Optimal Output Power Control of Switched Reluctance Generator at a Constant Speed

Liwei Shao， Lei Dong and Lulu Ling

（1. School of Automation, Beijing Institute of Technology, Beijing 100081, China；2. Zhongshan Research Institute, Beijing Institute of Technology, Zhongshan 528437,Guangdong, China）

Abstract: In order to control the output power of a switched reluctance generator(SRG) at a con?stant speed, the output power of SRG is theoretically analyzed by using freewheeling control. First,through a theoretical analysis, a finite element simulation and an experiment, it was verified that the output power of SRG cannot be improved by using freewheeling control with a single pulse con?trol method(SPCM). Then, the maximum output power can be obtained by optimizing the turn off angles of SPCM at a constant speed, and at the same time, the formula of the optimal turn?off angle was presented, which meets the criterion for the output power maximization. Finally, numer?ical simulation and experimental results demonstrated the validity of the theoretical analysis.

Key words: freewheeling technique；output power maximization；single pulse control；switched reluctance generator(SRG)

The simple structure without windings and permanent magnets on the rotor, which has the characteristics of low manufacturing cost and fault tolerance[1?3], make the switched reluctance machine (SRM) a viable candidate for hash en?vironments and high speed applications, such as aerospace[4?5], automotive[6?9]and wind power gen?eration systems[10?12].

A number of studies have been carried out to optimize the firing angles of the switched re?luctance generator(SRG) in order to maximize the generated power or generating efficiency. An approach to control the firing angles of the SRG operating at high speeds was presented in Ref. [13],in which the optimal?efficiency turn off angle was determined from a curve fitted by the speed and power in single pulse control. In Refs. [14?15], the optimal firing angles were calculated from formu?las that depend on the rotor speed and dc?link voltage and manage a best balance between iron and copper loss. The current chopping control and single pulse control were adopted respect?ively. In Refs. [16?17], an efficiency optimization system based on an optimal current waveform was presented. The control strategies for maxim?izing the efficiency were presented in Refs. [18?19],the behavior of the input control parameters was analyzed first through exhaustive data collection and it showed that the input control parameters which minimize the dc?link current ripple also maximize the generating efficiency, based on which, the controller for minimizing the dc?link current ripple was presented.

The freewheeling technique has been used in Refs. [20?23]. In Ref. [20], the increased producti?vity and output power were presented by using an intermediate freewheeling mode in the single pulse control method (SPCM). The freewheeling stage based on the PWM control method was in?troduced in Ref. [21], and the optimal set of turn off, turn on and freewheeling angles were determ?ined one by one in order to maximize the energy?conversion efficiency. The freewheeling interval was evenly distributed around the turn off angle in Ref. [22] to mitigate the dc bus current ripples, in which case it was believed that the freewheeling technique did not contribute to the output power enhancement. In Ref. [23], free?wheeling control method(FCM) was shown to be helpful for the improvement of torque ripple and dc current ripple. However, in this paper, the freewheeling technique was considered to have the capability to enhance the output power.

Whether using an intermediate freewheeling mode in SPCM or not will not influence the max?imum output power of SRG, which is proved in the theoretical analysis and also verified with nu?merical simulations and real?time experiments in this paper. Therefore, the output power optimiza?tion can be achieved just by optimizing firing angles in SPCM at a constant speed. The contri?butions of this paper can be summarized as fol?lows.

Firstly, this study provided a theoretical analysis to show that the intermediate freewheel?ing mode in SPCM is unable to increase the max?imum output power of SRG at a constant speed.Secondly, it demonstrated that by optimizing the turn off angle in SPCM, the output power can be maximized for a certain turn on angle. Thirdly,the formula of the optimal turn off angle for maximizing the output power is provided. Both numerical simulations and real?time experiments have been provided, which well demonstrated the validity of the proposed analyses and related for?mula.

This paper is organized as follows. Section 1 describes the analysis of SRG operation in SPCM and freewheeling control method(FCM). Section 2 presents the theoretical comparison of the two methods, SPCM and FCM, on output power, the formula of the optimal turn off angle for maxim?izing the output power is also given in Section 2.Numerical simulation and experimental results are given in Section 3. Section 4 presents the con?clusions.

1 Linear Analysis of SRG Operation

The voltage equation for each phase of SRG is given by[24]

Fig. 1 Typical waveforms of the idealized inductance and phase current

where K is the changing rate of inductance versus rotor position.

2 Theoretical Comparison of the Two Methods

Fig. 2 Waveforms of phase current in the two control methods

According to Eqs.(10)–(11), the following inequality can be derived

Inequality(24) means that the output power in FCM where the phase current is denoted with the red curve is smaller than that in FCM where the phase current is denoted with the purple curve. Considering the conclusion in case III, it can be concluded that the output power in FCM where the phase current is denoted with the red curve is smaller than that in SPCM where the phase current is denoted with the black curve.Therefore, in this case, FCM cannot enhance the output power.

3 Optimal Turn off Angles in SPCM

It has shown that the freewheeling tech?nique cannot enhance the output power of an SRG. Therefore, SPCM can be directly applied when the controller seeks the maximum power generation.

The output power of one phase is equivalent to the value obtained by calculating the time in?tegral of phase current when SRG operates at a constant speed, i.e.,

It can be seen from Eq. (27) that there is only one optimal turn off angle when the turn on angle is constant.

4 Simulation and Experimental Results

An 8/6 SRG is used to verify the aforemen?tioned conclusion and optimality condition. The SRG operates with the dc?link voltage of 16 V and the asymmetric bridge converter is used. Fig. 3 shows the magnetization characteristic of the SRG used in simulation. Turn on and turn off angles in SPCM are swept over a range in the generating region within one electrical period at a constant speed.

Fig. 3 Magnetization characteristics of the 8/6 SRG in simula?tion

The ranges of turn on and turn off angles swept are presented as follows:

Fig. 4 Normalized output power SPCM

Tab. 1 Orthogonal table in simulation 300 r/min

All the normalized output powers in Tab. 1 are smaller than 1, which means the output power in FCM is smaller than that in SPCM.

The optimal turn off angles in the calcula?tion and simulation are shown in Tab. 2. The in?ductance parameters used in calculation is ob?tained through magnetization characteristics in Fig. 3. It can be seen from the table, the calcu?lated optimal turn off angles are nearly equal to the optimal turn off angles in the simulation.

Tab. 2 Optimal turn-off angles by simulation and calculation

In order to verify that FCM cannot increase the output power of SRG, the SRG power gener?ation experimental system is built. Fig. 5 shows the block diagram of the experimental system.The experimental system mainly includes dc mo?tor, dc governor, switched reluctance generator,asymmetric half?bridge power converter, dc power supply, DSP controller, drive circuit, posi?tion detecting circuit, current detecting circuit and so on. The machine used in experiment is a 370 W, 220 V, 8/6 SRG. A separately excited 600 W, 220 V dc motor controlled by SIMOREG DC?MASTER 6RA70 drives the SRG. Fig. 6 shows the SRG system experimental platform.

Fig. 5 Block diagram of the experimental system

Fig. 6 SRG system experimental platform

Fig. 7 shows the normalized output power at a constant speed and a dc source in the experi?ment. The lines in different colors indicate differ?ent θonin SPCM. The points denoted with the pentagrams correspond to the operation points in the orthogonal experiment table which is shown in Tab. 3. The lines and the pentagrams in the same color indicate the same θonin SPCM and FCM. All the output powers in Fig. 7 are di?vided by the maximum value in SPCM.

It can be seen that each curve has a global maximum, and for each turn on angle, the abso?lute maximum output power connected with the line is larger than that denoted with pentagrams.

Fig. 8 shows the phase current waveform that can output the maximum power operation point under the two control methods, where the 143.33 mV of CH2 channel corresponds to the phase current of 1 A. Fig. 8a and Fig. 8e are the SPCM currents, and Fig. 8d and Fig. 8f are the FCM currents. It can be seen that although the exciting current controlled by FCM may be lar?ger than that controlled by SPCM, the integra?tion of the generating current of FCM is not lar?ger than that of SPCM. So FCM cannot increase the output power of SRG.

Fig. 7 Normalized output power in experiment

Tab. 3 Orthogonal table in FCM without invalid operation points

Fig. 8 Phase current waveforms of SRG under SPCM and FCM control

5 Conclusion

Based on the theoretical analysis, it is shown that using an intermediate freewheeling stage in SPCM cannot increase the maximum output power of SRG at a constant speed. However, by optimizing the turn off angle in SPCM, the out?put power maximization can be achieved for a certain turn on angle. The formula of the optim?al turn off angle which meets the criterion for the output power maximization is presented. Both numerical simulations and experiment results demonstrated the validity of the provided theor?etical analysis and the optimality condition for turn off angle.