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Advances in Mechanical Engineering
Volume 2013 (2013), Article ID 261241, 14 pages
http://dx.doi.org/10.1155/2013/261241
Research Article

Modeling, Simulation, and Experiment of Switched Reluctance Ocean Current Generator System

School of Information and Electrical Engineering, China University of Mining and Technology, Xuzhou 221116, China

Received 13 June 2013; Revised 23 August 2013; Accepted 10 September 2013

Academic Editor: Luigi Cappelli

Copyright © 2013 Hao Chen et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

This paper presents nonlinear simulation model of switched reluctance (SR) ocean current generator system on MATLAB/SIMULINK with describing the structure of generator system. The developed model is made up of main model, rotor position calculation module, controller module, gate module, power converter module, phase windings module, flux-linkage module, torque module, and power calculation module. The magnetization curves obtained by two-dimensional finite-element electromagnetic field calculation and the conjugated magnetic energy graphics obtained from the three-dimensional graphics of flux linkage are stored in the “Lookup Table” modules on MATLAB/SIMULINK. The hardware of the developed three-phase 12/8 structure SR ocean current generator system prototype with the experimental platform is presented. The simulation of the prototype is performed by the developed models, and the experiments have been carried out under the same condition with different output power, turn-off angle, and rotor speed. The simulated phase current waveforms agree well with the tested phase current waveforms experimentally. The simulated output voltage curves agree well with the tested output voltage curves experimentally. It is shown that the developed nonlinear simulation model of the three-phase 12/8 structure SR ocean current generator system is valid.

1. Introduction

DC generator, synchronous generator, and induction generator are used as ocean current generators now. DC generator has the armature with windings and drainage brushes. Its structure is complex, it has maintenance workload, and the life time is short because there exist the mechanical sliding mechanisms, such as the brushes and commutator. It is difficult for the rotor to manufacture the waterproof structure. There are two categories of synchronous generators, such as the electric excited synchronous generator and the permanent magnet synchronous generator. It is difficult for the electric excited synchronous generator to manufacture the waterproof structure because of the electric excited winding on the rotor. The structure and the power supply of the permanent magnet synchronous generator are more simple than those of the electric excited synchronous generator, but the permanent magnet materials are expensive due to the high overall cost of the permanent magnet synchronous generator system. The excitation of AC induction generator is complex, and it is difficult to regulate the excitation effectively. The permanent magnet materials are also used in brushless DC generator, so its cost is also high. The switched reluctance (SR) motor drive had been applied with high reliability for many years [19]. It can also be used as generator system [1012].

The switched reluctance (SR) generator system consists of an SR generator body, power converter, and controller [16]. The generator rotor is only laminated by electrical steel, and there are brushless, no winding, no permanent magnets on the rotor and concentrated windings on the stator. It is easy to manufacture the waterproof structure. It has advantages like its firm and durable structure, low manufacture cost, and easy maintenance. It is suitable for harsh outdoor environment operation, and other types of generators cannot match its long-life operation. The independence of each phase can be done on the magnetic paths and the circuit, and the system can ensure the continued safe operation by removing the fault phase when a phase fails. It has high operational reliability and fault tolerance. The SR generator system developed for ocean current generator system has a good prospect.

This paper presents for the first time the nonlinear simulation model of the developed switched reluctance ocean current generator system by MATLAB platform, which is integrated with the magnetization curves of switched reluctance generator calculated by the two-dimensional finite-element electromagnetic field calculation, the nonlinear electrical network model of the power converter, and the excitation/commutation control algorithms. The simulation results in phase current waveforms and the output voltage curves are compared with the measured waveforms and curves for the developed prototype. The developed prototype consists of the three-phase 12/8 structure doubly salient poles reluctance generator, the three-phase asymmetric bridge power converter, and the controller, which could be applied to ocean current energy systems.

2. Structure of Generator System

The developed SR ocean current generator adopts three-phase 12/8 structure doubly salient poles reluctance generator. The sketch map of the three-phase 12/8 structure SR generator is shown in Figure 1. There are 12 poles on the stator and 8 poles on the rotor. The concentrated windings are wound on each stator pole, and four diametrically opposite windings can be connected to make up a phase winding, such as , , , and for A phase, , , , and for B phase, and , , , and for C phase.

261241.fig.001
Figure 1: Sketch map of the three-phase 12/8 structure switched reluctance generator.

The SR generator works in separately excited mode, and the main circuit of the power converter adopts three-phase asymmetrical bridge structure as shown in Figure 2. MOSFETs are used as main switches, , , , , , and , and fast recovery diodes are adopted as freewheeling diodes, , , , , , and . The voltage rating of main switches and freewheeling diodes are 80 V; the current rating of main switches and freewheeling diodes are 80 A. Though the circuit seems to be complicated, it is convenient to control the generator system since the excited loop and the power generation loop are independent of each other, the excitation is supplied by the external DC power supply during the whole operation period, and the excited voltage, and the output voltage can be adjusted independently. As shown in Figure 2, is excited current, is generated current, is A phase current, is B phase current, is C phase current, is load, is the excited voltage and is the output voltage. The triggering signals of the down main switches, , , and , are modulated by the PWM signal. The phase winding average excited voltage could be adjusted by regulating the duty ratio of the PWM signal. So the output voltage and the output power are adjustable by regulating the duty ratio of the PWM signal. The excited voltage is DC 24 V, and the frequency of the PWM signal is set to 5 kHz.

261241.fig.002
Figure 2: Power converter main circuit.

The operating status of SR generator can be divided into the excitation stage and the power generation stage when the main switches are closed and opened, respectively, which are shown in Figure 3, according to the circuit-theoretic equations as follows.

fig3
Figure 3: Sketch map of one-phase circuit.

In the excitation stage when , where is real-time rotor angle, is turn-on angle, is turn-off angle, is phase voltage, is phase current, is phase resistance, and is flux linkage of phase .

In the power generation stage when ,

By Merging (1) and (2),

3. Simulation Models

In the paper, two-dimensional finite-element electromagnetic field calculation method is used to obtain the magnetization curves of SR generator and the magnetization curves are stored in the “Lookup Table” module on MATLAB/SIMULINK. While the rotor angle and the phase current are input to the “Lookup Table” module, the flux linkage at any instantaneous rotor angle and current can be obtained. Figure 4 shows the three-dimensional graphics of the obtained flux linkage at different rotor angles and phase current and its specific variations are shown in Figures 5 and 6. Figure 5 shows that the flux linkage varies with different phase currents at different rotor angles, and it can be seen that the flux linkage varies linearly with different phase currents when the rotor angles are close to the minimum phase inductance position 0°; the flux linkage saturation increases with the increase of the rotor angle, and the larger the phase current is, the larger the flux linkage is at a constant rotor angle. Figure 6 shows that the flux linkage varies with different rotor angle at different phase currents. It is shown that the flux linkage increases with the increase of the rotor angle at a constant phase current in the first half period. The three-dimensional graphics of the conjugated magnetic energy vary with different rotor angles and phase current can be obtained from the three-dimensional graphics of flux linkage which is shown in Figure 7.

261241.fig.004
Figure 4: Three-dimensional graphics of flux linkage.
261241.fig.005
Figure 5: Flux linkage varies with phase current at different rotor angles.
261241.fig.006
Figure 6: Flux linkage varies with rotor angle at different phase currents.
261241.fig.007
Figure 7: Three-dimensional graphics of conjugated magnetic energy.
3.1. Main Model

Figure 8 shows the main simulation model of SR generator system, including the rotor position calculation module, the controller module, the power converter module, the phase winding module, the power calculation module, the excited current, and the generated current calculation module. The rotor position calculation module “Rotor_position” simulates the rotor angle relative to the stator, “” is the generator angular velocity, the controller module “Controller” simulates the controller, the power converter module “Converter” simulates the power converter, and the phase winding modules “A phase”, “B phase”, and “C phase” simulate SR generator body. The power calculation module “Sum”, the excited current calculation module “Sum1”, and the generated current calculation module “Sum2” in the bottom of Figure 8 calculate the output power, the excited current, and the generated current of the system, respectively. The system output power is obtained by adding A phase output power , B phase output power , and C phase output power as follows:

261241.fig.008
Figure 8: Main model.

The sum of A phase excited current , B phase excited current , and C phase excited current is the total excited current in the excited loop as follows:

The sum of A phase generated current , B phase generated current , and C phase generated current is the total generated current in the power generation loop as follows:

The module between “Controller” and “Sum” is used to calculate and display A phase current “” and three-phase current “”.

3.2. Rotor Position Calculation Module

As shown in Figure 9, the rotor position calculation module is used to calculate the rotor salient pole angle relative to each phase stator. While the rotor “Angular velocity” is input to the module, the relative angle of each phase “Rotor position A,” “Rotor position B,” and “Rotor position C” can be output. The total turning angle of the rotor can be converted by the turning radius which is calculated through integrating the angular velocity “Transfer Fcn1”, subtracting the relative phase angle difference, and calculating the remainder through “mod” which limits the rotor angle between 0° and the cycle turning angle of the rotor , so that the rotor relative angle of each phase can be obtained. In the paper, the of three-phase 12/8 motor is 45° that “Constant 1,” “Constant 2,” and “Constant 3” are “45”. Since A, B, and C phase must be electrified, respectively, in one period, the phase angle difference between two adjacent phases can be calculated by where is the number of phase, which is three in the paper. So the phase angle differences between A phase and B phase, A phase and C phase are 15° and 30°, which are set to “15” and “30”, respectively.

261241.fig.009
Figure 9: Internal structure of rotor position calculation module.
3.3. Controller Module

The controller module with the three-phase main switches logic is shown in Figure 10. The controller module consists of the PWM signal module and the gate drive signal module of the power converter main switches which has three submodules “Gate A,” “Gate B,” and “Gate C”. The PWM signal “Duty” can be obtained by inputting “PWM duty ratio” in the PWM signal module. “Repeating sequence” module is used to generate periodic ramp signal, and the signal cycle should be the same as the PWM signal cycle whose frequency is set to 5 kHz. While the output of “Repeating sequence” is smaller than the “PWM duty ratio,” the “Switch” output is “1.” While the output of “Repeating sequence” is larger than the “PWM duty ratio,” the “Switch” output is “0.” Those can meet the requirements of the PWM signal “Duty”. PWM signal can control one or two main switches of each phase, which is the so-called single switch chopping mode or double switches chopping mode, and the single switch chopping mode is adopted in the paper. In the gate drive signal module, “Rotor_position_A,” “Rotor_position_B,” and “Rotor_position_C” are the rotor angles relative to the stator of each phase that are connected to the outputs of “Rotor_position” in main model. “Turn-on angle” and “Turn-off angle” denote the turn-on angle and the turn-off angle of the power converter main switches. “Duty” is the PWM signal obtained from the PWM signal module. “,” “,” and “” are the phase currents, and “” is the current protection limit. The gate drive signals of three-phase main switches “Gate” can be gained through logical judgment and operation, which consist of “Gate A+,” “Gate A−,” “Gate B+,” “Gate B−,” “Gate C+,” and “Gate C−”.

261241.fig.0010
Figure 10: The internal structure of controller.
3.4. Gate A Module

The submodule describes the internal logical operation of the gate drive signals module of each phase. Take “Gate A” as an example, it contains three components: the position logical judgment part, the current hysteresis part, and the combinational logical judgment part as shown in Figure 11. In the position logical judgment part, while the input value of “Rotor position A” is between the set values of “turn-on angle” and “turn-off angle,” which means that the rotor angle of phase A is in the opening angle range, the “Interval test dynamic” outputs 1, otherwise the “Interval test dynamic” outputs 0. In the current hysteresis part, the compared results of the phase current “” and the current protection limit “” is input to the hysteresis “Relay”, the width of hysteresis can be regulated through “Relay”. While A phase current “” exceeds current protection limit “” and “”-“” is greater than the width of the hysteresis, the output “Relay” is 0. While “” is less than “” and “”-“” is greater than the width of the hysteresis, the output “Relay” is 1. Finally, the gate drive signals of the main switches in each phase can be obtained through the combinational logical judgment parts “Logical operator” and “Logical operator1” with combining the position logical operation output, the PWM signal “Duty,” and the current hysteresis result as the down gate drive signal “Gate A−,” and the upper gate drive signal “Gate A+” is the output of position logical judgment part.

261241.fig.0011
Figure 11: Internal structure of submodule “gate A.”
3.5. Power Converter Module

The internal structure of power converter is shown in Figure 12, which is set up according to the power converter topology structure shown in Figure 2. The inputs are DC excited power voltage “”, the three-phase gate drive signals “Gate” which are connected to the output of the controller “Gate.” The outputs are the output voltage “” and three-phase voltages “A+” and “A−,” “B+,” and “B−”, “C+” and “C−” which are connected to “Phase A,” “Phase B,” and “Phase C” main model, respectively. “” denote the main switches, “” denote the fast recovery diodes, and “” are used to present fault information in the simulation process connected to the output ports of “.” In the system, the excited voltage “” is set to 24 V, the “” of the excitation circuit are set to 0.0001 Ω and 2200 μF to stabilize the voltage, the capacitor “” is set to 2200 μF and the resistance “” is set to 0.0001 Ω. The current flows through the freewheeling diodes “,” “,” and “” to the charge capacitor “” and supplies power to the load “” when the main switches are opened, where the capacitor “” plays the dual role of storage and voltage-stabilizing in the circuit.

261241.fig.0012
Figure 12: Internal structure of power converter main circuit.
3.6. Phase Windings Module

By taking A phase as an example, the internal structure of “A phase” module in main model consists of the current calculation module, the torque calculation module, and the power calculation module as shown in Figure 13. Submodule “B phase” and submodule “C phase” are similar to submodule “A phase”.

261241.fig.0013
Figure 13: Internal structure of phase A module.

Ignoring mutual inductance between phase windings, the voltage balance equation of -phase is as follows:

The flux linkage is the function of the phase current and the rotor position angle of -phase as follows:

Thus,

Transforming the above equation is as follows: where is the generator angular velocity.

The current calculation module of “A phase” is built according to (11) as shown in Figure 13. The inputs are the A phase voltage signals “A+” and “A−” which are connected to the outputs of the power converter, the rotor angular velocity “Angular velocity,” and the rotor angle relative to A phase “Rotor position A.” The outputs are the phase current “”, the instantaneous torque of A phase “”, the excited current “”, the generated current “,” and the A phase output power “.” Combine A phase voltage signals “A+” and “A−” to A phase voltage through “Voltage measurement” module, multiply the feedback phase current “” and the phase winding resistance “” to obtain the winding resistance voltage drop, calculate results of “” through “Sum” and “Divide” module, and then get A phase current through “Integrator” as the input of “Controlled current source,” which is used to connect the electrical ports and the signal ports to transport the A phase current “.” The “Switch 1” module and “Switch” are used to separate the phase current to the excited current “” and the generated current “” by setting the value of turn-off angle as boundary, which means the threshold of “Switch 1” and “Switch” is set to the same value with “turn-off angle.” While the “Rotor position A” is smaller than the threshold, the generator enters into the excitation stage, , . Otherwise while the “Rotor position A” is larger than the threshold, the generator enters into the power generation stage, , . The last submodules “Flux linkage,” “Torque,” and “Power” included in phase winding modules are used to calculate the partial derivatives of the flux linkage to phase current and to rotor angle , the instantaneous torque of A phase , and the A phase output power . The following will introduce them, respectively.

3.7. Flux Linkage Module

The partial derivatives are calculated by: where and are the instantaneous values of phase current and rotor angle; and are the increments of phase current and rotor angle.

As shown in Figure 14, the submodule “Flux linkage” in Figure 13 is built according to (12). The inputs are the instantaneous values of phase current “” and rotor relative angle “”, and and can be calculated which are denoted by “” and “”. The data of magnetization curves shown in Figure 4 are stored in “flux linkage,” “flux linkage 1,” and “flux linkage 2,” and the two-dimension sample insert method is adopted for calculating the flux linkage at the certain phase current and the certain rotor angle based on the magnetization curve data. “Constant” and “Constant2” which denote the current increment “” are both set to 0.01, “Constant1” and “Constant3” which denote the rotor angle increment “” are both set to 0.01. In addition, the proportion coefficient “” is used to unify the units of the rotor relative angle and the value in the lookup table of the flux linkage and conjugated magnetic energy, which is set to “.”

261241.fig.0014
Figure 14: Internal structure of “flux linkage” submodule.
3.8. Torque Module

The instantaneous torque of one phase is given by where “” is conjugated magnetic energy of SR generator.

The conjugated magnetic energy at different phase currents and rotor angles can be calculated by the following equation with its three-dimension graphics shown in Figure 7:

The “Torque” submodule can be built as shown in Figure 15 according to the previous equations. The conjugated magnetic energy data are stored in “Coenergy” and “Coenergy1.” Inputs are the instantaneous values of the phase current “” and the rotor relative angle “,” and output is the A phase torque “.” “Constant” and “Constant1” which denote the rotor angle increment are both set to 0.01. The proportion coefficient “” is set to “”, which plays the same role with the “” in Figure 14.

261241.fig.0015
Figure 15: Internal structure of torque calculation module.
3.9. Power Calculation Module

The “Power” module is shown in Figure 16. The inputs are the generated current “,” the phase voltage “,” and the excited current “.” The output is the output power of phase A “.” The generated power “” and the excited power “” can be obtained by the generated current “” and the excited current “” multiplied by the phase voltage “,” respectively, and then through the “Mean Value” and “Mean Value 1” to get the mean value. In addition, the generated power value is negative that can be transformed as positive value by setting “” as “−1.” Then the result of the generated power “” minus the excited power “” to get the value of the output power of A phase is as follows:

261241.fig.0016
Figure 16: Internal structure of power calculation module.

4. Simulation and Experimental Results

The simulation of the prototype is performed by the developed models on MATLAB. According to the designed hardware and software of the SR generator system prototype, the experiments have been carried out. The photograph of the three-phase 12/8 structure SR ocean current generator system prototype is shown in Figure 17 with SR generator and power converter-controller. The hardware experimental platform consists of the SR generator body, the power converter, the controller, the prime mover, and the torque/rotor speed instrument. The excited voltage is 24 V, the frequency of the PWM signal is set to 5 kHz, and the rotor cycle turning angle is 45°, while the maximum inductance position is at 22.5° and the minimum inductance position is at 0°. The turn-on angle is fixed at the maximum inductance position of 22.5°.

fig17
Figure 17: Photograph of prototype.

The tested phase current waveforms are shown as “2” lines, and the simulated phase current waveforms are shown as “1” lines. While the rotor speed is 1000 r/min and the turn-off angle is 30°, the phase current waveforms are shown in Figure 18 as follows: (a) the output power is 30.27 W, the efficiency is 81.66%, the abscissa is 0.0005 s/div, and the ordinate is 5.0 A/div, (b) the output power is 18.51 W, the efficiency is 79.34%, the abscissa is 0.0005 s/div, and the ordinate is 2.0 A/div, (c) the output power is 8.55 W, the efficiency is 68.12%, the abscissa is 0.0005 s/div, the ordinate is 1.0 A/div, (d) the output power is 1.63 W, the efficiency is 55.25%, the abscissa is 0.001 s/div, and the ordinate is 1.0 A/div, and (e) the output power is 0.6 W, the efficiency is 29.13%, the abscissa is 0.001 s/div, the ordinate is 1.0 A/div. It is shown that the phase current decreases with the decrease of the load.

fig18
Figure 18: Phase current waveforms I.

While the rotor speed is 1000 r/min, the phase current waveforms are shown in Figure 19 as follows: (a) the turn-off angle is 28°, the output power is 4.98 W, the efficiency is 74.77%, the ordinate is 2.0 A/div, and the abscissa is 0.0005 s/div, (b) the turn-off angle is 30°, the output power is 15.38 W, the efficiency is 73.30%, the ordinate is 2.0 A/div, and the abscissa is 0.0005 s/div, and (c) the turn-off angle is 33.75°, the output power is 22.56 W, the efficiency is 60.43%, the ordinate is 5.0 A/div, and the abscissa is 0.0010 s/div. The maximum of phase current increases significantly with the increase of the turn-off angle and the increase of the output power.

fig19
Figure 19: Phase current waveforms II.

While the turn-off angle is 30°, the ordinate is 1.0 A/div, the phase current waveforms are shown in Figure 20 as follows: (a) the rotor speed is 250 r/min, the output power is 2.47 W, the efficiency is 21.04%, and the abscissa is 0.0020 s/div, (b) the rotor speed is 500 r/min, the output power is 2.63 W, the efficiency is 46.55%, and the abscissa is 0.0010 s/div, (c) the rotor speed is 750 r/min, the output power is 2.47 W, the efficiency is 42.27%, the abscissa is 0.0005 s/div, and (d) the rotor speed is 1000 r/min, the output power is 2.36 W, the efficiency is 63.10%, and the abscissa is 0.0005 s/div. The phase current decreases with the increase of the rotor speed and the decrease of the output power.

fig20
Figure 20: Phase current waveforms III.

While the turn-on angle is 22.5°, the turn-off angle is 30°, the rotor speed is 1000 r/min, the abscissa is 0.5 s/div, and the ordinate is 10.0 V/div, the output voltage curves in establishing voltage process are shown in Figure 21 as follows: (a) the given output voltage is 7.0 V, the output power is 4.50 W, (b) the given output voltage is 30.0 V, the output power is 82.57 W, (c) the given output voltage is from 14.5 V to 30.0 V and the output power is from 19.29 W to 82.57 W, and (d) the given output voltage is from 30.0 V to 14.5 V and the output power is from 82.57 W to 19.29 W.

fig21
Figure 21: Output voltage curves.

It is shown that the simulated phase current waveforms are consistent with the experimental results. The simulated output voltage curves agree well with the tested output voltage curves experimentally. The nonlinear simulation model of the developed SR ocean current generator system by MATLAB platform is validated.

5. Conclusions

The SR generator system has a good prospect for ocean current generator system with high operational reliability and fault tolerance. The simulated phase current waveforms agree well with the tested phase current waveforms experimentally. The simulated output voltage curves agree well with the tested output voltage curves experimentally. The proposed nonlinear simulation model of the three-phase 12/8 structure SR generator system on MATLAB/SIMULINK is valid. The method of developed nonlinear simulation models can be adopted to set up the nonlinear simulation models of the other SR generator system with other structure switched reluctance generators, other topologies of the power converter, and other generator control schemes on MATLAB/SIMULINK. The developed nonlinear simulation model contributes to optimized control strategies and parameters of the SR ocean current generator system with saving developed period.

Acknowledgments

This work was supported in part by the National Natural Science Foundation of China under Grant no. 51277174, International S&T Cooperation Program of China under Grant no. 2011DFA61150, and the Specialized Research Fund for the Doctoral Program of Higher Education of China under Grant no. 20120095110019.

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