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On optimization for security and reliability of power systems with distributed

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Conference Paper · July 2003

DOI: 10.1109/PTC.2003.1304111 · Source: IEEE Xplore

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 Paper accepted for presentation at 2003 IEEE Bologna Power Tech Conference, June 23th-26th, Bologna, Italy

On Optimization for Security and Reliability of

Power Systems with Distributed Generation
J. A. Greatbanks, D. H. Popović, M. Begović, A. Pregelj and T. C. Green

Abstract— Electricity market restructuring and supra-national kept within given limits. Clearly, the effect of adding DG on
agreements on the reduction of global greenhouse gas emissions network security and reliability will vary depending on its type
have paved the way for an increase in the use of distributed gen- and position and (forecast) load at the connection point. Conse-
eration - the connection of generation to the lower voltage power quently, one or more sites on a given network may be optimal.
system. This paper formulates and discusses a methodology for the
In addition, optimal resource integration and utilization should
optimal siting and sizing of distributed generation a security con-
strained system can accept. Optimal siting is determined by sensi- allow distributed generators to best compete in the market. It
tivity analysis of the power flow equations. The sizing method for implies that the cost of incorporating distributed generation into
a set of loading conditions, generation penetration level and power power system, the cost of outages and the cost of maintenance
factor is formulated as a security constrained optimization prob- should be taken into account. Both security/reliability and eco-
lem. The information on optimal generation sites is used further to nomic issues should however be assessed subject to distributed
optimize system reliability assessed via reliability indices calcula- resource capacity, mode of operation (as needed, only when
tion. A genetic algorithm is designed to solve for optimal recloser economic or must-run), local grid stability and reliability crite-
positions when distributed generators are deployed in a securely
ria and the needs of the energy user (wrt energy, reliability and
optimal manner.
power quality) [1].
Index Terms: Distributed generation, genetic algorithm, opti- Preliminary studies have already shown that unless backup
mization, protection, reliability, static security capacity is provided, stand-alone distributed generation may
lower system reliability [2]. Similarly, it could harm system re-
I. I NTRODUCTION liability if it is not properly coordinated, located and designed
Recent years have seen a trend towards the development and to work with existing network protection. In a radial feeder,
deployment of distributed generation (DG) due to government protection devices are only expected to detect the unidirectional
policy changes and increased availability of small generation flow of current. In a majority of cases, only one device per fault
plant. The nature of distributed generation is smaller (≤ 100 operates. The control logic for protection devices is therefore
MW) plant with little or limited central control, connected to simple - the nearest recloser upstream from the fault location
the distribution system. Distribution systems have tradition- detects the fault current, trips, and goes into a predefined re-
ally been designed to operate with unidirectional power flow, closing sequence in order to restore service, in case the fault
from the source (transmission system) to the loads. Adding was of a temporary nature. If more reclosers are present on
DG to a distribution system imposes a different set of oper- the radial feeder, they are coordinated, usually via time lags,
ating conditions on the network, namely reverse power flow, such that the recloser closest to the fault operates. In a DG-
voltage rise, increased fault levels, reduced power losses, har- enhanced feeder, power flow is not unidirectional and conven-
monic distortion and stability problems. The presence of adi- tional protection logic must be altered in order for the fault-
tional generation on a feeder may also allow for a stand-alone, detecting devices to successfully perform their function [3]. A
island mode operation where DGs are supplying portions of the faulted branch may be energized from both sides and several
feeder load after fault has been isolated. Islanded operation protection devices may need to operate in order to completely
however requires significant coordination of distributed gener- interrupt the fault current. Several control strategies, using only
ators with feeder protection devices in order to create possible local or SCADA measurements, may be utilized. Distributed
self-supporting islands. generation and storage units, located on the feeder, may reduce
Extensive operations planning system analysis is needed for the number of faults and/or fault durations for customers within
distributed generation integration to be successful from both their protection zones, thus increasing the reliability of service.
system security and reliability point of view. This paper will This paper develops a methodology for systematic and ratio-
address the issue of coordinated and optimal placement of dis- nal placement of distributed resources and reclosers in distribu-
tributed generators and reclosers into a security constrained dis- tion networks. Both voltage sensitivity analysis and loss sen-
tributed power system. Connecting a DG source to the distri- sitivity analysis of the power flow equations are used to deter-
bution system has to be done so that operating conditions are mine the optimal sites for placement of distributed generators.
It is followed by the constrained optimisation method which
J. A. Greatbanks, D. H. Popovic´ and T. C. Green are with the Dept of Elec-
trical and Electronic Engineering, Imperial College, London SW7 2BT, UK calculates the quantity of DG that can be connected to specified
M. Begovic´ and A. Pregelj are with the School of Electrical and Computer points with the system remaining secure. The assessment takes
Engineering, Georgia Institute of Technology, Atlanta, GA 30332 0250, USA into account the distributed generator power factor character-

0-7803-7967-5/03/$17.00 ©2003 IEEE

istics and load profiles for various operating conditions. The tem. In a conventional (radial) feeder, protection device place-
information on optimal generation sites is used further to op- ment is designed to maximize network reliability, and therefore
timize system reliability assessed via calculation of reliability minimize the reliability indices assuming energy source(s) lo-
indices which include the DG units. A genetic algorithm is de- cated only at substation(s). As a brief reminder, the standard re-
signed to solve for optimal recloser positions when distributed liability performance indices, such as SAIFI, SAIDI and MAI-
generators are deployed in a securely optimal manner. A 114- FIe, and the composite index obtained as a combination of all
bus mixed urban and rural 11kV feeder in the UK is used to three will be considered. The system average interruption du-
verify and demonstrate the methodology. ration index (SAIDI) and the system average interruption fre-
quency index (SAIFI) are typically used to measure average ac-
cumulated duration and frequency of sustained interruptions per
II. O PERATION AND F EEDER D ESIGN O PTIMIZATION FOR
customer. The momentary average interruption event frequency
D ISTRIBUTED G ENERATION index (MAIFIe) measures the number of momentary interrup-
The introduction of generating sources into the distribution tions per customer. The recloser placement can be optimized
system can significantly impact the operating state and dynam- with respect to any of these three, or some other, indices. In
ics of both the transmission and distribution systems. While order to include the effects of both sustained and momentary
at low/modest levels of distributed generation penetration, the interruptions, a composite index may be used, with appropriate
impacts on the high voltage transmission system may not be choices of weighting factors and target values for the SAIFI,
significant, impacts at the lower voltage distribution level could SAIDI and MAIFIe.
be much larger especially in respect of fault current levels, the Conventional logic suggests placing a recloser at the halfway
magnitude and direction of real and reactive power flow, the point of a radial feeder with uniformly distributed load, which,
system voltage (both steady-state and transient) and the system in theory, would yield a 25% feeder-wide reliability improve-
stability under various small and large signal transient condi- ment. Similarly, locations at 1/3 and 2/3 of feeder length should
tions. The impacts and interactions can be both positive and be considered for placement of two reclosers. In realality, in the
negative depending on the distribution network operating char- presence of critical loads and non-uniform load distributions,
acteristics and the distributed generation characteristic, place- utilities often resort to engineering judgment to place reclosers.
ment and size. A proper placement plays a very important role As an example, Figure 1 shows a typical rural feeder, with sub-
since power flows at the interface substations and throughout station breaker and two reclosers. Assuming there is no DG at
the networks depend on geographic distribution of all genera- the end of the feeder, a fault anywhere on the line will lead to
tion sources with respect to demand irrespective of the voltage the opening of the first recloser upstream from the fault. For
at the connection point. For distributed generation to have a example, after a fault between reclosers 1 and 2, recloser 1 op-
positive effect, it must be at least suitably integrated and co- erates, leaving all customers downstream without service. If
ordinated with the distribution system operating practices and DG is present, recloser 2 would also operate, allowing the por-
feeder design [4]. In order to further the positive effect and tion of the feeder downstream from it to operate as an island.
enhance network capacity limits while contributing to system
security and quality of supply, local optimisation would be re-
quired accompanied with taking advantage of any inherent reg-
ulation capability of dispersed generation.
In short, adding generation will usually cause changes in
voltage magnitudes and power flows. These changes will affect
system losses. There are obvious implications for the current Fig. 1. Strategically placed reclosers increase reliability of the system by
rating of lines resulting from modified power flows, and voltage reducing the number of customers affected by the fault
changes could see voltages rise to undesirable levels. Genera-
tors operating with a leading power factor may compound the In order to operate in island mode, DG(s) have to be able
latter. In addition, DG injected power may result in voltage that to satisfy the islanded load, and therefore keep both the volt-
is within limits at the DG site but could be out of limits further age and frequency within acceptable ranges. Islanded operation
downstream. The addition of extra power sources to a network requires significant coordination of distributed generators with
also impacts on system fault levels and may increase fault cur- feeder protection devices. The sequence of events after the fault
rents beyond the rating of the circuit breakers. The essence is should be as follows:
that adding generators to a passive distribution system makes it • DG is tripped, and fault detected and isolated by one or
an active distribution system, almost a mini transmission sys- more protection devices.
tem, and extra thought must be given to its operation and con- • DG reconnects if not within the faulted zone.
trol. More specifically, in voltage profile and regulation studies, • After the fault is cleared, recloser synchronizes its reclos-
available transmission capacity studies, as well as cost studies, ing operation with DG.
the connection point, type, size and location of DG, the volt- The positions of protection devices and distributed genera-
age regulator settings and impedance characteristics of the line tors are therefore strongly dependent. Incorrect recloser place-
must all be considered for various load and load density levels. ment may lead to islands with not enough generation and would
Similar considerations must be given to islanding response not yield additional reliability benefits. On the other side, by
during upstream operation of protection and faults on the sys- strategically placing reclosers, one may be able to significantly
increase the reliability of service to customers in such islands. These values can be used to rank the overall voltage sensitiv-
Typically, there will be a momentary interruption to the cus- ity of each node to real or reactive power injection. A Voltage
tomers in the island, due to the need for the DG to disconnect Sensitivity Index (V SI) used in ranking is defined as [10]
after the fault in order not to interfere with protection devices’    
operation. If however, reclosers are able to disconnect immedi- ∂V ∂V
V SI = w + (1 − w) (3)
ately, there may not be even a momentary interruption, and thus ∂P ∂Q
MAIFIe index may also be reduced.
The diagonal elements of the Jacobian matrix represent the sen-
III. O PTIMAL P LACEMENT AND S IZE OF D ISTRIBUTED sitivity of one bus voltage magnitude to the injection of power
G ENERATORS at the same bus, whereas the off diagonal elements represent the
sensitivity to power injected at other buses. Since the purpose
Optimal placement of distributed generators for enhanced of adding dispersed generation is to bring about an improve-
reliability, reduced transmission and distribution costs and re- ment in network performance, the effect of power injection at
duced emissions can be realized only by considering all fac- a single bus on the voltage sensitivities of the whole network
tors, including the loss reduction achieved system wide and on must be considered. This is achieved by expressing the VSI
the feeders, security limits and cost/benefit analysis. It is a very for each node as an Euclidean norm normalized across all load
complex problem considering a high number of options in terms buses. The value of the weighting factor w will depend on the
of sites and units available and a need to account for a 8760h X/R ratio of the network under consideration.
load profile and generation profile and associated uncertain- The nodes are ranked according to the VSI value and the
ties [5–7]. In [8], the OPF-based optimal placement is proposed ranked set is used to define the optimum sites to accept injection
addressing the effect of DGs on the spot prices and stability lim- of P and/or Q.
its. Reference [9] investigates locational aspects of DG with re-
spect to transmission and distribution losses. In this study, costs Loss Sensitivity
related to adding the DG and transmission/distribution upgrades The majority of power losses are ohmic in nature caused by
and/or savings are not taken into account and the network ca- power flow through lines and transformers, i.e.,
pacity limits are evaluated based on the impacts of distributed
generation on the system losses, security and adequacy of sup- Ploss = P (δ, V )
(4)
ply. Qloss = Q(δ, V )
To assess network capability to absorb available distributed
resources safely, a steady-state system representation in the Combining equations (1) and (4) gives
form of power flow equations will be used. The inverse power " ∂Ploss # ∂Ploss
" #
flow Jacobian relates changes in power injections to changes in ∂P  T −1 ∂δ
angles and voltages, i.e., ∂P
= J (5)
loss ∂Ploss
∂Q ∂V
 ∂P ∂P
−1
The Loss Sensitivity Index (LSI) is defined as
   
∆δ ∂δ ∂V ∆P
=  (1)
∆V ∂Q ∂Q ∆Q    
∂δ ∂V ∂Ploss ∂Ploss
LSI = w + (1 − w) (6)
∂P ∂Q
A. Optimal DG siting
In order to determine the most suitable sites for DGs, two B. Sizing of DG
sensitivity based approaches related to voltage control and Determination of the optimal sites for DG placement in Sec-
power loss are proposed. Both a voltage sensitivity index (VSI) tion III.A is followed by determination of the amount of DG
and loss sensitivity index (LSI) are defined and used to identify that can be added at these sites without loss increase and oper-
and rank the nodes within the network with respect to receiv- ational constraints violation. The sizing method is formulated
ing new generation. It is assumed that generators can connect as a constrained optimization problem adapted from a reactive
to any point in the network subject to security constraints and power compensation sizing algorithm [11] and capacitor bank
are not restricted in their location by generator controllers or sizing algorithm [12, 13]. Given information on the available
existing protection devices. distributed generation and assuming no expected load growth
in the region of interest, the objective is to maximise the quan-
Voltage Sensitivity
tity of distributed generation connected to a system, i.e.,
Assuming that angle-related problems are not a concern, the
voltage sensitivity can be defined as n
X
    max (PGi + jQGi ) (7)
∂V ∂V
[∆V ] = [∆Q] + [∆P ] (2) i=1
∂Q ∂P
where PGi and QGi are the real and reactive power injections at
From (1), for each system node, there is an associated real each node i respectively. The equality constraints are the power
power sensitivity ( ∂V ∂V
∂P ) and reactive power sensitivity ( ∂Q ). flow equations. The inequality constraints are
 • voltage operational tolerance limits at all buses Start

Select Data File, Max Generator

Vimin ≤ Vi ≤ Vimax (8) Increment, Weighting Factors

• limit on losses Initial System Load Level

X X
PlossG ≤ Ploss (9) Initial Generator Type
ij ij

• limit on total power generated by DG subject to a pene- Calculate VSI & LSI
Solve Initial Load Flow and Fault Levels

tration level of 20% (e.g. it must not exceed 20% feeder

load). Normalize & Rank
Increment Generators at Viable Nodes

n n
X X Solve Load Flow and Fault Levels
PGi ≤ 0.2 PLi (10) No

i=1 i=1
n n Are Constraints
X X Breached?
QGi ≤ 0.2 Q Li (11)
Yes
i=1 i=1
Remove Last Generator Increment

• branch flows limits (e.g. they must remain below thermal

limits) Repeat for All Remaining Generator Types

Sij ≤ Sij max (12)

Repeat for All Remaining Load Levels
• fault current limits (e.g. they must be less than the maxi-
mum fault current rating of the switchgear on each line) Finish

Fig. 2. Solution Algorithm for Optimal Placement and Sizing

IFij ≤ IFij max (13)
The optimal placement and sizing methods are combined
to add DG penetration with generators connected at optimal
points. The proposed solution algorithm is shown in Fig. 1. The
sizing element is an iterative process, and involves repeatedly
solving load flow equations. Each iteration has a larger value
of DG source connected at predetermined (optimal) points. The
solution is reached when the next iteration fails to satisfy one or
more constraints. The loading of a system plays an important
role in determining the type of constraint to be violated. Con-
sequently, the methodology and solution algorithm are applied
over a range of loading conditions. Fig. 2 shows typical load
profiles for three representative days for a test feeder, winter
evening peak demand, summer night least demand and spring Fig. 3. Load Profile for Test Feeder
daytime average demand. These three levels are approximated
by the ratio 4:2:1, exploited by the algorithm. The methodology and solution algorithm are tested on sev-
eral distribution systems representing urban, rural and mixed
C. Numerical study use 11 kV networks. All networks are assessed for ‘intact’ con-
In order to evaluate the effects of adding DG to a system, the ditions (e.g. no contingencies). The results shown here are for
operating characteristics of the distributed generator should be a 114 bus mixed urban and rural 11 kV system from the United
taken into account, especially with respect to the network in- Kingdom. Fig. 4 shows a slightly modified version of the feeder
terface, whether it is synchronous or induction machine based, obtained by aggregating many of smaller (rural) loads located
directly coupled or connected via an inverter. The vast majority at lateral ends. Consequently, the number of buses is reduced
of distributed generation in the UK serves the single purpose to 75. Currently, there is no DG connected anywhere within
of exporting power to the power system for consumption [14]. the feeder. The total maximum feeder load is 17.4 MW, with
Little if any distributed generation is either controllable or dis- 13.8 MW concentrated down the main feeder as housing estates
patchable and is not used for any ancillary support. This, cou- and small industrial units supplied via 300- 1000 kVA substa-
pled with the regulatory and commercial arrangements for DGs tions. The two right hand laterals supply small housing clusters
means that there is no benefit or incentive for the generator to and farms via 10- 100 kVA transformers and their maximum
operate at a power factor other than unity (or as close to unity loads are 2.5 and 1.1 MW.
as possible). This analysis considers three generator power fac- Fig. 5 shows the VSI results of the optimal siting method
tors of unity, 0.95 leading and 0.95 lagging to represent likely with the highest ranked sites, as expected, being located to-
operating generator characteristics. wards the feeder extremities where nodal voltages are lowest.
 Fig. 5. Normalised Voltage Sensitivity Index (w = 0.5)

Fig. 6. Normalised Loss Sensitivity Index (w = 0.5)

Similarly, Fig. 6 shows the nodes’ LSI values. The highest pattern was observed for the spring and summer load levels,
ranked nodes are again located towards the feeder extremities. although not shown. However, voltage rises are still moder-
Relating Figs. 5 and 6 to Fig. 4, a clustering pattern can be ate enough so as not to cause overvoltage problems in any load
clearly observed whereby neighbouring nodes have very simi- state. In each case, the leading generator power factor gives rise
lar voltage and loss sensitivities. Hence, simply placing the DG to the greatest voltage improvement and the lagging to the least.
units at the highest ranked sites would lead to an undesirable Fig. 10 compares the relative improvement in voltage profile for
cluster of neighbouring generators. To avoid this situation and 20% penetration with generators placed by both LSI and VSI.
to distinguish between feasible and non feasible sites, a cutoff Over the bulk of the feeder, i.e. the large main section, there is
value of 0.015 was chosen for both the VSI and LSI. Of all the no difference in voltage improvement. However, on the later-
feasible sites identified by VSI, ten were chosen as viable gen- als, there is generally a greater voltage lift from placement by
erator sites with respect to their spatial distribution around the LSI. This is due to the LSI optimal generators being placed at
feeder as indicated in Fig. 5 and marked in Fig. 4. The loss sen- fewer sites and sized larger. The losses and efficiency results of
sitivities in Fig. 6 indicate an even stronger clustering pattern Figs. 8 and 9 all follow the same pattern for each load state of
and the eight most sensitive sites identified as optimal are cho- approximately a 40% reduction in losses with a 20% penetra-
sen as to coincide with the VSI-based sites. It is worth noting tion and winter load. A 40% reduction in losses gives rise to a
that within clusters buses are more sensitive to voltages than 2.3% improvement in efficiency. With a summer load, a 39%
losses, such as cluster 16 - 22 and 69 - 72. Within cluster 64 reduction in losses translates to only a 0.5% rise in efficiency.
- 67 the ranking order reverses with bus 64 at the lateral end Although results are only shown for a generator power factor of
being more sensitive to voltage yet all four buses show similar 1, similar results were seen for the other cases, with a leading
loss sensitivities. The results shown in Figs. 7, 8, 9 are obtained power factor leading to most significant loss reduction. (Note
using LSI based solution algorithm in Fig. 2 for the three load that the efficiency is the ratio of real power losses to real power
conditions (winter, summer, spring) and three generator power input. Real power input is the sum of real power losses and real
factors of 1, 0.95 leading and 0.95 lagging. In all cases, a so- power loads.)
lution was reached when 20% penetration was achieved, i.e., a
breach of constraint (10). The network performance is also analyzed for VSI-based op-
timal placement. As expected, due to similarity in optimal sites,
Fig. 7 shows a noticeable improvement in voltage profile the reduction in losses and hence improvement in system effi-
along the feeder. Note that in Fig. 7, all voltage profiles have ciency were virtually identical to those shown in Figs. 8 and 9.
been normalised so that the source voltage (node 1) is equal to The voltage profile comparison illustrated in Fig. 10 shows sig-
the winter level of 1.04 pu. Despite only a 20% penetration, nificant improvement in voltages along the feeder but no major
there is roughly a 2% rise in voltage, even in buses on the main differences arising from siting methods. Although not included,
feeder geographically distant from the generators. A similar a set of results for fault levels was obtained. These indicated
 Fig. 8. Real Power Losses for Unity Power Factor DG

Fig. 4. Test Feeder Schematic

Fig. 9. System Efficiency for Unity Power Factor DG

strictions on its placement.

IV. G ENETIC A LGORITHM FOR R ECLOSER P LACEMENT

In a DG-enhanced feeder, the optimization of reclosers is not
as straightforward as in the case of a conventional feeder, due
Fig. 7. Voltage Profile for Feeder with LSI Placed DG and Winter Load
to the presence of additional generators, which may be able to
satisfy portions of the feeder load after fault has been isolated,
an average rise of 7.9% with no line experiencing more than a as shown in the simple example presented above in Fig. 1. In a
20%increase. In Fig. 11, the ratio between loss reduction and large, meshed network, the task of locating optimal recloser po-
total installed DG capacity is shown giving a further insight into sitions that would create possible self-supporting islands is not
how the reduction of system losses due to DG can be exploited, trivial. The optimal recloser position(s) depend on the types,
especially during peak load. locations and sizes of distributed generators deployed at the
The case study yields a set of numerical results for optimally feeder. Conversely, if the reclosers are already placed on the
placed DG that the system can accept under particular load and feeder, optimal DG positions and sizes can also be determined.
generator power factor conditions. These represent a conser- Finally, both the placement of reclosers and DG can be opti-
vative estimate with DG added to the most sensitive nodes. If mized concurrently during the planning stage of the feeder de-
the same quantity of DG were added to less sensitive nodes, the sign. In this study, a simple genetic algorithm (GA)is proposed,
voltage rise or loss reduction will be less significant, although based on the algorithm presented in [15], to solve for optimal
line flows and fault levels may become limiting factors. For sys- recloser positions, by minimizing the composite reliability in-
tem planners and operators, this conservative estimate is likely dex (CRI), described in (14).
to be of much greater value than a ’best case scenario’ value (SAIF I − 1) SAIDI − 2.2 M AIF Ie − 7
showing that more DG could be accepted, but with greater re- CRI = 0.2
SAIF I
+ 0.4
2.2
+ 0.4
7
(14)
 subject of this paper. For each recloser configuration, a com-
posite index is calculated by determining the reliability zones
(zones bounded by the reclosers), simulating the faults in those
zones, determining the online and offline loads, and finally cal-
culating the composite index. For each reliability zone that has
a DG, after a fault in other zones, the maximum output of all
zone generators is compared with the load duration curve for
zone loads, and the number of faults is reduced by the percent-
age of time that the zone generation exceeds zone load.
The results of the algorithm are presented in Table I, which
shows the top three values for the composite index, and corre-
sponding branches at which reclosers are placed, when up to
four reclosers are strategically placed on the feeder. The branch
numbering corresponds with numbering shown in Fig. 4. Two
Fig. 10. Voltage Profile for Unity Power Factor and Winter Load cases are considered: the feeder without DG, and with 20% DG
penetration with the ten generators sited by the VSI. In the one
recloser case, the recloser placement is dominated by the ”con-
ventional” benefits obtained by placing the recloser towards the
middle of the feeder. The additional benefits, obtained by re-
ducing the number and duration of outages during islanded op-
eration, do not justify placing a recloser at a different location.
In the case with two reclosers, we note that the optimal re-
closer positions differ significantly. Without DG, reclosers are
optimally placed at branches 15-22 and 42-55, isolating two
portions of the feeder downstream from buses 15 and 55, and
allowing the remaining customers to continue receiving service
even after the fault in the isolated areas. In a DG-enhanced
feeder, reclosers are concentrated closer to the DGs, creating is-
lands of supply for customers downstream from bus 15. Similar
to the one-recloser case, for a fault upstream from bus 15, the
whole portion of the feeder downstream from bus 15 may op-
Fig. 11. Loss reduction / Installed DG
erate as an island. The placement of the second recloser at the
branch 12-68 creates additional possible island for customers
downstream from bus 12; they may now remain on-line even
Genetic algorithms are suitable candidates for such optimiza- after a fault between reclosers. As a result, the reliability index
tion problems, due to the nature of the optimization function. drops to 0.0037, as compared to the 0.0672 in the case without
The search space is spanned by mimicking the natural princi- DG. Note that if we placed reclosers at buses 15-22 and 42-55
ples of reproductive evolution. Starting from an initial popu- (optimal placement for a feeder without DG), the index in the
lation of individuals, GAs effectively implement the ’survival case with DG would be 0.0247.
of the fittest’ strategy - fitter individuals (those with higher val- A similar trend continues for the cases with more than two re-
ues of the optimization function) are more likely to reproduce closers. In some cases, the composite index becomes negative,
and/or survive to the next generation, thus improving the over- indicating the target values for reliability indices have been ex-
all population. The population evolves using two genetic op- ceeded. This is because target values for reliability indices used
erators, mutation and crossover. Various techniques exist for in the definition of the composite index in (14) represent suffi-
selecting the individuals that will continue on to the next gener- cient level of reliability for a conventional distribution network.
ation, and/or be chosen for mutation and crossover, which can
all be fine-tuned depending on the application. The GA termi-
V. C ONCLUSIONS
nates either after a pre-specified number of generations or after
population converges to a single solution. This paper has presented a methodology for optimizing and
The test feeder was used to demonstrate the algorthim, with coordinating the placement of distributed generators and re-
DG placed at the optimal nodes from the voltage sensitivity closers in a security constrained distribution network. A sys-
analysis - see Fig. 4. It is assumed that the fault incidence tematic and rational placement of distributed generation and re-
rate and the duration of faults (damage restoration time, DRT) closers is shown to be able to improve both system security and
are uniform over all feeder branches. Also, in the case of the reliability, by improving feeder voltage profile, reducing losses
fault, only the minimum number of reclosers closest to the fault and increasing efficiency, and providing energy to some of the
should operate, and isolate the fault. The actual implementation customers, even after the fault in the distribution system. The
of the control algorithm required for such operation is not the level of improvement depends on the type, number and size of
 TABLE I
T HE C OMPOSITE R ELIABILITY I NDEX FOR DG E NHANCED F EEDER AND VARIOUS R ECLOSER P LACEMENT S TRATEGIES

Number of Without DG With DG

Reclosers Index Value Recloser Positions Index Value Recloser Positions
0.1862 15-22 0.1351 15-22
1 0.5855 14-15 0.4717 14-15
0.6063 14-69 0.4840 14-69
0.0672 15-22, 42-55 0.0037 12-68, 15-22
2 0.0677 15-22, 4-55 0.0066 14-15, 15-16
0.0794 14-15, 15-16 0.0212 13-69, 15-16
-0.0397 42-55, 14-15, 15-16 -0.1648 2-53, 15-22, 46-75
3 -0.0391 4-55, 14-15, 15-16 -0.1610 2-22, 15-22, 46-75
-0.0276 42-55, 15-16, 15-22 -0.1534 2-53, 15-22, 27-58
-0.2519 2-53, 14-15, 15-16, 46-75 -0.2962 2-53, 12-68, 15-22, 46-75
4 -0.2494 2-22, 14-15, 15-16, 46-75 -0.2923 2-22, 12-68, 15-22, 46-75
-0.2429 2-53, 14-15, 15-16, 27-58 -0.2847 2-53, 12-68, 15-22, 27-58

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age needs. VI. B IOGRAPHIES
James Greatbanks (S’02) received his MEng degree from Imperial College
London in 2002. Currently he is working towards his PhD at Imperial College
London.
R EFERENCES Dragana Popović (M’99) received her BSc and MSc degrees from the
University of Belgrade, Yugoslavia in 1987 and 1991 respectively. In 1996
[1] F. Alvarado, “Locational aspects of distributed generation,” in Proceed- she received her PhD degree in Electrical Engineering from the University of
ings of the IEEE Power Engineering Society Summer Meeting, 2001. Newcastle, Australia. She is currently a Lecturer at Imperial College London.
[2] T. E. McDermott and R. C. Dugan, “Distributed generation impact on Miroslav Begović (S’87, M’89, SM’92) received the BSc and MSc degrees
reliability and power quality indices,” in Proceedings of the Rural Electric from Belgrade University, Yugoslavia, and the PhD degree from Virginia
Power Conference, vol. D3, pp. 1–7, 2002. Polytechnic Institute and State University, Blacksburg, all in electrical
[3] L. A. Kojovic and R. D. Willoughby, “Integration of distributed gener- engineering. Currently he is an Associate Professor in the School of Electrical
ation in a typical USA distribution system,” in Proceedings of the 16th and Computer Engineering at Georgia Institute of Technology, Atlanta.
CIRED, vol. 4, p. 5, 2001. Aleksandar Pregelj (S’98) received the BSc degree in electrical engineering
[4] L. Dale, “Modeling the reliability impact of distributed generation,” in from Belgrade University and the MSc degree in electrical engineering from
Proceedings of the IEEE Power Engineering Society Summer Meeting, Georgia Institute of Technology, Altlanta, in 1997 and 1998 respectively. He is
vol. 1, pp. 442–446, 2002. currently working towards his PhD at the School of Electrical and Computer
[5] M. Begovic et al, “Impact of renewable distributed generation on power Engineering, Georgia Institute of Technology.
systems,” in Proceedings of the 34th Hawaii International Conference on Tim Green (M’89, SM’02) studied Electrical Engineering at Imperial College
System Science, 2001. and obtained a PhD in Electrical Engineering from Heriot-Watt University,
[6] G. Carpinelli et al, “Distributed generation siting and sizing under un- Edinburgh in 1990. He is currently a Senior Lecturer and Deputy Head of the
certainty,” in Proceedings of the IEEE Porto Power Tech Conference, Control and Power Research Group at Imperial College London.
September 2001.

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