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Difference in analysis methods of tap changer instability in link and radial networks
Energy Conversion and Management 48 (2007) 1919–1922 www.elsevier.com/locate/enconman
Difference in analysis methods of tap changer instability in link and radial networks F. Karbalaei *, M. Kalantar Center of Excellence for Power System Automation and Operation, Department of Electrical Engineering, Iran University of Science and Technology, Tehran 1684613114, Iran Received 6 July 2006; accepted 30 January 2007 Available online 27 March 2007
Abstract One of the diagnosis methods for voltage instability due to tap changer operation is to use conventional power flow results. This paper discusses that divergence of conventional power flow calculations can show tap changer instability only in radial networks (i.e. in bulk power delivery transformers), but for analysis of tap changer instability in link networks (i.e. in transmission transformers), a new type of bus must be defined for those controlled by tap changers and, consequently, new power flow calculations must be performed. A wide range of tap changing is used in this study. Ó 2007 Elsevier Ltd. All rights reserved. Keywords: Tap changer instability; Loadability; Link and radial networks
1. Introduction In recent years, voltage collapse has drawn more attention. One of the important reasons for long term voltage instability and collapse is the tap changer operations [1,2]. Up to now, this has been predicted using the divergence of conventional power flow calculations. The tap changer function is voltage control in the buses that are connected to transformers having tap changers. When a disturbance occurs, the voltage decreases in all buses, which causes the tap changers to try to restore the voltage. Because of the voltage dependence characteristic of loads, voltage restoration causes the power consumed by the loads to be restored to the values before disturbance. If the loads are higher than the loadability of the disturbed system, the voltages can not be restored, and the tap changer operations finally cause voltage collapse [3]. For this reason, loadability is known as the voltage stability boundary, and many papers have been presented for fast compu-
*
Corresponding author. Tel.: +98 21 77240492. E-mail address: [email protected] (F. Karbalaei).
0196-8904/$ - see front matter Ó 2007 Elsevier Ltd. All rights reserved. doi:10.1016/j.enconman.2007.01.029
tation of loadability [4–6]. This paper discusses that loadability is only sufficient to diagnose tap changer instability in radial networks because in link networks, loadability varies when the taps are altered. In Ref. [7], the effects of tap changing in transmission transformers on the degree of voltage stability have been verified. This instability is related to the tap changers in bulk power delivery transformers and not to transmission transformers. In the following, the difference that must be considered in the analysis of tap changer instability in link and radial networks will be explained. 2. Diagnosis of tap changer instability Voltage control due to tap changer operation causes load characteristics to become constant power. If this power is higher than the system loadability, tap changers can not control voltages, and tap changer instability occurs. In this condition, with an increase of tap value, voltage decreases instead of increasing. Thus, the loadability is a criterion for diagnosis of tap changer instability in a given load. If under load tap changing (ULTC) is in a radial network (Fig. 1a), the loadability does not depend
1920
F. Karbalaei, M. Kalantar / Energy Conversion and Management 48 (2007) 1919–1922
3
2.15
P,Q 2.1
a 1
4
3
~
P,Q
Max imum Trans fer P ower, p. u.
~
2
1
2.05
2
1.95
2
~
1.9 0.8
b
0.85
0.9
0.95
1 1.05 Tap Value
1.1
1.15
1.2
1.25
Fig. 1. Tap changing transformers in radial and link networks. Fig. 2. The variation of loadability with the tap values.
3. Simulation results The simple system in Fig. 1b is first used as a test system to illustrate the loadability variation by tap changing. It is assumed that the tap is located on the secondary side. The reactance of lines 2–4, 1–3 and the transformer are 0.2 p.u. and Q is half of P. Fig. 2 shows the variation of loadability (Pmax) versus the tap values. It can be seen that with an increase of tap value, loadability decreases. The reason is that the tap increase causes more reactive power flow into line 1–3, and this decreases the loadability because the reactances of line 1–3 plus that of the transformer is more than that of line 2–4. Fig. 3 shows the load voltages corresponding to tap ratios at different load powers. When the voltage starts to decrease, conventional power flow solutions still converge. This indicates that conventional power flow convergence
0.86
0.84
Hidden instability
P=1.83p.u. 0.82
0.8
V o l t ag e, p. u .
on the tap value. Therefore, if conventional power flow converges in a given load, the tap changer can control voltage. However, in a link network (Fig. 1b), loadability depends on the tap value. For example, in Fig. 1b, the tap increase causes more reactive power flow into line 1–3, and this increases or decreases the loadability depending on the reactance of the lines. Therefore, the convergence of conventional power flow calculations in a given load for which the tap value is assumed to be fixed does not guarantee tap changer stability, and a new power flow calculation is required. In the proposed method, the tap value is included in the power flow equations as a variable, and instead, the voltage in the secondary side of the transformer is fixed. Thus, the bus becomes a PQV bus because the active load (P), reactive load (Q) and voltage (V) are specified, but the angle and tap value are unknown. Now, the convergence of the new power flow calculations for a given load and requested voltage indicates tap changer stability and determines the tap value.
P=1.9p.u. 0.78
0.76
P=2p.u. 0.74
0.72
0.7
0.68 0.8
0.9
1
1.1
1.2
1.3
1.4
1.5
1.6
1.7
1.8
Tap ratio
Fig. 3. The load voltages corresponding to tap ratios at different load powers.
cannot guarantee tap changer instability in link networks, contrary to that in radial networks. However, in the proposed power flow, bus 4 can be defined as a PQV bus, and if the power flow solutions converge in any specified voltage, voltage stability is guaranteed. The area in which the voltage starts to decrease until conventional power flow divergence occurs can be named a hidden instability area because this region cannot be identified by the indices that are based on conventional power flow results. Fig. 3 shows that the hidden instability starts when the tap ratios are higher than 1.2, which seems unpractical, but it can occur in a practical tap ratio range. For example, when high active power and low reactive power flow into a line, the critical voltage at the receiving end becomes a high value (even 0.95 p.u.). In this condition, hidden instability starts when the tap ratio is low. For example, in Fig. 1b, if P = 2.2 p.u., Q = 0.22 p.u. and the active power genera-
F. Karbalaei, M. Kalantar / Energy Conversion and Management 48 (2007) 1919–1922 2
V3=1p.u V3=0.95p.u. V3=0.9p.u.
1.8
1.6 Tap rat io
tion in bus 1 is three times as much as bus 2, the hidden instability starts when the tap ratio is 1, and the conventional power flow diverges when the tap ratio is 1.1, as shown in Fig. 4. Another test system is a six bus system (Fig. 5) for which the corresponding data is presented in Ref. [8]. Bus 3 is selected to be a variable load bus; its base case powers are P = 0.275 p.u. and Q = 0.065 p.u. There is a tap changing transformer in transmission line 4–3 that controls the voltage of bus 3. Fig. 6 shows the tap ratios corresponding to the load powers at different voltages. With an increase of load power, the proposed power flow finally diverges, which shows the maximum allowable power at the requested voltage. These results are confirmed using conventional power flow. The figure reveals that in link networks, on the contrary of radial networks, transformer tap variations affect the maximum transmitted power.
1921
Maximum allowable power at requested voltage
V3=0.85p.u
1.4
1.2
1
0.8 0.2
0.3
0.4
0.5 0.6 0.7 Load active power, p.u.
0.8
0.9
1
Fig. 6. Tap ratios corresponding to load powers at different voltages. 0.84
0.83
Voltage, p.u.
0.82
0.81
0.8
0.79
0.78 0.8
0.85
0.9
0.95
1
1.05
1.1
1.15
Tap ratio
Fig. 4. Beginning of hidden instability in low value of tap ratio.
Therefore, the calculation of maximum allowable power using conventional power flow (i.e. with tap fixed and voltage unspecified) guarantees tap changer stability in only the bulk power delivery transformer but not in the transmission transformer. In radial networks, for example, Fig. 1a, if a requested load power is lower than maximum allowable power, the corresponding tap changer can adjust the load voltage to any requested value provided that tap ratio limits are neglected, but in link networks, this is not correct. It is important to know that when voltage stability analyses of buses connected to transmission transformers are to be performed, Thevenin’s equivalent system must not be used because this converts link networks to radial ones and can not show the dependence of maximum allowable power on tap ratio. 4. Conclusions
~ 1
6
4
3
5
2
~ Fig. 5. Six bus test system.
This paper discusses the difference between analysis methods of tap changer instability in link and radial networks. The convergence of conventional power flow in a given load, with tap ratio fixed and load voltage unspecified, indicates tap changer stability only in radial networks because in link networks, tap variation changes the maximum allowable load power. To diagnose tap changer instability in link networks, a new power flow has been presented. In this method, the load voltages in the buses connected to tap changing transformers are specified. Therefore, these buses have been defined as PQV buses. Now, if this proposed power flow converges in a given load, tap changer stability is guaranteed. The simulations show that a hidden instability area is created when using conventional power flow. This area can occur inside the practical range of tap ratio variations.
1922
F. Karbalaei, M. Kalantar / Energy Conversion and Management 48 (2007) 1919–1922
References [1] Isaias Lima Lopes B, de Sousa ACZ. On multiple tap blocking to avoid voltage collapse. Int J Electric Power Syst Res 2003;67:225–31. [2] Vournas CD, Karystianos M. Load tap changers in emergency and preventive voltage stability control. IEEE Trans Power Syst 2004;19(February):492–8. [3] Cutsem T Van. An approach to corrective control of voltage in stability using simulation and sensitivity’’. IEEE Trans Power Syst 1995;10(May):616–22. [4] Karbalaei F, Jadid S, Kalantar M. A novel method for fast computation of saddle node bifurcation in power systems using an
[5] [6]
[7]
[8]
optimization technique. Int J Energy Conver Manage 2006:582–9. de Sousa ACZ, de Souza JCS, da Silva AML. On line voltage stability monitoring. IEEE Trans Power Syst 2000:1300–5. de Sousa ACZ, Canizares CA, Quintana VH. New techniques to speed up voltage collapse computations using tangent vectors. IEEE Trans Power Syst 1997:1380–7. El-Sadek MZ, Mahmoud GA, Dessouky MM, Rashed WI. Tap changing transformer role in voltage stability enhancement. Int J Electric Power Syst Res 1999;50:115–8. Pai MA. Computer techniques in power system analysis. New York: McGraw-Hill; 1986.
Difference in analysis methods of tap changer instability in link and radial networks F. Karbalaei *, M. Kalantar Center of Excellence for Power System Automation and Operation, Department of Electrical Engineering, Iran University of Science and Technology, Tehran 1684613114, Iran Received 6 July 2006; accepted 30 January 2007 Available online 27 March 2007
Abstract One of the diagnosis methods for voltage instability due to tap changer operation is to use conventional power flow results. This paper discusses that divergence of conventional power flow calculations can show tap changer instability only in radial networks (i.e. in bulk power delivery transformers), but for analysis of tap changer instability in link networks (i.e. in transmission transformers), a new type of bus must be defined for those controlled by tap changers and, consequently, new power flow calculations must be performed. A wide range of tap changing is used in this study. Ó 2007 Elsevier Ltd. All rights reserved. Keywords: Tap changer instability; Loadability; Link and radial networks
1. Introduction In recent years, voltage collapse has drawn more attention. One of the important reasons for long term voltage instability and collapse is the tap changer operations [1,2]. Up to now, this has been predicted using the divergence of conventional power flow calculations. The tap changer function is voltage control in the buses that are connected to transformers having tap changers. When a disturbance occurs, the voltage decreases in all buses, which causes the tap changers to try to restore the voltage. Because of the voltage dependence characteristic of loads, voltage restoration causes the power consumed by the loads to be restored to the values before disturbance. If the loads are higher than the loadability of the disturbed system, the voltages can not be restored, and the tap changer operations finally cause voltage collapse [3]. For this reason, loadability is known as the voltage stability boundary, and many papers have been presented for fast compu-
*
Corresponding author. Tel.: +98 21 77240492. E-mail address: [email protected] (F. Karbalaei).
0196-8904/$ - see front matter Ó 2007 Elsevier Ltd. All rights reserved. doi:10.1016/j.enconman.2007.01.029
tation of loadability [4–6]. This paper discusses that loadability is only sufficient to diagnose tap changer instability in radial networks because in link networks, loadability varies when the taps are altered. In Ref. [7], the effects of tap changing in transmission transformers on the degree of voltage stability have been verified. This instability is related to the tap changers in bulk power delivery transformers and not to transmission transformers. In the following, the difference that must be considered in the analysis of tap changer instability in link and radial networks will be explained. 2. Diagnosis of tap changer instability Voltage control due to tap changer operation causes load characteristics to become constant power. If this power is higher than the system loadability, tap changers can not control voltages, and tap changer instability occurs. In this condition, with an increase of tap value, voltage decreases instead of increasing. Thus, the loadability is a criterion for diagnosis of tap changer instability in a given load. If under load tap changing (ULTC) is in a radial network (Fig. 1a), the loadability does not depend
1920
F. Karbalaei, M. Kalantar / Energy Conversion and Management 48 (2007) 1919–1922
3
2.15
P,Q 2.1
a 1
4
3
~
P,Q
Max imum Trans fer P ower, p. u.
~
2
1
2.05
2
1.95
2
~
1.9 0.8
b
0.85
0.9
0.95
1 1.05 Tap Value
1.1
1.15
1.2
1.25
Fig. 1. Tap changing transformers in radial and link networks. Fig. 2. The variation of loadability with the tap values.
3. Simulation results The simple system in Fig. 1b is first used as a test system to illustrate the loadability variation by tap changing. It is assumed that the tap is located on the secondary side. The reactance of lines 2–4, 1–3 and the transformer are 0.2 p.u. and Q is half of P. Fig. 2 shows the variation of loadability (Pmax) versus the tap values. It can be seen that with an increase of tap value, loadability decreases. The reason is that the tap increase causes more reactive power flow into line 1–3, and this decreases the loadability because the reactances of line 1–3 plus that of the transformer is more than that of line 2–4. Fig. 3 shows the load voltages corresponding to tap ratios at different load powers. When the voltage starts to decrease, conventional power flow solutions still converge. This indicates that conventional power flow convergence
0.86
0.84
Hidden instability
P=1.83p.u. 0.82
0.8
V o l t ag e, p. u .
on the tap value. Therefore, if conventional power flow converges in a given load, the tap changer can control voltage. However, in a link network (Fig. 1b), loadability depends on the tap value. For example, in Fig. 1b, the tap increase causes more reactive power flow into line 1–3, and this increases or decreases the loadability depending on the reactance of the lines. Therefore, the convergence of conventional power flow calculations in a given load for which the tap value is assumed to be fixed does not guarantee tap changer stability, and a new power flow calculation is required. In the proposed method, the tap value is included in the power flow equations as a variable, and instead, the voltage in the secondary side of the transformer is fixed. Thus, the bus becomes a PQV bus because the active load (P), reactive load (Q) and voltage (V) are specified, but the angle and tap value are unknown. Now, the convergence of the new power flow calculations for a given load and requested voltage indicates tap changer stability and determines the tap value.
P=1.9p.u. 0.78
0.76
P=2p.u. 0.74
0.72
0.7
0.68 0.8
0.9
1
1.1
1.2
1.3
1.4
1.5
1.6
1.7
1.8
Tap ratio
Fig. 3. The load voltages corresponding to tap ratios at different load powers.
cannot guarantee tap changer instability in link networks, contrary to that in radial networks. However, in the proposed power flow, bus 4 can be defined as a PQV bus, and if the power flow solutions converge in any specified voltage, voltage stability is guaranteed. The area in which the voltage starts to decrease until conventional power flow divergence occurs can be named a hidden instability area because this region cannot be identified by the indices that are based on conventional power flow results. Fig. 3 shows that the hidden instability starts when the tap ratios are higher than 1.2, which seems unpractical, but it can occur in a practical tap ratio range. For example, when high active power and low reactive power flow into a line, the critical voltage at the receiving end becomes a high value (even 0.95 p.u.). In this condition, hidden instability starts when the tap ratio is low. For example, in Fig. 1b, if P = 2.2 p.u., Q = 0.22 p.u. and the active power genera-
F. Karbalaei, M. Kalantar / Energy Conversion and Management 48 (2007) 1919–1922 2
V3=1p.u V3=0.95p.u. V3=0.9p.u.
1.8
1.6 Tap rat io
tion in bus 1 is three times as much as bus 2, the hidden instability starts when the tap ratio is 1, and the conventional power flow diverges when the tap ratio is 1.1, as shown in Fig. 4. Another test system is a six bus system (Fig. 5) for which the corresponding data is presented in Ref. [8]. Bus 3 is selected to be a variable load bus; its base case powers are P = 0.275 p.u. and Q = 0.065 p.u. There is a tap changing transformer in transmission line 4–3 that controls the voltage of bus 3. Fig. 6 shows the tap ratios corresponding to the load powers at different voltages. With an increase of load power, the proposed power flow finally diverges, which shows the maximum allowable power at the requested voltage. These results are confirmed using conventional power flow. The figure reveals that in link networks, on the contrary of radial networks, transformer tap variations affect the maximum transmitted power.
1921
Maximum allowable power at requested voltage
V3=0.85p.u
1.4
1.2
1
0.8 0.2
0.3
0.4
0.5 0.6 0.7 Load active power, p.u.
0.8
0.9
1
Fig. 6. Tap ratios corresponding to load powers at different voltages. 0.84
0.83
Voltage, p.u.
0.82
0.81
0.8
0.79
0.78 0.8
0.85
0.9
0.95
1
1.05
1.1
1.15
Tap ratio
Fig. 4. Beginning of hidden instability in low value of tap ratio.
Therefore, the calculation of maximum allowable power using conventional power flow (i.e. with tap fixed and voltage unspecified) guarantees tap changer stability in only the bulk power delivery transformer but not in the transmission transformer. In radial networks, for example, Fig. 1a, if a requested load power is lower than maximum allowable power, the corresponding tap changer can adjust the load voltage to any requested value provided that tap ratio limits are neglected, but in link networks, this is not correct. It is important to know that when voltage stability analyses of buses connected to transmission transformers are to be performed, Thevenin’s equivalent system must not be used because this converts link networks to radial ones and can not show the dependence of maximum allowable power on tap ratio. 4. Conclusions
~ 1
6
4
3
5
2
~ Fig. 5. Six bus test system.
This paper discusses the difference between analysis methods of tap changer instability in link and radial networks. The convergence of conventional power flow in a given load, with tap ratio fixed and load voltage unspecified, indicates tap changer stability only in radial networks because in link networks, tap variation changes the maximum allowable load power. To diagnose tap changer instability in link networks, a new power flow has been presented. In this method, the load voltages in the buses connected to tap changing transformers are specified. Therefore, these buses have been defined as PQV buses. Now, if this proposed power flow converges in a given load, tap changer stability is guaranteed. The simulations show that a hidden instability area is created when using conventional power flow. This area can occur inside the practical range of tap ratio variations.
1922
F. Karbalaei, M. Kalantar / Energy Conversion and Management 48 (2007) 1919–1922
References [1] Isaias Lima Lopes B, de Sousa ACZ. On multiple tap blocking to avoid voltage collapse. Int J Electric Power Syst Res 2003;67:225–31. [2] Vournas CD, Karystianos M. Load tap changers in emergency and preventive voltage stability control. IEEE Trans Power Syst 2004;19(February):492–8. [3] Cutsem T Van. An approach to corrective control of voltage in stability using simulation and sensitivity’’. IEEE Trans Power Syst 1995;10(May):616–22. [4] Karbalaei F, Jadid S, Kalantar M. A novel method for fast computation of saddle node bifurcation in power systems using an
[5] [6]
[7]
[8]
optimization technique. Int J Energy Conver Manage 2006:582–9. de Sousa ACZ, de Souza JCS, da Silva AML. On line voltage stability monitoring. IEEE Trans Power Syst 2000:1300–5. de Sousa ACZ, Canizares CA, Quintana VH. New techniques to speed up voltage collapse computations using tangent vectors. IEEE Trans Power Syst 1997:1380–7. El-Sadek MZ, Mahmoud GA, Dessouky MM, Rashed WI. Tap changing transformer role in voltage stability enhancement. Int J Electric Power Syst Res 1999;50:115–8. Pai MA. Computer techniques in power system analysis. New York: McGraw-Hill; 1986.