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Power Loss Minimization in Radial Distribution System using Network Reconfiguration and Multiple DG Units
Sarfaraz Nawaz
Swami Keshvanand Institute of Technology Management & Gramothan, Jaipur, India
Sonali Singh
Thakur College of Engineering & Technology, Mumbai, India
Supriya Awasthi
Atharva College of Engineering, Mumbai, India
Abstract
A novel approach is anticipated in this paper for optimal feeder reconfiguration and allocation of DG and capacitor units in distribution system with an objective of reduction of real power losses while satisfying operating constraints. Selective Particle Swarm Optimization algorithm (SPSO) is used to obtain reconfigured distribution network. A new heuristic technique has been proposed to solve DG & Capacitor placement problem. A new mathematical expression, Power Voltage Sensitivity Constant (PVSC), has been formulated here. The value of PVSC decides the candidate bus location and size. The results of the proposed technique are validated on IEEE 33 bus test distribution system at different load level. The level of DG penetration is also considered in a range of 0–50% of total system load. A novel index is also proposed which incorporates level of DG penetration and % reduction in real power losses. The results are promising when compared with recently proposed algorithms.
Keywords: Radial distribution network, distributed generation, capacitors, network reconfiguration, SPSO (Selective Particle Swarm Optimization), heuristic technique, DG penetration
1. Introduction
Generation, transmission and distribution of electrical energy are the main function of electric power system. There is an increasing trend to automate the distribution system. It has become possible to install distribution operating center to monitor and control the distribution networks as well as reconfiguring the distribution system to minimize the active power losses and balance loads under normal operating conditions. The operation and control of distribution system is carried out by two types of switches namely as sectionalizing switches (normally close) and tie switches (normally open).
The distribution system has to run in a way that it must be radial, operating cost should be minimum as much as possible, all loads are serving and the bus voltages should be in the permissible limit. Merlin and H. Back [1] introduced the feeder reconfiguration method for real power loss reduction . Branch and bound technique was used to solve the problem. Civanlar et. al.[2] presented a novel method for determining the power loss by branch exchange method. D.Shirmohammadi, et.al [3] presented the power flow method to reduce line losses. S.K. Goswami et-al [4] presented a heuristic
Reconfiguration and Multiple DG Units 475
algorithm for the reconfiguration of feeders. G. J. Peponis et-al [5] developed two heuristic methods to minimize the line power losses as well as for load balancing. Y.H.Song et-al [6] presented a fuzzy controlled EP (FCEP) based approach for reconfiguration. From last two decades, so many optimization techniques have been proposed by researchers to obtain optimal reconfigured system. The various optimization techniques are simulated annealing (SA) [7], Refined Genetic algorithm [8], fuzzy multi objective approach [9], analytical approach [10] , Plant Growth Simulation Algorithm (PGSA) [11], branch exchange method[12], honey bee mating optimization (MHBMO) evolutionary algorithm[13], enhanced integer coded particle swarm optimization (EICPSO) [14], binary particle swarm optimization (BPSO)[15], PSO [16].
Distributed generation (DG) devices can be deliberately sited to reduce real or reactive power losses, to enhance bus voltage profile, to improve load factors, reliability and efficiency in power systems. The main function of the optimal DG placement (OPDG) is to offer the best locations and sizes of DG units while considering DG capacity constraints. To solve the problem, distributed generation (DG) placement is continuously being considered by researches. Various researchers applied different approaches and optimizing various objective functions. Such optimization methods can be classified into deterministic methods such as analytical methods and heuristic methods (like Genetic Algorithm (GA), Particle Swarm Optimization (PSO), Artificial Bee Colony (ABC) etc.) or into single- and multi- objective, based on the number of objectives. Kyu-Ho Kim et. al. [17] used a hybridized method (combination of GA & fuzzy set theory) to find out optimal DG size and location in radial distribution system. N. Acharya et. al. [18] proposed an analytical method to solve DG placement problem in radial distribution system. S. Kamalinia, et-al [19] offered MADM (Multi-Attribute Decision Making) and Genetic algorithm technique to determine DG size and location. In [20], authors used Particle Swarm Optimization (PSO) technique to calculate optimal size and position of multiple DG units. M. Abbagana et. al. [21] proposed a Differential Evolution technique to solve DG placement problem in a distribution network. Duong Quoc Hung et. al. [22] proposed an improved analytical (IA) method to attain high power loss reduction in large-scale primary distribution networks by multiple distributed generator (DG units) placement. In [23], author presented a meta heuristic Harmony Search Algorithm (HSA) for feeder reconfiguration and optimal DG placement in distribution network. Seyed Abbas Taher et.al. [24]
formulated a multi objective function to solve the feeder reconfiguration problem in the occurrence of DG units. Author anticipated GA method to solve the problem. Sayyid Mohssen Sajjadi et.al. [25]
proposed Memetic algorithm for simultaneous placement of DG and capacitors units to reduce power loss, energy loss and to improve voltage profile. In [30] authors presented a heuristic technique to solve capacitor allocation problem in real distribution system of India.
In this paper the objective of real power loss reduction and voltage profile improvement in distribution system is solved by network reconfiguration and by placing DG & capacitor units. A selective particle swarm optimization technique (SPSO) is used to solve feeder reconfiguration problem. A new heuristic technique is proposed to solve DG and capacitor allocation problem. A new constant, Power Voltage Sensitivity Constant (PVSC), has been proposed here. This constant is incorporated with real power loss and voltage of the system. The researchers did not consider DG penetration in their research. In their paper the size of the DG unit is very high. In many practical cases along with economic constraints the size of DG units are not pragmatic. The high size of DG units gives high cost of the system. Here, level of DG penetration is also considered in a range of 0–50% of total system load. A novel index, DG penetration Index (DGPI), has been proposed to incorporate the level of DG penetration and % loss reduction. The proposed approach is experimented on standard IEEE 33-bus test distribution network and obtained results are discussed.
The rest of the paper is organized as follows: section 2 gives the portrayal of problem statement. Section 3: gives the proposed approach for feeder reconfiguration and DG placement problem. Section 4 portrays the simulation results of test distribution systems used in this paper. A brief summary of the obtained results is also included in this section and the conclusions of the papers are summarized in Section 5.
2. Problem Formulation
This work presents a method to resolve feeder reconfiguration problem with DG & capacitor allocation in radial distribution system to minimize line losses and to get better bus voltage. The objective function of the problem is formulated in this section.
In figure 1, single line diagram of the feeder is shown. The equations mentioned below are obtained from the single line diagram of the feeder.
The impedance of line section between bus i and i+1 is given as
Zi,i+1= Ri,i+1 + j Xi,i+1 (1)
and load demand at bus i is
SLi=PLi+jQLi (2)
Figure 1: single line diagram of main feeder
Pi+1, Qi+1 are the real and reactive power flow at the receiving end of branch i+1. The recursive equations for receiving end voltage are given by [26]:
= − − , | | (3)
= − − , | | (4)
| | = | | − 2( , . + , . ) +
, + , .( | | ) (5)
Where,
: line real power flow from bus i.
: line reactive power flow from bus i.
: real power load at bus i.
: reactive power load at bus i.
, : resistance of the line between bus i and i+1.
, : reactance of the line between bus i and i+1.
Equations (3), (4) and (5) are known as distribution power flow equations. This procedure is known as forward update.
Similarly, a backward update is expressed as:
= + + , | | (6)
= + + , | | (7)
| | = | | + 2( , . + ,. ) +
, + , .( | | ) (8)
Where, Pi1=Pi+PLi and Qi1=Qi+QLi
Now, the real power loss of the line segment connecting among node i and i+1 is computed as:
WL(i,i+1) = R i,i+1 | | (9)
P 0 ,Q 0 P 1 ,Q 1 P i -1 ,Q i -1 P i ,Q i P i+1 ,Q i+1 P n ,Q n
P L1 ,Q L1 P L-1 ,Q L-1 P Li ,Q Li PL i +1 ,QL i +1 P Ln, Q Ln
0 1 i-1 i i+1 n
Reconfiguration and Multiple DG Units 477
Total network power loss is determined by adding the losses of all line sections of feeder.
Total feeder power loss (WT Loss) =
(10)
2.1 Real Power Loss Minimization using Feeder Reconfiguration
In a distribution system, the feeder reconfiguration problem is to determine optimal radial structure of the system which gives lowest amount of power loss whereas fulfilling the operating constraints under a certain load pattern. The operating constraints are voltage drop with in limit, current capability of the feeder should not exceed and radial configuration of the system should be maintained. The mathematical model of the feeder reconfiguration is presented as
Minimize f1 = min ( WT Loss ) (11) Subjected to ≤ ≤ "#
| $ | ≤ $ "#
System should be radial.
Where ,
Vmin ,Vmax are minimum and maximum bus voltage limits respectively.
Ii is current at ith bus.
I i,max is maximum current.
2.2 Power Loss Reduction using DG & Capacitor Placement
The aim of allocation of DG and capacitor units is the reduction in active and reactive power loss of radial distribution system to its minimum value. To achieve this objective, multiple Distributed Generation and capacitor units are used for allocation.
The problem is defined as:
Minimize f2 = min (WL ) (12)
% = ∑ ∑- ( )- | | | ' | | ||, ' | ()* +, ' (13)
a) Equality Constraints: The arithmetical summation of all incoming and outgoing powers together with power losses for distribution system and power generated by DG units should be equal to zero.
b) Inequality Constraints:
(i) The injected power by each DG units is restricted by its maximum and minimum limits as,
P/01213 ≤ P/01 ≤ P/01245 Q213/01 ≤ Q/01 ≤ Q/01245
(ii) Bus voltage limits (As per Indian standard ±5%) 0.95 pu ≤ V1 ≤ 1.05 pu (iii) The feeder should not go beyond the thermal limit of the line.
Where,
R: Line resistance between bus i and (i+1);
X: Line reactance between bus i and (i+1);
Z : Line impedance;
Vi : Magnitude of voltage at bus i ;
V(i+1): Magnitude of voltage at bus (i+1);
Vmin : Minimum bus voltage
δi: Angle of voltage at bus i; δi+1: Angle of voltage at bus (i+1) ; P and Q: Active and reactive power flow from bus i to (i+1)
> %?(@,@+1) A−1 @=0
2.3 Objective Function
The objective function of the problem is to minimize the line power loss of distribution system by satisfying operating constraints.
Minimize f= min. (f1 + f2 ) (14) Subjected to:
(i) V213 ≤ V1 ≤ V245 (ii) | I1| ≤ I1,245
(iii) The arithmetical sum of all incoming and outgoing powers together with line losses for distribution network and power generated by DG units should be equal to zero.
(iv) P/01213 ≤ P/01 ≤ P/01245 (v) Q/01213 ≤ Q/01 ≤ Q/01245 (vi) System should be radial.
(vii) DG penetration level should not exceed 50% of total system load.
3. Solution Methodology
In this paper, the feeder reconfiguration problem is solved by selective particle swarm optimization (SPSO) technique and optimal sizing and location of DGs is solved by analytical technique.
3.1 SPSO Technique for Feeder Reconfiguration
Selective particle swarm Optimization (SPSO) is recently proposed AI based approach. In [27] Tamer proposed selective particle swarm optimization technique to resolve network reconfiguration problem which is modified version of Binary Particle Swarm Optimization (BPSO) to search in selective space.
3.1.1 Steps to Solve the Feeder Reconfiguration Problem using SPSO There are three steps to solve feeder Reconfiguration problem using SPSO [28].
Step-I : Specifying the number of dimensions: Radial distribution network is designed as ring main but it is always operated in radial structure like an open loop to assure the network in form of a tree. To identify the number of dimensions for network reconfiguration problem, all tie switches (normally open switches) must be closed. It will confer the number of loops. In SPSO technique the number of loops equals the number of dimension.
Step-II : Finding the Search Space for Each Dimension: By closing all the tie switches, it will confer the number of loops. The branches non belonging to any of the loop will not be considered in the search space for any dimension. The search space for each dimension will be the branches belonging to the particular loop at this dimension. There may be possibility when some branches are common to two or more loop, than in that case the common branches will appear for one dimension only and this could be done randomly.
Step-III : Using Selective Particle Swarm Optimization to select the Optimal Solution from the Search Spaces: After the number of dimensions specified, and finding the search space for each dimension, the optimal solution from the search space for each dimension would be identified by Selective Particle Swarm Optimization.
The algorithm and flow chart of SPSO technique is used from [28].
3.2. Heuristic Technique
A new approach has been presented for DG and capacitor placement problem. The Power Voltage Sensitivity Constant (PVSC) is formulated to find out the size and position of DG and capacitor units.
This constant takes active power loss and voltage limits of individual buses in account and suggest the optimal location & size of DG and capacitor units.
Reconfiguration and Multiple DG Units 479
CD = EFGE H+ NO"KKLMMIJKLMM (15)
For optimal allocation of DG/capacitor bank the value of PVSC should be minimum. The flow chart of proposed approach is shown in figure 2.
Prealloss: base case real power loss.
Pdgloss: active power loss after DG placement at ith bus.
Vmax is rated bus voltage in pu after DG placement at ith bus (always be 1 pu).
Vmin is minimum bus voltage in pu after DG placement at ith bus.
Figure 2: Flow chart of proposed method
3.3 DG Penetration Index (DGPI)
Most of the researchers did not consider DG penetration in their research. In many practical cases along with economic constraints the size of DG units are not pragmatic. In their paper the size of DG unit is very high. But the high size of DG unit will lead to high cost of the system.
In this paper a novel index, called DG penetration index, is proposed. The DGPI gives the % power loss reduction for unit size of DG.
DGPI = (% Q)RST U)** TSVW(X1)3)
Y)X4U XZQS [ /0 *1\S (16)
Hence, for improvement of network performance the value of the DGPI should be maximum.
Start
Read System Data
Calculate Active Power Loss Paploss
by running base case load flow program
Set the Iteration count K=1
Set size of DG/capacitor as C=1
Set the Bus count P=1
Calculate active power loss Pcrloss, Vmax & Vmin by running load flow
program after placing DG/capacitor at P bus
Calculate PVSC = (Vmax/Vmin) + (Ploss/Prealloss)
Check if all the buses have been taken into account
Store the value of Bus count for minimum value of PVSC as BK and corresponding value of Ploss. Also set B0 = BK
Check if BK = BK-1
Value of the Bus Count BK-1 and value of capacitor in iteration (K-1) is the optimal location and size of capacitor
End Increse the value of
DG/ capacitor as C = C*1.005
and Iteration count K=K+1
Yes
No No
Yes Advance the
Bus count P=P+1
4. Test Results and Discussion
The proposed method has been tested on IEEE 33 bus test system at three different loading conditions i.e. light load (50%), nominal load (100%) & heavy load (160%). The proposed approach has been implemented using MATLAB 10 software.
Four cases are considered here:
Case I: Only Feeder reconfiguration (FR)
Case II: Only DGs placement after feeder reconfiguration Case III: Only capacitors placement after feeder reconfiguration
Case IV: Simultaneous placement of DGs and capacitors after feeder reconfiguration
The IEEE 33 bus radial distribution system [29] has five tie-switches and 32 sectionalizing switches. The system has total load of 3.715 MW and 2.30 MVAr. The base network power loss is 202.6762 kW and tie switches are 33,34,35,36,37. The selective particle swarm optimization technique is used to solve the reconfiguration problem. The parameters of SPSO algorithm used in the simulation of network are Number of Particles 25, Wmax (initial weight) 0.9, Wmin (final weight) 0.4, Maximum no of iterations 100, Acceleration constants 2.
The results of 33 bus system before and after compensation is shown in table 1. Three loading conditions and four different cases are considered here. For DG and capacitor installation only first three candidate buses are selected.
Table 1: Performance analysis of proposed method on IEEE 33-bus system at different load levels
Case Items Load Level
Light (50%) Nominal (100%) Heavy (160%) Base Case
Tie switches 33-34-35-36-37 33-34-35-36-37 33-34-35-36-37
Power Loss (kW) 47 202.7 575.3
Minimum Bus Voltage (pu) 0.959 0.91 0.853
(I) After Feeder Reconfiguration (FR)
Tie switches 7-9-14-32-37 7-9-14-32-37 7-9-14-32-37
Power Loss (kW) 33.2 139.55 380
Minimum Bus Voltage (pu) 0.97 0.943 0.90
% Loss reduction 29.9% 31.2% 34%
(II) DG placement after FR
DG size (Location)
340 (16) 310 (30) 230 (32)
680 (16) 670 (30) 420 (32)
950 (16) 720 (30) 780 (32)
Total DG size (kW) 880 1770 2450
Power Loss (kW) 18 73.8 198
Minimum Bus Voltage (pu) 0.985 0.9703 0.95
% Loss reduction 45.7 63.6 65.5
(III) Capacitor placement after FR
Capacitor size (Location)
140 (17) 320 (30) 120 (32)
280 (17) 510 (30) 280 (32)
460 (17) 630 (30) 440 (32)
Total Capacitor size (kVAr) 580 1070 1530
Power Loss (kW) 23.6 98.8 271
Minimum Bus Voltage (pu) 0.981 0.956 0.928
% Loss reduction 49.8 51.25 52.9
(IV) DG and Capacitor allocation after FR
Total DG size (kW) 880 1770 2450
Total Capacitor size (kVAr) 580 1070 1530
Power Loss (kW) 8.7 36.5 103
Minimum Bus Voltage (pu) 0.988 0.98 0.956
% Loss reduction 73.8 82 82
It is observed from table 1, at nominal load level, percentage power loss reduction is 31.2, 63.6, 51.25 & 82 for case I, II, III & IV respectively.
Similarly, at light and heavy load conditions, the percentage power loss reduction for case I to IV is 29.9, 45.7, 49.8 & 73.8 ; 34, 65.5, 52.9 &82. It is also observed that at all loading conditions the
Reconfiguration and Multiple DG Units 481
minimum bus voltage is also enhanced. The comparison of results with other latest optimization technique is shown in table 2. The proposed technique is compared with Improved GA, Improved PSO and Improved CSO algorithm [31]. In [31], authors did not consider any penetration level of DGs. The size of DG units is very high in their results. But, in proposed technique the size of DG and capacitor units is less as compared to others.
The value of DGPI (percentage loss reduction for per unit DG) is 0.046 in the proposed technique. In IGA, IPSO, ICSO the value of DGPI are 0.032, 0.033 and 0.033 which is in lower side.
Table 2: Comparison of Results for 33 bus system at nominal load level
Technique Tie Switch Total Capacitor size in kVAR
Total DG size in kW
% loss reduction
Min. bus
Voltage (pu) DGPI
IGA [31] 7, 9, 17, 35, 37 1700 2870 94.28 0.99 0.032
IPSO [31] 7, 9, 17, 25, 35 1800 2808 94.51 0.99 0.033
ICSO [31] 33, 34, 35, 36, 37 2000 2847 94 0.99 0.033
Proposed 7-9-14-32-37 1070 1770 82 0.98 0.046
The high size of DG and capacitor units gives high cost of the system. The proposed approach gives maximum percentage loss reduction at optimum size of DG and capacitor units.
The comparison of bus voltages at nominal load level for base case and other four cases is shown in figure 3 .
Figure 3: Comparison of bus voltage at nominal load for 33 bus system
5. Conclusion
In this paper a novel technique has been proposed to minimize active power loss and to improve voltage profile for distribution system. The objective is achieved by network reconfiguration and allocation of DG & capacitor units. Selective Particle Swarm Optimization algorithm (SPSO) is used to obtain reconfigured distribution network. A novel analytical technique has been proposed to solve DG
& Capacitor placement problem. A novel constant, Power Voltage Sensitivity Constant (PVSC), has been proposed for determining candidate bus location and size. The level of DG penetration is also considered in a range of 0–50% of total system load. A novel index (DGPI) is also proposed which incorporates level of DG penetration and % reduction in real power losses. For better coordination of DG units, the per unit size of DGs gives maximum percentage loss reduction. Two test systems are used to implement the proposed method. The results shown that the proposed approach give maximum percentage loss reduction for unit size of DG and capacitor units. For both test system, the size of DG
5 10 15 20 25 30
0.91 0.92 0.93 0.94 0.95 0.96 0.97 0.98 0.99 1 1.01
Bus Number
Bus voltage in pu
Base FR only FR & DG FR & OCP FR, DG & OCP
units are less as compared to other technique. In all other technique, the DG penetration is not considered. So, the high size of DG units gives high cost of system. The proposed approach give better percentage loss reduction & voltage profile at less DGs and capacitors size.
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