order to consider the alternative source(s) unavailability, the load points of classes D, E are divided into two groups. The first group is the load points which have no connection with a DG. Therefore, when an alternative is not available, their restoration time is equal to the repair time of failed component.
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Consequently, the modified restoration time of the first group of classes D and E are as follow: MRD1 = PAlternativ e .rD + (1 − PAlternativ e ).rH
(5)
MRE1 = PAlternativ e .rE + (1 − PAlternativ e ).rH
(6)
where: MRD1 —Modified restoration time of the first group in class D MRE1 —Modified restoration time of the first group in class E PAlternativ e —The availability of alternative source rD —Restoration time of class D rE —Restoration time of class E rH —The time of isolating the fault and repair the failed component (Restoration time of class H). The second group is the load points which are connected directly to a DG, or indirectly by a normally open switch. Therefore, when an alternative is not available, they belong to classes F or G and may be supplied by a DG. Therefore, the modified restoration time of the second group of classes D and E are as follow: MRD2 = PAlternativ e .rD + (1 − PAlternativ e ).PDG .(rF .WF + rG .WG ) + (1 − PAlternative ).(1 − PDG ).rH (7) MRE2 = PAlternativ e .rE + (1 − PAlternativ e ).PDG .(rF .WF + rG .WG ) + (1 − PAlternative ).(1 − PDG ).rH
(8)
where: MRD2 —Modified restoration time of the second group in class D MRE2 —Modified restoration time of the second group in class E PDG —The availability of DG. Furthermore, WF and WG are binary variable refer to the classes F and G, respectively. WF is equal to one if the second group belongs to class F in the case of alternative source unavailability and at the same time WG is equal to zero. Similarly, when WG is equal to one, WF is zeros. In other words, WF + WG = 1. It should be noted that part of nodes located in the second group of classes D and E which they do not satisfy the load flow constraints, must be shed and their restoration time are the same as the first groups of these classes. In addition to the nodes classified from classes D, E to classes G, F, there are some nodes in classes G, F, originally (classes F, G identified earlier in Section 5.2.) supplied by DG after isolation of the faulted area. The modified restoration time of these classes by consideration of DG unavailability is as follow: MRG = PDG .rG + (1 − PDG ).rH
(9)
MRF = PDG .rF + (1 − PDG ).rH
(10)
where: MRG —Modified restoration time of class G MRF —Modified restoration time of class F rF —Restoration time of class F rG —Restoration time of class G. 5.4. Reliability assessment algorithm Based on the description and the assumptions in the above sections, the proposed algorithm includes the following steps. 1. Read the reliability and load flow data. 2. Consider contingency state using contingency enumeration. 3. Determine the area affected using the shortest path [18] to form the separate subsystems. 4. Classify the nodes into classes A, B, C, D, E, F, G and H based on the location of protective devices, DGs, and alternative sources (Section 5.2). 5. Modify restoration time of the nodes in classes D, E, F, G. (Section 5.3). 6. Calculate load point indices for this contingency state. 7. Go to the next step if all contingencies are considered; otherwise go to Step 2 for new contingency. 8. Calculate the system indices.
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Table 1 Voltage magnitude and phase angle in 33 bus distribution in the base case system. Node no.
Voltage magnitude (p.u.)
Phase angle (deg)
Node no.
Voltage magnitude (p.u.)
Phase angle (deg)
Node no.
Voltage magnitude (p.u.)
0 1 2 3 4 5 6 7 8 9 10
1.0000 0.9970 0.9829 0.9755 0.9681 0.9497 0.9462 0.9413 0.9351 0.9292 0.9284
0 0.014 0.096 0.161 0.228 0.133 −0.096 −0.060 −0.133 −0.195 −0.188
11 12 13 14 15 16 17 18 19 20 21
0.9269 0.9208 0.9185 0.9171 0.9157 0.9137 0.9131 0.9965 0.9929 0.9922 0.9916
−0.177 −0.268 −0.347 −0.384 −0.408 −0.485 −0.495
22 23 24 25 26 27 28 29 30 31 32
0.9794 0.9727 0.9694 0.9477 0.9452 0.9337 0.9255 0.9219 0.9178 0.9168 0.9166
0.0037
−0.063 −0.082 −0.103
Phase angle (deg) 0.065
−0.023 −0.067 0.173 0.229 0.311 0.389 0.494 0.410 0.386 0.379
6. Simulation results Two standard distribution systems consisting of 33 and 69 busses are used to examine the effectiveness of the proposed reliability algorithm. At first, a risk analysis is performed in the test systems to determine whether the voltages of all nodes are in the determined limit. After that, the percentage (probability) that each node can be categorized in each of classes (classes A to H) is determined. Because of similar trend of results for both test systems, results related to node classification and risk analysis is only presented for 33-bus test system. Then, in each distribution system, the customer-oriented reliability indices such as SAIFI, SAIDI, CAIDI ASUI and load- and energy-oriented indices such as ENS and AENS are calculated. The effect of SSVR on these indices is considered and compared with the results of these test systems without any SSVR. In order to indicate and compare the effects of SSVR installation in the distribution system, different sizes and locations are selected for installation. The system reliability indices for typical distribution systems are computed for four cases. It should be noted that only one SSVR is used at a time while performing load flow calculations. Details of case studies are as follows: Case ‘1’: Alternative supply and DGs are 100% available; LV transformers are 100% available; Case ‘2’: Availability of alternative supply and DGs are 0.9 and 0.85, respectively and LV transformers are 100% available; Case ‘3’: Alternative supply and DGs are 100% available and failure rate of LV transformers is considered. Case ‘4’: Availability of alternative supply and DGs are 0.9 and 0.85, respectively and failure rate of LV transformers is considered. Restoration time (hour) of classes B, C, D, E, F, G in both test systems are considered as below [2,3,23]: rB = 1 , rG = 1.8
rC = 1.2, and
rD = 1.3,
rE = 1.5,
rF = 1.6,
rH = 5 .
The results obtained in these systems are briefly summarized in the following subsections. 6.1. 33-bus test system Fig. 3. shows single line diagram of the 12.66 kV, 33-bus, 4lateral radial distribution system. The total load of the system in the base case is (3715 + j 2300) kVA. The load flow data of the system are taken from [5]. The upper and lower bounds of acceptable voltage magnitudes are 1.05p.u. and 0.95p.u. , respectively. Furthermore, limits of line capacity are taken from IEEE standard test feeders [24]. Reliability parameters are from the RBTS-BUS2 [25] (length of all feeders is considered to be 0.75 km).
Fig. 3. Single line diagram of 33 bus distribution system.
Also, normally open switches data is taken from [5]. This system includes large user, industrial, commercial, agriculture, residential, government and institutions and, office and buildings customers. The customers’ data, with few modifications is obtained from RBTS-BUS2 [25]. For reliability studies of the system, one 500 kW and 100 kVAr standby DG in node 21, an alternative source in node 24, and also a breaker connecting to the source node are considered. 6.1.1. The system risk study A summery of the load flow results for the base case is taken in Table 1. The results show that 21 nodes out of 33 nodes of the distribution system are under 0.95p.u. . As shown in Table 1, some nodes have under-voltage problems in the base case before reliability assessment and therefore, risk of system in this situation is equal to 1. These nodes are: nodes 5–17 and also nodes 25–32. The other feeder of the system, i.e. feeder with nodes 18–21 and the other one with nodes 22–24, have voltage magnitude in acceptable limits (Table 1). Two DGs are installed in nodes 17 and 32 to solve the mentioned under voltage problem. The capacity of each DG is equal to 500 kW and 100 kVAr. It should be discussed that, the installation of two DGs in nodes 24 and 21 (healthy feeders) cannot completely mitigate the undervoltage problem of the nodes 5–17 and 25–32. This is due to the fact that the DGs location (nodes 24 and 21) are far from these nodes. Consequently the installation of DGs in nodes 21 and 24 seems not to be efficient in terms of under-voltage mitigation. Instead, if the DGs are installed in nodes 17 and 32, it is indicated that the under voltage problem of the mentioned nodes are mitigated as these nodes. The results of this case are taken in Table 2, showing that DGs in nodes 17 and 32 can efficiently mitigate the under-voltage problem as these two DGs are approximately located in the vicinity of the nodes with the under-voltage problem. 6.1.2. Classification of node points Table 3 shows the percentage (probability) that each node can be categorized in each of classes (class A–H). For cases 1 and 2, the percentage is calculated by considering all of the line outage. In the cases 3, 4, besides the line outage, all the LV transformer
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Table 2 Voltage magnitude and phase angle in 33 bus distribution after DG installations in nodes 17 and 32. Node no.
Voltage magnitude (p.u.)
Phase angle (deg)
Node no.
Voltage magnitude (p.u.)
Phase angle (deg)
Node no.
Voltage magnitude (p.u.)
Phase angle (deg)
0 1 2 3 4 5 6 7 8 9 10
1 0.9977 0.9875 0.9828 0.9784 0.9668 0.9644 0.9622 0.9599 0.9582 0.9581
0 0.024 0.157 0.262 0.368 0.483 0.375 0.427 0.460 0.505 0.517
11 12 13 14 15 16 17 18 19 20 21
0.9579 0.9576 0.9576 0.9585 0.96 0.9633 0.9655 0.9972 0.9936 0.9929 0.9923
0.537 0.620 0.665 0.710 0.766 0.978 1.052 0.013 −0.053 −0.072 −0.093
22 23 24 25 26 27 28 29 30 31 32
0.9839 0.9773 0.974 0.9656 0.9641 0.9571 0.9522 0.9506 0.9504 0.9508 0.952
0.127 0.039 −0.004 0.533 0.603 0.825 1.002 1.132 1.205 1.243 1.327
Table 3 The percentage (probability) that each node can be categorized in each of classes (class A–H) for the cases 1–4. Node no. Class A (%)
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32
Class B (%)
Class C (%)
Class D (%)
Class E (%)
Class F (%)
Class G (%)
Class H (%)
Case 1, 2
Case 3, 4
Case 1, 2
Case 3, 4
Case 1, 2
Case 3, 4
Case 1, 2
Case 3,4
Case 1, 2
Case 3, 4
Case 1, 2
Case 3, 4
Case 1, 2
Case 3, 4
Case 1, 2
Case 3,4
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
48.4 48.4 48.4 48.4 48.4 48.4 48.4 48.4 48.4 48.4 48.4 48.4 48.4 48.4 48.4 48.4 48.4 48.4 48.4 48.4 48.4 48.4 48.4 48.4 48.4 48.4 48.4 48.4 48.4 48.4 48.4 48.4
93.8 84.4 84.4 84.4 75.0 75.0 68.8 65.6 62.5 65.6 62.5 46.9 43.8 40.6 40.6 46.9 40.6 87.5 84.4 81.3 75.0 90.6 84.4 81.3 78.1 71.9 68.8 59.4 62.5 53.1 56.3 53.1
46.9 42.2 42.2 42.2 37.5 37.5 34.4 32.8 31.3 32.8 31.3 23.4 21.9 20.3 20.3 23.4 20.3 43.8 42.2 40.6 37.5 45.3 42.2 40.6 39.1 35.9 34.4 29.7 31.3 26.6 28.1 26.6
0 0 3.13 6.25 9.38 12.5 15.6 18.8 21.9 25.0 28.1 31.3 34.4 37.5 40.6 43.8 43.8 0 3.13 6.25 6.25 0 0 0 12.5 15.6 18.8 18.8 18.8 25.0 31.3 31.3
0 0 1.56 3.13 4.69 6.25 7.81 9.38 10.9 12.5 14.1 15.6 17.2 18.7 20.3 21.9 21.9 0 1.56 3.13 3.13 0 0 0 6.25 7.81 9.38 9.38 9.38 12.5 15.6 15.6
0 3.13 3.13 3.13 3.13 3.13 3.13 3.13 3.13 3.13 3.13 15.6 12.5 9.38 6.25 3.13 3.13 0 3.13 3.13 3.13 3.13 6.25 6.25 3.13 3.13 3.13 6.25 6.25 6.25 3.13 3.13
0 1.56 1.56 1.56 1.56 1.56 1.56 1.56 1.56 1.56 1.56 7.81 6.25 4.69 3.13 1.56 1.56 0 1.56 1.56 1.56 1.56 3.13 3.13 1.56 1.56 1.56 3.13 3.13 3.13 1.56 1.56
0 3.13 3.13 3.13 3.13 3.13 3.13 3.13 3.13 3.13 3.13 3.13 3.13 3.13 3.13 3.13 3.13 0 3.13 3.13 3.13 3.13 3.13 3.13 3.13 3.13 3.13 6.25 6.25 6.25 3.13 3.13
0 1.56 1.56 1.56 1.56 1.56 1.56 1.56 1.56 1.56 1.56 1.56 1.56 1.56 1.56 1.56 1.56 0 1.56 1.56 1.56 1.56 1.56 1.56 1.56 1.56 1.56 3.13 3.13 3.13 1.56 1.56
3.13 3.13 3.13 0 3.13 3.13 3.13 3.13 3.13 0 0 0 3.13 3.13 3.13 0 3.13 3.13 3.13 3.13 3.13 0 3.13 3.13 0 3.13 3.13 3.13 0 0 0 3.13
1.56 1.56 1.56 0 1.56 1.56 1.56 1.56 1.56 0 0 0 1.56 1.56 1.56 0 1.56 1.56 1.56 1.56 1.56 0 1.56 1.56 0 1.56 1.56 1.56 0 0 0 1.56
0 3.13 0 0 3.13 0 3.13 3.13 3.13 0 0 0 0 3.13 3.13 0 0 3.13 0 0 3.13 0 0 0 0 0 0 3.13 0 0 0 0
0 1.56 0 0 1.56 0 1.56 1.56 1.56 0 0 0 0 1.56 1.56 0 0 1.56 0 0 1.56 0 0 0 0 0 0 1.56 0 0 0 0
3.13 3.13 3.13 3.13 3.13 3.13 3.13 3.13 3.13 3.13 3.13 3.13 3.13 3.13 3.13 3.13 6.25 6.25 3.13 3.13 6.25 3.13 3.13 6.25 3.13 3.13 3.13 3.13 6.25 9.38 6.25 6.25
3.13 3.13 3.13 3.13 3.13 3.13 3.13 3.13 3.13 3.13 3.13 3.13 3.13 3.13 3.13 3.13 4.69 4.69 3.13 3.13 4.69 3.13 3.13 4.69 3.13 3.13 3.13 3.13 4.69 6.25 4.69 4.69
outages are also considered. From the table, it can be seen that the calculated percentage of all nodes for cases 1, 2 is equal to zero (the 2nd column of Table 3). This is due to the fact that there is only one breaker in the source node and therefore for any line outage in the system, the breaker operates. Accordingly no nodes can be categorized in class A and their calculated percentage for class A is zero. But in cases 3 and 4, for any LV transformer outage in the system, the transformer fuse operates and the rest of the nodes belong to class A. In [18], the effects of DG, reconfiguration, load adding and unavailability of alternative sources are not considered. Therefore, based on the definition for load point classes in our paper, the load points of [18] are classified to classes A, B, D, H. On the other hand, according to Table 3, a considerable number of load points are found in class C. Also, some load points are in class E, F, G. As a result, the reliability indexes obtained in this paper are more realistic and practical for real distribution systems. Although the percentage of load points in each class for the cases 1 and 2 and also cases 3 and 4 are the same (from Table 3), it is necessary
to modify the restoration time of classes D, E, F, G for cases 2, 4 for reliability indices calculation (based on Section 5.3). The results of reliability indices are presented in the following sections. 6.1.3. Reliability indexes with and without SSVR Reliability indices for each case in 33-bus distribution system before SSVR installation are calculated and presented in Table 4. Comparing the results of Cases ‘3’, ‘4’ with those of Cases ‘1’, ‘2’, it can be seen that there is a considerable difference between the results. As the repair time for a LV transformer (200 h [25]) is much longer than that of the other elements, the difference between the reliability indices for the cases is significant. Furthermore, a consideration of unavailability for the alternative supply and DGs in cases ‘2’ and ‘4’ causes the reliability to worsen as compared with cases ‘1’, ‘3’, respectively. The effect of SSVR installation on reliability indices is studied. For this purpose, one SSVR is installed in each line of the system and after that reliability indices are calculated. This process is
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Table 4 Reliability indices for 33 bus distribution system without SSVR. Case
SAIFI (int./cus.yr)
SAIDI (h/cus.yr)
CAIDI (h/cus.int)
ASUI
ENS (kWh/yr)
AENS (kWh/cus.yr)
Case ‘1’ Case ‘2’ Case ‘3’ Case ‘4’
1.56 1.56 1.575 1.575
1.9702 1.9808 4.9702 4.9808
1.2629 1.2698 3.1557 3.1624
0.00022491 0.00022612 0.00056737 0.00056859
7323 7413.5 18468 18559
3.7438 3.7901 9.4417 9.488
Table 5 Reliability indices for 33 bus distribution system with 50 kVA SSVR. Installation priority
Case
1 2 3 4 1 2 3 4 1 2 3 4 1 2 3 4 1 2 3 4
1
2
3
4
5
a
CAIDI (h/cus.int)
ASUI
Value
SAIDI (h/cus.yr) SLa
Value
SL
Value
SL
Value
ENS (kWh/yr) SL
Value
AENS (kWh/cus.yr) SL
1.8472 1.8596 4.8472 4.8596 1.8473 1.8597 4.8473 4.8597 1.8509 1.8632 4.8509 4.8632 1.8529 1.8653 4.8529 4.8653 1.853 1.8654 4.853 4.8654
5 5 5 5 4 4 4 4 27 27 27 27 7 7 7 7 6 6 6 6
1.1841 1.192 3.0776 3.0854 1.1842 1.1921 3.0799 3.0855 1.1865 1.1944 3.0812 3.0878 1.1878 1.1957 3.0813 3.0891 1.1972 1.1958 3.0906 3.0973
5 5 4, 5 5 4 4 27 4 27 27 7 27 6, 7 7 6 6, 7 2, 3 6 2, 3 2, 3
0.00021087 0.00021228 0.00055333 0.00055474 0.00021088 0.00021229 0.00055334 0.00055475 0.00021129 0.0002127 0.00055375 0.00055516 0.00021152 0.00021293 0.00055399 0.0005554 0.00021153 0.00021294 0.000554 0.00055541
5 5 5 5 4 4 4 4 27 27 27 27 7 7 7 7 6 6 6 6
7064.7 7161.8 18210 18307 7075.8 7172.9 18221 18318 7125.4 7198.2 18270 18343 7128.7 7219.3 18274 18364 7212.2 7289.2 18357 18434
5 5 5 5 4 4 4 4 3 3 3 3 2 2 2 2 27 27 27 27
3.6118 3.6614 9.3097 9.3593 3.6175 3.6671 9.3153 9.365 3.6428 3.6801 9.3407 9.3779 3.6445 3.6908 9.3424 9.3887 3.6872 3.7266 9.3851 9.4244
5 5 5 5 4 4 4 4 3 3 3 3 2 2 2 2 27 27 27 27
SL: SSVR Location.
Table 6 Reliability indices for 33 bus distribution system with 200 kVA SSVR. Installation priority
Case
1 2 3 4 1 2 3 4 1 2 3 4 1 2 3 4 1 2 3 4
1
2
3
4
5
a
SAIDI (h/cus.yr)
CAIDI (h/cus.int)
ASUI
Value
SLa
Value
SL
Value
SL
Value
ENS (kWh/yr) SL
Value
AENS (kWh/cus.yr) SL
1.8403 1.8533 4.8403 4.8533 1.8406 1.8536 4.8406 4.8536 1.8508 1.8631 4.8508 4.8631 1.8528 1.8652 4.8528 4.8652 1.853 1.8654 4.853 4.8654
5 5 5 5 3, 4 3, 4 3, 4 3, 4 25, 27 25, 27 25, 27 25, 27 7 7 7 7 6 6 6 6
1.1797 1.188 3.0732 3.0815 1.1798 1.1882 3.0734 3.0816 1.1864 1.1943 3.0798 3.0877 1.1877 1.1956 3.0812 3.089 1.1878 1.1958 3.0813 3.0891
5 5 5 5 3, 4 3, 4 3, 4 3, 4 25, 27 25, 27 25, 27 25, 27 7 7 7 7 6 6 6 6
0.00021008 0.00021156 0.00055254 0.00055403 0.00021011 0.0002116 0.00055258 0.00055406 0.00021127 0.00021268 0.00055374 0.00055515 0.00021151 0.00021292 0.00055398 0.00055539 0.00021153 0.00021294 0.000554 0.00055541
5 5 5 5 3, 4 3, 4 3, 4 3, 4 25, 27 25, 27 25, 27 25, 27 7 7 7 7 6 6 6 6
6899.7 6977.2 18045 18122 7025.6 7103.2 18171 18248 7025.6 7103.2 18171 18248 7116.5 7191.8 18261 18337 7132.2 7206.6 18277 18352
5 5 5 5 3 3 3 3 4 4 4 4 2 2 2 2 25 25 25 25
3.5274 3.5671 9.2253 9.2649 3.5918 3.6315 9.2897 9.3293 3.5918 3.6315 9.2897 9.3293 3.6383 3.6768 9.3361 9.3747 3.6463 3.6844 9.3442 9.3822
5 5 5 5 3 3 3 3 4 4 4 4 2 2 2 2 25 25 25 25
SL: SSVR Location.
done for all system nodes and reliability indices are calculated. Tables 5 and 6 show the reliability indices for five top best locations of SSVR which have considerable effect on the reliability index. The best location of SSVR in cases ‘1’–‘4’ is determined separately for each reliability index. The capacity of SSVR in Tables 5 and 6 are 50 kVA and 200 kVA, respectively. Comparing the results of Tables 5 and 6 with that of Table 4 show that SSVR can improve the reliability indices of the system. But its effectiveness depends on its capacity and location. Also, comparing the results shown in Tables 5 and 6, it is observed that the effect of 200 kVA SSVR is more than 50 kVA SSVR. For example for
the case ‘1’, in the best condition, 200 kVA SSVR can improve SAIDI, CAIDI, ASUI, ENS, AENS from 1.9702, 1.2629, 0.00022491, 7323 and 3.7438 (Table 4) to 1.8403, 1.1797, 0.00021008, 6899.7, 3.5274 (Table 6), respectively, whereas, 50 kVA SSVR improves these indices to 1.8472, 1.1841, 0.00021087, 7064.7 and 3.6118, respectively (Table 5). Furthermore, Tables 5 and 6 show that by SSVR installation, both customer-oriented indices (SAIDI, CAIDI, and ASUI) and also load- and energy-oriented indices (ENS and AENS) can be improved considerably. Also, the suitable location for SSVR installation in all four cases for the customer-oriented indices is almost the same.
M. Hosseini et al. / ISA Transactions 48 (2009) 98–106
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Table 7 Reliability indices for 69 bus distribution system without a SSVR. Case
SAIFI (int./cus.yr)
SAIDI (h/cus.yr)
CAIDI (h/cus.int)
ASUI
ENS (kWh/yr)
AENS (kWh/cus.yr)
Case ‘1’ Case ‘2’ Case ‘3’ Case ‘4’
3.315 3.315 3.33 3.33
5.0024 5.056 8.0024 8.056
1.509 1.5252 2.4031 2.4192
0.00057105 0.00057717 0.00091351 0.00091964
36 898 37 144 49 443 49 689
12.4952 12.5786 16.7435 16.8269
Table 8 Reliability indices for 69 bus distribution system with a 50 kVA SSVR. Installation priority
Case
1 2 3 4 1 2 3 4 1 2 3 4 1 2 3 4 1 2 3 4
1
2
3
4
5
a
CAIDI (h/cus.int)
ASUI
ENS (kWh/yr)
AENS (kWh/cus.yr)
Value
SAIDI (h/cus.yr) SLa
Value
SL
Value
SL
Value
SL
Value
SL
4.4528 4.5059 7.4528 7.5059 4.453 4.5063 7.453 7.5063 4.7952 4.8482 7.7952 7.8482 4.7967 4.8483 7.7967 7.8483 4.7968 4.8502 7.7968 7.8502
9, 10 9, 10 9, 10 9, 10 11 11 11 11 8, 12 12 8, 12 12 6 8 6 8 7 6 7 6
1.3432 1.3592 2.2381 2.254 1.3433 1.3594 2.3409 2.2541 1.4465 1.4625 2.3413 2.3568 1.447 1.4631 2.3414 2.3574 1.4487 1.4632 2.3431 2.3575
9, 10 9, 10 9, 10, 11 9, 10 11 11 8, 12 11 8, 12 8, 12 6 8, 12 6, 7 6 7 6 13 7 13 7
0.00050831 0.00051437 0.00085077 0.00085683 0.00050833 0.00051441 0.00085078 0.00085684 0.00054739 0.00055345 0.00085079 0.00085688 0.0005474 0.00055346 0.00088986 0.00089592 0.00054756 0.00055368 0.00088986 0.00089615
9, 10 9, 10 9 9 11 11 10 10 12 12 11 11 8 8 8 8, 12 6 6 12 6
35 233 35 475 47 778 48 021 35 236 35 478 47 781 48 023 35 811 35 479 48 356 48 024 35 814 36 054 48 359 48 599 35 819 36 057 48 364 48 602
9 9 9 9 10,11 10 10, 11 10 12 11 12 11 8 12 8 12 13 8 13 8
11.931 12.013 16.179 16.262 11.932 12.014 16.18 16.263 12.127 12.209 16.375 16.457 12.128 12.21 16.376 16.458 12.13 12.211 16.378 16.46
9 9 9 9 10, 11 10, 11 10, 11 10, 11 12 12 12 12 8 8 8 8 13 13 13 13
SL: SSVR Location.
This can be stated for load- and energy-oriented indices; however, the proper location of SSVR is not necessarily the same for both customer and load- and energy-oriented indices, simultaneously. It should be noted that since there is one breaker in the system, any outage in the system may result in the breaker action. Therefore, by SSVR installation, the frequency indices such as SAIFI are not changed as shown in Table 4. 6.2. 69-bus test system The 12.66 kV, 69-bus, 8-lateral radial distribution system with few modifications in active and reactive power demand is considered as another test system. Load flow data of the system are obtained from [26]. Base load of the system is considered as (4.0951 + j 2.8630) MVA. The upper and lower limits of voltage magnitude for the load points are considered 1.05p.u. and 0.95p.u. , respectively. Furthermore, the limits of line capacity are taken from IEEE standard test feeders [24]. The reliability parameters are from the RBTS-BUS2 [25] (length of all feeders is considered to be 0.75 km). This system has 48 load points. For this system, large user, industrial, commercial, agriculture, residential, government and institutions and, office and buildings are considered. The customer data, with few modifications is obtained from RBTSBUS4 [25]. Two DGs are considered in the nodes 47 and 53 with the same capacity of 500 kW and 100 kVAr. Furthermore, another DG is considered in node 26 with 600 kW and 120 kVAr capacity. Moreover, one breaker connecting to the source node and an alternative source is considered in node 68. Table 7 shows the reliability indices for each case in the 69bus distribution system before a SSVR installation. Moreover, After a SSVR installation in all lines of the system, results of Tables 8 and 9 are obtained. These tables show the reliability indices of the four cases for five top best locations of the SSVR which have considerable effects on the reliability index. The capacity of the SSVR in Tables 8 and 9 are 50 kVA and 500 kVA, respectively.
Comparing the results of Tables 8 and 9 with that of Table 7 show that a SSVR can improve the reliability indices of the system. Also, the result show that in 69-bus test system customer-oriented indices (SAIDI, CAIDI, and ASUI) improvement is almost the same for both 50 kVA and 200 kVA SSVR installation, whereas the effect of the 200 kVA SSVR on load- and energy-oriented indices (ENS and AENS) is more than that of the 50 kVA. For example for the case ‘4’, in the best condition, a 200 kVA SSVR can improve SAIDI, CAIDI, ASUI, ENS, AENS from 8.056, 2.4192, 0.00091964, 49689 and 16.8269 (Table 7) to 7.5059, 2.254, 0.00085683, 46929, 15.892 (Table 9), respectively, whereas, 50 kVA SSVR improves these indices to 7.5059, 2.254, 0.00085683, 48021 and 16.262, respectively (Table 8). Furthermore, the results show that the proper location of a SSVR is not exactly the same for both customer and load- and energyoriented indices, simultaneously. For case ‘2’, as an example, lines 9, 10, 11 are the best locations for a 200 kVA SSVR to improve SAIDI, CAIDI and ASUI indices, while the best location of a 200 kVA SSVR for the ENS, AENS indices improvement is line 47 (Table 9). This is due to ENS and AENS being strongly dependent on the active loads of customers whereas, SAIDI, CAIDI, ASUI never depend on the active load of customers [3]. Therefore, the best location of a SSVR installation for SAIDI, CAIDI, and ASUI decrement is not necessarily the same as the best location of a SSVR installation for the decrement of AENS and ENS. By comparing the effect of a SSVR installation in the two test systems, it is concluded that the performance of this device in the system as well as their effectiveness are similar. As the results show, the approach presented in this paper in using the SSVR seems to be effective in the reliability improvement of these systems. 7. Conclusion In this paper, a SSVR is utilized for the reliability improvement of distribution systems. For this purpose, an algorithm for the
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Table 9 Reliability indices for 69 bus distribution system with a 200 kVA SSVR. Installation priority
Case
1 2 3 4 1 2 3 4 1 2 3 4 1 2 3 4 1 2 3 4
1
2
3
4
5
a
CAIDI (h/cus.int)
ASUI
ENS (kWh/yr)
AENS (kWh/cus.yr)
Value
SAIDI (h/cus.yr) SLa
Value
SL
Value
SL
Value
SL
Value
SL
4.4528 4.5059 7.4528 7.5059 4.7952 4.8482 7.7952 7.8482 4.7954 4.8483 7.7954 7.8483 4.7967 4.8486 7.7967 7.8486 4.7999 4.8502 7.7999 7.8502
9, 10, 11 9, 10, 11 9, 10, 11 9, 10, 11 8, 12 12 8, 12 12 7 8 7 8 6 7 6 7 13 6 13 6
1.3432 1.3592 2.2381 2.254 1.4465 1.4625 2.3409 2.3568 1.4466 1.4626 2.341 2.3569 1.447 1.4631 2.3413 2.3574 1.4479 1.4643 2.3423 2.3586
9, 10, 11 9, 10, 11 9, 10, 11 9, 10, 11 8, 12 8, 12 8, 12 8, 12 7 7 7 7 6 6 6 6 13 13 13 13
0.00050831 0.00051437 0.00085077 0.00085683 0.00054739 0.00055345 0.00085078 0.00085684 0.0005474 0.00055346 0.00088986 0.00089592 0.00054742 0.00055349 0.00088989 0.00089596 0.00054756 0.00055368 0.00089003 0.00089615
9,10, 11 9, 10, 11 9, 11 9, 11 12 12 10 10 8 8 8, 12 8, 12 7 7 7 7 6 6 6 6
34 139 34 384 46 684 46 929 35 233 35 475 47 778 48 021 35 234 35 478 47 779 48 023 35 811 36 054 48 356 48 599 35 814 36 057 48 359 48 602
47 47 47 47 9, 11 9, 11 9, 11 9, 11 10 10 10 10 12 12 12 12 8 8 8 8
11.561 11.644 15.809 15.892 11.931 12.013 16.179 16.262 11.932 12.014 16.18 16.263 12.127 12.209 16.375 16.457 12.128 12.21 16.376 16.458
47 47 47 47 9, 11 9, 11 9, 11 9, 11 10 10 10 10 12 12 12 12 8 8 8 8
SL: SSVR Location.
reliability assessment is presented using the model of a SSVR in it. In the proposed algorithm, the effects of DGs, alternative source, system reconfiguration, load shedding and load adding are considered. In the algorithm, load points are divided into eight classes and also the effect of the DG and alternative source unavailability is expressed in restoration time of load point classes. Two standard distribution systems consist of 33 and 69 nodes are considered and some reliability indices such as SAIFI, SAIDI, CAIDI, ENS, AENS are calculated in different cases. The effect of the SSVR installation in reliability indices is considered and compared with the case of without a SSVR. Also, two different sizes and different locations are selected for its installation. The best location of a SSVR for each reliability index improvement in different cases is determined. The results show that, by SSVR installation, both customer-oriented indices (SAIDI, CAIDI, ASUI) and load- and energy-oriented can be improved noticeably. But its effectiveness depends on its capacity and location. Also, by categorizing the load points to eight classes, the reliability indexes obtained in this paper are more realistic and practical for real distribution systems. In total, these satisfactory results indicate the effectiveness of the proposed reliability algorithm and also the SSVR utilization for improving the reliability indices in large distribution systems. References [1] Billinton R, Wang P. Reliability-network-equivalent approach to distributionsystem-reliability evaluation. IEE Proc Gener Transm Distrib 1998; 145(March):149–53. [2] Billinton R, Allan RN. Probabilistic assessment of power systems. IEEE Proc 2000;88(2):140–62. [3] Billinton R, Allan RN. Reliability evaluation of power system. 2nd ed. New York: Plenum Press; 1996. [4] Momoh JA, Caven AC. Distribution system reconfiguration scheme using integer interior point programming technique. In: Transmission and distribution conference and exposition, 2003 IEEE PES, vol. 1. 2003. p. 234–41. [5] Baran ME, Wu FF. Network reconfiguration in distribution systems for loss reduction and load balancing. IEEE Trans Power Deliv 1989;4(2):1401–7. [6] Brown RE. Distribution reliability assessment and reconfiguration optimization. In: Transmission and distribution conference and exposition, 2001 IEEE/PES. 2001. p. 994–9. [7] Bae IS, Kim JO, Kim JC, Singh C. Optimal operating strategy for distributed generation considering hourly reliability worth. IEEE Trans Power Syst 2004; 19(1):287–92.
[8] Barker PP, de Mello RW. Determining impact of distributed generation on power systems: Part 1—radial distribution systems. In: Power engineering society summer meeting. IEEE Conference, vol. 3. 2000. p. 1645–56. [9] Pipattanasomporn M, Willingham M, Rahman S. Implications of on-site distributed generation for commercial/industrial facilities. IEEE Trans Power Syst 2005;20(1):206–12. [10] Haque MH. Compensation of distribution system voltage sag by DVR and DSTATCOM. In: 2001 IEEE porto power tech conference, vol. 1. 2001. p. 223–8. [11] Ramsay SM, Cronin PE, Nelson RJ, Bian J, Menendez FE. Using distribution static compensators (D-STATCOMs) to extend the capability of voltage-limited distribution feeders. In: Rural electric power conference, the 39th annual conference. 1996. p. A4/18–A4/24. [12] Ghosh A, Ledwich G. Compensation of distribution system voltage using DVR. In: Proceedings of the IEEE international symposium on industrial electronics, vol. 2. 1999. p. 515–20. [13] Joos G. Three-phase static series voltage regulator control algorithms for dynamic sag compensation. IEEE Trans Power Deliv 2002;17(October): 1030–6. [14] Fujita H, Akagi H. The unified power quality conditioner: The integration of series and shunt-active filters. IEEE Trans Power Electron 1998;13:315–22. [15] Shayanfar HA, Fotuhi-Firuzabad M, Hosseini M. Modeling of static series voltage regulator (SSVR) in distribution systems for voltage improvement and loss reduction. Leonardo Electron J Pract Technol 2008;(12):61–82. [16] Kjolle G, Sand K. An analytical approach for distribution system reliability assessment. IEEE Trans Power Deliv 1992;7(April):809–14. [17] Billinton R, Wang P. Distribution system reliability cost/worth analysis using analytical and sequential simulation techniques. IEEE Trans Power Syst 1998; 13(November):1245–50. [18] Xie K, Zhou J, Billinton R. Reliability evaluation algorithm for complex medium voltage electrical distribution networks based on the shortest path. IEE Proc Gener Transm Distrib 2003;150(6):686–90. [19] Ermolin YA. Reliability calculation under seasonally varying failure rate. ISA Trans 2007;46(1):127–30. [20] Knegtering B, Brombacher AC. A method to prevent excessive numbers of Markov states in Markov models for quantitative safety and reliability assessment. ISA Trans 2000;39(3):363–9. [21] Wang P, Billinton R. Optimum load-shedding technique to reduce the total customer interruption cost in a distribution system. IEE Proc Gener Transm Distrib 2000;147(1):51–6. [22] Haque MH. A general load flow method for distribution systems. Electr Power Syst Res 2000;54(July):47–54. [23] Zareipour H, Bhattacharya K, Canizares CA. Distributed generation: Current status and challenges. In: Annual North American power symposium. 2004. p. 1–8. [24] IEEE Distribution Planning Working Group Report. Radial distribution test feeders. IEEE Trans Power Syst 1991;6(3):975–85. [25] Billinton R, Jonnavithula S. A test system for teaching overall power system reliability assessment. IEEE Trans Power Syst 1996;11(4):1670–6. [26] Baran ME, Wu FF. Optimal capacitor placement on radial distribution systems. IEEE Trans Power Deliv 1989;4(1):725–32.
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Reliability improvement of distribution systems using SSVR Mehdi Hosseini a,∗ , Heidar Ali Shayanfar a , Mahmoud Fotuhi-Firuzabad b a
Center of Excellence for Power System Automation and Operation, Department of Electrical Engineering, Iran University of Science & Technology, Tehran, Iran
b
Department of Electrical Engineering, Faculty of Electrical Engineering, Sharif University of Technology, Tehran, Iran
article
info
Article history: Received 6 July 2008 Received in revised form 21 September 2008 Accepted 3 October 2008 Available online 11 November 2008 Keywords: Distribution system SSVR Reliability improvement
a b s t r a c t This paper presents a reliability assessment algorithm for distribution systems using a Static Series Voltage Regulator (SSVR). Furthermore, this algorithm considers the effects of Distributed Generation (DG) units, alternative sources, system reconfiguration, load shedding and load adding on distribution system reliability indices. In this algorithm, load points are classified into 8 types and separated restoration times are considered for each class. Comparative studies are conducted to investigate the impacts of DG and alternative source unavailability on the distribution system reliability. For reliability assessment, the customer-oriented reliability indices such as SAIFI, SAIDI, CAIDI ASUI and also load- and energy-oriented indices such as ENS and AENS are evaluated. The effectiveness of the proposed algorithm is examined on the two standard distribution systems consisting of 33 and 69 nodes. The best location of the SSVR in distribution systems is determined based on different reliability indices, separately. Results show that the proposed algorithm is efficient for large-scale radial distribution systems and can accommodate the effects of fault isolation and load restoration. © 2008 ISA. Published by Elsevier Ltd. All rights reserved.
1. Introduction The basic function of a distribution system is to provide customers demand to the entire load with an acceptable level of reliability and voltage constraint. Over the past few decades, power system reliability evaluation has been mainly concentrated on generation and transmission. The basic reason for this is that generation and transmission systems are capital intensive, and their inadequacy can cause widespread catastrophic consequences for both society and its environment [1]. However, analysis of the customer failure statistics of most utilities shows that the distribution system makes the greatest individual contribution to the unavailability of supply to a customer and the electrical distribution network failures account for approximately 80% of the average customer interruptions [2,3]. Therefore, distribution systems have begun to receive more attention for reliability assessment. During different contingencies in the distribution systems, loads may be interrupted; lines may be over-loaded or disconnected due to internal or external influences. These anomalies lead to a loss of revenue (especially in a competitive environment) and utility integrity. To overcome these problems, power engineers
∗
Corresponding author. Fax: +98 77240490. E-mail addresses: [email protected] (M. Hosseini), [email protected] (H.A. Shayanfar), [email protected] (M. Fotuhi-Firuzabad).
have proposed several methods such as feeder reconfiguration, capacitor switching for VAR control, series voltage regulator and dispersed generation installation [4]. Feeder reconfiguration is an important measure to improve the operational performance [4–6]. In restoring a process by feeder reconfiguration, the path connecting the loads and the topological structure of the distribution system are changed. In the new configuration, load voltages and line currents may be violated and therefore, the operator is forced to shed some load from the distribution system. Dispersed generations are used for the improvement of reliability of the distribution systems [7–9]. After experiencing an interruption, when the fault is isolated, distributed generators in the part of the feeder not affected by the fault may be allowed to reconnect and operate in a stand-alone or an island mode. Furthermore, most dispersed generators are operated between 0.85 lagging and 1.0 power factor [8] and reactive power compensation (leading current) is provided by other devices. In order to operate in the island mode, DG(s) should be able to meet the required load of the island and therefore, keep the voltage within an acceptable range. Accordingly, additional devices are needed for voltage improvement and reactive power compensation in the distribution systems. The development of electronics-based equipment for distribution systems leads to appearance of new devices for power quality improvement [10–15]. Since the topology of these devices is similar to those implemented for FACTS (Flexible AC Transmission systems) devices, they are also called Distribution FACTS (DFACTS).
0019-0578/$ – see front matter © 2008 ISA. Published by Elsevier Ltd. All rights reserved. doi:10.1016/j.isatra.2008.10.006
M. Hosseini et al. / ISA Transactions 48 (2009) 98–106
Despite the conventional devices such as series voltage regulators and shunt capacitors, D-FATCS have quick response and continuous operation to changes in the network [10,11]. Static Series Voltage Regulator (SSVR) is a series D-FATCS device used in distribution systems for power quality improvement such as voltage sag [14], and under-voltage [15]. Modeling of SSVR in distribution systems load flow is presented in [15]. In that work, it is shown that SSVR is an effective device for the steady-state voltage improvement and also active and reactive power loss reduction. This model is also used for reliability improvement in this paper. Several methods for assessing the distribution system reliability have been developed [1–3,16–20]. Ref. [18] presents an approach to search for the shortest paths between any two nodes of a distribution system. The classification of nodes has been made by considering the sections controlled by protection devices based on the shortest path. The algorithm is suitable for the large-scale distribution system with multiple sub feeders and is used in this paper. In [18], nodes have been classified into four types, whereas in our paper, load points in a distribution system are divided into eight classes. Also, the effect of DG and alternative source unavailability is expressed in restoration time of load points and used in the reliability algorithm. The rest of this paper is organized as follows: Section 2 presents effect of SSVR in voltage improvement in distribution systems, briefly. In Section 3, the effect of DG in reliability improvement, and also load shedding and load adding, and reconfiguration techniques used in this paper are briefly described. The reliability modeling of the distribution systems is explained in Section 4. Details of the proposed algorithm for the reliability assessment are illustrated in Section 5. In Section 6, the proposed algorithm is examined on 33-bus and 69-bus standard distribution using SSVR. Finally, Section 7 summarizes the main points and results of this paper. 2. Static Series Voltage Regulator (SSVR) Fig. 1 shows a typical model of a SSVR installed in a line connected between busses i and j of network. SSVR consists of DC capacitor, voltage source converter and series injection transformer. It can exchange reactive power with the system for voltage regulation and therefore the injected voltage by SSVR should be kept in quadrate with its current flow (Fig. 2). SSVR is used to compensate voltage of bus j, changing it from Vj to Vjnew by injecting a series voltage (VSSVR ) as shown in Fig. 2. The method for calculation of injected series voltage and reactive power by SSVR and also the modeling of SSVR in distribution systems load flow is presented in [15]. 3. Distributed generation; load shedding, and reconfiguration, and load adding techniques 3.1. Distributed generation The utilities evaluate different approaches to provide competitive rates and acceptable reliability levels to customers. DG consists of small generators typically ranging in capacity from several kilowatts to 10 MW connected to distribution systems [8]. The high cost associated with the power interruptions and considering that the costs of transmission and distribution systems are taking an increasingly large portion of the utility capital investment, use of DG in power industry could be a cost effective solution to enhance system reliability. When a fault occurs in the distribution system, by opening switches in the upstream and down stream side of DGs, an isolated area can be supplied. In other words, DGs can improve reliability through islanding operation. Furthermore, DGs can operate as on-site or backup units. In this paper both of these situations are considered.
99
Fig. 1. Single line diagram of two busses of a distribution system with SSVR consideration.
Fig. 2. Phasor diagram of voltages and current of the system shown in Fig. 1.
3.2. Load shedding For a distribution system consisting of M sections, the total number of sections sets is 2M − 1. A section is defined as group of loads which is connected to a protection device; consequently, M is the number of protection devices in local area for load shedding action. To select the best section for shedding, a Priority Weighting Factor (PWF) has been used based on the Sector Customer Damage Functions (SCDF) and feeder load [21] and is used in this paper. SCDF provides the customer interruption cost models for different customers consisting of large user, industrial, commercial, agriculture, residential, government and institutions and office and buildings categories. PWF for section j in the distribution system for the failure duration ri , is determined using the following equation [21]: PWFij =
N X
Lk ck (ri )
(1)
k=1
where, k represents load point k, N is the number of loads connected to section j, Lk is the load connected to load point k, and ck (ri ) is the per unit customer cost for duration ri . The load shedding procedure for determining which section or sections of load points should not be restored consists of the following steps: 1. The Priority Weighting factor (PWF) for each section is calculated and then the sections are sorted in ascending manner. 2. The first section from the sorted list is selected and the total load to be cut for this section is determined. 3. If load shedding action is used in an isolated area with some dispersed generators, the total load of the section must be smaller than or equal to the sum of generator capacities. Otherwise, this state is omitted from the sorted list. 4. The selected section is shed from the determined area and load flow is run. The voltage and current constraints must be checked after shedding this section from the system. If the constraints are satisfied, load shedding is stopped. Otherwise, the next section from the sorted list is selected and the process goes to step 2.
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The above procedure is repeated until the voltage and current constraints are reached by optimum load shedding with the minimum value of PWF index. 3.3. Reconfiguration and load adding Distribution systems are normally operated as radial systems; however, configuration of the system can be changed (reconfigured) by changing the state of some normally-closed switches placed on the line sections of the system. Different feeders are connected through normally-open tie switches, allowing certain interrupted customers to be temporarily transferred to adjacent feeders during maintenance and repair [6]. In this paper feeder reconfiguration is used to improve voltage regulation and reliability. The interrupted sections with maximum total interruption cost are firstly selected to be restored by normally-open switches. Also, load adding to the safe area is considered for reliability improvement. For this purpose, the section sets including at least one normally-open switches connected to the energized part of system, are selected and PWF index is calculated for them. If there is more than one normally open switch in the section, there are different options to add this section to the safe area. In this situation, the best option is obviously the section with the greatest interruption cost. It should be noted that load shedding, reconfiguration and load adding are applied in the distribution system while voltage constraints, capacity constraints of lines and radial structure constraint of the distribution system are satisfied. 4. Distribution reliability modeling 4.1. Reliability indexes The basic distribution system reliability indexes are the three Load Point (LP) indexes: (1) Average failure rate λs ; (2) average outage duration rs ; (3) annual outage duration Us . A radial distribution system consists of a set of series components, including lines, breakers, fuses, disconnected switches, and etc. A customer connected to a load point of such a system requires all components between himself and the supply point to be operating. Consequently, the principle of series systems can be applied directly to these systems is as below [3,17]:
λs =
X
λi
(2)
Us =
λi ri
(3)
i
rs =
Us
λs
.
5. Solution algorithm 5.1. Overall algorithm The overall algorithm is the determination of three areas of system, i.e. safe, interrupted and isolated. Then, the reliability indexes for each load point in these areas are calculated. For this purpose, at first, during system failure, the distribution system is divided into different classes by protective devices (will be described in 5.2). Then, the interrupted area is identified and load points that are fed with the main source, alternative source and distributed generators, are recognized after power flow, load shedding, reconfiguration and load adding techniques. These techniques are used to improve the reliability of the distribution system. The load shedding, reconfiguration and load shedding priority among sections of the distribution system are determined to minimize the total system interruption cost. It should be noted that this algorithm is based on the assumption that the distribution system has a radial structure. After a fault has been cleared, two kinds of switching operations may be done. The first action is isolating the failure point from the system. The second one is determination of the affected areas which are disconnected from the source and may be resupplied from the available sources (the source, the alternative source or DGs). The restoration procedure includes the process of decision making, and various switching and repairing actions using the switches. In this paper it is assumed that at first, the load points are re-supplied from the main source as far as possible by reconfiguration. In the next priority step, loads are however resupplied from an alternative source and finally, the interrupted loads are fed by DGs (island operation). Based on this assumption, different classifications for the load points are considered and described in the following section. 5.2. Load point classification
i
X
3. Only an overcurrent protection device such as breaker or fuse can interrupt fault currents. Also protective devices such as breakers, fuses, disconnectors, normally open and closed switches have the function of fault isolation. 4. A fault in a radial subsystem is interrupted by the nearest overcurrent protection device (fuse/breaker) on its source side and is isolated by the nearest protective devices. 5. Protection devices are 100% reliable. 6. The location of switches, alternative and DGs on the distribution system are known.
(4)
The customer-oriented reliability indices such as SAIFI, SAIDI, CAIDI ASUI and load- and energy-oriented indices such as, ENS and AENS can be calculated from the three basic LP indexes [3, 17]. In this paper, these indices are considered for the reliability evaluation of the test systems. 4.2. Basic assumption In this paper the following assumptions are considered in the proposed algorithm: 1. A two-state up/down representation for the operation/repair cycle of an element is used. 2. All failures in the distribution systems are independent.
The distribution system is divided into sections by the protection and isolation components. A section is a group of components whose entry component is a switch or a protection device. Therefore, each section has only one switch or protection device. When a failure occurs in the network, it must be isolated by the nearest upstream breaker or fuse. Then, the sections that are affected by this failure must be isolated from the system. When the faults are on the lines with switches, they are isolated by those switches and faults on lines without switches are isolated by opening proper downstream and upstream switches. Distribution system is divided into different areas in terms of the location of sectionalizers, normally open switch, alternative source location(s), and DG location(s). The restoration times of load points in each area will not be the same due to restoration switching sequence. In this paper, load in a distribution system is divided into eight classes as follows: Class A: Load points that are not affected by a fault (restoration time is equal to zero).
M. Hosseini et al. / ISA Transactions 48 (2009) 98–106
Class B: The upstream load points of faulted component whose outage duration is equal to the time of isolating the fault plus the reclosing time of the breaker. The load points in this class are restored through the main supply. Class C: The load points whose outage duration is equal to the time of isolating the fault plus the reconnection time of the breaker plus the switching time of a tie switch or normally open switch. The load points in this class are connected to the nodes in class A or B by normally open switching. Therefore, they are energized through the main supply. Class D: The load points whose outage duration is equal to the isolating time of the fault plus the breaker reclosing time of an alternative source. Class E: The load points whose outage duration is equal to the time of isolating the fault plus the breaker connection time of an alternative source plus the switching time of a tie switch or normally open. The load points in this class are connected to the nodes in class D by normally open and therefore, are energized through the alternative source. Class F: The load points whose outage duration is equal to the time of isolating the fault plus the starting time of DG. Class G: The load points whose outage duration is equal to the isolating time of the fault plus the starting time of DG plus the switching time of a tie switch or normally open. The load points in this class are connected to the nodes in class F by normally open and are energized through a DG. Class H: The load points whose outage durations are equal to the time of isolating the fault and repair the failed components. Furthermore, before the classification of nodes, a load flow calculation is performed. If the load flow is converged and the nodes voltages and line currents are in the acceptable limit then the classification is done. Otherwise, after reconfiguration and load shedding and finally load adding, the parts of the subsystem with voltage and current in the acceptable ranges are classified and the other nodes are considered as new subsystems which are candidate to be categorized to other classes. It should be mentioned that if the load flow calculation is performed for a part of system that include SSVR, its model [15] is considered in the load flow calculations. It should be noted that in classes A, B, C, D or E, if there are several distributed generators, the distribution system is first converted to an equivalent single source network with radial configuration [22] and then the load flow problem is solved. Similarly, in the isolated areas (class G or H) if there are several distributed generators, the DG unit with the highest capacity is modeled as a voltage source taking into account its capacity limit. Accordingly, using the method proposed in [22], the subsystem with several DGs can be converted to a radial structure. 5.3. Effect of alternative source and DG unavailability on restoration time As mentioned in Section 5.2., the restoration time of different classes is not the same and it increases from class A to class H. It is not always feasible that the alternative source and DG be available when they are required. Therefore, restoration of classes D, E (supplied by alternative source), F, G (supplied by DG) should be modified. In order to consider the alternative source(s) unavailability, the load points of classes D, E are divided into two groups. The first group is the load points which have no connection with a DG. Therefore, when an alternative is not available, their restoration time is equal to the repair time of failed component.
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Consequently, the modified restoration time of the first group of classes D and E are as follow: MRD1 = PAlternativ e .rD + (1 − PAlternativ e ).rH
(5)
MRE1 = PAlternativ e .rE + (1 − PAlternativ e ).rH
(6)
where: MRD1 —Modified restoration time of the first group in class D MRE1 —Modified restoration time of the first group in class E PAlternativ e —The availability of alternative source rD —Restoration time of class D rE —Restoration time of class E rH —The time of isolating the fault and repair the failed component (Restoration time of class H). The second group is the load points which are connected directly to a DG, or indirectly by a normally open switch. Therefore, when an alternative is not available, they belong to classes F or G and may be supplied by a DG. Therefore, the modified restoration time of the second group of classes D and E are as follow: MRD2 = PAlternativ e .rD + (1 − PAlternativ e ).PDG .(rF .WF + rG .WG ) + (1 − PAlternative ).(1 − PDG ).rH (7) MRE2 = PAlternativ e .rE + (1 − PAlternativ e ).PDG .(rF .WF + rG .WG ) + (1 − PAlternative ).(1 − PDG ).rH
(8)
where: MRD2 —Modified restoration time of the second group in class D MRE2 —Modified restoration time of the second group in class E PDG —The availability of DG. Furthermore, WF and WG are binary variable refer to the classes F and G, respectively. WF is equal to one if the second group belongs to class F in the case of alternative source unavailability and at the same time WG is equal to zero. Similarly, when WG is equal to one, WF is zeros. In other words, WF + WG = 1. It should be noted that part of nodes located in the second group of classes D and E which they do not satisfy the load flow constraints, must be shed and their restoration time are the same as the first groups of these classes. In addition to the nodes classified from classes D, E to classes G, F, there are some nodes in classes G, F, originally (classes F, G identified earlier in Section 5.2.) supplied by DG after isolation of the faulted area. The modified restoration time of these classes by consideration of DG unavailability is as follow: MRG = PDG .rG + (1 − PDG ).rH
(9)
MRF = PDG .rF + (1 − PDG ).rH
(10)
where: MRG —Modified restoration time of class G MRF —Modified restoration time of class F rF —Restoration time of class F rG —Restoration time of class G. 5.4. Reliability assessment algorithm Based on the description and the assumptions in the above sections, the proposed algorithm includes the following steps. 1. Read the reliability and load flow data. 2. Consider contingency state using contingency enumeration. 3. Determine the area affected using the shortest path [18] to form the separate subsystems. 4. Classify the nodes into classes A, B, C, D, E, F, G and H based on the location of protective devices, DGs, and alternative sources (Section 5.2). 5. Modify restoration time of the nodes in classes D, E, F, G. (Section 5.3). 6. Calculate load point indices for this contingency state. 7. Go to the next step if all contingencies are considered; otherwise go to Step 2 for new contingency. 8. Calculate the system indices.
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Table 1 Voltage magnitude and phase angle in 33 bus distribution in the base case system. Node no.
Voltage magnitude (p.u.)
Phase angle (deg)
Node no.
Voltage magnitude (p.u.)
Phase angle (deg)
Node no.
Voltage magnitude (p.u.)
0 1 2 3 4 5 6 7 8 9 10
1.0000 0.9970 0.9829 0.9755 0.9681 0.9497 0.9462 0.9413 0.9351 0.9292 0.9284
0 0.014 0.096 0.161 0.228 0.133 −0.096 −0.060 −0.133 −0.195 −0.188
11 12 13 14 15 16 17 18 19 20 21
0.9269 0.9208 0.9185 0.9171 0.9157 0.9137 0.9131 0.9965 0.9929 0.9922 0.9916
−0.177 −0.268 −0.347 −0.384 −0.408 −0.485 −0.495
22 23 24 25 26 27 28 29 30 31 32
0.9794 0.9727 0.9694 0.9477 0.9452 0.9337 0.9255 0.9219 0.9178 0.9168 0.9166
0.0037
−0.063 −0.082 −0.103
Phase angle (deg) 0.065
−0.023 −0.067 0.173 0.229 0.311 0.389 0.494 0.410 0.386 0.379
6. Simulation results Two standard distribution systems consisting of 33 and 69 busses are used to examine the effectiveness of the proposed reliability algorithm. At first, a risk analysis is performed in the test systems to determine whether the voltages of all nodes are in the determined limit. After that, the percentage (probability) that each node can be categorized in each of classes (classes A to H) is determined. Because of similar trend of results for both test systems, results related to node classification and risk analysis is only presented for 33-bus test system. Then, in each distribution system, the customer-oriented reliability indices such as SAIFI, SAIDI, CAIDI ASUI and load- and energy-oriented indices such as ENS and AENS are calculated. The effect of SSVR on these indices is considered and compared with the results of these test systems without any SSVR. In order to indicate and compare the effects of SSVR installation in the distribution system, different sizes and locations are selected for installation. The system reliability indices for typical distribution systems are computed for four cases. It should be noted that only one SSVR is used at a time while performing load flow calculations. Details of case studies are as follows: Case ‘1’: Alternative supply and DGs are 100% available; LV transformers are 100% available; Case ‘2’: Availability of alternative supply and DGs are 0.9 and 0.85, respectively and LV transformers are 100% available; Case ‘3’: Alternative supply and DGs are 100% available and failure rate of LV transformers is considered. Case ‘4’: Availability of alternative supply and DGs are 0.9 and 0.85, respectively and failure rate of LV transformers is considered. Restoration time (hour) of classes B, C, D, E, F, G in both test systems are considered as below [2,3,23]: rB = 1 , rG = 1.8
rC = 1.2, and
rD = 1.3,
rE = 1.5,
rF = 1.6,
rH = 5 .
The results obtained in these systems are briefly summarized in the following subsections. 6.1. 33-bus test system Fig. 3. shows single line diagram of the 12.66 kV, 33-bus, 4lateral radial distribution system. The total load of the system in the base case is (3715 + j 2300) kVA. The load flow data of the system are taken from [5]. The upper and lower bounds of acceptable voltage magnitudes are 1.05p.u. and 0.95p.u. , respectively. Furthermore, limits of line capacity are taken from IEEE standard test feeders [24]. Reliability parameters are from the RBTS-BUS2 [25] (length of all feeders is considered to be 0.75 km).
Fig. 3. Single line diagram of 33 bus distribution system.
Also, normally open switches data is taken from [5]. This system includes large user, industrial, commercial, agriculture, residential, government and institutions and, office and buildings customers. The customers’ data, with few modifications is obtained from RBTS-BUS2 [25]. For reliability studies of the system, one 500 kW and 100 kVAr standby DG in node 21, an alternative source in node 24, and also a breaker connecting to the source node are considered. 6.1.1. The system risk study A summery of the load flow results for the base case is taken in Table 1. The results show that 21 nodes out of 33 nodes of the distribution system are under 0.95p.u. . As shown in Table 1, some nodes have under-voltage problems in the base case before reliability assessment and therefore, risk of system in this situation is equal to 1. These nodes are: nodes 5–17 and also nodes 25–32. The other feeder of the system, i.e. feeder with nodes 18–21 and the other one with nodes 22–24, have voltage magnitude in acceptable limits (Table 1). Two DGs are installed in nodes 17 and 32 to solve the mentioned under voltage problem. The capacity of each DG is equal to 500 kW and 100 kVAr. It should be discussed that, the installation of two DGs in nodes 24 and 21 (healthy feeders) cannot completely mitigate the undervoltage problem of the nodes 5–17 and 25–32. This is due to the fact that the DGs location (nodes 24 and 21) are far from these nodes. Consequently the installation of DGs in nodes 21 and 24 seems not to be efficient in terms of under-voltage mitigation. Instead, if the DGs are installed in nodes 17 and 32, it is indicated that the under voltage problem of the mentioned nodes are mitigated as these nodes. The results of this case are taken in Table 2, showing that DGs in nodes 17 and 32 can efficiently mitigate the under-voltage problem as these two DGs are approximately located in the vicinity of the nodes with the under-voltage problem. 6.1.2. Classification of node points Table 3 shows the percentage (probability) that each node can be categorized in each of classes (class A–H). For cases 1 and 2, the percentage is calculated by considering all of the line outage. In the cases 3, 4, besides the line outage, all the LV transformer
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Table 2 Voltage magnitude and phase angle in 33 bus distribution after DG installations in nodes 17 and 32. Node no.
Voltage magnitude (p.u.)
Phase angle (deg)
Node no.
Voltage magnitude (p.u.)
Phase angle (deg)
Node no.
Voltage magnitude (p.u.)
Phase angle (deg)
0 1 2 3 4 5 6 7 8 9 10
1 0.9977 0.9875 0.9828 0.9784 0.9668 0.9644 0.9622 0.9599 0.9582 0.9581
0 0.024 0.157 0.262 0.368 0.483 0.375 0.427 0.460 0.505 0.517
11 12 13 14 15 16 17 18 19 20 21
0.9579 0.9576 0.9576 0.9585 0.96 0.9633 0.9655 0.9972 0.9936 0.9929 0.9923
0.537 0.620 0.665 0.710 0.766 0.978 1.052 0.013 −0.053 −0.072 −0.093
22 23 24 25 26 27 28 29 30 31 32
0.9839 0.9773 0.974 0.9656 0.9641 0.9571 0.9522 0.9506 0.9504 0.9508 0.952
0.127 0.039 −0.004 0.533 0.603 0.825 1.002 1.132 1.205 1.243 1.327
Table 3 The percentage (probability) that each node can be categorized in each of classes (class A–H) for the cases 1–4. Node no. Class A (%)
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32
Class B (%)
Class C (%)
Class D (%)
Class E (%)
Class F (%)
Class G (%)
Class H (%)
Case 1, 2
Case 3, 4
Case 1, 2
Case 3, 4
Case 1, 2
Case 3, 4
Case 1, 2
Case 3,4
Case 1, 2
Case 3, 4
Case 1, 2
Case 3, 4
Case 1, 2
Case 3, 4
Case 1, 2
Case 3,4
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
48.4 48.4 48.4 48.4 48.4 48.4 48.4 48.4 48.4 48.4 48.4 48.4 48.4 48.4 48.4 48.4 48.4 48.4 48.4 48.4 48.4 48.4 48.4 48.4 48.4 48.4 48.4 48.4 48.4 48.4 48.4 48.4
93.8 84.4 84.4 84.4 75.0 75.0 68.8 65.6 62.5 65.6 62.5 46.9 43.8 40.6 40.6 46.9 40.6 87.5 84.4 81.3 75.0 90.6 84.4 81.3 78.1 71.9 68.8 59.4 62.5 53.1 56.3 53.1
46.9 42.2 42.2 42.2 37.5 37.5 34.4 32.8 31.3 32.8 31.3 23.4 21.9 20.3 20.3 23.4 20.3 43.8 42.2 40.6 37.5 45.3 42.2 40.6 39.1 35.9 34.4 29.7 31.3 26.6 28.1 26.6
0 0 3.13 6.25 9.38 12.5 15.6 18.8 21.9 25.0 28.1 31.3 34.4 37.5 40.6 43.8 43.8 0 3.13 6.25 6.25 0 0 0 12.5 15.6 18.8 18.8 18.8 25.0 31.3 31.3
0 0 1.56 3.13 4.69 6.25 7.81 9.38 10.9 12.5 14.1 15.6 17.2 18.7 20.3 21.9 21.9 0 1.56 3.13 3.13 0 0 0 6.25 7.81 9.38 9.38 9.38 12.5 15.6 15.6
0 3.13 3.13 3.13 3.13 3.13 3.13 3.13 3.13 3.13 3.13 15.6 12.5 9.38 6.25 3.13 3.13 0 3.13 3.13 3.13 3.13 6.25 6.25 3.13 3.13 3.13 6.25 6.25 6.25 3.13 3.13
0 1.56 1.56 1.56 1.56 1.56 1.56 1.56 1.56 1.56 1.56 7.81 6.25 4.69 3.13 1.56 1.56 0 1.56 1.56 1.56 1.56 3.13 3.13 1.56 1.56 1.56 3.13 3.13 3.13 1.56 1.56
0 3.13 3.13 3.13 3.13 3.13 3.13 3.13 3.13 3.13 3.13 3.13 3.13 3.13 3.13 3.13 3.13 0 3.13 3.13 3.13 3.13 3.13 3.13 3.13 3.13 3.13 6.25 6.25 6.25 3.13 3.13
0 1.56 1.56 1.56 1.56 1.56 1.56 1.56 1.56 1.56 1.56 1.56 1.56 1.56 1.56 1.56 1.56 0 1.56 1.56 1.56 1.56 1.56 1.56 1.56 1.56 1.56 3.13 3.13 3.13 1.56 1.56
3.13 3.13 3.13 0 3.13 3.13 3.13 3.13 3.13 0 0 0 3.13 3.13 3.13 0 3.13 3.13 3.13 3.13 3.13 0 3.13 3.13 0 3.13 3.13 3.13 0 0 0 3.13
1.56 1.56 1.56 0 1.56 1.56 1.56 1.56 1.56 0 0 0 1.56 1.56 1.56 0 1.56 1.56 1.56 1.56 1.56 0 1.56 1.56 0 1.56 1.56 1.56 0 0 0 1.56
0 3.13 0 0 3.13 0 3.13 3.13 3.13 0 0 0 0 3.13 3.13 0 0 3.13 0 0 3.13 0 0 0 0 0 0 3.13 0 0 0 0
0 1.56 0 0 1.56 0 1.56 1.56 1.56 0 0 0 0 1.56 1.56 0 0 1.56 0 0 1.56 0 0 0 0 0 0 1.56 0 0 0 0
3.13 3.13 3.13 3.13 3.13 3.13 3.13 3.13 3.13 3.13 3.13 3.13 3.13 3.13 3.13 3.13 6.25 6.25 3.13 3.13 6.25 3.13 3.13 6.25 3.13 3.13 3.13 3.13 6.25 9.38 6.25 6.25
3.13 3.13 3.13 3.13 3.13 3.13 3.13 3.13 3.13 3.13 3.13 3.13 3.13 3.13 3.13 3.13 4.69 4.69 3.13 3.13 4.69 3.13 3.13 4.69 3.13 3.13 3.13 3.13 4.69 6.25 4.69 4.69
outages are also considered. From the table, it can be seen that the calculated percentage of all nodes for cases 1, 2 is equal to zero (the 2nd column of Table 3). This is due to the fact that there is only one breaker in the source node and therefore for any line outage in the system, the breaker operates. Accordingly no nodes can be categorized in class A and their calculated percentage for class A is zero. But in cases 3 and 4, for any LV transformer outage in the system, the transformer fuse operates and the rest of the nodes belong to class A. In [18], the effects of DG, reconfiguration, load adding and unavailability of alternative sources are not considered. Therefore, based on the definition for load point classes in our paper, the load points of [18] are classified to classes A, B, D, H. On the other hand, according to Table 3, a considerable number of load points are found in class C. Also, some load points are in class E, F, G. As a result, the reliability indexes obtained in this paper are more realistic and practical for real distribution systems. Although the percentage of load points in each class for the cases 1 and 2 and also cases 3 and 4 are the same (from Table 3), it is necessary
to modify the restoration time of classes D, E, F, G for cases 2, 4 for reliability indices calculation (based on Section 5.3). The results of reliability indices are presented in the following sections. 6.1.3. Reliability indexes with and without SSVR Reliability indices for each case in 33-bus distribution system before SSVR installation are calculated and presented in Table 4. Comparing the results of Cases ‘3’, ‘4’ with those of Cases ‘1’, ‘2’, it can be seen that there is a considerable difference between the results. As the repair time for a LV transformer (200 h [25]) is much longer than that of the other elements, the difference between the reliability indices for the cases is significant. Furthermore, a consideration of unavailability for the alternative supply and DGs in cases ‘2’ and ‘4’ causes the reliability to worsen as compared with cases ‘1’, ‘3’, respectively. The effect of SSVR installation on reliability indices is studied. For this purpose, one SSVR is installed in each line of the system and after that reliability indices are calculated. This process is
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Table 4 Reliability indices for 33 bus distribution system without SSVR. Case
SAIFI (int./cus.yr)
SAIDI (h/cus.yr)
CAIDI (h/cus.int)
ASUI
ENS (kWh/yr)
AENS (kWh/cus.yr)
Case ‘1’ Case ‘2’ Case ‘3’ Case ‘4’
1.56 1.56 1.575 1.575
1.9702 1.9808 4.9702 4.9808
1.2629 1.2698 3.1557 3.1624
0.00022491 0.00022612 0.00056737 0.00056859
7323 7413.5 18468 18559
3.7438 3.7901 9.4417 9.488
Table 5 Reliability indices for 33 bus distribution system with 50 kVA SSVR. Installation priority
Case
1 2 3 4 1 2 3 4 1 2 3 4 1 2 3 4 1 2 3 4
1
2
3
4
5
a
CAIDI (h/cus.int)
ASUI
Value
SAIDI (h/cus.yr) SLa
Value
SL
Value
SL
Value
ENS (kWh/yr) SL
Value
AENS (kWh/cus.yr) SL
1.8472 1.8596 4.8472 4.8596 1.8473 1.8597 4.8473 4.8597 1.8509 1.8632 4.8509 4.8632 1.8529 1.8653 4.8529 4.8653 1.853 1.8654 4.853 4.8654
5 5 5 5 4 4 4 4 27 27 27 27 7 7 7 7 6 6 6 6
1.1841 1.192 3.0776 3.0854 1.1842 1.1921 3.0799 3.0855 1.1865 1.1944 3.0812 3.0878 1.1878 1.1957 3.0813 3.0891 1.1972 1.1958 3.0906 3.0973
5 5 4, 5 5 4 4 27 4 27 27 7 27 6, 7 7 6 6, 7 2, 3 6 2, 3 2, 3
0.00021087 0.00021228 0.00055333 0.00055474 0.00021088 0.00021229 0.00055334 0.00055475 0.00021129 0.0002127 0.00055375 0.00055516 0.00021152 0.00021293 0.00055399 0.0005554 0.00021153 0.00021294 0.000554 0.00055541
5 5 5 5 4 4 4 4 27 27 27 27 7 7 7 7 6 6 6 6
7064.7 7161.8 18210 18307 7075.8 7172.9 18221 18318 7125.4 7198.2 18270 18343 7128.7 7219.3 18274 18364 7212.2 7289.2 18357 18434
5 5 5 5 4 4 4 4 3 3 3 3 2 2 2 2 27 27 27 27
3.6118 3.6614 9.3097 9.3593 3.6175 3.6671 9.3153 9.365 3.6428 3.6801 9.3407 9.3779 3.6445 3.6908 9.3424 9.3887 3.6872 3.7266 9.3851 9.4244
5 5 5 5 4 4 4 4 3 3 3 3 2 2 2 2 27 27 27 27
SL: SSVR Location.
Table 6 Reliability indices for 33 bus distribution system with 200 kVA SSVR. Installation priority
Case
1 2 3 4 1 2 3 4 1 2 3 4 1 2 3 4 1 2 3 4
1
2
3
4
5
a
SAIDI (h/cus.yr)
CAIDI (h/cus.int)
ASUI
Value
SLa
Value
SL
Value
SL
Value
ENS (kWh/yr) SL
Value
AENS (kWh/cus.yr) SL
1.8403 1.8533 4.8403 4.8533 1.8406 1.8536 4.8406 4.8536 1.8508 1.8631 4.8508 4.8631 1.8528 1.8652 4.8528 4.8652 1.853 1.8654 4.853 4.8654
5 5 5 5 3, 4 3, 4 3, 4 3, 4 25, 27 25, 27 25, 27 25, 27 7 7 7 7 6 6 6 6
1.1797 1.188 3.0732 3.0815 1.1798 1.1882 3.0734 3.0816 1.1864 1.1943 3.0798 3.0877 1.1877 1.1956 3.0812 3.089 1.1878 1.1958 3.0813 3.0891
5 5 5 5 3, 4 3, 4 3, 4 3, 4 25, 27 25, 27 25, 27 25, 27 7 7 7 7 6 6 6 6
0.00021008 0.00021156 0.00055254 0.00055403 0.00021011 0.0002116 0.00055258 0.00055406 0.00021127 0.00021268 0.00055374 0.00055515 0.00021151 0.00021292 0.00055398 0.00055539 0.00021153 0.00021294 0.000554 0.00055541
5 5 5 5 3, 4 3, 4 3, 4 3, 4 25, 27 25, 27 25, 27 25, 27 7 7 7 7 6 6 6 6
6899.7 6977.2 18045 18122 7025.6 7103.2 18171 18248 7025.6 7103.2 18171 18248 7116.5 7191.8 18261 18337 7132.2 7206.6 18277 18352
5 5 5 5 3 3 3 3 4 4 4 4 2 2 2 2 25 25 25 25
3.5274 3.5671 9.2253 9.2649 3.5918 3.6315 9.2897 9.3293 3.5918 3.6315 9.2897 9.3293 3.6383 3.6768 9.3361 9.3747 3.6463 3.6844 9.3442 9.3822
5 5 5 5 3 3 3 3 4 4 4 4 2 2 2 2 25 25 25 25
SL: SSVR Location.
done for all system nodes and reliability indices are calculated. Tables 5 and 6 show the reliability indices for five top best locations of SSVR which have considerable effect on the reliability index. The best location of SSVR in cases ‘1’–‘4’ is determined separately for each reliability index. The capacity of SSVR in Tables 5 and 6 are 50 kVA and 200 kVA, respectively. Comparing the results of Tables 5 and 6 with that of Table 4 show that SSVR can improve the reliability indices of the system. But its effectiveness depends on its capacity and location. Also, comparing the results shown in Tables 5 and 6, it is observed that the effect of 200 kVA SSVR is more than 50 kVA SSVR. For example for
the case ‘1’, in the best condition, 200 kVA SSVR can improve SAIDI, CAIDI, ASUI, ENS, AENS from 1.9702, 1.2629, 0.00022491, 7323 and 3.7438 (Table 4) to 1.8403, 1.1797, 0.00021008, 6899.7, 3.5274 (Table 6), respectively, whereas, 50 kVA SSVR improves these indices to 1.8472, 1.1841, 0.00021087, 7064.7 and 3.6118, respectively (Table 5). Furthermore, Tables 5 and 6 show that by SSVR installation, both customer-oriented indices (SAIDI, CAIDI, and ASUI) and also load- and energy-oriented indices (ENS and AENS) can be improved considerably. Also, the suitable location for SSVR installation in all four cases for the customer-oriented indices is almost the same.
M. Hosseini et al. / ISA Transactions 48 (2009) 98–106
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Table 7 Reliability indices for 69 bus distribution system without a SSVR. Case
SAIFI (int./cus.yr)
SAIDI (h/cus.yr)
CAIDI (h/cus.int)
ASUI
ENS (kWh/yr)
AENS (kWh/cus.yr)
Case ‘1’ Case ‘2’ Case ‘3’ Case ‘4’
3.315 3.315 3.33 3.33
5.0024 5.056 8.0024 8.056
1.509 1.5252 2.4031 2.4192
0.00057105 0.00057717 0.00091351 0.00091964
36 898 37 144 49 443 49 689
12.4952 12.5786 16.7435 16.8269
Table 8 Reliability indices for 69 bus distribution system with a 50 kVA SSVR. Installation priority
Case
1 2 3 4 1 2 3 4 1 2 3 4 1 2 3 4 1 2 3 4
1
2
3
4
5
a
CAIDI (h/cus.int)
ASUI
ENS (kWh/yr)
AENS (kWh/cus.yr)
Value
SAIDI (h/cus.yr) SLa
Value
SL
Value
SL
Value
SL
Value
SL
4.4528 4.5059 7.4528 7.5059 4.453 4.5063 7.453 7.5063 4.7952 4.8482 7.7952 7.8482 4.7967 4.8483 7.7967 7.8483 4.7968 4.8502 7.7968 7.8502
9, 10 9, 10 9, 10 9, 10 11 11 11 11 8, 12 12 8, 12 12 6 8 6 8 7 6 7 6
1.3432 1.3592 2.2381 2.254 1.3433 1.3594 2.3409 2.2541 1.4465 1.4625 2.3413 2.3568 1.447 1.4631 2.3414 2.3574 1.4487 1.4632 2.3431 2.3575
9, 10 9, 10 9, 10, 11 9, 10 11 11 8, 12 11 8, 12 8, 12 6 8, 12 6, 7 6 7 6 13 7 13 7
0.00050831 0.00051437 0.00085077 0.00085683 0.00050833 0.00051441 0.00085078 0.00085684 0.00054739 0.00055345 0.00085079 0.00085688 0.0005474 0.00055346 0.00088986 0.00089592 0.00054756 0.00055368 0.00088986 0.00089615
9, 10 9, 10 9 9 11 11 10 10 12 12 11 11 8 8 8 8, 12 6 6 12 6
35 233 35 475 47 778 48 021 35 236 35 478 47 781 48 023 35 811 35 479 48 356 48 024 35 814 36 054 48 359 48 599 35 819 36 057 48 364 48 602
9 9 9 9 10,11 10 10, 11 10 12 11 12 11 8 12 8 12 13 8 13 8
11.931 12.013 16.179 16.262 11.932 12.014 16.18 16.263 12.127 12.209 16.375 16.457 12.128 12.21 16.376 16.458 12.13 12.211 16.378 16.46
9 9 9 9 10, 11 10, 11 10, 11 10, 11 12 12 12 12 8 8 8 8 13 13 13 13
SL: SSVR Location.
This can be stated for load- and energy-oriented indices; however, the proper location of SSVR is not necessarily the same for both customer and load- and energy-oriented indices, simultaneously. It should be noted that since there is one breaker in the system, any outage in the system may result in the breaker action. Therefore, by SSVR installation, the frequency indices such as SAIFI are not changed as shown in Table 4. 6.2. 69-bus test system The 12.66 kV, 69-bus, 8-lateral radial distribution system with few modifications in active and reactive power demand is considered as another test system. Load flow data of the system are obtained from [26]. Base load of the system is considered as (4.0951 + j 2.8630) MVA. The upper and lower limits of voltage magnitude for the load points are considered 1.05p.u. and 0.95p.u. , respectively. Furthermore, the limits of line capacity are taken from IEEE standard test feeders [24]. The reliability parameters are from the RBTS-BUS2 [25] (length of all feeders is considered to be 0.75 km). This system has 48 load points. For this system, large user, industrial, commercial, agriculture, residential, government and institutions and, office and buildings are considered. The customer data, with few modifications is obtained from RBTSBUS4 [25]. Two DGs are considered in the nodes 47 and 53 with the same capacity of 500 kW and 100 kVAr. Furthermore, another DG is considered in node 26 with 600 kW and 120 kVAr capacity. Moreover, one breaker connecting to the source node and an alternative source is considered in node 68. Table 7 shows the reliability indices for each case in the 69bus distribution system before a SSVR installation. Moreover, After a SSVR installation in all lines of the system, results of Tables 8 and 9 are obtained. These tables show the reliability indices of the four cases for five top best locations of the SSVR which have considerable effects on the reliability index. The capacity of the SSVR in Tables 8 and 9 are 50 kVA and 500 kVA, respectively.
Comparing the results of Tables 8 and 9 with that of Table 7 show that a SSVR can improve the reliability indices of the system. Also, the result show that in 69-bus test system customer-oriented indices (SAIDI, CAIDI, and ASUI) improvement is almost the same for both 50 kVA and 200 kVA SSVR installation, whereas the effect of the 200 kVA SSVR on load- and energy-oriented indices (ENS and AENS) is more than that of the 50 kVA. For example for the case ‘4’, in the best condition, a 200 kVA SSVR can improve SAIDI, CAIDI, ASUI, ENS, AENS from 8.056, 2.4192, 0.00091964, 49689 and 16.8269 (Table 7) to 7.5059, 2.254, 0.00085683, 46929, 15.892 (Table 9), respectively, whereas, 50 kVA SSVR improves these indices to 7.5059, 2.254, 0.00085683, 48021 and 16.262, respectively (Table 8). Furthermore, the results show that the proper location of a SSVR is not exactly the same for both customer and load- and energyoriented indices, simultaneously. For case ‘2’, as an example, lines 9, 10, 11 are the best locations for a 200 kVA SSVR to improve SAIDI, CAIDI and ASUI indices, while the best location of a 200 kVA SSVR for the ENS, AENS indices improvement is line 47 (Table 9). This is due to ENS and AENS being strongly dependent on the active loads of customers whereas, SAIDI, CAIDI, ASUI never depend on the active load of customers [3]. Therefore, the best location of a SSVR installation for SAIDI, CAIDI, and ASUI decrement is not necessarily the same as the best location of a SSVR installation for the decrement of AENS and ENS. By comparing the effect of a SSVR installation in the two test systems, it is concluded that the performance of this device in the system as well as their effectiveness are similar. As the results show, the approach presented in this paper in using the SSVR seems to be effective in the reliability improvement of these systems. 7. Conclusion In this paper, a SSVR is utilized for the reliability improvement of distribution systems. For this purpose, an algorithm for the
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Table 9 Reliability indices for 69 bus distribution system with a 200 kVA SSVR. Installation priority
Case
1 2 3 4 1 2 3 4 1 2 3 4 1 2 3 4 1 2 3 4
1
2
3
4
5
a
CAIDI (h/cus.int)
ASUI
ENS (kWh/yr)
AENS (kWh/cus.yr)
Value
SAIDI (h/cus.yr) SLa
Value
SL
Value
SL
Value
SL
Value
SL
4.4528 4.5059 7.4528 7.5059 4.7952 4.8482 7.7952 7.8482 4.7954 4.8483 7.7954 7.8483 4.7967 4.8486 7.7967 7.8486 4.7999 4.8502 7.7999 7.8502
9, 10, 11 9, 10, 11 9, 10, 11 9, 10, 11 8, 12 12 8, 12 12 7 8 7 8 6 7 6 7 13 6 13 6
1.3432 1.3592 2.2381 2.254 1.4465 1.4625 2.3409 2.3568 1.4466 1.4626 2.341 2.3569 1.447 1.4631 2.3413 2.3574 1.4479 1.4643 2.3423 2.3586
9, 10, 11 9, 10, 11 9, 10, 11 9, 10, 11 8, 12 8, 12 8, 12 8, 12 7 7 7 7 6 6 6 6 13 13 13 13
0.00050831 0.00051437 0.00085077 0.00085683 0.00054739 0.00055345 0.00085078 0.00085684 0.0005474 0.00055346 0.00088986 0.00089592 0.00054742 0.00055349 0.00088989 0.00089596 0.00054756 0.00055368 0.00089003 0.00089615
9,10, 11 9, 10, 11 9, 11 9, 11 12 12 10 10 8 8 8, 12 8, 12 7 7 7 7 6 6 6 6
34 139 34 384 46 684 46 929 35 233 35 475 47 778 48 021 35 234 35 478 47 779 48 023 35 811 36 054 48 356 48 599 35 814 36 057 48 359 48 602
47 47 47 47 9, 11 9, 11 9, 11 9, 11 10 10 10 10 12 12 12 12 8 8 8 8
11.561 11.644 15.809 15.892 11.931 12.013 16.179 16.262 11.932 12.014 16.18 16.263 12.127 12.209 16.375 16.457 12.128 12.21 16.376 16.458
47 47 47 47 9, 11 9, 11 9, 11 9, 11 10 10 10 10 12 12 12 12 8 8 8 8
SL: SSVR Location.
reliability assessment is presented using the model of a SSVR in it. In the proposed algorithm, the effects of DGs, alternative source, system reconfiguration, load shedding and load adding are considered. In the algorithm, load points are divided into eight classes and also the effect of the DG and alternative source unavailability is expressed in restoration time of load point classes. Two standard distribution systems consist of 33 and 69 nodes are considered and some reliability indices such as SAIFI, SAIDI, CAIDI, ENS, AENS are calculated in different cases. The effect of the SSVR installation in reliability indices is considered and compared with the case of without a SSVR. Also, two different sizes and different locations are selected for its installation. The best location of a SSVR for each reliability index improvement in different cases is determined. The results show that, by SSVR installation, both customer-oriented indices (SAIDI, CAIDI, ASUI) and load- and energy-oriented can be improved noticeably. But its effectiveness depends on its capacity and location. Also, by categorizing the load points to eight classes, the reliability indexes obtained in this paper are more realistic and practical for real distribution systems. In total, these satisfactory results indicate the effectiveness of the proposed reliability algorithm and also the SSVR utilization for improving the reliability indices in large distribution systems. References [1] Billinton R, Wang P. Reliability-network-equivalent approach to distributionsystem-reliability evaluation. IEE Proc Gener Transm Distrib 1998; 145(March):149–53. [2] Billinton R, Allan RN. Probabilistic assessment of power systems. IEEE Proc 2000;88(2):140–62. [3] Billinton R, Allan RN. Reliability evaluation of power system. 2nd ed. New York: Plenum Press; 1996. [4] Momoh JA, Caven AC. Distribution system reconfiguration scheme using integer interior point programming technique. In: Transmission and distribution conference and exposition, 2003 IEEE PES, vol. 1. 2003. p. 234–41. [5] Baran ME, Wu FF. Network reconfiguration in distribution systems for loss reduction and load balancing. IEEE Trans Power Deliv 1989;4(2):1401–7. [6] Brown RE. Distribution reliability assessment and reconfiguration optimization. In: Transmission and distribution conference and exposition, 2001 IEEE/PES. 2001. p. 994–9. [7] Bae IS, Kim JO, Kim JC, Singh C. Optimal operating strategy for distributed generation considering hourly reliability worth. IEEE Trans Power Syst 2004; 19(1):287–92.
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