变压器励磁涌流的抑制变压器励磁涌流不仅导致继电保护误动，由其衍生的电网电压骤降、谐波污染、和应涌流、铁磁谐振过电压等都给电力系统运行带来不可低估的负面影响。

数十年来人们通过识别励磁涌流特征的方法来减少继电保护的误动率，但并未获得良好的回报，误动率仍居高不下。

至于对电压骤降、谐波污染、和应涌流等的消除更一筹莫展。

究其原因是人们认为励磁涌流的出现不可抗拒，只能采用“识别”的对策，即“躲”的对策。

其实，换个思路——“抑制”，是完全可以实现的，而且已经实现了。

引言变压器励磁涌流与电容器的充电涌流抑制原理完全相似，电感及电容都是储能元件，前者不容许电流突变，后者不容许电压突变，空投电源时都将诱发一个暂态过程。

在电力变压器空载接入电源时及变压器出线发生故障被继电保护装置切除时，因变压器某侧绕组感受到外施电压的骤增而产生有时数值极大的励磁涌流。

励磁涌流不仅峰值大，且含有极多的谐波及直流分量。

由此对电网及电器设备造成极为不利的影响。

1、励磁涌流的危害性1.1 引发变压器的继电保护装置误动，使变压器的投运频频失败；1.2 变压器出线短路故障切除时所产生的电压突增，诱发变压器保护误动，使变压器各侧负荷全部停电；1.3 A电站一台变压器空载接入电源产生的励磁涌流，诱发邻近其他B电站、C电站等正在运行的变压器产生“和应涌流”(sympathetic inrush)而误跳闸，造成大面积停电；1.4 数值很大的励磁涌流会导致变压器及断路器因电动力过大受损；1.5 诱发操作过电压，损坏电气设备；1.6 励磁涌流中的直流分量导致电流互感器磁路被过度磁化而大幅降低测量精度和继电保护装置的正确动作率；1.7 励磁涌流中的大量谐波对电网电能质量造成严重的污染。

1.8 造成电网电压骤升或骤降，影响其他电气设备正常工作。

数十年来人们对励磁涌流采取的对策是“躲”，但由于励磁涌流形态及特征的多样性，通过数学或物理方法对其特征识别的准确性难以提高，以致在这一领域里励磁涌流已成为历史性难题。

2、励磁涌流的成因抑制器的重要特点是对励磁涌流采取的策略不是“躲避”，而是“抑制”。

理论及实践证明励磁涌流是可以抑制乃至消灭的，因产生励磁涌流的根源是在变压器任一侧绕组感受到外施电压骤增时，基于磁链守恒定理，该绕组在磁路中将产生单极性的偏磁，如偏磁极性恰好和变压器原来的剩磁极性相同时，就可能因偏磁与剩磁和稳态磁通叠加而导致磁路饱和，从而大幅度降低变压器绕组的励磁电抗，进而诱发数值可观的励磁涌流。

由于偏磁的极性及数值是可以通过选择外施电压合闸相位角进行控制的，因此，如果能掌握变压器上次断电时磁路中的剩磁极性，就完全可以通过控制变压器空投时的电源电压相位角，实现让偏磁与剩磁极性相反，从而消除产生励磁涌流的土壤——磁路饱和，实现对励磁涌流的抑制。

长期以来，人们认为无法测量变压器的剩磁极性及数值，因而不得不放弃利用偏磁抵消剩磁的想法。

从而在应对励磁涌流的策略上出现了两条并不畅通的道路，一条路是通过控制变压器空投电源时的电压合闸相位角，使其不产生偏磁，从而避免空投电源时磁路出现饱和。

另一条路是利用物理的或数学的方法针对励磁涌流的特征进行识别，以期在变压器空投电源时闭锁继电保护装置，即前述“躲避”的策略。

这两条路都有其致命的问题，捕捉不产生偏磁的电源电压合闸角只有两个，即正弦电压的两个峰值点（90°或270°），如果偏离了这两点，偏磁就会出现，这就要求控制合闸环节的所有机构（包括断路器）要有精确、稳定的动作时间，因为如动作时间漂移1毫秒，合闸相位角就将产生18°的误差。

此外，由于三相电压的峰值并不是同时到来，而是相互相差120°，为了完全消除三相励磁涌流，必须断路器三相分时分相合闸才能实现，而当前的电力操作规程禁止这种会导致非全相运行的分时分相操作，何况有些断路器在结构上根本无法分相操作。

用物理和数学方法识别励磁涌流的难度相当大，因为励磁涌流的特征和很多因素有关，例如合闸相位角、变压器的电磁参数等。

大量学者和工程技术人员通过几十年的不懈努力仍不能找到有效的方法，因其具有很高的难度，也就是说“躲避”的策略困难重重，这一策略的另一致命弱点是容忍励磁涌流出现，它对电网的污染及电器设备的破坏性依旧存在。

图2-1为一单相变压器结构图，可写出空载时初级绕组的电压方程式中N1、R1分别为初级绕组的匝数及电阻（2.1）可改写为式中α为 t=0时U1的初相角如忽略电阻R1，即设R1=0，则得求解（ 2.3）式微分方程得磁通Φ的表达式为依据磁链守恒定理，合闸瞬间磁路中磁链不能突变，即可求出积分常数C。

式中可写出磁通Φ表达式式中为总磁通的幅值从式(2.6)中不难看出变压器外施电压u1在不同初相角α合闸时所产生的磁通Φ都不相同，将式(2.6)改写为式(2.7)中为暂态磁通，即偏磁，在合闸瞬间Φp的值与α有关，在90°或270°空投时Φp=0，在0°或180°空投时Φp可达峰值Φm。

式(2.7)中为稳态磁通，为一周期函数。

图2-2为空投合闸角α=0时的磁通变化曲线，图中Φs为稳态磁通，Φ为Φs和Φp合成的总磁通（未计及剩磁Φres），Φsat为变压器饱和磁通。

对于无损变压器（R1=0）偏磁Φp不会衰减，如实线所示，对于有损变压器（R1>0）Φp按时间常数衰减，如虚线所示。

从图2-2中可看出在电压相位角在θ1至θ2区间总磁通Φ大于饱和磁通Φsat，磁路饱和，因而产生励磁涌流iy，iy具有间断性。

对于无损变压器Φ和iy是关于的偶对称波形，而在iy=0的间断角区间Φ则是关于的偶对称波形。

对于有损变压器则Φ与iy将不再有对称关系。

当计及剩磁时，总磁通将由剩磁、偏磁（暂态磁通）及稳态磁通三者组成。

不难看出在图2-2偏磁的情况下，如剩磁为正，则总磁通曲线向上平移，即磁路更易饱和，励磁涌流幅值会更大。

如剩磁为负，则励磁涌流将被抑制。

图2-3是铁磁材料的磁滞回线，它描述在磁路的励磁线圈上施加交流电压时，磁势H 也相应的从-Hc到Hc之间变化，由H产生的磁通Φ（或磁通密度B=Φ/S）将在磁滞回线上作相应的变化。

如果H在回线上的某点突然减到零，则B将随即落到对应B轴的某点上，该点所对应的B值即为剩磁Br。

可以看出剩磁的数值和极性与切除励磁电压的相位角有关，如果在第Ⅰ、Ⅱ象限切断励磁电源（即H=0）则剩磁为正或零，在Ⅲ、Ⅳ象限切断励磁电源，则剩磁为负。

3、励磁涌流的抑制方法变压器在正常带电工作时，磁路中的主磁通波形与外施电源电压的波形基本相同，即是正弦波。

磁路中的磁通滞后电源电压90°，通过监测电源电压波形实现对磁通波形的监测，进而获取在电源电压断电时剩磁的极性。

变压器空投上电时产生的偏磁Φp也一样，因偏磁，电源电压上电时的初相角α在Ⅰ、Ⅳ象限区间内产生的偏磁极性为正，而初相角α在Ⅱ、Ⅲ象限区间内产生的偏磁极性为负。

显然，剩磁极性可知，偏磁极性可控，只要空投电源时使偏磁与剩磁极性相反，涌流即被抑制。

变压器初级电压u、主磁通Φ、剩磁ΦRes及偏磁Φp与分闸角和合闸角的关系曲线图,以及电源电压u分闸初相角α’与剩磁ΦRes的关系曲线。

变压器处于稳态时主磁通Φ滞后电源电压u 90°.变压器空载上电时所产生的偏磁一定与稳态时对应上电时电压u曲线上电点的稳态磁通大小相等，极性相反，其最大值可达稳态磁通Φ的峰值Φm，而剩磁ΦRes幅值与磁路材料的特性有关。

不难看出对应同一个合闸初相角α或分闸初相角α’所产生的偏磁和剩磁的极性正好相反，也就是说通过分闸时测量电源电压分闸角α’，并将α’保存下来，在下次空投变压器时选择在合闸角α等于α’时加上电源，偏磁就可与剩磁反向，它们的合成磁通将小于饱和磁通Φsat(曲线④)，（因饱和磁通一般选择大于稳态磁通峰值），磁路不会饱和，从而实现对励磁涌流的抑制。

由于三相电源电压在断路器三相联动切除时所得到的三相分闸相角各相差120°，剩磁极性也是三相各相差120°，而在三相联动合闸时三相的合闸初相角也是相差120°，三相偏磁极性也各相差120°，这样就自然实现了变压器三相磁路中的偏磁和剩磁都是抵消的，从而避免了一定要断路器分相分时操作才能抑制励磁涌流的苛求，也就是说三相联动断路器支持对三相涌流的抑制。

由于抑制励磁涌流只要偏磁和剩磁极性相反即可，并不要求完全抵消，因而当合闸角相对前次分闸角有较大偏差时，只要偏磁不与剩磁相加，磁路就不会饱和，这就大大降低了对断路器操作机构动作时间的精度要求，为这一技术的实用化奠定了基础。

将这种抑制器与快切装置和备自投装置联动即可实现备用变压器按冷备用方式运行，这将大大节约变压器热备用方式的空载能耗。

图3-1选录了四条励磁涌流Iy与分闸角α’和合闸角α的关系曲线，可以看到，在合闸角α为90°或270°时，空投变压器的励磁涌流与变压器的前次分闸角无关，原因是在变压器初级电压过峰值时上电不产生偏磁，不论变压器原来是否有剩磁都不会使磁路饱和。

当然，如果使用三相联动断路器是不可能做到三相的偏磁都为零。

而当合闸角α为0°或 180°时则空投变压器的励磁涌流与前次分闸角α’密切相关，当α与α’相近（大约相差±60°）时励磁涌流被抑制，此后α与α’偏离越大，励磁涌流也越大。

由此可以看到如断路器的合闸时间漂移在±3ms时对涌流的抑制基本无影响。

当今的真空断路器和SF6断路器的分、合闸时间漂移都在1ms之内，完全可以精确实现对励磁涌流的抑制。

分闸角α’与合闸角α对励磁涌流的影响曲线图3-1应该指出，变压器断电后留在三相磁路中的剩磁在正常情况下是不会衰减消失的，不会改变极性。

只有在变压器铁心受到高于材料居里点的高温作用后剩磁才会衰减或消失，但一般的电站现场不会出现这种情况。

退一步讲，剩磁消失是件好事，只要没有剩磁，仅靠偏磁是不会引起磁路饱和的。

4、结束语电力变压器空投充电相位角与前次切除电源相位角匹配原则，从理论及实践上都证明了在使用三相联动操作断路器时能彻底抑制励磁涌流。

同样，电力电容器空投充电相位角与前次切除电源相位角匹配原则，也能实现抑制三相联动断路器合闸时的电容器充电涌流。

这一技术对根除保护误动、改善电能质量、提高运行可靠性有重要意义。

同样对各种电压等级电力系统的无功补偿、远距离输电线路的串联补偿控制等也有重要意义。

Transformer inrush current suppressionTransformer inrush current leads not only to the protective relaying misoperation, derived from the power grid voltage sags, harmonic pollution, and the inrush current, ferromagnetic resonance overvoltage in power system operation, to bring the negative effect that cannot underestimate. For decades the people through the identification of inrush current feature method to reduce the relay misoperation rate, but did not gain a good return, malfunction rate is still high. As for the voltage sag, harmonic pollution, and the inrush current, elimination of the more be nonplussed over sth.. The reason is that people think the inrush current appears irresistible, can only use" recognition " countermeasure, namely "hide " countermeasure. In fact, change a train of thought --" inhibition", can be fully realized, and have achieved.IntroductionTransformer inrush and surge suppression capacitor chargingprinciple is completely similar to the inductance and capacitance are energy storage devices, the former does not allow current mutation, which does not allow voltage surge,power drop will induce a transient process. Access in the power transformer no-load transformer outlet power failure andprotection devices to be removed, because of a side of the transformer windings to feel the surge applied voltage values are sometimes generated a great inrush current. Inrush currentpeak is not only large, and contains very many harmonics andDC component. Electrical equipment on the grid and thusresult in an extremely negative impact.1. the danger of inrush current1.1 caused by the transformer protection devices malfunction,the frequent failure of the transformer and put into operation;1.2 removal of the transformer short-circuit fault outlet voltage generated when the sudden increase in the protection induced by transformermalfunction, so that each side of the transformer load all thepower;1.3 A power station access to a power transformer no-load inrush current generated, inducing other B power station nearby, C power station transformers are running a "and should surge" (sympathetic inrush) and false tripping, resulting in a large area power failure; large inrush currentvalue of1.4 would result in electric power transformers andcircuit breakers due to excessive damage;1.5-induced over-voltage, damaged electrical equipment;1.6 inrush current of the DC component lead to over-current transformermagnetization and magnetic significantly reduce themeasurement accuracy and the correct action rate ofprotection devices;1.7 magnetizing inrush current in a large number of harmonics on power quality caused by pollution.1.8 caused by voltage sags or swells, affecting the normal operation of other electrical equipment. For decades, people have taken to the inrush current approach is to "hide", butbecause of inrush current form and characteristics ofdiversity, through mathematical or physical methods toidentify its characteristics difficult to improve the accuracy ofthat inrush current in this field has been a historical problem.2. the magnetizing inrush currentcausesSuppressor is an important feature of the strategy adopted bymagnetizing inrush current is not "escape", but "suppression." Inrush current theory and practice that can suppress or even eliminate, because the source of inrush current is generated in the transformer windings on either side felt the applied voltage increases, based on fluxconservation theorem, the windings in the magnetic circuit will produce a single polarity of the magnetic bias, such as partial pole and transformer of exactly the same as the original remanence polarity, it may bias magnetic remanence andsteady-state flux superimposed with the result of magnetic saturation, thus greatly reducing the magnetizing reactance ofthe transformer windings , and then induced a significantinrush current value. As the partial magnetic polarity and the value is applied voltage switch by selecting the phase angle control, and therefore, if we can grasp the power transformer when the last of remanent magnetic polarity, they can drop by when the control transformer the supply voltage phase angle, which allows magnetic bias with opposite polarity remanence, which eliminate the inrush current of the soil -magnetic saturation, to achieve the inrush current .For a long time, people found it impossible to measure thetransformer polarity and remanence values, and thus had to abandon the use of the idea of partial remanence magneticoffset. Inrush current in response to the strategy does notappear on the two smooth road, a road through the control power transformer voltage drop closing phase angle, so that it does not produce magnetic bias, in order to avoid magnetic saturation occurs when the power drops . The other way is the use of physical or mathematical method foridentifying the characteristics of magnetizing inrush current, in order to lock in the power transformer protection devices drop, that the aforementioned "avoid" strategy. The two fatal road has its problems, capture does not produce magnetic bias voltage closing angle of only two, namely, the two sinusoidal voltage peak point (90 ° or 270 °), if you deviate from these two points, partial there will be magnetic, which requires control of the closing part of all institutions (including circuit breakers) should be accurate, stable operating time,because, as 1 millisecond time drift action, closing phaseangle of 18 ° will produce the error. In addition, three-phase voltage of the peak is not at the same time coming, but the difference between 120 °, to completely eliminate the three-phase inrush current, must be time-phase three-phase circuit breaker closing can be achieved, and the current operating rules prohibit such power will be lead to time-sharing-phasesplit-phase operation running, not to mention some circuit breakers in the sub-phase structure can not operate.dentification with the physical and mathematical methods of magnetizing inrush current rather difficult, because the characteristics of magnetizing inrush current and a lot of factors, such as closing phase angle, the electromagnetic parameters of the transformer and so on. A large number of scholars and engineers through decades of unremitting effortsstill can not find an effective way, because of its high degree of difficulty, that is to "avoid" strategy difficult, the Achilles heel ofthis strategy is to tolerate the other excitation inrush current occurs, the pollution of its power grid and electrical equipment,there is still destructive.Transformer diagram 2-1Figure 2-1 is a single-phase transformer structure, we can write the no-load voltage of the primary winding of the equationWhere N1, R1, respectively, for the primary winding turns and the resistance（2.2)(2.1) can be rewritten as Where α t = 0, U1, such as ignoring the initial phase angleresistor R1, whichLet R1 = 0, we obtain the solution (2.3)-type equations have an expression for the magnetic flux ΦBased on flux conservation theorem, in the closing momentsmagnetic flux can not change suddenly, you can find theintegration constant C.The amplitude of the total flux from equation (2.6) is not difficult to see that the applied voltage transformer u1 in the early phase angle α diffe rent when closing the magnetic fluxgenerated by Φ is not the same, the equation (2.6) is rewritten as(2.7) for the transient flux, that is, magnetic bias, in the closing moments Φp value of α for the 90 ° or 270 ° drop at Φp = 0, at 0 ° or 180 ° when dropped up to the peak Φm Φp . Equation(2.7) in f or the steady-state flux, as a periodic function. Figure 2-2 for the drop-closing angle α = 0, the flux curve, the steady-state flux diagram Φs, Φ is Φs and Φp total flux synthetic (not taking into account t he remanence Φres), Φsat for the transformer saturation flux. For the lossless transformer (R1 = 0) magnetic bias Φp will not decay, the solid line shows, for lossy transformer (R1> 0)Closing angle α = 0, the flux curve of Figure 2-2Dashed line. As can be seen from Figure 2-3 in the voltage phase angle range θ1 to θ2 greater than the total flux Φsaturation flux Φsat, magnetic saturation, resulting inrush current iy, iy has a discontinuity.For the lossless transformer Φ and iy is about even symmetry of thewaveform, while the discontinuity in theiy = 0 is the angular range of Φt he even symmetric waveform. For Φ and iy is detrimental tothe transformer will no longer symmetrical relationship.When taking into account the remanence, the remanence will be the total magnetic flux, magnetic bias (transient flux) andsteady-state flux of the three components. Difficult to see inFigure 2-2 Bias in the case, such as remanence is positive, the total flux curve upward shift,that more saturated magnetic circuit, inrush current amplitude will be greater. If remanence is negative, the inrush current is suppressed.Core material hysteresis loop in Figure 2-3 、Figure 2-2 is the hysteresis loops of ferromagnetic materials,which describes the excitation coil in the magnetic circuit on the AC voltage applied, the corresponding magnetic potential H-Hc to Hc from between the change in magnetic flux Φ generated by H (or magnetic flux density B = Φ / S) in the corresponding hysteresis loop changes. If the H line at some point suddenly back to zero, then B will then fall into the B-axiscorresponds to a certain point, the point corresponding to theB value is the remanence Br. Remanence values can be seenwith the removal of excitation voltage and polarity of the phaseangle, and if in the first Ⅰ, Ⅱexcitation power off quadrant (ie,H = 0) then the remanence is positive or zero, in Ⅲ, Ⅳquadrant cut off the excitation power, the remanence is negative.3.the magnetizing inrush current suppression methodTransformer energized during normal working hours, the main magnetic flux in the applied voltage waveform and the waveform is basically the same, that is a sine wave. Magnetic flux lags the supply voltage of90 °, by monitoring the supply voltage waveform to achieve the flux waveform monitoring,then get off when the supply voltage polarity remanence. Dropon the power transformer magnetic bias Φp also generatedas a result of magnetic bias, the power supply voltage when the initial phase angle α in Ⅰ, Ⅳquadrant bias generated within the range of magnetic polarity is positive, while the initial phase angle α in Ⅱ, ⅲquadrant bias generated within the range of magnetic polarity is negative. Clearly, the remanence polarity shows that the magnetic polarity bias control, so long as the power drop and remanence magneticpolarity opposite side, he incurs surge suppression.Figure 3-1for the transformer primary voltag e u, the main magnetic flux Φ, and the bias magnetic remanence ΦRes Φp with sub-gate the relationship between the angle and closing angle curve, and the sub-gate supply voltage u beginning ofthe phase angle α 'with the remanence ΦRes curve. The main transformer in the steady state flux Φ lag the supply voltage u 90 °, tTransformer no-load power generated when the magnetic bias must correspond with the steady state voltage u at power point on the curve of steady-state flux power equal,opposite polarity, The maximumsteady-state flux Φ up to the peak Φm, while theamplitude of magnetic remanence ΦRes material characteristics. Easy to see the early phase corresponds to the same angle α or closing the sub-gate initial phase angle α 'and the resulting magnetic remanence of the very partial.Transformer primary voltage u, the main magnetic flux Φ, and the bias magnetic remanence ΦRes Φp with sub-gate the relationship between the angle and closing angle curve of the opposite, that is measured by the sub-gate sub-gate voltage angle α ', and α ' preserved, the selection of the transformer in the next drop in the closing angle α equal to α', when coupled with power, and bias magnetic remanence can reverse, theywill be less than the synthesis of magnetic flux saturation f lux Φsat .(Due to saturation flux is generally larger than the steady-state flux peak selection), the magnetic circuit is not saturated, in order to achieve inrush current suppression. As the three-phase three-phase supply voltage of the circuit breaker when the linkage has been cut three-phase sub-phase of thedifference between the gate 120 °, the phase difference between the remanence polarity is 120 °, and when closing the three-phase three-phase co-linkage initial phase angledifference between the gate is 120 °, the phase difference between the partial pole is also 120 °, so that the naturalrealization of the three-phase transformer magnetic circuitbias magnetic and remanence are offset to avoid a circuit breaker must be with a time share in order to suppress inrush current demanding, that support for three-phase three-phasecircuit breaker linkage surge suppression.As long as the partial inhibition of inrush current and remanent magnetic polarity opposite to, are not required to fully offset,so when the closing angle relative to a greater angle of the previous sub-gate bias, as long as no magnetic bias and remanence are added together, the magnetic circuit not saturated, which greatly reduces the operating time of circuit breaker operating mechanism precision requirements for the practical application of this technology laid the foundation.Suppressor and fast cutting of such devices and equipmentcan be realized from the investment unit linked by cold stand by spare transformer run, which will greatly reduce no-load transformer hot standby mode energy consumption.Figure 3-3presents selected four inrush current Iy and thesub-gate angle α 'and the closing angle α of the curve, you can see, in the closing angle α of 90 ° or 270 °, drop the transformer inrush current and transformer before sub-sub-gate angle has nothing to do, because the transformer primary voltage over peak power does not produce magnetic bias, regardless of whether the original transformer magnetic saturation remanence will not. Of course, if you use three-phase circuit breaker is not possible linkage phase of themagnetic bias is zero. And when the closing angle α is 0 ° or180 ° when the drop the transformer inrush current and the previous sub-gate angle α 'is closely related to, when α and α'are similar (about a difference of ± 60 °) when the inrush current is suppressed, then α and α 'the greater the deviation,the greater the inrush current. It can be seen as closing the circuit breaker when the time shift at ±3ms surge suppression for no influence. Today's vacuum circuit breakers and SF6 circuit breaker, closing time drift are within1ms, can accurately achieve the inrush current suppression.Tripping angle α 'and closing angle α of the inrush current of Figure 3-1It should be noted, after a stay in the three-phase power transformer magnetic circuit remanence under normal circumstances will not decay away, and not to change polarity.Only in the transformer core material above the Curie point bythe high temperature will decay or disappear after the remanence, but generally the power station site will not happen. Say the least, remanence disappeared a good thing,as long as there is no residual magnetism, magnetic bias alone will not cause magnetic saturation.4.ConclusionDrop charging power transformer phase angle phase anglewith the previous removal of the power matching principle, in theory and practice have proved that the joint operation in the use of three-phase circuit breaker can be completely suppressed when the inrush current. Similarly, the power capacitor charging phase angle with the last drop cut powerphase angle matching principle, can be achieved when thecircuit breaker closing inhibit the interaction of three-phase capacitor charging surge. The technology protection malfunction eradication, improvement of power quality, improve operational reliability are important. The same variety of voltage levels of power system reactive power compensation, long-distance transmission line series compensation control is also important.。