IET Generation, Transmission & Distribution

Research Article

Network reconfiguration for the DG-integrated ISSN 1751-8687

Received on 7th January 2019
Revised 15th June 2019
unbalanced distribution system Accepted on 2nd July 2019
E-First on 6th August 2019
doi: 10.1049/iet-gtd.2019.0028
www.ietdl.org

Priyanka Gangwar1 , Sri Niwas Singh1, Saikat Chakrabarti1

1Department of Electrical Engineering, IIT Kanpur, Kanpur, India
E-mail: priyankg@iitk.ac.in

Abstract: Distribution system reconfiguration is a complex combinatorial optimisation problem. Finding a globally optimal
solution to this problem in a short span of time is a challenging task. Two different network reconfiguration methodologies,
namely a look-up table-based algorithm and a Pareto-optimisation-based algorithm have been discussed. Power loss
minimisation and reliability maximisation are taken as objectives for both the methodologies when the system is in the normal
operating state. The same algorithms also work for maximum service restoration under the post-fault condition. For reliability
assessment in the presence of distributed generators (DGs), an algorithm is also proposed using the probabilistic model of
components. In the other algorithm, reconfiguration is performed in the presence of DGs using a look-up table. The look-up
table is prepared with the help of the proposed Pareto-optimisation-based reconfiguration algorithm to train the system for
various loading conditions. The feasibility and effectiveness of the proposed methods are demonstrated using the IEEE 34- and
IEEE 123-bus unbalanced radial distribution systems under normal and faulty conditions. The algorithms are also tested on a
13-bus practical distribution system in the field.

 Nomenclature 1 Introduction
List of abbreviations In modern power systems, transmission and distribution networks
generally operate under heavily loaded conditions. Owing to the
a availability of a component heavy loading, the load current drawn from the source increases,
Ak set of buses adjacent to bus k leading to increased voltage drop and losses in the system. To
Ci index for the ith minimal cut set improve the performance of the distribution system and to enhance
f 1s, f 2s power loss and unavailability of the system the network efficiency, network reconfiguration (NR) of the
corresponding to the sth switch combination distribution system is needed [1]. Statistically, majority of the
μf , μm recovery rate and repair rate of a component service interruptions to customers come from distribution systems.
h index for iteration number Hence, reliability assessment has become a significant aspect in the
I¯mk branch current phasor between the buses m and k distribution system. Post-fault NR enhances system reliability with
i¯k load current phasor at bus k minimal investment. NR is a technique, in which the topological
p structure of the system can be altered by changing the open/closed
Ik , k + 1 current magnitude between the buses k and k + 1 for
states of the sectionalising (normally closed) and tie (normally
phase p
open) switches. It enables the transfer of loads from heavily loaded
IDG, k injected DG current at the kth bus
feeders to relatively less loaded feeders, thereby, improving the
k index for bus number voltage profile along the feeders and further reduces the system
L total number of load points in the system power loss (PL) [2]. The presence of distributed generator (DG)
npv total number of PV-type DGs influences the reconfiguration problem, because the power flow
N total number of buses in the system changes in the presence of DG, and the original network topology
p index for a set of phases p ∈ r, y, b may not be the optimal one.
p power loss between the buses k and k + 1 for phase p
PLk, k + 1
q unavailability of a component 1.1 Literature review
Q reactive power injection
S̄ phasor for complex power Significant research has been carried out for loss minimisation and
s index for switch combination reliability improvement of distribution systems. Reconfiguration
s total number of parent–child pairs for topology for loss minimisation in a distribution system was first proposed by
T pc Merlin and Back [3], in which the distribution system was
corresponding to the sth switch combination
U, Uavg unavailability of the load point and average system considered as a mesh network, by closing all the switches, and the
unavailability radial nature of the distribution system was maintained by opening
d c bus voltage phasor, desired voltage phasor and switches successively. Some researchers have suggested
V̄, V̄ , V̄ metaheuristic algorithm (MHA)-based NR algorithms. MHAs are
calculated voltage phasor
Vk voltage magnitude of bus k problem-independent techniques, unlike heuristic algorithms and
can be used as a black box. For example, harmony search (HMS)
z̄mk 3 × 3 impedance matrix of a branch between the buses algorithm-based (HSA) offline reconfiguration method is proposed
m and k in [4], which discusses DG placement using sensitivity analysis.
Zk sensitivity impedance matrix for bus k However, this work considers the distribution system as a balanced
λf , λm, λeol failure, maintenance and end of life rate of a one. For reliability improvement and loss minimisation, a binary
component particle swarm optimisation-based (PSO) technique is proposed in
μf , μm recovery rate and repair rate of a component [5], which includes a multi-objective problem formulation for
ϵ tolerance limit reconfiguration and dynamic programming is applied to obtain the
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 Table 1 NR methods
Reference number Objectives Unbalanced Online Service Method
feeder with DG restoration after
fault isolation
[21] reliability enhancement no no yes discrete PSO
[22] energy loss minimisation yes no no GA and branch exchange method
[23] minimisation of energy loss and no yes no disjunctive mixed integer model and
voltage deviation convex relaxations of the AC power
flow
[24] reliability enhancement and loss no no no artificial immune systems
minimisation optimisation
[25] losses minimisation no no no dynamic switches set heuristic
algorithm
[26] loss, transformer load balancing no no yes artificial immune systems and ACO
and voltage deviation
[19] reliability yes no no MCS
[27] loss minimisation no no no HSA
[20] loss minimisation and load yes yes no branch exchange method
balancing
proposed look-up loss minimisation, reliability yes yes yes depth-first-search, look-up table
table and Pareto- maximisation and maximum and probabilistic methods
optimisation-based service restoration
method

minimal cut set for each load point. Possible switch combinations decision-making tree algorithm. A three-stage algorithm is
are generated, and for each switch combination, PL and reliability presented in [14] for service restoration, i.e. restoration, NR and
are calculated. In [6], the hyper-cube (HC) ant-colony optimisation optimal load shedding. A sequential switch opening technique-
(ACO) method is proposed for loss minimisation. The aim of the based NR is carried out in [15]. An objective function is
proposed reliability-driven design is to reduce the frequency and formulated considering PL and voltage stability index and the line
duration of power interruptions for customers. Sequential switch which carries a minimum value of fitness function is opened
opening with metaheuristic methods such as PSO and ACO is used sequentially. Peng et al. [16] presented a heuristic algorithm for
in [7–9]. Sequential switch opening is the process, in which an NR based on the convex relaxation of the AC optimal power flow.
initially meshed network is considered; then, the switches are A two-stage heuristic technique is proposed by Raju and Bijwe
opened sequentially to eliminate the network loops. Abdelaziz et [17]. In the first stage, real PL sensitivity is computed with respect
al. [10] suggested an HC framework-based ACO optimisation to the branch impedances, and the branch exchange method is
algorithm to solve the reconfiguration problem. HC framework applied to derive the optimal solution in the second stage. Tang et
makes the ACO procedure more easy and robust. The limitation of al. [18] elaborate different heuristic methodologies that have been
ACO is the slow convergence speed and the solution may get implemented so far for NR considering different objectives. In [16,
trapped in local minima. Kumar et al. [11] proposed a heuristic and 17], fault-persistent analysis and DG integration is taken into
HMS technique for NR to reduce PL and improve node voltage consideration. The limitations of the above-stated heuristic
security and quality index. HMS is a simple technique and not optimisation methods are that these techniques are often too greedy
computationally very exhaustive, but the drawback of HMS is the and get trapped in local optima and fail to obtain an optimal global
weak local search ability. However, Abdelaziz et al. [10] and solution. For the reliability analysis, Monte Carlo simulation
Kumar et al. [11] have not considered DG integration, service (MCS) is carried out in [19], which is a time-consuming technique
restoration and unbalanced distribution system while performing and hard to implement on large systems. A drawback of the method
NR. Tyagi et al. [12] present a two-stage NR methodology. In the proposed in [20] is that the computation time increases with the
first stage, reactive PL is minimised, and in the second stage, HMS increase in the total number of tie switches and sectionalising
is implemented to improve the loadability limit. In [12], the branch switches in the system. A part of the literature is summarised in
exchange method is applied to open/close the switches. The Table 1.
limitation of the branch exchange method is that the final solution All the aforementioned research work is based on the
depends on the initial switch status. The limitation of the above- assumption that the distribution system is balanced. However,
stated MHAs is that a unique solution is not obtained at each practical distribution systems are rarely balanced. The degree of
iteration, and hence to obtain the optimal solution, several imbalance may vary depending on the power consumption pattern
simulations have to be carried out. The other limitation of MHA is of the end users, which again varies with the time of the day, the
that it depends on some initial parameters, and the solution quality season of the year and numerous other factors. Therefore, one
depends on the fine-tuning of these parameters. Another group of needs to take this unbalance into consideration to analyse a
researchers presented heuristic optimisation-based NR algorithms. distribution system. The reconfiguration problem of unbalanced
Heuristic optimisation methods are problem-dependent techniques distribution systems is not very well explored.
and usually take advantage of the problem particularities. For
example, Wen et al. [13] suggested a real-time NR technique. 1.2 Contributions
Graph theory is used in [13] to find the initial topology and
dynamic analysis is carried out to update the topological This paper attempts to overcome the above-stated limitations of the
parameters, restore network connectivity and identify the out-of- existing methods. The main contributions of this paper are as
service areas. The unbalanced feeder is taken for study in [12], but follows:
the integration of DG and service restoration is not taken into
consideration. However, Wen et al. [13] have taken post-fault- i. Most of the existing methods are proposed for offline
persistent analysis into consideration, but the DG integration is not reconfiguration, considering the distribution system as a
done and analysis is carried out only on a balanced system. balanced system. This paper proposes an NR methodology
Ghasemi et al. [14] suggested a restoration methodology in the with DG integration using a look-up table for the unbalanced
presence of DG for a balanced distribution system using a distribution system. It can be implemented in online

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 applications as well. The merits of this algorithm are as considers the unbalanced loading of the three phases, mutual
follows. coupling between the phases and the presence of capacitor banks.
The load flow algorithm is briefly given below:
• The computational time of this algorithm does not depend
on the total number of switches present in the system, unlike • Compute the load current ikp at each bus according to the load
most of the reconfiguration algorithms described above. model. For constant PQ-type load, current is calculated as
• A single algorithm can deal with both the conditions, i.e.
when the system is under normal operating conditions and p ∗

when a fault persists in the system. p S̄k

i¯k p
=
, k = 2, 3, …, N, p ∈ r, y, b (1)
ii. A multi-objective Pareto-optimisation-based reconfiguration V̄ k
algorithm is also developed. Reconfiguration is performed for • Backward sweep is carried out by calculating the branch current
the minimisation of losses and maximisation of reliability p
of each phase Imk starting from the farthest branch toward the
when a system is under normal operating conditions, and if a
fault persists, faulty line is isolated and reconfiguration is slack bus
performed for maximum service restoration. The merits of this
algorithm are given below:
p
I¯mk = i¯k +
p
∑ p
I¯kx (2)
x ∈ Ak
• This algorithm does not depend on the initial status of • Forward sweep is carried out by computing the voltage at the
switches, whereas most of the discussed algorithms depend receiving-end bus V k as
on the initial switch status.
• Most of the existing methodologies, during the search V̄ k = V̄ m − z̄mk Īmk (3)
process, generate switch status assuming meshed system, • Here, V̄ k is a vector of three-phase voltages, i.e. V kr V ky V kb ;
and then discard the switch status combinations that do not
r y b
satisfy radiality condition, which increases the overall Īmk is the vector of three-phase branch current, i.e. [Imk Imk Imk ].
execution time. This algorithm always maintains radiality of • Check the convergence criteria as stated in (4). If it is satisfied,
the system and generates only feasible switch combinations load flow is taken as converged; moreover, if not, update the
using the depth-first-search technique and graph theory. The voltages of each bus and repeat the above-stated steps
execution time of this algorithm is, therefore, significantly
small as compared with other existing methods. p p
max V̄ k, h + 1 − V̄ k, h ≤ ε (4)
iii. Reliability assessment of the unbalanced distribution system is
also proposed in the presence of DGs using the probabilistic
To enhance the reliability of the distribution system, DGs are
model of components. The merits of this algorithm are as
incorporated into the system. To incorporate the PV model of DGs
follows:
into the load flow algorithm, the following steps are required [28]:
• Reliability analysis is carried out for an unbalanced three-
i. In the beginning of the load flow, the generator is taken as a
phase distribution network. In the literature, the common
PQ bus with specified real power and power factor.
practise is to do so for single-phase equivalents.
ii. After the convergence of the load flow algorithm, calculate the
• Failure of each load point is calculated considering the
voltage mismatch vector for all PV buses in the system
failure of each phase using the minimal cut-set method. It is
to be noted that the minimal cut-set technique takes p d, p c, p
significantly less computational time because it focuses on ΔV̄ k = V̄ k − V̄ k (5)
the system contingencies, pertinent to the selected load iii. Calculate the injected DG current DG, k using Z̄ k. The size ofI¯
points and not to the complete system. Z̄ k depends on the total number of PV buses in the system
The look-up table is prepared with the help of the proposed Pareto- npv × npv . For example, a system shown in Fig. 1 consisting
optimisation-based reconfiguration algorithm. It is developed to of two PV buses Z̄ k is derived as
train the system for different loading patterns. A load flow
algorithm incorporating DGs is also developed for PL computation. t t
Z̄ g3 Z̄ g3 + g4
This paper is organised as follows. Section 2 discusses forward– Z̄ k = (6)
t t
backward sweep algorithm for the assessment of PL of unbalanced Z̄ g3 + g4 Z̄ g4
systems when DGs are incorporated into the system. In Section 3,
the reliability assessment technique for the three-phase unbalanced t
where Z̄ g3 is the 3 × 3 total impedance matrix of the path
system is discussed. In Section 4, the formulation of the Pareto-
t
optimisation-based reconfiguration is discussed. Section 5 explains between PV bus 1 and slack bus. Z̄ g3 + g4 is the total impedance
the look-up table-based reconfiguration algorithm considering matrix of the path which is shared by both the DGs. It can be
different loading patterns. Simulation results for the IEEE 34-bus, calculated as
IEEE 123-bus and 13-bus practical distribution system are
discussed in Section 6. The conclusion is summarised in Section 7. t
Z̄ g3 = Z̄ 1 + Z̄ 2 (7)

2 Three-phase power flow in an unbalanced t

Z̄ g4 = Z̄ 1 + Z̄ 3 (8)
distribution system
In this section, the power flow algorithm for three-phase t
Z̄ g3 + g4 = Z̄ 1 (9)
unbalanced systems is discussed to account for PL calculation in
the reconfiguration algorithm [28]. For usual power flow solutions
for the transmission system, it is assumed that the line currents and where Z̄ 1, Z̄ 2 and Z̄ 3 are 3 × 3 impedance matrices of each
voltages are balanced. It is also usually assumed that the branch. I¯DG, k is computed as
transmission lines are transposed, and therefore the line
impedances are the same for all the three phases. Distribution lines, [Z̄ k][I¯DG, k] = [ΔV̄] (10)
on the other hand, are rarely transposed, and the line loadings may
be heavily unbalanced. A three-phase load flow algorithm is where the size of I¯DG, k and ΔV̄ is npv × 1 and npv is the total
developed for the unbalanced distribution system using the number of PV buses in the system.
forward–backward sweep method. The developed algorithm
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 iv. Calculate the amount of reactive power injection that is outage and repair rates of a component, namely λf λm, λeol, μm and
required by the PV bus. It can be calculated as μf . The unavailability, q, of a component is denoted as

Qk = ∑ c, p p ∗
imag V̄ k I¯DG, k (11) q=1−a (14)
p ∈ [r, y, b]
The unavailability of each minimal cut set is given by the product
where Qk is the total three-phase injected reactive power. of unavailability of the components present in the minimal cut set,
Reactive power injected at each phase is equal to Qk /3. whereas the unavailability of each load point is given by the union
v. After the calculation of reactive power injections at PV bus, of unavailability of all the minimal cut sets between the source
check for the reactive power limits node and the load points [5]. The unavailability of a load point U is
calculated as
k k k
Qmin ≤ Qnew ≤ Qmax (12)

k k
U=P ⋃ Ci (15)
where Qmin and Qmax are the minimum and maximum reactive i
power limits at the kth bus, respectively.
where P(.) is the probability of occurrence of an event and Ci is the
failure event of the ith minimal cut set between the feeder and the
3 Probabilistic reliability evaluation of load point. The average system unavailability Uavg is computed as
unbalanced distribution systems L
MCS is a widely used method for probabilistic reliability Uavg = ∑ Ui (16)
assessment [5]. Owing to extensive computational time and large i=1
storage requirements, this approach is not appropriate for real-time
implementation. Most of the probabilistic methods are designed for While performing the reliability analysis of the unbalanced three-
balanced systems; hence, unbalanced systems need more attention phase distribution system with DG, the islanded mode of DG and
in this area. A key contribution of this paper lies in the reliability load shedding have not been considered.
assessment of an unbalanced distribution network in the presence The proposed methodology has been elaborated with the help of
of DGs. The execution time of this algorithm is substantially low. Fig. 2, having a three-phase unbalanced system with DG.
The proposed method in this paper is aimed at the reliability To calculate the availability at load point 4, the minimal cut set
assessment of three-phase unbalanced systems by identifying the between each generator and load point 4 is determined. The order
minimal cut set between each generator bus and load point, where of the minimal cut set depends on the total number of generators
the minimal cut set has been calculated using graph theory. present in the system and topology between each load point and
Probabilistic models of various components, appearing in the path generator. Subsequently, the availability of each component, which
of the minimal cut set, are derived considering outage history, lies in the minimal cut set of the load point 4 using (13), is
failure rate and maintenance rate. The availability, a, of a calculated. For Fig. 2, a second-order cut set has been formed as
component is defined as shown in Fig. 3.
In Fig. 3, X is a subsystem having a third-order cut set of
MTTF ∑i 1/λi components A1, B1 and C1 and Y is a subsystem having a second-
a= = (13) order cut set of components A2 and B2. The algorithm now
MTTF + MTTR ∑i 1/λi + ∑i 1/ μi
identifies the common components (subsystem 2) in both the cut
sets, as the failure of any common component causes the failure of
where MTTF is the mean time to failure and MTTR is the mean the load point. However, the simultaneous failure of the individual
time to repair for a component. λi and μi are different types of components from both the cut sets would lead to the failure of the
load point. Therefore, to calculate the availability of subsystem 1,
both cut sets have been considered in parallel, and the availability
of subsystem 2 has been calculated considering the components in
series. Now, the availability of load point 4 has been calculated
considering both subsystems in series. System unavailability can be
calculated using (16) after calculating the unavailability of each
load point using (15). For the system shown in Fig. 2,
unavailability at various load points has been calculated with the
help of the proposed algorithm, as illustrated in Table 2. The
Fig. 1  Single line diagram of a 4-bus system flowchart of the reliability assessment algorithm is shown in Fig. 4.

The key merits of the proposed algorithm are as follows:

i. Proposed algorithm's execution takes only a few seconds, and

hence, can be implemented in real-time applications.
ii. This algorithm can be carried out on both types of systems, i.e.
balanced and unbalanced.

Fig. 2  Single line diagram of three-phase unbalanced distribution system

4 Proposed methodology I – Pareto-optimisation-
with DG
based NR
Most of the existing methodologies focus on balanced distribution
systems. Moreover, the dependence of the existing methods on the
initial status of the switches limits their applications. In this paper,
a new approach is suggested for NR to overcome these drawbacks.
In the present work, an unbalanced system is considered, and the
proposed algorithm does not depend on the initial status of
Fig. 3  Second-order cut set of the load point 4 considering slack bus and switches. Further advantage includes the applicability of the
DG1

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 Table 2 Unavailability of the load points for a three-phase unbalanced system as shown in Fig. 2
Output node Minimal cut set Unavailability
Between Gen 1 and load point Between DG 1 and load point
1 G1,1 DG1, 3, A2, B2, 2, A1, B1, C1,1 1.13 × 10−6
2 G1,1, A1, B1, C1,2 DG1, 3, A2, B2, 2 6.72 × 10−7
3 G1,1, A1, B1, C1,2, A2, B2, 3 DG1,3 9.53 × 10−7
4 G1,1, A1, B1, C1,2, A2, B2,3, A3,4 DG1,3,A3,4 0.0031
system unavailability 7.84 × 10−4

Fig. 4  Flowchart for the reliability assessment of three-phase unbalanced distribution systems

algorithm under normal operating state and post-fault conditions. s

T pc > N−1 (17)
For reconfiguration, two conditions have been considered: • All the loads should be connected to the system to meet the
maximum demand
i. Normal (pre-fault) condition.
ii. Persistent post-fault condition.
T cs = N (18)
4.1 Reconfiguration under normal condition T cs
• Here, is the total number of the connected load corresponding
to the sth switch combination.
Reconfiguration can be performed with many objectives such as • Phase sequence from sending-end bus to receiving-end bus
minimisation of losses, load balancing, maximisation of reliability should be justified, i.e. the receiving-end bus should only have
etc. In this paper, a multi-objective reconfiguration problem has those phases which are already available in the sending-end bus.
been considered, which considers minimisation of losses and The phases of the sending-end bus k and the receiving-end bus k 
maximisation of reliability. Three-phase switches are taken into
+ 1 are expressed in vector form as ϕsk and ϕsk + 1, in which each
account for the reconfiguration. Every switch combination has to
satisfy some specific constraints for reconfiguration, as mentioned element is 1 or 0
below.
ϕsk = psk, r psk, y psk, b
4.1.1 Topological constraints:
ϕsk + 1 = psk, +r 1 psk, +y 1 psk, +b 1
• The system should be radial in nature. A binary tree is prepared
for topology corresponding to the sth switch combination. If If at the kth bus, the rth phase is present, then psk, r is 1;
(17) holds true, then a loop exists in the system otherwise, 0. If (19) is true, then the sth switch combination is not a
feasible solution

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 ϕsk, i < ϕsk + 1, i (19) generate reconfiguration solutions for varying relative importance
of the two objectives.
Here, ϕsk, i is the ith element of the vector ϕsk.
4.2 Reconfiguration under persistent post-fault condition
4.1.2 Operational constraints: In this case, the location of the fault is presumed to be known. The
proposed algorithm can consider multiple faults in the system. The
• The voltage of each bus at each phase and current in each dynamic connectivity matrix has been created for switch
branch should be within limits configurations satisfying the following constraints:

V min ≤ V kp ≤ V max k ∈ 1…N, p ∈ r, y, b (20) i. The faulty line should be removed from the system.
ii. Maximum load must be met.
p iii. The system has to be radial.
Ik, k + 1 ≤ Ikmax
k ∈ 1…N − 1, p ∈ r, y, b
, k+1 (21)
p
iv. Phase sequence of the sending-end bus and the receiving-end
• Penetration of DG, PDG, k , at bus k phase p should be within bus should be the same after faulty-line isolation.
limits
PL and unavailability of the system have been calculated for each
p p switch combination. The combination, for which the objective
0 ≤ PDG , k ≤ Pk k ∈ 1…N, p ∈ r, y, b (22)
function defined in (27) is minimum, is taken as the optimal
p p solution. A graph-theory-based approach has been adopted to find
0 ≤ QDG , k ≤ Qk k ∈ 1…N, p ∈ r, y, b (23) the switch combination which justifies all the given conditions.
• Here, Pkp and Qkp are maximum allowable active power and Flowchart for the proposed methodology is shown in Fig. 5.
reactive power penetration limits of the DG at bus k and phase p,
respectively. 5 Proposed methodology II – look-up table-based
NR
4.1.3 Objective function formulation: The PL and reliability
This paper proposes a reconfiguration methodology using a look-
calculations have been carried out for the switch combinations,
up table for unbalanced three-phase systems. This algorithm
which satisfy the above-listed topological constraints. The first
applies for the minimisation of losses and maximisation of
objective, the minimisation of losses, is mathematically formulated
reliability, considering various loading conditions and weighing
as
factors, when the system operates under normal condition.
N−1 Maximum service restoration has been carried out, considering the
minimise f 1s = ∑ ∑ PL pk k ( , + 1)
(24)
minimisation of losses and maximisation of reliability, after the
removal of the faulty line from the system following a fault. In this
p ∈ [a, b, c] k = 1
algorithm, a look-up table has been utilised to determine the
s.t. : (20) and (21)
optimal solution. The look-up table stores various loading
p conditions for each phase, and the corresponding optimal solution
PL(k, k + 1) between the buses k and k + 1 is computed as is derived using Pareto-optimisation-based reconfiguration
algorithm. This algorithm takes substantially less memory and
p p p∗ p p∗
PL(k, k + 1) = Re V̄ k I¯k, k + 1 − V̄ k + 1I¯k, k + 1 (25) computational time even for a large system. The format of the
look-up table is shown in Table 3.
Maximisation of reliability, the second objective, has been already The first row consists of the details of all probable faulty lines
discussed in the previous section. It is mathematically formulated available in the system, and the next two rows hold all the
as predefined weighing factor combinations (scaled between 0 and 1).
The first three columns contain the total load at each phase,
L followed by an index of optimal switch combination against each
1
L p ∈∑ ∑ Ukp
minimise f 2s = (26) faulty line, considering different weighing factors. Here, the index
[r, y, b] k = 1 of optimal solution represents different switch combinations.
Different loading conditions have been used to train the system.
Normalised linear weighted-sum approach has been used for the The algorithm of the proposed methodology is given below:
optimisation. In multi-objective linear weighted-sum approach, all
the objectives should have a comparable numerical value. The i. System reads the input data, namely look-up table, load data
objective functions are, therefore, normalised to have a numerical and switch status, i.e. index of the optimal solution
value between 0 and 1. The multi-objective reconfiguration representing different switching combinations.
problem is formulated as ii. Initialise the faulty-line number, if fault persists in the system,
else initialise it to zero.
f = minimise w1 f 1∘ s + w2 f 2∘ s (27) iii. Weighing factor w1 is selected between 0 and 1 to obtain the
optimal solution. The second weighing factor w2 is computed
where w1 and w2 are the weights such that w1 + w2 = 1. as 1 − w1 .
The normalised values f 1∘ s and f 2∘ s corresponding to the iv. Different arrays are derived with the help of the look-up table
objective functions f 1s and f 2s are obtained as follows: corresponding to common switch combinations, considering
different faulty lines and weighing factors. Each array contains
f 1s − min f 1 upper and lower bounds of load data for each switch
f 1∘ s = combination, considering different faulty lines and weighing
max f 1 − min f 1
(28) factors.
∘ f 2s − min f 2 v. All common switch combinations are listed out from the
f =
2s
max f 2 − min f 2 derived array with upper and lower bounds for further
processing.
Here, f 1 is the vector of PL values and f 2 is the vector of system vi. The system calculates the total load on each phase from the
unavailability for different switch combinations, respectively. The input load data.
normalisation ensures comparable numerical values of both the
objectives. The weights w1 and w2 are varied in the range (0,1) to

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 vii Classify the input load pattern into the load range class bus test system, deployed as part of the project at the Amrita
. mentioned in step 5 above, and note the corresponding switch University campus, Kollam, India, has been considered.
combination.
vii Select the above switch combination as the optimal solution of 6.1 Test on IEEE standard systems
i. the reconfiguration problem.
The proposed Pareto-optimisation-based and look-up table-based
The merits of the proposed method are summarised below: reconfiguration methodologies have been implemented on the
IEEE 34-bus and IEEE 123-bus systems. For the IEEE 34-bus
i. The computational time of the proposed algorithm does not system, 9 switches and for the IEEE 123-bus system and 11
depend on the number of switches present in the system. switches are considered for the reconfiguration. All the buses have
Hence, its execution time is small even for a large system. been considered as load buses, apart from the substation bus. The
ii. It can be applied for both healthy and post-fault conditions. line and load data have been taken from [29] and the component
data along with failure and recovery rate have been taken from [5],
iii. It can be applied to both balanced and unbalanced systems.
to calculate the reliability of the system. The single line diagrams
iv. Multiple objectives (in this work, the minimisation of losses of the IEEE 123-bus and IEEE 34-bus system are shown in Figs. 6
and maximisation of reliability) can be handled using this and 7, respectively.
method. For better visualisation, different cases and scenarios are
considered as listed below:
6 Case studies
To see the effectiveness of the proposed algorithms, two cases have • Case 1 – Normal (pre-fault) condition.
been considered. In the first case, proposed algorithms are tested • Case 2 – Persistent post-fault condition.
on IEEE standard test systems. In the second case, a practical 13- • o Scenario 1 – Reconfiguration without DG integration.
• o Scenario 2 – Reconfiguration considering DG integration.

Fig. 5  Flowchart for Pareto-optimisation-based NR

Table 3 Format of the look-up table

Total loading Faulty line 1 Faulty line 2 —
w11 w12 — w11 w12 — —
w21 w22 — w21 w22 — —
phase a phase b phase c optimal solution optimal solution — optimal solution optimal solution — —

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 higher value compared with w1. Tables 5 and 6 present the results
of the Pareto-optimisation-based NR methodology for the IEEE
34-bus and IEEE 123-bus systems, respectively. For case 1 and
scenario 1, the reduction in PL is observed at 23 and 54%, and
reduction in downtime is observed at 18 and 27% for the IEEE 34-
bus and the IEEE 123-bus systems, respectively. The results also
conclude that the integration of DG into the system significantly
reduces the PL and enhances the system reliability. For case 1 and
scenario 2, the maximum reduction in loss and downtime is noted
at 78 and 93% for the IEEE 34-bus system. About 88% reduction
in loss and 91% reduction in downtime are noted for the IEEE 123-
bus system. For case 2, a single line outage is taken to study the
persistent post-fault condition. The proposed methodology restores
all the loads for both the system; moreover, NR improves the
system performance by reducing losses and downtime. The
execution time of the proposed Pareto-optimisation-based
reconfiguration algorithm is 13 and 21 s for the IEEE 34 and IEEE
123-bus systems, respectively, in a core i5, 2.9 GHz, 4 GB RAM
computer. All the simulations are carried out in MATLAB 2015b.
Fig. 6  Single line diagram of IEEE 123-bus system considering tie and
Tables 7 and 8 present the results for the look-up table-based
sectionalising switches
reconfiguration technique. Different loading patterns and weighing
factor combinations are taken to perform the NR. In Tables 7 and
8, w1 and w2 are weighing factors for PL and reliability and NRL is
the total number of restored load after faulty-line isolation. The
result shows that PL and Energy not supplied (ENS) are reduced
significantly for different loading conditions and different line
outage conditions. All the loads have been restored after single line
outage, but after multiple line outages, all the loads cannot be
restored for both the systems. A significant improvement in the
system performance is noted when NR takes place in the presence
of DGs. Moreover, this algorithm can incorporate any loading
condition, i.e. same increment/decrement in the load at all buses or
Fig. 7  Single line diagram of IEEE 34-bus system considering tie and different increment/decrement in the load at each bus. This
sectionalising switches algorithm can also deal with multiple line outage conditions. The
computation time of the proposed look-up table-based
Table 4 Location and capacity of DGs reconfiguration algorithm has been found out to be <0.31 and 0.63 
IEEE 123-bus system s for the IEEE 34- and IEEE 123-bus systems, respectively.
The proposed reliability evaluation method is compared with
Bus number Capacity, MW Power factor Number of phases
the MCS method [30]. To compute the system unavailability of an
48 0.279 0.9 3 unbalanced distribution system using MCS, some assumptions are
65 0.168 0.9 3 considered as listed below:
76 0.348 0.85 3
109 0.267 0.85 1 i. Load point failure is calculated by considering the failure of
IEEE 34-bus system each phase.
820 0.096 0.9 1 ii. Single- and three-phase DGs are connected into the system.
890 0.146 0.9 3
While calculating load point failure, the failure of the generator
in each phase has been considered.
844 0.144 0.85 3
The execution times for reliability evaluation for IEEE 34-bus and
IEEE 123-bus systems using MCS are 157 and 615 s, respectively,
The DGs are taken as constant power output and are integrated at compared with the computation times of 0.39 and 0.78 s for the
the weak buses in the system. To find the weak buses, power flow proposed reliability assessment method. For Pareto-optimisation-
is run for the base case, and a priority list is created in the based reconfiguration algorithm, load flow needs to be run for each
ascending order of the bus voltage. The penetration of the DGs can loading condition, to find the optimal solution, whereas in the case
be calculated as of the look-up table-based reconfiguration algorithm, the optimal
solution does not require load flow analysis for different loading
SDG conditions. This reduces the computational time for finding the
DG penetration level(%) = (29)
Sload optimal configuration. Post reconfiguration, in each case and
scenario, a reduction in total PL has been observed. Figs. 8 and 9
where SDG is the total real power output of the DGs and Sload is the show the voltage profile of the IEEE 123-bus and IEEE 34-bus
total load of the system. Initially, 20% DG penetration level is systems for the three phases in three different cases: (i) system
assumed and the output power of DG Pdg is varied with the before reconfiguration, (ii) system after reconfiguration without
penetration level of the DG, considering the varying load profile. DG integration and (iii) system after reconfiguration in the
PQ-type three-phase and single-phase DGs have been placed at presence of DG. It is evident from this figure that the node voltages
different buses as presented in Table 4. are increasingly improved from case (i) to case (iii). From the
Two extreme cases are taken for broader analysis. For loss results, it can be concluded that after reconfiguration, the efficiency
minimisation, w1 and w2 are taken as 1 and 0, respectively, and for of the system is improved as the PL is reduced. The operational
reliability maximisation, w1 and w2 are taken as 0 and 1, efficiency of the system is also improved by reducing the
respectively. The system operator decides the values of the downtime of the system.
weighing factors w1 and w2 based on the operating condition of the The proposed Pareto-optimisation-based algorithm is compared
current system. For example, in the event of a line outage, service with different existing algorithms such as HSA [4], genetic
restoration is given a higher priority over PL. Hence, w2 will have a algorithm (GA) [31] and discrete PSO [32]. The results are
summarised in Table 9. The result depicts that the proposed

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 methodology gives better voltage profile with reduced PL. The PL and iteration, whereas the proposed methodology generates only
is reduced by ∼22% for the IEEE 34-bus system as compared with feasible solution, and it is not an iterative process. That is why the
other methods. The result shows that the computational time of the proposed methodology has significantly smaller execution time.
proposed method is relatively small as compared with other The proposed algorithm is also implemented on a 33-bus
methods, and in the case of other methods, it increases sharply as balanced distribution system. All the lines and load data of the
the system size increases. Metaheuristic methodologies such as system are taken from [5], and it is also compared with several
PSO, HSA and GA may generate solutions that are not feasible, existing methodologies. The performance of the proposed
thereby increasing the execution time by performing further search methodology is presented in Table 10, and the results show better

Table 5 Optimal solution for the IEEE 34-bus system for Pareto-optimisation-based NR
Case/scenario Base case Scenario 1 Scenario 2
For losses For reliability For losses For reliability
minimisation maximisation minimisation maximisation
case 1 closed switches 9, 8, 6, 7, 1 8, 7, 2, 4, 5 8, 6, 3, 4, 5 8, 6, 3, 4, 5 9, 8, 6, 1, 4
PL, kW 312.91 227.94 240.49 67.07 110.81
reliability 0.99571 0.99656 0.99688 0.99951 0.99971
down time, h/year 37.56 30.12 27.31 4.28 2.46
minimum voltage, pu 0.89 0.92 0.91 0.99 0.98
case 2 faulty line (between — 832–858 832–858 832–858 832–858
the buses)
total restored load — 34 34 34 34
closed switches 9, 8, 6, 7, 1 8, 7, 2, 3, 4, 5 8, 6, 2, 3, 4, 5 8, 6, 2, 3, 4, 5 8, 6, 1, 3, 4, 5
PL, kW 312.91 227.23 227.47 65.74 65.95
reliability 0.99571 0.99697 0.99699 0.99961 0.99974
down time, h/year 37.56 26.46 26.31 3.49 2.22
minimum voltage, pu 0.89 0.92 0.92 0.99 0.99

Table 6 Optimal solution for IEEE-123-bus system for Pareto-optimisation-based NR

Case/scenario Base case Scenario 1 Scenario 2
For losses For reliability For losses For reliability
minimisation maximisation minimisation maximisation
case 1 closed switches 9, 3, 4, 5, 7, 8, 9, 1, 2, 3, 5, 7, 8 1, 2, 3, 5, 8, 10, 11 9, 1, 2, 3, 5, 8, 11 1, 2, 4, 5, 7, 8, 10
10
PL, kW 571.84 260.11 274.62 67.25 88.05
reliability 0.99322 0.99477 0.99501 0.99923 0.99932
down time, h/year 59.38 45.73 43.73 6.67 5.91
minimum voltage, 0.86 0.94 0.94 0.98 0.97
pu
case 2 faulty line (between — 28–29 28–29 28–29 28–29
the buses)
total restored load — 123 123 123 123
closed switches 9, 3, 4, 5, 7, 8, 9, 1, 2, 3, 5, 7, 8, 10 9, 1, 2, 3, 5, 8, 10, 11 9, 1, 2, 3, 5, 8, 10, 11 9, 1, 2, 4, 5, 7, 8, 10
10
PL, kW 571.84 261.74 268.54 66.86 82.66
reliability 0.99322 0.99472 0.99493 0.99924 0.99928
down time, h/year 59.38 46.24 44.35 6.63 6.29
minimum voltage, 0.86 0.93 0.93 0.98 0.97
pu

Table 7 Optimal solution for IEEE 34-bus system using look-up table-based reconfiguration
Before/after reconfiguration Faulty line NRL Load level w1 Closed switches PL, kW ENS, kWh
base case — — 0.5 0.2 9, 8, 7, 1, 4 169.28 33,693.35
after (without DG) 8, 6, 3, 4, 5 122.78 24,205.82
after (with DG) 9, 8, 6, 1, 4 116.57 2181.11
base case — — 1.1 0.5 9, 8, 7, 1, 4 493.31 64,017.69
after (without DG) 8, 7, 3, 4, 5 382.71 46,128.61
after (with DG) 6, 1, 3, 4, 5 71.68 5586.11
base case 854–852 34 0.9 0.6 9, 8, 7, 1, 4 352.47 53,909.63
after (without DG) 8, 6, 1, 2, 4, 5 256.99 42,238.44
after (with DG) 8, 6, 1, 2, 3, 4 64.74 4633.78
base case 814–850 33 1.5 0.8 9, 8, 7, 1, 4 666.92 74,125.74
after (without DG) 850–816 9, 8, 6, 2, 4, 5 490.43 61,347.23
after (with DG) 9, 8, 6, 3, 4, 5 69.22 6200.32

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 Table 8 Optimal solution for the IEEE 123-bus system using look-up table-based reconfiguration
Before/after reconfiguration Faulty line NRL Load level w1 Closed switches PL, kW ENS, kWh
base case — — 0.5 0.2 4, 5, 7, 8, 9, 10, 11 253.69 158,110.81
after (without DG) 1, 2, 3, 5, 8, 10, 11 132.97 120,203.01
after (with DG) 1, 2, 3, 4, 5, 8, 10 42.98 16,820.04
base case - - 1.3 0.9 4, 5, 7, 8, 9, 10, 11 1012.79 29,334.37
after (without DG) 1, 2, 3, 5, 7, 8, 9 451.61 233,451.85
after (with DG) 1, 2, 3, 5, 8, 10, 11 102.61 31,920.21
base case 108–300 123 0.7 0.3 4, 5, 7, 8, 9, 10, 11 356.55 185,215.52
after (without DG) 1, 2, 3, 5, 7, 8, 9, 11 177.67 141,657.71
after (with DG) 1, 2, 3, 4, 5, 7, 8, 10 51.14 20,076.03
base case 40–42 121 1.5 0.8 4, 5, 7, 8, 9, 10, 11 1452.84 338,808.89
after (without DG) 42–44 1, 2, 3, 5, 8, 9, 10, 11 631.23 252,191.34
after (with DG) 1, 2, 3, 4, 5, 8, 9, 10 125.07 35,419.84

Fig. 8  Improvement in the voltage profile of each phase of IEEE 123-bus system after reconfiguration

performance of the proposed method over other existing Amrita University, 13 student hostels are considered as 13 buses.
methodologies for a balanced distribution system as well. On each bus, the smart monitoring and control unit is installed as
Adaptive weighted-sum method (AWSM) is used to obtain the shown in Fig. 12. This unit has two boxes, i.e. electrical protection
Pareto front. In the AWSM approach, the weights are not and switching unit (EPS) and the metering communication and
predetermined, but evolve according to the nature of the Pareto processing unit (MCP). The EPS unit operates 4-pole power
front of the problem. Initially, a smaller step size of weight is contractors, which connect or disconnect a line to or from a node.
taken, and after obtaining several nearly identical solutions, the The contractors can be controlled (open–close) from the smart
step size is increased accordingly. The detailed algorithm of metre through interposing relays residing in the MCP unit. These
AWSM is given in [33]. The weight variation has been taken in contractors allow complete flexibility to open/close any power line
steps of size 0.1 to plot the Pareto front because the optimal going in–out from that particular node. This aids in the remote
solution obtained for weighing factor variation with a smaller step isolation of a particular section of the grid in the event of a fault;
size, e.g. 0.01 gives almost the same Pareto front as with a step size thereby allowing for the reconfiguration of the power network to
of 0.1, as shown in Fig. 10. Step size higher than 0.1, e.g. 0.2 restore power. The MCP unit is responsible for the data acquisition
missed some of the optimal solutions. from the electrical loads, storing and processing of data and
wireless transmission of data. Smart metres are installed inside the
6.2 Application in field pilot MCP unit. Fig. 13 details the components and interfacing between
the EPS and MCP units.
To analyse the performance of the proposed techniques in a The test results on the Amrita University system are shown in
practical environment, a three-phase 13-bus test system, deployed Table 11. The proposed algorithms restore all the loads after faulty-
in the Amrita University, Kollam, India, has been considered. The line isolation, improve voltage profile, reduce losses and improve
schematic diagram of the system is shown in Fig. 11. Resistance, the overall reliability of the system. Figs. 14 and 15 show the
reactance and capacitance of the lines are measured as 0.62 Ω/km, voltage profile and power flow of the 13-bus system before and
0.078 Ω/km and 0.24 μF/km. A 4 kW solar DG exists at bus 6. The after reconfiguration. After reconfiguration, the voltage magnitude
maximum current carrying capacity of the line is 70 A. In the of most of the buses has been improved, and a reduction in power
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 Fig. 9  Voltage profile of the IEEE 34-bus system for different cases

Table 9 Comparison of the proposed methodology with different methods

Different IEEE 34-bus system IEEE 123-bus system
methodology Closed switches PL, kW ENS, Minimum Run Closed switches PL, kW ENS, kWh Minimum Run
kWh voltage, pu time, s voltage, pu time, s
base case 1, 4, 9, 8, 7 395.78 57,279 0.89 — 3, 4, 5, 7, 8, 9, 10 571.85 233,170.17 0.9 —
HSA 3, 4, 5, 8, 6 306.7 41,150 0.91 33 1, 2, 3, 4, 5, 7, 8 340.59 191,735.78 0.91 90
GA 1, 2, 3, 4, 7 309.51 45,657 0.9 70 1, 3, 4, 5, 8, 9, 10 279.34 181,955.59 0.93 130
discrete PSO 1, 3, 4, 5, 6 309.77 44,379 0.9 30 1, 3, 4, 5, 8, 9, 10 279.34 181,955.59 0.93 80
proposed Pareto- 3, 4, 5, 7, 8 305.8 41,273 0.92 13 1, 2, 3, 5, 7, 8, 10 273.28 176,781.12 0.94 21
optimisation-
based method

Table 10 Comparison of the proposed methodology with existing methods for the 33-bus balanced distribution system
Different Closed switches (switch number) PL, kW ENS, kWh Minimum voltage, pu Run time, s
methodologies
HSA 3, 6, 7, 9, 10, 11, 12 288.22 28,668 0.91 21
GA 3, 4, 5, 6, 7, 10, 11 273.39 34,604 0.91 35
discrete PSO 2, 3, 4, 5, 6, 7, 10 170.11 29,560 0.92 20
proposed method 2, 4, 5, 6, 7, 9, 10 190.08 27,487 0.92 18
switch number 1 (11–12), 2 (12–13), 3 (14–15), 4 (17–18), 5 (24–25), 6 (29–30), 7 (32–33), 8 (21–8), 9 (9–15), 10 (12–22), 11 (18–33),
(between the buses) 12 (25–29)

7 Conclusion
This paper has presented two different methodologies for
distribution NR: one is Pareto-optimisation-based NR and another
is look-up table-based NR. Both the algorithms work under healthy
and persistent post-fault conditions. The proposed algorithms have
shown better performance and less computational time as
compared with the existing algorithms. The computational time of
the proposed techniques is small even for a large system because
the computational time does not depend on the total number of
switches in the system. Another advantage of the proposed method
over the existing method is that it does not depend on the initial
Fig. 10  Pareto front for the different configurations with different switch status of the system. Another contribution of this paper is
weighing factor variation for the IEEE 34-bus system the reliability assessment algorithm for an unbalanced distribution
system. The advantage of this algorithm is that it is
flow has been observed in most of the branches. This signifies that computationally less exhaustive as compared with the MCS
the capacity of most of the feeders is increased to handle load method and the execution time is less as compared with MCS. All
growth. The proposed algorithms are implemented in the Metered the simulations are carried out on an unbalanced distribution
Data Management System of the 13-bus field pilot deployed at the system without simplifying it to single-phase equivalents. The
Amrita University, India. proposed methodologies have been successfully applied on IEEE
34- and IEEE 123-bus test distribution systems, as well as on a real

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 Fig. 11  Single line diagram of the 13-bus system of the Amrita University

Fig. 12  Installed smart monitoring and control unit in the Amrita University campus to perform NR

Fig. 13  Components and interfacing of the MCP and EPS units

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 Table 11 Test results of the 13-bus Amrita University system after reconfiguration
Cases Before After
faulty line (between the buses) — 6–7
closed switches — 3
PL, kW 10.21 6.97
minimum voltage (V) 404.18 409.51
ENS, kWh 35.72 28.69
number of restored load — 13

Fig. 14  Voltage profile of the 13-bus Amrita University system

Fig. 15  Power flow of the 13-bus Amrita University system

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