Excitation Control and Voltage Regulation of Switched Reluctance Generators Above Base Speed Operation. W.U.N Fernando, Mike Barnes, and Ognjen Marjanovic School of Electrical and Electronic Engineering The University of Manchester Manchester, M60 1QD, UK. Email:
[email protected],
[email protected],
[email protected]
Abstract—Switched reluctance (SR) generators are a candidate technology in vehicle electric power generation applications that require operation under harsh conditions such as high temperature and high speed. This paper presents the excitation control and DC link voltage regulator design for a SR generator system. Excitation control is designed with consideration of the machine electrical dynamics in single pulse mode of operation at different speeds, and dynamically locates the conduction period to a predefined region of the inductance profile for higher efficiency. This excitation controller is compared with a fixed turn-on angle and variable turn-off angle based excitation controller. The discrete nature of the SR generator excitation and per-stroke average DC link dynamics control issue is treated in discretetime domain. The DC link voltage regulation is formulated as a multirate proportional integral (PI) control scheme. The proposed controller is validated and analyzed by means of a finite element (FE) model based dynamic simulation of a three phase SR generator.
I. I NTRODUCTION Electrical systems for vehicle power and propulsion have become a major area of interest due to their benefits in the transportation industry, e.g., high efficiency, high fuel economy, low maintenance, and enhanced life time. The SR machine is an option for the more-electric aero-engine starter/generator [1]–[4], automotive starter/generator [5], [6], regenerative braking [7], and hybrid electric vehicle applications [8], [9]. The SR machine is an option in such applications due to its simple construction, low manufacturing cost, brushless operation, wide operational speed range, high torque density, high efficiency and the independency from rare earth permanent magnet (PM) metals [10]. However, the control of SR machines is complex in both the motoring and power generation modes of operation. This is mainly due to the inherent nonlinear nature and the difficulty in adopting standard linear control methods for the excitation control of the machine. Furthermore, the optimization of SR machine control for high efficiency and performance requires more complex analysis compared with that of the PM machine. As a result, the adoption SR machine technology to the transportation industry has been hindered. The majority of vehicle power and propulsion applications require high speed operation. SR machines perform best in
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Asymmetric half bridge converter
SR Generator b
c
a a a'
vdc
b
b'
c
a'
c' c'
Fig. 1.
b'
SR generator and asymmetric half bridge converter
single pulse mode, during high speed operation. The instantaneous output current of the system cannot be directly controlled and average current production during each stroke period of the SR generator is manipulated via the excitation voltage turn-on and turn-off positions with respect to rotor position. The commanded excitation pulse is issued in each stroke period, which can be represented as discrete-time signal. The stroke period varies proportionately with speed and the voltage regulator can be developed as a multirate system. The objective of this paper is to develop a simple excitation control strategy and multirate DC link voltage regulator in single pulse mode of SR generator operation with wide primemover speed variations. A 2 : 1 ratio of speed range in the region of 15000rpm to 60000rpm is typically seen in aeroengine operation [2]. This paper considers a scaled down SR generator with a speed range of 2000rpm to 6000rpm for control design. The proposed excitation control strategy achieves considerable optimality without the need for rigorous mathematical optimization and thereby offer the ease of adaptability to other SR machines. The SR generator system considered in this paper is shown in figure 1. Each phase of the SR machine is interfaced with an asymmetric half bridge converter. The operational dynamics of this system in generation mode is briefly explained in section II . Section III presents a brief review of classical excitation control methods and the rationale for the proposed excitation control strategy. Section IV develops a multirate DC link voltage regulator. The proposed excitation control strategies are compared and the DC link voltage regulation scheme is
validated in section V via FE model based dynamic simulation of a SR generator system. II. SR GENERATOR OPERATION bs
L
iph for a
br
iph for b iph for c
qst phase-A
phase-B
qu
excitation pulse - a
qext
qoff
qon
excitation pulse - b excitation pulse - c
qref q3 qu+ qrpp q
qa q2
q1
qon
qoff
q qext
qext qon
qoff
q
q
Fig. 2. Idealized inductance profile for one phase of a typical SR machine. Current waveforms of cases a and b are below base speed and case c is above base speed
Two classes of current control methods are available for SR generators, viz., current chopping operation and single pulse mode of operation. Current chopping is successful in low speeds where the generator back-EMF is significantly lower than the DC link voltage vdc . However, when the magnitude of the back-EMF is in the same range of vdc , chopping operation becomes difficult due to insufficiency of DC link voltage. In such situations, instantaneous current control is typically relinquished and per-stroke average current control via single pulse mode of operation is established. The SRM excitation in single pulse mode of operation is controlled by manipulation of the turn-on (θon ) and turn-off (θof f ) angles with respect to the rotor angle θ. Figure 2 shows the idealized inductance profile of a typical SR machine and the current waveforms for three cases of excitation pulses. Parameters βs and βr represents the stator pole angle and the rotor pole angle respectively. θu and θa represents the unaligned and aligned positions. θrpp represents the rotor pole pitch angle where θu + θrpp corresponds with the consequent unaligned position in phase A. The stroke angle θst represents the phase shift of the adjacent phase, at which a similar inductance profile is repeated. Given the applied voltage on a certain phase vph , the instantaneous dynamics is governed by, vph = Riph +
dψ dt
Equation (1) can also be written as: ∂ψ diph ∂ψ dθ vph = Riph + + ∂iph dt ∂θ dt
(1)
(2)
and e = ∂ψ The two partial differentials L = ∂i∂ψ ∂θ are ph considered as the inductance and back-EMF terms which are functions of iph and θ. For a typical SR machine, negative back-EMF (e < 0) results during the region dL dθ < 0 as shown in figure 2 and is utilized for power generation. The SR machine current is built-up during the period from θon to θof f while the switches are turned on. Following turn-off, energy is returned to the DC link via the free-wheeling diodes until the phase current extinguishes at θext . The selection of the excitation parameters θon and θof f is a challenging task since these parameters are not unique for the same average DC current production. Techniques used for the calculation of these excitation parameters are briefly reviewed in the section III. Figure 2 shows three cases where the same average DC current is produced. While current waveforms a and b are for the same speed with e < vdc and different excitation times, waveform c represents a typical situation where e > vdc . In waveform a and b, the back-EMF e < vdc and as a result the current decays following θ > θof f . In contrast, waveform c increases for a certain duration beyond θ > θof f due to the back-EMF e > vdc condition. Although, the three waveforms in figure 2 produce the same average DC current, the efficiencies and the power electronic converter stresses are at three different levels. Four parameters that can be used to characterize the SR generator and converter performance are the excitation penalty ε, root mean square (RMS) current level Irms , peak phase current value Ipk , and peak flux-linkage ψpk . The excitation penalty is defined by [11],
Iin = ε= Iout
1 θrpp 1 θrpp
θR of f
iph dθ
θ=θon θR ext
(3) iph dθ
θ=θof f
The per-stroke per-phase RMS current, peak current and peak flux-linkage values are calculated by, v u θ Zext u 1 u i2ph dθ Irms = t (4) θrpp θ=θon
Ipk = maximum {iph } θu τi . Assuming piecewise constant speed, the sampling period of the control can be found by: ∆τk = τk+1 − τk =
θst ωk
(13)
Continuous time DC link voltage dynamics is given by, C
dvdc = idc,avg − iload dt
(14)
By integrating the continuous time dynamics (14) over a stoke period assuming piecewise constant speed ωk , average DC link current per-stroke period idc,avg,k and load disturbance iload,k , the discrete time dynamic model can be derived as, vdc,k+1 = vdc,k +
1 1 ∆τk idc,avg,k − ∆τk iload,k C C
(15)
Substitution of (11), (13) and subtraction from a reference ∗ voltage vdc , the error system can be written as, ek+1 = ek −
θst ∗ θst i + iload,k Cωk dc,avg,k Cωk
(16)
θst ∗ where xk = [ek , ϑk ] , uk = Cω i , and wk represents k dc,avg the effective of load disturbance. 1 0 −1 Ak = , and Bk = . ∆τk 1 0 The feedback control law can be written with feedback gain F as uk = F xk . The multirate controller feedback gain F is calculated via discrete linear quadratic optimization (LQR) technique for a maximum τk value of τk = 0.0025s which yields a linear model. LQR method is known to provide superior system gain and phase margins, and minimizes a quadratic cost function of the form, X J= (xTk Qxk + uTk Ruk ) (19)
V. R ESULTS A FE model based high-fidelity continuous-time simulation replicating the SR generator and converter dynamics has been simulated with the discrete-time multirate controller. The associated SR generator and converter parameters are given in table I. The multirate controller feedback gain is calculated for the cost function (19) with R = 100 and Q = diag(1, 1000) as F = [0.1557, 2.9182]. TABLE I PARAMETERS OF THE SR GENERATOR AND CONVERTER SYSTEM .
Symbol Prated ωrated ωmax Nr Ns m La Lu ∗ vdc C
Quantity Rated power Rated speed Maximum speed No of rotor poles No of stator poles No of phases Aligned inductance Unaligned inductance Nominal DC-link voltage DC-link capaciatnce
Value 0.45kW 2000rpm 6000rpm 4 6 3 4.30mH 0.48mH 24V 20mF
Two sets of results are presented in figure 6, i.e., for the excitation controller with optimal variation of turn-on and turn-off angles (black-line) and for the excitation controller with optimal fixed turn-off angle at (θon = −50 ) and variable turn-off angle startgy (red line). The speed was varied from 2000rpm to 4000rpm and to 6000rpm. A step loading of 60%, 80% and 100% of the maximum power generation capability (Pmax ) was applied at each speed, and is shown in figure 6. The corresponding DC link voltage response, load current supplied by the system, variation of the excitation parameters, excitation penalty, and the RMS phase currents are shown in figure 6. The voltage response is within acceptable limits
Speed [rpm]
via FE model based dynamic simulations of a SR generator system. The proposed control scheme is shown to work well and achieves near optimal performance.
6000 4000 2000
(a)
Load [A]
30 20
Excitation penalty
DC link Voltage [V]
10 (b)
0 30 20 10
(c)
0 1 0.5
(d)
Peak flux-linkage [Vs]
Phase RMS current [A]
0 40 20
(e)
0 0.1
0.05 0
(f)
0
1
2
3 4 5 6 time [s] fixed turn-on angle based excitation controller variable turn-on and turn-off angle based excitation controller
Fig. 6. Variation of (a) DC link voltage (b) Speed (c) load (d) Excitation penalty (e) RMS current (f) Peak flux-linkage (g) θon and (h) θof f variation
in both excitation control methods. The excitation penalty of the fixed turn-on angle controller is higher than that of the optimal excitation controller which achieves an excitation penalty below 0.4 for all steady state conditions. In addition, the optimal excitation angle controller achieves lower RMS phase current for all load and speed steady-state conditions in contrast with the fixed turn-on strategy. The peak flux-linkage levels of both methods are near the achievable optimum. VI. C ONCLUSION The optimal variation of turn-on angle and turn-off angles for a SR generator under minimized excitation penalty, RMS current, or peak flux-linkage has been presented. A simple excitation control strategy to achieve near optimal efficiency is developed by considering the modification of turn-off angle value based on load demand and dynamic saturation of turnon angle based on the operational speed. The DC link voltage regulator is developed in the form of a discrete time multi-rate controller. The performance of the optimal excitation control method is compared with a fixed turn-on and variable turn-off angle based excitation control method. Both the excitation control methods and the DC link voltage regulator are validated
ACKNOWLEDGMENT The authors would like to thank the University of Manchester and the Overseas Research Student Award Scheme (ORS). R EFERENCES [1] C. Ferreira, S. Jones, W. Heglund, and W. Jones, “Detailed design of a 30-kw switched reluctance starter/generator system for a gas turbine engine application,” in Industry Applications Society Annual Meeting, 1993., Conference Record of the 1993 IEEE, Oct. 1993, pp. 97 –105 vol.1. [2] S. MacMinn and W. Jones, “A very high speed switched-reluctance starter-generator for aircraft engine applications,” in Aerospace and Electronics Conference, 1989. NAECON 1989., Proceedings of the IEEE 1989 National, May 1989, pp. 1758 –1764 vol.4. [3] W. Fernando, M. Barnes, and O. Marjanovic, “Modelling and control of variable frequency multiphase multi-machine ac-dc power conversion systems,” Power Electronics, Machines and Drives (PEMD 2010), 5th IET International Conference on, pp. 1 –6, april 2010. [4] ——, “Direct drive permanent magnet generator fed ac–dc active rectification and control for more-electric aircraft engines,” IET Electric Power Applications, vol. 5, no. 1, pp. 14–27, 2011. [5] B. Fahimi, A. Emadi, and J. Sepe, R.B., “A switched reluctance machinebased starter/alternator for more electric cars,” Energy Conversion, IEEE Transactions on, vol. 19, no. 1, pp. 116 – 124, march 2004. [6] A. de Vries, Y. Bonnassieux, M. Gabsi, F. d’Oliveira, and C. Plasse, “A switched reluctance machine for a car starter-alternator system,” in Electric Machines and Drives Conference, 2001. IEMDC 2001. IEEE International, 2001, pp. 323 –328. [7] H. Chen, D. Zhang, and Y. Guo, “A novel green electric drive system,” in Systems, Man, and Cybernetics, 2001 IEEE International Conference on, vol. 5, 2001, pp. 3157 –3162 vol.5. [8] N. Schofield and S. Long, “Generator operation of a switched reluctance starter/generator at extended speeds,” in Vehicle Power and Propulsion, 2005 IEEE Conference, sept 2005, p. 8 pp. [9] P. Watterson, W. Wu, B. Kalan, H. Lovatt, G. Prout, J. Dunlop, and S. Collocott, “A switched-reluctance motor/generator for mild hybrid vehicles,” in Electrical Machines and Systems, 2008. ICEMS 2008. International Conference on, oct 2008, pp. 2808 –2813. [10] M. Barnes and C. Pollock, “Power electronic converters for switched reluctance drives,” Power Electronics, IEEE Transactions on, vol. 13, no. 6, pp. 1100 –1111, Nov. 1998. [11] I. Kioskeridis and C. Mademlis, “Optimal efficiency control of switched reluctance generators,” Power Electronics, IEEE Transactions on, vol. 21, no. 4, pp. 1062 – 1072, july 2006. [12] D. Cameron and J. Lang, “The control of high-speed variable-reluctance generators in electric power systems,” in Applied Power Electronics Conference and Exposition, 1992. APEC ’92. Conference Proceedings 1992., Seventh Annual, feb 1992, pp. 121 –125. [13] H. Chen and Z. Shao, “Turn-on angle control for switched reluctance wind power generator system,” in Industrial Electronics Society, 2004. IECON 2004. 30th Annual Conference of IEEE, vol. 3, nov 2004, pp. 2367 – 2370 Vol. 3. [14] W. Heglund and S. Jones, “Performance of a new commutation approach for switched reluctance generators,” in Energy Conversion Engineering Conference, 1997. IECEC-97., Proceedings of the 32nd Intersociety, vol. 1, jul,aug 1997, pp. 574 –579 vol.1. [15] E. Mese, Y. Sozer, J. Kokernak, and D. Torrey, “Optimal excitation of a high speed switched reluctance generator,” in Applied Power Electronics Conference and Exposition, 2000. APEC 2000. Fifteenth Annual IEEE, vol. 1, 2000, pp. 362 –368 vol.1. [16] J. Faiz and R. Fazai, “Optimal excitation angles of a high speed switched reluctance generator by efficiency maximization,” in Power Electronics and Motion Control Conference, 2006. EPE-PEMC 2006. 12th International, sept 2006, pp. 287 –291. [17] Y. Sozer and D. Torrey, “Closed loop control of excitation parameters for high speed switched-reluctance generators,” Power Electronics, IEEE Transactions on, vol. 19, no. 2, pp. 355 – 362, march 2004.
