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1、同步发电机灭磁电阻的吸能容量李自淳 彭辉 符仲恩 夏维珞(中国科学院等离子体物理研究所科聚公司，安徽 合肥 230031)摘要 本文探讨了同步发电机采用快速移能灭磁时，其灭磁电阻吸收能量容量的计算及选择方法。关键词 发电机、灭磁电阻、吸能容量1 概述目前大中型同步发电机的快速灭磁普遍采用移能灭磁，故灭磁电阻必须快速吸收在各种工况下的磁场能量。据分析：最严重的工况是发电机空载失控误强励及定子出线端突然短路。这两种工况的转子电流都可以达到额定励磁电流的34.5倍，转子的磁场能量也达到最大。以下以国内最大的三峡电站水轮发电机为例，分别探讨这二种工况下的磁场能量。由于电机的瞬态过渡过程十分复杂，又因发
2、电机的电磁参数提供不全，故只能从电机学1的基本理论出发，忽略一些次要因素，作某些简化假定，对以上两种工况作粗略的分析，再以长江水利委员会（以下简称“长委”）提供的一些发电机基本参数（见表1）为依据，作一初步的计算，以供参考。计算均以ABB公司发电机为例，取最大容量时的饱和值参数作计算原始数据，励磁方式为机端自并励，三相全控桥式整流。2 发电机空载失控误强励工况下的磁场能量2.1 励磁电流的计算此工况是指发电机不并网，但由于功率整流柜脉冲变压器击穿等原因，造成励磁调节失控，控制角a = 0，发电机误强励，定子电压升高，以致励磁变次级电压也升高，假定升高到额定值的1.3倍（考虑因励磁电流增大而使励
3、磁变压降增大因素），此时励磁电流可达到Ifm = 1.31.35Ua / Rf (1)式中: Ua 励磁变次级额定线电压有效值(V)；Rf 转子励磁绕组电阻(W)。据“长委”提供：Ua=1243V，Rf = 0.1144W；代入（1）式得Ifm = 1.31.351243 / 0.1144 = 19069A。2.2 转子漏磁通的能量本工况时转子等值电路如图1所示，图中定子电阻Ra、定子漏抗Xs、及定子直轴电枢反应电抗Xad均折算到转子边。由于定子输出开路，故Ra及Xs不起表1 “长委”提供的三峡发电机基本参数序号参数名称数 值单 位备 注VGSABB1额定容量777.8777.8MVA2最大容
4、量840840MVA3额定电压2020kV4额定功率因数0.90.95额定转速7575R/min6定子绕组连接方式YY7直轴同步电抗Xd0.97/0.881.05/0.950.939/0.8351.014/0.902标么值不饱和/饱和,额定容量时不饱和/饱和,最大容量时8直轴瞬变电抗X，d0.32/0.300.35/0.320.315/0.2950.340/0.319标么值不饱和/饱和,额定容量时不饱和/饱和,最大容量时9直轴超瞬变电抗X，d0.22/0.200.23/0.210.240/0.2000.259/0.216标么值不饱和/饱和,额定容量时不饱和/饱和,最大容量时10直轴瞬变开路时间
5、常数T，do11.110.1S11直轴瞬变短路时间常数T，d4.03.2S12定子绕组短路时间常数Ta0.320.28S13转子绕组电阻0.096430.1144VGS90时,ABB130时14励磁变二次侧电压10241243V顺德联络会上确定15空载励磁电压211191.8V16空载励磁电流21902352A17负载励磁电压364/409475.9/497.1V额定容量时/最大容量时18负载励磁电流3779/39404158/4345A额定容量时/最大容量时19励磁顶值电压12801556V20励磁顶值电流78808690A21允许强励时间2020S励磁顶值电流下22转子过电压值0.5Us0
6、.5UsUs为绕组出厂对地耐压试验时的电压幅值作用。转子等效电抗Xf = Xfs+Xad（式中Xfs为转子漏抗），因为定子绕组及阻尼绕组开路时励磁绕组时间常数Td0 = （为电角频率，对50Hz电机来说=250=314弧度/秒）。“长委”提供T d0 = 10.1s，Xf = T d0wRf = 10.13140.1144 = 363W，转子等效电感Lf = Xf/= T d0 Rf = 10.10.1144 = 1.16H （不饱和值）。这里Rf取“长委”提供的130时的电阻值，此温度应与电机设计时T d0 取的对应温度一致，国内电机厂一般取75，ABB取多少不知，偏高选取较安全。 由于没有
7、Xfs及Xad的数据，只能主观假设转子漏感Lfs = 0.1Lf = 0.11.16 = 0.116H（不饱和值）。由于漏磁通的磁路大部分经过空气，如不考虑磁路的饱和，则Lfs为常数，漏磁能量W fs =LfsI fm2 = 0.50.116190692 = 21MJ（不饱和值）。偏大! 图1 定子空载时转子等值电路图 图2 发电机空载特性曲线实际上漏磁通的磁路有一部分在铁心里，在特大的励磁电流下，铁心高度饱和，磁阻增大，使漏磁通增长率减少，表现为等效电感L fs减小。设饱和系数为0.2，则Wfs = 0.221 = 4.2MJ（饱和值）。2.3 转子主磁通的能量转子激磁电感（交链定子绕组产生
8、感应电势e0的主磁通0的电感）Lad = Lf - Lfs = 1.16 - 0.116 = 1.044H（不饱和值）。根据电工学2理论，主磁通的能量W0 = KHdB，而H = ifwf / l，B =0 / S。式中：K常数；H磁场强度；B磁通密度；if励磁电流；wf励磁绕组每极串联匝数；l磁路长度；S磁路截面积；0主磁通。因对某一台电机而言，wf、l及S均为固定参数，故H if，B 0，W0 = K1if d0 （K1为常数） (2)又因发电机空载端电压（线电压有效值）u0 = e0=4.44fwaka0 (3)式中：e0 定子空载相电势（有效值）；f 定子额定电频率，f = 50Hz；
9、wa 定子绕组每相串联匝数；ka 定子绕组系数；0 定子每极主磁通。对某一台发电机，f、wa及ka均为固定参数，故u0 0，(2)式可等效为W0 = K2（K2为常数） (4)式(4)表明主磁通的能量正比于发电机空载特性曲线u0-if与u0轴之间的面积（图2中阴影部分）。图3为“长委”提供的ABB公司为三峡设计发电机的特性曲线，图中曲线1为空载特性曲线。该图纵座标为定子空载电压标么值，基值UN=20000V（定子额定电压），横座标为励磁电流标么值，基值IN=1982A（假定磁路不饱和时，在气隙线3上量得的额定空载励磁电流，见图3右下角英文说明）。现在可以利用此图来求出励磁电流高达Ifm = 1
10、9069A时主磁通的能量，方法如下： (1) 算出标么值I = Ifm/IN = 19069/1982 = 9.62(2) 由于图3的曲线1只画到2.6P.U.，需要外推到9.62P.U.，我们将原图缩小，并按曲线1末端（2.6P.U.处）的斜率作延长直线到9.62P.U.处（见图4）。由于铁心饱和的加深，磁化曲线（形状与空载特性曲线相同）的斜率只会随励磁电流的加大而减小，我们当作斜率不变是偏安全的（计算能量偏大）。(3) 计算发电机额定空载时主磁通的能量。此时发电机磁路不饱和，认为转子激磁电感为常数Lad = 1.044H，“长委”提供发电机空载励磁电流If0 = 2352A，故空载时主磁通
11、的能量W0 = Lad I=0.51.04423522 = 2.89MJ。此能量相当于图4中曲边三角形OAB的面积SOAB 4.23cm2。(4) 失控误强励灭磁时，励磁电流增大到19069A（9.62P.U.），相当于空载特性曲线上的D点，求得曲边三角形OCD的面积SOCD32.49cm2。(5) 根据上述主磁通能量正比于发电机空载特性曲线与u0轴之间的面积的结论。可求出失控误强励时主磁通的能量W0m = W0SOCD/SOAB = 2.8932.49/4.23 = 22.2MJ。图3 ABB公司三峡发电机特性曲线图4 外推延长的ABB发电机空载特性曲线2.4 空载失控误强励时转子储能量通过
12、以上计算，可知空载失控误强励时转子储能量Wf = Wfs + W0m = 4.2 + 22.2 = 26.4MJ。2.5 考虑磁路进一步饱和时的转子储能量图4中按磁化曲线斜率不变外推到D点，定子电压将升高到额定值的1.78倍，一般认为由于磁路进一步饱和，磁化曲线斜率将进一步下降，失控误强励时，定子电压最高升到额定值的1.5倍，这样可求得F点，曲边三角形OEF的面积小于OCD的面积，求得SOEF = 19.39cm2。主磁通的能量W0m = W0 SOEF/SOAB = 2.89 19.39/4.23 = 13.25MJ。空载失控误强励时转子储能量Wf = Wfs + W0m = 4.2+13.
13、25 = 17.45MJ。3 定子出线端突然短路工况下的转子磁场能量3.1励磁电流的计算为了使问题不至过于复杂，仅考虑三相对称短路的工况。由电机学1分析，由于闭合回路磁链守恒的原理，定子短路后，电枢三相绕组内立即感应出周期分量及非周期分量的短路电流，其作用是要保持闭合的电枢绕组内磁链不变。但短路电流产生的磁场穿过转子，使转子的磁链发生变化，所以经励磁电源短路（只要励磁电流不等于零，功率整流桥处于导通状态，就可视作短路）的转子励磁绕组及本身就短路的阻尼绕组中也立即感应出周期及非周期性的电流，以保持其磁链不变。该电流幅值很大，如果这时跳灭磁开关灭磁，则转子将释放出很大的能量。由于阻尼绕组的时间常数
14、较小，而继电保护动作时间一般在0.1秒以上，此时阻尼绕阻电流已基本衰减完毕，故分析灭磁能量时，可近似将阻尼绕组视作开路。定子短路后0.1秒时转子电流最大值Ifm的计算可有两种方法：(1) 据瑞典ASEA工厂提供公式3Ifm = K（2-1）If0 (5)式中：K 系数，1.05 1.10，取K = 1.1；Xd 直轴同步电抗，“长委”提供Xd = 0.902；Xd 直轴瞬变电抗，“长委”提供Xd = 0.319;If0 空载励磁电流，“长委”提供If0 = 2352A。将已知数据代入（5）式，算出Ifm=1.1(20.902/0.319-1)2352=12044A。(2) 据美国国家标准ANS
15、I/IEEE C37.18-1979(R1997)4中表5推荐： Ifm = 3IfN (6)式中：IfN 额定励磁电流，“长委”提供IfN = 4345A。Ifm = 34345 = 13035A，与上述结果相近，为安全计取较大值 Ifm = 13035A。3.2 转子储能量的计算定子短路时，由于磁链守恒的作用，定子绕阻、阻尼绕组及转子绕组内均感应出很大电流，它们产生的磁场互相抵消，才能维持原来的磁链不变，所以定子短路时，电机内总的磁通并没增加。但是单独从转子侧看，它的磁通及磁场能量是大大增加了。定子短路时转子等值电路如图5所示，图中各量与图1相同，只是定子出口由开路转为短路。因为RaXs，
16、两者并联，可将Xad忽略不计。这样图5就可以简化成图6，这时励磁绕组的时间常数T=。“长委”已提供该Td = 3.2s，转子电阻Rf = 0.1144W，故此时转子等效电感L f = T dRf = 3.20.1144 = 0.366H（不饱和值）。因为转子等效电抗Xf = wLf = Xfs + Xs，为转子和定子漏抗之和，漏磁通大部分在空气中通过，如不考虑磁路饱和，L f当作常数，则磁场能量（不饱和值），偏大！ 图5 定子短路时转子等值电路图 图6 定子短路时转子简化等值电路图实际上漏磁通的磁路有一部分在铁心里，所以还是应考虑磁路饱和的影响，这里磁力线要经过转子漏磁路和定子漏磁路两部分空气
17、隙，故饱和深度较小，设饱和系数为0.6（上述2.2节取为0.2，因只考虑转子漏磁路，空气隙小，故饱和较深，饱和系数小），则Wf = 0.631.1 = 18.7MJ(饱和值)。4 总结以上计算的是在极端工况下的转子磁场储能量，还作了很多偏安全的假设，所以计算结果应该是偏大的。另外在灭磁过程中转子绕组电阻、励磁回路电阻及磁场断路器也吸收部分能量，故灭磁电阻实际吸能比上述计算结果要小，另外根据中国电力行业标准DL/T 583-19955要求，还要保证1.2倍安全裕量。根据我们多年来对300MW及以下大中型水轮发电机转子灭磁电阻选配及试验的经验，感觉三峡发电机灭磁电阻的吸能容量可选为1620MJ为宜
18、！由于三峡发电机可靠性的要求特别高，故以上计算按发电机空载失控误强励及定子出线端突然短路这两种最严重的极限工况来考虑，以致计算出的灭磁电阻吸能容量非常大。但这两种极限工况出现的几率非常小，如对一般发电机均按此设计，将使灭磁电阻的体积和造价大大增加，不符合经济性要求。建议常规设计仅考虑空载有控误强劢工况，这时的励磁电流一般为额定值的2倍，计算方法同上述第2节。我公司从八十年代至今已为国内外各电厂提供了700台左右的发电机快速灭磁装置，其灭磁电阻均以空载有控误强励的磁场能量配置，至今仅发现3台发电机发生失控误强励，结果使灭磁电阻吸能过量而烧毁（或因移能不良而烧毁磁场断路器），但发电机完好，我公司给
19、予更换灭磁电阻（或磁场断路器）后即恢复正常运行。从安全经济的全面观点来考虑，这样的选择应该是合适的。但安全和经济有矛盾，具体选择由发电机安全的重要性和用户的经济能力来决定。 其他同步水轮发电机灭磁电阻的吸能容量可以参照上述的计算方法及选择原则来确定。汽轮发电机由于转子整锻铁心内有强烈的涡流阻尼作用，大部分磁场能量转入转子铁心的涡流中衰耗，使灭磁电阻的吸能大大减少。据实验分析6，空载灭磁时ZnO灭磁电阻吸能不到磁场储能量的10%。为安全计，可取汽轮发电机灭磁电阻（一般同时兼作转子过电压保护）的吸能容量为计算磁场储能量的30%50%。参考文献1 华中工学院 许实章，电机学，机械工业出版社，1981
20、年4月第1版2 上海交通大学，电工学（上册），人民教育出版社，1961年7月第2版3 瑞典ASEA工厂，大型发电机的灭磁，低压电器，1994年第1期4 ANSI/IEEE C37.18-1979(R1997),American National Standard Requirements for Field Discharge Circuit Breakers for Rotating Electric Machinery5 中国电力行业标准，DL/T 583-1995大中型水轮发电机静止整流励磁系统及装置技术条件6 中国科学院等离子体物理研究所 东方电机厂，黄台电厂300MW汽轮发电机灭磁试
21、验工作报告，1987年12月作者照片：李自淳在秦山电站310MW汽轮机前留影Editors note: Judson Jones is a meteorologist, journalist and photographer. He has freelanced with CNN for four years, covering severe weather from tornadoes to typhoons. Follow him on Twitter: jnjonesjr (CNN) - I will always wonder what it was like to huddle ar
22、ound a shortwave radio and through the crackling static from space hear the faint beeps of the worlds first satellite - Sputnik. I also missed watching Neil Armstrong step foot on the moon and the first space shuttle take off for the stars. Those events were way before my time.As a kid, I was fascin
23、ated with what goes on in the sky, and when NASA pulled the plug on the shuttle program I was heartbroken. Yet the privatized space race has renewed my childhood dreams to reach for the stars.As a meteorologist, Ive still seen many important weather and space events, but right now, if you were sitti
24、ng next to me, youd hear my foot tapping rapidly under my desk. Im anxious for the next one: a space capsule hanging from a crane in the New Mexico desert.Its like the set for a George Lucas movie floating to the edge of space.You and I will have the chance to watch a man take a leap into an unimagi
25、nable free fall from the edge of space - live.The (lack of) air up there Watch man jump from 96,000 feet Tuesday, I sat at work glued to the live stream of the Red Bull Stratos Mission. I watched the balloons positioned at different altitudes in the sky to test the winds, knowing that if they would
26、just line up in a vertical straight line we would be go for launch.I feel this mission was created for me because I am also a journalist and a photographer, but above all I live for taking a leap of faith - the feeling of pushing the envelope into uncharted territory.The guy who is going to do this,
27、 Felix Baumgartner, must have that same feeling, at a level I will never reach. However, it did not stop me from feeling his pain when a gust of swirling wind kicked up and twisted the partially filled balloon that would take him to the upper end of our atmosphere. As soon as the 40-acre balloon, wi
28、th skin no thicker than a dry cleaning bag, scraped the ground I knew it was over.How claustrophobia almost grounded supersonic skydiverWith each twist, you could see the wrinkles of disappointment on the face of the current record holder and capcom (capsule communications), Col. Joe Kittinger. He h
29、ung his head low in mission control as he told Baumgartner the disappointing news: Mission aborted.The supersonic descent could happen as early as Sunday.The weather plays an important role in this mission. Starting at the ground, conditions have to be very calm - winds less than 2 mph, with no prec
30、ipitation or humidity and limited cloud cover. The balloon, with capsule attached, will move through the lower level of the atmosphere (the troposphere) where our day-to-day weather lives. It will climb higher than the tip of Mount Everest (5.5 miles/8.85 kilometers), drifting even higher than the c
31、ruising altitude of commercial airliners (5.6 miles/9.17 kilometers) and into the stratosphere. As he crosses the boundary layer (called the tropopause), he can expect a lot of turbulence.The balloon will slowly drift to the edge of space at 120,000 feet (22.7 miles/36.53 kilometers). Here, Fearless
32、 Felix will unclip. He will roll back the door.Then, I would assume, he will slowly step out onto something resembling an Olympic diving platform.Below, the Earth becomes the concrete bottom of a swimming pool that he wants to land on, but not too hard. Still, hell be traveling fast, so despite the
33、distance, it will not be like diving into the deep end of a pool. It will be like he is diving into the shallow end.Skydiver preps for the big jumpWhen he jumps, he is expected to reach the speed of sound - 690 mph (1,110 kph) - in less than 40 seconds. Like hitting the top of the water, he will beg
34、in to slow as he approaches the more dense air closer to Earth. But this will not be enough to stop him completely.If he goes too fast or spins out of control, he has a stabilization parachute that can be deployed to slow him down. His team hopes its not needed. Instead, he plans to deploy his 270-s
35、quare-foot (25-square-meter) main chute at an altitude of around 5,000 feet (1,524 meters).In order to deploy this chute successfully, he will have to slow to 172 mph (277 kph). He will have a reserve parachute that will open automatically if he loses consciousness at mach speeds.Even if everything
36、goes as planned, it wont. Baumgartner still will free fall at a speed that would cause you and me to pass out, and no parachute is guaranteed to work higher than 25,000 feet (7,620 meters).It might not be the moon, but Kittinger free fell from 102,800 feet in 1960 - at the dawn of an infamous space race that captured the hearts of many. Baumgartner will attempt to break that record, a feat that boggles the mind. This is one of those monumental moments I will always remember, because there is no way Id miss this.
