外文翻译风力发电中的自我激励与谐波

Self-Excitation and Harmonics in Wind Power Generation
E. Muljadi ，C. P. Butterfield
National Renewable Energy Laboratory, Golden, Colorado 80401
H. Romanowitz
Oak Creek Energy Systems Inc.,Mojave, California 93501
R. Yinger
Southern California Edison,Rosemead, California 91770 Traditional wind turbines are commonly equipped with induction generators because they are inexpensive, rugged, and require very little maintenance. Unfortunately, induction generators require reactive power from the grid to operate，capacitor compensation is often used. Because the level of required reactive power varies with the output power, the capacitor compensation must be adjusted as the output power varies. The interactions among the wind turbine, the power network, and the capacitor compensation are important aspects of wind generation that may result in self-excitation and higher harmonic content in the output current. This paper examines the factors that control these phenomena and gives some guidelines on how they can be controlled or eliminated.
1．Introduction
Many of today’s operating wind turbines have fixed speed induction generators that are very reliable, rugged, and low cost. During normal operation, an induction machine requires reactive power from the grid at all times. The most commonly used reactive power compensation is capacitor compensation. It is static, low cost. Different sizes of capacitors are generally needed for different levels of generation.
Although reactive power compensation can be beneficial to the overall operation of wind turbines, we should be sure the compensation is the proper size and provides proper control. Two important aspects of capacitor compensation, self-excitation and harmonics ,are the subjects of this paper.
2．Power System Network Description
A diagram representing this system is shown in Fig(1). The power system components analyzed include the following:
• An infinite bus and a long line connecting the wind turbine to the substation
• A transformer at the pad mount
• Capacitors connected in the low voltage side of the transformer • An induction generator
For the self-excitation, we focus on the turbine and the capacitor compensation only the right half of Fig. For harmonic analysis, we consider the entire network shown in Fig.
3. Self-Excitation
3.1 The Nature of Self-Excitation in an Induction Generator.
Self-excitation is a result of the interactions among the induction generator, capacitor compensation, electrical load, and magnetic saturation. This section investigates the self-excitation process in an off-grid induction generator, knowing the limits and the boundaries of self-excitation operation will help us to either utilize or to avoid self-excitation.
Fixed capacitors are the most commonly used method of reactive power compensation in a fixed-speed wind turbine. An induction generator alone cannot generate its own reactive power; it requires reactive power from the grid to operate normally, and the grid dictates the voltage and frequency of the induction generator.
One potential problem arising from self-excitation is the safety aspect. Because the generator is still generating voltage, it may compromise the safety of the personnel inspecting or repairing the line or generator. Another potential problem is that the generator’s operating voltage and frequency may vary. Thus, if sensitive equipment is connected to the generator during self-excitation, that equipment may be damaged by
over/under voltage and over/ under frequency operation. In spite of the disadvantages of operating the induction generator in self-excitation, some people use this mode for dynamic braking to help control the rotor speed during an emergency such as a grid loss condition. With the proper choice of capacitance and resistor load, self-excitation can be used to maintain
the wind turbine at a safe operating speed during grid loss and mechanical brake malfunctions 。

3.2 Steady-State Representation.
The steady-state analysis is important to understand the conditions required to sustain or to diminish self-excitation. As explained above, self-excitation can be a good thing or a bad thing, depending on how we encounter the situation. Figure 2 shows an equivalent circuit of a capacitor compensated induction generator. As mentioned above, self-excitation operation requires that the balance of both real and reactive power must be maintained. Equation （1）gives the total admittance of the system shown in Fig(2):
S Y +'M Y +'R Y =0 （1）
where
S Y = effective admittance representing the stator winding, the capacitor, and the load seen by node M
'M Y = effective admittance representing the magnetizing branch as seen by node M,referred to the stator side
'R Y = effective admittance representing the rotor winding as seen by node M, referred to the stator side
Equation 1 can be expanded into the equations for imaginary and real parts as shown in Eqs.2and3:
（2）
Fig. 2 Per phase equivalent circuit of an induction generator under self-excitation mode
Fig.3 A typical magnetization characteristic
S R = stator winding resistance
LR L = stator winding leakage inductance
'R R = rotor winding resistance
'
LR L = rotor winding leakage inductance
'
M L = stator winding resistance
S = operating slip
= operating frequency
L R = load resistance connected to the terminals
C = capacitor compensation
S R =阻抗
One important aspect of self-excitation is the magnetizing characteristic of the induction generator. Figure 3 shows the relationship between the flux linkage and the magnetizing inductance for a typical generator; an increase in the flux linkage beyond a certain level reduces the effective magnetizing inductance '
L. This graph can be derived from the
M
experimentally determined no-load characteristic of the induction generator.
The voltage at the terminals of the induction generator presented in Fig . （5） shows the impact of changes in the capacitance and load resistance. As shown in Fig. （5）, the load resistance does not affect the terminal voltage,
especially at the higher rpm （higher frequency）, but the capacitance has a significant impact on the voltage profile at the generator terminals. A larger capacitance yields less voltage variation with rotor speed, while a smaller capacitance yields m ore voltage variation with rotor speed. As shown in Fig. 6, for a given capacitance, changing the effective value of the load resistance can modulate the torque-speed characteristic.
These concepts of self-excitation can be exploited to provide dynamic braking for a wind turbine as mentioned above to prevent the turbine from running away when it loses its connection to the grid; one simply needs to choose the correct values for capacitance （a high value） and load resistance to match the turbine power output. Appropriate operation over a range of wind speeds can be achieved by incorporating a variable resistance and adjusting it depending on wind speed.
3.3 Dynamic Behavior.
This section examines the transient behavior in self-excitation operation. We choose a value of 3.8 mF capacitance and a load resistance of 1.0 for this simulation. The constant driving torque is set to be 4500 Nm. Note that the wind turbine aerodynamic characteristic and the turbine control system are not included in this simulation because we are more interested in the self-excitation process itself. Thus, we focus on the electrical side of the equations.
Figure 7 shows time series of the rotor speed and the electrical output power. In this case, the induction generator starts from rest. The speed increases until it reaches its rated speed. It is initially connected to the grid and at t=3.1 seconds （s）, the grid is disconnected and the induction generator enters self-excitation mode. At t=6.375 s, the generator is
reconnected to the grid, terminating the self-excitation. The rotor speed increases slightly during self-excitation, but, eventually, the generator torque matches the driving torque （4500 Nm）, and the rotor speed is stabilized. When the generator is reconnected to the grid without synchronization, there is a sudden brief transient in the torque as the generator resynchronizes with the grid. Once this occurs, the rotor speed settles at the same speed as before the grid disconnection.
Figure 8 (a) plots per phase stator voltage. It shows that the stator voltage is originally the same as the voltage of the grid to which it is connected. During the self-excitation mode 3.1 s<t<6.375 s, when the rotor speed increases as shown in Fig. 7, the voltage increases and the frequency is a bit higher than 60 Hz. The voltage and the frequency then return to the rated values when the induction generator is reconnected to the grid. Figure 8(b) is an expansion of Fig. 8(a) between t=3.0 s and t=3.5 s to better illustrate the change in the voltage that occurs during that transient. 4．Harmonic Analysis
4.1 Simplified Per Phase Higher Harmonics Representation. In order to model the harmonic behavior of the network, we replace the power network shown in Fig. 1 with the per phase equivalent circuit shown in Fig. 9（a）. In this circuit representation, a higher harmonic or multiple of 60 Hz is denoted by h, where h is the integer multiple of 60 Hz. Thus h=5 indicates the fifth harmonic （300 Hz）. For wind turbine applications, the induction generator, transformer, and capacitors are three phase and connected in either Wye or Delta configuration, so the even harmonics and the third harmonic do not exist [5,6]. That is, only h=5,7,11,13,17, . . ., etc. exist.
Fig.8 The terminal voltage versus the time.（a）Voltage during
self-excitation.（b） Voltage before and during self-excitation , and after reconnection.
4.1.1 Infinite Bus and Line Feeder. The infinite bus and the line feeder connecting the wind turbine to the substation are represented by a simple Thevenin representation of the larger power system network. Thus, we consider a simple RL line representation.
Fig.9 The per phase equivalent circuit of the simplified model for harmonic analysis
4.1.2 Transformer.
We consider a three-phase transformer with leakage reactance （
X）
xf
of 6 percent. Because the magnetizing reactance of a large transformer is usually very large compared to the leakage reactance （'
X→open circuit）,
M
only the leakage reactance is considered. Assuming the efficiency of the transformer is about 98 percent at full load, and the copper loss is equal to the core loss （a general assumption for an efficient, large Transformer）, the copper loss and core loss are each approximately 1 percent or 0.01 per unit. With this assumption, we can compute the copper loss in per unit at
I=1.0 per unit）, and we can determine the total full load current （
full load
1_
winding resistance of the primary and secondary winding （about one percent in per unit）.
4.1.3 Capacitor Compensation. Switched capacitors represent the compensation of the wind turbine. The wind turbine we consider is equipped with an additional 1.9 MVAR reactive power compensation（1.5 MVAR above the 400 kVAR supplied by the manufacturer）. The wind turbine is compensated at different levels of compensation depending on the level of generation. The capacitor is represented by the capacitance C in series with the parasitic resistance（Rc）, representing the losses in the capacitor. This resistance is usually very small for a good quality capacitor.
4.1.4 Induction Generator. The induction generator （1.5 MW,480 V,60 Hz）used for this wind turbine can be represented as the per phase equivalent circuit shown Fig. 9（a）. The slip of an induction generator at any harmonic frequency h can be modeled as
where
S= slip for h th harmonic
h
H = harmonic order
ω= synchronous speed of the generator
s
ω= rotor speed of the generator
r
S=1) Thus for higher harmonics ( fifth and higher) the slip is close to 1 (
h
and for practical purposes is assumed to be 1.
4.2 Steady State Analysis. Figure 9(b) shows the simplified equivalent circuit of the interconnected system representing higher harmonics. Note
that the magnetizing inductance of the transformers and the induction generator are assumed to be much larger than the leakages and are not included for high harmonic calculations. In this section, we describe the characteristics of the equivalent circuit shown in Fig. 9, examine the impact of varying the capacitor size on the harmonic admittance, and use the result of calculations to explain why harmonic contents of the line current change as the capacitance is varied.
From the superposition theorem, we can analyze a circuit with only one source at a time while the other sources are turned off. For harmonics analysis, the fundamental frequency voltage source can be turned off. In this case, the fundamental frequency voltage source(infinite bus), Vs, is short circuited.
Fig. 10(a) The total admittance for higher harmonics as a function of reactive compensation. (b) Total harmonic distortion of the current as a function of the reactive compensation in per unit.
where
line Z = line R + j line X = line impedance
xf Z = xf R + j xf X = transformer leakage impedance
C Z = c R +()1
jh C ω-= capacitor impedance
gen Z = gen R + j gen X = generator impedance The admittance at any capacitance and harmonic frequency can be found from the impedance:
For a given harmonic, the harmonic current is proportional to the admittance shown in Eq. (6) multiplied by the corresponding harmonic voltage. Because the field data only consist of the total harmonic distortion of the capacitor current, and do not provide information about individual harmonics, we can only compare the trends from the admittance calculation to the measured data.
Fig. 11 (a) Per-phase equivalent circuit of a transformer. (b) Phasor diagram for P>0,Q>0. (c) Phasor diagram for P>0,Q <0.
From Fig. 10, we can say that the circuit will resonate at different frequencies as the capacitor C is varied. Two harmonic components must exist to generate harmonics currents in the systems —a harmonic source (due to magnetic saturation as shown in Fig. 3) and a circuit that will resonate at certain levels of capacitance compensation.
4.3 Dynamic Simulation. Now consider how the harmonic sources are generated in the transformer. Most utility-size wind turbines are equipped with a pad-mount step-up transformer that connects them to the utility. When the transformer is saturated, the nonlinear characteristic of the magnetic circuit generates a nonsinusoidal current.
Figure 11(a) shows the per-phase equivalent circuit of a transformer. The iron core loss of a transformer is usually represented as an equivalent
resistance,'CORE R , in parallel with the magnetizing reactance 'M X . In this
study, the core loss is small enough to be neglected (i.e., the value of
'CORE R =∞ represents an open circuit; thus, the equivalent resistance 'CORE R is not drawn in the equivalent circuit). The magnetizing flux linkage is proportional to the ratio of the voltage and the frequency:
where
'M E = the magnetizing voltage
'M λ= flux linkage
B ω= the base frequency
'M E = 磁化的电压
The flux linkage of the transformer can be found from Eq.(7). The
relationship between the flux linkage and the magnetizing inductance '
M L due
to the magnetizing current is nonlinear. When the magnetizing current is low, the flux (and flux linkage) varies linearly with the magnetizing current, but eventually saturation is reached and the nonlinear characteristic starts;
further increases in magnetizing current 'M I will produce smaller increases
in the flux linkage. In the saturation region, the resulting output current '2I will be nonsinusoidal , as shown in Fig. 12, due to the nonlinearity of the magnetizing inductance.
Fig. 12 The output voltage and current of a transformer under light load condition
There are two types of operation that can cause saturation. The first one occurs when the transformer operates at a higher voltage level. One
example of this operation is when the transformer is lightly loaded. As a
result, the magnetizing branch is exposed to a high voltage 'M E , producing
a large magnetizing current 'M I in the magnetizing branch.
The second type of operation that can result in high saturation is when the transformer is operated with a leading power factor (supplying reactive power to the grid Vs).
The voltage across the magnetizing reactance 'M X (referred to the primary side) can be expressed as
where
line Z =line R + j line X = line impedance connecting the transformer to the voltage source VS
1Z = 1R + j 1X = primary winding impedance of the transformer
1R =2R = /2xf R = resistance of the primary and secondary winding of the transformer
1X =2X = /2xf X = leakage reactance of the primary and secondary winding of the transformer
S V = voltage at the infinite bus
1I = current flowing in the primary winding
line X = reactance of the line
line R = line resistance
As an illustration, we can use the phasor diagrams shown in Figs. 11(b) and 11(c). For the case of simplicity in the phasor diagram illustrations, we can simplify the equivalent circuit shown in Fig. 11(a) as an ideal transformer with only its leakage reactance represented. In Fig. 11(a), the real power P and reactive power Q are considered to be flowing from the right to the left (positive values flow from the turbine to the grid). When P >0,
Q<0 (the turbine generates real power but absorbs reactive power), then 'M E <
S V , and we have normal operation. On the other hand, when P>0, Q>0 (the
turbine generates both real and reactive power), then 'M E < S V and we may
experience saturation.
风力发电中的自我激励与谐波
1．介绍
传统的风力涡轮机通常安装的是感应发电机，因为它廉价，耐用，而且只需要很少的维护。

然而，电感应发电机需要的无功功率通常通过电容器补偿来得到。

因为输出功率各不相同，所以电容补偿必须随之调整。

风力发电机组的电力网络中，相互的电容补偿作用是导致输出电流中产生自我激励和高次谐波的一个重要原因。

这篇文章探讨产生这些现象的原因，并对如何控制或消除这些现象提出一些方法。

现在大部份风力发电机的性能是非常可靠的，并且维修简单，费用低。

一台感应发电机在正常工作期间始终需要得到无功功率。

使用最普遍的无功功率补偿是电容器补偿，因为它是静态的, 而且成本低。

不同型号的电容器可以提供不同的电容补偿。

虽然无功的动力补偿可能对风轮机总的操作有利，但是我们必须确保补偿是恰当的，并且不影响控制。

自我激励和谐波是电容器补偿的两个重要部分也是这篇文章的主题。

2．动力系统网络描述
如图1所示描述的这个系统。

动力系统的部件分析包括如下内容：
•连接风机各部分的总线和输入线路。

•一台安装在衬垫上的变压器
•连结在变压器低电压的电容器
•一台电感应发电机
图1.系统各部件图
对于自我激励，我们关注的是在涡轮上的电容补偿。

对于谐波分析，我们用图表来表示整个网络。

3．自我激励
3.1感应发电机的自我激励。

自激是在感应发电机和电容器补偿之中负电荷和磁性浸透交互作用的一个结果。

自我激励过程这部分是在一台离栅栏的电感应发电机里进行研究的，知道极限和自激操作的边界将会帮助我们去利用或者避免自激。

在固定速度的风轮机中应用最普遍的是固定电容器无功的动力补偿方法。

只有一台电感应发电机是不能得到它自己需要的无功动力的，它要求来自电网正常操作的无功动力，并且栅栏口接电感应发电机的电压和频率。

安全是自我激励的一个潜在问题。

因为发电机可以产生电压，它可能伤害检查或者修理这台发电机的人员。

另一个潜在的问题是发电机的工作电压和频率可能变化。

因此，在自我激励期间连接在发电机上的易损设备可能在过高或过低的电压和频率下被损坏。

尽管这是自我激励
过程中电感应发电机的缺点，然而一些人把这种方式应用于动态的刹车系统中，帮助在栅栏损失的紧急情况时控制转子速度。

因此，适当的选择电容和电阻器可以在栅栏损失和机械刹车故障期间控制风轮机速度。

3.2 稳态表现。

稳态分析中关键是理解哪些条件对自我激励有增强或削弱作用。

如上面解释的那样，自我激励可能是一件好事情也可能是一件坏事情，这取决于我们遇到什么样的形势。

图2为一个电容器补偿电感应发电机。

如上所述，自我激励操作要求必须保持完全的无功平衡。

S Y +'M Y +'R Y =0 （1）
S
Y =电容器节点的有效输入 'M Y =磁化部分的有效输入
'
R Y =转子节点的有效输入
方程式1的实部和虚步可以被扩展为方程式2 和3。

（2）
图2.自我激励方式下的等效电路
图3. 典型的磁化特性
S
L=渗漏电感
LR
'
R =转子阻抗
R
'
L=转子渗漏电感
LR
'
L=阻抗
M
S =操作损失
=操作频率
R =终端负载电阻
L
C =电容器补偿
自我激励的一个重要方面是电感应发电机的磁化特性。

图3所示为一台典型的励磁电感发电机和输出电流之间的关系；这图由实验得来反映了发电机的特性。

图5为电感应发电机的终端电压受电容和负载电阻变化的影响而变化的示意图。

如图5所示，负载电阻不影响终端电压，特别是在发电机转速很高时，但是电容对发电机的输出电压有显著影响。

一个大的电容在转子转动过程中产生较少的电容变化，而较小的电容在转子转动过程会产生很大的电容变化。

如图6所示，对规定的电容来说，改变负载电阻的有效值能调节力矩速度。

自我激励这个概念可以被利用在涡轮机上，如上所述，当它失去对栅栏连接时可以提供动态刹车从而防止飞车现象发生。

只要正确选择电容和负载电阻使其与涡轮机输出电源相匹配，就能在一定的风速范围内来调节阻抗。

3.3 动态反应。

这部分可以在自我激励过程中检查瞬时的变化。

对于这次模拟来说我们选择3.8毫法电容和1.0欧的负载电阻。

驱动力矩的常量被调整为4500纳米。

但是，空气动力学的风轮机特性控制系统不包括在这个模拟中，我们关注的是自我激励的过程。

因此，我们重视方程式电的方面。

图7显示连续时间内转子速度和输出功率的关系。

在这种情况下，电感应发电机由静止启动，速度逐渐增加，直到达到它自身的额定速度。

最初连接栅栏在开始的t = 3.1秒s，栅栏被断开，电感应发电机进入自我激励方式。

在t = 6.375 s时，发电机被再接通到栅栏，终止自我激励。

在自我激励期间转子速度逐渐增加，但是，最后发电机力矩达到4500牛米，并且转子速度变为稳定。

当发电机没有同步而被再接通到栅栏时，在发电机的力矩会突然发生简短的瞬间变化。

这种情况一旦发生，转子速度会与栅栏之前有相同的速度。

图8(a)显示每个时期电压的状况。

它显示最初电压与被连结栅栏后的电压相同。

如图7所示，在自我激励方式下3.1 s<t<6.375 s期间，转子速度逐渐增加，电压逐渐增加，最终频率比60赫兹高一点。

当电感应发电机再次被接通到栅栏时，电压和频率返回额定值。

图8（b）是对图8（a）中t=3.0s和t=3.5s的扩展，举例说明在这期间电压存在的瞬间的变化。

图5. 终端电压对转子速度的影响
图6. RL和C对发电机转速的影响
4．谐波分析
4.1 简化每个时期的谐波。

为了模拟谐波网络的变化，我们用图9（a）中显示的每个时期的线路替换图1 中显示等效电路。

在这电路表现中，h 指示60赫兹或更高频率的谐波，在这里h是60赫兹的整数倍。

因此h = 5 表明第5 谐波（300赫兹），对于风轮机应用来说，电感应发电机、变压器和电容器是三相的字母Y型连接或三角形连接，因此，谐波和第3谐波不存在[5，6] ，即，只是h = 5，7，11，13，17，…，等等存在。

图7. 发电机的输出功率和转子速度
图8 终端电压与时间(a)在自我激励期间的电压(b)在自我激励期间的电压
4.1.1 总线和输入线路。

用大型的动力网络系统来描述连接风机各部分的总线和输入线路。

因此，我们用简单的RL图线来表示。

图9. 等效电路模型的简单谐波分析
4.1.2 变压器
我们认为三相变压器有大约百分之6的电抗被泄露 。

因为一台大的变压器的磁化电杭远远少于渗漏电抗，所以我们只考虑渗漏电抗。

假定变压器的效率在满负荷时大约是百分之98，铜损与核心损失基本相等，铜损失和核心损失大约都占百分之1。

在这个假设下，我们能计算出铜损在全部负载电流占多大比例， 并且我们能确定主要和次级绕组的总电阻。

电容补偿。

变换电容代表风轮机的补偿。

我们考虑的风轮机装有额外的1.9 MV 无功动力补偿。

风轮机按不同的标准进行补偿。

电容器通过电容器里的损失串联电容进行描述。

质量好的电容器阻抗通常非常小。

4.1.4 电感应发电机。

应用1.5兆瓦， 480 V ，60赫兹的电感应发电机，这台风轮机的情况可以被等效电路描述，如图（a ）所示。

这台电感应发电机在任何谐频h 时的谐波可以表示为
h S = h 频率时的谐波
H = 假设谐波频率
s =发电机的同步速度
r =发电机的转子速度
因为h S 都接近于1 ，所以在应用公式时按照h S =1计算。

4.2 稳态分析。

连接系统等效电路的主要谐波通过图9(b)描述。

注意，假设变压器和电感应发电机的励磁电感远远大于损失的电感，并且不对很高谐波情况进行计算。

在这部分中，我们通过对图9进行分析，检查电容器尺寸的变化对等效电路谐波特性的影响, 并且通过计算来解释为什么会出现这些变化。

在这个定理的基础上，我们每次只分析一个因素，把其它的因素都关闭。

对谐波分析来说，基本频率的电压源可以被关上。

在这种情况下，基本频率电压源头是短路的。

图10(a)无功功率的谐波 (b)与无功功率补偿相关的谐波失真
line Z = line R + j line X = 线路阻抗
xf Z = xf R + j xf X = 变压器渗漏阻抗
C Z = c R +()1
jh C ω-=电容器阻抗
gen Z = gen R + j gen X = 发电机阻抗
通过阻抗我们能发现任何电容和谐波频率之间的关系：
对已确定的谐波来说，谐波电流与谐波电压成正比。

因为该数据只由电容器电流的总谐波失真组成， 并且不提供关于个别谐波的信息，我们只能通过对被测量数据进行计算来得到变化谐波的趋势。

图.11(a)一台变压器每时期的等效电路(b) 图解法表示P>0，Q>0。

(c)图解法表示p>0，Q<0。

从图10中我们可以看出当电容器C 被改变时，电路将产生不同频率的共振。

此时两谐波一定会产生谐波电流， 原因可能是谐波源磁饱和或者是在对电容进行补偿时电路产生共振。

4.3 动态模拟。

现在分析在变压器里如何产生谐波。

在大多数实用的风轮机中，变压器是安装在一个衬垫上再与风力发电机连接在一起的。

当变压器饱和时，磁路的非线性特性产生一个非正弦电流。

图11(a)描述一台变压器的每阶段的等效电路。

变压器的铁芯损失通常被表示为等效抵抗，类似于磁化电杭。

在这项研究中，变压器的铁损非常小，所以被忽略。

磁化了的磁链中电压和频率成正比：
'M E = 磁化的电压
'M λ= 磁链
B ω = 基础频率 通过公式7可以发现变压器的磁链。

磁链和励磁电感'
M L 之间存在上述关系是因为磁化电流是非线性的。

当磁化电流很低的时，磁化电流也随着改变，但是最终达到饱和时，开始非线性的特性； 这时进一步增加磁化电流会产生更小的流联系。

在饱和区，如图12所示，由于非线性的磁化电感，将产生非正弦的输出电流。

图12 一台变压器在低负荷状态下的输出电压和电流
有两种运行方式能引起饱和。

第一种方式是当变压器在很高的电压电平操作时。

这里举的例子中操作变压器负载很小。

因此，在暴露于高电压的磁化分部将生产较大的磁化电流。

能引起高饱和的第二种运行方式是变压器操作领先功率因数。

交叉磁化电抗的电压可以表示：
line Z =line R + j line X =线路阻抗连接变压器电压
1Z = 1R + j 1X =初级绕组阻抗变压器
1R =2R = /2xf R =主要的电阻和变压器的次级绕组
1X =2X = /2xf X =主要的渗漏电抗和变压器的次级绕组
S V = 电压
1I =初级绕组电流
line X =线电抗
line R =线电阻
在这个例子中，我们对简单的情况通过图11(b)和11(c)进行分析，并且利用一些插图简化等效电路。

图11(a)描述的是一个理想变压器的泄漏阻抗。

在图11(a)中，实际功率P 与无功功率是相互联系的。

当p > 0 ，q < 0 时，'M E < S V ，当 P > 0， q > 0时 ，'
M E < S V 。

文章来自：
北京信息科技大学校园网-图书馆藏-电子期刊-美国机械工程师学会电子期刊全文数据库 作者和文献出处： E. Muljadi ， C. P. Butterfield
National Renewable Energy Laboratory, Golden, Colorado 80401
H. Romanowitz
Oak Creek Energy Systems Inc.,Mojave, California 93501
R. Yinger
Southern California Edison,Rosemead, California 91770
付：外文翻译
电火花加工
电火花加工法对加工超韧性的导电材料（如新的太空合金）特别有价值。

这些金属很难用常规方法加工，用常规的切削刀具不可能加工极其复杂的形状，电火花加工使之变得相对简单了。

在金属切削工业中，这种加工方法正不断寻找新的应用领域。

塑料工业已广泛使用这种方法，如在钢制模具上加工几乎是任何形状的模腔。

电火花加工法是一种受控制的金属切削技术，它使用电火花切除（侵蚀）工件上的多余金属，工件在切削后的形状与刀具（电极）相反。

切削刀具用导电材料（通常是碳）制造。

电极形状与所需型腔想匹配。

工件与电极都浸在不导电的液体里，这种液体通常是轻润滑油。

它应当是点的不良导体或绝缘体。

用伺服机构是电极和工件间的保持0.0005~0.001英寸（0.01~0.02mm ）的间隙，以阻止他们相互接触。

频率为20000Hz 左右的低电压大电流的直流电加到电极上，这些电脉冲引起火花，跳过电极与工件的见的不导电的液体间隙。

在火花冲击的局部区域，产生了大量的热量，金属融化了，从工件表面喷出融化金属的小粒子。

不断循环着的不导电的液体，将侵蚀下来的金属粒子带走，同时也有助于驱散火花产生的热量。

在最近几年，电火花加工的主要进步是降低了它加工后的表面粗糙度。

用低的金属切除率时，表面粗糙度可达2—4vin.(0.05—0.10vin)。

用高的金属切除率[如高达15in3/h(245.8cm3/h)]时，表面粗糙度为1000vin.(25vm)。

需要的表面粗糙度的类型，决定了能使用的安培数,电容,频率和电压值。

快速切除金属（粗切削）时，用大电流,低频率,高电容和最小的间隙电压。

缓慢切除金属（精切削）和需获得高的表面光洁度时，用小电流,高频率,低电容和最高的间隙电压。

与常规机加工方法相比，电火花加工有许多优点。

1 . 不论硬度高低，只要是导电材料都能对其进行切削。

对用常规方法极难切削的硬质合金和超韧性的太空合金，电火化加工特别有价值。

2 . 工件可在淬火状态下加工，因克服了由淬火引起的变形问题。

Electrical discharge machining
Electrical discharge machining has proved especially valuable in the machining of super-tough, electrically conductive materials such as the new space-age alloys. These metals would have been difficult to machine by conventional methods, but EDM has made it relatively simple to machine intricate shapes that would be impossible to produce with conventional cutting tools. This machining process is continually finding further applications in the metal-cutting industry. It is being used extensively in the plastic industry to produce cavities of almost any shape in the steel molds.
Electrical discharge machining is a controlled metal removal technique whereby an electric spark is used to cut (erode) the workpiece, which takes a shape opposite to that of the cutting tool or electrode. The cutting tool (electrode) is made from electrically conductive material, usually carbon. The electrode, made to the shape of the cavity required, and the workpiece are both submerged in a dielectric fluid, which is generally a light lubricating oil. This dielectric fluid should be a nonconductor (or poor conductor) of electricity. A servo mechanism maintains a gap of about 0.0005 to 0.001 in. (0.01 to 0.02 mm) between the electrode and the work, preventing them from coming into contact with each other. A direct current of low voltage and high amperage is delivered to the electrode at the rate of approximately 20 000 hertz (Hz). These electrical energy impulses become sparks which jump the dielectric fluid. Intense heat is created in the localized area of the park impact, the metal melts and a small particle of molten metal is expelled from the surface of the workpiece . The dielectric fluid, which is constantly being circulated, carries away the eroded particles of metal and also assists in dissipating the heat caused by the spark.
In the last few years, major advances have been made with regard to the surface finishes that can be produced. With the low metal removal rates, surface finishes of 2 to 4 um. (0.05 to 0.10um) are possible. With high metal removal rates finishes of 1 000uin. (25um) are produced.
The type of finish required determines the number of amperes which can be used, the capacitance, frequency, and the voltage setting. For fast metal removal。