IEEJ TRANSACTIONS ON ELECTRICAL AND ELECTRONIC ENGINEERINGIEEJ Trans 2012; 7: 471–477Published online in Wiley Online Library (wileyonlinelibrary.com). DOI:10.1002/tee.21760
Paper
Power Loss Minimization Considering Short-Circuit Capacity in DistributionSystem with Decentralized Distributed Generation
Recently, in order to mitigate global warming, many researchersaround the world are making efforts to reduce greenhouse gasemission. In electric power system, distributed generation (DG),which can reduce the energy exhausted and CO2 emission,becomes more and more attractive. However, with increase inthe penetration of DG, the distribution network will becomemore complex and more difficult to control, and some technicalproblems will appear such as steady-state voltage raised by reversepower flow from DG, power quality deterioration by flickers andharmonics, etc. [1–4]. In the future, with a large number ofrotary DGs, two problems may emerge in the distribution powersystem. One is that the profile of power flow will change andvoltage will rise because of the reverse power flow from DGs innormal operation. Also, the quantity of reverse power flow will bealso differ with load variation during the day, and therefore lossoptimization has to consider this load variation also. The other isthat the short-circuit capacity (SCC) will increase and may becomehigher than the rated maximum of the existing circuit breaker(CB) due to the connection of DG. These may cause system costincreases and damage to the devices; furthermore, the reliability ofthe power system will be also impacted. Therefore, these problemsshould not be ignored.
Network reconfiguration is the process of changing the topologyof distribution systems by altering the on/off status of switches.This method is usually done for loss minimization, load balanc-ing, Volt/Var support, and restoration [2,3]. Distribution networkreconfiguration is a combinatorial optimization problem. In orderto resolve the problem of a suitable pair of switches to obtainthese objectives, many methods have been proposed. They are
Graduate School of Engineering, Yokohama National University, 79-5Tokiwadai, Hodogaya, Yokohama, Kanagawa 240-8501, Japan
mathematical programming (e.g. linear programming, sequentialquadratic programming, dynamic programming) and heuristicsmethods, such as neural network [4], simulated annealing [5],genetic algorithm [6], tabu search [7], and so on.
In the past 15 years, the particle swarm optimization (PSO) [8]algorithm in heuristics research has been proposed and improved.It has also been utilized to solve the various problems of thedistribution network gradually [9,10]. It is much simpler and easierto implement than other methods. And, binary PSO (BPSO), abinary version of PSO for discrete problems [11], has been shownto be powerful in realizing distribution network reconfigurationand achieving the best suitable combination of switches.
Currently, with regard to the approaches of SCC reduction, thefollowing main methods are recommended:
1. Change the CB with a larger interrupting capacity;2. Change the devices with larger impedance;3. Divide the system by a back to back (BTB) DC system;4. Utilize a reactor;5. Change the network configuration.
Methods 1–4 are probably effective in decreasing SCC, but theyall lead to increase in equipment cost. Method 5 involves only achange in the operating mode of the network and is economical.It can be implemented by network reconfiguration.
In this paper, network reconfiguration is used for loss minimiza-tion and SCC reduction. The optimal combination of sectionalizingtie switch pairs is determined by the BPSO algorithm. Moreover,a new treatment of inequality constraints based on double fitnessesis proposed during the simulation. The calculation of fault currentduring SCC reduction utilizes the original prefault data. Therefore,the calculation time can be reduced. This paper also proposes thedivided-stage load method to resolve the problem of power lossincrease with load variation. In addition, the divided point of timeis also selected by the BPSO algorithm. The details are describedin the following sections.
2.1. OPF formulation Because of a large number ofconnected distributed generators, the distribution network ischanged from a single source into multiple sources. It increasesthe complexity of the existing network. The power loss in the lightload condition will be increased, and voltages of some nodes willbe also raised because of the large amount of reverse power flowin the branches. During a fault, the fault current flowing throughthe CB will also increase because of the current not only from theupper system but also from the distributed generators. In this paper,we consider power loss minimization as the objective and SCC asone of constraint conditions during distribution network reconfig-uration with DGs. Mathematically, the problem can be formulatedas follows:
[Objective]
Minimizef (X ) = Ploss =T2∑
i=T1
Nb∑j=1
kij I2ij rj (1)
whereIij is the current of branch j at i o’clock,rj is the resistance of branch j ,Nb is the number of branches in the system,X is the switch status array,T1, T2 are the time, andkij is the switch status of branch j at io’clock; if branch j isenergized, kij = 1, else kij = 0.
[Constraints](Power flow equations)
PGi − PLi − Vi
N∑k=1
vk {Gik cos(θi − θk )
+ Bik sin(θi − θk )} = 0 (2)
QGi − QLi − Vi
N∑k=1
vk {Gik sin(θi − θk )
− Bik cos(θi − θk )} = 0 (3)
(Voltage limit)
Vij min ≤ Vij ≤ Vij max (4)
(Switch status)
SWi ={
0 (if switch i is open)
1 (if switch i is closed)(5)
(Branch capacity limit)
Iij < Ib max (6)
(SCC limit)
SCC < SCCmax (7)
(Radial distribution system)
Neb = N − 1 (8)
Rank (A) = N − 1 (9)
whereN is the number of nodes,PGi , QGi are the generation active and reactive power output atnode i ,PLi , QLi are the load active and reactive power at node i ,Vi , θ i are the voltage and phase of node i ,vk , θ k are voltage and phase of node k ,
Gik , Bik are the conductance and susceptance between nodes iand k ,Vij min, Vij max are the maximum and minimum voltage limits ofnode j at i o’clock,Ibmax is the maximum branch current,SWi is the status of switch i ,SCCmax is the maximum of SCC,Rank(A) is the row rank branch-to-node incidence matrix A, andNeb is the number of energized branches.
2.2. Calculation of Short-Circuit Capacity SCC atany location d in power system is the result of short-circuit currentmultiplied by the voltage. It can be obtained as
Ssccd =√
3Ifd Uld (10)
where Ssccd is SCC at location d , Ifd is the three-phase short-circuitcurrent flowing through location d , and Uld is the line voltage atlocation d . In (10), the line voltage can be got by power flowcalculation and Ifd can be calculated by the node voltage of post-fault and branch impedance. In order to get the post-fault data, thefault current of the fault point must be calculated first. Therefore,the key point of the calculation of SCC is the calculation of thethree-phase short-circuit current Ifp of the fault point. In this paper,the short-circuit current of the fault point is calculated by nodeimpedance elements [12], expressed as
Ifp = Uf |0|Zff + zf
(11)
whereUf |0| is the the pre-fault voltage of the fault point, which can begot by power-flow calculation,zf is the grounding impedance of the fault point, andZff is the the self-impedance element of fault point f in the post-fault node impedance matrix.Zff can be calculated from (12). Here, we suppose that the three-phase short-circuit fault has taken place at fault point f of branchjk in which the start node is j and end node is k , and the distancejf is d times (d < 1) the length of branch jk.
where Zjj , Zkk are the self-impedances of nodes j and k in thepre-fault node impedance matrix, Zjk are the mutual impedance ofnodes j and k in the pre-fault node impedance matrix, and zjk isthe branch impedance of branch jk.
Through the above description, the post-fault self-impedanceZff is obtained by the pre-fault data of the node impedance. Thenew node impedance matrix need not to be regenerated. Hence thecalculation time can be decreased.
2.3. DG type and fault type In the future, two connectmodes of rotary DG will appear. One is that the scale of theDGs is small and the distribution is strongly decentralized, such ascombined heat and power; the other is that DG is large-scale andcentralized, such as wind power generation. In this paper, we takeinto account that the free electricity market is enlarging and theenergy cost reducing, and the former mode is used for simulation.
With regard to the fault point and type, because the purpose offault calculation is to find out whether the current through the CBexceeds the the interrupting capacity of the CB, only the maximumshort-circuit currents should be considered in the worst condition.As is known, in all kinds of faults, the fault current of the three-phase short-circuit is maximum, thus the fault type is three-phaseshort-circuit when SCC is calculated. Moreover, in distributionnetworks with a radial configuration, fault point should be close toupper system because the capacity of the upstream system is large.
472 IEEJ Trans 7: 471–477 (2012)
LOSS MINIMIZATION CONSIDERING SCC WITH DECENTRALIZED DG
2.4. Loss minimization with load variation The lossis more because the load variation is large during a day. Therefore,it is not economical to operate by the same mode during the day.In order to reduce the loss in a day, we have proposed a solutionin which the actual load is simulated by the average load duringnetwork reconfiguration [13]. In that method, the time in a day isdivided into several stages and the average load is calculated ineach stage. Based on the average load, the optimal network andloss minimum in each stage can be found. Finally, the total lossminimization is obtained. However, the precision of this method islimited when the number of divided stages is small (such as 2 or1); in the worst case, the optimal network satisfying the constraintsmay not exist. In order to solve this problem, in this paper, basedon the idea of divided stages, a novel method is proposed. In detail,this method is to calculate the sum of the loss in each stage usedthe actual load and seek the optimal network of loss minimizationin each stage by BPSO; finally, the sum of loss in a day can beobtained. Moreover, to make the loss optimum, the divided timepoint is also implemented by the optimal algorithm.
3. Optimization Algorithm
3.1. Optimization method In this paper, BPSO is usedfor the optimal combination of switches. BPSO is an optimizationmethod of a discrete problem based on PSO [8] and was proposedby Kennedy and Eberhart in 1997 [11]. The major differencebetween BPSO and PSO is that the relevant variables (velocitiesand positions of the particles) are defined in terms of the changesof probabilities and the position of particles by integers in {0, 1}.BPSO can be described in general by
vk+1id = ω∗vk
id + c1∗ rand()∗ (pbestid − xki ) + c2∗ rand()∗
× (gbestd − xkid ) (13)
S (vk+1id ) = 1
1 + e−vk+1id
(14)
if (rand() < S (vk+1id )) then xk+1
id = 1
else xk+1id = 0 (15)
wherevk
id is the velocity of the i th particle in the d th dimension atiteration k ,xk
id is the position of the i th particle in the d th dimension atiteration k (in this paper, the switch status),ω is the inertia weight,rand() is a random number between 0 and 1,c1, c2 are the acceleration coefficients, which are usually set to2.0,pbest i is the personal best position in the i th dimension,gbest i is the global best position in the i th dimension, andS (vk+1
id ) is the logistic sigmoid transformation function.Equation (13) is to update the velocity of particle, and (14) and
(15) are to update the position of the particle. Moreover, in thispaper, in order to avoid local convergence and to accelerate theconvergence, the inertia weight (ω) is assumed to decrease linearlyduring the course of iteration, which is calculated by [14].
ωk = ωmax − k(ωmax − ωmin)
Tk max(16)
whereωk is the inertia weight at iteration k ,ωmax, ωmin are the maximum and minimum inertia weights, andTk max is the maximum iteration time.The decreasing ω-strategy is a near-optimal setting for manyproblems, since it allows the swarm to explore the search space in
the beginning of the run, and still manages to shift towards a localsearch when fine-tuning is needed. Usually, the inertia weight isin the range [0, 1]. ωmax should be near 1 because setting a highvalue contributes to the global search; on the other hand, in orderto speed up the local search, ωmin should be low. Moreover, theminimum is adequate in range [0.2, 0.5] [15]. Tkmax affects thecalculation time and the accuracy of the results. The calculationtime may become long if Tkmax is too large; on the contrary, if it istoo small, the iteration may end before better results are obtained.Hence, most of time, the value for Tkmax is selected empirically.
As described above, it is clear that the BPSO algorithm cannotbe applied to a network reconfiguration directly. The reason isthat the BPSO does not take into account the constraints. Hence,constraints must be dealt with separately. The equation constraintswill be satisfied in the network configured and power flowcalculated. In this paper, we focus on treatment of the inequalityconstraints. The double fitnesses will be formed to resolve thisproblem: namely, one is the loss-minimized fitness, the other is theconstraint fitness. That can be defined according to (17). Moreover,we assume that the constraint fitness plays a more important rolethan loss fitness. The reason is that the loss fitness can surelyconverge quickly to the solution zone.
xmin − x x < xmin
fconstraint(x) = 0 xmin ≤ x ≤ xmax (17)
x − xmax x > xmax
wherex is the variable of the constraint andfconstraint is the fitness of the constraint.
3.2. Algorithm of proposed method Not only thealgorithm of loss minimization considering SCC reduction andload variation by network reconfiguration but also the algorithmof optimal time division is based on the BPSO. It can be describedin detail as follows:
1. Input the data and initial parameters. For example, theimpedances of branches, active and reactive power of loads,initial status of switches, the number (Ns ) of divided stages,number of particles, and so on;
2. Iteration of optimal divided time begins;3. Confirm the divided stages number of each particle;4. Calculate the loss minimum of particle i in stage j , and
flowchart is shown in Fig. 1;5. Calculate the sum of loss for particle i in a day;6. Get the pbest of each particle and gbest of all of particles;7. Get the new divided time mode of each particle by (10)–(12);8. Confirm whether the condition of iteration end is satisfied; if
not, time of iteration plus 1, then go to step 3;9. Continue until a termination criterion [M < maximum of
iteration (Mmax)] is satisfied;10. Put out the gbest, which includes the loss minimum in a day,
the optimal switch combination in each time stage, and theoptimal divided time mode in a day.
Figure 1 is the flowchart of the network reconfiguration basedon BPSO for loss minimization and SCC reduction in a stage. Thewhole flowchart of our proposed method is shown in Fig. 2.
4. Case Study
Based on the configuration in Ref. [2], the data of the test systemis modified. The test system is a 6.6-kV distribution system with33 nodes and 37 branches (including 5 tie branches). The peak loadincludes 6.17 MW active power and 3.96 MVar reactive power.
473 IEEJ Trans 7: 471–477 (2012)
C. LIU, T. TSUJI, AND T. OYAMA
Obtain the new switch statusby equations (13)~(15)
Yes
Nok>Tkmax?
Power flow calculation
Short circuit capacity calculation
Calculate the constraints fitness
Calculate the loss fitness in this stage
Read data
k = k+1
Write optimal network
If fconstraints(X) < fconstraints (pbest) then X ⇒ pbestIf fconstraints (pbest) < fconstraints (gbest) then pbest ⇒ gbest
If fconstraints (pbest) = fconstraints (gbest) and
floss (pbest) < floss (gbest) then pbest ⇒ gbest
If fconstraints (X) = fconstraints (pbest) and
floss (X) < floss (pbest) then X ⇒ pbest
Fig. 1. Flowchart of network reconfiguration by BPSO
The initial network configuration is shown in Fig. 3. In the figure,solid lines represent the branches in service with closed switchesand dotted lines represent the cut-off branches with open switches.The numbers 0–32 represent the nodes 0–32 and the number with‘s’ represents a line switch. In the test system, the same rotary DGunits are installed in nodes 2–17 and nodes 22–24 because theloads are heavier in these two feeders than in other feeders. Thecapacity of each DG is 300 kW, and power factor of DG is 0.85and lagging. The subtransient reactance of DG is 0.161 p.u. relativeto its capacity. In the test system, the maximum of short-circuitcurrent through the CB is the same as through CB1 as CB1 is nearthe upper system and all of the fault currents from generators flowthrough it. Hence three-phase short-circuit is supposed to occur atthe outlet of CB1 (lines side) in location A (Fig. 3). The maximumof interrupting capacity of CB1 is also considered as a constraintof SCC during simulation.
The system constants is given in Table I.In the following simulations, the load variation will be consid-
ered when loss and SCC are calculated. The daily load curve insummer is shown in Fig. 4. The direct-axis value is the ratio oftime load to the maximum of daily load (at 14 o’clock).
4.1. Results of pre-reconfiguration The power loss,SCC, and voltage of the pre-reconfiguration are calculated. Thereare two cases for pre-reconfigured network during simulation. Theyare the initial network without DGs and the initial network withDGs whose data were described above.
4.1.1. Results of loss and short-circuit capacity In theinitial network without DGs, the total power loss is 8145.2 kWhand about 10% of the total load. SCC of CB1 is 121–123.5 MVAand under the limitation of SCC (143 MVA). When DGs areconnected, the reverse power flow occurs because the total capacity
No i = Ns ?
No
Obtain the loss minimumin this stage by BPSO
Yes
Start
Read data of system
Divided stage i = 1
Divided mode M = 1
i = i+1
Obtain the loss minimumin this mode
YesM< Mmax
M = M+1
Get the next divided mode
Write data(loss minimum optimal network
optimal divided time)
End
Fig. 2. Flowchart of loss minimization and SCC reduction withload variation
0
A
1 3 10 11 12 13 14 15 16 17
18 19 20 21
22 23 24
25 26 27 28 29 30 31 32
Swingnode
66kV/6.6kV
S1 S2 S3S4
S5 S6 S7S8 S9
S10 S11 S12 S13S14
S15 S16S17
S19 S20
S21
S18
S22
S23 S24
S25
S26 S27S28 S30
S31 S32S29
S33
S34
S35
S36
S37
CB12 54 6 7 8 9
Fig. 3. Initial network configuration of test system
of connected DGs is large (about 90% peak load). Moreover, thereverse power flow changes with the load variation. Though thepower loss is decreased to 4539.1 kWh, the initial network is stilllossy (about 5% of the total load). Especially under light load, thepower loss with DGs is increased compared to when the DGs arenot connected. The SCC of CB1 (SCC1) is 147.03–147.55 MVA,which is above the interrupting capacity of the CB. Loss and SCCof each hour in initial network with DGs and without DGs areshown in Figs 5 and 6, respectively.
4.1.2. Results of voltage profile The node voltage profilesduring 3-h interval in two cases of initial network are shown inFigs 7 and 8. From the two diagrams, the following result is
474 IEEJ Trans 7: 471–477 (2012)
LOSS MINIMIZATION CONSIDERING SCC WITH DECENTRALIZED DG
0.45
0.55
0.65
0.75
0.85
0.95
1.05
0 4 8 10 12 14 16 18 20 22
Time (h)
Rat
io to
max
imum
Load
2 6
Fig. 4. Daily load curve in summer
100
200
300
400
500
600
0 4 8 10 12 14 16 18 20 22
Time (h)
Los
s (k
W)
Without DGs
With DGs
2 6
Fig. 5. Loss of initial network
120
125
130
135
140
145
150
155
0 6 10 12 14 16 18 20 22
Time (h)
SCC
(M
VA
)
Without DGs With DGs
2 4 8
Fig. 6. SCC1 of initial network
known: The variation of the node voltage profile in the initialsystem is large. As shown in Fig. 7, most of the node voltages arelower than the lower limit (0.95) because of the low load powerfactor (about 0.85). On the contrary, when a large number of DGsare connected (Fig. 8), voltages of some nodes are above the upperlimit at any time because a large amount of reverse reactive powerfrom DGs is flowing through the lines. Hence, the profile of thenode voltage in the initial network must be improved.
4.2. Results of reconfiguration In order to minimizepower loss in the test system with DGs considering the loadvariation, the algorithm described in Section 3.2 is used. Certainly,the more the number of divided stages, the better the results.However, the operation modes will increase with increase in thenumber of divided stages. Therefore, the frequency of switchchange and the probability of equipment damage will increase. Tooptimize the network and the changed number of operation mode,in this paper, the following three cases are considered. Case I iswhere the daily load is divided into three stages; Case II is wheretwo stages are divided; and Case III is where there is only oneoperation mode in a day. Moreover, to obtain better results, theoptimal divided time is also found.
Fig. 8. Node voltage profile of initial network with DGs
4.2.1. Results of loss and short-circuit capacity Thenetwork reconfiguration optimization is performed for each stagein the three cases using the load data shown in Fig. 4. The optimalcombination of switches is shown in Table II. The loss and SCC1at any time are calculated using optimal networks, and the resultsare shown in Table III. The optimal divided time is shown inTable IV. From these tables, all of SCC1 are below the limit(143 MVA) and power loss has decreased sharply (over 60%).Furthermore, compared to the operation mode of Case III, theother two cases are more efficient for loss reduction (about 8%).Obviously, the proposed method is effective.
Table II. Open switches in each stage for the three cases
Case II Stage 1 S7, S10, S13, S22, S34Stage 2 S5, S10, S14, S33, S34
Case III S7, S11, S14, S26, S34
Table III. Optimization results
TCTOS SCC1 (MVA) Ploss (kWh) LRR (%)
Case I 10 140.6–142.9 1289.1 71.6Case II 6 138.6–142.3 1324.2 70.8Case III 0 140.4–141.2 1662.8 63.4
TCTOS = number of total changing times of the switch, LRR = lossreduced ratio.
475 IEEJ Trans 7: 471–477 (2012)
C. LIU, T. TSUJI, AND T. OYAMA
Table IV. Optimal divided time point for three cases
Divided time point
Case I 0, 8, and 19 o’clockCase II 7 and 23 o’clockCase III —
0
50
100
150
200
250
0 6 10 12 14 16 18 20 22
Time (h)
Los
s (k
W)
2 4 8
Initial network Case I Case II Case III
Fig. 9. Loss comparisons before and after reconfiguration
136
138
140
142
144
146
148
0 6 10 12 14 16 18 20 22
Time (h)
SCC
(M
VA
)
2 4 8
Initial network Case I Case II Case III
Fig. 10. SCC1 comparisons before and after reconfiguration
The detailed 24-h loss and SCC1 before and after network recon-figuration are shown in Figs 9 and 10, respectively. The data iswith DGs.
Figure 9 shows that the loss is more when the load is light andthe loss is less when load is heavy. However, the state of SCC1is the opposite, no matter which case in Fig. 10.
4.2.2. Results of voltage profile The voltage profiles ofthe 3-h interval in optimal load model for the three cases afterreconfiguration are shown in Figs 11–13. Comparing the data, thevoltage profile after reconfiguration has improved very well andvalue is distributed between 0.97 and 1.05 p.u. However, at latenight, some node voltages will be be close to the upper limit eventhough the network is reconfigured. The reason is that the largereverse power flow from DGs makes some node voltages rise toomuch.
With respect to optimal operation model in a day, as mentionedabove, multiple factors must be taken into account. According tothe comparative results, in Case II, the number of total changingtimes of the switch (TCTOS) is 6 and the most changed times ofthe same switch is twice. Loss reduced ratio is 70.8% and onlyincreases 0.8% compared to the minimum (Case I) of the threecases in a day but the TCTOS decreases 40% compared to thatin Case I. Moreover, the node voltage profile of Case II is alsosmooth and distributed in 0.98–1.05 p.u. In summary, Case II isconsidered as the optimal operation model with load variation inthis case study.
5. Conclusion
As is known, the power loss will decrease when appropriate DGsare connected to the distribution system. However, if the capacity
0.95
0.96
0.97
0.98
0.99
1
1.01
1.02
1.03
1.04
1.05
0 6 10 12 14 16 18 20 22 24 26 28 30 32
Node
Vol
tage
(p.
u.)
0 o'clock 3 a.m. 6 a.m. 9 a.m.
12 o'clock 3 p.m. 6 p.m. 9 p.m.
2 4 8
Fig. 11. Voltage profile after network reconfiguration in Case I
0.95
0.96
0.97
0.98
0.99
1
1.01
1.02
1.03
1.04
1.05
0 6 10 12 14 16 18 20 22 24 26 28 30 32
Node
Vol
tage
(p.
u.)
0 o'clock 3 a.m. 6 a.m. 9 a.m.
12 o'clock 3 p.m. 6 p.m. 9 p.m.
2 4 8
Fig. 12. Voltage profile after network reconfiguration in Case II
0.95
0.96
0.97
0.98
0.99
1
1.01
1.02
1.03
1.04
1.05
0 6 10 12 14 16 18 20 22 24 26 28 30 32
Node
Vol
tage
(p.
u.)
0 o'clock 3 a.m. 6 a.m. 9 a.m.
12 o'clock 3 p.m. 6 p.m. 9 p.m.
2 4 8
Fig. 13. Voltage profile after network reconfiguration in Case III
of the connected DGs is very large, it will increase the powerloss inversely during light load and bring about the short-circuitcurrent through some CBs above the interrupting capacity of CBin fault. In order to resolve the problem, in this paper, networkreconfiguration with decentralized DG considering SCC constraintand load variation was performed for power loss minimizationand SCC reduction. In order to confirm the method, a 33-bussystem was tested. By the proposed method, the optimal operationmodes with the daily load variation were obtained. The resultsshowed that the proposed method could decrease drastically thepower loss, and the SCC anywhere could be suppressed effectivelybelow the interrupting capacity of the CB. Moreover, the nodevoltage profile also improved very well. Therefore, the reliability
476 IEEJ Trans 7: 471–477 (2012)
LOSS MINIMIZATION CONSIDERING SCC WITH DECENTRALIZED DG
of power system could be enhanced. The simulation results ofdividing load into two stages (Case II) were better than those ofthe other two cases (Case I, Case III) when load variation wasconsidered in this test system with DGs. However, when loadwas excessively light (late at night), power loss became more andvoltages of some nodes were be near the upper limit in any case.The reason is that the reverse power flow from DGs is large.Although the results are used only for the case study, the proposedmethod in this paper can apply to any radial distribution system.Namely, in a general radial distribution system, loss and SCCcan be reduced, and voltage profiles can also be improved bynetwork reconfiguration. Moreover, considering the load variationin a day, the method, which is to divide a day into several intervalswith optimal time-divided point algorithm to perform optimalcombination of switches for each interval, can decrease furtherloss. The distinction for each system is the difference of detailedresult data. In future research, this problem under low load will befollowed with interest and the solution will be worked out.
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Chang Liu (Non-member) was born in Liaoning province, China,in 1979. She received the B.S. and M.S. degreesin electric power engineering from the North-east Institute of Electric Power, China, in 2001and 2004, respectively. At present, she is pur-suing the Ph.D. degree at the Graduate Schoolof Engineering, Yokohama National University.Her research interests include distribution sys-
tems with distributed generation automation and optimization.
Takao Tsuji (Member) was born in Japan on November 22,1977. He received the Dr Eng. degree fromthe Yokohama National University in 2006.In April of the same year, he was appointedResearch Associate at the Graduate School ofInformation Science and Electrical Engineering,Kyushu University. Since April of 2007, he hasbeen an Assistant Professor in the Faculty of
Engineering, Yokohama National University. His research interestsinclude planning, operation, and control of electric power systems.Dr Tsuji is a member of the IEEE.
Tsutomu Oyama (Senior member) received the B.S., M.S., andDr Eng. degrees in electrical engineering fromthe University of Tokyo, Tokyo, Japan, in 1978,1980, and 1983, respectively. Since 1983, he hasbeen with Yokohama National University, wherehe is currently a Professor. His research interestsinclude analysis, operation, and planning ofpower systems. He is a member of CIGRE,
IEEE, and the Japan Society of Energy and Resources.
