OPTIMUM ALLOCATION OF CAPACITOR AND DG IN MV
DISTRIBUTION NETWORK USING PSO AND OPENDSS
Naji Eltawil
1, Marizan Sulaiman
2, Meysam Shamshiri
2and Zulkiflie Bin Ibrahim
21
Higher Institute for Water Technology, Agelat, Libya
2
Centre for Robotics and Industrial Automation, Faculty of Electrical Engineering Universiti Teknikal Malaysia Melaka Hang Tuah Jaya Durian Tunggal, Melaka, Malaysia
E-Mail: [email protected]
ABSTRACT
The optimum capacitor and distributed generation (DG) allocation in medium voltage (MV) distribution network utilizing particle swarm optimization (PSO) for selecting the optimum size and placement of (DG) units can significantly affect the distribution network. Capacitor installation is a standard method for reactive power compensation within a distribution network. The placement and sizing of the capacitor have been optimized in the distribution network for a number of capacitors with the objective of the voltage profile improvement and power loss minimization. Maximum and minimum bus voltage and possible maximum capacitor size were the constraints of the optimum capacitor and sizing problems, which take into account as a penalty factor (PF) within the objective function (OF) and the allocation of DG units. To solve the obtained OF, PSO and Open DSS engines were used in this research to analyse power flow results that obtained from the standard IEEE14 Bus system. The performance evaluation of PSO model was carried out by showing the results that the PSO algorithm. PSO can obtain the optimal solution of the size and location also find the optimum DG size for the loss minimization and voltage profile improvement compared to the standard case without DG and capacitor compensation. All simulations had been performed using MATLAB software.
Keywords: distributed generation, particle swarm optimization and open DSS engine, power losses, optimization, objective function,
placement, sizing, power flow.
1. INTRODUCTION
Distributed Generations (DGs) are an essential part of the electric power system. The distribution network can enhance DGs in order to avoid network reinforcement and huge investment of installing new transmission lines. It is predicted that DG would have a share of about 20% of new generating units in the future distribution network. The distribution network consists of several various elements such as generators, bus bars, transmission lines, switches, overhead lines, circuit breakers, active and passive compensators, etc. Researchers have been carried out at various essential research centres such as the Electric Power Research Institute (EPRI); it has seen that more than 25% capacity of new installed DGs was installed the unit in 2010 [1-2]. Through the previous explanation about DGs that is connected to distribution networks, most of the studies and plans related to the networks should have been reviewed one more time to take into account the optimal management of distribution networks [1-2]. DG placement and sizing is one of the leading problems because of the integrations of possible buses, size, and a number of generators. Many algorithms have been proposed to place DGs such as PSO, Ant colony, optimal power flow and Analytical methods. Nowadays, several Evolutionary Computation Techniques have been sophisticated to determine the optimum capacitor placement and sizing of distributed generation. Different algorithms such as evolutionary Programming and Genetic Algorithms (GA) have been tempted to find the optimum capacitor placement and sizing. Particle Swarm Optimization (PSO) and OpenDSS engines are the other evolutionary computational techniques that can be utilized to solve the optimum allocation and to size-obtain
better results compared to the classical methods with less computational effort, and the application of PSO Algorithm is very efficient in handling the DG placement and sizing problems [3-4].
The main aim of this work is to show the enforcement of PSO technique for optimum allocation and sizing of DG and capacitor using OpenDSS engine, used to analyse data collection obtained from IEEE14 Bus system as an example of the methodology. Also, the minimization of power losses after using the PSO technique.
2. METHODOLOGY
In this paper, the PSO algorithm has been utilized to find the optimum solution for capacitor placement and sizing as well as a DG unit allocation. Hence, the following subsections describe the methods to overcome optimum solution and power flow calculation.
A. Network modelling
Figure-1. Single line diagram of the 14 Bus systems.
B. Data collection and implementation of power flow Engine (OpenDSS)
The data collection and implementation can be divided into four categories. The first is load demand, the loads are not voltage-dependent but have constant active P and reactive power Q demand in Table-1. Second, generator” G_0001” is the slack generator. Therefore the voltage magnitude and voltage angle are given (1.06 p.u, zero degrees). The generators are configured to control the P injection and voltage magnitudes at the connected buses as shown in Table-2 and Table-3. Third, data of lines are given in per unit (p.u) and based on the base power S_ (b) =100 MVA and as represented in Table-4. Fourth, data of transformers are given in per unit (p.u) as represented in Table-5 base power S_ (b) =100 MVA.
Tables 4 and 5 have a summary of the transmission lines and transformers. The system has 16 lines. The line data are taken in per unit (p.u) with base S_ (b) = 100MVA. The transmission lines work at various voltage levels, 132kv, 33kv, 1kv, and 11kv. The system operating at Bus1-Bus5 with 132kv; Bus6, Bus9-14 at 33kv; Bus7 at 1kv and Bus 8 at 11kv are represented under Table-4. The system has 5 transformers. The transformed data are taken in per unit (p.u) with base S_ (b) = 100MVA.
Table-1. Load demand.
Load Bus P (MW) Q
(Mvar)
Load 0002 Bus 0002 21.7 12.7
Load 0003 Bus 0003 94.2 19.0
Load 0004 Bus 0004 47.8 -3.9
Load 0005 Bus 0005 7.6 1.6
Load 0006 Bus 0006 11.2 7.5
Load 0009 Bus 0009 29.5 16.6
Load 0010 Bus 0010 9.0 5.8
Load 0011 Bus 0011 3.5 1.8
Load 0012 Bus 0012 6.1 1.6
Load 0013 Bus 0013 13.5 5.8
Load 0014 Bus 0014 14.9 5.0
Table-2. Generator dispatch.
Generator Bus
Type
Voltage (p.u)
Minimum capability (MVA)
Maximum capability (MVA)
Gen 0001 Slack 1.060 N.A. N.A.
Gen 0002 PV 1.045 -40.0 50.0
Gen 0003 PV 1.010 0.0 40.0
Gen 0006 PV 1.070 -6.0 24.0
Gen 0008 PV 1.090 -6.0 24.0
Table-3. Generator controller settings.
Generator Bus P (MW) Q (Mvar)
Gen 0001 Bus 0001 N.A. N.A.
Gen 0002 Bus 0002 40.0 N.A.
Gen 0003 Bus 0003 0.0 N.A.
Gen 0006 Bus 0006 0.0 N.A.
Table-4. Data of lines in the power factory model.
Line From bus To bus Un (kV) R (Ω) X (Ω) B (µS)
Line 0001 0002/1 1 2 132 6.7535 20.620 151.515
Line 0001 0002/2 1 2 132 6.7535 20.620 151.515
Line 0001 0005 1 5 132 9.4142 38.862 282.369
Line 0002 0003 2 3 132 8.1875 34.494 251.377
Line 0002 0004 2 4 132 10.1251 30.722 214.647
Line 0002 0005 2 5 132 9.9230 30.297 195.133
Line 0003 0004 3 4 132 11.6758 29.800 198.577
Line 0004 0005 4 5 132 2.3261 7.337 73.462
Line 0006 0011 6 11 33 1.0343 2.166 0.000
Line 0006 0012 6 12 33 1.3385 2.786 0.000
Line 0006 0013 6 13 33 0.7204 1.419 0.000
Line 0009 0010 9 10 33 0.3464 0.920 0.000
Line 0009 0014 9 14 33 1.3842 2.944 0.000
Line 0010 0011 10 11 33 0.8935 2.092 0.000
Line 0012 0013 12 13 33 2.4058 2.177 0.000
Line 0013 0014 13 14 33 1.8614 3.790 0.000
Table-5. Data of transformers given in based on 100 MVA, with rated voltages added to the power factory model.
Transformer From
Bus
To Bus
Ur HV in kV
Ur LV in kV
r in p.u.
x In p.u.
x ohms
Transformer final turns ratio
Trf-0004-0007 4 7 132.0 1.0 0.0 0.20912 36.4371 0.978
Trf-0004-0009 4 9 132.0 33.0 0.0 0.55618 96.9088 0.969
Trf-0005-0006 5 6 132.0 33.0 0.0 0.25202 43.9170 0.932
Trf-0007-0008 7 8 11.0 1.0 0.0 0.17615 0.2131 0.000
Trf -0007-0009 7 9 33.0 1.0 0.0 0.11001 1.0900 0.000
C. Load flow analysis uses OpenDSS
Load flow analysis in operation and planning power system studies voltage angles and magnitude information for each bus; in particular, the load, the real generator power, and voltage condition. Load Flow analysis proposes for distribution network can be categorized in branch-based and node-based approaches [2]. Some of the parameters inject into the system such as injection active and reactive, current injection and bus voltage is used in a node-based approaches while in the node-based methodologies, current or power of the branch is utilized. The Open Source Distribution System Simulator (OpenDSS) which is an inclusive electrical power system simulation engine was utilized in the research. The OpenDSS software program has then had been utilized to solve the power flow through mat lab coding interface and simulation programs such as MATLAB, C#, Visual Basic (VBA), etc. It can help the researchers find a number of grid parameters, which involves losses, branch current, bus voltage, etc. In this work, the OpenDSS engine was used to obtain the power
system features such as power losses, voltage profile, power factor, active and reactive power flowing in every line, etc. [6]. In this work, the OpenDSS engine was used to solve the load flow analysis for data collection obtained from IEEE14 Bus system. The OpenDSS engine has been developed to provide a very flexible research Platform and to serve as a base for distribution analysis, enforcement such as Distributed Generation (DG) [5]. OpenDSS engine is a valuable tool to determine the optimum allocation (sizing and sitting) for both DG and Capacitor in the distribution system network; the OpenDSS engine was developed to provide a very flexible research Platform, and as a base for distribution analysis enforcement such as Distributed Generation (DG), the power flow analysis is required.
D. Particle swarm optimization (PSO)
complex non-linear Engineering issue control system; a particular control system in distribution system planning, multi-objective optimization problems with various fetters, etc. The most popular and widely used PSO algorithm is one of the accurate methods to solve the capacitor and DG location and sizing problem. The general picture of PSO particle movement Is shown in Figure-2. The optimal movement of every particle through particle movement based on best personal position, global position, and velocity of particles from the previous position to the next position. The related equation of PSO that can be elaborated from Figure-2 is shown in Equation 1 and Equation 2, respectively [7].
Figure -2. Basic structure of PSO [7].
V it+1 = ( w ∗ Vit )+∝ ( Xpbest− Xit ) + β( XGbest− Xit )(1)
Xit+1= Xit + Vit+1 (2)
Where,
Xit Refers to the current position of the particle I at iteration t
Xpbest Refers to the best personal position of the particle
Xpbest= {
Xpbest(i) if OFj+1≥ OFj
Xit if OFj+1≤ OFj (3)
X
Gbest
Refers to the best global position of particthele
X
Gbest
= {
XGbest(j) if OFj+1≥ OFj
Xpbest(j+1) if OFj+1≤ OFj (4)
Vit = Refers to the velocity of particle I at iteration t
Vit+1= Refers to the velocity of particle I towards next position
∝&β= Refers to the Acceleration coefficient W = Denote the inertia weight factor OF = Denote the Objective Function.
Where = C1 refers to the cognitive factor
= C2 refers to the social factor and r_1&r_2~ U (0, 1) are the uniformly distributed random number [8].
3. PROPOSED ALGORITHM FOR CAPACITOR ALLOCATION
The main target of the proposed algorithm is to obtain the allocation and sizing of the capacitor bank. There are two objectives for problem formulation; one is the optimum placement capacitor, and the other is the optimum sizing of the capacitor. This is a discrete optimization problem where the outcome will determine the optimum capacitor that must be installed in optimum buses.
The MATLAB software is used in this research to initialize the model and communicate to power flow engine (OpenDSS) iteratively to find the optimum solution for the related objective function. In this case, the problem formulation and details of the developed algorithm and procedure are provided as follows:
A. Input data: the data to be fed as input are listed below
a) Number of buses, bus data, and load demand (active power and reactive power) at each bus, line data and other power variables.
b) Node voltage constraint Vmin≤ Vbus≤ Vmax
The minimum voltage is 0.9, and the maximum voltage is 1.1 (±5%)
c) Select the suitable range of capacities from table 1 such that. Qic≤ Qcmax≤ Qtotal
d) Generator Operation constraint. Pimin≤ Pg≤ pimax
e) Every data is conveyed to power flow, which is executed via the OpenDSS engine, and the outcomes of power flow sent to the MATLAB software for analysis.
B. From the result, the maximum reactive power (Q) at the system is obtained by power flow; after that, injection into every bus is computed.
In this step, the lowest bus voltage in every buse will be chosen. It also finds the sensitive buses to choose the capacitor placement.
C. Initialization
placement and sizing which take into account the problem constraints.
D. Evaluation
After that, the process will evaluate the obtained results by solving the power flow during the Open DSS to determine two parameters, one of them the personal best and other global best.
E. Updates
At this stage the two parameters will be updated; one of them is the personal best and others are the global best particles.
F. PSO main loop
Steps (3 to 5) will be implemented after that until the end of the population loop in step (6). The PSO main loop starting in this step and updates of the position and velocity of particles is performed at this step. Also to find the optimal placement and bus in the distribution system as well as sizing of the DG -[11].
a) Objective Function for capacitor allocation
In capacitor placement and sizing, the total cost is included in the power losses and the capacitors costs. The objective function can be expressed as[12]:
Min OF = ∑ Cnbi=1 L . pLossi (5)
Where OF refers to the total cost function,
CL refers to the total capacitor which is provided in
PLoss i [KW] which refers to the active power losses on the bus; I and nb refer to the number of buses.
PLossi = ∑[Vi2+ Vj2− 2Vi2 . Vj2 cos(δi+ δj)]. Yijcos θij (6)
Element voltages, magnitudes, and angles are referred to as Vi , δi , Vj and δjof bus i and j. Element line admittance magnitude and the angle to referred as Yij andθij between the buses i and j, respectively.
b) Placement and sizing of capacitor in the distribution network
The utilization of capacitors in power distribution networks has several benefits of power system that include voltage profile improvement and power loss minimized due to the compensation of the reactive component of power flow. Maximum and minimum bus voltage are effected indirectly by capacitor size, which is one pf the main constraint in finding the optimum capacitor placement, and sizing, that is taken into account as a penalty factor (PF).
4. PLACEMENT AND SIZING OFDG IN THE DISTRIBUTION NETWORK
Distributed Generation (DG) is one of the critical considerations in the distribution network. DGs can reduce the total losses of the network, which are mitigated by environmental pollution. DGs can connect directly to
the network via asynchronous generator or asynchronous or indirectly by power electronic interfaces. The control method of the electrical machine and the inverter are determined via one type of DG units and its operational principle. The optimizing placement and sizing of DG in distribution networks are one of the significant issues of the distribution system. The optimizing placement and sizing of distributed generation can help to reduce the real and reactive power losses and improve the bus voltage profile in the system. In this paper, PSO technique is used to evaluate objective function for capacitor placement [9].
a) Objective function for DG allocation
The main objective function of DG allocation in this paper can be written as follows:
OF = ∑busesi=1 Plossesi + PF (7)
where OF is the objective function of DG allocation that needs to be minimized, Plossesi Are the power losses at bus I, and PF is the penalty factor of the problem constraints that can be obtained from the violations of the following inequality constraints.
∑numi=1 DGi <MaxDGnum (8)
∑Sizei=1 DGi< MaxDGsize (9)
MinDGi < DGiMaxDGi (10)
0.95 < Vi < 1.05 (11)
b) Assumptions of DG
The following assumptions are considered in the development of the objective function (PF).
(a) Max DG numbers: 3
(b) Max total size of DGs: 25.9 MW 10% of total loading.
DG unit size: 0 < 𝐷𝐺 < 50
5. RESULTS AND DISCUSSIONS
The proposed method is executed using program MATLAB that performed on IEEE- 14 standard bus case shown in Figure-1. This network consists of swing/slack bus, generators at buses 3, 6, 8 and 14 transmission lines. There are loads in 11 nodes, which are nodes 2, 3, 4, 5, 6, 9, 10, 11, 12, 13 and 14. The following subsection shows the power flow results in the standard case, after optimum capacitor placement and sizing as well as DG allocation.
a) Results of OpenDSS
case [13] in order to validate the functionality of the utilized power flow engine as results are shown in Figures 3 and 4. As it can be observed from the results, there is a minor mismatch between the OpenDSS results and standard existing results for IEEE 4 Bus test case.
Figure-3. Voltage comparison between OpenDSS and standard results.
Figure-4. Power losses comparison between OpenDSS and standard results.
b) Results after optimum capacitor placement and sizing using PSO
In this section, the optimum capacitor placement and sizing have been performed using the proposed PSO technique on IEEE 14 bus test system [13] to obtain the best possible size and location of the capacitor. Figure-5 shows the voltage comparison results after optimum capacitor placement and sizing using PSO. It indicates that by installing a capacitor at the optimum location, the voltage profile is acceptable and even improved in some of the busses. A bus 14 the voltage was violated from the standard limit before capacitor bank 1.082 p.u. Has changed to 1.0266 p.u. After installing the optimum capacitors at buses 10, 11, 13 and 14 with sizes (4300, 1050, 5250 and 4900 kvars), respectively. Moreover, the total power losses of the network have been reduced after installing the capacitor that can be seen in Figure 6 and Table-6. The power losses have been mitigated to 13304.73kW after capacitor, installation compared to 13412.2kW before installation that concluded with 107.47kW loss reduction. Also, Figure-7 shows the loss
minimization towards PSO iteration during the optimum capacitor placement and sizing.
Figure-5. Voltage comparison between before and after capacitor placement and sizing.
Figure-6. Power losses comparison between before and after capacitor placement and sizing.
Figure-7. Cost function minimization.
Table-6. Losses comparison between before and after capacitor placement and sizing.
Line name After Cap Before Cap Difference
(kW)
Line.1-2 2132.893 2147.4 -14.507
Line.1-1-2 2132.893 2147.4 -14.507
Line.1-5 2810.374 2763.8 46.574
Line.2-4 1656.84 1677 -20.16
Line.2-5 915.8718 902.3 13.5718
Line.3-4 377.3314 371.4 5.9314
Line.4-5 461.7681 516.5 -54.7319
Line.6-11 65.53716 54.7 10.83716
Line.6-12 68.91735 71.7 -2.78265
Line.6-13 213.1915 211.5 1.6915
Line.9-10 6.311715 13.1 -6.78829
Line.9-14 93.72312 116.8 -23.0769
Line.10-11 20.1528 12.3 7.8528
Line.12-13 6.439776 6.2 0.239776
Line.13-14 66.39906 53.6 12.79906
Total Losses 13304.73 13412.2 -107.47
c) Results after optimum DG placement and sizing using PSO
The connection of DG allocation in power distribution networks using the PSO Technique on IEEE 14 bus test system [13] can reduce the real power losses and voltage profile improvement. The main target of this research is to determine the optimum allocation (sizing and sitting) of DG. The DGs are installed on buses 3, 12 and 4 with sizes of 1000, 4969 and 8700 kW respectively. Furthermore, the total power loss of the network has been reduced after installing the DG and voltage profile improvement that can be seen in Figures 8 and 9. The power loss has been mitigated to 11774.1 kW after installation of DG compared to 13314.45 kW before the installation, giving 1540.35 kW losses reduction.
Figure-8. Voltage comparison between before and after DG.
Figure-9. Power losses comparison between before and after DG.
d) Results after optimum DG and capacitor placement and sizing using PSO
In this section, the optimum DG and Capacitor (placement and sizing) have been performed using the proposed PSO technique on IEEE 14 bus test system [13] to obtain the best possible size and location of the capacitor. Figure-10 shows the voltage comparison results after optimum Capacitor using PSO. It indicates that by installing Capacitor at the optimum location, the voltage profile is acceptable and even improved in some of the busses after installing the optimum Capacitor at buses 10, 11, 13 and 14 with sizes 4300, 1050, 5250 and 4900KW, respectively. Moreover, the total power losses of the network have been reduced after installing the DG at buses 4, 7 and 10 with sizes 8900, 8700 and 8300kW that can be seen in Figure-11 and Table-7. The power losses have been mitigated to 10736.27kW after DGs installation compared to 13412.2kW before installation that concluded with 1872.32kW loss reduction. Also, Figure-10 shows the loss minimization towards PSO iteration during the optimum DG allocation.
Figure-10. Voltage comparison between before and after DG and Cap placement and sizing.
Figure-12. Cost function minimization.
Table-7. Losses comparison between before and after DG placement and sizing.
Line name
After DG and Cap
Before DG and Cap
Difference (kW)
Line.1-2 1635.78 2147.4 -327.282
Line.1-1-2 1635.78 2147.4 -327.282
Line.1-5 2180.984 2763.8 -282.87
Line.2-3 2002.131 2320.2 -407.117
Line.2-4 1241.751 1677 -189.952
Line.2-5 717.1084 902.3 -63.1738
Line.3-4 546.9651 371.4 -82.6373
Line.4-5 307.86 516.5 -122.8948
Line.6-11 33.46746 54.7 -9.00947
Line.6-12 64.90024 71.7 -4.13821
Line.6-13 196.9435 211.5 -4.2817
Line.9-10 1.733241 13.1
-12.9873745
Line.9-14 104.8806 116.8 -18.67387
Line.10-11 7.404138 12.3 -0.88924
Line.12-13 5.613869 6.2 -0.13172
Line.13-14 52.96314 53.6 7.3088
Total
Losses 10736.27 13412.2 -1872.32
Table-8 shows the summary of the results that could be obtained from all above results. It illustrates that the combination of DG and capacitors can bring lots of power Losses reduction for power system as well as improvement voltage profile.
6. CONCLUSIONS
The results have shown that PSO algorithm is more efficient compared to other traditional load flow methods. The real power losses obtained via the PSO algorithm are reduced and time taken is less to calculate the real power losses. The optimal allocation (sizing and sitting) of DG using PSO technique was examined for an IEEE 14 bus system. It also studied the effects of optimally reinforcing the variables such as voltage profile improvement and loss reduction. The simulation results show that the total losses in the system without DG and capacitor is 13314.45kw compared to 10736.3kW after installing optimum capacitor and DG in the system, the power losses have reduced. In general, the power quality of the distribution system is improved.
Table-8. DG sizing and optimum capacitor placement and sizing using PSO result.
Types Selected
bus
Size (KW)
Total (KW)
Line loss at standard case (KW)
Line loss after installation (KW)
Power loss reduction, saving
Capacitor
10 4300
15500 13314.45 13304.7 9.75
11 1050
13 5250
14 4900
DG
3 10000
24952 13314.45 11774.1 1540.35
12 4969
4 9983
Capacitor + DG
DG
4 8900
25900
13314.45 10736.3 2578.15
7 8700
10 8300
Cap
10 4300
15500
11 1050
13 5250
ACKNOWLEDGEMENT
The authors are grateful to the Universiti Teknikal Malaysia Melaka (UTeM) for providing the necessary platform for this research to Centre for Robotics and Industrial Automation (CeRIA) and the Higher Institute for Water Technology, Agelat.
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![Figure -2. Basic structure of PSO [7].](https://thumb-us.123doks.com/thumbv2/123dok_us/9040880.975289/4.595.51.317.249.788/figure-basic-structure-of-pso.webp)
