# Research on the Brushless Excitation System with Linear Current Amplifier Characteristics

Authors: Wei Fan; Yiqun Fang; Yuanyuan Yang; Xiangsheng Liu; Xiutao Ji
Journal: Mathematical Problems in Engineering
 (2022)

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## Abstract

In terms of improving the dynamic response characteristics of brushless AC synchronous generators, the concept of integrated design of AC exciter and rotating rectifier and their electromagnetic characteristics are studied, and the conditions and judgment methods for determining their operating modes are obtained in theoretical design and simulation design, pointing out that when the brushless excitation system operates in or is close to mode III, i.e., the rectifier always has three or four diodes in each operating cycle. The linear current amplifier characteristics can be basically achieved when the brushless excitation system is operated in mode III or is close to mode III, i.e., the rectifier always has three or four diodes alternating in each operating cycle. The impact of the key parameters of the AC exciter at different rotational speeds and temperatures on the characteristics of the linear current amplifier was explored, and an engineering prototype was manufactured. The related test verified the correctness of the concept of integrated electromagnetic design and simulation calculation. This study provides an engineered design method for enhancing the dynamic response properties of the brushless AC synchronous generators.


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## Body

## 1. Introduction

The brushless AC synchronous generator, which was developed with the rapid development of power electronics technology, is a new type of motor based on the combination of disciplines such as electrical engineering, electronics, and automation control technology [1]. It uses AC exciter and rotating rectifier as the brushless excitation system to replace the traditional carbon brush and slip ring to provide excitation current for the synchronous generator so that the brushless excitation system no longer has moving contacts, thus the maintenance of carbon brush and slip ring can be avoided. In this way, the reliable, safe, and economical operation of the brushless AC synchronous generator can be achieved.The brushless AC synchronous generator is usually composed of two parts: the main motor, which can be used as a generator or motor, and a brushless excitation system. It requires an external DC power supply as the excitation power supply for the brushless excitation system, which is called a two-stage brushless AC synchronous generator; some brushless AC synchronous generators also have the third part, namely, the permanent magnet generator, also called pilot exciter, whose main function is to provide excitation power for the brushless excitation system and drive power for the controller. This form can realize the self-excited pressure build-up of the brushless AC synchronous generator without relying on the external power supply, and it is called the three-stage brushless AC synchronous generator. The structure of the two-stage or three-stage brushless AC synchronous generator is shown in Figure1. The brushless excitation system, composed of the AC exciter and rotating rectifier, is the core part of the synchronous generator to realize brushlessness. The AC exciter is usually designed as a rotating armature electric excitation synchronous generator, and the rotating rectifier is usually designed in the form of three-phase full-bridge uncontrolled diode rectification.Figure 1
Principle of the two-stage or three-stage brushless AC synchronous generator.The function of the brushless excitation system composed of an AC exciter and a rotating rectifier is to convert the exciter’s excitation currentIef to the main motor’s excitation current IF. The stability of the main motor’s external output voltage is mainly achieved by the adjustment of Ief. Therefore, the goal of designing the brushless excitation system is to meet the excitation needs of the main motor under full working conditions, and at the same time, to reduce the burden of the voltage regulator as much as possible and improve the dynamic response speed of the system, Ief is required to have a small range of variation under full working conditions; that is, the brushless excitation system should have the linear current amplifier characteristics [2, 3].Reference [2] proposed and analyzed the design concept of a single-phase AC exciter, studied its operating characteristics in two modes: power generation and start, and concluded that such single-phase AC exciter has linear current amplifier characteristics and approximate constant current source in power generation mode. In the starting mode, the excitation current Ief of the exciter is almost independent of the speed. Reference [4] proposed a magnetic pole structure with additional short-circuit coils from the perspective of improving the starting output capability of the AC exciter, and pointed out that the short-circuit coil will not affect its performance in the DC excitation power generation mode. However, in reference [2, 4], the focus of the research is laid on the starting performance, and the power generation performance of the AC exciter and the rotating rectifier has not been studied. Reference [3] investigated the basic principles of the linear amplifier of brushless excitation systems at constant speeds and pointed out that the reactance load factor XR is the dominant factor for determining the operating modal. Reference [5] mainly studied the commutation process of rotating rectifier and analyzed commutation waveform theoretically. Reference [6] explored the operating modal of the brushless excitation system at constant speed and the magnification and linearity of the current amplifier at different temperatures and different loads. However, references [3, 5, 6] have not studied the typical electrical characteristics and the judgment method of each operating modal and how the operating modal affects the current amplifier characteristics under variable speed conditions. In reference [7], the output characteristics and commutation mechanism of the AC exciter as well as rotating rectifier were analyzed, but the judgment method of each operating modal and how the electromagnetic parameters of the AC exciter affect the operating modal were not examined. Reference [8] analyzed and predicted the commutation voltage drop of the diode in the three-phase full-bridge rectifier bridge and used the optimized structure parameters of the AC exciter to achieve smaller commutation voltage drop and higher output capacity, but the operating modal of the rectifier was not discussed in the article.Although there are a number of researches that have explored the electromagnetic characteristics of AC exciters and rotating rectifiers from different perspectives, they either focus on AC exciters or rotating rectifier. Based on the previous studies, a combination of theoretical analysis and simulation calculation was used in this paper to study the concept and electromagnetic characteristics of the integrated electromagnetic design of the AC exciter and the rotating rectifier, and the conditions and methods for determining its operating modal were summarized. Besides, the influence of the key parameters of the AC exciter at different speeds and temperatures on the linear current amplifier characteristics was analyzed, and it was concluded that when the brushless excitation system works in the modal III or close to this modal, the linear current amplifier characteristics can be basically achieved so that the dynamic response characteristics of the brushless excitation system can be improved.


## 2. Theoretical Design

The following two indicators are usually used to quantitatively describe the linear current amplifier characteristics of the brushless excitation system:(1)IF=K·Ief,ΔK=K1−K2K1×100%,where K is the current amplification, K1 and K2 are the current amplification factors under two different operating conditions, respectively, and △K is the linearity, which is the relative change value of K under the two load conditions. When △K = 0, it means that K is not related to the load state, and the current amplifier is completely linear at this time.


### 2.1. Theoretical Design of the AC Exciter

The load of the brushless excitation system is the excitation winding of the main motor, which is a large inductive load, and its resistance and inductance are represented byRF and LF, respectively. Then the excitation current IF flowing through the excitation winding of the main motor can be approximated as the direct current, and its pulsation component is so small that it can be ignored.When the brushless AC synchronous generator works at different speeds and temperatures and under different loads, the excitation currentIF of the main motor may vary within a relatively large range. Therefore, it is required that the output voltage of the AC exciter should vary within a relatively large range, and to achieve linear output characteristics at the same time, the AC exciter can be designed to work in a linear (unsaturated magnetic circuit) state.After the design of the main motor, since temperature is the only factor that causes the change in the resistanceRF of the excitation winding of the main motor, when the temperature rise leads to an increase in RF, in order to keep IF output unchanged, the output voltage of the AC exciter needs to be increased. Although the output voltage of the exciter can be increased by increasing Ief, it expands the variation range of Ief, which is inconsistent with the design goal. On the other hand, the electromagnetic parameters of the exciter can be appropriately designed, and the commutation reactance Xc of the winding of each phase can be increased, thereby changing the operating modal of the brushless excitation system, and achieving the purpose of increasing the output voltage of the exciter while keeping Ief basically unchanged.(1)
It can be found from references [5, 9] that when the AC exciter is connected to a large inductive load via a three-phase bridge rectifier circuit, the commutation overlap caused by the commutation reactance Xc of the three-phase armature winding results in short-circuit between the two commutation windings, which reduces the average rectified output voltage. The greater the reactive load factor XR, the larger the commutation angle γ, and the greater the loss of commutation voltage drop. The reactive load factor XR is defined as(2)XR=XcRF.When the temperature rises,RF also increases. The smaller the XR, the smaller the γ, and the smaller the loss of commutation voltage drop, which can improve the rectified output voltage.(2)
The potential vector during the stable operation of the exciter is shown in Figure2. According to reference [7], the internal power factor angle ψ has the following relationship with the commutation angle γ:(3)ψ≈γ2.Figure 2
Potential vector during the stable operation of the exciter.It can be known that the smaller theγ, the smaller the ψ, and the smaller the direct-axis current Id; that is, the weaker the D-axis demagnetizing magnetic field, thus, the air gap magnetic field of the exciter increases when Ief remains unchanged and the rectified output voltage is improved.Due to the compensation effect of the above two factors, whenRF increases with the temperature, the corresponding output voltage of the exciter also increases, which is the theoretical basis for the exciter to realize the characteristics of the linear current amplifier.


### 2.2. Theoretical Design of the Rotating Rectifier

In order to deeply analyze the operating characteristics of the three-phase bridge uncontrolled diode rectifier circuit, theoretical analysis was combined with simulation calculation in this paper. The simulated circuit is shown in Figure3. According to the difference in the time interval of commutation current conversion, the external characteristics expressing the rectified voltage and rectified current can be divided into three operating modals.Modal I: the commutation angle γ < π/3, the rectifier always has two or three diode elements working alternately in each operating period; Modal II: the commutation angle γ = π/3, the rectifier always has three diode elements working at any time in each operating period; Modal III: commutation angle π/3 ＜ γ ≤ 2π/3, the rectifier always has three or four diode elements working alternately in each operating period. The electrical characteristics of each operating modal are displayed in Table 1, and the voltage source with a certain internal impedance was used to express the external characteristics of the three-phase full-bridge rectifier. α′ in the table is the delay angle. (4)Ud=U0−Id×Req,U0=32πE,where Ud is the output DC voltage of the rectifier, U0 is the no-load output DC voltage of the rectifier, Req is the equivalent output impedance of the rectifier, and E is the effective value of the three-phase line voltage. The rectifier circuit can be divided into two states, conduction and commutation according to the number of rectifier components that are simultaneously conducting. The commutation state includes two-phase commutation (two-phase short-circuit) and three-phase commutation (three-phase short-circuit). The equivalent circuit is shown in Figure 4.Figure 3
Simulated model of the three-phase full-bridge diode uncontrolled rectifier circuit.Table 1
Three operating modals.
Working modesCommutation angleDelay angleElectrical characteristicsExternal characteristicsConditionReqIγ < π/3α′ = 0Conduction and commutationUd=32/πE−3xγ/πIdXR ≤π/93Xc/πIIγ = π/30 <α′ < π/3Commutation (two-phase short-circuit)2π2/27×Ud2/E2+2Id2xγ2/E2=1π/9 < XR≤π/33Xc/π∼9Xc/πIIIπ/3 < γ ≤ 2π/3α' = π/3Commutation (three-phase short-circuit)Ud=3·32/πE−3·3xγ/πIdπ/3 < XR9Xc/πFigure 4
Equivalent circuit: (a) two-phase conduction equivalent circuit, (b) two-phase commutation equivalent circuit, and (c) three-phase commutation equivalent circuit.
(a)(b)(c)From Figure4(c), it can be seen that the rectifier voltage is 0 because there are four rectifier elements conducting at the same time, resulting in a short-circuit state on the AC side and DC side. This condition can be used as a basis for judging that the rectifier is working in the IIIrd mode, and the expression of the average rectified voltage and current in this mode can be obtained by analyzing the circuit as follows:(5)Ud=92/πcosα′−π/6−9/πIdxγId=Ex/2xγcosα′−π/6−cosα′+γ−π/6..By solving the two-phase commutation equivalent circuit, the short-circuit current amplitude can be obtained:(6)Is2=2E2Xγ.To facilitate analysis, the external characteristics of the rectifier are expressed by per-unit values, andU0 and Is2 were used as the base value of voltage and current, respectively. The equation of the external characteristics of the rectifier expressed by per-unit value is shown in Table 2, and Figure 5 shows the external characteristic curve of the rectifier expressed by per-unit value.Table 2
The external characteristics expressed by per-unit values.
Working modesExternal characteristicsConditionIUd∗=1−1/2Id∗0<Id∗≤1/2II4/3Ud∗2+Id∗2=11/2<Id∗≤3/2IIIUd∗=3−3/2Id∗dId∗>3/2IFigure 5
External characteristic curve (expressed by per-unit value).It can be seen from Tables1 and 2 and Figure 5 that when IF changes, Req is related to the commutation reactance Xc and the operating modal of the rectifier and increases as the operating modal of the rectifier increases. When the reactive load factor XR increases to a certain extent, the equivalent output impedance Req increases significantly. At this time, the change of load impedance has a relatively small impact on the output DC current, and it can be approximated as a current source. When the rotation speed and load resistance change (temperature change), the current amplification K is basically constant; that is, it has linear amplifier characteristics. Therefore, the three-phase full-bridge diode uncontrolled rectifier circuit should be designed with the operating modal III.


## 2.1. Theoretical Design of the AC Exciter

The load of the brushless excitation system is the excitation winding of the main motor, which is a large inductive load, and its resistance and inductance are represented byRF and LF, respectively. Then the excitation current IF flowing through the excitation winding of the main motor can be approximated as the direct current, and its pulsation component is so small that it can be ignored.When the brushless AC synchronous generator works at different speeds and temperatures and under different loads, the excitation currentIF of the main motor may vary within a relatively large range. Therefore, it is required that the output voltage of the AC exciter should vary within a relatively large range, and to achieve linear output characteristics at the same time, the AC exciter can be designed to work in a linear (unsaturated magnetic circuit) state.After the design of the main motor, since temperature is the only factor that causes the change in the resistanceRF of the excitation winding of the main motor, when the temperature rise leads to an increase in RF, in order to keep IF output unchanged, the output voltage of the AC exciter needs to be increased. Although the output voltage of the exciter can be increased by increasing Ief, it expands the variation range of Ief, which is inconsistent with the design goal. On the other hand, the electromagnetic parameters of the exciter can be appropriately designed, and the commutation reactance Xc of the winding of each phase can be increased, thereby changing the operating modal of the brushless excitation system, and achieving the purpose of increasing the output voltage of the exciter while keeping Ief basically unchanged.(1)
It can be found from references [5, 9] that when the AC exciter is connected to a large inductive load via a three-phase bridge rectifier circuit, the commutation overlap caused by the commutation reactance Xc of the three-phase armature winding results in short-circuit between the two commutation windings, which reduces the average rectified output voltage. The greater the reactive load factor XR, the larger the commutation angle γ, and the greater the loss of commutation voltage drop. The reactive load factor XR is defined as(2)XR=XcRF.When the temperature rises,RF also increases. The smaller the XR, the smaller the γ, and the smaller the loss of commutation voltage drop, which can improve the rectified output voltage.(2)
The potential vector during the stable operation of the exciter is shown in Figure2. According to reference [7], the internal power factor angle ψ has the following relationship with the commutation angle γ:(3)ψ≈γ2.Figure 2
Potential vector during the stable operation of the exciter.It can be known that the smaller theγ, the smaller the ψ, and the smaller the direct-axis current Id; that is, the weaker the D-axis demagnetizing magnetic field, thus, the air gap magnetic field of the exciter increases when Ief remains unchanged and the rectified output voltage is improved.Due to the compensation effect of the above two factors, whenRF increases with the temperature, the corresponding output voltage of the exciter also increases, which is the theoretical basis for the exciter to realize the characteristics of the linear current amplifier.


## 2.2. Theoretical Design of the Rotating Rectifier

In order to deeply analyze the operating characteristics of the three-phase bridge uncontrolled diode rectifier circuit, theoretical analysis was combined with simulation calculation in this paper. The simulated circuit is shown in Figure3. According to the difference in the time interval of commutation current conversion, the external characteristics expressing the rectified voltage and rectified current can be divided into three operating modals.Modal I: the commutation angle γ < π/3, the rectifier always has two or three diode elements working alternately in each operating period; Modal II: the commutation angle γ = π/3, the rectifier always has three diode elements working at any time in each operating period; Modal III: commutation angle π/3 ＜ γ ≤ 2π/3, the rectifier always has three or four diode elements working alternately in each operating period. The electrical characteristics of each operating modal are displayed in Table 1, and the voltage source with a certain internal impedance was used to express the external characteristics of the three-phase full-bridge rectifier. α′ in the table is the delay angle. (4)Ud=U0−Id×Req,U0=32πE,where Ud is the output DC voltage of the rectifier, U0 is the no-load output DC voltage of the rectifier, Req is the equivalent output impedance of the rectifier, and E is the effective value of the three-phase line voltage. The rectifier circuit can be divided into two states, conduction and commutation according to the number of rectifier components that are simultaneously conducting. The commutation state includes two-phase commutation (two-phase short-circuit) and three-phase commutation (three-phase short-circuit). The equivalent circuit is shown in Figure 4.Figure 3
Simulated model of the three-phase full-bridge diode uncontrolled rectifier circuit.Table 1
Three operating modals.
Working modesCommutation angleDelay angleElectrical characteristicsExternal characteristicsConditionReqIγ < π/3α′ = 0Conduction and commutationUd=32/πE−3xγ/πIdXR ≤π/93Xc/πIIγ = π/30 <α′ < π/3Commutation (two-phase short-circuit)2π2/27×Ud2/E2+2Id2xγ2/E2=1π/9 < XR≤π/33Xc/π∼9Xc/πIIIπ/3 < γ ≤ 2π/3α' = π/3Commutation (three-phase short-circuit)Ud=3·32/πE−3·3xγ/πIdπ/3 < XR9Xc/πFigure 4
Equivalent circuit: (a) two-phase conduction equivalent circuit, (b) two-phase commutation equivalent circuit, and (c) three-phase commutation equivalent circuit.
(a)(b)(c)From Figure4(c), it can be seen that the rectifier voltage is 0 because there are four rectifier elements conducting at the same time, resulting in a short-circuit state on the AC side and DC side. This condition can be used as a basis for judging that the rectifier is working in the IIIrd mode, and the expression of the average rectified voltage and current in this mode can be obtained by analyzing the circuit as follows:(5)Ud=92/πcosα′−π/6−9/πIdxγId=Ex/2xγcosα′−π/6−cosα′+γ−π/6..By solving the two-phase commutation equivalent circuit, the short-circuit current amplitude can be obtained:(6)Is2=2E2Xγ.To facilitate analysis, the external characteristics of the rectifier are expressed by per-unit values, andU0 and Is2 were used as the base value of voltage and current, respectively. The equation of the external characteristics of the rectifier expressed by per-unit value is shown in Table 2, and Figure 5 shows the external characteristic curve of the rectifier expressed by per-unit value.Table 2
The external characteristics expressed by per-unit values.
Working modesExternal characteristicsConditionIUd∗=1−1/2Id∗0<Id∗≤1/2II4/3Ud∗2+Id∗2=11/2<Id∗≤3/2IIIUd∗=3−3/2Id∗dId∗>3/2IFigure 5
External characteristic curve (expressed by per-unit value).It can be seen from Tables1 and 2 and Figure 5 that when IF changes, Req is related to the commutation reactance Xc and the operating modal of the rectifier and increases as the operating modal of the rectifier increases. When the reactive load factor XR increases to a certain extent, the equivalent output impedance Req increases significantly. At this time, the change of load impedance has a relatively small impact on the output DC current, and it can be approximated as a current source. When the rotation speed and load resistance change (temperature change), the current amplification K is basically constant; that is, it has linear amplifier characteristics. Therefore, the three-phase full-bridge diode uncontrolled rectifier circuit should be designed with the operating modal III.


## 3. Electromagnetic Design of the Brushless Excitation System

### 3.1. Integrated Electromagnetic Design Implementation and Operating Mode Determination

The above theoretical analysis and simulation calculation show that the brushless excitation system composed of the AC exciter and rotating rectifier should have the characteristics of linear current amplifier; that is,Ief can meet the variation of IF within a small range of variation under full load conditions so that the dynamic response ability of the brushless AC synchronous generator system can be enhanced. The reactive load factor XR of the brushless excitation system completely determines its operating modal, and further determines its characteristics of linear current amplifier.The expression of the definition ofXR reveals that the factors affecting the characteristics of the linear current amplifier are the resistance RF of the excitation winding of the main motor and the commutation reactance Xc of the AC exciter. When the electromagnetic parameters of the main motor are constant, the temperature is the only determinant of RF; Xc is determined by the electromagnetic parameters of the AC exciter. Reference [3] provides the analytical expression of the commutation reactance of the undamped winding exciter:(7)Xc=Xd+Xq2.Due to the extreme complexity of the electromagnetic equation of the AC exciter and the equation of the external characteristics of the rectifier, as well as the electromagnetic inter-relationship, they should be considered as a whole in the design process. Finite element simulation software can calculate the electromagnetic model and circuit model simultaneously and can provide sufficiently accurate numerical solution in a short period of time, which can save time and cost and improve design efficiency. Thus, it is favored by a majority of engineering designers.In this study, the influence of the key parameters of the AC exciter on the characteristics of the linear current amplifier was studied through the finite element simulation calculation. Figure6 shows a simulation model of the original electromagnetic scheme of the AC exciter, denoted by 0#, and its basic parameters are displayed in Table 3. An external circuit model for the integrated simulation calculation of the AC exciter and the rotating rectifier was built according to Figure 3, According to reference [10], the three-phase bridge rectifier circuit has higher energy conversion efficiency.Figure 6
Finite element electromagnetic simulation model of AC exciter.Table 3
Basic parameters of the original scheme (0#) of AC exciter.
Motor formRotating armatureSlot-pole combination10p48sSpeed (rpm)8000∼16000Temperature (°C)−40∼180Load resistance (Ω)0.153∼0.325Load inductance (mH)25Outer diameter of the stator (mm)155Inner diameter of the stator (mm)107.7Pole body height (mm)14Pole body width (mm)12Pole shoe width (mm)25Pole shoe height (mm)2Field winding wire gauge1 −φ0.8/80Air gap length (mm)0.5Outer diameter of the rotor (mm)106.7Inner diameter of the rotor (mm)80Armature winding wire gauge10 −φ0.56/2Parallel branches1In order to accurately identify the operating modal of the brushless excitation system, the typical characteristics of operating modals I, II, and III were first analyzed.Operating modal I: according to the above analysis, there are only conduction and two-phase commutation in this modal. Figure7 shows the curve of the three-phase armature current waveform, where θ is the conduction angle and γ is the commutation angle. In the conduction phase, no current flows through one phase winding, and DC current IF passes through the two-phase windings, respectively; in the commutation phase, IF passes through one phase winding. As shown in Figure 4(b), IF passes through the two-phase windings participating in the commutation.Operating modal II: in this modal, only two-phase commutation exists, and there is no conduction. Figure8 shows the curve of the three-phase armature current waveform, where γ = 60°. At any time, IF passes through one of the phase windings, and IF flows through two-phase windings participating in the commutation.Operating modal III: in this modal, there is only commutation, and two-phase commutation (two-phase short-circuit) and three-phase commutation (three-phase short-circuit) alternately appear [11]. Figure 9 shows the curve of the three-phase armature current waveform, where ε angle is the electrical angle corresponding to the time interval of two-phase commutation, ζ angle is the electrical angle corresponding to the time interval of three-phase commutation, and the commutation angle is 60° < γ < 120°. It can be seen from Figure 4(c) that when the AC side of the rectifier is three-phase short-circuited, the DC side will also be short-circuited. Considering the voltage drop of the diode, the DC voltage Ud will be negative within the interval of ζ angle. As shown in Figure 10, the negative value of Ud in a certain interval can be used as the basis for judging whether the rectifier is working in modal III.Figure 7
Three-phase current waveform in operating modal I.Figure 8
Three-phase current waveform in operating modal II.Figure 9
Three-phase current waveform in operating modal III.Figure 10
Three-phase voltage waveform in operating modal III.


### 3.2. Influence of the Main Electromagnetic Parameters on the Characteristics of Current Linear Amplifiers

The inductance parameter of the armature winding of the AC exciter is proportional to the square of the number of series turns per phase, and it is sensitive to the influence of the commutation reactanceXR. In this paper, the impact of the number of turns of the armature winding on the linear current amplifier characteristics was first studied. A total of three electromagnetic schemes were simulated for calculation: 0#, 1#, and 2#. The 0# scheme is the original electromagnetic scheme, and the number of serial turns of winding per phase is 32. Based on the 0# scheme, the 1# scheme sets empty slots to form a three-phase symmetrical winding with 20 series turns of winding per phase. The 2# scheme sets the number of turns per coil of the 0# scheme to 1 to constitute a three-phase symmetrical winding with 16 series turns of winding per phase. The remaining electromagnetic structure parameters of the three schemes are the same.Figure11 shows the curve of the DC output current IF of the rectifier changing with the excitation current Ief of the exciter under the working condition where the speed is 16000 rpm and temperature is −40°C in the 0# scheme. Under this working condition, the brushless excitation system works in modal III. It can be seen from the figure that IF and Ief are approximately linear.Figure 11
The curve ofIF varying with Ief in scheme 0#.Tables4–6 provide the operating modal and the parameters of linear current amplifier characteristics of the three electromagnetic schemes. n represents the rotating speed of the generator, T is the operating temperature, and the subscripts min and max represent the minimum and maximum value of the corresponding parameters, respectively. △Kn@Tmin means the relative change value of the current amplifier magnification factor K when the brushless excitation system changes from the minimum speed to the maximum speed at the lowest temperature, that is, linearity. Other parameters have similar meaning. The following conclusions can be drawn from the previous theoretical analysis and simulation calculation.(1)
Under the same working condition, the more the number of series turns of winding per phase, the greater the Table5 commutation reactance XC, the larger the reactive load factor XR, the greater the commutation angle γ, and the more the improvement of the operating modal of rectifier;(2)
At the same speed in each electromagnetic scheme, the higher theT, the larger the RF, the smaller the XR, the smaller the γ, and the more the operating modal of the rectifier can be reduced. The K decreases with the increase of RF;(3)
At the same temperature in each electromagnetic scheme, the higher then, the higher the electrical frequency of the generator, the larger the Xc, the greater the XR, the larger the γ, and the more the operating modal of the rectifier can be improved. The K increases with the increase of n;(4)
Under the four simulation conditions, the 0# scheme works in modal III, the 1# scheme works in modals II and III due to the difference inXR, and the 2# scheme works in modals I, II, and III. It can be seen from the data in Table 6 that the current magnification of the 0# scheme has relatively small changes, with the maximum linearity of △K < 10%. The maximum linearity of the 1# scheme is about 30%, and the maximum linearity of the 2# scheme is about 55.5%. In fact, owing to the influence of the structure and volume of the AC exciter, it is impossible to fully realize linear current amplifier characteristics. In engineering, when △K < 10%, it is considered that the linear current amplifier characteristics have been basically realized.Table 4
Operating modal.
Electromagnetic schemesnminTmaxnmaxTmaxnminTminnmaxTmin0#IIIIIIIIIIII1#IIIIIIIII2#IIIIIIIITable 5
Linear current amplifier magnification.
Electromagnetic schemesnminTmaxnmaxTmaxnminTminnmaxTmin0#11.6612.7412.6713.351#13.2817.2616.9819.262#12.1918.9518.3223.13Table 6
Linearity of linear current amplifier.
Electromagnetic schemes△Kn@Tmin△Kn@Tmax△KT@nmin△KT@nmax0#5.379.268.664.791#13.4329.9727.8611.592#26.2655.4650.2922.06The air gap lengthδ affects the exciter’s magnetic circuit reluctance and armature inductance parameters, thereby influencing the commutation reactance XC. When RF remains unchanged, the reactive load factor XR changes, and the operating modal of the rectifier changes accordingly, leading to the changes in the linear current amplifier characteristics. Based on the 0# scheme, the influence of different air gap length δ on the linear current amplifier characteristics was studied in this paper. To facilitate description, 3#∼6# schemes were used. All electromagnetic schemes have basically the same electromagnetic parameters except for the air gap length δ.Table7 shows the operating modal of each electromagnetic scheme under different working conditions. Figure 12 shows the curves of Figure 13 current magnification K and linearity △K of each electromagnetic scheme changing with the air gap length δ at the same speed and temperature. The following conclusions can be obtained: at the same speed and temperature, the smaller the air gap length δ, the smaller the air gap magnetic resistance, the larger the commutation reactance Xc, the larger the XR, the greater the γ, and the more the improvement of rectifier’s operating modal, the larger the K, the smaller the △K, and the more the linear current amplifier characteristics can be realized. However, due to the limitation of motor structure and technology, the air gap length should not be further reduced.Table 7
Operating modal.
Electromagnetic schemesnminTmaxnmaxTmaxnminTminnmaxTmin3#:δ = 0.2 mmIIIIIIIIIIII0#:δ = 0.35 mmIIIIIIIIIIII4#:δ = 0.6 mmIIIIIIIIIII5#:δ = 0.8 mmIIIIIIIIIII6#:δ = 1 mmIIIIIIIIIFigure 12
The curve of current magnificationK changing with air gap length δ.Figure 13
The curve of the linearity of current amplifier changing with air gap lengthδ.The axial lengthL of the exciter affects the area of the magnetic flux per pole and the total permeability, thereby influencing the commutation reactance Xc. When RF remains unchanged, the reactive load factor XR changes and the linear current amplifier characteristics of the rectifier will also change. Based on the 0# scheme, this study explored the influence of different axial lengths L on the characteristics of linear current amplifier. To facilitate description, 7#–10# schemes were used. All electromagnetic schemes have basically the same electromagnetic parameters, except for the axial length L.Table8 shows the operating modal of each electromagnetic scheme under different conditions. Figure 14shows the variation curves of current amplification K and linearity △K of each electromagnetic Figure 15scheme with the axial length L under the same speed and temperature. The following conclusions can be drawn: at the same speed and temperature, the greater the L, the greater the total permeability, the larger the Xc, the greater the XR, the larger the γ, the greater the improvement of the rectifier’s working mode, the larger the K, and the smaller the △K, so that the linear current amplifier characteristics can be achieved. Besides, with the increase of L, the changes in K and △K tend to be smooth, but the volume and weight also increase, resulting in a decrease in the utilization rate of the iron core. Therefore, the length of the iron core cannot be increased blindly under the premise of improving the dynamic response performance.Table 8
Operating modal.
Electromagnetic schemesnminTmaxnmaxTmaxnminTminnmaxTmin7#:L = 7 mmIIIIIIIIIII8#:L = 9.5 mmIIIIIIIIIII0#:L = 12 mmIIIIIIIIIIII9#:L = 14.5 mmIIIIIIIIIIII10#:L = 17 mmIIIIIIIIIIIIFigure 14
The curve of current magnification changing with the axial lengthL.Figure 15
The curve of the linearity of current amplifier changing with the axial lengthL.The load of the brushless excitation system is the excitation winding of the main motor, which is a large inductive load. Its DC current ripple is so small that it can be ignored. The reactive load factorXR is inversely proportional to RF. The value of RF is related to the structure of the excitation winding, wire gauge, and operating temperature. Thus, the impact of RF on the linear current amplifier characteristics should be fully considered in the design of the main motor. Based on the 2# electromagnetic scheme, this study investigated the influence of RF on the linear current amplifier characteristics. Table 9 shows the influence of RF on the operating modal of the rectifier when the electromagnetic structure of the exciter is fixed. Figure 16 exhibits how the current amplification changes with RF. It can be seen that when the electromagnetic structure of the exciter is fixed, XR is inversely proportional to RF. The smaller the RF, the larger the XR, the more significant the improvement of the rectifier’s operating modal, and the current amplification factor K decreases with the increase of RF.Table 9
Operating modal @2# scheme.
RF (ohm)0.8870.750.60.4430.350.2960.2220.1770.1480.111Working modeIIIIIIIIIIIIIIIIIIIIFigure 16
The curve of current amplifier magnification factor changing withRF.


## 3.1. Integrated Electromagnetic Design Implementation and Operating Mode Determination

The above theoretical analysis and simulation calculation show that the brushless excitation system composed of the AC exciter and rotating rectifier should have the characteristics of linear current amplifier; that is,Ief can meet the variation of IF within a small range of variation under full load conditions so that the dynamic response ability of the brushless AC synchronous generator system can be enhanced. The reactive load factor XR of the brushless excitation system completely determines its operating modal, and further determines its characteristics of linear current amplifier.The expression of the definition ofXR reveals that the factors affecting the characteristics of the linear current amplifier are the resistance RF of the excitation winding of the main motor and the commutation reactance Xc of the AC exciter. When the electromagnetic parameters of the main motor are constant, the temperature is the only determinant of RF; Xc is determined by the electromagnetic parameters of the AC exciter. Reference [3] provides the analytical expression of the commutation reactance of the undamped winding exciter:(7)Xc=Xd+Xq2.Due to the extreme complexity of the electromagnetic equation of the AC exciter and the equation of the external characteristics of the rectifier, as well as the electromagnetic inter-relationship, they should be considered as a whole in the design process. Finite element simulation software can calculate the electromagnetic model and circuit model simultaneously and can provide sufficiently accurate numerical solution in a short period of time, which can save time and cost and improve design efficiency. Thus, it is favored by a majority of engineering designers.In this study, the influence of the key parameters of the AC exciter on the characteristics of the linear current amplifier was studied through the finite element simulation calculation. Figure6 shows a simulation model of the original electromagnetic scheme of the AC exciter, denoted by 0#, and its basic parameters are displayed in Table 3. An external circuit model for the integrated simulation calculation of the AC exciter and the rotating rectifier was built according to Figure 3, According to reference [10], the three-phase bridge rectifier circuit has higher energy conversion efficiency.Figure 6
Finite element electromagnetic simulation model of AC exciter.Table 3
Basic parameters of the original scheme (0#) of AC exciter.
Motor formRotating armatureSlot-pole combination10p48sSpeed (rpm)8000∼16000Temperature (°C)−40∼180Load resistance (Ω)0.153∼0.325Load inductance (mH)25Outer diameter of the stator (mm)155Inner diameter of the stator (mm)107.7Pole body height (mm)14Pole body width (mm)12Pole shoe width (mm)25Pole shoe height (mm)2Field winding wire gauge1 −φ0.8/80Air gap length (mm)0.5Outer diameter of the rotor (mm)106.7Inner diameter of the rotor (mm)80Armature winding wire gauge10 −φ0.56/2Parallel branches1In order to accurately identify the operating modal of the brushless excitation system, the typical characteristics of operating modals I, II, and III were first analyzed.Operating modal I: according to the above analysis, there are only conduction and two-phase commutation in this modal. Figure7 shows the curve of the three-phase armature current waveform, where θ is the conduction angle and γ is the commutation angle. In the conduction phase, no current flows through one phase winding, and DC current IF passes through the two-phase windings, respectively; in the commutation phase, IF passes through one phase winding. As shown in Figure 4(b), IF passes through the two-phase windings participating in the commutation.Operating modal II: in this modal, only two-phase commutation exists, and there is no conduction. Figure8 shows the curve of the three-phase armature current waveform, where γ = 60°. At any time, IF passes through one of the phase windings, and IF flows through two-phase windings participating in the commutation.Operating modal III: in this modal, there is only commutation, and two-phase commutation (two-phase short-circuit) and three-phase commutation (three-phase short-circuit) alternately appear [11]. Figure 9 shows the curve of the three-phase armature current waveform, where ε angle is the electrical angle corresponding to the time interval of two-phase commutation, ζ angle is the electrical angle corresponding to the time interval of three-phase commutation, and the commutation angle is 60° < γ < 120°. It can be seen from Figure 4(c) that when the AC side of the rectifier is three-phase short-circuited, the DC side will also be short-circuited. Considering the voltage drop of the diode, the DC voltage Ud will be negative within the interval of ζ angle. As shown in Figure 10, the negative value of Ud in a certain interval can be used as the basis for judging whether the rectifier is working in modal III.Figure 7
Three-phase current waveform in operating modal I.Figure 8
Three-phase current waveform in operating modal II.Figure 9
Three-phase current waveform in operating modal III.Figure 10
Three-phase voltage waveform in operating modal III.


## 3.2. Influence of the Main Electromagnetic Parameters on the Characteristics of Current Linear Amplifiers

The inductance parameter of the armature winding of the AC exciter is proportional to the square of the number of series turns per phase, and it is sensitive to the influence of the commutation reactanceXR. In this paper, the impact of the number of turns of the armature winding on the linear current amplifier characteristics was first studied. A total of three electromagnetic schemes were simulated for calculation: 0#, 1#, and 2#. The 0# scheme is the original electromagnetic scheme, and the number of serial turns of winding per phase is 32. Based on the 0# scheme, the 1# scheme sets empty slots to form a three-phase symmetrical winding with 20 series turns of winding per phase. The 2# scheme sets the number of turns per coil of the 0# scheme to 1 to constitute a three-phase symmetrical winding with 16 series turns of winding per phase. The remaining electromagnetic structure parameters of the three schemes are the same.Figure11 shows the curve of the DC output current IF of the rectifier changing with the excitation current Ief of the exciter under the working condition where the speed is 16000 rpm and temperature is −40°C in the 0# scheme. Under this working condition, the brushless excitation system works in modal III. It can be seen from the figure that IF and Ief are approximately linear.Figure 11
The curve ofIF varying with Ief in scheme 0#.Tables4–6 provide the operating modal and the parameters of linear current amplifier characteristics of the three electromagnetic schemes. n represents the rotating speed of the generator, T is the operating temperature, and the subscripts min and max represent the minimum and maximum value of the corresponding parameters, respectively. △Kn@Tmin means the relative change value of the current amplifier magnification factor K when the brushless excitation system changes from the minimum speed to the maximum speed at the lowest temperature, that is, linearity. Other parameters have similar meaning. The following conclusions can be drawn from the previous theoretical analysis and simulation calculation.(1)
Under the same working condition, the more the number of series turns of winding per phase, the greater the Table5 commutation reactance XC, the larger the reactive load factor XR, the greater the commutation angle γ, and the more the improvement of the operating modal of rectifier;(2)
At the same speed in each electromagnetic scheme, the higher theT, the larger the RF, the smaller the XR, the smaller the γ, and the more the operating modal of the rectifier can be reduced. The K decreases with the increase of RF;(3)
At the same temperature in each electromagnetic scheme, the higher then, the higher the electrical frequency of the generator, the larger the Xc, the greater the XR, the larger the γ, and the more the operating modal of the rectifier can be improved. The K increases with the increase of n;(4)
Under the four simulation conditions, the 0# scheme works in modal III, the 1# scheme works in modals II and III due to the difference inXR, and the 2# scheme works in modals I, II, and III. It can be seen from the data in Table 6 that the current magnification of the 0# scheme has relatively small changes, with the maximum linearity of △K < 10%. The maximum linearity of the 1# scheme is about 30%, and the maximum linearity of the 2# scheme is about 55.5%. In fact, owing to the influence of the structure and volume of the AC exciter, it is impossible to fully realize linear current amplifier characteristics. In engineering, when △K < 10%, it is considered that the linear current amplifier characteristics have been basically realized.Table 4
Operating modal.
Electromagnetic schemesnminTmaxnmaxTmaxnminTminnmaxTmin0#IIIIIIIIIIII1#IIIIIIIII2#IIIIIIIITable 5
Linear current amplifier magnification.
Electromagnetic schemesnminTmaxnmaxTmaxnminTminnmaxTmin0#11.6612.7412.6713.351#13.2817.2616.9819.262#12.1918.9518.3223.13Table 6
Linearity of linear current amplifier.
Electromagnetic schemes△Kn@Tmin△Kn@Tmax△KT@nmin△KT@nmax0#5.379.268.664.791#13.4329.9727.8611.592#26.2655.4650.2922.06The air gap lengthδ affects the exciter’s magnetic circuit reluctance and armature inductance parameters, thereby influencing the commutation reactance XC. When RF remains unchanged, the reactive load factor XR changes, and the operating modal of the rectifier changes accordingly, leading to the changes in the linear current amplifier characteristics. Based on the 0# scheme, the influence of different air gap length δ on the linear current amplifier characteristics was studied in this paper. To facilitate description, 3#∼6# schemes were used. All electromagnetic schemes have basically the same electromagnetic parameters except for the air gap length δ.Table7 shows the operating modal of each electromagnetic scheme under different working conditions. Figure 12 shows the curves of Figure 13 current magnification K and linearity △K of each electromagnetic scheme changing with the air gap length δ at the same speed and temperature. The following conclusions can be obtained: at the same speed and temperature, the smaller the air gap length δ, the smaller the air gap magnetic resistance, the larger the commutation reactance Xc, the larger the XR, the greater the γ, and the more the improvement of rectifier’s operating modal, the larger the K, the smaller the △K, and the more the linear current amplifier characteristics can be realized. However, due to the limitation of motor structure and technology, the air gap length should not be further reduced.Table 7
Operating modal.
Electromagnetic schemesnminTmaxnmaxTmaxnminTminnmaxTmin3#:δ = 0.2 mmIIIIIIIIIIII0#:δ = 0.35 mmIIIIIIIIIIII4#:δ = 0.6 mmIIIIIIIIIII5#:δ = 0.8 mmIIIIIIIIIII6#:δ = 1 mmIIIIIIIIIFigure 12
The curve of current magnificationK changing with air gap length δ.Figure 13
The curve of the linearity of current amplifier changing with air gap lengthδ.The axial lengthL of the exciter affects the area of the magnetic flux per pole and the total permeability, thereby influencing the commutation reactance Xc. When RF remains unchanged, the reactive load factor XR changes and the linear current amplifier characteristics of the rectifier will also change. Based on the 0# scheme, this study explored the influence of different axial lengths L on the characteristics of linear current amplifier. To facilitate description, 7#–10# schemes were used. All electromagnetic schemes have basically the same electromagnetic parameters, except for the axial length L.Table8 shows the operating modal of each electromagnetic scheme under different conditions. Figure 14shows the variation curves of current amplification K and linearity △K of each electromagnetic Figure 15scheme with the axial length L under the same speed and temperature. The following conclusions can be drawn: at the same speed and temperature, the greater the L, the greater the total permeability, the larger the Xc, the greater the XR, the larger the γ, the greater the improvement of the rectifier’s working mode, the larger the K, and the smaller the △K, so that the linear current amplifier characteristics can be achieved. Besides, with the increase of L, the changes in K and △K tend to be smooth, but the volume and weight also increase, resulting in a decrease in the utilization rate of the iron core. Therefore, the length of the iron core cannot be increased blindly under the premise of improving the dynamic response performance.Table 8
Operating modal.
Electromagnetic schemesnminTmaxnmaxTmaxnminTminnmaxTmin7#:L = 7 mmIIIIIIIIIII8#:L = 9.5 mmIIIIIIIIIII0#:L = 12 mmIIIIIIIIIIII9#:L = 14.5 mmIIIIIIIIIIII10#:L = 17 mmIIIIIIIIIIIIFigure 14
The curve of current magnification changing with the axial lengthL.Figure 15
The curve of the linearity of current amplifier changing with the axial lengthL.The load of the brushless excitation system is the excitation winding of the main motor, which is a large inductive load. Its DC current ripple is so small that it can be ignored. The reactive load factorXR is inversely proportional to RF. The value of RF is related to the structure of the excitation winding, wire gauge, and operating temperature. Thus, the impact of RF on the linear current amplifier characteristics should be fully considered in the design of the main motor. Based on the 2# electromagnetic scheme, this study investigated the influence of RF on the linear current amplifier characteristics. Table 9 shows the influence of RF on the operating modal of the rectifier when the electromagnetic structure of the exciter is fixed. Figure 16 exhibits how the current amplification changes with RF. It can be seen that when the electromagnetic structure of the exciter is fixed, XR is inversely proportional to RF. The smaller the RF, the larger the XR, the more significant the improvement of the rectifier’s operating modal, and the current amplification factor K decreases with the increase of RF.Table 9
Operating modal @2# scheme.
RF (ohm)0.8870.750.60.4430.350.2960.2220.1770.1480.111Working modeIIIIIIIIIIIIIIIIIIIIFigure 16
The curve of current amplifier magnification factor changing withRF.


## 4. Test Verification

Based on the electromagnetic simulation data, the exciters in 0# (the number of series turns per phase is 32) and 1# (the number of series turns per phase is 20) electromagnetic schemes were produced, which were combined with the same main motor to form a two-pole brushless AC synchronous generator, respectively. In the test, a 200 kW DC motor was used as the prime motor to drive the prototype to rotate, and a 60 V/10A DC power supply was used as the excitation power supply of the AC exciter. The ambient temperature was 15°C, and the generator speed was 12000 rpm. The generator cooling method is oil-cooled, the oil feed pressure is 300 kPa, the oil feed temperature is 70°C, and the oil feed flow rate is 8 L/min. Figure17 shows the three-phase voltage waveform curve of the main motor with 0.98 A DC current connected to the 0# AC exciter, and its effective value is 115 V. Figure 18 shows the no-load characteristic curve of the generator (the variation curve of phase terminal voltage U0 of the main motor and the excitation current Ief of the AC exciter): in the same exciter electromagnetic scheme, due to the difference in the manufacturing and assembly of the components of the motor, the value of the no-load saturation voltage test is slightly lower than the simulation value, but it can meet the requirement for engineering accuracy. Compared with the 1# scheme since the 0# scheme has more series turns per phase, the commutation reactance Xc is larger, the commutation angle γ is greater, and the voltage drop loss caused by the commutation overlap is also larger. The average output voltage of the rotating rectifier is small, the average output current is also small, and the current amplification K is relatively small accordingly. Therefore, under the condition of the same U0, the required Ief is relatively large.Figure 17
No-load voltage waveform curve of main generator @Ief = 0.98 A (0# AC exciter).Figure 18
No-load characteristic curve.The simulation value of the generator’s no-load characteristic curve is basically consistent with the test value, indicating that the idea and the simulation method for the integrated electromagnetic design of the AC exciter and the rotating rectifier are correct, and the accuracy meets the requirement of engineering design.


## 5. Conclusion

In order to enhance the dynamic response characteristics of the brushless AC synchronous generator, the excitation currentIef of the brushless excitation system composed of an AC exciter and a rotating rectifier should be able to meet the need of the excitation current IF of the main motor under full load condition within a small variation range, which means that the brushless excitation system should have the linear current amplifier characteristics. In this paper, the theoretical basis for realizing the linear current amplifier characteristics and the determinant, typical characteristics, and judgment basis of each operating modal of the rectifier were analyzed first. The main contribution is that finite element simulation was adopted to realize the integrated electromagnetic design of the AC exciter and the rotating rectifier, and the influence of the key parameters of the exciter on the linear current amplifier characteristics was explored. When the brushless excitation system works in modal III or close to modal III, the linear current amplifier characteristics can be basically realized. The basis for judging the rectifier operating in mode III is obtained from theory and simulation design and providing a concrete engineering design approach for improving the dynamic response characteristics of brushless AC synchronous generators. Finally, a prototype was made and related test was conducted to verify the correctness of the integrated electromagnetic design and simulation calculation. This study presents an effective design method for improving the dynamic response performance of the AC brushless synchronous generator.



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*Source: 9271302-2022-08-02.xml*