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398 IEEE Transactions on Power Systems, Vol. 12, No. 1, February
1997
UTION NETWORK RECONFIGURATION FOR ENERGY LOSS REDUCTION
Kubin Taleski, Member IEEE Dragoslav RajiCid, Member IEEE
University "Sv. Kiril i Metodij," Faculty of Electrical Engineering
Skopje
Skopje, Republic of Macedonia
Abstract A new method for energy loss reduction for distribution
networks is presented. It is based on known techniques and algo-
rithms for radial network analysis -- oriented element ordering,
power summation method for power flow, statistical representation
of load variations, and a recently developed energy summation
method for computation of energy losses. These methods, com- bined
with the heuristic rules developed to lead the iterative proc- ess,
make the energy loss minimization method effective, robust and
fast. It presents an altemative to the power minimization methods
for operation and planning purposes.
Keywords: Daily load curve, Energy losses, Energy loss
reduction, Energy summation, Oriented ordering, Power losses, Power
loss reduction, Power summation, Radial network,
Reconfiguration.
INTRQDUCTION
Radial networks have some advantages over meshed net- works such
as lower short circuit currents and simpler switching and
protecting equipment. On the other hand, the radial structure
provides lower overall reliability. Therefore, to use the benefits
of the radial structure, and at the same time to overcome the
difficulties, distribution systems are planned and built as weakly
meshed networks, but operated as radial networks.
The radial structure of distribution networks is achieved by
placing a number of sectionalizing switches in the net- work
(usually referred to as tie switches) used to open the loops that
would otherwise exist. These switches, together with the circuit
breakers at the beginning of each feeder, are used for
reconfiguration of the network when needed. Obvi- ously, the
greater the number of switches, the greater are the possibilities
for reconfiguration and the better are the effects.
Generally, network reconfiguration is needed to: i) provide
service to as many customers as possible following a fault
condition, or during planned outages for maintenance purposes, ii)
reduce system losses, and balance the loads to avoid overload of
network elements [l].
There have been a number of works concerning resistive line
losses reduction in distribution networks through recon- figuration
[ 1-91. Generally there are two approaches to the
96 WM 305-3 PWRS A paper recommended and approved by the IEEE
Power System Engineering Committee of the IEEE Power Engineering
Society for presentation at the 1996 IEEE/PES Winter Meeting,
January 21- 25, 1996, Baltimore, MD. Manuscript submitted July 25,
1994; made available for printing December 15, 1995.
reconfiguration problem. The first approach would be to de-
termine the status of all switches in the network simultane- ously.
Due to the combinatorial nature of the problem, very complicated
mathematical techniques should be used and large computational time
is needed. Usually, the solution ob- tained by methods using this
approach represents a global optimum of the loss optimization
problem.
The second approach would be to deal with each possible loop
(determined by an open tie switch) one at a time. Methods based on
this approach are simpler and faster. The simplicity and speed are
achieved by introducing heuristic techniques and approximations.
Sometimes these methods lead to a local optimum that closely
approximates the global optimum.
Traditionally optimal configurations are obtained by minimizing
power losses. For a given period, a moment of time is chosen as a
representative state of the load conditions in the network (usually
the system peak) and a power loss optimization method is used to
determine the configuration of the network.
The problem of loss minimization becomes very complex if energy
losses are to be optimized. Since loads change on an hourly basis
or even shorter, configuration of the network may need to be
changed accordingly. In [7,8,9] the problem of non-coincidence of
peak loads, and diversity of load c gories was addressed and
implemented in energy loss mini- mization methods.
To provide operation with minimum power and energy losses, the
network should be equipped with remotely oper- ated tie switches,
preferably in every line of the network to accomplish the highest
level of flexibility. Even though such an operation can provide
significant savings [7], it requires increased investment and
operational costs needed for highly automated control and
monitoring system.
The method proposed in this paper can be used to deter- mine the
configuration with minimum energy losses for a given period. It is
based on several favorable characteristics of methods and
techniques specially developed for radial network analysis --
oriented ordering of the network ele- ments, power summation method
for power flow, and statis- tical representation of load
variations, all together combined in the energy summation method
for computation of energy losses [lo].
Basically, the method belongs to the methods known as "branch
exchange techniques." Possible loops in the net- work (or feeder
pairs) are analyzed and reconfigured one at a time. The
reconfiguration is performed by closing the open tie switch that
defines the loop, and opening the switch in the branch that
produces maximum savings in energy losses.
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399
' _ _ _ _ ) I
The candidate branch to be opened is chosen using a similar
approximate technique found in [3], but applied for energy losses,
rather than power losses. The order by which the loops are analyzed
and reconfigured is determined by heu- ristic rules. A number of
power loss minimization methods based on the branch exchange
technique have used heuristics to determine the open switch to be
closed, for example [ 1,3,5,6]. However, since those methods deal
with a particu- lar moment of time, the same heuristic rules can
not be ap- plied, as loads and voltages vary with time.
The proposed method may have advantages over tradi- tional
methods that take into account only power losses. On the other
hand, it requires more input data to describe varia- tions of
loads, daily load curves (DLC) for typical consumer types in
particular. However, it is not necessary to know DLCs for every
load point in the network. Usually there are arbitrary number of
different typical consumer types, much less than the number of load
points. Consumers of a certain type have DLCs of equal or similar
shape, but with different magnitude (peak active and reactive
power). If DLCs are expressed in p.u. of their peak active power,
the only data needed to represent the load at a load point is the
maximum active and reactive powers, and the DLC type. Furthermore,
the proposed method allows the load at a load point to be expressed
as a combination of different consumer types.
GLOSSARY OF SYMBOLS
- Branch
T - duration of the load curves; nt - number of time intervals
in T; n - number of consumer types in the network;
P and Q - active and reactive power, respectively; p and q -
active and reactive power in p.u. of peak load for
load curves, respectively; I and V - current and voltage,
respectively;
R - line resistance; W - energy;
e,f- components of typical loads at load points (in P.u.) for
active and reactive power, respectively;
- second statistical moment of a random variable. The following
symbols are used combined with the gen-
eral symbols: A - denotes energy or power losses, or time
interval;
'I - denotes a quantity at the receiving end of an ele-
ment;
P and Q - as superscript denote that the variable is associ-
ated with active and reactive power or energy, re- spectively;
m - lower case letter as subscript denotes that the vari- able
is associated with an element;
M - upper case letter as subscript denotes that the vari- able
is associated with a node;
i, j and k - as sub-subscripts denote that the variable is asso-
ciated with load curve of type i, j or k;
t - as sub-subscript denote that the variable is associ- ated
with a particular moment of time (interval) t;
- bar over a variable denotes average value (power); - - bar
under a variable denotes a complex quantity. -
orientation
Z' A
Link b _ _ _
Lx
Fig. 1 Two feeder (one loop) distribution network
We will assume that every branch in the network is equipped with
a switch. To maintain the radiality of the net- work the switch in
one of the branches (branch a in Fig. 1) is open. Network elements
are numbered using the oriented ordering algorithm described in
[lo]. As a result of the or- dering, a branch (and its receiving
node) is assigned a num- ber (index) in the ordered list that is
always greater than the index of the sending end. The orientation
of branches in the network is positive fi-om the sending node
(lower index) to the receiving node (higher index).
If the open switch in line a is at the side of node Z, intro-
ducing the fictitious node Z', branch a can be treated as a branch
of the network with no load flowing in it. The posi- tive
orientation af the loop is defined fi-om the node with lower index
(Z) to the node with higher index (2'). Through- out the paper we
will use the term loop as a synonym for an open tie line. The same
terminology will be used instead of the termfeederpair, because a
single feeder may have a loop within.
It is assumed that peak loads and corresponding typical DLCs are
known at each load point, and that there are n dif- ferent consumer
types. We will also assume that at each load point the resulting
load can be represented as a sum of n dif- ferent consumer types
(1). Furthermore, each load can be of constant power, constant
current, or constant impedance type [lo]. Similarly, the proposed
method in this paper assumes balanced three-phase loads and network
elements, but it can be adapted for use in case of unbalanced
networks.
n n
t = 1, ..., nt .
The purpose of the reconfiguration is to determine which branch
in the loop should be opened, instead of branch A-2, to obtain
minimum energy losses. Let us assume that branch x is the branch we
are looking for. If the network is analyzed only at a particular
moment, the effect of the reconfiguration (change in power losses
in the loop) can be estimated by us- ing (2), as in [3]:
The reconfiguration, or in other words the load transfer from
feeder a-nl to feeder z-n2, can be simulated by injec-
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400
tion of complex current equal to the current flowing through
branch x at nodes Z and Z', with directions shown on Fig. 1. By
doing this, the current in branch x will become zero -- which is
equivalent to the effect of closing the switch in branch a, and
opening the switch in linex.
However, (2) can not be applied if energy losses are to be
estimated. But, a similar formula can be derived if the en- ergy
summation method [lo] is used. Briefly, if statistical
characteristics of the DLCs are calculated (second moments of
random variables that compose DLCs), the average power losses in a
particular branch m (defined as a quotient of ac- tive energy
losses and period r ) can be calculated from (3):
According to [IO], voltage magnitude V, in (3) is the av- erage
voltage at the receiving end of line m, obtained from a power flow
calculation with average loads (average power) applied at load
points.
Let us, for the time being, assume that (average) node voltages
will not change significantly due to the load transfer performed by
the reconfiguration. By analogy, the recon- figuration can be
simulated if an average complex power, equal to the average complex
power at the receiving end of branch x, is injected at nodes 2 and
2'. But the location of the switch to be opened is not known, so we
will fmd the amount of complex energy (average complex power)
needed to achieve minimum energy losses in the network. The branch
to be opened will be the one whose average complex power flow
equals the average complex power oktained.
Since there can be n different load types in the network, the
injected average complex power 6P+ j6e can be decom- posed into n
different components:
The active energy losses (or the average active power losses) in
branch m, after the injection of the complex power sP+ J ~ Q at
nodes Z and Z', can approximately be calculated using (5).
According to the use tation, the plus sign in (5) is orientation
coincides with the
The apount of average power loss change in line m can be
applied for branches orientation of the loop (branches hom n2 to
z in Fig. 1).
estimated from (5) and (3), resulting into (6): change - upnew -
upold = -
M m - m m
and the amount of average power loss change for the loop can be
calculated from (7):
Function (7) reaches extreme if its first partial derivatives,
with respect to 6P and @ , are equal to zero:
, Equations (8) represent two sets of n linear equations
and,
after rearranging, they can be written as (9.a) and (9.b). I
m=a V&
k = l , ..., n ; ( 9 4
- 2 m=a V ,
k = l , ,n. (9.b) Right hand sides of (9.a) and (9.b) can be
calculated fiom
the average power flows in branches of the loop. Note that the
positive sign indicates a branch with opposite orientation in
respect to the loop orientation, and that (9.a) needed only for
those consumer types that are loop -- the remaining c complex power
are set t
matical solution of the problem. minimized if a branch in the
loo power flow satisfies relation (10).
Linear equations (9.a) and (9.b) losses can be
Obviously, it would be very hard, if not impossible, to find a
branch whose all n components meet the requirements from (10).
Therefore, the solution obtained fiom (9.a) and (9.b) has little
practical implementation, and it is presented only to justify the
technique proposed in this paper.
Since the direct solution of the problem is very compli- cated
to obtain, we will apply the technique used in [3]. With respect to
(I I), eq. (7) can be rewritten as in (12).
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401
Element ordering Set al l LOFs to .FALSE.
Optimize independent loops
The similarity between (2) and (12) is obvious. Equation (12)
can be used to estimate the amount of energy loss changes over
period T, achieved by closing branch a and opening the branch with
average complex power at the re- ceiving end equal to 6P + j6Q.
The change in configuration will alter the power flows in
branches affected by that change. At this point it would be
rational to test branches for possible overloads. For exam- ple,
current magnitude in branch n2 in every interval At can be
approximately calculated with (1 3) using average power flow at its
receiving end (14). Furthermore, if all branches in the feeder have
equal current limits, only the first branch should be tested
(branch n2 in Fig. 1).
Since node voltages are not known for every interval At, we can
use average node voltages, similarly to ( 3 ) . Tests showed that
errors produced by approximate formula (1 3) are of the same
magnitude as errors produced by (3) when branch energy losses are
calculated. According to [ 101 those errors are less than 5%, even
for heavily loaded networks.
THE ENERGY LOSS MINIMIZATION METHOD
The procedure described in the previous section would be
sufficient if applied simultaneously to all loops in the net- work,
but only if the loops do not have mutual branches. The problem
becomes more complicated if some branches in the network belong to
more than one loop. It is because load transfer in one loop can
affect power flows in the loops that share mutual branches.
The simplified flow-chart of the energy loss minimization method
is shown in Fig. 2.
At the beginning of the procedure, after the oriented or-
dering, loops (open tie switches) are identified, and for each loop
a loop optimality flag (LOF) is assigned. LOF when TRUE indicates
that the loop has been optimized. Then, the
~
I
Calculate average node voltages and average power flows Set LOFs
to .FALSE. for loops with changed power flows
i
I
r Select next loop for optimizaaon ' Estimate energy loss
changes Select a branch to be opened
I / \
_ _ _ _ ~ i.
~ Change configuration and reorder network elements I I
17- ,:L-- Optimal configuration found 1
L
Fig 2 Simplified flow-chart for the proposed algorithm
independent loops are identified -- we will use the term inde-
pendent loops for those loops that do not have any mutual branches.
For these loops the procedure for selection of a branch to be
opened is applied simultaneously, and the loops are marked as
optimized (their LOFs set to TRUE), because they do not have to be
further analyzed.
The remaining of the procedure is iterative. At the be- ginning
of each iteration a power flow is performed to calcu- late average
node voltages needed for the energy loss calcu- lation that
follows. (Note that energy loss calculation is also performed in
the previous step for optimization of the inde- pendent loops.)
Then, the active energy losses for each loop are tested to
determine which loops were affected by the re- configuration in the
previous iteration. If such loops exist, their LOFs are set to
FALSE. At this stage branch current limits can be tested, and if
necessary take appropriate action.
The process continues by selection of the next loop to be
optimized. At this point it should be noted that the order by which
loops are selected and optimized may significantly af- fect the
efficiency of the method. To avoid unnecessary it- erations
efficient criteria for loop selection must be estab- lished.
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Various power loss minimization methods based on the branch
exchange technique use different criteria to determine the order by
which the loops are analyzed. Usually, it is the voltage difference
across the open switches, or the power loss difference across the
two sub paths of the loop -- branches with coincident orientation
with the loop orienta- tion and the branches with oppmite
orientation.
For this method a set of specific heuristic rules was set up.
These rules are based on the analysis of the network topol- ogy and
the active energy losses for each loop. Parts of a complex radial
distribution network shown in Fig. 3 and Fig. 4 will be used to
explain the basic principles for selec- tion of the switch to be
closed.
The part of the network in Fig. 3 has one open tie switch (loop
Ll). A characteristic of loop L1 is that one of the sub paths does
not contain any branches. Let us assume, for the moment, that all
network elements are with identical parame- ters and that loads are
uniformly distributed. If this were true, the configuration with
minimum losses for a single loop could have been achieved by
opening the switch in the branch at the middle sf the loop. Even if
none of the as- sumptions above is true, it is normal to expect
that, eventu- ally, id the minimization process, the open switch
A-A would have to be moved on sub path A'-M-A, towards node A .
Therefore, loops like loop L1 should have priority for opti-
mization in the reconfiguration process.
The part of the network shown in Fig. 4 includes two open tie
switches: consequently, there are two loops (L2 and L3), oriented
as indicated by the arrows. Both loops have same root (node B), and
they overlap -- a part of loop L2 (branches between nodes B and
N> i s a subset of loop L3. We will refer to loops L2 and L3 as
an inner-outer loop pair (IOLP).
The relation between loops L2 and L3 (inner and outer loop) is
also used for construction of the heuristic rules. In most cases,
as tests showed, it is more efficient to optimize the inner loop
first. If the relation between those two loops has not changed (the
open switch in the new configuration is on the path B-C-C'-N), then
optimize the outer loop. The oriented ordering technique used for
the element ordering provides an efficient and fast detection of
IOLPs.
Note that, generally, more than two loops may have simi- lar
relationship. If more than two loops have at least one mu- tual
branch, they are considered as an innedouter loop group.
Furthermore, the identification of the most inner and the most
outer loop is accomplished by comparison of the energy losses
associated with the loops. The Ioop with the lowest energy losses
is declared as the most inner loop, while the loop with the highest
losses, as the most outer loop. For ex- ample, if loop L2 in Fig. 4
has lower energy losses than loop L3, L2 is an inner loop, whileL3
is an outer loop.
The selection of the loop to be optimized (or the open tie
switch to be closed) is performed by the following rules, listed by
descending order of precedence:
Select and optimize first loops with characteristics like loop
L1 in Fig. 3 (highly unbalanced energy losses over both loop's sub
paths). As described ear- lier, these loops are the most likely
candidates for op- timization. If these loops are not optimized at
this
Fig 3 Part of a radial distribution network with one loop
To substation Loop L3
Fig. 4 Part of a radial distribution network with two loops
early stage of the process, their later optimization can affect
the configuration in loops, thus requiring extra iterations.
exists, the se1 trary. When a pair or group is or group is not
selected until all optimized. The or mized in the group is from
outer loop. Due to the app (12), the accuracy o higher if the chan
modest changes in energy losses. Therefore, by op- timizing the
loops with lower losses (inner loops) the possibilities for false
estimates are lower. Select the next loop in the list of ordered
elements.
The application of these rules provides fewer iterations to be
performed. However, for networks in which many loops overlap, some
loops need to be optimized more than once.
The next step in the minimization procedure is to deter- mine
the branch to be opened. To avoid testing all the branches in the
loop, the first two branches adjacent to the open switch are
tested. If there are no power sources in the network (other than at
the slack ) the results of the tests will have opposite signs.
Equati the active energy loss change if branches z and b are opened
(Fig. 1). This is accomplished by substituting in (1 1):
Detect all IOL
Then, the branches on the path on which the first branch has
negative changes are checked. The energy loss changes become
positive, or i The branch with highest negative energy loss changes
so far is selected to be opened. sources at nodes other than the
slack nod energy and power flows in parts of the network can be
dis- turbed. If this is the case, the swi to be opened is deter-
mined by testing all branches in th
Finally, the last step in the procedure is the reordering of the
network elements. oted before, the proposed method, as well as the
pro s it uses (power and energy
However,
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403
lem of non-coincident peak loads is solved simpler -- their
magnitude is what counts, not the timing.
The problem of network reconfiguration is not solely a technical
problem. Usually it is a matter of utility compa- nies' policies.
Some utilities change their network configu- rations on a seasonal
basis, while other utilities reconfigure their networks more
fiequently. The methodology presented in this paper allows to
evaluate the benefits of more fiequent reconfiguration, for example
on weekdaylweekend basis, in addition to seasonal changes. Even
periods shorter than 24 hours can be used, for example off-peak and
peak load peri- ods [7].
TEST RESULTS
summation methods), are based on the oriented ordering of the
network elements. After a change in the configuration is performed,
it is necessary to update the indices in the list of ordered
elements.
The reordering can be simply accomplished by a full or- dering
such as the one performed at the top of the procedure. However, for
large networks this task could be time consum- ing. On the other
hand, only small segments of the ordered list are affected by the
reconfiguration, and it is rational to take advantage of that fact.
Therefore, a special technique for partial reordering was
developed. Tests performed on a 150-node (28 loops) radial network
suggest that speed gains over a full ordering are 5 to 10 times,
depending on the scale of the changes in the configuration.
A special characteristic of the proposed method is that it can
be used, with minor modifications in (12), as a power loss
minimization method as well. Note that if n=1, and the DLC is flat
( F&,) = Q = 1 ), average power losses become
power losses. Hence, equation (12) can be considered as a
general form of equation (2). Both minimization versions of the
method were tested on numerous networks, and they pro- duced
configurations with lowest energy or power losses, re-
spectively.
The proposed method for energy loss reduction is very simple and
fast. Both characteristics are achieved by the as- sumption that
average node voltages do not change much with each load transfer.
However, there are situations when this assumption can produce
false estimates in (12) and lead to a change in configuration with
higher energy losses. But, since energy losses are recalculated in
every iteration, such situations are easily detected, and the
changes are ignored by marking the current loop as optimized and
proceeding with the next one. The price to pay for that is an extra
iteration.
At this point it must be emphasized that the configuration of
the network with minimum energy losses over a period does not
necessarily mean it provides the most cost savings. There are
several issues to be considered, among them costs for switching.
For example, there are cases, as it happens with power loss
optimization methods, when expected sav- ings are marginal and
overwhelmed by switching costs. In addition, there are situations
when savings in energy losses may not be greater than the price
difference between lost power and lost energy.
On the other hand, the proposed method is capable of dealing
with networks and loading conditions in which maximum power losses
do not occur at system peak (example network in AppendixA), or when
maximum (energy) savings are expected during off-peak periods
[7,9].
Even though the proposed method deals with energy, it does not
require load curves for all load points. At most load points there
will be only one consumer category. Once typi- cal consumer groups
are determined, and they are assigned to load points, only
additional data, except peak loads, are the types of DLCs at load
points. Loads that do not conform to a single consumer category can
be mathematically decom- posed into n typical consumer load curves
(l), requiring knowledge of components e andfonly. Likewise, the
prob-
%,l)
The effectiveness of the proposed method for energy loss
reduction was tested for convergence and ability to provide
configuration with lowest energy losses. The method has not been
compared with other methods, since, by the authors' knowledge,
there are no similar methods suitable for com- parison.
Computer programs, Written in FORTRAN, were devel- oped and ran
on a 66MHz 486DX2 PC/AT compatible per- sonal computer. The power
and energy summation methods [lo] were used for all power flow and
energy loss calcula- tions. The nominal voltage was chosen as a
base voltage and as the voltage at the slack bus. In all cases
(power summa- tion method) the iterative process finishes if, in
two con- secutive iterations, changes in both network active and
reac- tive power losses are lower than 0.01 kWkvar.
Test results presented in this paper include two networks. The
first test network (10 kV, 16-nodes and 2 loops) is non existent,
but was constructed for demonstration purposes using realistic
data. Two types of consumer were adopted fi-om [ l 11: Urban
Residential Load (URL,), and Commercial Load (CL). The data for the
network elements, as well as for the loads, is presented in Table
I.
The results of the optimization for both energy and power losses
at system peak are presented in Table 11, and complex network load
and loss curves are presented in Figs. A.2 and A.3. The results
show that two optimal configurations differ significantly. Power
losses at system peak (8 p.m.) for both configurations are almost
identical. But, the configuration obtained for minimum power losses
at system peak has 6% higher energy losses, and 14% higher maximum
power, losses (10 a.m.) than the configuration obtained for minimum
en- ergy losses. However, not always the two minimization methods
result in configurations that differ that much, as proven with the
second test network.
The second test network (12.66 kV, 32-nodes and 5 loops) was
used in [IO], but originally found in [l]. Since the network in [l]
was used for power loss reduction, it had to be modified. Two
consumer types were assigned to the load points in the following
way: every odd node was as- signed URL type, while every even node,
CL type. Loads fiom [l] were used as peak loads. Also, nodes were
given names with the letter N preceding the number.
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TABLE I DATA FOR THE 10 KV TEST NETWORK
Branch Sending Receiving
node node I 0 0.00 0 55
030 012 025 010 025 010 0.25 0.10 025 010 0.30 0 12 025 010 030
012 050 020
Load at receiving node E G 7 G F E - I
kW h a r type
500 200 URL 500 200 URL 500 200 URL 500 200 URL 400 150 CL 450
150 CL 500 200 CL 400 150 CL 400 150 CL 400 150 CL 500 200 CL 400
150 CL 600 200 URL 600 200 URL 600 200 URL 600 200 CL
0 0
TABLE II COMPARISON OF BOTH OPTIMAL. CONFIGURATIONS
If the power loss minimization algorithm is applied (for the
moment when system peak occuss -- 8 p.m.), it leads to the
configuration defined by the following open lines: N6-N7, N8-N9,
N13-Nl4, N27-N28 and N31-N32. The number of iterations varies
depending on the starting con- figuration, but the final (optimal)
configuration is always identical. The power losses for the optimal
configuration are 105.6 kW, while energy losses over a 24 hour
period, are 1735.9 kWh. In this case, the same configuration is
achieved if the energy minimization algorithm is applied.
Many factors influence the differences between confgu- rations
obtained by the power and energy loss minimization methods, such
as: loads and types of loads, voltage variation at the slack node,
variances and covariance of DLCs, and network element parameters.
Since it is almost impossible to predict the outcome of both
minimization methods, the fmal decision about which configuration
should be used for most economical operation should consider
factors such as costs for power, energy, and switching.
To illustrate the effects of the heuristic rules used for se-
lection of the switch to be closed, the intermediate results of the
energy minimization algorithm for the second test net- work are
presented in Table 111. The starting configuration for this test is
defined by the following open lines: N7-N20, NS-Nl4, Nll-N21,
N17-N32 and N24-N28. The energy losses for this configuration are
2477.8 kWh. The results ob- tained using the heuristic rules are
presented in the first half of the table. The second half of the
table shows the results when no rules are applied -- the order by
which loops are
TABLE J l l INFLUENCE OF THE HEURISTIC RULES ON SELECTION OF
SWITCH TO BE OPENED
Iteration/ I Closeline I Open line I Energy losses (no ofloops
tested) I kWh
1 /(I) 1 N8 - N14 I N13 - N14 [ 2411.3 Loop selection by
heuristic rules
2 / (1) N7 - N20 N6 - N7 1897 9 3 /(1) N11 - N21 N8 - N9 1779.9
4 IC31 N17 - N32 N31 - N32 1744.1 5 l(4) N24 - N28 N27 - N28
1735.9
Loop selection by thelr position in the ordered list N24 - N28
N27 - N28 2141 0
1809 8 1 /(I) 2 I (2.) N21 - N11 N9 - N10
1795 8 1812 6 1780 5 1772 0 1753 2 1761 9 1735 9
selected is determined by their position in the list of ordered
elements. The numbers in parentheses show how many loops were
tested in each iteration before a decrease in the energy losses was
achieved.
Results in Table 111 show that the order by which loops are
optimized directly affects the performance of the pro- posed
algorithm. Note that if no heuristic is applied, the number of
iterations depends on the positions of the loops in the ordered
list of elements. Also note that in the 4. iteration and 7.
iteration there are false estimates resulting into energy loss
increase, requiring repetition with another loop.
Finally, some remarks about the speed of the energy loss ization
method. Most of the computational time in each iteration is used
for calculation of the energy losses. The number of loops tested
and the number of branches tested for (1 2) does not significantly
affect the time required for one iteration. For example, for the
second test network when heuristic rules are used, the average time
was 0.050 seconds per iteration.
CONCLUSIONS
A method for distribution network reconfiguration for en- ergy
loss reduction is presented. The method can be used to obtain the
configuration with minimum active energy losses over a period of
time and can be used as an advantageous al- ternative to the power
loss minimization methods. Its ro- bustness, effectiveness and
accuracy are inherited &om the energy summation method and
further improved by the heu- ristic rules used to lead the
minimization process. The com- putational time is almost identical
to the time needed by power loss minimization methods that makes
this method suitable for operation, as well for planning
purposes.
ACKNOWLEDGMENT
This work was supported in part by the Ministry of Sci- ence,
Republic of Macedonia.
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APPENDIX A: NUMERICAL EXAMPLE
LOOP LOF Awloop AW+ AW- AW+/AW- kWh kWh kWh
I
405
MI0 MI1 MI2 In this section we will present a brief numerical
example for optimization of the first test network (Table1 and Fig.
A.l). There are two loops in the network and they can be considered
as a loop pair, similar to the example in Fig. 4 (same root -- M,
and mutual line M-M6). Second moments p2 for DLCs (URI, and CL)
used in the tests are calculated fiom (A. 1) [ l I] and are
presented in Table A.1 in p.u. of av- erage power for the
corresponding DLC.
I = 1 ,..., n;/= 1 ,..., n , (A. 1 ) where all quantities in the
right hand sides of (A.l) are ex- pressed in p.u. of peak active
power for the corresponding DLC.
The next step is to determine the loop to be optimized first.
Active energy losses for each loop, as well as energy losses for
branches on the positive and negative path ( AW+ and AW- ), are
calculated and they are shown in Table A.11 (1. iteration).
Loop M15-Ml6 is chosen to be optimized first for the following
reasons: it is considered as an inner loop (lower energy losses,
47.8 kwh) and it has higher unbalanced losses across both paths
(0.281 11).
TABLE A.1 SECOND MOMENTS FOR DLCS USED IN THE TESTS h 1
1. Iteration Active network losses: 1729.2 kWh M15-Ml6 I FALSE I
47.8 I 10.5 I 37.3 I 0.28111 M5 -M9 I FALSE I 49.2 I 20.1 I 29.1 I
0.68920
2. Iteration Active network losses: 1632.2 kWh
Next, it should be determined which branch in the loop provides
highest energy loss reductions if opened. Estimates for energy loss
reductions if adjacent lines to line M15-Ml6 are opened, are
calculated using (12):
Open line Estimates for energy loss reduction (kWh) M12 - MI6
96.0 MI4 - MI5 -318.3
lese L MI M2 M3 M4 M5
Fig. A.l Graph of the 10 kV test network
Estimates show that branches on the path M15-M if opened would
produce increase in energy losses. Next, line Mll-M12 is tested and
the test shows that, if opened, that line will produce energy loss
reduction equal to 9.3 kwh. Line M12-Ml6 is the best candidate
since it yields to highest reduction if opened.
The next iteration starts with calculation of energy losses for
the new configuration. Results of the calculations are shown in
Table A.11 (2. iteration). Note that loop M12-Ml6 is marked as
optimized (LOF'TRUE). Estimates for energy loss reduction for
adjacent lines to line M5-M9 are:
Open line Estimates for energy loss reduction (kWh) M8 - M9
-77.6 M4 - M5 -56.1
Since opening neither line produces energy loss reduction, this
loop is marked as optimized, leaving us with no loop to be further
optimized.
In the configuration determined for minimum power losses at
system peak, the most loaded branch is M-M6. At 10 a.m. it is
loaded at 93% of its thermal limit (255 A), while at 8 p.m. (system
peak) it is loaded at 64% (Fig. A.4). In the final configuration
obtained for mi&" energy losses the same branch is loaded at
77% of its limit (10 a.m. Fig. AS). Minimal voltages for both
configurations are 0.9543 and 0.9636 P.u., respectively.
S (kVA) 8000
AP (kW) S,,=7247.1 kVA 2oo
2000 50
1000 t t O
0 2 4 6 8 10 12 14 16 18 20 22 24 Time
Fig. A.2 Apparent load and active power loss curves for the
network in the configuration with minimum power losses at system
peak
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406
S (kVA)
8ooo i AP (kW
S,,=7247.5 W A T 2oo
0 2 4 6 8 10 12 14 16 18 20 22 24 Time
Fig A 3 Apparent load and active power loss curves for the
network in the configuration with minimum energy losses
kW, kvar 4000 T
Line M-M6
3000
2000
1000
-P -Q 0 - 9 : , / # : I / 8 I 8 ; 8 : # I > l , I > : I
/
0 2 4 6 8 10 12 14 16 18 20 22 24 Time
Fig A 4 Load curves for the most loaded branch in the network in
the configuration with minimum power losses
kW, kvar
4000 i Line M-M6
P -Q - i 07-3 : ' I , I ' I ' : ' I , I , I , ~, I I : I I 0 2 4
6 8 10 12 14 16 18 20 22 24
Time
REFERENCES
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Rubin Taleski (M '90) was born in 1957. He received his B.S. and
M.S. degrees, both in Electrical Engineering, from the University
"Sv. Kiril i Metodij" in Skopje in 1980 and 1990, respectively.
During the period 1981-1987 he worked at the Institute for Energy
in Skopje. In 1987 he joined the Faculty of Electrical Engineering
in Skopje, and presently he is a teaching assistant in Power
Systems at the same University. His subjects of interest are
computer appli- cations in power and distribution system
analysis.
Drugoslav Rujicic (M '86) was born in 1935. He received his B.S.
from University "Sv. Kiril i Metodij" in Skopje and M.S. and Ph.D.
from the University of Belgrade, all in Electrical Engineering.
Presently he is a Professor at the Faculty of Electrical
Engineering at the University "Sv. Kiril i Metodij" in Skopje. His
current area of interest is analysis of transmission and
distribution systems.
Fig. A.5 Load curves for the most loaded branch in the network
in the configuration with minimum energy losses
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