臺灣博碩士論文加值系統

本論文提出一個在台灣各類型發電廠之開關場採用阻尼電抗器成功抑制 161 kV氣封絕緣開關設備(Gas Insulated Switchgear，簡稱GIS)電磁感應型比壓器(Potential Transformer，簡稱PT)鐵磁共振(Ferroresonance，簡稱FR)的經驗。由於量測與計費之需要，比壓器必須具備低容量與高精確度，因此，低鐵芯損耗是必要的，但也同時降低其阻尼能力，並增加了鐵磁共振發生的可能性。在本論文研究案例，同一個開關場曾在九個月內發生兩次肇因於鐵磁共振的比壓器事故。為了深入了解鐵磁共振的行為與抑制方法，在民國96年至100年間，共執行了四次現場試驗，其中前二次在台灣西部的燃氣火力發電廠，第三次在台灣中部的水力發電廠，第四次在台灣東北部興建中的核能發電廠，經由在電力系統中的實地測試，取得了比壓器鐵磁共振的完整波形，第一次實地測試經由11次隨機操作，重現了鐵磁共振的現象，最長的共振持續了22.9秒，第二次至第四次實地測試，經由29次隨機操作，證實了採用阻尼電抗器可抑制並縮短鐵磁共振的時間在4.36秒以內，此外，從西部的燃氣火力發電廠 SCADA系統之操作紀錄統計，自民國97年11月至99年9月間共23個月82次可能發生鐵磁共振的操作，證實得到長期良好的運轉實績。本論文證明採用電磁暫態解析程式(ElectroMagnetic Transients Program)EMTP/ATPDraw 的模擬可以有效預測鐵磁共振發生與否與鐵磁共振之型態，並證明規格適當的阻尼電抗器可以成功抑制鐵磁共振。本論文為台灣電力系統中首次為了了解電磁感應型比壓器鐵磁共振的行為，投入五年的時間進行深入廣泛的研究與實地測試，對於未來更高電壓等級非線性行為的研究，極具價值。
雖然第一篇有關鐵磁共振的文獻早在1920年即被發表，但是此一特殊的現象至今仍然未被完全了解，本論文討論了電力系統中之氣封絕緣開關設備，由於斷路器的極間電容和電磁感應型比壓器的非線性電感所構成的單相鐵磁共振；理論上，鐵磁共振是由電容和非線性電感所構成的非線性串聯共振，造成電壓和電流波形明顯的畸變。鐵磁共振的振盪模式可分為基波模式、次諧波模式、類週期模式、及混沌模式，鐵磁共振產生之過電壓與過電流可能導致高壓設備和PT因絕緣與過熱等問題而損壞；雖然電磁感應型比壓器在某些GIS架構中有發生鐵磁共振的風險，但是因為電磁感應型比壓器在長期使用下，不論可靠性、精確度與電壓轉換比等特性都優於電容分壓型比壓器，因此電磁感應型比壓器比電容分壓型比壓器更廣泛被使用在GIS設備上，為此，本論文結合相關文獻之理論基礎及GIS、PT專業廠家的經驗與技術，對GIS各種可能的架構進行完整之檢視，討論各個參數對鐵磁共振行為的影響，並介紹相關的分析流程與方法，提出避免鐵磁共振發生之方法和有效之抑制措施，本論文就一個161 kV GIS發生鐵磁共振之實際案例進行探討，先建立詳細的系統參數模型，再透過EMTP/ATPDraw模擬，最後將電腦程式模擬的結果與現場試驗的量測結果進行比較分析，確認分析流程與方法的正確性與實用性，提供電力工程師們在規劃和設計時之參考。

This dissertation presents a successful mitigation experience of ferroresonance (FR) with a Damping Reactor(DR) involving electromagnetic type Potential Transformers(PTs) of a 161 kV Gas Insulated Switchgear(GIS) in Taiwan. PTs have a typically low thermal capacity and high accuracy due to their measuring functions. Low core losses are necessary to obtain high accuracy, but they also reduce its damping ability and therefore increase the possibility of FR. FR happened twice and destroyed PTs for just nine months in the study case. Complete FR waveforms of 161 kV PT were obtained via field tests never conducted before in Taiwan. The first field test had a reappearing FR which sustained up to 22.9 seconds in 11 random operations and the second to fourth field tests confirmed the validity of DR which shortened FR less than 4.36 seconds in 29 random operations which are carried out in thermal power plant, hydro power plant and nuclear power plant. A reliable prediction by EMTP/ATPDraw simulation and a useful mitigation method with a proper DR were proved by both field tests and the following 23 months satisfactory operations for 82 times which extracted from SCADA system in a thermal power plant since Nov., 2008. The five years study would prove valuable for further research in higher voltage level GIS.
Although the first paper on FR was published in 1920, FR is still not a fully understood phenomenon. This dissertation focuses on single phase FR in GIS with PT, fed by the circuit breaker grading capacitance. In principle, FR is a forced oscillation in a nonlinear series resonance circuit including a capacitance and nonlinear inductance, which shows significantly distorted voltage and current waveforms. The complex nonlinear behavior of the saturable inductance can cause fundamental FR, subharmonic FR, quasi-periodic and even chaotic oscillations. FR can result in high overvoltage and high overcurrent, which can finally damage the high voltage equipment or PTs due to dielectric and thermal problems. Even if there is the risk of ferroresonance for specific GIS configurations, electromagnetic PTs are used rather than capacitive ones because of their reliability, higher accuracy and stable transformation ratio during the entire lifetime. However, combine the theory, GIS and PT maker’s experiences, this dissertation provides an overview of network configurations, parameters influencing the FR behavior and a number of methods to avoid or suppress FR are discussed. A very comprehensive analysis is performed by detailed modeling using time domain simulation with a digital computer transient analysis program such as the EMTP/ATPDraw and compares them with field tests and measurements. It would be valuable on planning and designing for electrical engineers.

Contents

中文摘要 i
Abstract iii
誌謝 v
Contents v
List of Tables viii
List of Figures ix
Chapter 1 INTRODUCTION 1
1.1 Motivation 1
1.2 Research objectives 2
1.3 Importance and significance of the study 2
1.4 Dissertation organization 3
Chapter 2 RELATED LITERATURE REVIEW 5
2.1 Introduction of GIS and PT 5
2.1.1 Introduction of GIS 5
2.1.2 Introduction of PT 6
2.2 Introduction of FR and linear resonance 7
2.2.1 Operational circumstances of FR 11
2.2.2 The symptoms of FR 11
2.2.3 Main characteristics of FR 12
2.2.4 Classification of FR modes 14
2.2.5 Operating point of power system 20
2.2.6 Typical circuit configurations with high FR risk 22
2.3 Commonly used tools for analyses 25
2.3.1 TNA 26
2.3.2 EMTP 26
2.4 Preventing or suppressing ferroresonance 27
Chapter 3 FR ANALYSIS AND SUPPRESSION 28
3.1 The scope of study 28
3.2 Typical configuration of 161 kV PT with FR risk 28
3.2.1 Configuration A 29
3.2.2 Configuration B 33
3.2.3 Configuration C 36
3.2.4 Configuration D 39
3.3 Methods for preventing or suppressing FR 40
3.3.1 Adding damping resistor 40
3.3.2 Adding damping reactor 42
3.3.3 Adding active damping device 44
3.3.4 PT relocation 44
3.3.5 Interlocking or revise switching procedures 45
3.3.6 Adding Metal Oxide Surge Absorber(MOSA) 45
3.3.7 Adding neutral resistance to PT 45
3.3.8 Adding both damping resistor and reactor 45
3.4 Flow chart of FR analysis 48
Chapter 4 CASE STUDY AND SIMULATION 50
4.1 Background of the study case 50
4.1.1 Configuration and single line diagram of power system 50
4.1.2 FR events 52
4.1.3 Conditions of damaged PT 53
4.2 Numerical simulation by EMTP/ATPDraw 55
4.2.1 Established detail system parameters 55
4.2.2 Numerical simulation of the study case 59
4.2.3 Summary of simulation results and discussion 84
Chapter 5 FIELD TEST RESULTS AND DISSCUSSION 86
5.1 Field tests and measurements 86
5.1.1 The first field test of a thermal power plant in western
Taiwan 86
5.1.2 The second field test in the same power plant 101
5.1.3 The third field test in a hydro power plant 107 5.1.4 The fourth field test in a nuclear power plant 108
5.1.5 Summary of four times field tests in Taiwan 111
5.2 Design criteria and thermal capacity of PT and DR 111
5.2.1 Thermal capacity of PT of the study case 111
5.2.2 Thermal capacity of damping reactor of the study case 113
5.2.3 Design criteria of PT and damping reactor 113
Chapter 6 CONCLUSIONS AND FUTURE WORKS 114
6.1 Conclusions 114
6.2 Future works 115
REFERENCES 117
ATTACHMENT 1 125
ATTACHMENT 2 136
ATTACHMENT 3 148
ATTACHMENT 4 160
ATTACHMENT 5 178
Author’s Introduction 189
Publication List 190



List of Tables

Table 4.1 Operation mode ............................................. 51
Table 4.2 Specifications of MOF PT and Line PT..............…..................... 53
Table 4.3 Detail parameters of the study case in Taiwan...........................55
Table 4.4 Details of analysis case ........................................... 59
Table 4.5 Parameters of MOF PT ........................................... 60
Table 4.6 Parameters of damping reactor type DR1.................................... 61
Table 4.7 Summary of EMTP/ATP simulation results of phase C................ 84
Table 5.1 The test results of the first field test ........................................... 90
Table 5.2 Parameters of damping reactor type DR2 .................................. 101
Table 5.3 The test results of the second field test....................................... 103
Table 5.4 Accumulative 82 times operations according to bay number and
month order since Nov., 2008.......................................... 105
Table 5.5 A summary of operations according to date sequence since Nov.,
2008 ........................................... 106
Table 5.6 The test results of the third field test......................................... 108
Table 5.7 The test results of the fourth field test...................................... 110
Table 5.8 Summary of four times field tests ........................................... 111














List of Figures

Figure 2.1 Outline of 161 kV GIS ................................................ 5
Figure 2.2 Structure of PT (a) single phase type (b) three phase type........... 6
Figure 2.3 Ferroresonance (a) schematic diagram of L-C series resonance
(b) simplified characteristicψ(i)................................................ 9
Figure 2.4 Free oscillation of a series ferroresonant circuit..................... 10
Figure 2.5 Main characteristics of FR (a) basic series RLC circuit (b)
sensitivity to system parameters and the jump phenomenon....... 13
Figure 2.6 Sensitivity to initial conditions.................... 14
Figure 2.7 Fundamental mode (a) time domain of fundamental mode (b) spectrum of fundamental mode............................ 16
Figure 2.8 Subharmonic mode (a) time domain of subharmonic mode (b) spectrum of subharmonic mode............................ 17
Figure 2.9 Quasi-periodic mode (a) time domain of quasi-periodic mode (b) spectrum of quasi-periodic mode............................ 18
Figure 2.10 Chaotic mode (a) time domain of chaotic mode (b) spectrum of chaotic mode............................ 19
Figure 2.11 Single phase L-C circuit............................ 20
Figure 2.12 The impact of source voltage E on operating point (E2＞E1＞
E0)............................ 21
Figure 2.13 The impact of frequency ω on operating point (ω1＜ω2＜ω3)... 21
Figure 2.14 The impact of capacitance C on operating point (C1＜C2＜C3). 22
Figure 2.15 Single phase switching of delta and ungrounded wye windings
(a) two phases energized on delta winding and its equivalent
network (b) one phase energized on delta winding and its
equivalent network (c) one phase energized on ungrounded
wye winding and its equivalent network................................. 23
Figure 2.16 Single phase switching of grounded wye transformers with
ungrounded capacitor banks (a) two phases energized on
grounded wye winding with ungrounded system capacitance
and its equivalent network (b) one phase energized on grounded
wye winding with ungrounded system capacitance and its
equivalent network................................................................. 24
Figure 2.17 Circuit breaker with grading capacitor feeding a PT.............. 25
Figure 3.1 Configuration A (a) single line diagram (b) its equivalent circuit ................................. 30
Figure 3.2 Possible FR region of configuration A........... ....................... 32
Figure 3.3 Single line diagram of configuration B.......... ....................... 34
Figure 3.4 Simplified circuit of configuration B (a) equivalent RLC circuit
(b) simplified by Thevenin’ s theorem.... ....................... 35
Figure 3.5 Single line diagram of configuration C.......... ....................... 37
Figure 3.6 FR experiences in UK (a) single line diagram of UK 400 kV
substation (b) single line diagram of another UK 400 kV
substation................................................................................. 38
Figure 3.7 Single line diagram of configuration D...................................... 39
Figure 3.8 Adding damping resistor(R) for PTs (a) with one secondary (b)
with two secondaries.................................................. ............ 41
Figure 3.9 Simplified circuit of PT with a damping reactor(DR)................. 42
Figure 3.10 The excitation characteristic of PT and damping reactor(DR)... 42
Figure 3.11 Details of a damping reactor (a) its structure (b) its equivalent circuit............. 43
Figure 3.12 Outline of a damping reactor.......... 44
Figure 3.13 Adding damping resistor(R) and damping reactor(DR) for PTs
with one secondary............. 46
Figure 3.14 Adding damping resistor(R) and damping reactor(DR) for PTs
with two secondaries.......... 47
Figure 3.15 Adding damping resistor(R) and damping reactor(DR) for PTs with three secondaries.......... 48
Figure 3.16 Flow chart of FR analysis for GIS with PT............................... 49
Figure 4.1 System configuration of the study case in Taiwan...................... 50
Figure 4.2 Partial single line diagram of the study case ......................... 51
Figure 4.3 Conditions of damaged MOF PT (a) its wiring connection (b)
photos of damaged MOF PT ................................................ 54
Figure 4.4 EMTP/ATPDraw model of the study case (a) phase A & C (b)
phase B ................................................ 56
Figure 4.5 Structure of GIS of the study case ......................... 57
Figure 4.6 Structure of MOF PT..... 58
Figure 4.7 Grounded shield between primary and secondary winding..... 59
Figure 4.8 Measuring scheme of capacitance Cpg and Csg............ 59
Figure 4.9 EMTP/ATPDraw model of case 1 in Table 4.4 (a) phase A & C
(b) phase B ................................................ 61
Figure 4.10 Simulation results of Case 1A (a) primary voltage response (b) partial enlargement of primary voltage response (0.965-1.1s).. 62
Figure 4.10 Continued. (c) primary current response (d) partial enlargement
of primary current response (0.965-1.1s).... 63
Figure 4.10 Continued. (e) secondary voltage response (f) partial
enlargement of secondary voltage response (0.965-1.1s).... 64
Figure 4.10 Continued. (g) partial enlargement of secondary voltage
response (1.5-2s) (h) secondary current response.... 65
Figure 4.10 Continued. (i) partial enlargement of secondary current
response (0.965-1.1s) (j) partial enlargement of secondary
current response (1.5-2s) .. 66
Figure 4.11 Simulation results of Case 1B (a) primary voltage response (b) partial enlargement of primary voltage response (0.99-1.2s).... 67
Figure 4.11 Continued. (c) primary current response (d) partial enlargement
of primary current response (0.99-1.2s).... 68
Figure 4.11 Continued. (e) secondary voltage response (f) partial
enlargement of secondary voltage response (0.99-1.2s).... 69
Figure 4.11 Continued. (g) partial enlargement of secondary voltage
response (1.5-2s) (h) secondary current response.... 70
Figure 4.11 Continued. (i) partial enlargement of secondary current
response (0.99-1.2s) (j) partial enlargement of secondary
current response (1.5-2s) .. 71
Figure 4.12 EMTP/ATPDraw model of case 2 in Table 4.4 (a) phase A & C
(b) phase B ................................................ 72
Figure 4.13 Simulation results of Case 2A (a) primary voltage response (b) partial enlargement of primary voltage response (0.965-1.1s).. 73
Figure 4.13 Continued. (c) primary current response (d) partial enlargement
of primary current response (0.965-1.1s).... 74
Figure 4.13 Continued. (e) secondary voltage response (f) partial
enlargement of secondary voltage response (0.965-1.1s).... 75
Figure 4.13 Continued. (g) partial enlargement of secondary voltage
response (1.5-2s) (h) secondary current response.... 76
Figure 4.13 Continued. (i) partial enlargement of secondary current
response (0.965-1.1s) (j) partial enlargement of secondary
current response (1.5-2s) .. 77
Figure 4.14 Simulation results of Case 2B (a) primary voltage response (b) partial enlargement of primary voltage response (0.99-1.2s).... 78
Figure 4.14 Continued. (c) primary current response (d) partial enlargement
of primary current response (0.99-1.2s).... 79
Figure 4.14 Continued. (e) secondary voltage response (f) partial
enlargement of secondary voltage response (0.99-1.2s).... 80
Figure 4.14 Continued. (g) partial enlargement of secondary voltage
response (1.5-2s) (h) secondary current response.... 81
Figure 4.14 Continued. (i) partial enlargement of secondary current
response (0.99-1.2s) (j) partial enlargement of secondary
current response (1.5-2s) .. 82
Figure 4.15 EMTP/ATPDraw model of phase A & C of case 3 in Table 4.4 ......................... 83
Figure 4.16 Simulation results of Case 3A consider thermal effect of Rz (a) secondary voltage response (b) secondary current response.....83
Figure 5.1 Wiring connection of MOF PT(MPT) ......................... 87
Figure 5.2 Measuring circuit of field test ......................... 88
Figure 5.3 Photos of the first field test (a) phase C MOF PT....................... 88
Figure 5.3 Continued (b) secondary terminal box of MOF PT (c) outline of digital recorder ......................... 89
Figure 5.4 Secondary voltage and current response of operation No. 2
mode A in Table 5.1 (a) complete waveforms (b) the beginning
part of complete waveforms ...................................................... 91
Figure 5.4 Continued. (c) the ending part of complete waveforms .............. 92
Figure 5.5 Secondary voltage and current response of operation No. 6
mode B in Table 5.1 (a) complete waveforms..... 92
Figure 5.5 Continued. (b) the beginning part of complete waveforms (c)
the ending part of complete waveforms..... 93
Figure 5.6 Secondary voltage and current response of operation No. 9
mode A in Table 5.1 (a) complete waveforms (b) the beginning
part of complete waveforms..... 94
Figure 5.6 Continued. (c) the ending part of complete waveforms..... 95
Figure 5.7 Secondary voltage and current response of operation No. 11
mode B in Table 5.1 (a) complete waveforms..... 95
Figure 5.7 Continued. (b) the ending part of complete waveforms..... 96
Figure 5.8 Simulation results of Case 2A with DR2 (a) secondary voltage
response (b) secondary current response..... 97
Figure 5.8 Continued. (c) partial enlargement of voltage response (2.5-3s)
(d) partial enlargement of current response (2.5-3s)..... 98
Figure 5.9 Simulation results of Case 2B with DR2 (a) secondary voltage
response (b) secondary current response..... 99
Figure 5.9 Continued. (c) partial enlargement of voltage response (4-4.5s)
(d) partial enlargement of current response (4-4.5s)..... 100
Figure 5.10 The excitation characteristics of MPT, DR1, DR2.................... 101
Figure 5.11 Secondary voltage and current response of operation No.9 mode A in Table 5.3.................... 104
Figure 5.12 Secondary voltage and current response of operation No. 12 mode B in Table 5.3.................... 104
Figure 5.13 Single line diagram of a hydro power plant 161 kV substation.. 107
Figure 5.14 Single line diagram of a nuclear power plant 161 kV substation........... 109
Figure 5.15 Allowable short time current of PT (a) primary winding (b) secondary winding......... 112
Figure 5.16 Allowable short time current of damping reactor........... 113

REFERENCES

[1] 中興電工機械股份有限公司，161 kV SF6 氣體絕緣開關設備型錄REF.NO.：PED-CAGIS15，林口：中興電工，2008，第10-12 頁。
[2] T. Oyabu, A. Nakahashi, "Application of the Gas Insulated Voltage Transformer," 日新電機技報, vol. 30, no. 4（’85.11）, 1985, pp. 22-28.
[3] Boucherot, "Existence de deux r’egimes en ferroresonance," Rev.Gen.de L’Elec, vol. 8, no. 24, 1920, pp. 827-828.
[4] B.A. Mork, D.L. Stuehm, "Application of nonlinear dynamics and chaos to ferroresonance in distribution systems," IEEE Trans. on Power Delivery, vol. 9, no. 2, 1994, pp. 1009-1017.
[5] J. Bethenod, "Sur le transformateur et résonance, " L’Eclairae Electrique, Nov. 30, 1907, pp. 289-296.
[6] J.W. Butler , C. Concordia, "Analysis of series capacitor application problems," AIEE Trans., vol. 56, 1937, pp. 975-988.
[7] R.G. Andrei, B.R. Halley, "Voltage transformer ferroresonance from an energy transfer standpoint," IEEE Trans. on Power Delivery, vol. 4, no. 3, 1989, pp. 1773-1778.
[8] Z. Emi, B.A.T. Al Zahawi, Y.K. Tong, "Voltage transformer ferroresonance in 275 kV substation," IEE High Voltage Engineering Eleventh International Symposium, Conference Publication No. 467, 22-27 August 1999, pp. 283-286.
[9] David A.N. Jacobson, Peter W. Lehn, Robert W. Menzies, "Stability domain calculations of period-1 ferroresonance in a nonlinear resonant circuit," IEEE Trans. on Power Delivery, vol. 17, no. 3, 2002, pp. 865-871.
[10] Yunge Li, Wei Shi, Rui Qin, and Jilin Yang, "A systematical method for suppressing ferroresonance at neutral-grounded substations," IEEE Trans. on Power Delivery, vol. 18, no. 3, 2003, pp.1009-1014.
[11] Yunge Li, Wei Shi, and Furong Li, "Novel analytical solution to fundamental ferroresonance-PartΙ：power frequency excitation characteristic," IEEE Trans. on Power Delivery, vol. 21, no. 2, 2006, pp. 788-793.
[12] J. Wisniewski, E. Anderson, J. Karolak, "Search for network parameters preventing ferroresonance occurrence," 9th International Conference on Electrical Power Quality and Utilisation, Baecelona, 9-11 Oct. 2007, pp. 1-6.
[13] C. Charalambous, Z.D. Wang, M. Osborne and P. Jarman, "Sensitivity studies on power transformer ferroresonance of a 400 kV double circuit," IET Journal of Generation, Transmission & Distribution, vol. 2, no. 2, 2008, pp. 159-166.
[14] G. Mokryani and M.-R.Haghifam, "Application of wavelet transform and MLP neural network for Ferroresonance identification," IEEE Conference of Conversion and Delivery of Electrical Energy in the 21st Century, 2008, pp. 1-6.
[15] A. Rezaei-Zare, R. Iravani, and M. Sanaye-Pasand, "Impacts of transformer core hysteresis formation on stability domain of ferroresonance modes," IEEE Trans. on Power Delivery, vol. 24, no. 1, 2009, pp. 177-186.
[16] C.A. Charalambous, Z.D. Wang, P. Jarman, and M. Osborne, "2-D Finite-Element Electromagnetic Analysis of an Autotransformer Experiencing Ferroresonance," IEEE Trans. on Power Delivery, vol. 24, no. 3, 2009, pp. 1275-1283.
[17] P.G. Khorasani, A. Deihimi, "A new modeling of Matlab transformer for accurate simulation of ferroresonance," International Conference on Power Engineering, Energy and Electrical Drives, Lisbon, Portugal, 18-20 March, 2009, pp. 529-534.
[18] H. Radmanesh, M. Rostami, A. Abassi, "Effect of circuit breaker shunt resistance on chaotic ferroresonance in voltage transformer," Advances in Electrical and Computer Engineering, vol. 10, no. 3, 2010, pp. 71-77.
[19] Radmanesh. Hamid, "Controlling ferroresonance in voltage transformer by considering circuit breaker shunt resistance including transformer nonlinear core losses effect," Journal of International Review on Modeling and Simulations (IRMS), vol. 3 N. 5, Part A, 2010.
[20] Radmanesh. Hamid, "Controlling chaotic ferroresonance oscillations in autotransformers including linear and nonlinear core losses effect," International Review of Electrical Engineering (I.R.E.E), vol. 5 N. 6, Part A, 2010.
[21] International Electrotechnical Commission, INTERNATIONAL STANDARD 60044-5: Capacitor voltage transformer, Geneva, Switzerland：IEC, 2004.
[22] International Electrotechnical Commission, INTERNATIONAL STANDARD 60044-2: Inductive voltage transformer, Geneva, Switzerland：IEC, 2003.
[23] IEEE Power Engineering Society, IEEE Std C57.13: IEEE Standard Requirements for Instrument Transformers, New York, USA：IEEE, 2008.
[24] Ph. Ferracci, Ferroresonance, USA: Group Schneider Cahier Technique n0 190, 1998, pp. 1-28.
[25] Marta Val Escudero, Ivan Dudurych, Miles Redfem, "Understanding ferroresonance," 39th International Universities Power Engineering Conference (UPEC), 6-8 Sept. 2004, pp. 1262–1266.
[26] 寧家慶，電力系統非線性共振之研究，博士論文，國立中山大學電機系，高雄，台灣，2005。
[27] Ta-Peng Tsao and Chia-Ching Ning, "Analysis of ferroresonant overvoltages at Maanshan nuclear power station in Taiwan," IEEE Trans. on Power Delivery, vol. 21, no. 2, 2006, pp. 1006-1012.
[28] M. Roy, and C. K. Roy, "Experiments on ferroresonance at various line conditions and its damping," Joint International Conference on Power System Technology and IEEE India Conference, India, 2008, pp. 1-8.
[29] B. Peter Daay, "Ferroresonance destroys transformers," IEEE Proceedings of Southeastcon ''91, 7-10 April 1991 , pp. 568-578.
[30] S.M. Miri, A. Keyhani, "Solution to the ferroresonance jump problem in three-phase power conditioning systems," Industrial and Commercial Power Systems Technical Conference, May 1989, pp. 87-92.
[31] S. Mozaffari, M. Sameti, A.C. Soudack, "Effect of initial conditions on chaotic ferroresonance in power transformers," IEE Proc. Generation, Transmission and Distribution, vol. 144, no. 5, 1997, pp. 456-460.
[32] M. Sanaye-Pasand, H. Mohseni, Sh. Farhangi, A. Rezaei-Zare, and R. Iravani, "Effects of initial conditions on ferroresonance in power transformers using Preisach theory," 39th International Universities Power Engineering Conference (UPEC) , 6-8 Sept., 2004, pp. 845-850.
[33] Madhab Roy, Chinmay Kanti Roy, "A study on ferroresonance with a varying initial conditions using a nonlinear model of transformer," 2009 Third International Conference on Power Systems, Kharagpur, India, 27-29 December, 2009, pp. 1-6.
[34] S.R. Naidu and B.A. Souza, "Analysis of ferroresonance circuit in the time and frequency domains," IEEE Trans. on Magnetic, vol. 33, no. 5, 1997, pp. 3340-3342.
[35] 曹建福、韓崇昭、方洋旺，非線性系統理論及應用，西安：西安交通大學出版社，2001。
[36] T. Van Craenenbroeck, W. Michiels, D. Van Dommelen, K. Lust, "Bifurcation analysis of three-phase ferroresonant oscillations in ungrounded power systems," IEEE Trans. on Power Delivery, vol. 14, no. 2, 1999, pp. 531-536.
[37] P.S. Bodger, G.D. Irwin, D.A. Woodford, A.M. Gole, "Bifurcation route to chaos for a ferroresonant circuit using an electromagnetic transients program," IEE Proc. Generation, Transmission & Distribution, vol. 143, no. 3, 1996, pp. 238-242.
[38] Frank Wornle, David K. Harrison, and Chengke Zhou, "Analysis of a ferroresonant circuit using bifurcation theory and continuation techniques," IEEE Trans. on Power Delivery, vol. 20, no. 1, 2005, pp. 191-196.
[39] 韓茂安、顧經士，非線性系統的理論和方法，北京：科學出版社，2001。
[40] Ralph H. Hopkinson, "Ferroresonance overvoltage control based on TNA tests on three-phase delta-wye transformer banks," IEEE Trans. on Power Apparatus and Systems, vol. Pas-86, no. 10, 1967, pp. 1258-1265.
[41] P.G. McLaren, R Kuffel, R. Wierckx, J. Giesbrecht, L. Arendt, "A digital TNA for testing relay," Wescanex ’91 IEEE Western Canada Conference on Computer, Power, Communication Systems in a Rural Environment, Canada, 1991, pp. 47-50.
[42] Klaus Bergmann, keith Stump, William H. Elliott, "Digital simulation, transient network analyzer and field tests of the closed loop control of the EDDY COUNTY SVC," IEEE Trans. on Power Delivery, vol. 8, no. 4, 1867, pp. 1867-1873.
[43] Yan Guo, Boon-Teck Ooi, Howard C. Lee, "Integration of turbo-generator modules in digital transient network analyzer," IEEE Trans. on Power Systems, vol. 9, no. 2, 1994, pp. 653-659.
[44] Elizabeth R. Pratlco, Murray A. Eitzmann, "A microcomputer-based data acquisition system for transient network analyzer operation," IEEE Trans. on Power Systems, vol. 9, no. 2, 1994, pp. 812-818.
[45] O. Devaux, L. Levacher, O. Huet, "An advanced and powerful real-time digital transient network analyzer," IEEE Trans. on Power Delivery, vol. 13, no. 2, 1998, pp. 421-426.
[46] Yuan Chen, and Venkata Dinavahi, "An iterative real-time nonlinear electromagnetic transient solver on FPGA," IEEE Trans. on Industrial Electronics, vol. 58, no. 6, 2011, pp. 2547-2555.
[47] ATPDraw Windows version 4.0p2, Copyright c 1998-2003, SINTEF Energy Research, Norway.
[48] X.S. Chen, Paul Neudorfer, and Simon Cheng, "Simulation of ferroresonance in low-loss grounded wye-wye transformers using a new multi-legged transformer model in EMTP," IEE 2nd International Conference on Advances in Power System Control, Operation and management, Hong Kong, Dec. 1993, pp. 718-724.
[49] E. S. Jin, X. F. Chen, G. W. Xia, Z. Q. BO, A. Klimek, "Research on subharmonic resonance," International Conference on Intelligent System Design and Engineering Application(ISDEA), 2010, pp. 257-260.
[50] L. B. Viena, F. A. Moreira, N. R. Ferreira, A. C. de Castro, and N. C. de Jesus, "Analysis and application of transformer models in the ATP program for the study of ferroresonance," 2010 IEEE/PES Transmission and Distribution Conference and Exposition, Latin America, 2010, pp. 738-744.
[51] Zhu Xukai, Yang Yihan, Lian Hongbo, Tan Weipu, "Study on ferroresonance due to electromagnetic PT in ungrounded neutral system," 2004 International Conference on Power System Technology-POWERCON 2004, Singapore, 21-24 Nov., 2004, pp. 924-928.
[52] K. Laohacharoensombat, K. Tuitemwong, S. Jaruwattanadilok, C. Wattanasakpubal, K. Kleebmek, "Case study of ferroresonance in 33 kV distribution network of PEA Thailand," TENCON 2004 IEEE Region 10 Conference, 2004, pp. 417-420.
[53] Huawei Li, Yu Fan, Rong Shi, "Chaos and Ferroresonance," Canadian Conference on Electrical and Computer Engineering(CCECE), Ottawa, Canada, 2006, pp. 494-497.
[54] M. Sanaye-Pasand, H. Mohseni, Sh. Farhangi, A. Rezaei-Zare, and R. Iravani, "Effects of grading capacitors of CBs on inception ferroresonance in power transformers," 39th International Universities Power Engineering Conference (UPEC), 2004, pp. 860-868.
[55] D. Ray Crane, and Geroge W. Walsh, "Large mill power outages caused by potential transformer ferroresonance," IEEE Trans. on Industry Application, vol. 24, no. 4, 1988, pp. 635-640.
[56] D. Shein, S. Zissu, W. Schapira, "Voltage transformer ferroresonance in one 400 kV GIS substation," Sixteenth Convention of Electrical and Electronics Engineers in Israel, Israel, 1989, pp. 1-5.
[57] William S. Vilcheck, Michael V. Haddad, "Voltage transformer ferroresonance in cogeneration substation," Pulp and Paper Industry Technical Conference, 1992, pp. 148-158.
[58] Z. Emin, B.A.T.Al Zahawi, D.W. Auckland, Y.K. Tong, "Ferroresonance in electromagnetic voltage transformer: A study based on nonlinear dynamics," IEE Proc. Generation, Transmission & Distribution, vol. 144, no. 4, 1997, pp. 383-387.
[59] David A. N. Jacobson, "Examples of ferroresonance in a high voltage power system," IEEE Power Engineering Society Meeting, 2003, pp. 1206-1212.
[60] S. Hassan, M. Vaziri, S. Vadhva, "Review of ferroresonance in a power distribution grids," IEEE IRI 2011, Las Vegas, Nevada, USA, 3-5 August, 2011, pp. 444-448.
[61] H. Radmanesh, M. Rostami, A. Abassi, "Effect of circuit breaker shunt resistance on ferroresonance phenomena in voltage transformer," IEEE Southeastcon, 2009, pp. 183-188.
[62] Zhang Bo, Lu Tiecheng, "Application of nonlinear dynamic on ferroresonance in power system," Asia-Pacific Power and Energy Engineering Conference (APPEEC), 2009, pp. 1-4.
[63] Zhao-ming Lei, Zuo-jun Liu, He-xu Sun, Hong-xun Liu, "Control and application of chaos in electrical system," Proceedings of the Fourth International Conference on Machine Learning and Cybernetics, Guangzhou, 18-21 August, 2005, pp. 1477-1481.
[64] Yunge Li, Wei Shi, and Furong Li, "Novel analytical solution to fundamental ferroresonance-PartⅡ：criterion and elimination," IEEE Trans. on Power Delivery, vol. 21, no. 2, 2006, pp. 794-800.
[65] Zia Emin, Yu Kwong Tong, "Ferroresonance experience in UK：simulations and measurements," Procs. of the 4th International Conference on Power System Transients, Rio de Janeiro, 24-28 June, 2001, pp. 1-6.
[66] D.A.N. Jacobson, D.R. Swatek, R.W. Mazur, "Mitigating potential transformer ferroresonance in a 230 kV converter station," IEEE Proceedings Transmission and Distribution Conference, 1996, pp. 269-275.
[67] M. Sanaye-Pasand, A. Rezaei-Zare, H. Mohseni, Sh. Farhangi, and R. Iravani, "Comparison of performance of various ferroresonance suppressing methods in inductive and capacitive voltage transformer," IEEE Power India Conference, India, 2006.
[68] D. Shein, S. Zissu, "Domains of ferroresonance occurrence in voltage transformers with or without damping reactors," Eighteenth Convention of Electrical and Electronics Engineers in Israel, Israel, 1995, pp. 1.5.2/1-1.5.2/5.
[69] Y. K. Tong, "NGC experience on ferroresonance in power transformers and voltage transformers on HV transmission systems," IEE Colloquium on Warning! Ferroresonance Can Damage Your Plant(Digest No: 1997/349), 1997, pp. 4/1-4/3.
[70] A. Ben-Tal, D. Shein, "Domains of ferroresonance occurrence by bifurcation diagrams," Nineteenth Convention of Electrical and Electronics Engineers in Israel, Israel, 1996, pp. 87-90.
[71] 張右龍，比壓器鐵磁共振之研究，碩士論文，私立逢甲大學資訊電機工程碩
士在職專班，台中，台灣，2006。
[72] Gao Qiang, Lai Tianyu, Lai Qingbo, "Study on features of ferromagnetic resonance of 110 kV substation and it’s elimination method," CIRED 14th International Conference on Electricity Distribution, 1997, pp. 16/1-16/7.
[73] W. Piasecki, M. Florkowski, M. Fulczyk, P. Mahonen, W. Nowak, "Mitigating ferroresonance in voltage transformers in ungrounded MV networks," IEEE Trans. on Power Delivery, vol. 22, no. 4, 2007, pp. 2362-2369.
[74] John Horak, "A review of ferroresonance," 57th Annual Conference for Protective Relay Engineers, 2004, pp. 1-29.
[75] Hamid Radmanesh, Seyed Hamid Fathi, Rozbeh Kamali, Mehrdad Rostami, "Controlling ferroresonance oscillations in potential transformer: PartΙ," 19th Iranian Conference on Electrical Engineering(ICEE), Iran, 2011, pp. 1-4.
[76] Hamid Radmanesh, Seyed Hamid Fathi, Rozbeh Kamali, Mehrdad Rostami, "Controlling ferroresonance oscillations in potential transformer: PartⅡ," 19th Iranian Conference on Electrical Engineering(ICEE), Iran, 2011, pp. 1-5.
[77] Meng Hui, YanBin Zhang, ChongXin Liu, "Elimination of chaotic ferroresonance in power system with nonlinear core loss," The Ninth International Conference on Electronic Measurement & Instruments, 2009, pp. 3-568-572.
[78] K. P. Kadomskaya, A. V. Ivanov, O. I. Laptev, "Ferroresonance process in electrical networks caused by saturation of voltage-transformer cores," IEEE Power Tech, Russia, 2005, pp. 1-4.
[79] Madhab Roy, Chinmay Kanti Roy, "A study on ferroresonance and its dependence on instant of switching angle of the source voltage," 2009 Third International Conference on Power Systems, Kharagpur, India, 27-29 December, 2009, pp. 1-6.
[80] Li Huawei, Fan Yu, "Impact of breaker operations on ferroresonance in power systems," The Eighth International Conference on Electronic Measurement and Instruments(ICEMI), 2007, pp. 3-680-682.
[81] Wang Chunbao, Tian Lijun, Qin Yinglin, "A study on factors influencing ferroresonance in distribution system," 4th International Conference on Electric Utility Deregulation and Restructuring and Power Technologies(DRPT) , 2011, pp. 583-588.
[82] Japanese Standard Association, JIS Std C1736: Instrument Transformers for metering, Tokyo, Japan：Japanese Standard Association, 2003.
[83] Maria BROJBOIU, Virginia IVANOV, Silvia Maria DIGA, "Implementation of the optical current and voltage transducers in the power systems," The 7th International Conference on Electromechanical and Power Systems, Iasi, Romania, 8-9 October, 2009, pp. 27-33.
[84] Mladen Kezunovic, Levi Portillo, Jorge Karady, Sadik Kucuksari, "Impact of optical instrument Transformer characteristics on the performance of protective relays and power quality meters," 2006 IEEE PES Transmission and Distribution Conference and Exposition, Latin America, Venezuela, 2006, pp. 1-7.
[85] F. FARIA DA SILVA, W. WIECHOWSKI, C. LETH BAK, U. STELLA, "Full scale test on a 100 km, 150 kV AC cable," CIGRE 2010, Paris, 2010, pp. 1-8.
[86] Wen-Lung Yang, Jonq-Chin Hwang, Sheng-Nian Yeh, "Analysis and improvement of line-capacitance effect on three-phase 161 kV bus potential transformers," IEEE Trans. on Power Delivery, vol. 24, no. 2, 2009, pp. 837-843.
[87] Syuya Hagiwara, Yasuro Hori, Yasuaki Suzuki, Toshimitsu Obata, "Vibration analysis of a large capacity shunt reactor," IEEE Trans. on Power Apparatus and Systems, vol. PAS-101, no. 3, 1982, pp. 737-745.
[88] Yanhui Gao, Masahide Nagata, Kazuhiro Muramatsu, Koji Fujiwara, Yoshiyuki Ishihara, Shigemasa Fukuchi, "Noise reduction of a three-phase reactor by optimization of gap between cores considering electromagnetism and magnetostriction," IEEE Trans. on Magnetics, vol. 47, no. 10, 2011, pp. 2772-2775.
[89] Tetsuhiro Ishikawa, Hiroo Sugiyama, Emiko Baba, Ryusuke Oka, Yutaka Suzuki, Yoshihiro Kawase, Michio Tatsuno, "Reactor vibration analysis in consideration of coupling between the magnetic field and vibration," 39th IAS Annual Meeting, IEEE Industry Applications Conference, 2004, pp. 872-877.