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A New Approach for Locating and Adjustment of Phase Shifters
ELSEVIER
Copyright © IFAC Power Plants and Power Systems Control, Seoul, Korea, 2003
IFAC PUBLICATIONS www.elsevier.com/locale/ifac
A NEW APPROACH FOR LOCATING AND ADJUSTMENT OF PHASE SHIFfERS A. Yazdani, G.B. Gharehpetian, S. M. Kouhsari
Electrical Engineering Faculty Amirkabir University of Technology
Abstract: Phase Shifting Transformers (PSTs) are powerful tools for controlling power flow in HV and EHV networks. The locating of PSTs in these networks can be considered as an optimization problem with a special objective function. This paper aims at locating of PSTs. The objective function is the transmission losses and PST must be used to minimize this function. To solve this optimization problem, different types of solutions have been presented, which are based on direct or indirect searching methods. This paper presents a new, simple and practical solution, which is a combination of both searching methods. Copyright © 2003 IFA C Key words: Phase shifters, losses, loss minimization, Power flow, adjustment.
I. INTRODUCTION
In this paper the concept of the best power flow pattern has been used. This pattern has the minimum transmission losses. The suggested algorithm of the paper tries to achieve this power flow pattern by using PSTs. The result of the algorithm is PST's best location and proper adjustment. The suggested approach is examined with the IEEE l4-bus test system and also there is a comparison between this method and the one which is presented in (Xing and Kusic, 1988) in a 5-bus sample system.
One of the most important applications of Phase Shifting Transformers (PSTs) is the control of the power flow in steady state conditions. To use this ability, it is important to install PST in a suitable place and then adjust it properly. The locating and adjustment of PST can be considered as an optimal power flow (OPF) problem. The OPF problem is formulated as a non-linear optimization problem. The solution of this problem means the determination of the optimal settings by adjusting control variables (PSTs' angles) in a power system. Solving such problems with numerical methods has several disadvantages e.g., divergence. Using distribution and sensitivity factors, a method has been developed in (Xing and Kusic, 1988) to adjust and allocate PSTs. Applying such methods in large networks will result in large matrices and will yield a new program besides other numerical disadvantages.
JJ. Modeling ofPST
Consider a PST connected between nodes i and k with an ideal turn ratio T = I .OL 1jI' in series with y' =
l'ILa'
transformer admittance Y as shown in figure 1. To model PST in a load flow program, the method of (YoussefR. D.,1993) has been used.
In (Paterni , et a1.,1999), the genetic algorithm is used to allocate PST. The characteristic of this method is such that there is no need to use the usual complex optimization techniques and formulations. But in this method calculation may spend too much time and it presents the suitable locations of installation but not the proper PST's adjustment. This paper proposes a new and convenient method to overcome the above mentioned problems.
J
v ]. I
I
£.I
Fig. 1: Model ofPST in a transmission line.
457
V-]
In this method the following equation is the starting point:
!..L = E
Where R b is the resistance of branch b, and J b is the current flow phasor in the branch b. J b can be divided into real (Jb) and imaginary (J~) parts:
.- t
T
= l. - t I
j
Jb=Jb+jJ~
j
These equations can be rewritten by (m x 1) vectors:
(1)
J=Jr+jJi
This can be written in the following matrix form:
[1~1:]= Yt[-T-1 -TIJIi] 1 ~
Applying equation AJ = I, in which A is the network incidence matrix and I is the vector of nodal injection currents (n x 1), we have: 1= r + jIi (2)
Now equation (6) can be decoupled into real and imaginary components and the Lagrangian associated with these decoupled equations can be written as follow (Shirmohammadi and Hong, 1989):
It can be shown that for the fast-decoupled Newton
Raphson load flow, the mismatch functions are:
bP;
= p;sp - V/Gii -
L(Gik
Vi
m
Min F r = Min(LR b(J b)2 - Ar ([A]l' - I r » r
COs8ik+Bik sin8ik ),Vk
J'.A
b=1
(7)
kEi
k*i
m
Min Fi =Min(LRb(J~)2-Ai([A]Ji _I i
(3)
J'.X
liQi = Q? -
vl Bij - V;
(4) Based on these functions, the Jacobean elements have been determined (Youssef R. D.,1993). It is obvious that with minimum efforts PST has been modeled in an AC load flow program. It must be noted that for a (p.. ) known power flow of PST lj , the proper adjustment of PST's angle can be determined by using (5). Vi JI).cos(Oij ).sin(Oij)
=
» (8)
Where X and }./ are the row vectors of Lagrange multipliers having dimension n. The solutions for these equations are:
~) Gik sin Bik + Bik cosBik ),Vk
f).Sij
b=\
2RbJ;
+A; -~ =0 2RbJb +ip -iq =0
b=I,2, ... ,m
(9) Which p and q denote the nodes of the branch b. Summing equations (9) all over the network loops yields:
:::
Xij
(10)
LRbJ~ =0
(5)
(11) L is the set of branches that are in the network loops. Multiplying (11) by the operator j and adding it to (10) yields: beL
Best Power Flow Pattern Concept For each generation and load condition, the power system has one special power flow pattern, which can be determined by a load flow analysis. PSTs can change not only the power flow pattern but also the transmission losses. Among different possible patterns, one of them has the minimum resistive losses, which is named in this paper "the best power flow pattern". In this section this concept will be introduced in detail.
LRb(Jb + jJ~)=O bEL
(13)
Assuming that the nodal current injections due to loads are known, the optimization problem can be formulated as follows: m
2
MinLR b lJ b l J'
(12) or
The interpretation of the equation (13) is very important. This equation is the Kerchief Voltage Law (KVL) for the network loops with the branch impedances replaced by their resistive components.
(6)
b=\
458
cases and the searching space is the same as before. So among these 1cases, the fIrst n load flow patterns (installation places) can be selected for a system with n PSTs. It must be noted that if the chosen places for PSTs are not suitable, the power flow pattern in the system will not tend the best power flow pattern and may increase the transmission losses. It can be said that this method for the placement and adjustment of PSTs is a practical one and user will not face numerical problems like divergence. The problem can be solved with a load flow program and there is no need for developing a new OPF program.
This idea has been used in (Shinnohammadi and Hong,1989) for the reconfiguration of the distribution system to reduce the losses. In this paper this concept has been used to determine the best solution and adjustment of PST for the minimization of the losses in transmission systems. The solution procedure is as follows: a) Convert the network into a pure resistive form of it, i.e. reactive generations and reactive loads must be equal to zero and the reactance and suseptance of transmission lines are neglected. b) Calculate the power flow of the purely resistive network by using a load flow
Case Studies and Discussion In this part two networks have been studied. The fIrst one is a 5-bus system Fig. 2. This system is completely presented in (. To show the validity of the suggested method it has been compared with a sensitivity method presented in (Xing and Kusic, 1988). The minimum loss of this system with the best power flow pattern is 3.02MW. Table 1 shows the results of two methods. Considering column 4 and 6 of this table, i.e. transmission losses, it can be said that lines no. 2, 3 and 6 are not so sensitive. The results of two methods are different for line 1. For
PST Allocation and Adjustment In the previous 1>ection, the concept of the best power flow pattern has been introduced. Using this pattern the flow of each line in this special condition is known. This flow is named "optimal power flow" of each line. For each line of a power system, PST must change each line normal power flow and set it to its "optimal power flow". As a result for a power system with 1 lines and one PST, there will be 1 installation candidates with 1 optimal power flows. For a known optimal power flow, the proper setting and adjustment ofPST can be determined· by using the PST model presented in section 11. Now, comparing results of 1 load flows, we have a very restricted searching space. The most proper place for PST installation is in this space and has minimum transmission losses. The procedure of fmding the most proper place to install a PST in a network is as follows: a) Convert the network to its pure resistive from, b) Determining the best power flow pattern of the converted system, by applying a simple load flow, c) Save the optimal flow of all lines, d) Test the installation of a PST in every line of the system and try to set the line power flow to its optimal power flow, e) Save the results (transmission losses) for each installation setting, f) Find the minimum of all cases, g) Adjust PST on the selected line.
line 7 adjusting PST on - 6.91° results in total losses of 4.980 MW but the other method will reach to 5.046 MW by adjusting PST on - 5.980° . It can be said that two methods may lead to almost the same results but the suggested method represents a better one. 4
3 Line No. 2 Line No. 6
Line No. 4 ,---
ro Z
.s
-' -l
5
2 Line No. 5
Fig. 2: Single Line Diagram of 5-Bus System Table1 Comparison of the two methods for PST adjustment
Line No.
It must be noted that a PST, which is installed in line i, not only changes the power flow of line i but also affect the power flow in other lines. Therefore it is obvious that the use of 2 or more PSTs can result in a more proper pattern which is much closer to the best power flow pattern and can cause more loss reduction in the system.
Line optimal
Best power flow concept
P:~
flow lJ (MW)
!iq)
floss
Sensitivity Method (Xing and Kusic, 1988) !il{J0
(MW)
1 2 3 4 5 6 7
Another important point is to fmd the desired number of PSTs for a power system. By using this method two or more PSTs can be adjusted in the same manner. In this case the losses of the system are known for alll
459
53 29.594 21.586 64.441 28.977 5.363 31.916
-8 -2.5 -0.05 -8.1 -5.8 -2.2 -6.91
7.281 5.790 5.606 5.046 5.046 5.753 4.980
floss (MW)
0.04 -0.04 -0.08 -5.68 5.89 -0.12 -5.89
5.706 5.706 5.706 5.119 5.046 5.706 5.046
Table4 rp variations and its effect on loss reduction
The other test network is the IEEE 14-bus system To test the effectiveness of the proposed method three cases have been studied, Case I is an optimal locating prob.le~ of one PST in the system. In case 11 the applIcatIon of two PSTs have been studied, And in case III sensitivity analysis for a phase shift angle is investigated.
10 9 8 7.1 6.5 5.5 5 4
Table 2 shows the most proper places for PST installation, which is suggested by the proposed meth?~. T?tal transmission loss of the system in normal co.ndItIon .IS 9.166 MW, but in the pure resistive form, this .loss IS 6.00~ MW. Considering the table 3, it is obVIOUS that the Installation of PSTs on lines 8 12 and 9 is sug~ested,. respectively. For line 8, adjusting PST ?n the Ime optImal flow (i. e., 87.401 MW) will result m 6.628 MW total power losses, i.e. 27.69% losses reduction in ~e s~stem. For lines 9 and 12, adjusting PSTs on theIr optImal flows, (i. e., 14.020 MW and 13.982 MW respectively) result in 11.06% and 11.49% losses reduction.
7 8 9 11 12 13 14 17 18 20
-2.95 -12.2 -5.68 -4.11 -6.06 7.21 7.21 -7.81 7.18 6.64
Line i
11 11 12
Linej 9 18 11 13 12 13 13
(MW)
8.886 8.772 8.706 8.673 8.658 8.660 8.672 8.715
0.300 0.394 0.460 0.493 0.508 0.506 0.494 0.451
tlPross
-19 -18 -17 -15 -14 -13 -12
-11
(MW)
(MW)
6.317 6.315 6.329 6.406 6.472 6.553 6.628 6.765
2.849 2.851 2.837 2.760 2.694 2.613 2.538 2.401
Vitet S., ~ena M. and Yokoyama A.(1999), OptImal LocatIon of Phase Shifters in the French Netwok by Genetic Algorithm", IEEE Trans, on Power System, Vol. 14, No. 1, pp. 37-42.
Shirmohamrnadi D. and Hong H. W.(1989), "Reconfiguration of Electric Distribution Networks for Resistive Line Losses Reduction" IEEE Trans. On Power Delivery, Vol. 4, No. 2, pp. 1492-1498.
8.875 6.628 8.152 8.724 8.113 8.673 8.674 8.808 8.673 8.760
Taranto G. N. and Pereira L. M. (1992),"Presentation of FACTS Devices in Power System Economic Dispatch", IEEE Trans. on Power System, Vol. 7, No. 2, pp. 572-576. Xing K. and Kusic G. (1988),"Application ofThyristor Controlled Phase Shifters to Minimize Real Power Losses and Augment Stability of Power System" IEEE Trans. on Power Systems, Vol. 3, No. 4 pp. 792-798. '
Table3 Simultaneous Installation of PSTs in two different lines
8 8 9 9
(MW)
Pate~i P.~
Pross 90.456 87.401 14.020 8.044 13.982 8.871 22.017 1.321 18.115 13.877
tlPross
REFERENCES
(MW)
(MW)
f}oss
~oncl,!sion: !he ~ocating and adjustment of PSTs is mvestIgated m this paper. The main idea, which has been used in this paper, is the concept of the best power flow pa~e!D' It. has been shown that applying this concept It IS pOSSIble to fmd a load flow pattern that has the minimum transmission losses. Based on this idea, a new method to allocate and adjust a PST in a power s~stem has ~e~~ presented. This method is compared With the senSItIvIty method and it is shown that the new procedure is effective and practical. The suggested method can be used with a simple load flow program and there is no need for a new OPF program.
~e second case study is the application of two PSTs in this system. Table 3 shows the simulation results. In !?is case it can be said that the most proper places are lInes 8 and 9. Comparison of this table and table 2 indicates that in each case we have more than 1 MW losses reduction. It verifies the idea that with more than one PST it is possible to achieve more losses reduction. It verifies the idea that with more than one PST it is possible to achieve more reduction of losses i~ the system Table 4 s~ows the )'c-s~lt of case III test. In this case the phase ShIft angle t rp) IS changed in lines 8 and 13. Table2 PST installation in only one line
Line No.
Line No. 8
Line No. 13
F:ossCMW)
YoussefR. D. (1993),"Phase Shifting Transformer in Load Flow and Short Circuit Analysis Modeling and Control", IEEE Proceedings C, Vol. 140, No. 4, pp. 331-336.
6.600 6.602 6.669 8.076 6.671 8.443 8.078
460
Copyright © IFAC Power Plants and Power Systems Control, Seoul, Korea, 2003
IFAC PUBLICATIONS www.elsevier.com/locale/ifac
A NEW APPROACH FOR LOCATING AND ADJUSTMENT OF PHASE SHIFfERS A. Yazdani, G.B. Gharehpetian, S. M. Kouhsari
Electrical Engineering Faculty Amirkabir University of Technology
Abstract: Phase Shifting Transformers (PSTs) are powerful tools for controlling power flow in HV and EHV networks. The locating of PSTs in these networks can be considered as an optimization problem with a special objective function. This paper aims at locating of PSTs. The objective function is the transmission losses and PST must be used to minimize this function. To solve this optimization problem, different types of solutions have been presented, which are based on direct or indirect searching methods. This paper presents a new, simple and practical solution, which is a combination of both searching methods. Copyright © 2003 IFA C Key words: Phase shifters, losses, loss minimization, Power flow, adjustment.
I. INTRODUCTION
In this paper the concept of the best power flow pattern has been used. This pattern has the minimum transmission losses. The suggested algorithm of the paper tries to achieve this power flow pattern by using PSTs. The result of the algorithm is PST's best location and proper adjustment. The suggested approach is examined with the IEEE l4-bus test system and also there is a comparison between this method and the one which is presented in (Xing and Kusic, 1988) in a 5-bus sample system.
One of the most important applications of Phase Shifting Transformers (PSTs) is the control of the power flow in steady state conditions. To use this ability, it is important to install PST in a suitable place and then adjust it properly. The locating and adjustment of PST can be considered as an optimal power flow (OPF) problem. The OPF problem is formulated as a non-linear optimization problem. The solution of this problem means the determination of the optimal settings by adjusting control variables (PSTs' angles) in a power system. Solving such problems with numerical methods has several disadvantages e.g., divergence. Using distribution and sensitivity factors, a method has been developed in (Xing and Kusic, 1988) to adjust and allocate PSTs. Applying such methods in large networks will result in large matrices and will yield a new program besides other numerical disadvantages.
JJ. Modeling ofPST
Consider a PST connected between nodes i and k with an ideal turn ratio T = I .OL 1jI' in series with y' =
l'ILa'
transformer admittance Y as shown in figure 1. To model PST in a load flow program, the method of (YoussefR. D.,1993) has been used.
In (Paterni , et a1.,1999), the genetic algorithm is used to allocate PST. The characteristic of this method is such that there is no need to use the usual complex optimization techniques and formulations. But in this method calculation may spend too much time and it presents the suitable locations of installation but not the proper PST's adjustment. This paper proposes a new and convenient method to overcome the above mentioned problems.
J
v ]. I
I
£.I
Fig. 1: Model ofPST in a transmission line.
457
V-]
In this method the following equation is the starting point:
!..L = E
Where R b is the resistance of branch b, and J b is the current flow phasor in the branch b. J b can be divided into real (Jb) and imaginary (J~) parts:
.- t
T
= l. - t I
j
Jb=Jb+jJ~
j
These equations can be rewritten by (m x 1) vectors:
(1)
J=Jr+jJi
This can be written in the following matrix form:
[1~1:]= Yt[-T-1 -TIJIi] 1 ~
Applying equation AJ = I, in which A is the network incidence matrix and I is the vector of nodal injection currents (n x 1), we have: 1= r + jIi (2)
Now equation (6) can be decoupled into real and imaginary components and the Lagrangian associated with these decoupled equations can be written as follow (Shirmohammadi and Hong, 1989):
It can be shown that for the fast-decoupled Newton
Raphson load flow, the mismatch functions are:
bP;
= p;sp - V/Gii -
L(Gik
Vi
m
Min F r = Min(LR b(J b)2 - Ar ([A]l' - I r » r
COs8ik+Bik sin8ik ),Vk
J'.A
b=1
(7)
kEi
k*i
m
Min Fi =Min(LRb(J~)2-Ai([A]Ji _I i
(3)
J'.X
liQi = Q? -
vl Bij - V;
(4) Based on these functions, the Jacobean elements have been determined (Youssef R. D.,1993). It is obvious that with minimum efforts PST has been modeled in an AC load flow program. It must be noted that for a (p.. ) known power flow of PST lj , the proper adjustment of PST's angle can be determined by using (5). Vi JI).cos(Oij ).sin(Oij)
=
» (8)
Where X and }./ are the row vectors of Lagrange multipliers having dimension n. The solutions for these equations are:
~) Gik sin Bik + Bik cosBik ),Vk
f).Sij
b=\
2RbJ;
+A; -~ =0 2RbJb +ip -iq =0
b=I,2, ... ,m
(9) Which p and q denote the nodes of the branch b. Summing equations (9) all over the network loops yields:
:::
Xij
(10)
LRbJ~ =0
(5)
(11) L is the set of branches that are in the network loops. Multiplying (11) by the operator j and adding it to (10) yields: beL
Best Power Flow Pattern Concept For each generation and load condition, the power system has one special power flow pattern, which can be determined by a load flow analysis. PSTs can change not only the power flow pattern but also the transmission losses. Among different possible patterns, one of them has the minimum resistive losses, which is named in this paper "the best power flow pattern". In this section this concept will be introduced in detail.
LRb(Jb + jJ~)=O bEL
(13)
Assuming that the nodal current injections due to loads are known, the optimization problem can be formulated as follows: m
2
MinLR b lJ b l J'
(12) or
The interpretation of the equation (13) is very important. This equation is the Kerchief Voltage Law (KVL) for the network loops with the branch impedances replaced by their resistive components.
(6)
b=\
458
cases and the searching space is the same as before. So among these 1cases, the fIrst n load flow patterns (installation places) can be selected for a system with n PSTs. It must be noted that if the chosen places for PSTs are not suitable, the power flow pattern in the system will not tend the best power flow pattern and may increase the transmission losses. It can be said that this method for the placement and adjustment of PSTs is a practical one and user will not face numerical problems like divergence. The problem can be solved with a load flow program and there is no need for developing a new OPF program.
This idea has been used in (Shinnohammadi and Hong,1989) for the reconfiguration of the distribution system to reduce the losses. In this paper this concept has been used to determine the best solution and adjustment of PST for the minimization of the losses in transmission systems. The solution procedure is as follows: a) Convert the network into a pure resistive form of it, i.e. reactive generations and reactive loads must be equal to zero and the reactance and suseptance of transmission lines are neglected. b) Calculate the power flow of the purely resistive network by using a load flow
Case Studies and Discussion In this part two networks have been studied. The fIrst one is a 5-bus system Fig. 2. This system is completely presented in (. To show the validity of the suggested method it has been compared with a sensitivity method presented in (Xing and Kusic, 1988). The minimum loss of this system with the best power flow pattern is 3.02MW. Table 1 shows the results of two methods. Considering column 4 and 6 of this table, i.e. transmission losses, it can be said that lines no. 2, 3 and 6 are not so sensitive. The results of two methods are different for line 1. For
PST Allocation and Adjustment In the previous 1>ection, the concept of the best power flow pattern has been introduced. Using this pattern the flow of each line in this special condition is known. This flow is named "optimal power flow" of each line. For each line of a power system, PST must change each line normal power flow and set it to its "optimal power flow". As a result for a power system with 1 lines and one PST, there will be 1 installation candidates with 1 optimal power flows. For a known optimal power flow, the proper setting and adjustment ofPST can be determined· by using the PST model presented in section 11. Now, comparing results of 1 load flows, we have a very restricted searching space. The most proper place for PST installation is in this space and has minimum transmission losses. The procedure of fmding the most proper place to install a PST in a network is as follows: a) Convert the network to its pure resistive from, b) Determining the best power flow pattern of the converted system, by applying a simple load flow, c) Save the optimal flow of all lines, d) Test the installation of a PST in every line of the system and try to set the line power flow to its optimal power flow, e) Save the results (transmission losses) for each installation setting, f) Find the minimum of all cases, g) Adjust PST on the selected line.
line 7 adjusting PST on - 6.91° results in total losses of 4.980 MW but the other method will reach to 5.046 MW by adjusting PST on - 5.980° . It can be said that two methods may lead to almost the same results but the suggested method represents a better one. 4
3 Line No. 2 Line No. 6
Line No. 4 ,---
ro Z
.s
-' -l
5
2 Line No. 5
Fig. 2: Single Line Diagram of 5-Bus System Table1 Comparison of the two methods for PST adjustment
Line No.
It must be noted that a PST, which is installed in line i, not only changes the power flow of line i but also affect the power flow in other lines. Therefore it is obvious that the use of 2 or more PSTs can result in a more proper pattern which is much closer to the best power flow pattern and can cause more loss reduction in the system.
Line optimal
Best power flow concept
P:~
flow lJ (MW)
!iq)
floss
Sensitivity Method (Xing and Kusic, 1988) !il{J0
(MW)
1 2 3 4 5 6 7
Another important point is to fmd the desired number of PSTs for a power system. By using this method two or more PSTs can be adjusted in the same manner. In this case the losses of the system are known for alll
459
53 29.594 21.586 64.441 28.977 5.363 31.916
-8 -2.5 -0.05 -8.1 -5.8 -2.2 -6.91
7.281 5.790 5.606 5.046 5.046 5.753 4.980
floss (MW)
0.04 -0.04 -0.08 -5.68 5.89 -0.12 -5.89
5.706 5.706 5.706 5.119 5.046 5.706 5.046
Table4 rp variations and its effect on loss reduction
The other test network is the IEEE 14-bus system To test the effectiveness of the proposed method three cases have been studied, Case I is an optimal locating prob.le~ of one PST in the system. In case 11 the applIcatIon of two PSTs have been studied, And in case III sensitivity analysis for a phase shift angle is investigated.
10 9 8 7.1 6.5 5.5 5 4
Table 2 shows the most proper places for PST installation, which is suggested by the proposed meth?~. T?tal transmission loss of the system in normal co.ndItIon .IS 9.166 MW, but in the pure resistive form, this .loss IS 6.00~ MW. Considering the table 3, it is obVIOUS that the Installation of PSTs on lines 8 12 and 9 is sug~ested,. respectively. For line 8, adjusting PST ?n the Ime optImal flow (i. e., 87.401 MW) will result m 6.628 MW total power losses, i.e. 27.69% losses reduction in ~e s~stem. For lines 9 and 12, adjusting PSTs on theIr optImal flows, (i. e., 14.020 MW and 13.982 MW respectively) result in 11.06% and 11.49% losses reduction.
7 8 9 11 12 13 14 17 18 20
-2.95 -12.2 -5.68 -4.11 -6.06 7.21 7.21 -7.81 7.18 6.64
Line i
11 11 12
Linej 9 18 11 13 12 13 13
(MW)
8.886 8.772 8.706 8.673 8.658 8.660 8.672 8.715
0.300 0.394 0.460 0.493 0.508 0.506 0.494 0.451
tlPross
-19 -18 -17 -15 -14 -13 -12
-11
(MW)
(MW)
6.317 6.315 6.329 6.406 6.472 6.553 6.628 6.765
2.849 2.851 2.837 2.760 2.694 2.613 2.538 2.401
Vitet S., ~ena M. and Yokoyama A.(1999), OptImal LocatIon of Phase Shifters in the French Netwok by Genetic Algorithm", IEEE Trans, on Power System, Vol. 14, No. 1, pp. 37-42.
Shirmohamrnadi D. and Hong H. W.(1989), "Reconfiguration of Electric Distribution Networks for Resistive Line Losses Reduction" IEEE Trans. On Power Delivery, Vol. 4, No. 2, pp. 1492-1498.
8.875 6.628 8.152 8.724 8.113 8.673 8.674 8.808 8.673 8.760
Taranto G. N. and Pereira L. M. (1992),"Presentation of FACTS Devices in Power System Economic Dispatch", IEEE Trans. on Power System, Vol. 7, No. 2, pp. 572-576. Xing K. and Kusic G. (1988),"Application ofThyristor Controlled Phase Shifters to Minimize Real Power Losses and Augment Stability of Power System" IEEE Trans. on Power Systems, Vol. 3, No. 4 pp. 792-798. '
Table3 Simultaneous Installation of PSTs in two different lines
8 8 9 9
(MW)
Pate~i P.~
Pross 90.456 87.401 14.020 8.044 13.982 8.871 22.017 1.321 18.115 13.877
tlPross
REFERENCES
(MW)
(MW)
f}oss
~oncl,!sion: !he ~ocating and adjustment of PSTs is mvestIgated m this paper. The main idea, which has been used in this paper, is the concept of the best power flow pa~e!D' It. has been shown that applying this concept It IS pOSSIble to fmd a load flow pattern that has the minimum transmission losses. Based on this idea, a new method to allocate and adjust a PST in a power s~stem has ~e~~ presented. This method is compared With the senSItIvIty method and it is shown that the new procedure is effective and practical. The suggested method can be used with a simple load flow program and there is no need for a new OPF program.
~e second case study is the application of two PSTs in this system. Table 3 shows the simulation results. In !?is case it can be said that the most proper places are lInes 8 and 9. Comparison of this table and table 2 indicates that in each case we have more than 1 MW losses reduction. It verifies the idea that with more than one PST it is possible to achieve more losses reduction. It verifies the idea that with more than one PST it is possible to achieve more reduction of losses i~ the system Table 4 s~ows the )'c-s~lt of case III test. In this case the phase ShIft angle t rp) IS changed in lines 8 and 13. Table2 PST installation in only one line
Line No.
Line No. 8
Line No. 13
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YoussefR. D. (1993),"Phase Shifting Transformer in Load Flow and Short Circuit Analysis Modeling and Control", IEEE Proceedings C, Vol. 140, No. 4, pp. 331-336.
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