Control of a Switched Reluctance Generator for Variable-Speed Wind ...

IEEE TRANSACTIONS ON ENERGY CONVERSION, VOL. 20, NO. 4, DECEMBER 2005

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Control of a Switched Reluctance Generator for Variable-Speed Wind Energy Applications Roberto C´ardenas, Member, IEEE, Rube´n Pe˜na, Member, IEEE, Marcelo Pe´rez, Jon Clare, Senior Member, IEEE, Greg Asher, Senior Member, IEEE, and Patrick Wheeler, Member, IEEE

Abstract—This paper presents a novel control system for the operation of a switched reluctance generator (SRG) driven by a variable speed wind turbine. The SRG is controlled to drive a wind energy conversion system (WECS) to the point of maximum aerodynamic efficiency using closed loop control of the power output. In the medium and low speed range, the SRG phase current is requlated using pulsewidth-modulation (PWM) control of the magnetizing voltage. For high speeds the generator is controlled using a single pulse mode. In order to interface the SRG to the grid (or ac load) a voltage-source PWM inverter is used. A 2.5-kW experimental prototype has been constructed. Wind turbine characteristics are emulated using a cage induction machine drive. The performance of the system has been tested over the whole speed range using wind profiles and power impacts. Experimental results are presented confirming the system performance. Index Terms—Reluctance generators, variable-speed drives, wind energy, wind power generation.

Fig. 1.

The 8/6 SRM.

I. INTRODUCTION HE switched reluctance machine (SRM) is robust and is appropriate for both high speed operation and operation in harsh environments due to the absence of windings and permanent magnets on the rotor [1]–[5]. The stator of the SRM is simple to wind; the end-turns are short and have no phaseto-phase crossovers. The bulk of the losses occur in the stator, which is relatively easy to cool, and this helps to produce a small machine for a given power [3]. Because of these characteristics the SRM may be used as a generator in many applications where a robust machine is required. Fig. 1, shows an 8/6 SRM. The winding A-A’ in Fig. 1 is one of the machine phases. Fig. 2 shows the idealized inductance profile of a SRM. If saturation is neglected then the inductance varies linearly with respect to the overlap between the stator and rotor poles. The inductance is maximum when the rotor and stator poles are fully aligned and minimum when the poles are completely unaligned. Motoring action is obtained when the phase is excited during the positive slope of the inductance profile. For generation, the machine phases are excited during the negative slope of the inductance profile. More information about the operation of SRMs can be found in [3].

T

Manuscript received July 27, 2004; revised December 2, 2004. This work was supported in part by the British Council and in part by the Chilean Research Council (Fondecyt) under Grant 1020721. Paper no. TEC-00215-2004. R. C´ardenas, R. Pe˜na, and M. Pe´rez are with the Electrical Engineering Department, University of Magallanes, Punta Arenas, Chile (e-mail: rcd@ieee. org). J. Clare, G. Asher, and P. Wheeler are with the School of Electrical and Electronics Engineering, University of Nottingham, Nottingham, NG7 2RD, U.K. (e-mail: [email protected]). Digital Object Identifier 10.1109/TEC.2005.853733

Fig. 2. Illustrative shape and position of current waveforms with respect to inductance profiles for SRM operation as generator or motor.

Despite its robustness and low cost, there are few publications related to the application of the SRM in variable-speed generation. Previously, applications of the switched reluctance generator (SRG) have been reported mostly for aerospace [4] and automotive [5], [6] applications. In [7], however, the possible application of SRGs in wind energy conversion systems (WECS) was discussed, highlighting the advantages of the machine for this particular application. However, control methods were not discussed, and no results were presented (simulation or experimental). In [8], the authors experimentally evaluated an 8/6 SRM of 7.5 kW for the case of dc generation using single pulse mode operation. This paper extends that work: ac grid connection is considered; a dual-voltage power converter topology is introduced; and an adaptive pulsewidth-modulation current control is used up to base speed. Additionally, the paper considers in detail the SRG power control design for optimum energy capture, for low and medium wind speed, and addresses the system implementation required for the operation of a variable speed SRG operating over a realistic speed range. Overspeed protection, for operation at high wind speed, is also considered. In this work, two power converters are used for the connection of the SRG to the grid. The machine-side power converter

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Fig. 4.

Fig. 3.

where Ct (λ, β) is the torque coefficient, ρ is the air density, R is the blade radius, β is the blade pitch angle, V is the wind velocity, and λ is the tip-speed ratio defined as

Control system proposed.

controls the current in the SRG phases, where, for the low and medium speed range, the SRG current is regulated using PWM control. In the high speed range the current is controlled using single pulse mode. For the grid side a vector-controlled frontend PWM inverter is used. The performance of the proposed generation system is studied experimentally using several wind profiles and step changes in the power reference. Section II presents the WECS system control strategy. Section III analyzes the control of the SRG and grid-side converters. Finally, in Section IV experimental results for the full system are presented and discussed. II. CONTROL SYSTEM PROPOSED The control system proposed in this paper is shown in Fig. 3. The SRG is driven by a variable-speed wind turbine and the reference output power for the SRG is calculated using a non linear function of the rotational speed ωr . A power control loop is used to regulate the current in the SRG phases. The gain of the power controller is varied as a function of the rotational speed to ensure a good dynamic response in the whole speed range of the WECS. The output of the power controller is the machine phase current demand. Signals from optical sensors (S1 . . . S4 in Fig. 3) are used to detect the overlapping between the rotor and stator poles. The power generated by the SRG is supplied to the grid using a voltage source PWM inverter that is vector controlled using a reference frame oriented along the grid voltage vd . This converter controls the dc-link voltage Edc using a proportional plus-integral (PI) controller acting on the d-axis (real power) component of the grid current. This paper only considers generation into the utility. However with some changes in the front-end converter control [9], the SRG may also be employed for ac generation into a stand-alone load.

The mechanical torque produced by a wind turbine is [10], [11] 1 πρCt (λ, β)R3 V 2 2

ωT R (2) V where ωT is the rotational speed of the blades. The power captured from the wind turbine is obtained as 1 Pm = πρCp (λ, β)R2 V 3 2 Cp (λ, β) = λCt (λ, β) (3) λ=

where Cp (λ, β) is the power coefficient. B. Control System for Low and Medium Wind Speed For low and medium wind speed, the variable speed wind turbine is controlled to operate at maximum Cp (λ, β) most of the time. In Fig. 4, V1 and V2 are wind velocities. For each wind velocity there is a point of maximum power capture which is obtained when the turbine is operating at the optimal power coefficient (Cp max ). It can be shown [10], [11] that the optimal power curve (segment OP in Fig. 4) can be calculated as Popt = kopt ωr3

(4)

where Popt is the optimal power, ωr is the rotational speed (generator side) and kopt depends on the blade aerodynamic, gear box ratio, and wind turbine parameters. In order to drive the WECS to the point of maximum aerodynamic efficiency, the power supplied by the SRG is regulated according to Pe∗ = kopt ωr3

(5)

where Pe∗ is the demanded SRG output power. Therefore, in steady state, and neglecting the losses, the power captured by the wind turbine is balanced by the power generated by the SRG. This simple control strategy drives the WECS to the optimal curve OP shown in Fig. 4. C. Control Systems for High Wind Speed

A. Variable-Speed Wind Turbines

Tm =

Power control of the wind turbine.

(1)

When the wind speed increases, the captured power also increases until the maximum rating of the power converter and electrical generator is reached. To avoid the overloading of the generator, pitch control of the blades can be used to reduce the aerodynamic efficiency of

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Fig. 5. Cp (λ, β) curves used in this work. Fig. 6.

the wind turbine. In this case the pitch angle of the blade is varied, reducing the power coefficient Cp (λ, β) and limiting the captured power [see (3)]. Since the pitch control rate is limited, it is useful to use the generator torque to force the wind turbine to stall by reducing the tip-speed ratio (see Fig. 5) for high wind speed conditions. When the rotational speed reaches ωpitch , pitch control is activated and the generator torque is increased to its limit, moving the operating point from P to S. The generator now operates at maximum torque along ST until the speed falls back to ωpitch . In practice, a small speed difference is needed between S and P to avoid excessive switching between the two operating modes. In Fig. 4, ωmax corresponds to the maximum operating speed for the WECS. The gap ωmax − ωpitch is selected depending on the pitch rate available to the pitch control system [11]. A complete discussion of pitch control and power limitation of variable speed wind turbines is outside the scope of this paper. More information about pitch control can be found in [11]. For the experimental work of this paper, the power coefficient curves shown in Fig. 5 are used [12].

III. CONTROL OF THE SRG A. SRG Power Converter The power converter arrangement used in this application is shown in Fig. 6. The grid-side converter is entirely conventional. The machine side converter has a topology in which a different voltage is used for magnetizing the machine phases (Ph1 , Ph2 . . . Ph4 ) to that for supplying energy to the dc link of the PWM inverter. When the transistor feeding any one of the machine phases (for instance Q1 in Fig. 6) is turned on at an appropriate time, energy is transferred from the capacitor Cm to the machine phase to magnetise it. When the transistor is turned off, energy (including that gained from the mechanical system) is transferred to the inverter dc link. A simple buck converter (Qm , Lm ), operating with current mode control, regulates the voltage Em by circulating some energy back to Cm . This buck converter switches at 2 kHz in the prototype. The power converter shown in Fig. 6 is appropriate for the machine used in the experimental prototype discussed in

Power converter for grid-connected SRG drive.

Section IV. However the control systems proposed in this work can be applied to other power converter topologies. B. Current Control of the SRG For the converter of Fig. 6, the equation describing the dynamics of phase j, when the transistor is turned on, is [2], [13], [14] dij ∂ψj + ωr (6) dt ∂θ where Rph and Lph are the phase resistance and inductance, respectively, ψ is the flux and ωr is the rotational speed. When the transistor is turned off, the phase dynamics is described by Em = Rph ij + Lph

dij ∂ψj + ωr . dt ∂θ The machine back-EMF is defined as [2] Em − Edc = Rph ij + Lph

(7)

∂ψ . (8) ∂θ At low speeds (where the machine back electromotive force (EMF) is small) the current can be regulated using PWM or delta modulation control [13], [14]. For PWM and considering a duty cycle d, the average current during a switching period is d¯ij ∂ ψ¯j Em − (1 − d)Edc = Rph¯ij + Lph + ωr . (9) dt ∂θ Equation (9) can be used to design the phase current controller. However, in (9) the inductance Lph and the machine backEMF have a large variation with respect to the phase current and rotor position and, in practice, a fixed PI controller cannot provide a good dynamic response. However, if the Lph and eback variations are compensated, a good dynamic response can be obtained [13]. Fig. 7 shows the back-EMF, estimated from the experimental rig for a rotational speed of 700 r/min. The aligned and unaligned positions are 30◦ and 60◦ , respectively. For low currents (2A in Fig. 7) the back-EMF is fairly constant across a wide range of rotor positions. However, at high currents the effects of saturation are evident. Another important consideration is the timing of the machine phase energization. In the aligned position the inductance is a maximum and the energization must be advanced in order to provide sufficient time for the current to be established in eback = ωr

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Fig. 7.

IEEE TRANSACTIONS ON ENERGY CONVERSION, VOL. 20, NO. 4, DECEMBER 2005

Machine back-EMF characteristics at 700 r/min.

Fig. 9.

Fig. 8.

Proposed current controller.

the phase winding [4]. Using (6), neglecting the resistance and assuming a low or zero value for eback close to the aligned position (see Fig. 7), the advance angle can be calculated as Em = Lph

∗ ωr Iph dij dθ ⇒ ∆θ = La dθ dt Em

(10)

∗ is where La is the inductance in the aligned position and Iph the phase current demand. Equation (10) is used to calculate the angle of advance for both PWM mode and single pulse mode. A similar equation can be used to turn off in advance to avoid motoring torque [6]. Fig. 8 shows the current control system proposed in this paper, which is based on the systems proposed in [13], [14]. There are three modes of operation: mode 1: PWM regulation of phase current; mode 2: hysteresis regulation of phase current; mode 3: single pulse control of phase current. Mode 1 is the normal mode at low and medium speeds and uses the duty cycle, acted on by a PI controller, to control the instantaneous phase current according to the phase current de∗ . As discussed above, the PI controller gains are made mand Iph. variable and the machine back-EMF is fed forward to compensate for measured nonlinearities. The phase current demand during PWM control varies over a small range in normal operation (due to the WECS characteristic in Fig. 4) and, therefore, the back-EMF and inductance profile are only stored for the nominal value of 6 A. Mode 2 is also used at low and medium speeds and becomes active when the phase current error exceeds specified bounds.

Supply-side converter control schematic.

Under these conditions, the PI performance is impaired due to poor compensation of nonlinearities, and the hysteresis controller is employed to ensure rapid convergence to the reference value. Mode 3 is used at high speeds when the machine back-EMF is such that there is not sufficient voltage available from the converter for effective PWM control [4]. In this single pulse mode, the instantaneous current is not controlled directly and ∗ is used only to calculate instead the phase current demand Iph the angle of advance of turn-on according to (10). The three-mode control described above is very convenient for a complete digital implementation using timer/counter devices and provides for seamless transitions between the various modes. C. Control of the Front-End Converter The aim of the boost type PWM converter is to regulate the dc link voltage Edc supplying the energy generated from the SRG into the grid. The use of vector control techniques allows the control of the ac currents with high bandwidth. In this application the reference frame is oriented along the grid voltage rotating vector. Therefore, the power supplied to the utility is controlled using the direct current id . The reactive power is controlled using the quadrature current iq . For this application the system shown in Fig. 9 is proposed [17], for the control of the front-end converter. A PI controller is used to regulate the dc-link voltage Edc . The output of this controller is the reference current i∗d . The controller is augmented by a feedforward compensation term that relates the direct current with the current idc supplied from the SRG. The feedforward compensation term is calculated from the power balance between the dc-link side and the front-end converter output. Neglecting the losses the relationship between idf and idc is idf = −

Edc idc kvd

(11)

´ CARDENAS et al.: CONTROL OF A SRG FOR VARIABLE-SPEED WIND ENERGY APPLICATIONS

Fig. 10.

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Power and voltage control loops.

where vd is the grid voltage, k arises from the two to three axes scaling and idf is the feedforward compensation current. The front-end direct current is defined as positive when the grid supplies energy to the front-end converter. Further discussion of the control of the front-end converter can be found in [9], [10], and [17]. D. Design of the Power and Voltage Control Loop In the experimental system, the electrical power is calculated as Pe = Edc idc .

(12)

Fig. 11. Small-signal model corresponding to Fig. 10.

where µE is the output from the voltage controller. Assuming that the dynamics of the power control loop are much slower than the dynamics of the machine currents, the SRG machine can be represented by the small-signal model   ∂idc ∗ . (16) ∆idc = ∗ ∆Iph ∂Iph ∗ ω r 0 ,I ph0

The power generated by the SRG is supplied to the grid by the front-end converter. Using the power balance, neglecting the converter losses and the dynamic of the direct current control loop, the current idc1 (see Figs. 6 and 9) is obtained as idc1 = −i∗d

kvd . Edc

(13)

The dc-link voltage is calculated as Cd

dEdc = idc − idc1 . dt

(14)

Using (11)–(14) the control diagram of Fig. 10 is obtained (where the symbols π and ÷ represent multiplication and division, respectively). Note that a low-pass filter is applied to the idc measurement before the power calculation to eliminate switching noise. The control system of Fig. 10 is strongly nonlinear. Linearizing around a quiescent point ∗ ) yields (Edc0 , idc0 , idc1 , ωr 0 , Iph0
 Edc0 idc0 ∆idf = − ∆idc + ∆Edc kvd kvd ∆Pe = ∆Edc idc0 + ∆idc Edc0 ∆idc1 = − ∆Edc =

kvd kvd i∗d0 ∆i∗d + ∆Edc0 2 Edc0 Edc0

(∆idc − ∆idc1 ) sCd

∆i∗d = ∆µE + ∆if

(15)

Using (15) and (16), the small-signal model of Fig. 11 is obtained. As shown in Fig. 11, there is some coupling between the power control loop and the voltage control loop. However, under the assumptions of lossless converters, the feedforward term ensures that variations in current injected into the dc link from the SRG are exactly compensated by variations in current drawn by the grid side converter. Hence, the voltage control loop is essentially decoupled from the power control loop and only has to ensure steady state accuracy and trim for the effects of losses. With these considerations, the plant for the voltage control loop becomes kvd ∆Edc = ∆µE sEdc0 Cd

(17)

a simple PI controller with a natural frequency of 6.5 Hz and damping factor of 0.8 is designed using (17). When considering design of the power control loop, it can be assumed that the dc link represents a stiff voltage source into which the SRG generates. This is again primarily due to the feedforward compensation term which ensures that variations in generated power have virtually no influence on the dc link voltage (∆Edc ≈ 0). In this case the transfer function between ∗ , and the measured power ∆Pe the power controller output, Iph (including the idc filter) is   ∆Pe 1 ∂idc Edc0 . (18) ∗ = 1 + sτ ∗ ∆Iph ∂Iph ∗ ω r 0 ,I ph0

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Fig. 12.

IEEE TRANSACTIONS ON ENERGY CONVERSION, VOL. 20, NO. 4, DECEMBER 2005

Experimental rig.

Again a PI controller can be employed. However, the term   ∂idc (19) Kdc = ∗ ∂Iph ∗ ω r 0 ,I ph0

is nonconstant and its variations must be compensated for to achieve good performance over the entire operating range. Considering that the objective is to operate the WECS along the power–speed characteristic of Fig. 4, a gain-scheduling controller of the form Gpc (s) = Ksch (ωr )[Kp + KI /s]

Fig. 13. Current waveforms at 20% rated power (6 A, 600 r/min). (a) Without back-EMF feedforward and (b) with back-EMF feedforward.

(20)

is used. In (20), Kp and KI are the proportional and integral gains of the PI power controller, Ksch (ωr ) is a variable gain, evaluated according to values of Kdc , measured experimentally by setting the output power along the power characteristic of ∗ Fig. 4 and applying small variations in the current demand Iph while the rotational speed is maintained at a constant value. Using this approach, a PI controller is designed to give a natural frequency of 2 Hz and damping factor of 0.7 for power control. Due to the gain scheduling in (20), this response is obtained for any operating point on the optimum curve of Fig. 4. For a given rotational speed and away from the optimum curve, the response varies since the gain scheduling does not account for variations in Kdc with current. However these variations are small compared to the influence of speed and satisfactory performance is achieved across the entire operating envelope of the WECS using gain scheduling based only on rotational speed. IV. EXPERIMENTAL RESULTS The control strategies described above have been implemented in the experimental system shown in Fig. 12. For the grid-side converter, a PWM voltage-source inverter, with 1-kHz switching frequency is used. The line inductance is 20-mH/phase and the dc-link voltage is regulated to 500 V. For the machine side, a 2.5-kW prototype of the power converter shown in Fig. 6 is used with the magnetizing voltage Em regulated to 250 V. A sampling frequency of 4 kHz is used for the control of the SRG currents. For the Edc and Em voltage and power control loops, the sampling frequency is 200 Hz. The system is implemented digitally in a digital signal processor (DSP) board based on the TMS320C31 processor. External DSP interfaces, implemented using timer/counter devices, are used

to provide the PWM signals to the power converters. Further parameters of the experimental rig are given in the Appendix. The SRG used in the experimental system is an 8/6 machine (see Fig. 1) with a nominal speed of 1500 rpm. Four current transducers and two voltage transducers are used to measure the phase currents and Edc , Em , respectively. A speed encoder of 2500 ppr is used to measure the rotor angle and speed. However, sensorless operation of the SRM is also feasible. According to [3, pp. 133–168], sensorless operation, with high resolution, can be obtained using observers of the SRM phase current. Sensorless operation of SRMs is beyond the scope of this paper. The variable-speed wind turbine is emulated using a vector controlled, speed regulated, cage induction machine. To implement the emulation, a wind speed profile is sent from the host PC to a second order model of the WECS implemented in the DSP. The power coefficient curves of Fig. 5 have been discretized and stored in a look up table. Linear interpolation is used to obtain the power coefficient Cp (λ, β) from the look-up table. A pitch control system with a limited pitch rate variability has also been implemented in order to emulate the operation of the wind turbine at high wind speed [11]. From the wind turbine model and considering pitch control when necessary, the rotational speed of the WECS generator (ωr∗ ) is calculated in each sampling time. The induction machine forces the SRG speed to this value. With this emulation technique the SRG rotates at the same speed as that of a generator driven by a real wind turbine. A complete discussion of the emulation technique can be found in [10] and [18] where a dc machine was used in place of the induction machine. The principle is, of course, the same. Fig. 13 shows the performance of the SRG current control system at 20% rated power, 6 A, and 600 rpm. Fig. 13(a) shows

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Fig. 15. Wind profile and rotational speed for emulated turbine inertia of 2 kg · m2 .

Fig. 14. Typical phase current waveforms illustrating advance angle. (a) 300 rpm and (b) 1500 rpm.

the response without the machine back-EMF feed forward term implemented (see Fig. 8). The PI controller is unable to compensate the fast variations of eback in the last part of the generation period (see Fig. 7) and the current drops to around 3 A. Fig. 13(b) shows the response obtained when the controller is augmented by back-EMF feedforward. In this case, the current is stable and close to the reference value of 6 A for the whole of the generating period. Clearly, back-EMF feedforward is beneficial and necessary to achieve good current regulation at all but very low speeds. For the test of Fig. 13, the hysterisis controller of Fig. 8 is not implemented. Fig. 14 shows typical phase current waveforms for PWM control (low rotational speed) and single pulse control (high rotational speed). Fig. 14(a) shows the waveform at 300 rpm with PWM control, illustrating the advance angle calculated from (10). Since the controller gain is relatively large when the poles are close to alignment, the controller saturates in a couple of sampling periods and the insulated gate bipolar transistor (IGBT) transistor is on permanently during most of the advance angle. The current reaches the reference value (6 A) when the poles are fully aligned. Fig. 14(b) illustrates the phase current waveform at 1500 rpm and approximately rated power (2.4 kW). The SRG is controlled using single pulse mode because of the large machine backEMF. Note that the peak current is produced after the transistor is turned off. In order to test the performance of the system for variable speed wind energy generation, various different wind profiles have been applied to the wind turbine emulator and the effective inertia of the emulated turbine has also been varied. Fig. 15 shows a wind profile of 60 s duration with relatively high turbulence and the corresponding rotational speed for an emulated turbine with a total inertia of 2 kgm2 . The variation in rotational

Fig. 16. Power output of SRG and dc-link voltage corresponding to conditions of Fig. 14.

speed is between 1200–1550 rpm, and the SRG power output is controlled according to (5) (pitch control is not considered during this test). For this wind profile, the average wind speed is v¯ = 8.19 ms −1 with a dispersion coefficient of σv = 2.034 ms−1 . For this wind profile, the mean turbulence intensity, dev is ≈25%. fined as σv /¯ Fig. 16 shows the power delivered by the SRG machine to the inverter dc link and the corresponding dc link voltage for the wind profile and turbine emulation of Fig. 15. The dc link voltage is very well regulated by the front-end converter, with variations of less than ±5 V around the reference value of 500 V. The variation of the power is between 700–1500 W. These results justify the earlier assumption that the influence of SRG power on the dc link voltage is small during normal operation. Fig. 17 shows some additional results for the conditions of Fig. 15. Fig. 17(a) shows the reference for the current Im , supplied to the magnetizing dc link capacitance, and the voltage Em . This voltage is well regulated with small fluctuations around the reference value of 250 V. For this power range the magnetizing current fluctuates between 12.5 A to almost 15 A. The shape of the magnetizing current fluctuations is similar to that of the output power Pe shown in Fig. 16. Fig. 17(b) shows the direct-axis (grid) voltage and the direct and quadrature currents supplied by the front-end converter. The reference frame is oriented along the grid voltage vector and in this instance iq is regulated to zero (zero reactive power). The waveform of id is determined by the voltage control loop that regulates the dc-link voltage. As expected the variations in id are essentially the same as those in the SRG power output Pe .

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Fig. 17. Voltages and currents corresponding to conditions in Fig. 14. (a) Machine-side converter and (b) grid-side converter. Fig. 19. Performance of the system corresponding to the wind profile of Fig. 18. (a) Power output and tracking error and (b) voltages and currents in the front-end converter.

Fig. 18. Wind profile and corresponding rotational speed for emulated turbine inertia of 0.5 kg · m2 .

When variable speed wind turbines are used for electrical generation, part of the power fluctuations are absorbed as inertial energy by the relatively high inertia of the blades, i.e., the wind turbine is equivalent to a narrow low-pass filter, filtering out the high-frequency components of the wind turbulence. In order to test the robustness of the proposed control system, the effects of wind turbulence are increased by emulating a wind turbine with a very low inertia (for this power rate) of 0.5 kgm2 . For this emulation, the wind profile of Fig. 18 is used. The average wind v) speed is v¯ = 7 ms−1 with a mean turbulence intensity (σv /¯ of ≈30%. Pitch control of the blades is not activated during this test. Since the inertia has been reduced, for this wind profile the rotational speed, has a large variation (between 900–1550 rpm in Fig. 18). Fig. 19(a) shows the power output of the SRG and the power tracking error Pe∗ − Pe corresponding to the conditions in Fig. 18. Good tracking is demonstrated, with a maximum tracking error of ±40 W (≈1.8% of nominal power) for the

entire wind profile, corresponding to a variation in output power between ≈300–1550 W. This illustrates that even for relatively high rotational speed variability the performance of the proposed control system is good. Fig. 19(b) shows the dc link voltage and the voltages and currents corresponding to the front-end converter. Because of the feedforward compensation term, the regulation of Edc is quite good even when the id current has large and fast variations. Although not shown here, the regulation of Em is similar to that obtained in Fig. 17 for these conditions. Fig. 20 shows the performance of the proposed control system for high wind speed operation. A pitch control system with a pitch rate of 5◦ /s is emulated. For this test the wind profile of Fig. 18 is used but with an average wind speed of v¯ = 13 ms−1 and a variation between ≈9 ms−1 to ≈17 ms−1 . For the emulated wind turbine the nominal wind speed is about 10 ms−1 for a maximum power of about 2.15 kW. For this test ωpitch is ≈1575 rpm. From the point P to S, there is a speed gap of 30 rpm (see Fig. 4). The maximum rotational speed of the system is just below 1700 rpm [see Fig. 20(c)]. A wind turbine with inertia of 2 kgm2 is emulated. Fig. 20(a) shows the SRG power output with the corresponding dc link voltage Edc and power tracking error. The output power has large and fast variations when the rotational speed is increased beyond ωpitch . This effectively drives the wind turbine to stall operation while the pitch control system reacts. Even for the relatively fast variations in the SRG output power the dc link voltage is well regulated. The power tracking is also good with a maximum power error of ≈ ± 55 W (less than 2.5% of the nominal power) for the entire wind profile.

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Fig. 21. Performance of the SRG for power steps of (a) 1 kW at 1150 rpm and (b) 2 kW at 1600 rpm.

Fig. 20. Performance of the control system for high wind speed. (a) Power error and power tracking, (b) currents and voltages in the front-end converter, and (c) rotational speeds.

Fig. 20(b) shows the direct axis (grid) voltage and the direct and quadrature currents supplied by the front-end converter. As expected the variations in id are essentially the same as those in the SRG power output Pe . Fig. 20(c) shows the variation in the rotational speed for a pitch rate of 5◦ /s. The rotational speed is below the maximum rotational speed for the entire wind profile. The power control system was also experimentally tested using power steps as illustrated in Fig. 21. For these experimental tests, the rotational speed is maintained constant (no wind turbine is emulated) and a large step is applied to the power reference Pe∗ . Fig. 21(a) shows a power step of 1 kW (40% of full load) for operation at 1150 rpm. At t≈1 s the power reference is varied from 300 W to 1.3 kW. The settling time is about ∗ ) varies from about 0.6 s and the phase reference current (Iph 3.7 A to 7 A. At 1.3 kW and 1150 rpm the machine is operating well outside the power curve of Fig. 4. However, the response is still good, justifying the use of a gain-scheduling controller based only on rotational speed.

Fig. 21(b) shows a power step of about 2 kW (80% of full load) at 1600 rpm. At t = 1 the power reference is varied from 200 W to 2.2 kW. The settling time is about 0.7 s and the phase reference current varies from 2.5 to 6.2 A. Again, very good performance is obtained for operation well outside the power curve, further justifying the approach taken. The experimental results presented in this section have confirmed the excellent performance of the proposed control strategies over a wide range of WECS operating conditions. V. CONCLUSION This paper has presented a novel control system for a switched reluctance generator as part of a WECS. Two power converters are used; one to control the machine phase currents and the other to supply the energy captured by the wind turbine into the grid. For low and medium wind speed, the output power is controlled in order to drive the WECS to the point of maximum aerodynamic efficiency. For high wind speed, the output power is controlled to drive the wind turbine to stall operation. A three-mode current controller is used, employing compensation for machine nonlinearities, which provides good current control over the full speed and current range. A novel power control system is designed, using a linearized model, which employs gain-scheduling to maintain excellent power control characteristics for the full operating envelope of the WECS by compensating for machine nonlinearities. The proposed generation system has been tested for rotational speeds between 300–1750 r/min. Several wind profiles, with high and low average speed, were used to test the performance of the system for wind energy generation. The system was also tested with power impacts and operation with wind turbines

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IEEE TRANSACTIONS ON ENERGY CONVERSION, VOL. 20, NO. 4, DECEMBER 2005

with relatively low inertia. For all these experimental tests the dynamic performance of the proposed control system was very good, justifying the approaches taken.

Roberto C´ardenas (S’95–M’97) was born in Punta Arenas, Chile. He received the Electrical Engineering degree from the University of Magallanes, Punta Arenas, Chile, in 1988, and the M.Sc. and Ph.D. degrees from the University of Nottingham, Nottingham, U.K., in 1992 and 1996, respectively. From 1989 to 1991, he was a Lecturer with the University of Magallanes. He is currently with the Electrical Engineering Department, University of Magallanes. His main interests are in control of electrical machines and variable-speed drives and renew-

APPENDIX SRM 8/6 2.5 kW, La ≈ 55 mH, Lu = 12 mH, Cm = Cdc = 2200 uF. Em and Edc voltage control loops are designed for a natural frequency of 6.5 Hz, ζ = 0.8. The Im , id, and iq current control loops are designed for a natural frequency of 70 Hz.

able energy systems.

REFERENCES [1] P. J. Lawrenson, J. M. Stephenson, P. T. Blenkirsop, J. Corda, and N. N. Fulton, “Variable speed switched reluctance motors,” Proc. Inst. Elect. Eng., vol. 127, pt. B, no. 4, pp. 253–265, 1980. [2] D. Torrey, “Switched reluctance generators and their control,” IEEE Trans. Ind. Electron., vol. 49, no. 1, pp. 3–13, Feb. 2002. [3] T. J. E. Miller, Electronic Control of Switched Reluctance Machines. ser. Newnes Power Engineering Series, Oxford, U.K.: Newnes, 2001. [4] D. E. Cameron and J. H. Lang, “The control of high-speed variablereluctance generators in electric power systems,” IEEE Trans. Ind. Appl., vol. 29, no. 6, pp. 1106–1109, Nov./Dec. 1993. [5] M. Besbes, M. Gasbi, E. Hoang, M. Lecrivian, B. Grioni, and C. Plasse, “SRM design for starter-alternator system,” in Proc. Int. Conf. Electric Machines, 2000, pp. 1931–1935. [6] C. Ferreira, S. R. Jones, W. Heglund, and W. D. Jones, “Detailed design of a 30-kw switched reluctance starter/generator system for a gas turbine engine applications,” IEEE Trans. Ind. Appl., vol. 31, no. 3, pp. 553–561, May/Jun. 1995. [7] D. A. Torrey, “Variable reluctance generators in wind-energy systems,” in Proc. IEEE Power Electronics Specialists Conf., 1993, pp. 561–567. [8] R. C´ardenas, W. F. Ray, and G. M. Asher, “Switched reluctance generators for wind energy applications,” in Proc. IEEE Power Electronics Specialists Conf. (PESC95), 1995, pp. 559–564. [9] R. Pena, R. C´ardenas, G. M. Asher, and J. C. Clare, “Vector controlled induction machines for stand-alone wind energy applications,” in Conf. Rec. IEEE-IAS Annu. Meeting, vol. 3, Oct. 2000, pp. 1409– 1415. [10] R. C´ardenas and R. Pe˜na, “Sensorless vector control of induction machines for variable speed wind energy applications,” IEEE Trans. Energy Convers, vol. 19, no. 1, pp. 196–205, Mar. 2004. [11] E. Muljadi and C. P. Butterfield, “Pitch-controlled variable-speed wind turbine generation,” IEEE Trans. Ind. Appl., vol. 37, no. 1, pp. 240–246, Jan./Feb. 2001. [12] J. Craig, “Dynamics of wind generators on electric utility network,” IEEE Trans. Aerosp Electron. Syst., vol. 12, pp. 483–493, Jul. 1976. [13] S. Schulz and K. M. Rahman, “High-performance digital PI current regulator for EV switched reluctance motor drives,” IEEE Trans. Ind. Appl., vol. 39, no. 4, pp. 1118–1126, Jul./Aug. 2003. [14] H. K. Bae and R. Krishnan, “A study of current controllers and development of a novel current controller for high performance SRM drives,” in Conf. Rec. IEEE-IAS Annu. Meeting, vol. 1, 1996, pp. 68–75. [15] Y. Sozer and D. Torrey, “Closed loop control of excitation parameters for high speed switched-reluctance generators,” IEEE Trans. Power Electron., vol. 19, no. 2, pp. 355–362, Mar. 2004. [16] R. Inerka and R. W. A. A. De Doncker, “High-dynamic direct average torque control for switched reluctance machines,” IEEE Trans. Ind. Appl., vol. 39, no. 4, pp. 1040–1045, Jul./Aug. 2003. [17] R. Pe˜na, R. C´ardenas, J. Clare, and G. Asher, “Control strategies for voltage control of a boost type PWM converter,” in Proc. IEEE Power Electronics Specialist Conf., vol. 2, Vancouver, BC, Canada, Jun. 2001, pp. 730–735. [18] R. C´ardenas, R. Pe˜na, G. Asher, and J. Clare, “Emulation of wind turbines and flywheels for experimental purposes,” in Proc. Eur. Power Electronics. Conf., Graz, Austria, Aug. 2001.

˜ (S’95–M’97) was born in Coronel, Rube´n Pena Chile. He received the Electrical Engineering degree from the University of Concepcion, Chile, in 1984, and the M.Sc. and Ph.D. degrees from the University of Nottingham, Nottingham, U.K., in 1992 and 1996, respectively. From 1985 to 1991, he was a Lecturer at the University of Masgallanes, Punta Arenas, Chile. He is currently with the Electrical Engineering Department, University of Magallanes. His main interests are the control of power electronics converters, ac drives, and renewable energy systems.

Marcelo Pe´rez was born in Punta Arenas, Chile. He received the Electrical Engineering degree from the University of Magallanes, Punta Arenas, Chile, in 2003. He is currently a Research Assistant in the Electrical Engineering Department, University of Magallanes. His main interests are in power electronics and digital control using DSP processors.

Jon Clare (M’90–SM’04) was born in Bristol, England. He received the B.Sc. and Ph.D. degrees in electrical engineering from The University of Bristol, U.K. From 1984 to 1990, he worked as a Research Assistant and Lecturer at The University of Bristol involved in teaching and research in power electronic systems. Since 1990, he has been with the Power Electronics, Machines, and Control Group at the University of Nottingham, U.K., and is currently Professor in power electronics and Head of Research Group. His research interests are: power electronic converters and modulation strategies, variable speed drive systems, and electromagnetic compatibility. Prof. Clare is a member of the Institution of Electrical Engineers and is an Associate Editor for IEEE Transactions on Industrial Electronics.

´ CARDENAS et al.: CONTROL OF A SRG FOR VARIABLE-SPEED WIND ENERGY APPLICATIONS

Greg Asher (M’98) graduated in electrical & electronic engineering from Bath University, in 1976. He received his Ph.D. in 1979, in Bond Graph structures and General Dynamic Systems. He was appointed lecturer in Control in the School of Electrical and Electronic Engineering at University of Nottingham, in 1984, where he developed an interest in motor drive systems, particularly the control of AC machines. He was appointed Prof. of Electrical Drives in 2000 and is currently Head of the School of Electrical and Electronic Engineering at Nottingham. Prof. Asher has published over 180 research papers, has received over $5M in research contracts and has supervised 29 Ph.D. students. He was a member of the Executive Committee of European Power Electronics (EPE) Association until 2003. He is a member of the Institution of Electrical Engineers and is an Associate Editor of the IEEE Industrial Electronics Society. He is currently Chair of the Power Electronics Technical Committee for the Industrial Electronics Society.

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Patrick Wheeler (M’00) received the Ph.D. degree in electrical engineering for his work on matrix converters from the University of Bristol, Bristol, U.K., in 1993. In 1993, he moved to the University of Nottingham, Nottingham, U.K., and worked as a Research Assistant in the Department of Electrical and Electronic Engineering. In 1996, he was appointed Lecturer (Senior Lecturer in 2002) in power electronic systems with the Power Electronics, Machines, and Control Group at the University of Nottingham. His research interests are in variable-speed ac motor drives, particularly different circuit topologies, power converters for power systems, and semiconductor switch use. Dr. Wheeler is a Member of the Institution of Electrical Engineers, U.K.