Comparative study of the reluctance machines with and without field winding for generator and starter applications

Abstract

The switched reluctance starter generator (SRSG) without field winding and the doubly salient electromagnetic starter generator (DSESG) with field winding are compared in this paper. The influences of two arrangements of each variable winding and spacing variable winding for the performance of the starter generator were studied. Mathematical models of start mode and power generation mode were established respectively, and the influencing factors of starting torque and power generation phase voltage were derived. Next, the finite element simulation software was used to simulate the electromagnetic characteristics of machine. Finally, prototype experiment was made. The finite element simulation and prototype experiment results proved that spacing excitation DSESG has a better prospect as automotive starter generator.

Keywords

Switched reluctance starter generator (SRSG)doubly salient electromagnetic starter generator (DSESG)variable winding

1. Introduction

The starter generator integrates the starter and generator independently installed in the car into one machine, and can work in starter mode or generator mode, realizing the integrated integration of the starter and generator, reducing the weight of the car and improving the reliability [1,2]. Therefore, starter generator has important research value and development prospects.

There are many research institutions and scholars around the world who have studied switched reluctance starter generators (SRSG). The US General Electric Company designed 12/8 SRMSG for fifth-generation fighter F-35. The Northwestern Polytechnical University and Nanjing University of Aeronautics and Astronautics demonstrate and study the application of switched reluctance starter power generation system in aviation field. However, the switched reluctance machine (SRM) requires rotor position information and corresponding control signals whether it is as a starter or a generator, especially when it is high-speed power generation [3]. Many researchers have studied the position sensorless of switched reluctance machines, but they have not been able to use them for higher speeds [4] designed a position sensorless technology at high speed, but the control algorithm is very complicated, and puts higher requirements on the processor.

The doubly salient electromagnetic machine (DSEM) is also one of the important choices for a new generation of brushless DC starter generators [5]. The University of Sheffield developed a doubly-fed variable reluctance doubly salient machine, which is equivalent to each excitation doubly salient starter generator. Nanjing University of Aeronautics and Astronautics tested the doubly salient electromagnetic starter generator (DSESG) on the aeroengine, and studied its control strategy and voltage regulation strategy. The School also developed the 18 Kw DSESG, which greatly promoted the integration process of electric excitation doubly salient start-up power generation. However, as a starter, the traditional DSEM needs to increase the excitation current and armature current in a short time to provide sufficient torque, which will cause over-saturation of the core and demagnetization effect of the armature reaction, reducing the efficiency of the machine [7–10].

Both SRSG and DSESG have their own advantages and disadvantages. The existing literature does not compare and analyze which of the above two starter generators is better. Therefore, it is very necessary to compare the starting and generating states of the SRSG without field winding and the DSESG with field winding to provides a basis for further design.

2. Basic topology and mathematical analysis

2.1. Basic topology

The DSEM is developed from SRM, the essential difference is that DSEM has field windings and SRM has no field winding. Adding field windings to the SRSG or turning part of the armature windings of the SRSG into field windings can form DSESG. For convenience of comparison, two three-phase starter generator schemes as shown in Fig. 1 can be obtained by setting a variable winding method.

Figure 1(a) shows each variable winding starter generator (EVW-SG) with armature windings and variable windings on each stator pole. The number of armature winding and variable winding turns on each stator pole is the same. The winding directions of the windings on the same stator pole are the same, and the winding directions of the windings on the adjacent stator poles are opposite. Each variable winding SRSG (EVW-SRSG) is formed when the armature windings are connected in series with the variable windings. In this case the variable windings are as the armature windings; Each variable winding DSESG (EVW-DSESG) is formed when the armature windings are connected in parallel with the variable windings. In this case the variable windings are as the field winding. Figure 1(b) shows spacing variable winding starter generator (SVW-SG) with armature windings and variable windings on spacing stator pole. The same number of armature windings and variable windings are wound on the spaced stator poles, and the winding directions on the adjacent two stator poles are opposite. The spacing variable winding SRSG (SVW-SRSG) is formed when the variable windings are as armature windings, and the spacing variable winding DSESG (SVW-DSESG) is formed when the variable windings are as field winding.

Fig. 1.

Machine configuration of EVW-SG and SVW-SG.

2.2. Mathematical analysis

2.2.1. Electric analysis

At low speed start mode, the output torque T_SRM of the SRSG is $\begin{eqnarray}\displaystyle T_{SRM}={\displaystyle \frac{i_{p}^{2}}{2}}{\displaystyle \frac{dL_{p}}{d{\theta}}} & & \displaystyle\end{eqnarray}$ (1) where, i_p is the phase current; L_p is the phase self-inductance of the SRM; and θ is the rotor position angle. Using the equivalent magnetic circuit method to obtain L_p $\begin{eqnarray}\displaystyle L_{p}=4N_{p}^{2}G_{p} & & \displaystyle\end{eqnarray}$ (2) where, N_p is the number of turns of phase p (p represents A, B, C) winding; G_p is the air gap permeability of phase p. Substituting Eq. ((2)) into Eq. ((1)) $\begin{eqnarray}\displaystyle T_{SRM}=2i_{p}^{2}{\displaystyle \frac{d(N_{p}^{2}G_{p})}{d{\theta}}}=2i_{p}^{2}N_{p}^{2}{\displaystyle \frac{dG_{p}}{d{\theta}}}. & & \displaystyle\end{eqnarray}$ (3)

The phase torque of DSEM is $\begin{eqnarray}\displaystyle T_{p}={\displaystyle \frac{1}{2}}i_{p}^{2}{\displaystyle \frac{dL_{p}}{d{\theta}}}+i_{p}i_{f}{\displaystyle \frac{dL_{pf}}{d{\theta}}}=T_{pr}+T_{pf} & & \displaystyle\end{eqnarray}$ (4) where, T_p is the output torque of phase p; T_pr is the phase reluctance torque; T_pf is the phase electromagnetic torque; L_pf is the mutual inductance between the armature and the field windings. The output torque is mainly the $\begin{eqnarray}\displaystyle T_{p}\approx T_{pf}=i_{p}i_{f}{\displaystyle \frac{dL_{pf}}{d{\theta}}}. & & \displaystyle\end{eqnarray}$ (5)

The DSESG starts with a full-bridge converter to achieve two-phase conduction, and the total output torque is $\begin{eqnarray}\displaystyle \text{} & \text{} & \displaystyle T_{DSEM}=T_{a}+T_{c}=2i_{p}i_{f}{\displaystyle \frac{dL_{pf}}{d{\theta}}}\end{eqnarray}$ (6) $\begin{eqnarray}\displaystyle \text{} & \text{} & \displaystyle L_{pf}={\displaystyle \frac{N_{f}{\varphi}_{p}}{i_{f}}}=N_{f}N_{p}{\displaystyle \frac{G_{p}G_{f}}{G_{f}+G_{u}}}\end{eqnarray}$ (7) where, T_a is the output torque of phase A; T_c is the output torque of phase C; N_f is the number of field winding turns; φ_p is the flux of the phase p winding; G_f is field permeability; G_p is air gap permeability of phase p; G_u = G_a + G_b + G_c is synthetic air gap permeability. Ideally, DSEM’s G_f approximates infinity, Eq. (7) can be written as $\begin{eqnarray}\displaystyle L_{pf}\approx N_{f}N_{p}G_{p}. & & \displaystyle\end{eqnarray}$ (8)

Substituting Eq. (8) into Eq. (6) $\begin{eqnarray}\displaystyle T_{DSEM}=2i_{p}i_{f}{\displaystyle \frac{d(N_{f}N_{p}G_{p})}{d{\theta}}}=2i_{p}N_{p}i_{f}N_{f}{\displaystyle \frac{dG_{p}}{d{\theta}}}. & & \displaystyle\end{eqnarray}$ (9)

From Eqs ((3)) and ((9)), we can draw the conclusion that if we change half of the SRM phase windings into DSEM fielding windings, and keep the same current density, the ratio of torques between SRM and DSEM will be approximately equal to 1, which is $\frac{T_{SRM}}{T_{DSEM}}\approx 1$ . Considering the saturation effect of the magnetic circuit in the actual motor, although the torque is no longer proportional to the square of the current, it increases with the increase of the current. Therefore, it is possible to increase the electromagnetic torque by increasing the current effectively. In other words, SRSG is more suitable for low-speed starting conditions than DSESG.

2.2.2. Power generation analysis

The phase voltage equation of DSESG during power generation is $\begin{eqnarray}\displaystyle u_{p}=i_{f}{\displaystyle \frac{dL_{pf}}{dt}}+i_{p}{\displaystyle \frac{dL_{p}}{dt}}-L_{p}{\displaystyle \frac{di_{p}}{dt}}. & & \displaystyle\end{eqnarray}$ (10)

The phase voltage equation of SRSG during power generation is $\begin{eqnarray}\displaystyle u_{p}=i_{f}{\displaystyle \frac{dL_{p}}{dt}}-L_{p}{\displaystyle \frac{di_{p}}{dt}} & & \displaystyle\end{eqnarray}$ (11)

For DSESG, the magnetomotive force F_a = F_b = F_c = 0 at no load, the magnetic flux of the field windings φ_f is $\begin{eqnarray}\displaystyle {\varphi}_{f}=F_{f}\frac{G_{f}G_{u}}{G_{f}+G_{u}} & & \displaystyle\end{eqnarray}$ (12)F_f is the magnetomotive force of field windings.

The self-inductance of field windings L_f is $\begin{eqnarray}\displaystyle L_{f}={\displaystyle \frac{N_{f}{\varphi}_{f}}{i_{f}}}=N_{f}^{2}{\displaystyle \frac{G_{f}G_{u}}{G_{f}+G_{u}}}. & & \displaystyle\end{eqnarray}$ (13)

The flux linkage of phase A𝜓_a is $\begin{eqnarray}\displaystyle {\psi}_{a}=N_{a}{\varphi}_{a}=N_{a}{\varphi}_{f}{\displaystyle \frac{G_{a}}{G_{u}}}. & & \displaystyle\end{eqnarray}$ (14)

The self-inductance L_a of phase A is $\begin{eqnarray}\displaystyle L_{a}={\displaystyle \frac{N_{a}{\varphi}_{a}}{i_{a}}}=N_{a}^{2}{\displaystyle \frac{G_{a}(G_{a}+G_{c}+G_{f})}{G_{f}+G_{u}}}\approx N_{a}^{2}G_{a}. & & \displaystyle\end{eqnarray}$ (15)

So the self-inductance of phase p is $\begin{eqnarray}\displaystyle L_{p}\approx N_{p}^{2}G_{p}. & & \displaystyle\end{eqnarray}$ (16)

Mutual inductance L_pf between p-phase windings and field windings is $\begin{eqnarray}\displaystyle L_{pf}={\displaystyle \frac{N_{f}{\varphi}_{f}}{i_{f}}}=N_{f}N_{p}{\displaystyle \frac{G_{f}G_{p}}{G_{f}+G_{u}}}\approx N_{f}N_{p}G_{p}. & & \displaystyle\end{eqnarray}$ (17)

$\frac{L_{pf}}{L_{p}}=\frac{N_{f}N_{p}G_{p}}{N_{p}^{2}G_{p}}=\frac{N_{f}}{N_{p}}$ can be get from Eqs (14) and (15). For SRSG, The self-inductance L_p of phase p is $\begin{eqnarray}\displaystyle L_{p}={\displaystyle \frac{{\psi}_{p}}{i_{p}}}={\displaystyle \frac{N_{p}(N_{p}i_{p}/R)}{i_{p}}}=N_{p}^{2}G_{p} & & \displaystyle\end{eqnarray}$ (18)

It can be seen from Eqs. (16), (17), (18) that both i_pdL_p and i_fdL_pf in Eqs (10) and (11) are proportional to the multiplied value of winding turns and winding current. Therefore, with the same excitation magnetic motive force, both of the DSEM and SRM have the same output voltage. However, when the DSEM is used as a generator, the voltage regulation can be easily realized by regulating the dc excitation current, as well as it needn’t position sensors. Therefore, DSESG is more suitable for high-speed power generation than SRSG.

In summary, DSESG is superior to SRSG for automotive starter generators because the vehicle starter generators operate much longer in power generation conditions than in the starting conditions.

3. Simulation analysis and experimental verification

Table 1
Basic design parameters of machine

Item Parameter

Outer diameter of the stator (mm) 137

Outer diameter of the rotor (mm) 81.8

Stator pole Number 12

Rotor pole Number 8

Air-gap (mm) 0.4

Iron stack length (mm) 100

Armature winding turns 20

Field winding turns 20

Number of machine phases 3

Rated voltage (V) 48

Item	Parameter
Outer diameter of the stator (mm)	137
Outer diameter of the rotor (mm)	81.8
Stator pole Number	12
Rotor pole Number	8
Air-gap (mm)	0.4
Iron stack length (mm)	100
Armature winding turns	20
Field winding turns	20
Number of machine phases	3
Rated voltage (V)	48

When EVW-SRSG and SVW-SRSG are used as SRSG, they can be regarded as the same SG. There is no need to compare. The finite element simulation models of EVW-DSESG and SVW-DSESG are established respectively. Figure 2 shows the flux linkage. The main parameters of the machines are the same, as shown in Table 1.

Fig. 2.

Flux linkage of EVW-DSESG and SVW-DSESG.

Fig. 3.

Starting characteristics.

Figure 3 shows the starting characteristics of SVW-SRSG when the machine speed is 500 r/min in the electric mode. With current chopping control, the current waveform of each phase is close to a square wave. Compared with the DSEM, the power supply only provides the forward voltage, and the current per phase is always positive. There is no negative torque due to the improper current commutation time, which reduces the starting performance.

Fig. 4.

No-load simulation. (a) Flux linkage of EVW-DSESG. (b) Flux linkage of SVW-DSESG. (c) Electromotive force of EVW-DSESG. (d) Electromotive force of SVW-DSESG.

Figure 4 shows the no-load electromotive force and flux linkage waveforms of the three-phase 12/8 EVW-DSESG and SVW-SRSG with an excitation potential of 100 AT and a rotational speed of 3000 r/min. Both the field windings and the armature windings are concentrated windings. In the power generation mode, the armature windings of each phase are in the same position with respect to the field windings, and the electromotive force and flux linkage of each phase are kept symmetric, also the back electromotive force of each armature winding is oblique trapezoidal. The three phases are symmetrical and differ by 120°. In Fig. 4(a), the peak value of the flux linkage is 0.0127 Wb, the peak value of the flux linkage in Fig. 4(b) is 0.0123 Wb, the peak value of the electromotive force in Fig. 4(c) is 15.43 V, and the peak value of the electromotive force in Fig. 4(d) is 15.22 V. The difference between the no-load flux linkage and the no-load electromotive force of EVW-DSESG and SVW-SRSG is small under the same magnetic potential. The simulation results are consistent with the theoretical analysis above.

Fig. 5.

Load simulation. (a) Voltage of EVW-DSESG. (b) Voltage of SVW-DSESG. (c) Current of EVW-DSESG. (d) Current of SVW-DSESG.

Fig. 6.

Experimental platform and waveforms.

Figure 5 shows the electromotive force and current waveforms of a three-phase 12/8-pole EVW-DSESG and SVW-SRSG with an excitation potential of 100 AT, a rotational speed of 3000 r/min, and an external 1 ohm load circuit. In the power generation mode, it can be observed that the phase current and phase voltage of EVW-DSESG are slightly higher than SVW-SRSG. Since SVW-SRSG has fewer windings than EVW-DSESG, it is much easier to manufacture. More importantly, SVW-SRSG can save switching devices because of fewer windings.

In order to verify the theoretical and simulation analysis of the machine, the two prototypes of EVW-DSESG and SVW-DSESG were trial-produced for comparative test research based on the basic parameters of Table 1, and then the experimental platform shown in Fig. 6(a) is constructed.

In Fig. 6(a), two prototypes are coaxially mounted on the platform to form an experimental unit. Both prototypes can be used as both a generator and a starter. Figure 6(b) is voltage of EVW-DSESG at 1 ohm. Figure 6(c) is voltage of SVW-DSESG at 1 ohm. Figures 6(d) and (e) reflect the current and voltage waveforms of the starter mode and the power generation mode of EVW-DSESG. Figures 6(f) and (g) reflect the current and voltage waveforms of the starter mode and the power generation mode of SVW-DSESG. Due to the current chopping control, the armature winding current is close to a square wave. However, during the current drop phase, a negative voltage pulse is induced across the windings. At the same time, in the relevant disconnection phase, the induced electromotive force generates a certain fluctuation due to the mutual inductance. In this case, the switch tube is still in the off state, and the entire circuit cannot form a loop, so the current in the windings is still zero. The experimental results are in accordance with the results of finite element analysis, which verifies the rationality of the prototype design.

4. Conclusion

In this paper, a comparative study of the reluctance machines with and without field winding was carried out. Through theoretical analysis of the performance of the two machines, and then using finite element simulation and experimental verification, the conclusions are obtained:

(1) In the starter mode, it can be seen that if half of the switched reluctance machine (SRM) phase windings is changed to the doubly salient electromagnetic machine (DSEM) fielding windings and keep the same current density, the ratio of torques between the machine with field winding and the machine without field winding will be approximately equal to 1.

(2) In the power generation mode, no matter what value the number of turns of the field windings are, as long as the excitation magnetic motive force is constant, the induced electromotive force of the machine remains unchanged.

(3) The doubly salient electromagnetic starter generator (DSESG) with field winding is superior to the switched reluctance starter generator (SRSG) without field winding for automotive starter generators.

The results of simulation and theoretical analysis verify the correctness of the theoretical analysis.

Footnotes

Acknowledgements

This work was supported by the National Natural Science Foundation of China (51975340, 51775320), and Shandong Key R&D Program (2019GGX104063).

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