Efficient and Automatic Reconfiguration and Service Restoration in Radial Distribution System Using Differential Evolution D. Pal, S. Kumar, B. Tudu, K.K. Mandal, and N. Chakraborty Power Engineering Department, Jadavpur University, Kolkata: 700098, India {dptndpal0,sajjan.pradhan48}@gmail.com, {bhimsen_ju,kkm567}@yahoo.co.in,
[email protected]
Abstract. This paper addresses two complex optimization problems in the form of radial distribution system reconfiguration and service restoration using a novel optimization technique called differential evolution. For distribution feeder reconfiguration (DFR) problem, the close and open statuses of sectionalizing and tie switches are changed to find minimum loss configuration. During any sudden outage of any section of the distribution system, the quickness of the restoration is checked with the help of basic optimization technique while feeding all the load points. A standard IEEE 3 feeder, 16 bus distribution system is chosen to simulate the dual problem of optimization. The feasibility and novelty of the optimization is also checked in a comparatively more complex IEEE 33 bus distribution system. Differential Evolution is chosen to find alternative topologies for feeder system and simplified forward Dist-Flow Equation is implemented to do power flow study and it is seen that differential evolution is quite capable of solving this type of complex, non-linear optimization problem with less time which is a basic requirement for the service restoration (SR) of the network system. Keywords: Radial distribution system, Network reconfiguration, Service restoration, Power loss reduction, Differential Evolution, Dist flow equation.
1
Introduction
In distribution system automation, the topological structure of distribution system is changed from a distant control center. The topological structure of any radial system can be changed by altering the statuses of (normally close) sectionalizing switches and (normally open) tie-switches for the purpose of reconfiguration and service restoration of the network system. The reconfiguration procedure is done at the time of service maintenance and service testing to find minimum loss configuration or optimum alternative configuration by exchanging the heavily loaded section with lightly loaded portion. Service restoration is a process of restoring power flow immediately after any kind of disturbance in the power system. In both cases, any kind of islanding S.C. Satapathy et al. (Eds.): Proc. of Int. Conf. on Front. of Intell. Comput., AISC 199, pp. 365–372. DOI: 10.1007/978-3-642-35314-7_42 © Springer-Verlag Berlin Heidelberg 2013
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of region and looping in between the sub-tree structures have to be avoided. To check the feasibility of the procedure, customer reliability factors are also considered over different topological structures. Because of many candidates switching, the reconfiguration and service restoration are complex, combinatorial, non-differentiable constrained optimization problem. The first ever approach on distribution feeder configuration is done by Civanlar et al. [1]. Ji-Pyng Chiou et al. have come up with this loss minimization for network configuration using modified Differential Evolution [2]. Ahmed A. Hossam-Eldin et al. [3] have worked on a twofold objective of feeder reconfiguration and service restoration using simulated annealing method. To observe any kind of voltage instability due to branch exchange in reconfiguration, Marcos A. N. Guimaraes et al. have introduced a voltage stability calculation in reconfiguration procedure [4].
2
Radial Distribution System and Problem Statement
The term “radial” in radial distribution system comes from the process of nuclear fission of radioactive heavy material. In that process the radioactive material splits into lighter nucleuses and radiates huge energy. The same radiation of electric energy happens from one end of the radial distribution system. Here the power system is handled in tree topology and looping of any topological structure is strictly avoided. For paper work, the test systems IEEE 3 feeder, 16 bus system (13 sectionalizing switches, 3 tie switches) and IEEE 33 bus distribution system (32 sectionalizing switches, 5 tie switches) are operated in radial structure to execute dual problem of reconfiguration and service restoration. 2.1
Problem Statement
To calculate active power, reactive power, voltage and power loss the simplified forward dist-flow equations are chosen [2]. This work aims to minimize the power loss, subject to operating constraints under certain load pattern. The mathematical term is expressed as follow: f = min PT,
(1)
Where PT,loss is the total loss in all connected branches to the system. Here, node voltage value should be maintained as per the upper (Vmax) and lower (Vmin) limits of node voltage and ( Ii,j ) current in each branch should be under the maximum current capacity of that branch. Equality Constraint: V
V
V
(2)
Inequality Constraint: I,
I
(3)
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Power Flow Equations Power flow in Radial distribution networks are expressed with the help of Dist-Flow equations. A set of simplified feeder-line flow formulas are employed. The equations are as follow:
|V
P
=P
Q
=Q
| = |V |
2
PL,
P + Q )/|V |
R,
Q L,
R,
(4)
P + Q )/|V |
X, P +X,
Q )+ R ,
+ X
(5) P
Q
(6)
|V |
Pi and Qi are real and reactive power flowing out of ith bus. PLi and QLi are active and reactive power loads at ith bus. Ri, i+1 and Xi, i+1 are resistance and reactance in between ith and i+1th bus. Power loss in the section connecting ith and i+1th bus is computed as: P + Q )/|V |
i, i + 1) = R ,
PL
(7)
The total loss (PT,loss) is found out by summing all branch losses in the feeder section. ∑
i, i + 1)
PT,
=
PL
i = 0,1,2, … . . n
3
Differential Evolution
(8)
The formulation of simple differential evolution is proposed by Storn and Price [7]. Differential Evolution is a population (P) and generation-based (G) optimization method, and here population is formulated on the control variables of switching statuses. During the optimization process, target vectors (sik) , donor vectors ( wik ) and trial are created to find the best suitable variable value for fitness function vector [7]. Step1) Initialization s i = 1,2 … N;
=s 0
+ σ σi
s
s
1;
)
(9)
k=1, 2……G
step2) Mutation w i = 1, 2, 3, … … . . N;
= s + F F
s .4, .5
s
(10) k = 1,2, … … . G
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0, 1 )
Step 3) Cross-over u
=
w s
if σ
CR) ; CR . 8 , .9 ) if σ
(11)
Step 4) Evolution and Selection s
=
if f u
u
s if f u
f s
(12)
f s
Here (f) is the objective function or fitness value. Among target and trail vectors new target vectors (sik+1) are created for the next generation or for the next iteration.
4
Optimization Procedure
To simulate the procedure, the validity of the switching combination and reliability factors are to be maintained. 4.1
Checking Validity
Every switching combination can be represented into branch vs. node matrix form [8]. Here the radial distribution system works as a directed tree. Outgoing branch from any node is represented using ‘-1’. Incoming branch to any node is represented by ‘+1’. If a node is not connected with any branches, then the connection is represented by ‘0’. In a matrix, if any node contains all zeros in its column then it is presumed as islanding of that node. Hence the switching combination is invalid. If certain matrix representation is not suffered of this above explained problem, then the respective switching combination is valid one. 4.2
Penalty Function
A penalty function is added with fitness value if some invalid switching combination gives infeasible result [9]. Penalty Function =
∑
V
V) +
∑
I
I)
(13)
Fitness function is formulated on penalty value in case of infeasible solution. and are user defined penalty factors. 4.3
Voltage Stability Index for Distribution System
Branch exchange phenomena in reconfiguration and service restoration, may cause serious voltage stress on some nodes in the system. To see the node voltage stability, different authors have proposed different methods. A power flow method based stability index calculation is adapted in this work [10].
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It is a calculation of stability index of mth node on the basis of voltage of kth node and active and reactive power of mth node. If stability index of node gives higher value than zero then it is secure node in the voltage profile point of view. SI = |V |
4.4
P r + Q x )|V |
4
4
P r
Q x )
(14)
Reliability Factors for Customer Satisfaction
Either process of reconfiguration or the strategy of service restoration, main purpose of these two is to satisfy the customers. Customer’s reliability on power system may be hampered due to capacity reduction of feeder and distribution transformer, voltage deviation and switching surge [11]. Feeder Capacity Margin (FCM) Min f = 1
I
min
IL
R
IR
i = 1,2, … … … Nbr
(15)
i = 1,2, … … … N
(16)
Transformer Capacity Margin (TCM) Min f = 1
min
S
SL
R
SR
Maximum Voltage Deviation (MVD) f = max|V
V
|
i = 1,2, … … … … . n
(17)
Minimum Switching Reconfiguration and service restoration should be done using minimum number of switching operation so that there would not be any kind of switching surge in the system.
5
Simulated Results and Comparative Study
Simulated results of reconfiguration and service restoration of both the systems are discussed below. 5.1
System 1: IEEE 3 Feeder, 16 Bus Distribution System
For system 1, IEEE 3 feeder, 16 bus distribution system, there are 13 sectionalizing switches and3 tie switches. The programming is done on the active power inputs of 10, 16, 6 MW and reactive power inputs of 6, 10, 4 MVAr [12]. 100MVA is base MVA and 20kV is base kV.
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Comparative Result Switches open
Minimum Loss Configuration
15,21,26
17,18,23
Loss(kW)
579.9
421.37
Feeder Capacity Margin (p.u)
0.6075
0.7475
Transformer Capacity Margin (p.u)
1
1
Maximum Voltage Deviation (p.u)
0.059015
0.0448307
-
27.33
% Loss minimization
Table 2. Result of system 1 (3 feeder system) in SR Conditions
Cut off switch
18 G=100 P=10 F=.5 CR=.9
Out of service nodes
Sectionalizing off
Tie off
Total Loss(kW)
Reliability Factors
9,11,12
14,17,18
-
431.46
FCM=.7475 TCM=1 M.V.D=.039
13.55
Run Time (sec)
14
7
17,19,14
-
443.69
FCM=.6075 TCM=1 M.V.D=.056
11.21
17
10
17,19,23
-
433.6
FCM=.6075 TCM=1 M.V.D=.056
9.15
From the comparative study on the loss reduction for system 1, it is found out that in optimized configuration the loss is reduced about 27.33 % from its original configuration. In case of service restoration, switches 18, 14 and 17 are cut in different cases to see the restoration of the system in minimum time. 5.2
System 2: IEEE 33 Bus Distribution System
For system 2, IEEE 33 bus distribution system, there are 32 sectionalizing switches and 5 tie switches. The programming is done on the active power input of 2520 kW Table 3. Result of system 2 (33 bus distribution system) on DFR Conditions
G=100,P=40 F=.5, CR=.9
Sectionalizing Off Original Configuration 8,15,18
Tie Off
Loss (kW)
Critical Nodes
Reliability Factor
-
384.75
3,6,20
33,36
163.34
6,20
FCM=1 TCM=1 MDV=.05
Time(s) 66.81
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Table 4. Result of system 2 (33 bus distribution system) on SR Outage Branch 3 8 17 28
Sectionalizing Off 3,12,17,18,21 8,11,18,22 2,8,9,17 11,18,28
Tie off 37 37 35,37
Loss (kW) 194.95 155.94 201.73 205.05
Critical Nodes 3 3,6 20,21,22 3,6
Reliability Factors FCM=1 TCM=1 MDV=.05
Time (s) 60.62 66.55 69.73 45.58
and reactive power input of 1073 kVAr. 10MVA is base MVA and 12.66 kV is base kV. The current limits for the branches 1 to 9 and 10 to 37 are taken 400A and 200A respectively [3]. In case of reconfiguration in system 2, for constant input the optimize configuration gives 163.34 kW of loss and that is near about 60% lower than its loss from original configuration. In service restoration, 3, 18, 17, 28 are cut off in different cases to see the same restoration of system in minimum time.
Fig. 1. Stability Index vs. Node and Optimization Curve Loss vs. Iteration of System 1
From Stability Index vs. nodes graph node number 11 is more insecure in term of voltage stability. The system is optimized that can be observed from optimization curve (Figure 1 for system 1, 3 feeders, 16 bus system).
6
Conclusion
It can be concluded that the loss reduction and quick responsive feature of the network system can be achieved using DE. For both the feeder systems (3 feeder system and 33 bus distribution system) restoration is achieved in more or less than one minute. This kind of intellectual programming can be put into the controlling strategy of distribution feeder system quite efficiently.
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Acknowledgments. The work described in this article has been supported by “University Grants Commission (UGC)” under the scheme of “University with Potential for Excellence, Phase-II (UPE-II)”.
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