CPPM混合励磁同步电动机的基本原理与特性

CPPM混合励磁同步电动机的基本原理与特性
TAKAYUKI MIZUNO, KAZUTOSHI NAGAY AMA,
TADASHI ASHIKAGA and TADAO KOBAY ASHI
日本明电舍公司（MEIDENSHA CORP.）
摘要永磁同步电动机在工业上得到了广泛应用。

众所周知，由于不需要励磁输入，电机
运行效率高。

然而，由永磁材料特性决定的磁通大致保持恒定，导致永磁电机的气隙磁场
难以调节。

另一方面，电励磁同步电动机的气隙磁场容易调节，但在额定负载时励磁铜耗
较大。

为使磁通易于控制并改善传统同步电机的性能，作者提出了一种带永磁体和励磁绕
组的混合励磁同步电动机（HSY），HSY的主要优点有：①无刷（免维护），②所需的励
磁容量很小（高效率），③容易实现较强的磁场控制等。

正因如此，混合励磁同步电动机
在不同领域都有良好的应用前景。

本文主要讨论和分析混合励磁同步电动机的基本原理与
特性。

SUMMARY Permanent magnet type synchronous machines have been widely used for industrial
applications. It is commonly known that they are operated at high efficiency since no excitation
input is required. However, it is difficult to control the air-gap magnetic flux, because the
magnetic flux is determined by the property of the permanent magnet and approximately kept
constant. On the other hand, synchronous machines with the field winding make it easy to control
the air-gap magnetic flux. But the copper loss of the field winding becomes large at the rated
load.
In order to realize the magnetic flux control easily and improve the performance of the conventional synchronous machine, we propose a hybrid excitation type synchronous machine
(HSY) with the permanent magnets and the field winding. Advantages of HSY are (1) it has no
brushes (maintenance free), (2) required excitation input is small (high efficiency), (3) it is easy
to get a sufficient magnetic flux control, and others. Therefore, HSY has a great possibility of use
for various applications.
In this paper, basic principles and characteristics of HSY are mainly discussed and made clear.
关键词同步电机，永磁，励磁绕组，混合励磁，磁场控制，有限元方法
Keywords: Synchronous machine; permanent magnet; field winding; hybrid excitation; field
control; finite element method.
1.引言
与其它旋转电机相比，永磁同步电动机（PMSY）的特点是无刷设计，并且不需要电励磁，可以实现高效率。

正因如此，随着稀土永磁材料的出现，永磁同步电动机在工业领域得到了广泛应用，而且容易制造出数十千瓦的PMSY。

然而，PMSY也有明显的缺点。

如前述，由于永磁体特性所决定的电机气隙磁场几乎不变，绕组感应电压随转速变化，这妨碍了作为电动机使用时的恒输出运行，或作为发电机使用时的恒压运行。

对于电动机，可采用具有弱磁控制的嵌入式永磁（flush-magnet）电机实现宽范围的恒输出运行。

然而，若采用高性能的稀土永磁，即使在空载情况下，也需要很大的电枢电流来实现弱磁控制，这意味着电机轻载时的性能会变坏。

此外，由直流电供电的PMSY需要按其额定容量选择晶闸管和逆变器，从而加大了体积。

Permanent magnet synchronous machines (PMSY) feature brushless design, and need no excitation which provides higher efficiency compared to other types of rotating machines. Because of this, PMSY have found a wide industrial application in a variety of fields, and with the advent of rare-earth magnets, PMSY of several tens
of kilowatts are easily manufacturable. However, PMSY suffer from a considerable drawback. Since magnetic flux is dictated by the characteristics of the permanent magnet being nearly constant, voltage induced in windings varies with the number of revolutions, which hinders constant-output operation when used as a motor or constant-voltage operation when used as a generator. In case of motors, constant-output operation in a wide range is achieved by using flush-magnet motors with field-weakening control [l,2]. However, when employing high-performance magnets such as rare-earth magnets, large armature current is required for this field-weakening control, even with no load, which means deterioration in performance at light-load operation [3]. Besides, PMSY-based dc power plants [4] require choppers and converters, according to the rated capacity, with a consequent large size.
另一方面，通过通入励磁绕组的直流励磁电流，电励磁同步电动机（FWSY）可以容易地控制气隙磁通，于是能解决前述PMSY与磁场相关的控制问题，特别是对于基于电力供电的FWSY，采用小体积、低容量的励磁电源，可以方便地实现电压控制。

然而，对于FWSY，需要额外增加如励磁绕组、电刷和光滑环，这将导致设计上的复杂、励磁损耗带来的效率恶化以及需要维护。

尽管与PMSY不同，然而FWSY也有本身的问题。

On the other hand, field-winding synchronous machines (FWSY) allow for easy control of magnetic flux by means of dc field current flowing through field winding, thus alleviating the aforementioned problems of PMSY related to the field control. Particularly, it is common knowledge that with FWSY-based power plants. V oltage control can easily be performed by a small-size low-capacity exciter. In case of FWSY, however, additional parts are required such as field windings, brushes and slip rings. This results in complicated design, deterioration of efficiency due to magnetic loss, and the need for maintenance. Thus, FWSY have their own problems, even though different from those of PMSY.
于是可以说，同步电动机可能的应用范围主要取决于其励磁方案。

也就是说，如果在拟开发的同步电机中结合PMSY和FWSY的优点，同步电动机的应用范围将被极大拓宽。

本文中，我们提出一种带有永磁励磁和直流励磁绕组励磁的混合励磁同步电动机（以下简称为HSY），并从理论和试验两方面讨论它的运行原理、基本特性以及应用。

Therefore, we can say that the possible range of application of synchronous machines depends heavily on excitation schemes, and that use of synchronous machines could be widened significantly if a synchronous machine was developed that combines advantages of permanent magnets and field windings. In this context, we have proposed a hybrid excitation synchronous machine featuring both permanent magnets and dc field windings [5, 6] (below referred to as HSY), and discussed its operating principle and basic characteristics in theoretical and experimental terms, as well as possible applications.
首先，本文介绍了带有永磁极和励磁绕组HSY的基本结构、采用直流励磁电流对气隙磁通有效控制以及与其它同步电机相比较的优缺点。

HSY的显著特点是它的永磁极磁路和励磁绕组磁路基本上相互独立，并可以用较小的励磁安匝实现对气隙磁通的合理调节。

因此，HSY在能提供免维护运行的同时还可以确保高效率的磁控制。

本文研究了基于有限元分析的一个实用二维有限元模型，并分析了样机的空载和负载特性。

为了建立实际系统中有限元计算结果和控制性能之间的关系，电压方程和转矩公式用于负载特性分析中。

其次，将分析值与空载和负载的测量值进行比较，同时证明了HSY作为同步电动机和同步发电机使用的可行性。

First, basic construction of HSY is described that uses both permanent magnets and field windings, and ensures control of air gap magnetic flux by means of dc field current, as well as its operating principle and comparative pros and cons against other synchronous machines. The distinctive feature of HSY is that magnetic circuits of permanent magnets and field windings basically are independent of each other, and appropriate
regulation of the gap magnetic flux can be performed with a small mmf of field winding. Hence, HSY ensures high-efficiency magnetic control while providing for maintenance-free operation. A practicable two-dimensional model was developed for finite element analysis, and both load and no-load characteristics of the prototype machine were analyzed. V oltage equations and a torque formula were employed in load characteristics analysis to establish the relation between FEM results and control performance in an actual system. Further, measured values of load and no-load characteristics were compared to analytical results, and the feasibility of using HSY as a synchronous motor [7] or a synchronous generator [8] was proved.
2. HSY 的基本结构和原理
2.1 基本结构
HSY 的基本结构如图1所示，图1（a ）、（b ）分别为HSY 的定子和转子。

HSY 的电枢与单极同步电机（homopolar synchronous machine ）基本相同，电枢铁心分成两部分，在铁心的中间嵌放了励磁绕组，在励磁绕组中通入直流励磁电流可以有效地控制气隙磁通。

通过导磁机壳将两部分铁心进行机械和磁路上的耦合。

定子铁心槽内安放传统的三相交流绕组。

Basic construction of the proposed HSY is shown in Fig.1. Specifically, Figs. 1(a) and (b) show the cross section of HSY and the design of the rotor, respectively.
HSY’s armature is basically the same as that of a homopolar synchronous machine [9]. The armature core is divided in two, and field winding is mounted in a space in the central part of the core. Passing dc current (field current) through this winding ensures appropriate regulation of the gap magnetic flux. The two armature cores are coupled, mechanically and magnetically, through an external back yoke. Also, slots are provided in the armature core to lay conventional three-phase ac windings.
类似，转子部分也分成两段。

为简化起见，图中转子左边和转子右边分别称之为N 极边和S 极边。

在N 极边，气隙由交替的永磁极和铁心叠片的凸极部分构成，以下由永磁极构成的极简称为磁极，由铁心构成的极简称为铁极。

S 极边的极配置是这样安排的，即S 极边的磁极与N 极边的铁极同轴，反之亦然。

同样，通过转子内部磁轭将两段转子铁心进行机械和磁路上的耦合起来。

Similarly, the rotor unit also is divided in two. For the sake of simplicity, the left-hand side and the right- hand side in the diagram will be referred to as N-pole side and S-pole side, respectively. At the N-pole side, the air gap is formed with alternate permanent magnet poles, and salient parts of the laminated core. Below, the poles with magnets will be referred to as magnet poles, and the poles formed by the core will be referred to as core poles. The pole configuration at the S-pole side is arranged so that S-side magnet poles are coaxial to N-side core poles, and vice versa. Also, both rotor cores are coupled mechanically and magnetically through the internal back yoke.
铁极 永磁极 导磁机壳 直流励 磁绕组 交流绕组 定子铁心 图1 HSY 的基本结构
（a ）定子 （b ）转子 N
2.2 运行原理
由于永磁体的高磁阻，在图1（a ）电枢中间的励磁绕组中通入励磁电流，几乎所有的磁通都走铁极。

这样所产生直流磁通的路径为：导磁机壳→S 极边电枢铁心→S 极边铁极→转子轭→N 极边铁极→S 极边电枢铁心→导磁机壳。

改变励磁电流的大小和方向可以控制直流磁通的大小和方向。

When field current flows through the field winding in the central part of the armature as shown in Fig. l(a), almost all the magnetic flux comes through the armature core poles because the permanent magnets show a high reluctance. Thus, dc magnetic flux is generated in the circuit of ( armature back yoke →S-side armature core →S-side core pole →rotor back yoke →N-side core pole →N-side armature core →mature back yoke).The magnitude and direction of this magnetic flux can be controlled in agreement with the magnitude and direction of the field current.
另一方面，如果永磁体具有大矫顽力，如采用稀土永磁材料，某些外部磁场作用下不会出现退磁问题，在磁极方向上产生几乎为恒值磁通，并确认是安全的。

因此，不考虑励磁电流的漏磁通及其它漏磁通，可以大致认为从N 极边磁极出来的磁通通过导磁机壳进入S 极边的磁极。

On the other hand, if permanent magnets with large coercive force, such as rare-earth magnets, are employed, there is no problem of demagnetization under application of some external magnetic field which makes it safe to believe that nearly constant flux is generated in the direction of the magnet polarity. Therefore, ignoring the magnetic flux produced by field current, and allowing for some leakage flux, it may basically be considered that the flux that goes out from the N-side magnet enters into the S-side magnet via the armature back yoke.
于是，可以认为励磁磁通和永磁磁通走相互独立的路径，然而实际上这二个磁通合成构成气隙磁通，通过励磁电流控制实现对气隙磁通的合理调节，分别讨论如下：
Thus, magnetic flux of field winding and that of the permanent magnet may be considered as going along independent routes. In practice, however, these fluxes combine, and appropriate adjustment of the air-gap flux can be performed through field current control, as will be shown below.
（1）无励磁情况（励磁电流I f = 0）
这种情况下，气隙磁通由永磁材料的特性和电机磁路，即仅由永磁极决定。

转子旋转时，电枢绕组切割N 极边，或S 极边下的磁通，在绕组中感应电流。

此时磁通的方向如图2（a ）所示（图中磁通的路径是示意的，没有画出电枢铁心和导磁机壳）。

In this case, the gap flux is governed by characteristics of permanent magnets and magnetic circuit, that is, it depends on magnet poles only. When the rotor is rotating, however, the armature winding cuts across magnetic flux at either the N-pole ，or S-pole side, and current is induced in the winding. Hence, the direction of magnetic flux is as shown in Fig. 2(a). (In the diagram, the magnetic flux route is shown schematically; the armature core and back yoke are omitted.)
图2 HSY 运行原理 (a) 无励磁电流 (c) 增磁励磁电流
(b) 去磁励磁电流
（2）去磁情况（励磁电流I f < 0）
这里励磁电流的方向如图2（b）所示，永磁体产生的磁通与情况（1）相同，并与励磁磁通相叠加。

如前所述，几乎所有的励磁磁通全部走铁极，但S极边与N极边的磁通方向相反，于是在电枢绕组中感应一个反向电压分量，这意味着感应电压比无励磁电流情况低。

因此，气隙磁通相应减小。

此时的合成磁通（永磁极磁通和励磁磁通产生的）路径相当复杂，特别地，永磁极磁通和铁极磁通相等时的磁场分布如图2（b）所示。

Here, the direction of field current is as shown in Fig. l(a). The flux produced by the magnets is the same as with case (l), while the flux produced by field winding is superimposed. As was stated in the foregoing, almost all the flux produced by field winding goes through core poles. However, magnetic fluxes at the S-pole and N-pole sides are opposing each other, and a reverse component arises in the voltage induced in the armature winding, which means that the induced voltage is lower compared to the case of zero field current. Therefore, the gap magnetic flux becomes weakened accordingly. The distribution of the resulting magnetic flux (produced by magnets, and field winding) is rather complicated. Particularly, when fluxes of core poles and of magnet poles are of the same magnitude, this distribution is as shown in Fig. 2(b).
（3）增磁情况（励磁电流I f > 0）
励磁电流方向与如图2（c）方向相反。

此时在N极边和S极边的磁通方向相同，电枢绕组中感应电压高于励磁电流为零时的情况。

图2（c）显示这种情况下的磁通分布，图中永磁极和铁极的磁通相等。

上述原理表明，通过改变直流励磁电流，可以连续地控制HSY的气隙磁通和绕组感应电压。

Here, the direction of field current is opposite compared to Fig. 1(a). In this case, magnetic fluxes at the S-pole and N-pole sides are of the same direction, and the voltage induced in the armature winding is higher compared to the case of zero field current. Therefore, the gap magnetic flux becomes weakened accordingly. Shown in Fig. 2(c) is the flux distribution in the case that fluxes of core poles and of magnet poles are of the same magnitude.
The above principle suggests that the gap flux and the voltage induced in armature winding of HSY can be controlled adequately and continuously by varying dc field current.
2.3 HSY的优缺点
上面介绍了HSY的结构和运行原理，其优点和缺点总结如下：
（1）电机体积
对于HSY来说，为了产生励磁磁场，需要励磁绕组和导磁机壳，因此，若电机容量相等，HSY的体积要比PMSY的大。

然而，直流励磁可以使HSY的气隙磁密比PMSY的大，同时可用机座作为导磁机壳，这样可使HSY与PMSY的体积设计得大致相当；另一方面，与FWSY相比，HSY消除了转子绕组、电刷和滑环，因此减小了电机体积。

With HSY, field winding and back yokes are required to generate dc magnetic field. Thus, it may be thought that, generally, HSY will be of larger size than PMSY, with the capacity being equal. However, dc magnetic field makes it possible to increase the gap magnetic flux density compared to PMSY, while frames can be employed as back yokes. Nevertheless, it seems possible to design HSY of the same size as PMSY. On the other hand, if compared to FWSY, the proposed HSY eliminates rotor windings, brushes and slip rings, which contributes to smaller design.
（2）控制单元
HSY作为电动机使用时，由于需要直流磁场，与普通PMSY的驱动单元相比，应额外增加一个励磁电路。

如前所述，HSY所需要的励磁容量很小，这样一个微小的励磁电路可放在电动机的驱动电路中，与PMSY相比，电路体积并没有明显增加；从控制效率方面讲，由于新型HSY采用励磁绕组进行磁场控制取代了传统的弱磁控制，控制效率大为改善；此外，HSY作为发电机使用时仅需要一个小的励磁电路，这意味着控制单元很小，而PMSY 则需要控制芯片和开关管。

与FWSY相比，HSY用永磁提供所需的励磁安匝，降低了励磁输入，从而减小了控制单元体积。

Since HSY requires dc magnetic field, an exciter with control circuitry is needed in addition to the conventional PMSY drive unit when employed as a motor. However, as was explained above, HSY requires relatively small excitation, and a miniature exciter can be built into the drive unit of the motor without significant increase in size compared to PMSY. Speaking in terms of efficient control, the new HSY offers considerable improvement, because in addition to magnetic field control with field winding, a conventional control scheme using armature current such as field-weakening control [l, 2] can be implemented as well. On the other hand, when used as a generator, PMSY calls for choppers and converters [4], while HSY requires only a small-size low-capacity simple exciter [8], which means a considerably smaller control unit. If compared to FWSY, much of the required mmf is provided by permanent magnets, which implies lower excitation input, and smaller size of control unit.
（3）励磁输入和效率
事实上，HSY额定负载运行时励磁损耗相当大，与PMSY相比效率下降。

然而，HSY 需要的励磁容量相当小（样机只需要160W），总效率并没有明显下降。

特别地，当电机轻载实现弱磁控制时，HSY的励磁损耗可忽略不计，与此同时，PMSY采用电枢电流弱磁控制的铜损耗则很大，效率下降。

因此，可使用HSY改善电机轻载时的效率。

与FWSY相比，HSY需要的励磁输入很小，总效率会有所提高。

The fact is that when HSY is operated at rated load, magnetic loss is rather high, and efficiency drops compared to PMSY. However, since magnetic field requires relatively low power (at most 160 W with prototype machine to be described below), the overall efficiency is not likely to be degraded significantly. Particularly, when performing field-weakening control under light loads, magnetic loss is negligible with HSY, whereas in case of PMSY, copper loss due to the armature current performing weakening-field control prevails and efficiency drops [3]. Therefore, the use of HSY is assumed to improve efficiency in the light-load area. Compared to FWSY, the proposed HSY requires smaller excitation input, and the overall efficiency is expected to improve.
可用不同的方式考察HSY的优缺点，取决于比较的角度。

总的来说，HSY结合了PMSY 和FWSY两种电机的特性，是一种中间的解决方案，适用于有磁场控制需求的场合。

Thus, pros and cons of HSY might be considered in different ways depending on the basis of comparison. On the whole, HSY can be classified as an intermediate solution combining characteristics of both PMSY and FWSY that is appropriate for applications calling for active magnetic control.
2.4 样机
样机的主要技术数据见表1。

分析原理时，作为例子讨论的是6极电机，但电机设计时极数是可以灵活选择的。

综合考虑电机的额定功率、电源频率和每极的磁体尺寸，样机采用了8极方案。

与文献[6]所报告的结果一样，磁体型式、励磁绕组的匝数和其它一些参数作了修正。

Brief specifications of the prototype machine are listed in Table 1. When explaining the operations principle,
example, but designs are feasible with an
arbitrary number of poles. With the prototype
machine, an 8 pole design was used from
considerations of balance between rated output,
power source frequency, and size of magnet per
pole. Also, type of magnet, number to turns of
field winding, and some other parameters were
revised in accord with the results reported in [6].
3. HSY的特性
表1样机磁场的有限元分析如下。

对于HSY，磁通的路径是三维的，这需
要精确的三维分析。

然而，从实用的角度出发，这里采用二维非线性分析。

Described below is FEM analysis of the magnetic field system of the prototype machine as specified in
Table 1. With HSY, the route of magnetic flux is three-dimensional, which calls for strict 3-D analysis. For the
sake of practicability, however, a two-dimensional nonlinear analysis was performed.
3.1 分析模型与假定
在HSY中，磁极和铁极是交替排列的，且样机为分数槽电枢绕组，应考虑选择一个一对极区域的分析模型；此外，励磁绕组产生的磁动势绝大部分作用于气隙，故近似认为该磁动势是仅作用在气隙处的一个等效磁动势。

基于上面假定，可以采用二维模型完成下面的分析。

文献[6]给出了一个可接受的空载特性分析模型，即一个一对极定子区域，转子处于任意位置，通入电流流过气隙两端以等效励磁绕组磁动势。

上面的方法不能用于负载特性分析，原因在于不能确定周期性的边界条件。

Since magnet poles and core poles are located alternately in HSY, while the armature winding of the
prototype machine is fractionated by slots, an analytical model should be considered in terms of 2-pole fragment.
Besides, the mmf produced by field winding acts mostly in the gap, and can be approximated with the equivalent
force applied in the gap only. With the above assumptions made, adequate analysis can be performed using a
two-dimensional model. As shown in [6], acceptable analysis of no-load characteristics can be conducted provided
the cross section of the 2-pole fragment is considered at an arbitrary location on the rotor, while passing electric
current through both ends of the gap to obtain mmf of the field winding. However, this approach cannot be used
for analysis of load characteristics because it proves impossible to specify periodic boundary conditions.
为此，引入二个分离模型，一个是含N边、S边的磁极模型，另一个是仅含铁极模型，如图3（a）、（b）所示。

这样气隙磁通可从两个模型分析结果合成得到，并用于电机特性的计算，无论电机是否加负载。

这种方法是合理的假设：即磁通从N极边磁极通过导磁机壳流向S极边磁极；与此同时，磁通从S极边铁极流向N极边铁极。

实际上，不能用图（3）所示的模型合理计算通过电枢和转子轭的磁通，这个模型可以视为导磁机壳足够厚，磁路不易饱和。

As a result, two separate models were provided involving N-side and S-side magnet poles, and core poles,
respectively, as shown in Figs. 3(a) and (b). As a result, the gap magnetic flux was found by combining analytical
results to be then used in calculation of characteristics no matter what load was applied. This method is justified
assuming that the flux out flowing from the N-side magnet pole goes to an S-side magnet pole via back yoke,
while similarly, the flux out flowing from the S-side core pole goes to the N-side core pole. Actually, magnetic flux going through the armature and rotor back yoke cannot be accounted for properly in terms of the model shown in Fig. 3. This model, however, may be recognized as acceptable since the back yoke is thick enough, and not susceptible to magnetic saturation.
如图所示，等位周期性边界条件施加在边界线上，零磁位的约束条件施加在铁心内外圆周上。

另外，用两极之间的电流表示励磁绕组磁动势，对应于各极之间磁场的大小和方向。

对于空载下的两个模型，这些电流假定为在各自槽内的电枢电流。

事实上，N 极边和S 极边由相同的励磁绕组励磁，这意味着模型中的磁动势只是实际磁动势的一半。

在下面的讨论中，为了避免在模型和样机涉及励磁电流和磁动势之间发生混淆，所有的值都转换为用样机的值来表示。

As shown in the diagram, periodic boundary conditions of equal potential are imposed at the boundary lines, while limiting conditions of zero potential are imposed along the inner and outer circumferences of the core. Also, mmf of the field winding is represented as electric currents in the gap between poles, with regard to magnitude and direction of magnetic field at respective poles. These currents are assumed to be armature currents in respective slots for both models under no-load operation. In fact, however, the N-pole side and the S-pole side are excited through the same field winding, which means that this model shows mmf that is only half the actual value. Therefore, to avoid confusion between the model and the prototype machine in the following considerations involving field current and mmf, all the values will be converted in terms of the prototype machine.
3.2 空载特性分析
作为图3所示空载模型分析结果的例子，图4画出了励磁
电流10A 时的磁力线分布图。

由于空载，永磁极和励磁绕组
所产生的电动势共同作用于所有的磁极，两个模型中所画的磁
通几乎相同。

在电机空载运行条件下，磁通的大小随励磁电流
而变，然而所画的磁通模型却保持不变。

正是由于这个原因，
本文省去了不同励磁电流下的磁场分布图。

Shown in Fig. 4 are magnetic flux plots at the field current of 10 A, as
examples of analytical results obtained for the models shown in Fig. 3 under
no-load operation. With no-load, electromagnetic forces produced by
permanent magnets and field winding are applied uniformly at all poles, and 图3 二维有限元分析模型
图4 空载磁场分布
the flux plots are nearly the same for both models. Also, in case of no-load operation, the magnitude of magnetic flux varies with field current, but the pattern of magnetic flux plot remains unchanged. For this reason, flux plots for different field currents have been omitted from this paper.
采用有限元方法计算了励磁电流为-5A、0、5A时电机的气隙磁密，计算结果见图5，从左列至右列分别为磁极模型和铁极模型的气隙磁密分布。

所有磁密分布只考虑一个周期，起点从模型的左边端点开始。

FEM analysis was performed for field winding under currents of -5, 0 and 5 A to find flux density distribution in the air gap. The results are given in Fig. 5, where the left and right columns pertain to flux density distribution for the models of magnet poles and core poles, respectively. With all flux density distributions, one period was considered starting from the left end of the model.
对于实际电机，N极边磁极与S极边铁极对齐，反之亦然。

正由于此，电枢绕组的感应电压正比于磁通密度（图中左列和右列）的合成值（平均值），这一合成值的基波分量称之为等效气隙磁密，此等效气隙磁密也在图5中给出了。

With the actual machine, N-side magnet poles are in line with the S-side core poles, and vice versa. Because of this, the voltage induced in armature winding is directly proportional to the resultant value (average value) of the flux densities given in the left and right columns in the diagram. The fundamental component of this resultant value will be referred to as equivalent gap flux density. The values of this equivalent gap flux density are given in Fig. 5 as well.
显而易见，当励磁电流变化时，永磁极下的磁密几乎不变，而铁极处的磁密则是变化的。

这表明，合成磁密，即等效气隙磁密是可控的。

As is evident from Fig. 5, when varying field current magnetic flux remains nearly unchanged at magnet poles while changing at core poles, which means that the resulting value, that is equivalent gap flux density can be controlled.
图5 空载分析结果
图6给出了不同励磁电流时上述分析的结果，一个等效气隙磁密曲线。

由图显见，等效气隙磁密正比于励磁电流，尔后达到在最大电流时的极限值，那是由于电枢铁心凸极部分磁
饱和所引起的。

Presented in Fig. 6 are results of the above analysis with varying field current, in the form of an equivalent flux density curve. As is obvious from the diagram, the equivalent gap flux density varies linearly with field current, but then reaches its limit at large currents, which is attributable to magnetic saturation at the armature core's salient parts.
图6 等效气隙磁密图7 导磁机壳磁密另一方面，气隙N极边和S极边的合成磁通是环绕导磁机壳的直流磁通。

这个磁通值可以容易地从图5中永磁极的磁密和铁极磁密之间的差值和气隙面积求出。

也就是说，导磁机壳的磁通密度可以由该磁通和导磁机壳的截面积计算得到。

图7给出了导磁机壳磁密与励磁电流的关系曲线。

由图可见，通过导磁机壳的直流磁密随着等效气隙磁密的增加而下降，反之亦然。

励磁电流为零时，导磁机壳的磁密为 1.2T。

由于导磁机壳磁饱和的原因，实际样机气隙磁密的有效控制区间是I f ≥0。

因此，为了进一步降低气隙磁密，从考虑磁饱和的角度出发，应合理选择导磁机壳的厚度。

On the other hand, resulting flux at the N-side or S-side of the gap is a dc flux circulating through the back yoke. The value of this flux can easily be deduced from the difference between flux densities at magnet poles and core poles shown in Fig. 5, and the gap area. Also, the flux density at the back yoke can be found from this flux, and the back yoke cross-section area. The flux density curve vs. field current is shown in Fig. 7 for the armature back yoke. As may be seen from the diagram, dc flux going through the back yoke decreases with increasing equivalent gap flux, and vice versa. With zero field current, armature back yoke flux density is 1.2 T. Because of magnetic saturation at the back yoke, with the actual prototype machine, efficient control of the equivalent gap flux is feasible at field current I f ≥0. Therefore, if further lowering of equivalent gap flux is required, appropriate thickness of the back yoke must be selected with regard to magnetic saturation.
上述计算结果是基于二维非线性分析，没有考虑导磁机壳的饱和问题。

因此，与反向励磁电流区间的测量值（下面讨论）存在一个显著差异。

The above calculated results were based on two-dimensional nonlinear analysis, which did not allow for magnetic saturation at the back yoke. Hence, there is a significant discrepancy with measured results (to be discussed below) in the area of negative field current.
3.3 负载特性的分析方法
HSY可用作电动机和发电机。

然而，本文着眼于分析HSY的运行原理和基本特性，这样做有助于弄清楚电枢绕组感应电压和电流之间的相位关系。

基于这个目的，重点放在分析HSY负载同步运行时的感应电压和电流。

特别地，这种同步化几乎可以实现使发电机的功率因数为1，或如永磁型交流伺服电动机广泛使用的控制策略（仅通入q 轴电流，以下简称。