Apr 2, 2014 - Alexandria, EGYPT. Abstract:- Unified power flow controller (UPFC) is an advanced member of the group of flexible AC transmission systems.
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April 2014
Power Flow Control using UPFC Device Gehan Gouda.M. A.1, Abdel-Moamen M. A.1 and Gaber Shabib. 2 1
Faculty of Energy Engineering, Aswan University, P.O. Box: 81528, Aswan, EGYPT. 2 King Marriott Academy for Engineering & Technology. Alexandria, EGYPT
Abstract:- Unified power flow controller (UPFC) is an advanced member of the group of flexible AC transmission systems (FACTS). This paper is focused on the steady-state modeling of UPFC for the implementation of the device in the conventional Newton-Raphson (NR) power flow algorithm. Performance of the proposed model has been tested for IEEE 6 bus systems. Suitable methods to determine the best locations of UPFC have been suggested in this paper. UPFC can be theoretically located anywhere along transmission line. In this respect, the effects of UPFC allocation on power system steady-state operation have also been investigated in detail. Index Terms — Index Unified Power Flow Controller (UPFC), FACTS Devices, Newton- Raphson, SSSC, TCSC and STATCOM.
I.
INTRODUCTION
The rapid development of power electronics has made it possible to design power electronic equipment of high rating for high voltage systems, improved by use of the equipment well-known as Flexible AC Transmission Systems (FACTS) controllers. Power flow is a function of transmission line impedance, the magnitude of the sending and receiving end voltages, and the phase angle between the voltages. By controlling one or a combination of the power flow arguments, it is possible to control the active, as well as the reactive power flow in the transmission line.
Fig. 1. Structure of UPFC.
Gyugyi [1] has proposed the concept of using the UPFC to control independently the real and reactive power flows at both the sending and receiving ends of the transmission line. Gyugyi [2] also compared the performance and equipment of the UPFC to the more conventional, but related power flow controllers, such as the Thyristor controller Series Capacitor and the Thyristor controller Phase Angle Regulator and concluded that due to the flexible capability and performance of the UPFC in controlling the power flow, this device would become the most important FACTS device.
During the last decade, continuous and fast improvement of power electronics technology has made flexible AC transmission systems (FACTS) a promising concept for power system applications. With the application of FACTS technology, power flow along transmission lines can be more flexibly controlled. Among a variety of FACTS controllers, UPFC is one of the more interesting and potentially the most versatile. it can provide simultaneous and independent control of important power system parameters: line active power flow, line reactive power flow, impedance; and voltage . Thereby, it offers the necessary functional flexibility for the combined application of phase angle control with controlled series and shunt compensation.
The UPFC is implemented practically by using two similar solid-state phase voltage source converters (shunt compensation block and series compensation block) which are connected through a common DC link capacitor as shown in Figure. 1 and each converter is coupled with a transformer. In the last few years, a number of publications have appeared in the literature, which described the basic operating of the UPFC [5–8]. In Ref. [9-10] a comparison of different models for UPFC using load flow study has been performed. The paper illustrated the necessity of modeling the controller as well as studying the individual function offered by various FACTS devices.
In recent years UPFC has been proposed to increase power flow as well as an aid for system stability through the proper design of their controllers [1–4]. It is becoming to be one of the most important FACTS devices since it can provide various types of compensation, i.e. voltage regulation, phase shifting regulation, impedance compensation and reactive compensation.
The basic function of Inverter 1 is to supply or absorb the real power demanded by Inverter 2 at the common dc link. This dc link power is converted back to ac and coupled to the transmission line via a shunt connected transformer. Inverter 1
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1 can also generate or absorb controllable reactive power, if it is desired, and thereby it can provide independent shunt reactive compensation for the line. It is important to note that whereas there is a closed “direct” path for the real power negotiated by the action of series voltage injection through inverter 1 and 2 back to the line, the corresponding reactive power exchanged is Supplied or absorbed locally by Inverter 2 and therefore it does not flow through the line. Thus Inverter 1 can be generated at a unity power factor or can be controlled to have a reactive power exchange, with the line independently of the reactive power exchanged by Inverter 2 [11].
B. Model of the Shunt Converter The shunt converter voltage Vp and the associated transformer impedance Zp of the UPFC are separately shown in Figure 3(a). The converter injects a complex power Sp (=Pp+jQp) into the network at the bus f. The power injection model of the converter is shown in Figure 3(b). For a given Vp, the shunt converter current Ip can be derived from Figure 3(a) as, f
I
Zs I fm m
mt
Is
Is
Is
f I m If
S mt
(b)
V Vp Vf f Z p
*
S ms (c)
Zs
V s s +
m
t
S
c
Fig. 2. Representation of series converter model of UPFC. Transm ission
Sf = Sfs + Ps
The active power injection (Ps) into the system by the series converter can be derived as;
V V V s m Ps Re Vs I m Re Vs f Z s *
*
(4)
The overall model of the UPFC can now be obtained by combining the equivalent circuits of the series converter (Figure2) and shunt converter (Figure3). The ultimate circuit is shown in Figure 4 and it represents the proposed UPFC model for load flow studies. It consists of a synchronous condenser (with P = 0), two fictitious loads (Sf and Sm), and an impedance (Zs). All of these elements can easily be incorporated into any standard load flow and optimal power flow programs. P=0 f I s
(a)
*
C. Overall Model of the UPFC
Z Sfm m s Smf
(3)
Zp
Where the reactive power Qp of the converter is used to maintain the desired voltage magnitude at bus f. However, the active power Pp of the converter needs to satisfy the active power balance of the UPFC as stated in equation (4).
(1) f
Vf Vp
S p Pp Q p Vf I p
The series injected voltage source Vs. of the UPFC can be easily transformed into a current source, Is, as shown in Figure 2. The value of Is is given by [14]
If
(c)
And shunt converter complex power Sp can be expressed by
Model of the Series Converter
m
Qp = 0 (b)
Ip
UPFC has three controllable parameters, namely the magnitude and the angle of inserted series voltage (Vs, s) and the angle of the inserted shunt voltage (p).
Zs
Pp - Ps = 0
Fig. 3 Representation of shunt converter model of UPFC.
However, both the series and shunt converters are capable of absorbing or supplying reactive power independently. The reactive power of the shunt converter can be used to regulate the voltage magnitude of bus f in the AC system.[13,15,7,8]
f
f
If
Sp = Pp + j Qp
(a)
Ps + P p = 0
V Is s Zs
f
Zp + Ip
Vp
The steady state model of UPFC consists of two ideal voltage sources, one in series and one in parallel with the associated during transmission line. Neglecting the losses of the converters and the associated coupling transformers steadystate operation it neither absorbs nor injects real power into the system the active power balance of the UPFC becomes;
If
If
If
II. UPFC STEADY-STATE MODEL
A.
April 2014
(2)
S = S m ms
Fig. 4 Overall UPFC model for load flow study
From Figure (4), 2
Line
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I fm I p I m
Vf Vp Vf Vs Vm Zp Zs
Pmf
(5)
1 1 1 1 1 Vf Vm Vs Vp Z Z Zs Zs Z p p s
Q mf
The relation between If and Im as a function of Vf and Vm are; I fm I mf
1 1 Z Z s p 1 Zs
Vf 1 Zs 1 1 Zs Vm Zs
1 Zs
Vf Vp Zp
and Y =
Vf Vs Vm Zs
Vf 1 Zs 1 1 Zs Vm Zs
1 Zs
Similarly, relation between Imt and Itm as a function of Vm and Vt can be obtained as;
I m Yff I Y t tf
V s (9) 0 V p
1 Zp
If Yff + 1 1+ Y Z Z ff s p = Ytf It 1+ Yff Zs
going through line f-m can be formulated by the following equations (for simplicity, neglecting resistances).
(11)
I f I t
Where:
where
2
Yff
Similarly, the real and reactive power going through line mf are;
Yft Vf Yff 1+ Yff Zs 1+ Yff Zs + Yft Ytf Zs Ytf Ytt 1+ Yff Zs Vt 1+ Yff Zs
Yff Yp Yftt Vf Yff = Y V + Y Y tf tt t tf
VV VV VV Q fm V f f m cos fm f p cos fp f s cos fs X sX p Xs Xp Xs
X s X p
(14)
By using equations (9), (13) and (14), the relation between
(10)
By using equations (9) and (10), the real and reactive power
V fV p VV V fV m sin fm sin fp f s sin fs Xs Xp Xs
(13)
1 1 Vf Yft Vt Vs Z Zs V Z Y V V Vm s f s ft t s 1 1 Zs Yff Yff Zs
I fm and I mf obtained from
Sfm Vf Ifm * and Smf Vm I mf *
Yf t Vm Ytt Vt
By equalizing Im from above equations the relation between Vm as a function of Vf and Vt can be obtained as;
equation (9) and are given by;
Pfm
Bc 2
Yft Ytf G ft jB ft Y
(8)
Complex powers can be determined by substituting the values of
(12)
1 Z
Yff Ytt G ff jB ff Y j
The relation between If and Im as a function of Vf and Vm are; 1 I fm 1 Z Z p s 1 I mf Zs
V V V 2 VV m f m cos mf m s cos ms Xs Xs Xs
(6)
(7)
1 1 1 1 1 Vf Vm Vs Vp Z Z Z Z s s s p Zp
V V V fV m sin mf m s sin fs Xs Xs
Vf V f f , Vt V t t , Z = R + jX
V s 0 V p
1 Zp
Sfm Vf I fm * and Smf Vm I mf * I fm I p I m
April 2014
G ff jB ff
Yp Vs 0 Vp
YYZ Yff , Ytt Gtt jB tt Ytt - ft tf s 1+ Yff Zs 1+ Yff Zs
Y 1 Yftt Ytf G ft jB tf ft and Yp 1+ Yff Zs Zp
3
1 V s Zp 0 Vp
(15)
(16)
(17)
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S finj Vf I finj *
The power flow equations from bus-f to bus-t and from bus-t to bus-f are as follows,
Sft Pft jQft Vf I*ft Vf Yff Vf Vs Yft Vt Yp Vp Vf
Stinj Vt Itinj *
*
Stf Ptf jQtf Vt Itf* Vt Ytf Vf Vs Yttt Vt
*
PfinjUPFC V f 2G ff V f V t G ft cos ft B ft sin ft +V f V s G ff cos fs B ff sin fs +V f V p G p cos fp -B p sin fp
Pft G ff (V f 2 +V f V s cos fs )+G ft (V f V t cos ft )+G p (V f V p cos fp ) Q ft G ff (V f V s sin fs )+G ft (V f V t sin ft )+G p (V f V p sin fp )
(25)
From equations (23) and (25) the injected real power at bus-f (Pfinj) and reactive power (Qfinj) of a transmission line having a UPFC are as follows,
(18)
Active and reactive power flows of the line with UPFC are,
B ff (V f V s sin fs ) B ft (V f V t sin ft ) B p (V f V p sin fp )
April 2014
Q
(19)
UPFC finj
(26)
V f B ff V f V t G ft sin ft B ft cos ft 2
+V f V s G ff sin fs B ff cos fs +V f V p G p cos fp +B p cos fp
B ff (V f V f V s cos fs ) B ft (V f V t cos ft ) B p (V f V p cos fp ) 2
Similarly, Ptf Gtf (V tV f cos tf +V tV s cos ts )+Gtt V t 2 Btf (V tV f sin tf +V tV s sin ts ) Qtf Gtf (V tV f sin tf +V tV s sin ts ) +Btt V t 2 Btf (V tV f cos tf +V tV s cos ts )
And the real power
injections at bus-t can be expressed by
PtinjUPFC V t 2Gtt V f V t Gtf cos tf Btf sin tf +V tV s Gtf cos ts - B tff sin ts
(20)
QtinjUPFC V t 2Btt V f V t Gtf sin tf Btf cos tf +V tV s Gtf sin ts - B tff cos ts
Hence from equations (19) and (20), the real power loss ( PLl ) in line-l connected between bus-f and bus-t is:
PLl V f 2G ff V t 2Gtt 2V f V t G ft cos ft +V f V p G p cos fp -B p sin fp V f V s G ff cos fs B ff sin fs +V tV s Gtf cos ts - B tff sin ts
I finj Yff = Itinj Ytf
Y YZ V Y ff ft s f ff 1 Yff Zs 1 Y Z ff s Yft Ytf Zs Ytf 1 Yff Zs Vt 1 Yff Zs
Yftt Vf Yff + Ytt Vt Ytf
1 V s Zp 0 Vp
Yp Vs 0 Vp
Pft Pft Pft spec 0
(21)
Q ft Q ft Q ft spec 0
Yftt Ytf G ft jB tf
(28)
Where PftSpec , Q ftSpec are specified active and reactive power flows, respectively.
Pft and Q ft are the calculated active
and reactive power flows in the line l. It may be expressed by;
Pft V f 2G ff +V f V t G ft cos ft B ft sin ft
+V f V s G ff cos fs B ff sin fs +V f V p G p cos fp -B p sin fp
(22)
Q ft V f 2B ff +V f V t G ft sin ft B ft cos ft
(29)
+V f V s G ff sin fs B ff cos fs +V f V p G p cos fp +B p cos fp
Where, Yff
(23)
Where,
G ff jB ff
Yftt Ytf G ft jB tf
Y 2Z YYZ 1 Yff G ff jB ff ff s , Ytt Gtt jB tt ft tf s 1 Yff Zs Z p 1 Yff Zs
(27)
The active and reactive power flow control constraints of the UPFC are,
The injected currents [14] Ifinj and Itinj can be obtained by subtracting equation (2) from equation (21) and their relationship with Vs and Vp is: 2 I finj Yff Zs 1 1 Y Z Z ff s p Yff Yft Zs Itinj 1 Yff Zs
UPFC UPFC Ptinj and reactive power Qtinj
Ytt G tt jB tt Ytt -
(24)
Yff Yft Zs 1 Yff Zs
Yp
Yff , and Yp defined in equation (20).
Yff 1+ Yff Z s
Yft 1+ Yff Z s
(30)
Yft Ytf Z s 1+ Yff Z s
1 Zp
A compact Newton-Raphson power flow algorithm is presented as follows: (31) F ( X)i J i .Xi
The injected powers at bus-f ( S finj ) and bus-t ( Stinj ) may
Where ∆X is the solution vector and J is the matrix of partial derivatives of F(X) with respect to X, Jacobian matrix, and they can be calculated as:
be formulated as;
4
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Pf V t
Pf s
Pf V s Pt Pt Pt Pt V t s p V s Q f Q f Q f Q f V t s p V s Qt Qt Qt Qt V t s p V s Pft Pft Pft Pft V t s p V s Q ft Q ft Q ft Q ft V t s p V s PE PE PE PE V t s p V s
(32)
Pf p
Fig. 5 Model of 6 bus system in PSAT[15]
UPFC devices are installed in Line # 2, Line # 6, Line # 8 and Line # 9 one by one respectively as shown in Fig. 6 to control the power flow for the following different cases: Case a: Control power flow in particular line by 17.5% series compensation Case b: Control power flow in particular line by 20 % series compensation Case c: Control power flow in particular line by -20 % series compensation 2 6
(33)
UPFC
1
5
UPFC
P , Q , P and Q
4
f f t t , are the active and Where reactive power mismatches at the terminal buses f and t
UPFC
f t V f ΔX V t s p V s
UPFC
Pf P t Q f F ( X ) Q t , Pft Q ft PE Pf Pf Pf V t f f Pt Pt Pt f t V f Q Q Q f f f f t V f Qt Qt Qt J f t V f Pft Pft Pft V t f f Q ft Q ft Q ft f t V f PE PE PE f t V f
April 2014
P , Q , P and Q
f t t are the sum of active and respectively. f reactive power flows leaving the terminal buses f and t respectively. Pft and Q ft are the active and reactive
Fig. 6 Six-Bus Test System with Different UPFC
power flow mismatches for the line l respectively. And PE is the active power exchange between the converters via the common DC link.
Adopted limitations of branches for all cases of study are as given in Table 1.
III. RESULTS AND DISCUSSION
Table 1. Line Data and Base Case Power Flows
In order to demonstrate the performance of the N-R power flow Line From To R X B Rating with UPFC devices, Six Bus system [8] is considered. UPFC has # Bus Bus p.u. p.u. p.u. MW a working range between -70% and 20% of line impedance [12] 2 3 6 0.02 0.1 0.02 50 (i.e. -0.7X: 0.2 X), where X is the reactance of the transmission 6 2 4 0.05 0.1 0.02 20 line where the UPFC installed, without violating the thermal 8 1 4 0.05 0.2 0.04 20 rating limit of the particular lines. 9 1 5 0.08 0.3 0.06 60 Figure 5 show the 6 bus- system test developed in PSAT software. In this system, there are using 3 generators, 11 Voltages results in different buses are tabulated in Table 2 and transmission lines, 6 busses and 3 loads [16]. they plotted in Fig 7, Fig 8 and Fig 9 5
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TABLE 2 Buses Voltages with and without UPFC for Different Cases Voltage
UPFC installed in Line # w/o
V4
0.986
0.986
0.986
0.985
1.009
1.010
0.985
0.995
0.996
0.986
0.987
0.987
0.986
V5
0.969
0.971
0.971
0.967
0.972
0.972
0.969
0.970
0.970
0.969
0.978
0.979
0.969
V6
0.991
1.003
1.004
0.989
0.992
0.992
0.991
0.992
0.991
0.991
0.993
0.993
0.991
c
a
9 b
c
a
2 b
c
a
6 b
c
a
8 b
c
a
9 b
c
TABLE 3 power flow results with and without UPFC for different cases
2
6
a
b
c
a
UPFC INSTALLED IN LINE # 8 b c a b
Vq
(pu)
0.013
0.015
-0.013
0.013
0.015
-0.013
0.018
0.021
-0.017
0.026
0.029
-0.023
Iq
(pu)
0.755
0.761
0.685
0.769
0.774
0.703
0.431
0.438
0.345
0.449
0.457
0.362
CP
(%)
17.5
20
-20
17.5
20
-20
17.5
20
-20
17.5
20
-20
49.68
49.68
49.68
60.50
60.50
60.50
39.79
39.79
39.79
37.82
37.82
37.82
50.53
50.99
44.59
58.98
59.50
52.11
41.64
42.26
34.16
39.82
40.51
31.64
6.29
6.28
6.43
4.47
4.46
4.64
5.67
5.61
6.48
5.48
5.41
6.37
Power flow (w/o) (MW) power flow (with) (MW) Total Power loss (MW)
1.02 1.01 1
0.97
#9 Li ne
w/ o
# Li ne
# Li ne
# Li ne
# Li ne
9
0.94
8
0.94 6
0.95
2
0.95
#8
0.96
Li ne
0.96
0.98
#6
0.97
V6
Li ne
0.98
0.99
V4 V5
#2
0.99
w/ o
Voltage pu
1
V4 V5 V6 Voltage pu
1.01
Li ne
1.02
Fig.8 buses voltages with different placement of UPFC (case b)
Fig.7 buses voltage with different placement of UPFC (case a)
6
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70
1.02
Voltage PU
1
V4 V5 V6
60 Power Flow MW
1.01
0.99 0.98 0.97 0.96
40 30 20
0 9
Line #2
Line #6
Line #8
Line #9
Li ne
#
8 Li ne
#
6 Li ne
#
2 # Li ne
w/ o
0.94
Fig.11
Fig.9 buses voltages with different placement of UPFC (case c)
Line Power Flow with and without UPFC case (b)
According to Table (2) and Figs. 7, 8 and 9, if UPFC installed in Line # 6, V4 is decreased from 0.985924 to 0.9852 pu , also V5 increased from 0.968541 to 0.9686 pu and V6 decreased from 0.991211 to 0.9911 pu.
70 60 power Flow MW
Comparing this change with the other UPFC placement. From above it is shown that the best rate of increasing voltage for all buses happened with UPFC which installed in Line # 6. To compare the power flow results with and without UPFC for different cases which can be concluded in Table 3 and plotted in Figs. 10 to15, which indicates that when power flows for all lines are increased, the total real power loses will increased.
W/O With
50 40 30 20 10 0 Line #2
From Figs. 10 to 15, Line # 6 has the smallest total power losses with different cases where the real power loss of line # 6 decreased to 0 with different cases. If UPFC is installed in Line # 6 the system reaches to its minimum power loss
Fig.12
Line #6
Line #8
Line #9
Line Power Flow with and without UPFC case(c)
7 70
case (a)
Total power loss
6.5 W/O With
60
Power Flow MW
W/O With
50
10
0.95
50 40
6 5.5 5 4.5 4
30
3.5 20
Line # 2
10
Fig.13
0 Line #2
Fig.10
April 2014
Line #6
Line #8
Line #9
Line Power Flow with and without UPFC case (a)
7
Line # 6
Line # 8
Line # 9
Total power loss with different UPFC placement (case a)
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REFERENCES 7
[1]. Gyugyi L. Unified power flow controller concept for flexible AC transmission systems. IEE Proc-C 1992; 139(4):323–31, 1992.
case (b)
Total power loss MW
6.5
[2]. Gyugyi L, Schauder CD. The unified power flow controller: a new approach to power transmission control. IEEE/PES, Summer Meeting, San Francisco, CA; July 24–28, 1994.
6 5.5
[3].
5
[4]. S.A. Nabavi-Niaki, M.R. Iravani, “Steady State and Dynamic Models of Unified Power Flow Controller (UPFC) for Power System Studies”, IEEE trans. on power systems, Vol. 11, No. 4, November, pp.19371943, 1996.
4.5 4
[5]. Muwaffaq I. Alomoush, “Exact Pi-Model of UPFC-Inserted Transmission Lines in Power Flow Studies”, IEEE Power Engineering Review, pp. 5456, December 2002.
3.5 Line # 2
Fig.14
Line # 6
Line # 8
Line # 9
[6]. Fang Dazhong, Dong Liangying and T.S.Chung, “Power Flow Analysis of Power System with UPFC Using Commercial Power Flow Software”, PES Winter Meeting, pp. 2922-2925, 2000.
Total power loss with different UPFC placement (case b)
[7]. Fang Dazhong and T.S.Chung, “Development of New Techniques for Power Flow Analysis of Power System with UPFC”, Proceeding of the 5th International Conference on Advances in Power System Control, Operation and Management, APSCOM, Hong Kong, October 2000.
7 Total power loss MW
case (c)
6.5
[8]. F.M.El-Kady, “Preventive/Corrective Control to Enhance Security Level Using Unified Power Flow Controllers”, Proceedings of the 8th International- -231- References Middle-East Power Systems Conference (MEPECON’2001), Cairo-Egypt, December 29-31, pp. 697-704, 2001.
6 5.5 5
[9]. Alireza Farhangfar, S. Javad Sajjadi, and Saeed Afsharnia “ Power Flow Control and Loss Minimization with Unified Power Flow Controller (UPFC)”Electrical and Computer Engineering, 2004, Canadian Conference, Vol.1, pp.385-388, May, 2004.
4.5 4
[10]. A.M. Vural and M. Tumay, “Steady State Analysis of Unified Power Flow Controller: Mathematical Modeling and Simulation Studies”, IEEE Bologna Power Tech Conference, Bologna, Italy, Vol. 4, Pages (6), June 23- 26, 2003.
3.5 Line # 2 Fig.15
Fuerte-Esquivel CR, Acha E. Unified power flow controller: a critical comparison of Newton–Raphson UPFC algorithms in power studies. IEE Proc-C Generation Transmission Distribut; 144(5), 1997.
Line # 6
Line # 8
Line # 9
Total power loss with different UPFC placement (case c)
[11]. Rusejla Sadikovic, “Power Flow Control with UPFC”, Internal Report, pp.1-20, available at www.eeh.ee.ethz.ch
IV. CONCLUSION In this paper, UPFC model is presented and incorporated to N-R power flow solution. The proposed model and algorithm were implemented on 6-bus test system for different case studies. UPFC improves system voltage regulation and the losses are minimized . the optimum location of the UPFC in IEEE 6-bus systems using PSAT (Power System Analysis Toolbox) software is obtained. Load flow results with and without UPFC proved effectiveness of their incorporation in improving networks voltage profiles and in decreasing total system losses. Line # 6 is proved to be the best location for the UPFC in the studied system specimens of Ni-DI showed reasonable values of friction coefficient and wear which recommend them for wide application .
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