Vol. 4, No. 8, August 2019
Abstract—In this paper, the optimal sitting and sizing of photovoltaic (PV) based distributed generator (DG) and distribution static synchronous compensator (DSTATCOM) are assigned separately and simultaneously under multi-load levels in radial distribution grid. Grey wolf optimizer (GWO) is an efficient optimization technique which is applied for solving the allocation problem of PV based DG and DSTATCOM in standard IEEE 85 bus distribution system. Six load levels are considered including 25%, 50%, 75%, 100%, 125 % and 150%
of rated loading for power loss minimization. Encourage results are obtained with inclusion of PV based DG or DSTATCOM in addition of that the superior case are captured with inclusion of PV units along with DSTATCOM in terms of the power losses minimization. Moreover, the simulation results verify the applicability and efficiency of GWO technique for solving the allocation problem of PV and DTSTACOM.
Index Terms—Radial Distribution Networks, D-STATCOM, Distributed Generator, Grey Wolf Optimizer.
I. INTRODUCTION
The load requirements are increased continuously in power system which leads the transmission lines be congested and the electrical systems suffer from poor power quality. Thus, flexible AC transmission systems (FACTS) devices and distributed generators (DGs) are included into the electric power system to enhance system power quality, loadability, security, as well as for cost consideration.
Different members of distributed flexible AC transmission systems (DFACTS) have been embedded in radial distribution grids (RDGs) such as; distributed static compensator (DSTATCOM), distribution static var compensator (D-SVC) and unified power quality conditioner (UPQC). DSTATCOM is a powerful device where, it has ability to provide the controllability of the bus voltage by injection or absorption of reactive power from system based on the generated voltage by converters [1-2].
Thereby, DSTSTCOM is utilized for minimizing the power loss, mitigating the harmonics, improving the network
Published on August 29, 2019.
M. A. E. Mohammed is with El-Minia High Institute of Engineering and Technology, El-Minia, Egypt (Email: [email protected]).
A. A. E. Mohammed is with Faculty of Engineering, Minia University, El Minia, Egypt (Email: [email protected]).
A. M. Abd El Hamed is Faculty of Industrial Education, Sohag University, Sohag, Egypt (Email: [email protected]).
M. E.Hessean is with Faculty of Engineering, Sohag University Sohag, Egypt (Email: [email protected]).
stability and amended the system operation [3]. Renewable based distributed generators (DGs) are wildly inserted in radial distribution grid (RDG) as an alternative solution instead of the conventional based DGs which are mainly depends upon the fossil fuels. Several technologies are emerged for renewable energy generation; the most common used technologies are solar thermal, solar photovoltaic (PV), wind and hydro types. It is well known that the renewable resources are incorporated for many economical and technical concerns [4-5].
Several algorithms have been used in RDG to determine the best placements and ratings of compensation device. The applied optimization techniques are based on nature-swarm inspired methods, human-inspired methods, physics inspired methods and evolutionary inspired algorithms which have been listed in [6-8]. As well as several algorithms have been also implemented for optimal inclusion of DG in RDGs such as; cuckoo search algorithm [9], symbiotic organisms search algorithm [10], differential evolution [11], particle swarm optimizer [12], moth-flame optimization [13], etc.
Grew wolf optimizer (GWO) is an effective technique which mimics the hunting technique and hierarchy of grey wolves [14]. In this paper, GWO is implemented to find the optimal sizing and placement of PV based DG and DSTATCOMs in IEEE 85-bus RDG. The influences of insertion the PV and DSTATCOM in this network are investigated in terms of the power quality and power loss where PV based DG and DSTATCOM under multi load ranges from 25% to 150% of the rated load. The rest of the paper is organized in four sections: Section I shows the problem formulation including the objective function.
Section II presents the procedure of the GWO technique.
Section III presents the simulation results and the corresponding discussions. Section IV shows the conclusion of this work.
II. PROBLEM FORMULATION
The radial distribution grids (RDGs) include series branches which denote the distribution lines, balanced power nodes and constant loads in Ref. [15] Eqs. (1-2) are used to obtain the power flow solution in the RDG with inclusion PV units and DSTATCOM shown in Fig. 1.
Pn+1= Pn− PL,n+1− Rn,n+1(P|Vn2+jQn2
n|2 ) + PPV (1)
Optimal Allocation of Photovoltaic Based and
DSTATCOM in a Distribution Network under Multi Load Levels
Montaser Abd El Sattar Mohammed, Adel A. Elbaset Mohammed, Amal M. Abd El Hamed and Mohamed E. Hessean
Qn+1 = Qn− QL,n+1− Xn,n+1(Pn2+jQn2
|Vn|2 ) + QDSTATcom (2)
n n jX R
1
V
nn L n
L jQ
P, , PL,n1jQL,n1
1
1
n
n jQ
P
V
nn
n
jQ
P
DSTATCOM
I
nPV QSTATCOM
PPV
Fig. 1. RDG with PV and DSTATCOM.
where, Xn,n+1 and Rn,n+1 are reactance and resistance of the line between buses n and n + 1, respectively. Qnand Pn are the real and reactive powers flows, respectively. The active power losses and reactive power losses are given as follows:
Ploss(n,n+1)= Rn,n+1(Pn2+jQn2
|Vn|2 ) (3)
The voltage stability index can be found as follows:
VSI(n+1)= |Vn|4− 4(Pmn+1Xn− Qn+1Rn)2− 4(Pn+1Xn+ Qn+1Rn)|Vn|2 (4) where, VSI(n+1) is the voltage stability index, voltage deviations of RDG can be found as follows:
VD = ∑nh=1|Vn− 1| (5) where, n is number of system buses. The system equality and insulate constraints are considered as follows:
A. Equality constraints Ps+ ∑ PPV
np
i=1 = ∑n PD
h=1 (h) + ∑nlj=1P loss(j) (6) Qs+ ∑nci=1QDSTATcom(i) ∑nh=1QD(h) ∑nlj=1Q loss(j) (7)
B. Inequality constraints
Vmin≤ Vi≤ Vmax (8)
∑nc QDSTATCO
i=1 (i) ≤ ∑n QD
i=1 (i) (9)
∑ PPV np
i=1 (i) ≤ ∑n PD
i=1 (i) (10) In≤ Imax,n n = 1,2,3 … , Nb (11) where, Ps and Qs are the supplied active power and the supplied reactive powers at substation, respectively.
PD and QD are the active load and reactive load, respectively.
nl is number of transmission lines in RDG. nc is number of DSTATCOMs. np is the number of PV units. Vmin and Vmax are the lower and the upper voltage limits. PD and QD are the active reactive loads. QDSTATCOM is injected reactive power by the DSTATCOM. PPV is injected reactive power by the PV units.
III. GREY WOLF OPTIMIZER ALGORITHM
The Grey wolves are predators living together in groups (pack). The pack of grey wolves has a special social hierarchy where the leadership in the pack is divided into four levels which are alphas, beta, omega and delta. Alpha wolf (α) is the first level in social hierarchy hence alpha wolf is the leader where it guides the pack and the other wolves respond to its orders. Beta wolf (β) is being in the second level of leadership where it helps the alpha wolf directly for the activities of the pack. Delta (δ) wolves come in the third level of hierarchy where, it follows α and β wolves [14]. The rest of wolves are the omegas (ω) which submit to whole group Fig. 2.
Fig. 2. Hierarchy of grey wolves.
A. Social hierarchy
The best solution is considered as the alpha (α). Hence, the second and the third solution are considered as β and δ and the other solutions will be treated as ω wolf.
B. Surrounding the prey
The grey wolves encircle the prey in hunting process which can be mathematically modeled as follows:
D = |C. kp(t) − X(t)| (12) X(t + 1) = Xp(t) − A. D (13) where, t is the current iteration Xp is the position vector of the prey, and X indicates the position vector of a grey wolf. A and C are coefficient vectors which can be calculated as follows by.
A = 2a. r1− a (14) C = 2. r2 (15) where, a is value that is decreased linearly from 2 to 0 with iterations.r1and r2are random numbers in range [0, 1].
C. Hunting the prey
In hunting process, the pack is affected by α, β and δ hence, the first three best solutions are saved as best agents (α,β, δ) and the other search agents are updated their positions according to the best agents as follows:
D = |C. Xp(t) − X(t)| (16)
Vol. 4, No. 8, August 2019
Dα= |C1. Xα− X| (17)
Dβ= |C2. Xβ− X| (18)
Dδ= |C3. Xδ− X| (19)
X1= Xα− A1. (Dα) (20)
X2= Xβ− A2. (Dβ) (21)
X3= Xδ− A3. (Dδ) (22)
X(t + 1) =X1+X2+X3 3 (23) D. Attacking the prey
The last stage in hunting is attacking the prey where the grey wolf attack when the prey stop moving. It can be achieved mathematically by reducing the value of a is gradually from 2 to 0 consequently, A is varied randomly with variation of a and it will be in range [-1, 1], hence the next location of search agents will be between its current position and the position of the prey.
IV. SIMULATION RESULTS
In this section GWO is applied for determining the optimal ratings and sizes of PV based DG and DSTATCOM in 85-bus system. The system data are given in [16-17]. The system load is 25.703+ j 26.220 MVA with 12.66-kV base voltage and the single line diagram is shown in Fig. 3. At the base case (100 % loading) the active and reactive power losses equal to 316.103 kW and 198.593 kVar, respectively.
The minimum voltage value is 0.87131 p.u at bus 54.
Several load levels are taken into considerations which are;
25%, 50%, 75%, 100%, 125 % and 150%. The active power losses without incorporating of PV or DSTATCOM for the previous load levels are 16.635 kW, 70.095 kW, 166.957 kW, 316.103 kW, 316.103 kW and 827.329 kW, respectively. However, the simulation results without PV and DSTATCOM are tabulated in Table I. Judging from Table I, the most severe case at the highest load level (150%) where the power losses increased with increasing of the load levels as well as the voltage stability decreased with increasing of the load level. Fig. 4 shows the voltage profile without PV or DSTATCOM. Referring to Fig. 4, the minimum value of the voltage magnitude is 0.79053 p.u at bus number 54 at 150% load level.
In case of inclusion the PV unit only, the power losses are reduced to 10.517 kW for the light load level (25%) and 445.197 kW for the most severe case (150 %), respectively.
Thus, insertion the PV unit can minimize the power losses considerably as depicted in Table II. The optimal location for this case at bus no. 28 and the selected best size of PV unit under different load levels are listed in Table II. Judging from Table II and Fig.5, it is obvious that, the voltage profile and the voltage stability are enhanced compared to the aforementioned case.
In case of inclusion the DSTATCOM optimally, the power losses are reduced to 10.817kW for the light load level (25%) and 827.329kW for the most serve case (150
%), respectively compared to first case (without PV or DSTATCOM). Thus, insertion the DSTATCOM can minimize the power losses considerably as depicted in Table III as well as the system stability is enhanced compared to first case. The best location of DSTATCOM is situated at bus no. 29. Judging from Table III and Fig.6, it is obvious that the voltage profile and the voltage stability are enhanced considerably compared to first case.
In case of optimal integration, the PV unit and the DSTATCOM simultaneously. The optimal ratings and locations of PV and DSTATCOM and the simulation results for this case are listed in Table IV. The power losses are reduced to 8.996kW for the light load level (25%) and 166.275kW for the most severe case (150 %), respectively as depicted in Table IV. The voltage profile of system for this case is shown in Fig. 7, it is clear that, the voltage profile is enhanced considerably where the minimum voltage at the most severe case is improved to 0.93245 p.u.
As well as the voltage stability enhanced compared to all the aforementioned cases. Table V shows the power losses for the presented cases, it is clear that; insertion of PV along with DSTATCOM is superior compared to other case.
1
s
2 16
10 11 9 7 8 6 4
3 5 13 14
17
12 15 19
20 21
47 46 18
27 28 25 26 22
4041
31 32
29 30 33 34
42 43
35 36
45 44
50 49
56
51 48
52 53 54
55
80 81 82
83 84 59 58 57
61
62 63
60
65
66 64
68 67 79 77
70 69
73 72 74
75 71
1 2 3 4 5 6 7 8 9 10 11 12 13 14
15 16 18 19 20 21
25 26 27 28 29 30 31 32 33 34 35
39 40 41
42
44 43 46 45
47
48
49
50 51
52 53
54
57 56 58
60
61 63 62 64 65
68 67 70 69
71
72 73
74 78 76
79 80 81
82 83
Fig. 3. Single line diagram of 85-bus system.
TABLEI:SIMULATION RESULTS OF THE BASIC CASE
Load Level 25 % 50 % 75 % 100 % 125 % 150 %
𝐏𝐥𝐨𝐬𝐬(𝐤𝐖) 16.635 70.095 166.957 316.103 316.103 827.329
𝐕𝐃(𝐩. 𝐮) 1.7840 3.6650 5.6610 7.7963 10.1050 12.6376
𝐕𝐦𝐢𝐧(𝐩. 𝐮)@
bus No.
0.97068 @ bus 54
0.93968 @ bus 54
0.90671 @ bus 54
0.87131 @ bus 54
0.83289 @ bus 54
0.79053 @ bus 54
∑ 𝐕𝐒𝐈 77.1168 70.3893 63.8143 57.3865 51.0974 44.9335
Total Reactive
Loss (KVAR) 10.465 44.081 104.946 198.593 332.798 519.062
TABLEII:SIMULATION RESULTS WITH INCLUSION PVONLY
Load Level 25 % 50 % 75 % 100 % 125 % 150 %
𝐏𝐥𝐨𝐬𝐬(𝐤𝐖) 10.517 43.282 100.342 184.076 297.245 445.197
𝐕𝐃(𝐩. 𝐮) 0.9887 1.9501 2.9600 3.9421 4.9794 6.4872
𝐕𝐦𝐢𝐧(𝐩. 𝐮)@ bus No. 0.98293 @ bus 76
0.96592 @ bus 76
0.94812 @ bus 76
0.93034 @ bus 76
0.91164 @ bus 76
0.88732 @ bus 76
∑ 𝐕𝐒𝐈 80.1227 76.4982 72.8418 69.4306 65.9780 61.2224
Optimal PV
Location (Size kW) 28(406.0287) 28(850.3208) 28(1.2958) 28(1.7837) 28(2.2749) 28(2.5703) TABLEIII:SIMULATION RESULTS WITH INCLUSION DSTATCOMONLY
Load Level 25 % 50 % 75 % 100 % 125 % 150 %
𝐏𝐥𝐨𝐬𝐬(𝐤𝐖) 10.817 43.826 103.037 191.956 331.834 827.329
𝐕𝐃(𝐩. 𝐮) 1.3945 2.6025 3.9805 5.4647 6.2784 12.6376
𝐕𝐦𝐢𝐧(𝐩. 𝐮)@ bus No. 0.97745 @ bus 54
0.95819 @ bus 54
0.93602 @ bus 54
.91205 @ bus 54
0.89906 @ bus 76
.79053 @ bus 54
∑ 𝐕𝐒𝐈 78.5767 74.1221 69.3070 64.4264 61.8738 44.9335
Optimal DSTATCOM
Location (Size kVar) 29(300.4717) 29(793.8665) 29(1.2045) 29(1.5915) 29(2.5775) 29(0)
TABLEIV:SIMULATION RESULTS WITH INCLUSION DSTATCOM AND PV UNITS
Load Level 25 % 50 % 75 % 100 % 125 % 150 %
𝐏𝐥𝐨𝐬𝐬(𝐤𝐖) 8.996 22.079 37.859 68.085 107.708 166.275
𝐕𝐃(𝐩. 𝐮) 1.2367 1.6998 1.2711 1.6751 1.9215 3.5612
𝐕𝐦𝐢𝐧(𝐩. 𝐮)@ bus No. 0.97910 @ bus 54
0.97072 @ bus 54
0.97293 @ bus 76
0.96402 @ bus 76
0.95712 @ bus 76
0.93245 @ bus 76
∑ 𝐕𝐒𝐈 79.1758 77.4330 79.0569 77.5450 76.6790 70.7882
Optimal PV
Location (Size kW)
26(57.3190) 26(687.2352) 26(1.4554) 26(1.9515) 26(2.5218) 26(2.5703)
Optimal DSTATCOM Location (Size kVar)
26(384.1478) 26(591.5697) 26(1.3855) 26(1.8866) 26(2.4419) 26(2.5975)
TABLEV:SIMULATION RESULTS OF TOTAL POWER LOSSES
Values without PV or DSTATCOM with PV only with DSTATCOM only DSTATCOM and PV units
Total P losses (kW) 316.103 445.197 827.329 107.708
Total Q loss (kVar) 198.593 266.221 519.062 48.692
Fig. 4. Voltage profile of system without PV or DSTATCOM.
Vol. 4, No. 8, August 2019
Fig. 5. Voltage profile of system with PV only.
Fig. 6. Voltage profile of with DSTATCOM only.
Fig. 7. Voltage profile of system with insertion of PV along with DSTATCOM.
V. CONCLUSION
In this paper, the optimal sitting and sizing of PV and DSTATCOM are assigned separately and simultaneously under multi-load levels. Grey wolf optimizer (GWO) was applied for solving the allocation problem of PV based DG and DSTATCOM in standard IEEE 85 bus distribution system. Six load levels are considered include 25%, 50%, 75%, 100%, 125 % and 150% of the rated loading for power minimization. The investigations are performed with four studied cases which include the system without PV or compensation, with incorporating PV based DG only, with incorporating DSTATCOM only and with incorporating PV along with DSTATCM. The simulation results indicated that inclusion of PV units or DSTATCOM separately or simultaneously where the superior case is captured with inclusion of PV units along with DSTATCOM in terms of the total power losses. In addition of that the simulation results verified the effectiveness of the proposed technique for solving the allocation problem of PV and DSTATCOM in RDGs.
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