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The effect of unified power flow controller location in power systems
Electrical Power and Energy Systems 26 (2004) 561–569 www.elsevier.com/locate/ijepes
The effect of unified power flow controller location in power systems Mehmet Tu¨maya, A.M. Vuralb,*, K.L. Loc a Department of Electrical and Electronic Engineering, C ¸ ukurova University, Baliai-Adana, Turkey Department of Electrical and Electronic Engineering, Gaziantep University, 27310 Gaziantep, Turkey c Department of Electrical and Electronic Engineering, University of Strathclyde, Royal College Building, 204 George Street, Glasgow G1 1XW, UK b
Received 18 October 2001; accepted 1 April 2004
Abstract The Unified Power Flow Controller (UPFC) is a device that is capable of providing control of voltage magnitude, active and reactive power flows. This paper represents the effect of UPFC location in steady-state analysis and to demonstrate the capabilities of UPFC in controlling active and reactive power flow within any electrical network. In this paper, a complete power injection model of UPFC including both the series injection branch and the shunt exciting branch is derived in rectangular form. An injected power model method is used to represent UPFC in load flow program. Finally, different types of simulation tasks are carried out based on IEEE 30-bus test system. q 2004 Elsevier Ltd. All rights reserved. Keywords: Flexible AC transmission; Unified power flow controller; Power quality
1. Introduction UPFC is the most comprehensive device which has arisen so after the Flexible AC Transmission Systems (FACTS) initiative, is capable of providing simultaneous active and reactive power flow control, as well as voltage magnitude control [1]. The versadility provided by UPFC makes it an advanced power system device and an important member of FACTS family to provide a number of control functions required to solve a wide range of steady-state problems encountered in electrical power networks [2,3]. Basic circuit configuration of UPFC is shown in Fig. 1. Performance analysis of UPFC in load flow studies requires its steady-state modelling. There are many papers concerned with the issue of UPFC mathematical modelling in open liturature for various study purposes. Ref. [2] introduces a steady-state UPFC model based on a single, ideal, series voltage source. Ref. [4] utilizes two ideal voltage sources, one in series and one in parallel as UPFC steady-state model. The steady-state model suggested in Ref. [5] is based upon one ideal, series voltage source, and one ideal, shunt current source. Refs. [6,7] provides an injected power model concept for UPFC. In this model, UPFC is * Corresponding author. Tel.: þ90-342-360-1200-2113; fax: þ 90-342360-1103. E-mail address: [email protected] (A.M. Vural). 0142-0615/$ - see front matter q 2004 Elsevier Ltd. All rights reserved. doi:10.1016/j.ijepes.2004.04.006
represented by two ideal voltage sources with series source impedances, connected in series and parallel with the transmission line, representing the output voltages of series and shunt branches of UPFC. This model is highly suitable for steady-state representation of UPFC in load flow program. Although considerable progress has been made in the area of developing a realistic UPFC model suitable for efficient load flow studies, a very little effort has been made for the investigation of the effects of UPFC location on transmission asset in electrical power networks. In this respect, this paper provides comprehensive simulation tasks concerning with the location of UPFC.
2. UPFC modelling [6,7] Steady-state investigation of UPFC involves power flow studies which include the calculation of busbar voltages, branch loadings, real and reactive transmission losses, and the impact of UPFC on the above mentioned system parameters. In order to evaluate UPFC overall steady-state performance, an adequate model is required. In this section, a UPFC model using power injection concept is derived for power flow studies. In this model, two voltage sources are used to represent the fundamental components of the pulse width modulated controlled output voltage waveforms of the two
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M. Tu¨may et al. / Electrical Power and Energy Systems 26 (2004) 561–569
Fig. 1. Basic circuit configuration of UPFC.
branches in the UPFC. The impedance of the two coupling transformers are included in the proposed model and losses of UPFC is taken into account. Fig. 2 depicts voltage source equivalent circuit of UPFC. The series injection branch, a series injection voltage source, performs the main functions of controlling power flow whilst the shunt branch is used to provide real power demanded by the series branch and the losses in UPFC, i.e. balancing the real power between the two branches. However, in the proposed model, the function of reactive compensation of shunt branch is completely neglected, this function can be taken into account for future studies. As shown in Fig. 2, the series and shunt injection branch are modelled with two ideal controllable voltage sources, Vse and Vsh ; respectively, while Xse and Xsh ; respectively, denote the leakage reactance of the two coupling transformers. IL represents transmission line current. Series voltage source Vse ; can be mathematically expressed as follows V~ se ¼ r V~ i ejg
ð1Þ
where 0 # r # rmax and 0 # g # 2p For the purpose of simplifying the formulation procedure of the power injection model, which has been derived in
rectangular form and verified in the authors’ previous work [7] is adopted here as shown in Fig. 3. The components of equivalent power injections at buses i and j; Pi;upfc ; Qi;upfc ; Pj;upfc ; and Qj;upfc are formulated as follows: Pi;upfc ¼ 0:02rbse Vi2 sin g 21:02rbse Vi Vj sinðui 2 uj þ gÞ
ð2Þ
Qi;upfc ¼ 2rbse Vi2 cos g
ð3Þ
Pj;upfc ¼ rbse Vi Vj sinðui 2 uj þ gÞ
ð4Þ
Qj;upfc ¼ rbse Vi Vj cosðui 2 uj þ gÞ
ð5Þ
In Eqs. (2)–(5), Pi;upfc þjQi;upfc and Pj;upfc þjQj;upfc are, respectively, the equivalent complex power injected into the two busbars, buses i and j; which are practically the resultant power injections contributed by both the series and shunt branches of UPFC. Vi ; Vj are, respectively, the voltage magnitude components of the voltages on buses i and j; while ui and uj are, respectively, the phase angle components of the voltages on buses i and j: bse is the leakage susceptance of the series coupling transformer. r and g are, respectively, magnitude and phase angle of series voltage source, UPFC parameters, shown in Fig. 2.
Fig. 2. Voltage source equivalent circuit of UPFC.
M. Tu¨may et al. / Electrical Power and Energy Systems 26 (2004) 561–569
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Fig. 3. Complete UPFC power injection model.
3. Power flow embedded with UPFC When a transmission line of an electrical power network is equipped with a UPFC, the implementation of UPFC model in power system software is an essential tool for investigating the impact of UPFC. Whilst power flow problem involves solving a set of nonlinear algebraic equations, representing the network under steady-state conditions, its solution is expected to provide not only the information of system states, i.e. busbar voltages, real and reactive power flows, transmission losses, but also the impact of UPFC under assorted system operating conditions. Proposed power injection model is incorporated inside the Jacobian and mismatch equations of Newton –Raphson algorithm, leading to iterative solutions. Many commercialgrade power system analysis programs integrated with userdefined modelling function are now available to provide different approaches for the solution of networks equipped with such advanced devices. Power System Analysis Software Package (PSASP) [8] is one of these commercial programs used to investigate the various impacts of UPFC to the different types of power systems. However, concerned modification of Newton– Raphson algorithm is not carried out in PSASP directly. Instead, UPFC power injection model is defined in its user-defined model interface. Real and reactive power injections at the buses, Pi;upfc ; Qi;upfc ; Pj;upfc ; and Qj;upfc at which UPFC is located, are used in user-defined model. This model of UPFC can be seen in Appendix A. The linearized system model based on Newton –Raphson algorithm, written in matrix form is as follows: "
DP DQ
#n
" ¼
H
N
J
L
#n "
Du
#n
In Eq. (6), DP ¼ Pspe 2 Pcal is the real power mismatch vector and DQ ¼ Qspe 2 Qcal is the reactive power mismatch vector. Du and DV are vectors of incremental changes in nodal voltages. H; N; J and L denote the basic elements in the Jacobian matrix. They corresponds partial derivatives of the real and the reactive powers with respect to the phase angles and the magnitudes of the nodal voltages given in Eqs. (7) and (8), n indicates iteration number H¼
›P ; ›u
N¼V
J¼
›Q ; ›u
L¼V
›Q ›V
Hii ¼ Hiin þ Hiiupfc ¼
›Pi;upfc › Pi þ ›ui ›ui
Nii ¼ Niin þ Niiupfc ¼ Vi
›Pi;upfc ›P i þ Vi ›V i › Vi
›Qi;upfc ›Qi þ ›ui ›ui
DV=V Lii ¼ Lnii þ Lupfc ¼ Vi ii
Fig. 4. UPFC located near bus 6 in the line between buses 2 and 6.
ð7Þ ð8Þ
The impact of UPFC can be treated as two controllable power sources or loads, ðPi;upfc þ jQi;upfc Þ and ðPj;upfc þ jQj;upfc Þ; injected into or absorbed from bus i and j; respectively. Since the two power injections ðPi;upfc þ jQi;upfc Þ and ðPj;upfc þ jQj;upfc Þ of UPFC vary with the connected busbar voltage amplitudes and phases, the relevant elements of the Jacobian matrix, given in Eqs. (7) and (8), should be modified at each iteration. Based on Eqs. (2) – (5), the following additional elements of the Jacobian matrix owing to the injections of the UPFC at the i and j busbars, between where the UPFC is installed, can be derived as follows: For bus i; when i ¼ j
Jii ¼ Jiin þ Jiiupfc ¼ ð6Þ
›P ; ›V
›Qi;upfc ›Q i þ Vi ›V i ›Vi
Fig. 5. UPFC located at the middle of line.
ð9Þ
ð10Þ
ð11Þ
ð12Þ
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Table 1 The percentage changes as UPFC moved from near bus 6 to at middle of line Active power flow change increase (%)
Reactive power flow change increase (%)
Total transmission real loss change increase (%)
Total transmission reactive loss change increase (%)
r Fixed
r Fixed
r Fixed
r Fixed
r Fixed
r Fixed
r Fixed
r Fixed
6.33
2.4
2120.81
30.91
1.94
20.72
230.22
230.72
When i – j Hij ¼ Hijn þ Hijupfc ¼
›Pi;upfc › Pi þ ›uj ›uj
Nij ¼ Nijn þ Nijupfc ¼ Vj Jij ¼ Jijn þ Jijupfc
›Pi;upfc ›P i þ Vj ›V j ›Vj
›Qi;upfc ›Qi ¼ þ ›uj ›uj
Lij ¼ Lnij þ Lupfc ¼ Vj ij
›Qi;upfc ›Q i þ Vj ›Vj › Vj
ð13Þ ð14Þ ð15Þ ð16Þ
In the above equations, UPFC related terms concerning the partial derivatives of UPFC power injections, Pi;upfc ; Qi;upfc ; Pj;upfc ; and Qj;upfc ; with respect to busbar voltages, Vi /ui ; and Vj /uj ; respectively. The related power mismatches equations for bus i and j must also be modified as: DPi ¼ Pi;G 2 Pi;L þ Pi;upfc 2 Pi;Cal
ð25Þ
DPj ¼ Pj;G 2 Pj;L þ Pj;upfc 2 Pj;Cal
ð26Þ
DQi ¼ Qi;G 2 Qi;L þ Qi;upfc 2 Qi;Cal
ð27Þ
DQj ¼ Qj;G 2 Qj;L þ Qj;upfc 2 Qj;Cal
ð28Þ
For bus j; when j ¼ i Hjj ¼ Hjjn þ Hjjupfc ¼
›Pj;upfc › Pj þ ›uj ›uj
Njj ¼ Njjn þ Njjupfc ¼ Vj Jjj ¼ Jjjn þ Jjjupfc ¼
›Pj;upfc ›P j þ Vj ›V j ›Vj
›Qj;upfc ›Qj þ ›uj ›uj
Ljj ¼ Lnjj þ Lupfc ¼ Vj jj
›Qj;upfc ›Q j þ Vj ›Vj › Vj
ð17Þ
4. Simulation examples
ð18Þ
Simulation tasks are performed on IEEE 30-bus system, as shown in Appendix B, consisting of 30 buses, 37 lines, four transformers, and two shunt capacitors. Also system data is given in Appendix B. Behind the idea of the simulation examples is to investigate the effects of location of UPFC on important system parameters. Two different UPFC locations are considered. One is near bus 6 in the line between buses 2 and 6, as shown in Fig. 4, and other is at the middle of line between the same buses, as shown in Fig. 5. The efficiency of UPFC is taken as 98%, series leakage reactance Xse is taken as 0.025 pu. For each simulation task, magnitude of series injected voltage of UPFC is changed from 0.005 to 0.1 pu, and phase angle of series injected voltage is changed from 0 to 3608, respectively. Two different locations were considered in simulations. For all simulation tasks, when a UPFC parameter was controlled, the other one was kept constant. Namely, magnitude of series inserted voltage of UPFC, r; was controlled, while phase angle of that voltage, g; was kept constant, and vice versa. Table 1 summarizes the percentage changes as UPFC is moved from near bus 6 location to at
ð19Þ ð20Þ
When j – i Hji ¼ Hjin þ Hjiupfc ¼
›Pj;upfc › Pj þ ›ui ›ui
Nji ¼ Njin þ Njiupfc ¼ Vi Jji ¼ Jjin þ Jjiupfc ¼
›Pj;upfc ›P j þ Vi ›V i ›Vi
›Qj;upfc ›Qj þ ›ui ›ui
¼ Vi Lji ¼ Lnji þ Lupfc ji
›Qj;upfc ›Q j þ Vi ›Vi › Vi
ð21Þ ð22Þ ð23Þ ð24Þ
Fig. 6. Comparison of active power flow by changing UPFC parameter.
Fig. 7. Comparison of active power loss by changing UPFC parameter.
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Fig. 8. Comparison of reactive power flow by changing UPFC parameter. Fig. 11. Comparison of total reactive losses by changing UPFC parameter.
Fig. 9. Comparison of reactive power flow by changing UPFC parameter. Fig. 12. Comparison of total reactive losses by changing UPFC parameter.
middle of line between buses 2 and 6 location. The data points labelled by symbols –V – and – B – (Figs. 6– 13) denote the location of UPFC as in Figs. 4 and 5, respectively.
4.1. Simulation task A The uncompensated active power flow in line between buses 2 and 6 is 0.5555 pu. The effect of UPFC location is investigated. Comparative results concerning this study are graphically represented in Figs. 6 and 7.
4.3. Simulation task C The total real transmission losses for the IEEE 30-bus test system is 0.1560 pu. Figs. 10 and 11 show the effect of UPFC location on total real power losses. 4.4. Simulation task D With the same configuration as in task C, the total reactive transmission losses is now 2 0.0164 pu and Figs. 12 and 13 depict the effect of UPFC location on total reactive power losses.
4.2. Simulation task B 5. Conclusions In this task, the same configuration is used. But this time the uncompensated reactive power flow is 0.0155 pu. Figs. 8 and 9 show the effect of UPFC location by changing the magnitude and phase angle of series inserted voltage, respectively.
UPFC can theoretically be located anywhere along a line in an electrical power network. In this work, effects of UPFC location on power system steady-state operating conditions
Fig. 10. Comparison of total real losses by changing UPFC parameter.
Fig. 13. Comparison of total reactive losses by changing UPFC parameter.
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have been investigated in detail. From the practical applications point of view, factors influencing the choice of location include cost, accessibility, fault level, protective relaying considerations, and effectiveness in improving power system operation. If the UPFC system is located at midpoint of the line, it will not be very convenient in terms of access for maintenance, monitoring, security, etc. If it is considered to be located at either end of the line, this
configuration provides more accessibility and availability of station service and other auxiliaries. The choice of location for any application requires a detailed study with regard to overall economy and system operation.
Appendix A. UPFC user-defined model for PSASP
M. Tu¨may et al. / Electrical Power and Energy Systems 26 (2004) 561–569
Appendix B. IEEE 30-bus system
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See Tables B1 – B4.
Table B2 (continued)
Table B1 Bus data Bus number
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30
Bus voltage
Bus generation
Bus load
Magnitude per unit
Phase angle (8)
Real MW
Reactive MVAR
Real MW
Reactive MVAR
1.0600 1.0450 1.0229 1.0142 1.0100 1.0122 1.0036 1.0100 1.0535 1.0489 1.0820 1.0584 1.0710 1.0460 1.0394 1.0472 1.0433 1.0307 1.0286 1.0329 1.0400 1.0398 1.0300 1.0257 1.0194 1.0018 1.0241 1.0085 1.0043 0.9938
0.00 25.01 26.96 28.57 213.53 210.21 212.10 210.92 212.56 213.79 212.56 213.67 213.67 213.66 214.27 213.98 214.06 214.79 214.91 214.69 213.86 213.93 214.56 214.59 214.53 214.94 214.23 210.78 215.46 216.34
243.25 40.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00
217.91 51.57 0.00 0.00 34.86 0.00 0.00 31.57 0.00 0.00 14.82 0.00 9.65 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00
0.00 21.70 2.40 7.60 94.20 0.00 22.80 30.00 0.00 5.80 0.00 11.20 0.00 6.20 8.20 3.50 9.00 3.20 9.50 2.20 7.50 0.00 3.20 8.70 0.00 3.50 0.00 0.00 2.40 10.60
0.00 12.70 1.20 1.60 19.00 0.00 10.90 30.00 0.00 2.00 0.00 7.50 0.00 1.60 2.50 1.80 5.80 0.90 3.40 0.70 11.20 0.00 1.60 6.70 0.00 2.30 0.00 0.00 0.90 1.90
Line number and between buses
Line impedance
Line No.
Buses
R (pu)
X (pu)
15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37
12 and 15 12 and 16 14 and 15 16 and 17 15 and 18 18 and 19 19 and 20 10 and 20 10 and 17 10 and 21 10 and 22 21 and 22 15 and 23 22 and 24 23 and 24 24 and 25 25 and 26 25 and 27 27 and 29 27 and 30 29 and 30 8 and 28 6 and 28
0.0662 0.0945 0.2210 0.0824 0.1070 0.0639 0.0340 0.0936 0.0324 0.0348 0.0727 0.0116 0.1000 0.1150 0.1320 0.1885 0.2544 0.1093 0.2198 0.3202 0.2399 0.0363 0.0169
0.1304 0.1987 0.1997 0.1932 0.2185 0.1292 0.0680 0.2090 0.0845 0.0749 0.1499 0.0236 0.2020 0.1790 0.2700 0.3292 0.3800 0.2087 0.4153 0.6027 0.4533 0.2000 0.0599
Half-line charging susceptance, B=2 (pu)
0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0214 0.0065
Table B3 Transformer data Transformer data
Between buses
Tap setting
1 2 3 4
6 and 9 6 and 10 4 and 12 28 and 27
1.0155 0.9629 1.0129 0.9581
Table B4 Shunt capacitor data
Table B2 Line data Line number and between buses
Line impedance
Line No.
Buses
R (pu)
X (pu)
1 2 3 4 5 6 7 8 9 10 11 12 13 14
1 and 2 1 and 3 2 and 4 3 and 4 2 and 5 2 and 6 4 and 6 5 and 7 6 and 7 6 and 8 9 and 11 9 and 10 12 and 13 12 and 14
0.0192 0.0452 0.0570 0.0132 0.0472 0.0581 0.0119 0.0460 0.0267 0.0120 0.0000 0.0000 0.0000 0.1231
0.0575 0.1852 0.1737 0.0379 0.1983 0.1763 0.4140 0.1160 0.0820 0.0420 0.2080 0.1100 0.1400 0.2559
Half-line charging susceptance, B=2 (pu)
0.0264 0.0204 0.0184 0.0042 0.0209 0.0187 0.0045 0.0102 0.0085 0.0045 0.0000 0.0000 0.0000 0.0000
Bus number
Susceptance (pu)
10 24
0.019 0.04
References [1] IEEE Power Engineering Society/Cigre, FACTS overview. Piscataway, NJ: IEEE Service Center; 1995. [special issue, 95TP108]. [2] Gyugyi L. Unified power-flow control concept for flexible AC transmission systems. IEE Proc-C 1992;139(4):323– 31. [3] Mihalic R, Zunko P, Povh D. Improvement of transient stability using unified power flow controller. IEEE Trans Power Deliv 1996;11(1): 485– 92.
M. Tu¨may et al. / Electrical Power and Energy Systems 26 (2004) 561–569 [4] Iravani MR, Dandeno PL, Nguyen KH, Zhu D, Maratukulam D. Applications of static phase shifters in power systems. IEEE Trans Power Deliv 1994;9(3):1600– 8. [5] Noroozian M, Anderson G. Power flow control by use of controlled series components. IEEE Trans Power Deliv 1993; 8(3):1420–9.
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[6] Ma T-T, Lo KL, Tu¨may M. A robust UPFC damping control scheme using PI and ANN based adaptive controllers. COMPEL 2000;19(3):878–902. [7] A. Mete Vural. Flexible AC transmission, a unified power flow controller. MSc Thesis; June 2001. [8] Power system analysis software package (PSASP) user manual. Electric Power Research Institute (China); 1993.
The effect of unified power flow controller location in power systems Mehmet Tu¨maya, A.M. Vuralb,*, K.L. Loc a Department of Electrical and Electronic Engineering, C ¸ ukurova University, Baliai-Adana, Turkey Department of Electrical and Electronic Engineering, Gaziantep University, 27310 Gaziantep, Turkey c Department of Electrical and Electronic Engineering, University of Strathclyde, Royal College Building, 204 George Street, Glasgow G1 1XW, UK b
Received 18 October 2001; accepted 1 April 2004
Abstract The Unified Power Flow Controller (UPFC) is a device that is capable of providing control of voltage magnitude, active and reactive power flows. This paper represents the effect of UPFC location in steady-state analysis and to demonstrate the capabilities of UPFC in controlling active and reactive power flow within any electrical network. In this paper, a complete power injection model of UPFC including both the series injection branch and the shunt exciting branch is derived in rectangular form. An injected power model method is used to represent UPFC in load flow program. Finally, different types of simulation tasks are carried out based on IEEE 30-bus test system. q 2004 Elsevier Ltd. All rights reserved. Keywords: Flexible AC transmission; Unified power flow controller; Power quality
1. Introduction UPFC is the most comprehensive device which has arisen so after the Flexible AC Transmission Systems (FACTS) initiative, is capable of providing simultaneous active and reactive power flow control, as well as voltage magnitude control [1]. The versadility provided by UPFC makes it an advanced power system device and an important member of FACTS family to provide a number of control functions required to solve a wide range of steady-state problems encountered in electrical power networks [2,3]. Basic circuit configuration of UPFC is shown in Fig. 1. Performance analysis of UPFC in load flow studies requires its steady-state modelling. There are many papers concerned with the issue of UPFC mathematical modelling in open liturature for various study purposes. Ref. [2] introduces a steady-state UPFC model based on a single, ideal, series voltage source. Ref. [4] utilizes two ideal voltage sources, one in series and one in parallel as UPFC steady-state model. The steady-state model suggested in Ref. [5] is based upon one ideal, series voltage source, and one ideal, shunt current source. Refs. [6,7] provides an injected power model concept for UPFC. In this model, UPFC is * Corresponding author. Tel.: þ90-342-360-1200-2113; fax: þ 90-342360-1103. E-mail address: [email protected] (A.M. Vural). 0142-0615/$ - see front matter q 2004 Elsevier Ltd. All rights reserved. doi:10.1016/j.ijepes.2004.04.006
represented by two ideal voltage sources with series source impedances, connected in series and parallel with the transmission line, representing the output voltages of series and shunt branches of UPFC. This model is highly suitable for steady-state representation of UPFC in load flow program. Although considerable progress has been made in the area of developing a realistic UPFC model suitable for efficient load flow studies, a very little effort has been made for the investigation of the effects of UPFC location on transmission asset in electrical power networks. In this respect, this paper provides comprehensive simulation tasks concerning with the location of UPFC.
2. UPFC modelling [6,7] Steady-state investigation of UPFC involves power flow studies which include the calculation of busbar voltages, branch loadings, real and reactive transmission losses, and the impact of UPFC on the above mentioned system parameters. In order to evaluate UPFC overall steady-state performance, an adequate model is required. In this section, a UPFC model using power injection concept is derived for power flow studies. In this model, two voltage sources are used to represent the fundamental components of the pulse width modulated controlled output voltage waveforms of the two
562
M. Tu¨may et al. / Electrical Power and Energy Systems 26 (2004) 561–569
Fig. 1. Basic circuit configuration of UPFC.
branches in the UPFC. The impedance of the two coupling transformers are included in the proposed model and losses of UPFC is taken into account. Fig. 2 depicts voltage source equivalent circuit of UPFC. The series injection branch, a series injection voltage source, performs the main functions of controlling power flow whilst the shunt branch is used to provide real power demanded by the series branch and the losses in UPFC, i.e. balancing the real power between the two branches. However, in the proposed model, the function of reactive compensation of shunt branch is completely neglected, this function can be taken into account for future studies. As shown in Fig. 2, the series and shunt injection branch are modelled with two ideal controllable voltage sources, Vse and Vsh ; respectively, while Xse and Xsh ; respectively, denote the leakage reactance of the two coupling transformers. IL represents transmission line current. Series voltage source Vse ; can be mathematically expressed as follows V~ se ¼ r V~ i ejg
ð1Þ
where 0 # r # rmax and 0 # g # 2p For the purpose of simplifying the formulation procedure of the power injection model, which has been derived in
rectangular form and verified in the authors’ previous work [7] is adopted here as shown in Fig. 3. The components of equivalent power injections at buses i and j; Pi;upfc ; Qi;upfc ; Pj;upfc ; and Qj;upfc are formulated as follows: Pi;upfc ¼ 0:02rbse Vi2 sin g 21:02rbse Vi Vj sinðui 2 uj þ gÞ
ð2Þ
Qi;upfc ¼ 2rbse Vi2 cos g
ð3Þ
Pj;upfc ¼ rbse Vi Vj sinðui 2 uj þ gÞ
ð4Þ
Qj;upfc ¼ rbse Vi Vj cosðui 2 uj þ gÞ
ð5Þ
In Eqs. (2)–(5), Pi;upfc þjQi;upfc and Pj;upfc þjQj;upfc are, respectively, the equivalent complex power injected into the two busbars, buses i and j; which are practically the resultant power injections contributed by both the series and shunt branches of UPFC. Vi ; Vj are, respectively, the voltage magnitude components of the voltages on buses i and j; while ui and uj are, respectively, the phase angle components of the voltages on buses i and j: bse is the leakage susceptance of the series coupling transformer. r and g are, respectively, magnitude and phase angle of series voltage source, UPFC parameters, shown in Fig. 2.
Fig. 2. Voltage source equivalent circuit of UPFC.
M. Tu¨may et al. / Electrical Power and Energy Systems 26 (2004) 561–569
563
Fig. 3. Complete UPFC power injection model.
3. Power flow embedded with UPFC When a transmission line of an electrical power network is equipped with a UPFC, the implementation of UPFC model in power system software is an essential tool for investigating the impact of UPFC. Whilst power flow problem involves solving a set of nonlinear algebraic equations, representing the network under steady-state conditions, its solution is expected to provide not only the information of system states, i.e. busbar voltages, real and reactive power flows, transmission losses, but also the impact of UPFC under assorted system operating conditions. Proposed power injection model is incorporated inside the Jacobian and mismatch equations of Newton –Raphson algorithm, leading to iterative solutions. Many commercialgrade power system analysis programs integrated with userdefined modelling function are now available to provide different approaches for the solution of networks equipped with such advanced devices. Power System Analysis Software Package (PSASP) [8] is one of these commercial programs used to investigate the various impacts of UPFC to the different types of power systems. However, concerned modification of Newton– Raphson algorithm is not carried out in PSASP directly. Instead, UPFC power injection model is defined in its user-defined model interface. Real and reactive power injections at the buses, Pi;upfc ; Qi;upfc ; Pj;upfc ; and Qj;upfc at which UPFC is located, are used in user-defined model. This model of UPFC can be seen in Appendix A. The linearized system model based on Newton –Raphson algorithm, written in matrix form is as follows: "
DP DQ
#n
" ¼
H
N
J
L
#n "
Du
#n
In Eq. (6), DP ¼ Pspe 2 Pcal is the real power mismatch vector and DQ ¼ Qspe 2 Qcal is the reactive power mismatch vector. Du and DV are vectors of incremental changes in nodal voltages. H; N; J and L denote the basic elements in the Jacobian matrix. They corresponds partial derivatives of the real and the reactive powers with respect to the phase angles and the magnitudes of the nodal voltages given in Eqs. (7) and (8), n indicates iteration number H¼
›P ; ›u
N¼V
J¼
›Q ; ›u
L¼V
›Q ›V
Hii ¼ Hiin þ Hiiupfc ¼
›Pi;upfc › Pi þ ›ui ›ui
Nii ¼ Niin þ Niiupfc ¼ Vi
›Pi;upfc ›P i þ Vi ›V i › Vi
›Qi;upfc ›Qi þ ›ui ›ui
DV=V Lii ¼ Lnii þ Lupfc ¼ Vi ii
Fig. 4. UPFC located near bus 6 in the line between buses 2 and 6.
ð7Þ ð8Þ
The impact of UPFC can be treated as two controllable power sources or loads, ðPi;upfc þ jQi;upfc Þ and ðPj;upfc þ jQj;upfc Þ; injected into or absorbed from bus i and j; respectively. Since the two power injections ðPi;upfc þ jQi;upfc Þ and ðPj;upfc þ jQj;upfc Þ of UPFC vary with the connected busbar voltage amplitudes and phases, the relevant elements of the Jacobian matrix, given in Eqs. (7) and (8), should be modified at each iteration. Based on Eqs. (2) – (5), the following additional elements of the Jacobian matrix owing to the injections of the UPFC at the i and j busbars, between where the UPFC is installed, can be derived as follows: For bus i; when i ¼ j
Jii ¼ Jiin þ Jiiupfc ¼ ð6Þ
›P ; ›V
›Qi;upfc ›Q i þ Vi ›V i ›Vi
Fig. 5. UPFC located at the middle of line.
ð9Þ
ð10Þ
ð11Þ
ð12Þ
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564
Table 1 The percentage changes as UPFC moved from near bus 6 to at middle of line Active power flow change increase (%)
Reactive power flow change increase (%)
Total transmission real loss change increase (%)
Total transmission reactive loss change increase (%)
r Fixed
r Fixed
r Fixed
r Fixed
r Fixed
r Fixed
r Fixed
r Fixed
6.33
2.4
2120.81
30.91
1.94
20.72
230.22
230.72
When i – j Hij ¼ Hijn þ Hijupfc ¼
›Pi;upfc › Pi þ ›uj ›uj
Nij ¼ Nijn þ Nijupfc ¼ Vj Jij ¼ Jijn þ Jijupfc
›Pi;upfc ›P i þ Vj ›V j ›Vj
›Qi;upfc ›Qi ¼ þ ›uj ›uj
Lij ¼ Lnij þ Lupfc ¼ Vj ij
›Qi;upfc ›Q i þ Vj ›Vj › Vj
ð13Þ ð14Þ ð15Þ ð16Þ
In the above equations, UPFC related terms concerning the partial derivatives of UPFC power injections, Pi;upfc ; Qi;upfc ; Pj;upfc ; and Qj;upfc ; with respect to busbar voltages, Vi /ui ; and Vj /uj ; respectively. The related power mismatches equations for bus i and j must also be modified as: DPi ¼ Pi;G 2 Pi;L þ Pi;upfc 2 Pi;Cal
ð25Þ
DPj ¼ Pj;G 2 Pj;L þ Pj;upfc 2 Pj;Cal
ð26Þ
DQi ¼ Qi;G 2 Qi;L þ Qi;upfc 2 Qi;Cal
ð27Þ
DQj ¼ Qj;G 2 Qj;L þ Qj;upfc 2 Qj;Cal
ð28Þ
For bus j; when j ¼ i Hjj ¼ Hjjn þ Hjjupfc ¼
›Pj;upfc › Pj þ ›uj ›uj
Njj ¼ Njjn þ Njjupfc ¼ Vj Jjj ¼ Jjjn þ Jjjupfc ¼
›Pj;upfc ›P j þ Vj ›V j ›Vj
›Qj;upfc ›Qj þ ›uj ›uj
Ljj ¼ Lnjj þ Lupfc ¼ Vj jj
›Qj;upfc ›Q j þ Vj ›Vj › Vj
ð17Þ
4. Simulation examples
ð18Þ
Simulation tasks are performed on IEEE 30-bus system, as shown in Appendix B, consisting of 30 buses, 37 lines, four transformers, and two shunt capacitors. Also system data is given in Appendix B. Behind the idea of the simulation examples is to investigate the effects of location of UPFC on important system parameters. Two different UPFC locations are considered. One is near bus 6 in the line between buses 2 and 6, as shown in Fig. 4, and other is at the middle of line between the same buses, as shown in Fig. 5. The efficiency of UPFC is taken as 98%, series leakage reactance Xse is taken as 0.025 pu. For each simulation task, magnitude of series injected voltage of UPFC is changed from 0.005 to 0.1 pu, and phase angle of series injected voltage is changed from 0 to 3608, respectively. Two different locations were considered in simulations. For all simulation tasks, when a UPFC parameter was controlled, the other one was kept constant. Namely, magnitude of series inserted voltage of UPFC, r; was controlled, while phase angle of that voltage, g; was kept constant, and vice versa. Table 1 summarizes the percentage changes as UPFC is moved from near bus 6 location to at
ð19Þ ð20Þ
When j – i Hji ¼ Hjin þ Hjiupfc ¼
›Pj;upfc › Pj þ ›ui ›ui
Nji ¼ Njin þ Njiupfc ¼ Vi Jji ¼ Jjin þ Jjiupfc ¼
›Pj;upfc ›P j þ Vi ›V i ›Vi
›Qj;upfc ›Qj þ ›ui ›ui
¼ Vi Lji ¼ Lnji þ Lupfc ji
›Qj;upfc ›Q j þ Vi ›Vi › Vi
ð21Þ ð22Þ ð23Þ ð24Þ
Fig. 6. Comparison of active power flow by changing UPFC parameter.
Fig. 7. Comparison of active power loss by changing UPFC parameter.
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Fig. 8. Comparison of reactive power flow by changing UPFC parameter. Fig. 11. Comparison of total reactive losses by changing UPFC parameter.
Fig. 9. Comparison of reactive power flow by changing UPFC parameter. Fig. 12. Comparison of total reactive losses by changing UPFC parameter.
middle of line between buses 2 and 6 location. The data points labelled by symbols –V – and – B – (Figs. 6– 13) denote the location of UPFC as in Figs. 4 and 5, respectively.
4.1. Simulation task A The uncompensated active power flow in line between buses 2 and 6 is 0.5555 pu. The effect of UPFC location is investigated. Comparative results concerning this study are graphically represented in Figs. 6 and 7.
4.3. Simulation task C The total real transmission losses for the IEEE 30-bus test system is 0.1560 pu. Figs. 10 and 11 show the effect of UPFC location on total real power losses. 4.4. Simulation task D With the same configuration as in task C, the total reactive transmission losses is now 2 0.0164 pu and Figs. 12 and 13 depict the effect of UPFC location on total reactive power losses.
4.2. Simulation task B 5. Conclusions In this task, the same configuration is used. But this time the uncompensated reactive power flow is 0.0155 pu. Figs. 8 and 9 show the effect of UPFC location by changing the magnitude and phase angle of series inserted voltage, respectively.
UPFC can theoretically be located anywhere along a line in an electrical power network. In this work, effects of UPFC location on power system steady-state operating conditions
Fig. 10. Comparison of total real losses by changing UPFC parameter.
Fig. 13. Comparison of total reactive losses by changing UPFC parameter.
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have been investigated in detail. From the practical applications point of view, factors influencing the choice of location include cost, accessibility, fault level, protective relaying considerations, and effectiveness in improving power system operation. If the UPFC system is located at midpoint of the line, it will not be very convenient in terms of access for maintenance, monitoring, security, etc. If it is considered to be located at either end of the line, this
configuration provides more accessibility and availability of station service and other auxiliaries. The choice of location for any application requires a detailed study with regard to overall economy and system operation.
Appendix A. UPFC user-defined model for PSASP
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Appendix B. IEEE 30-bus system
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See Tables B1 – B4.
Table B2 (continued)
Table B1 Bus data Bus number
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30
Bus voltage
Bus generation
Bus load
Magnitude per unit
Phase angle (8)
Real MW
Reactive MVAR
Real MW
Reactive MVAR
1.0600 1.0450 1.0229 1.0142 1.0100 1.0122 1.0036 1.0100 1.0535 1.0489 1.0820 1.0584 1.0710 1.0460 1.0394 1.0472 1.0433 1.0307 1.0286 1.0329 1.0400 1.0398 1.0300 1.0257 1.0194 1.0018 1.0241 1.0085 1.0043 0.9938
0.00 25.01 26.96 28.57 213.53 210.21 212.10 210.92 212.56 213.79 212.56 213.67 213.67 213.66 214.27 213.98 214.06 214.79 214.91 214.69 213.86 213.93 214.56 214.59 214.53 214.94 214.23 210.78 215.46 216.34
243.25 40.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00
217.91 51.57 0.00 0.00 34.86 0.00 0.00 31.57 0.00 0.00 14.82 0.00 9.65 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00
0.00 21.70 2.40 7.60 94.20 0.00 22.80 30.00 0.00 5.80 0.00 11.20 0.00 6.20 8.20 3.50 9.00 3.20 9.50 2.20 7.50 0.00 3.20 8.70 0.00 3.50 0.00 0.00 2.40 10.60
0.00 12.70 1.20 1.60 19.00 0.00 10.90 30.00 0.00 2.00 0.00 7.50 0.00 1.60 2.50 1.80 5.80 0.90 3.40 0.70 11.20 0.00 1.60 6.70 0.00 2.30 0.00 0.00 0.90 1.90
Line number and between buses
Line impedance
Line No.
Buses
R (pu)
X (pu)
15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37
12 and 15 12 and 16 14 and 15 16 and 17 15 and 18 18 and 19 19 and 20 10 and 20 10 and 17 10 and 21 10 and 22 21 and 22 15 and 23 22 and 24 23 and 24 24 and 25 25 and 26 25 and 27 27 and 29 27 and 30 29 and 30 8 and 28 6 and 28
0.0662 0.0945 0.2210 0.0824 0.1070 0.0639 0.0340 0.0936 0.0324 0.0348 0.0727 0.0116 0.1000 0.1150 0.1320 0.1885 0.2544 0.1093 0.2198 0.3202 0.2399 0.0363 0.0169
0.1304 0.1987 0.1997 0.1932 0.2185 0.1292 0.0680 0.2090 0.0845 0.0749 0.1499 0.0236 0.2020 0.1790 0.2700 0.3292 0.3800 0.2087 0.4153 0.6027 0.4533 0.2000 0.0599
Half-line charging susceptance, B=2 (pu)
0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0214 0.0065
Table B3 Transformer data Transformer data
Between buses
Tap setting
1 2 3 4
6 and 9 6 and 10 4 and 12 28 and 27
1.0155 0.9629 1.0129 0.9581
Table B4 Shunt capacitor data
Table B2 Line data Line number and between buses
Line impedance
Line No.
Buses
R (pu)
X (pu)
1 2 3 4 5 6 7 8 9 10 11 12 13 14
1 and 2 1 and 3 2 and 4 3 and 4 2 and 5 2 and 6 4 and 6 5 and 7 6 and 7 6 and 8 9 and 11 9 and 10 12 and 13 12 and 14
0.0192 0.0452 0.0570 0.0132 0.0472 0.0581 0.0119 0.0460 0.0267 0.0120 0.0000 0.0000 0.0000 0.1231
0.0575 0.1852 0.1737 0.0379 0.1983 0.1763 0.4140 0.1160 0.0820 0.0420 0.2080 0.1100 0.1400 0.2559
Half-line charging susceptance, B=2 (pu)
0.0264 0.0204 0.0184 0.0042 0.0209 0.0187 0.0045 0.0102 0.0085 0.0045 0.0000 0.0000 0.0000 0.0000
Bus number
Susceptance (pu)
10 24
0.019 0.04
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