Optimal Directional Relay Placement in Microgrids Considering
Coordination Constraints
Bahare Salehi
Department of Electrical and
Computer Engineering
Isfahan University of Technology
Isfahan, Iran
Mahdi Tadayon
Distribution Network
Department
Behrad Consulting Engineers
Isfahan, Iran
Hamid Reza Karshenas
Department of Electrical and
Computer Engineering
Isfahan University of Technology
Isfahan, Iran
B.salehi70@gmail.com
Mahdi.tadayon@gmail.com
karshen@cc.iut.ac.ir
Abstract: — This paper is concerned with the optimal
placement of protection devices in a microgrid (MG) using
genetic algorithms. The occurrence of power outages in
distribution networks is higher than that of other parts of
the grid. This phenomenon may impose substantial damage
on customers with sensitive loads. The new concepts of
distributed generation (DG) and microgrid (MG) in modern
distribution systems can reduce the number of outages and
associated damages by supplying a feeder from multiple
sources. However, microgrids and distribution networks
with DG require significant effort for the coordination of
DGs and their protection devices. Therefore, the placement
of protective equipment in order to limit the scope of the
fault is one of the important issues which power engineers
face. Adding DGs to a distribution system creates different
sets of operating conditions such as reverse power flow and
increased fault levels. In this paper, using the graph theory,
various branches of a feeder are identified and the
constraints for using genetic algorithm to optimize the
location of protective equipment are derived. In the
proposed algorithm, the location, type and direction of
relays are optimized simultaneously. The results of
implementing the proposed approach on a 33-bus test
network confirm the performance and accuracy of this
method.
Keywords: Microgrid, Genetic Algorithm, Protection
Coordination, Graph theory.
I.
INTRODUCTION
Power outages (also known as interruptions and
blackouts) are one of the most damaging power quality
problems if properly is not taken care of. The amount of
damage depends on the number and duration of outages
and the sensitivity of customer loads. High-tech
industries, hospitals and information technology (IT)
sectors are usually affected more than others and are
more likely to suffer from such losses. In some countries
such losses are being reimbursed after an assessment of
clients' contracts and duration and numbers of imposed
outages [1].
The reimbursement of such damages, in addition to
significant loss of sales, results in considerable
recompense for electric distribution companies, which
persuades them to seek methods to reduce power outages.
For instance, optimized placement of devices such as
monitoring and protective equipment and remote
controllable breakers can enhance system operation and
improve reliability and power quality indices of the
system [2]. This optimization, however, is considered a
very difficult task because it is a combinatorial
constrained problem described by a nonlinear and
nondifferential objective function [3].
Using distributed generation (DG) to improve system
reliability is a known concept these days. An important
aspect of distribution networks with DG is that the power
flow can be bidirectional and thus the traditional
protection strategies should be properly modified in order
to rectify the operation of protective equipment. In other
words, a branch on which the fault has occurred may be
fed from two sides and protective equipment should be
able to cover such faults completely [4]. Consequently,
relay placement in distribution systems with DG is
always a challenge.
One of the most important stages of relay placement is
its coordination with other relays in the grid. Based on
factors such as short circuit level, the type of relay and
the type of circuit breakers, the number of series relays
which can be coordinated is limited. By series relays, we
mean those relays that can see the same faults occurred at
the end of each branch. Identifying series relays seen by
each source needs special algorithms.
The fault current seen by a particular relay in forward
direction (i.e. when a fault occurs downstream to the
relay) is much higher than that of seen in the reverse
direction. Therefore the relays must have the ability to
distinguish between forward and reverse fault currents
[4]. In other words, it necessitates different relay settings
in forward and reverse directions. Therefore directional
overcurrent relays are proposed to isolate the faulted
sections.
Preliminary studies have already shown that Graph
theory can simplify the representation of switching
procedures in a complex power system [5]. This method
is also used in this paper in order to identify series relays.
In doing so, all directions and sources are considered to
find the candidate locations for various series
configurations.
Some papers have proposed the multi-objective
optimization for design problems of power distribution
system protection planning. Reference [6] has proposed a
Genetic Algorithm for finding optimal location of
Recloses on the feeder equipped with power constrained
DGs. In [7], risk analysis is used to optimize the location
of circuit breakers on the distribution feeders. In [9], the
reactive tabu search algorithm is proposed to optimally
place both control and protective devices in the same
optimization process on radial distribution feeders.
In this paper, Graph Theory and Genetic Algorithm are
used to optimize the location, type and direction of relays
in a microgrid and distribution network with DG. The
objective function used in this optimization is energy not
supplied (ENS) and the constraints are based on relays
coordination and islanding operation of distributed
generations. The results of implementing the proposed
approach on a 33 bus test network are described and
discussed.
II.
MATHEMATICAL FORMULATION
Mathematical formulation consists of optimization
constraints and defining objective function.
A. Optimization constraints
Relays coordination and islanding operation in the
optimized plan are considered as optimization constraints.
• Relays coordination
When a fault occurs, it should be cleared as fast as
possible with minimal affected area in the rest of system.
In addition, time coordination among protective devices
are also essential. Primary devices, which are close to the
fault location, should take action before backup devices
which are located farther. The direction in which the fault
occurs is detected by measuring the direction of current
flow, which can be recognized by the phase displacement
between the current and voltage.
The inverse definite minimum time (IDMT)
characteristics defined by:
1
where:
t = operating time for constant current I (seconds),
I = energizing current (amps),
Is = overcurrent setting (amps),
TMS = time multiplier setting,
k, a, c = constants of defining curve.
(1)
In the situations where the fault current does not
significantly vary relative to fault location, i.e. the
impedance between the relay and the power source is
large; the advantages of IDMT characteristics are not
fully utilized. In such cases, definite time overcurrent
protection is applied. The operating time can be constant
irrespective of the magnitude of the fault current [10].
Every primary protection needs a backup for
guaranteeing a dependable protective system. The two
protective schemes should be coordinated together, i.e. a
predefined coordination time interval (CTI) should
collapse before the backup scheme comes into action.
This CTI depends on the type of the relays
(electromechanical or microprocessor based), speed of
the circuit breakers and other system parameters.
Typically, the CTI used for electromechanical relays is
0.3 to 0.4 s, while a CTI in the order of 0.1 to 0.2 s is
used in the case of microprocessor based protective relays
[11]. In summary, protection coordination between
primary and backup relays can be described by
(2)
where
Tbackup : operating time of the backup relay
Tprimary : operating time of the primary relay
Therefore if the time delay for the circuit breaker at the
beginning of the line is set at 0.5 second, we can
coordinate 5 series relays in the best condition. We
should coordinate series relays for best performance and
reduce energy not supplied.
Based on this fact, a new constraint for optimal
protection device placement is developed and formulated
by
i=1,2,…,n
(3)
where
: Number of series relays in each branch of graph
n: Number of branch in the graph
: Maximum number of relays that can be
coordinated together
• Islanding operation conditions
One of the technical issues to be solved in an islanded
zone of distribution network is generation and load
balancing. The fluctuations in both these quantities
depend on customer needs and the type of generation.
Demand side management (DSM) is a well-established
technique to control the levels of electricity consumption,
both in island and grid-connected networks [12]. DSM
has been used for controlling network operators to
maintain power system frequency and voltage and
stability in the islanded zone. For each islanded zone, this
constraint is formulated as
(4)
where
n: Number of loads in each zone
: Loads in each zone
: Distributed Generator capacity inn each zone
These constraints have been checkeed for each source
including main source and DGs.
Objective function
In this paper, minimizing ENS is the objective
function which is defined as
various operators on some of genes in each generation.
Fig. 2 demonstrates the proposeed algorithm.
The objective function is caalculated for each of these
chromosomes, and the best of them is determined. If the
conditions are met, the algoriithm terminates; otherwise
the genetic operators are appplied again and the next
generation is created. Genetic operators are described as
follows:
B. Selection
This function transfers bestt chromosomes from each
generation into the next. The number of chromosomes
that are selected is proportionnal to the total number of
chromosomes.
(5)
where
NIL: Number of isolated load points due to
contingency j;
NC: Number of contingencies;
Lkj: Curtailed load at load point due to
t contingency j;
rj :Average outage time due to continngency j;
λj :Average failure rate of contingenccy j;
III.
PROPOSED METTHOD
The proposed algorithm was impllemented using a
code
utilizing
hybrid
MATLAB-DIgSILENT
DIgSILENT Programing Language (D
DPL) feature. This
combination of DPL and MATLAB has
h been used for
writing scripts to use advantages of DIIgSILENT in load
flow and reliability calculations and ease of Genetic
Algorithm and Graph Theory coding in MATLAB.
In order to reduce the complexity and run-time, the
possible locations for placing protectiive equipment are
first refined by an expert to find best caandidate locations.
Consequently, by forming approppriate trees, the
impossible combinations for the coordination of
protective equipment are determined ussing Graph-theory.
These combinations have been defineed based on short
circuit levels and the length of lines annd will be checked
continuously throughout the execution of
o the algorithm.
The method used for eliminaating impossible
candidates of the trees is illustratedd in Fig 1. This
algorithm is implemented using a self-calling subroutine.
The next step is to find the best locaation for protective
equipment using genetic algorithm. In this
t regard, a gene
in each chromosome signifies a candidaate location. Genes
can pick up integer values 0, 1, 2 or 3.
3 “0” is used for
candidate locations that is not selectedd for placement of
protective equipment, “1, 2 and 3” are used
u
for candidate
locations that are selected for placem
ment of protective
equipment as a forward relay, reverse relay and both of
them respectively. These chromosomees are filtered by
graph theory output to satisfy the coorddination constraint.
To produce a new generation, this algorithm applies
Figure 1. Flowchart of series relays determination
C. Perturbation
This function makes a small changee in a near perfect
chromosome. In other words, it's a muutation with a very
low probability [13].
Figure 2. Perturbation operaator
Test network specificatioons corresponding to 8
conditions are considered in thhis paper. These conditions
are shown by letters A to H in Table 2. The optimal
locations of nondirectional or forward-reverse relays for
each condition is named by nuumber and shown in Table
3. If a DG is connected in this test network, relays
between DG and main sourcee will sense different short
circuit currents for downstreeam and upstream faults.
Therefore directional relays aree placed in these candidate
locations.
D. Mutation
This function changes the genes in a chromosome. The
number of mutated points and thee probability for
mutation are flexible. If the number off mutated genes is
high versus to total number of geness, each generation
inherits fewer properties from their prrevious generation
and instead more chromosomes are being
b
studied. To
increase the speed of this method, The
T
number of
mutated points and the probability for mutation are
reduced as it approaches to the stoppingg criterion [13].
Figure 3. Mutation operatoor
E. Crossover
c
and
This function operates on two chromosomes
randomly exchanges some of their genes.
g
The result
chromosomes inherit most of their parennt's qualities.
Figure 4. Crossover operatoor
IV.
RESULTS AND DISC
CUSSIONS
The proposed algorithm has been tessted on several real
distribution networks in Iran. In this papper, the 33Bus test
network[14] is used to demonstrate and verify the optimal
locations of protective equipment. In this system, one DG
has been considered in several conditioons and reliability
data such as failure rate and repair duuration are defined
equally for all contingencies on the linees. Failure rate is 1
for each kilometre in one year and the
t corresponding
repair duration is 10 hours. The test neetwork along with
the name of nodes and branches aree shown in Fig6.
Several conditions are considered foor evaluating the
performance of proposed algorithm andd the effect of load
priorities and distributed generation on the optimal
locations, types and directions of relays.
Figure 5. Flowchart of proposed algorithm
STUDIED CONDITIONS
locations for expanding the islanded zone of DG. The
probability of fault in the expanded zone will be
increased and the positive effect of DG decreased. As can
be seen, if the priority of loads is considered in the
optimal protection device placement, optimal locations
will be changed to decrease the outages in the important
customers’ zone by allocating relays near to these
customers in the upstream and downstream of the feeder.
Condition
Description
Loads importance
Location of
DG
Capacity
of DG
A
All equal
Busbar 12
0
B
All equal
Busbar 12
1
C
All equal
Busbar 12
2
D
All equal
Busbar 12
3
E
Importance of Load
15 is 10 times more
than others
Busbar 12
1
All equal
Busbar 6
3
G
All equal
Busbar 6
2
H
Importance of Load
13 is 10 times more
than others
Busbar 12
1
03
023
024
003
022
22
21
021
25
23
020
24
019
002
018
20
001
02
004
04
028
029
030
031
33
32
31
30
29
28
027
032
006
026
007
07
08
09
10
1
3 6
8 18 20 21 22 23 24 25 30
A,G
2
3 7 11 18 20 21 22 23 24 25 30
B,E
3
3 6 11 18 20 21 22 23 24 27 31
C,D
4
5 6
5
7 11 14 18 20 21 22 23 24 25 28 31
TABLE III.
8 18 20 21 22 23 24 25 30
12
013
014
015
016
18
17
16
15
13
012
14
11
011
Number of lines on which relays are installed
010
Condition
Number of
arrangement
009
RESULTS OF OPTIMAL PLACEMENT OF RELAYS
025
008
The optimal location of relays in each condition is
tested on other conditions and ENS has been calculated
and presented in Table 3. These results in a 3D view have
been shown in Fig 7.
27
05
06
TABLE II.
19
01
005
F
main
26
TABLE I.
017
Figure 6. 33Bus test network
F
H
ENS IN EACH CONDITION FOR OPTIMUM PLANS
ENS for different number of arrangement
Condition
1
2
3
4
5
A
365.40
370.94
388.94
392.15
411.01
B
351.87
311.93
358.64
378.99
334.93
C
320.42
311.93
306.22
368.50
334.93
D
276.83
268.34
262.63
288.34
334.93
E
351.87
311.93
358.64
378.99
334.93
F
321.45
327.30
344.90
311.99
411.01
G
365.04
370.94
388.49
392.15
411.01
H
351.87
311.93
358.64
378.99
334.93
By comparing the results of B to D conditions, the
effect of DG’s capacity can be observed. Increasing in the
size of DG leads to a small displacement in relays
Figure 7. ENS in each condition for optimum plans
Figure 8 shows the normalized load points
corresponding to energy not supplied (NLPENS) for
several load points. The normalization is performed based
on the results of condition A. By comparing these results,
it can be seen that primary branches are not affected by
DG’s locations, because relays on thesee branches are not
displaced and these branches are not islanded in each
outage. Also we find that NLPEN
NS of important
customer is decreased by optimizing rellay’s locations.
25
H
F
D
B
5.
Conclusion
This paper presents a methhod for optimal placement
and coordination of protectivee equipment in distribution
networks with distributed geneeration. It was shown how
to identify the branches of the network with series relays
and to find the tentative locatioons for them. The proposed
algorithm in this paper use a Graph Theory based
algorithm for this purpose and a robust Genetic
Algorithm with dynamic muutation for optimizing the
type, direction and location of relays. The criteria used
for optimization is the energyy not supplied (ENS). The
results on a test network shhows that load priorities,
location and direction of relaays between sources have
impact effect on ENS.
30
29
ween the main source and
of other directional relays betw
DG.
20
12
11
6
nces
Referen
1
0
1
2
3
4
Figure 8. NLPENS for several loads inn 4 conditions
Often, relays between DG and sourcce have significant
effects on ENS as they generate islaanded zones if an
outage occurs on the upstream. Figg. 9 shows ENS
according to the location of a directioonal relay that has
been added to network in zone A. Coordination
constraints will be observed by settiing this relay for
operating on reverse fault current. As can
c be seen, if this
relay generates a wrong islanded zone for DG (when the
total load of zone is more than capacityy of DG), the total
ENS will increase.
Figure 9. ENS variations depend on reverrse relay location
In the “D” condition, the best locattion of directional
relay between the main source and DG
G is Terminal 05 at
the beginning of Branch 05. When a fault
f
occurs on the
upstream of this point, this relay willl operate and an
islanded zone will be created around thhe DG. The sum of
loads in the created zone is 945kW less than DG capacity,
hence total ENS increases. But whhen this relay on
terminal05 is placed between Terminall01 to Terminal04,
the total ENS increases, because efficiiency of this relay
depends on LPENS of upstream load pooints and locations
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