作者: 保罗Ç. Buddingh, P.Eng. 成员, IEEE Universal Dynamics Limited 100 - 13700 International Place Richmond, BC V6V 2X8 Canada
Copyright Material IEEE – Paper No. PCIC 2002-11
我. 引言
This case study describes an investigation by the author of harmonic filter failures at a Chemical plant in North America. The plant utilizes large static converters to take incoming High Voltage low current 60 赫兹, AC power and rectify it into to Low Voltage, very high current DC power for operation of the electrochemical cells. Harmonic current generation is expected in this type of power system and harmonic filters are commonly used to limit harmonic levels and protect power system components.
A call from the plant indicated that they were experiencing what appeared to be overheating of a set of reactors used in a harmonic filter associated with one of the plant’s converter systems. The reactors in the 5日 harmonic branch of the filter had discolored, and dark bands were evident on the glassfiber surface of the reactors.
The filter was originally installed in 1988 and had a history of problems. “ 5日 harmonic reactors had failed before, and a clear cause was never identified. As historical information was reviewed and measurement data collected, it became apparent that something unusual was occurring.
This paper outlines the power and harmonic filter systems at the plant, discusses how uncharacteristic harmonics are generated, analyzes the difficulty, identifies the cause and provides an action plan used to correct the problem.
II. POWER SYSTEM CONFIGURATION
The plant has two production lines, Lines A and B, each consisting of a series of electrochemical cells.
Line A consists of a 1978 vintage 6-pulse rectifier in a single-way ANSI 45 configuration with inter-phase transformer. The primary voltage is 13.8 千伏. Each of the 6 phases or “legs” has eight parallel thyristors. A phase lock loop (PLL) type control system using discrete analog electronics is implemented.
无花果. 1: Line A Harmonic Filter
A three-branch harmonic filter is installed, consisting of branches tuned precisely to the 5日, 7日 和 11日 harmonic with 6.9 effective MVAR of capacitors.
The Line B rectifier system is supplied directly at 66 千伏, in an ANSI 45/46 12-pulse configuration shifted an extra 15° apart to make a 24-pulse system. The rectifiers are equipped with a single branch harmonic filter, also at 66 千伏, tuned at the 4.7日 harmonic and rated at 15 MVAR effective.
III. BACKGROUND
It has been well known, since at least the 1930’s, that rectifiers produce harmonic currents as they convert electric power from AC to DC. A classic paper from the days of the mercury arc rectifiers, still relevant today, was written in 1945 by J. Ç. 阅读. [1]. The proliferation of large thyristor rectifiers in the late 1960s and early 1970s created a resurgence and exacerbation of harmonics issues, largely a result of the increased size of the converters (在 20 MW to 30 MW range). These new larger rectifiers typically required large capacitor banks for power factor correction, creating an ideal environment for parallel resonance disturbances. In response, a number of excellent papers were produced addressing this new twist on an old problem [2] [3].
无花果. 2: Electrical Single Line Drawing Showing Main Power Distribution
This paper is not intended to be a primer or theoretical treatise on harmonics. There are many excellent works referenced that explain power system harmonics in detail. In particular, Ĵ. Arrillaga et al, “Power System Harmonics” [4], 建议. A few highlights pertinent to this case, 但, will be summarized.
IV. SOME THEORY
Half-controlled converters consisting of a mix of diodes and thyristors will not contemplated in this paper. Half-controlled converters inherently produce even harmonics and are not used in high power applications.
As discussed in detail in the reference papers, a wellbalanced “ideal” static converter – 就是说, a converter with equal currents in each phase of the rectifier will produce harmonics on the AC side of the converter according to:
h = kp ± 1 (1)
哪里: h harmonic order k any integer (1, 2, 3,...) p pulse number of the circuit with a magnitude:
我Ĥ = I1/Ĥ (2)
哪里: Ih harmonic current I1 fundamental current magnitude h harmonic order
在实践中, the commutating reactance and phase retard angle of the thyristors will somewhat reduce the amplitude of the current at each of the following characteristic harmonics:
谐波 5 7 11 13 17 19 23 25
当前 0.175 0.111 0.045 0.029 0.015 0.01 0.009 0.008 (单位)
These normal or “characteristic” harmonic frequencies starting at the 5日 和 7日 harmonics are expected from a 6pulse rectifier. 同样, a 12-pulse system will have characteristic harmonics starting at the 11日 和 13日 and a 24-pulse will have characteristic harmonics starting at the 23路 和 25日 谐波, 等. The rectifier acts as a harmonic current source, injecting these harmonic currents back into the AC system. If the AC system is reasonably symmetrical and timing of the rectifier firing is exact, the resulting harmonic currents will be equal in all three phases.
Jean Babtiste Fourier’s theory is used to mathematically explain the resulting harmonic spectrum. A 6-pulse rectifier is made up of two single-way, 3-pulse rectifiers, either connected in series in the form of a bridge configuration, or in parallel, as in this case. Fourier’s theory shows that for 3pulse systems the 3路, 9日, 15日…harmonics are zero. A singleway, 3-pulse system is not half-wave symmetrical about the zero axis and produces even harmonics 2, 4, 6,…. The 180° configuration of the two parallel rectifiers creates a 6-pulse symmetrical system, which ordinarily eliminates the even frequencies.
无花果. 3: Schematic of a 6-pulse Double Wye Connection with Inter-Phase Transformers
在现实世界中, there are always some residual abnormal odd and even harmonics on the AC power supply side. These are classified as “uncharacteristic” harmonic frequencies.
Commonly, “uncharacteristic” harmonics are caused by imperfections in the AC power supply system including tolerances in transformer winding phase angles, commutation reactance and the presence of incoming AC power supply harmonic voltages. These imperfections in the AC power side affect the thyristor firing timing, as its synchronization signal is taken from the AC fundamental frequency. Normally, the asymmetry is minor, the resulting distortion is small and the effects minimal.
It is assumed that phase-control timing or firing is identical for all semi-conductors on a phase, phase-to-phase timing is coordinated and that each phase group is precisely fired with respect to each other. For cancellation, we need precise and repeatable firing. This is another area where tolerances play a large part. Deviations in firing will also generate uncharacteristic harmonic currents. In a properly designed and operating rectifier, the “uncharacteristic” harmonics are normally minimal, and are not a concern.
Harmonic filters are designed, 因此, based on accepted “theory”, only to treat the normal characteristic harmonics. For cost reasons, they are not normally designed to handle excessive “uncharacteristic” harmonic currents.
在. ANALYSIS
There were a number of obstacles in the investigation and analysis of the plant converter system. One was analyzing the overheating problem without the ability to directly measure the 5日 harmonic filter branch current. This made it difficult to get a complete picture of the existing harmonic conditions. The harmonic filter consists of three branches tuned precisely to the 5日, 7日 和 11日 谐波. Each branch consists of an air-core reactor with a set of capacitors for phases A, 乙, 和
Ç. The filter is supplied by one metal clad “Teck” cable via a circuit breaker equipped with current transformers. The only practical point of connection for taking measurements was at the current transformer that supplies all three branches of the filter.
TABLE 1 Measured Harmonic Currents at Line A Rectifier Input
The harmonic currents produced by the rectifier were reasonable with the uncharacteristic components higher than ideal, but not that unusual for a 1978-vintage rectifier. It was notable, 但, that measurements at the input of the rectifier had a lower amount of 4日 harmonic current than at the input of the filter. This provided the first hint that uncharacteristic harmonic currents were the source of the reactor distress.
Measurements at the Line A circuit breaker indicated that the AC power supply system was acceptable and not a point of concern.
When measurements were taken on the Line A filter, everything looked reasonable. The currents measured did not exceed the rating of the reactors and ambient temperatures were within the 30° C test rating of the reactor.
所以, what was causing the overheating? Additional clues were uncovered as we reviewed the history of rectifier operation. Discussions with plant maintenance personnel indicated that an extensive retrofit of the rectifier power section had recently been completed, with oversize devices installed. This had eliminated the repeated thyristor failures that occurring prior to the retrofit and was a strong indication that the problem was associated with control irregularities.
If firing timing is not identical for a parallel set of thyristors, uneven loading can result producing individual semiconductor failures and gravitate towards a subsequent cascade of failures through the system as fewer devices carry more and more of the load. By installing larger oversize devices, the plant had eliminated the symptom.
未来, the power system was analyzed with particular emphasis on pinpointing any abnormal harmonic resonance conditions.
Various power system configurations used during normal plant operations were checked. An interesting discovery was made when Line A was operating with the Line B rectifier and filter shut down. “ 5日 filter branch in Line A (series tuned to exactly 300 赫兹) was found to exhibit strong parallel resonance with the power system at the 4日 harmonic when the Line B system is out of service. When the Line B system is operating, the parallel resonance is still present, but not nearly as significant.
Subsequent analysis indicated that if Line B is shut down and the rectifier produces as little as 5% 4日 谐波电流, it is amplified and causes a 40% current overload in the 5日 branch of the Line A filter.
This finding provided the theoretical basis for a growing suspicion that an even harmonic resonance was the source of the reactor overheating. One question remained: the plant normally operates at full capacity, 24 hours per day, all year long — could a short annual maintenance outage on Line B be sufficient to cause the overheating and resulting dark bands on the reactors?
Reactors have a normal maximum temperature rise of 60°C over a 30°C ambient temperature. The manufacturer reports that reactor insulation will not discolor until it reaches 130°C. To reach this temperature, the total current in the reactor would need to increase to 140% of the reactor rating. Since the reactors have little thermal mass, this temperature would occur in the order of minutes.
Armed with this data, the theory that high, uncharacteristic harmonics were causing the overheating could be tested. Another set of measurements was taken on Line A to quantify intermittent, uncharacteristic harmonic currents coming from the rectifier and their amplification in the 5日 harmonic branch of the filter.
A careful measurement protocol confirmed that amplification was in fact taking place. Measurements of 20% 至 58% 的 4日 谐波电流 (as a percentage of the total filter current) were recorded for a period of approximately 13 seconds at the Line A filter. It was found that the 5日 branch filter was drawing almost half the total filter current, 和 70% 的 4日 谐波电流. 其结果, for short periods these reactors are loaded with more than 200% of rated current. With Line B down, the effect would likely be considerably worse.
This last piece of data completed the picture.
无花果. 5: Series & Parallel Resonance of 5日 过滤器 & 13.8 kV Bus
VI. MORE THEORY
As discussed above, even harmonics can be created in rectifier systems by firing timing irregularities. Galloway [7] describes harmonic instability as the abnormal operation of a converter system due to the harmonic voltage distortion of the power source caused by the harmonic currents itself. J.D. Ainsworth wrote a classic paper on this same topic 35 年前 [8].
Galloway [7] explains the various modes of timing irregularities. The irregularities are defined into three types.
Type 1 — Pulse Deviation — One of the six pulses does not occur in the correct time or manner. This results in an “across the board” increase in harmonic currents, with poor cancellation of odd harmonics and production of even harmonic currents due to half-wave dissymmetry about zero.
Type 2 - 相不平衡 - 相不平衡不会产生找齐,,en,它的作用就像一个单相整流器，并产生奇次谐波的全谱，具有±的调制分量,,en,正常的谐波频率的,,en, - 集团不平衡 - 豆类,,en,移位相等的量从,,en,这导致偶次谐波的产生,,en,的倍数,,en,在工厂进行的测量似乎表明，A型,,en,问题发生由于随机定时变化,,en,作为整个频谱的谐波升高的时期,,en,包括偶次谐波，注意到,,en,随着旧的电子控制装置,,en,失效模式是很难分离,,en,和类型,,en,与相间饱和,,en,可能会发生,,en; it acts like a single-phase rectifier and produces the full spectrum of odd harmonics with modulation components of ± 2 of normal harmonic frequencies.
Type 3 — Group Unbalance — Pulses 1, 3 和 5 are displaced an equal amount from 2, 4 和 6. This results in the generation of even harmonics, 就是说, multiples of 3 ±1.
Measurements made in the plant seemed to indicate that a Type 1 problem was occurring due to random timing variations, as periods of elevated harmonics across the spectrum, including even harmonics were noted. With the older control electronics, 但, the failure mode was hard to isolate, and a Type 3 问题, with inter-phase saturation, could be occurring.
该相间变压器通常被设计成只吸收整流器半之间的不平衡量小，可以迅速进入饱和,,en,当整流系统没有很好的平衡,,en,在相间相反方向流动的两个3脉冲组的输出电流产生所述芯的显著直流磁化,,en,因为它进入饱和，变得无效,,en,整流器作为两工作,,en,分离,,en,与所连接的星点和半导体脉冲组仅进行超过一半的正常120°的,,en,将得到的60°的导通角的结果在大约,,en,增加半导体功率,,en,这导致了大量增加晶闸管加热,,en,熔断器以及次级变压器的,,en. When the rectifier system is not well balanced, the output currents of the two 3-pulse groups flowing in opposite directions in the interphase produce significant dc magnetization of the core. As it goes into saturation and becomes ineffective, the rectifier operates as a two, separate, 3-pulse groups with the star points connected and semi-conductors only conducting over half of the normal 120°. The resulting 60° conduction angle results in about a 17% increase in semi-conductor power (瓦) 损失. This results in a substantial increase in heating of thyristors, fuses as well as the secondary of the transformers.
这种不平衡还导致有效的DC电流，所述变压器次级必须携带,,en,变压器可以进入饱和,,en,增加损失和产生大量的热和第三高次谐波电流的量不成比例,,en,七,,en,发现,,en,拼图的碎片已经开始走到一起,,en,越来越多的证据指向一个偶次谐波共振作为过滤器的原因过热,,en,中遇到的困难的起源是晶闸管触发电路问题,,en,控制系统的年龄和所得的电子部件“漂移”,,en,似乎已经创建了一个类型,,en,定时不规则,,en,射击不对称不再直接影响到整流器的操作与最近已安装的特大型晶闸管,,en. The transformer can go into saturation, increasing losses and creating large amounts of heat and a disproportionate amount of third harmonic current.
VII. FINDINGS
The pieces of the puzzle were starting to come together. More and more evidence pointed to an even harmonic resonance as the cause of the filter overheating.
The origin of the difficulties experienced is a thyristor firing circuit problem. The age of the control system and resulting electronic component “drift”, appears to have created a Type 1 timing irregularity.
Firing asymmetry was no longer directly affecting the operation of the rectifier with the oversize thyristors that had been recently installed, 但仍影响在某些设备的运转状态的谐波滤波器,,en,行了整流器结束,,en,岁,,en,虽然早已过了最初的设计寿命,,en,这些强大的机器继续运转是在电化学工业中常见的,,en,跟腱医治这些单元通常是控制系统的老化电子,,en,电子设备具有bathtubshaped可靠性曲线和该设备有可能在该曲线的斜率向上,,en,简而言之,,en,控制系统问题与旧的整流器预期,,en,测量表明，与线B的操作,,en,大量的,,en,谐波电流过载的线A滤波器,,en,分支短时间,,en,反应器具有小的热质量,,en,并且可以在几分钟的数量级达到极端温度,,en.
The Line A rectifier is over 30 years old and, while well past its original design life, continued operation of these robust machines is common in the electrochemical industry. The Achilles heal of these units is typically the aging electronics of the control system. Electronic equipment has a bathtubshaped reliability curve and this equipment is likely on the upward slope of that curve. In short, control system problems are to be expected with older rectifiers.
Measurements demonstrated that with Line B operating, large amounts of 4日 harmonic current overloaded the Line A filter 5日 branch for short periods. The reactors have little thermal mass, and can reach extreme temperatures in the order of minutes. 对于至少13秒的时间段,,en,将反应器暴露在,,en,加载,,en,如果B线在这些条件下关闭,,en,电流很可能是显著较高,,en,一个可取之处是，B线为维持很短的间隔频繁关闭,,en,随着时间的推移重复过热的累积效应已经强调反应堆,,en,其中一个,,en,谐波电抗器被替换,,en,这就解释了为什么只有两三个现有反应堆都出现损坏迹象,,en,较新的反应器没有被暴露到相同的程度反复过热作为两个大的第五谐波的反应器,,en,次要问题是DC偏移在变压器的相间和次级电路的效果,,en,虽然变压器处于良好状态,,en, the reactors were exposed to a 200% load. If Line B is shut down under these conditions, the currents are likely to be significantly higher. A redeeming feature is that Line B is shut down infrequently for short intervals of maintenance. The cumulative effects of repeated overheating over time has stressed the reactors.
在 1992, one of the 5日 harmonic reactors was replaced. This explains why only two of the three existing reactors are showing signs of damage. The newer reactor has not been exposed to the same degree of repeated overheating as the two older fifth harmonic reactors.
A secondary concern is the DC offset effects on the interphase and secondary circuit of the transformer. While the transformer is in good condition, 升高的DC电流可能会大幅增加加热并导致长期降解,,en,分接开关,,en,芯夹具和其它内部硬件可以具有局部化与高次谐波电流增加的水平的加热效果,,en,特别是与机器从未被设计的量，不寻常的高次谐波电流,,en,八,,en,行动计划,,en,的物理检查,,en,A线电抗器已经完成，并强调虽然,,en,没有在失败的直接危险,,en,尤其是当B线保持上线,,en,新整流器控制系统的安装是一个庞大的资本支出,,en,和工厂目前正在考虑这一步,,en,同时,,en,下列措施已到位,,en,行整流控制系统,,en. Tap changers, core clamps and other internal hardware can have localized heating effects with increased levels on harmonic currents [10], particularly with the uncharacteristic harmonic currents for which the machine was never designed.
VIII. ACTION PLAN
A physical inspection of the 5日 reactors on Line A was completed and although stressed, were not in immediate danger of failing, particularly if Line B is kept on-line.
The installation of a new rectifier control system is a substantial capital expenditure, and the plant is now considering this step. In the meantime, the following measures have been put into place.
无花果. 6: Line A Rectifier Control System
第一, 峰值检测保护继电器被替换为现代可编程继电器也就是低次谐波频率在此系统上经历敏感,,en,这将提供报警和滤波器组跳闸，如果反应堆是在超载的危险,,en,该继电器还测量和记录谐波水平,,en,重新设计,,en,谐波滤波电抗器被安装到移动过滤器和所述电力系统到低于之间的并联谐振,,en,新的设计将大大降低敏感度共振,,en,新的核反应堆已经订购并更换已定,,en,变压器溶解气体样本之间的间隔已被降低到改善的变压器状态监测,,en. This will provide alarming and tripping of the filter bank if the reactors are in danger of overload. This relay also measures and records harmonic levels.
第二, redesigned 5日 harmonic filter reactors are being installed to move the parallel resonance between the filter and the power system to below the 4日. The new design will greatly decrease the sensitivity to resonance. New reactors have been ordered and the replacement has been scheduled.
最后, the interval between transformer dissolved gas samples has been decreased to improve monitoring of the transformer condition. 溶解气体分析是评估变压器的条件一个伟大的工具,,en,特别是当面对不确定谐波应力,,en,然后可以根据需要采取纠正措施,,en,IX,,en,结论,,en,的持续整流器,,en,谐波水平,,en,或者更多,,en,而此时线B是关闭,,en,已经超负荷的反应堆和使他们运行热点和褪色,,en,这些年来,,en,出现了加剧的条件的累积效应,,en,如果没有做,,en,工厂的经营历史已经确定，故障将遵循,,en,作为第一步,,en,过滤器保护继电器被修改，以检测一,,en,谐波电流过载，并报警和跳闸根据需要,,en,在待处理的原设计不被认为准确调谐线A谐波滤波器对每个谐波频率的共振效应,,en,微调每一个的,,en, particularly when faced with uncertain harmonic stress. Corrective action can then be taken as required.
IX. CONCLUSIONS
A sustained rectifier 4日 harmonic level of 5% or more, at a time when Line B is off, has overloaded the reactors and caused them to run hot and discolor. Over the years, there has been a cumulative effect intensifying the condition. If nothing was done, plant operating history has established that failure would follow.
As a first step, the filter protection relay was modified to detect a 4日 harmonic current overload and to alarm and trip as required.
The resonant effects of tuning the Line A harmonic filter exactly to each harmonic frequency to be treated was not considered in the original design. Tuning each of the 5日, 7日 和 11日 分支到频率,,en,低于目标频率会缓解了并联谐振,,en,损坏的滤波电抗器的重新设计已经完成，新的反应堆计划安装,,en,新的更大的晶闸管,,en,最近被取代,,en,能够承受控制系统不规则更大的程度,,en,与可靠性的改善所得,,en,控制系统违规较早引起整流问题,,en,仍影响交流电源系统,,en,偶次谐波也将导致整流变压器通过磁路的饱和运行较热,,en,金属夹子,,en,固定装置和其它组件可以在变压器内部过热,,en,创造局部热点,,en,这可以显著降低变压器的生活,,en 2% 至 10% below the target frequency would have alleviated the parallel resonance.
A redesign of the damaged filter reactors is complete and the new reactors are scheduled for installation.
The new larger thyristors, which were recently replaced, are able to withstand control system irregularities to a much greater degree, with a resulting improvement in reliability. Control system irregularities that earlier caused rectifier problems, 但, still affect the AC power system.
Even harmonics will also cause the rectifier transformer to run hotter by saturation of the magnetic circuit. Metal clamps, fixtures and other components can overheat inside the transformer, creating localized hot spots. This can significantly reduce transformer life.
已采取措施来缓解眼前的问题，如注意和更换控制系统是正在审议厂,,en,致谢,,en,我要感谢约翰·基里猜恩科和工厂员工有机会在这个非常有趣的挑战和我的同事贝恩德·施密特克工作,,en,他的出色工作和洞察力在这个项目上,,en,XI,,zh-CN,J.C.,,fr,整流器和逆变器性能特性的计算,,en,在LEEE论文集,,jw,A.P,,en,Jacobs和毛重,,en,沃尔什,,en,“应用注意事项可控硅直流电源系统,,en,” IEEE跨,,en,4- EVERY,,et,7月/月,,en,D.E.,,es,陡，R.P,,en,“无功补偿及使用工业电力系统谐波抑制晶闸管转换器,,en,IA-12,,id,电源转换器手册,,en,加拿大通用电气公司,,en,有限公司,,en,J.H,,en,“在相控整流器谐波不稳定性,,en.
X. ACKNOWLEDGEMENTS
I would like to thank John Kirichenko and the Plant Staff for the opportunity to work on this very interesting challenge and my colleague Bernd Schmidtke, P.Eng. for his outstanding work and insight on this project.
XI. 参考
[1] J.C. 阅读, “The Calculation of Rectifier and Inverter Performance Characteristics”, Proceedings of the lEEE, 飞行. 92, 部分 2, 不. 29, 十月 1945, PP. 495-509. [2] A.P. Jacobs and G.W. Walsh, “Application considerations for SCR dc power systems,” IEEE Trans. IGA-4, July/Aug 1968. [3] D.E. Steeper and R.P. 斯特拉特福, “Reactive Power Compensation and Harmonic Suppression for Industrial Power Systems using Thyristor Converters,” IEEE Trans. IA-12, 5/76 PP. 235-255. [4] Ĵ. Arrillaga et al, “Power System Harmonics”, 约翰·威利 & 儿子, 国际标准书号 0471906409, 1985. [5] Power Converter Handbook, Canadian General Electric Co. Ltd., 1976. [6] IEEE 519-1992 “IEEE推荐做法和谐波控制要求在电力系统”. [7] J.H. Galloway, “Harmonic Instability in Phase Controlled Rectifiers,” IEEE PCIC的conf,,en,记录,,en,安斯沃思,,en,控制静态转换器和交流网络之间的“谐波不稳定性,,en,”过程,,en,7号pp.949-957七月,,en,Arillaga等,,en,“电力系统谐波分析,,en,”约翰·威利,,en,S.P,,en,肯尼迪,,en,“设计和半导体整流变压器的应用,,en,记录页,,en,Shaefer“整流电路,,en,B.M,,pl,Bird等,,en,“介绍给电力电子,,en,克洛斯,,no,“一个基本的指南电力电子,,en,P.C。,,ro,火星“新生活使用现代数字控制晶闸管老功率整流器,,en,” IEEE IAS交易月/ 2000年10月,,en,XII,,en,VITA,,en,Buddingh从桑德湾湖首大学毕业,,en,安大略,,en,加拿大拥有电子工程学位,,en,毕业后,,en,他花了几年的工作了多伦多,,en,加拿大作为电咨询工程师重工业工作,,en. record 1999, PP. 171-175. [8] J.D. Ainsworth, “Harmonic Instability between Controlled Static Converters and AC Networks,” Proc. IEE, No.7 pp.949-957 July 1967. [9] Ĵ. Arillaga et al, “Power System Harmonic Analysis,” John Wiley, 国际标准书号 0471975486, 1998. [10] S.P. Kennedy, “Design and Application of Semiconductor Rectifier Transformers,” IEEE PCIC的conf,,en,记录,,en,安斯沃思,,en,控制静态转换器和交流网络之间的“谐波不稳定性,,en,”过程,,en,7号pp.949-957七月,,en,Arillaga等,,en,“电力系统谐波分析,,en,”约翰·威利,,en,S.P,,en,肯尼迪,,en,“设计和半导体整流变压器的应用,,en,记录页,,en,Shaefer“整流电路,,en,B.M,,pl,Bird等,,en,“介绍给电力电子,,en,克洛斯,,no,“一个基本的指南电力电子,,en,P.C。,,ro,火星“新生活使用现代数字控制晶闸管老功率整流器,,en,” IEEE IAS交易月/ 2000年10月,,en,XII,,en,VITA,,en,Buddingh从桑德湾湖首大学毕业,,en,安大略,,en,加拿大拥有电子工程学位,,en,毕业后,,en,他花了几年的工作了多伦多,,en,加拿大作为电咨询工程师重工业工作,,en. 2001 record pp. 153-159. [11] Ĵ. Shaefer “Rectifier Circuits – 理论 & 设计,” John Wiley & 儿子, 1965. [12] B.M. Bird et al, “An introduction to Power Electronics,” John Wiley & 儿子, 国际标准书号 10430 2 1983. [13] 一. Kloss, “A basic guide to Power Electronics,” John Wiley, 国际标准书号 0471904325 1985. [14] P.C. Buddingh & Ĵ. 圣. Mars “New Life for Old Thyristor Power Rectifiers using Contemporary Digital Control,” IEEE IAS transactions Sep/Oct.2000, PP. 1449-1454.XII. VITA
保罗Ç. Buddingh graduated from Lakehead University in Thunder Bay, Ontario, Canada with a degree in Electrical Engineering. Upon graduation, he spent several years working out of Toronto, Canada as an electrical consulting engineer working in heavy industry. 在 1991, 他创立的是开发出一种新的磁性的方法来解决低电压系统的零个序谐波问题公司,,en,他搬到温哥华,,en,加拿大并加入通用动力,,en,他一直在设计并安装了谐波滤波器,,en,他的工作是集中在设计高可靠性电力系统负荷难,,en,电源转换器的问题和解决电力系统问题，为在美洲许多行业客户,,en,他是安大略省的注册工程师,,en,曼尼托巴省和不列颠哥伦比亚省和几个IEEE论文的作者,,en,精密声学提升开发团队与新的软件工程师的任命,,en. 在 1997, he moved to Vancouver, Canada and joined Universal Dynamics. He has been designing and installing harmonic filters for 15 岁月. His work is centered on designing high reliability power systems for difficult loads, power converter issues and resolving power system problems for a number of industrial customers across the Americas. He is a registered Engineer in the provinces of Ontario, Manitoba and British Columbia and an author of several IEEE papers.