CN118508816A - Permanent magnet linear generator optimal control method applied to single-degree-of-freedom direct-drive wave energy power generation system - Google Patents
Permanent magnet linear generator optimal control method applied to single-degree-of-freedom direct-drive wave energy power generation system Download PDFInfo
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Abstract
The invention discloses a permanent magnet linear generator optimal control method applied to a single-degree-of-freedom direct-drive type wave energy power generation system, relates to the field of permanent magnet linear generators for wave energy power generation, and is mainly used for energy conversion and efficiency improvement of wave energy power generation devices. The invention comprises the following steps: s1, establishing a mathematical model of a permanent magnet linear generator; s2, establishing a mathematical model of the maximum wave energy capturing condition; s3, setting parameters of the permanent magnet linear generator and optimizing the control method; the invention improves the running stability and the power generation conversion efficiency of the motor by optimizing the structure and the control method of the linear motor.
Description
Technical Field
The invention relates to the technical field of single-degree-of-freedom direct-drive wave energy power generation, in particular to a permanent magnet linear generator optimal control method applied to a single-degree-of-freedom direct-drive wave energy power generation system.
Background
The permanent magnet linear generator has the advantages of simple structure, reliable operation, high efficiency and the like, so that the permanent magnet linear generator has wide application prospect in the field of wave energy power generation. The environment for wave energy power generation is ocean, and the environment conditions are complex and changeable, including the influence of wind waves, ocean currents, tides and other factors. Such an environment may cause the permanent magnet linear motor to be subjected to large impact and vibration during the operation, which affects the stability and reliability thereof. Due to the characteristics of instability, randomness, intermittence and the like of wave energy, the running process of the permanent magnet linear generator is faced with complex dynamic characteristics and nonlinear characteristics, so that the power generation running performance is unstable, the power generation conversion efficiency of the wave energy is further influenced, and the method brings challenges to the optimal control of the permanent magnet linear generator.
In order to solve the defects in the background art, the invention aims to provide a motor optimal control method applied to a single-degree-of-freedom direct-drive wave power generation system, and the optimal control method aims to reduce the loss of a motor and improve the operation efficiency and stability of the motor by optimizing the structural design and operation parameters of the motor.
Disclosure of Invention
The invention aims at realizing the motor optimization control method applied to the single-degree-of-freedom direct-drive wave energy power generation system, and the method comprises the following steps:
s1, establishing mathematical model of permanent magnet linear generator
S2, establishing a mathematical model of maximum wave energy capturing conditions
S3, parameter setting and optimal control experimental method for permanent magnet linear generator
The establishment of the mathematical model of the permanent magnet linear generator comprises the following steps:
The permanent magnet synchronous linear motor (PMSLG) may be modeled mathematically as a permanent magnet synchronous motor (PMSG). The stator windings are symmetrically distributed in three phases, and the axial lines of the windings are different by 120 degrees in electrical angle; the generated air gap magnetomotive force and magnetic flux density are distributed in a sine wave manner; neglecting the influence of the ventilation grooves and the winding grooves, and assuming that the stator and rotor surfaces are smooth; neglecting the influence of magnetic circuit saturation, hysteresis loss and eddy current loss;
The park transformation is performed to transform the electromagnetic quantities represented by stationary three-phase coordinate systems a, b, c into electromagnetic quantities represented by two-phase rectangular coordinate systems d, q rotating with the rotor and a stationary 0-axis coordinate system (collectively referred to as dq0 coordinate system). The coordinate transformation does not change the electromagnetic relationship inside the generator.
The park transformation changes a variable coefficient differential equation into a constant coefficient differential equation, adopts the park transformation with equal power, and has the functions of:
Under a three-phase static coordinate system, the voltage function of the PMSG stator three-phase loop is as follows:
Wherein R a、Rb、Rc is a three-phase resistor, and R a＝Rb＝Rc＝Rs;ia、ib、ic is stator three-phase current because of the symmetry of three-phase windings; phi a、φb、φc is a three-phase stator flux linkage, and the corresponding flux linkage function is:
Wherein L is self-inductance and equal; m is mutual inductance and equal; phi f is the permanent magnet flux linkage; θ is the angle between d-axis and a-axis, θ=ω et;ωe is the electrical angular velocity, N p is the motor pole pair number and τ is the motor pole pitch. After the transformation of the equal power park, the voltage function under the dq axis rotation coordinate system is as follows:
u d、uq、id、iq is dq axis stator voltage and current, respectively; l d、Lq is dq axis equivalent inductance, and L d＝Lq＝Ls;Ψd、Ψq is equivalent flux linkage of the stator flux linkage under dq axis. The equivalent flux linkage function is:
The complete expression of the voltage function of the permanent magnet synchronous generator under d and q coordinate axes can be obtained by the formula:
SVPWM control of the generator based on i d =0 can be achieved by the above formula.
The generator electromagnetic force F pto can be obtained in analogy to the electromagnetic force under the motor, and its functional form is:
Because of i d＝0,Ld＝Lq＝Ls, the reduced function is:
the induced electromotive force E of the PTO device is as follows:
the voltage difference between the stator voltage U and the induced electromotive force E of the PTO device is:
further, the establishing the maximum wave energy capturing condition includes the steps of:
Float kinetic function:
z b is the displacement of the float relative to the hydrological zero; Acceleration of the float
M b is the total mass of the float body and the linear generator rotor
F e is wave force
F hs is hydrostatic recovery: f hs＝-Khs·Zb
K hs is the equivalent elastic coefficient of seawater and is related to the geometric structure of the floater
F pto is the thrust of the PTO device, namely the electromagnetic thrust of the linear motor
F rad is the radiation force to which the float body is subjected
According to the research on wave force, under irregular waves, a convolution integral formula of a Cummins equation is introduced to describe the fluid memory effect, and the corresponding radiation force function is as follows:
after the above formula is finished, the kinetic equation of the single-degree-of-freedom direct-drive wave power generation device can be obtained:
further, a frequency domain equation of the direct-drive wave power generation system is obtained:
Wherein F g is a counter electromagnetic force, and is the interaction force of electromagnetic thrust F pto; b 0 is the radiation force damping coefficient, which is obtained by the formula:
when the back electromagnetic force of the direct-drive wave energy power generation system is only in a linear relation with the speed of the floater, the back electromagnetic force can be expressed as follows:
wherein R e is the optimal damping coefficient of the direct-drive wave energy power generation system.
The wave and float velocity phase difference angles θ, R e, ω can be expressed as:
The method can be obtained after Lawster transformation:
The maximum wave energy capture condition is derived when the damping Z e of the energy output system is equal to the conjugate of the impedance Z 1 within the wave energy conversion system:
The optimal speed for obtaining the float body is:
the system dynamics model can be equivalent to a second-order resonance circuit, and the response form of the system can be compared with series resonance.
Under the condition that the device achieves maximum wave energy capture, resonance can be achieved under any wave energy environment as long as the motion stroke, acting force and output power of the permanent magnet linear generator of the wave energy power generation device are within the allowable range, so that the device captures the maximum wave energy, and the application area is wide. PMLG in operation, energy is often transferred bi-directionally, and the electric machine outputs electrical energy as a generator when energy is flowing in a forward direction, whereas the input electrical energy is input as an electric motor to the PTO.
Further, the experimental method for parameter setting and optimal control of the permanent magnet linear generator comprises the following steps:
Furthermore, the primary pole structure is selected, the permanent magnet with the long secondary structure is longer than the stator winding, and the whole stator winding is an effective winding although the permanent magnet is made of more materials, so that the energy conversion efficiency is high. Long secondary structure studies were chosen herein from the perspective of high energy conversion.
Further, parameters are selected, the direct-drive type PTO device float body is connected with a rotor of the linear motor through a connecting rod, and the float body is driven by wave force to move to drive the linear motor rotor to do up-down heave motion. In an ideal case, the equation of motion of a wave can be described as:
H is the wave height and lambda is the wavelength. When the sea wave level is 4, h=2.5m, λ=30m, and under ideal conditions (neglecting factors such as motor friction and wave reflection, Φ=0), the motion velocity equation of the wave can be expressed as:
v＝0.26sin0.21t
The maximum wave motion speed obtained by the method is 0.26m/s, and the linear generator is optimized and controlled by the constant speed of 0.26m/s for the purpose of conveniently processing data and verifying the motor performance.
Further, the permanent magnet linear motor is a 9-pole 12-slot, m=3, the modeling linear generator is the same as the long secondary model, and only the right side is modeled for convenience of analysis because the linear generator model is completely symmetrical left and right. The motor is designed as a three-phase permanent magnet linear motor, and the label groups of A, B, C three-phase windings are arranged.
Furthermore, the existence of the auxiliary groove structure enables the magnetic flux distribution at the side end of the stator to be greatly different, and the existence of the auxiliary groove can convert part of leakage magnetic flux into effective magnetic flux, so that the change rate of air gap magnetic resistance is greatly reduced, and the positioning force born by the rotor can be theoretically reduced. In order to reduce the positioning force applied to the rotor, the stator structure is improved, and the tooth grooves at the edge are widened, which is equivalent to the function of an auxiliary groove.
Further, compared with the prior motor improvement, the no-load induced electromotive force amplitude of the linear motor without the auxiliary groove is increased; the difference in induced electromotive force between the C phase and A, B phase is reduced. After the auxiliary groove is added, the electromechanical energy conversion efficiency of the linear motor is enhanced under the same condition, the working efficiency and performance of the motor are improved, and the correctness and rationality of the improvement of the stator tooth slot structure of the linear motor are verified.
Further, when the linear motor is loaded, the three phases of load-induced electromotive forces are different from each other and smaller than when no load is applied, which is caused by the inherent longitudinal side effect of the linear motor and the armature reaction when loaded. The phases of the phases are shifted from those of the no-load induced electromotive force, because the phase of the no-load induced electromotive force is determined only by the magnetic field generated by the permanent magnet, and the phase of the no-load induced electromotive force is determined by the magnetic field which reacts and acts together with the permanent magnet and the armature when the load is applied.
Further, the initial movement direction of the test rotor is downward, the rotor of the linear motor is at the highest position at the moment 0, then the rotor starts to move downward, the speed is faster and faster, and the maximum speed of the rotor reaches 0.26m/s at the moment 0.5 s. At this time, no-load induced electromotive force generated around the stator is also maximized. Thereafter, the mover continues to move down while the speed is gradually reduced, and the magnitude of the induced electromotive force is also gradually reduced. When 1s, the mover moves to the lowest point, the speed of the mover is 0, and the induced electromotive force is also 0. The mover then follows the wave upward, which induces an electromotive force and changes in speed similar to when the mover moves downward.
The invention has the beneficial effects that: the linear motor with improved stator tooth slot has less positioning force to the rotor during motion. Under no-load and load, the three-phase winding can generate induced electromotive force at the constant speed and the sinusoidal speed at the rotor speed of the linear motor, and the amplitude and the phase change of the induced electromotive force are consistent with the normal theory, so that the correctness and rationality of the structural design of the linear motor are proved, and the high-efficiency conversion from wave energy to electric energy can be further realized.
Drawings
For a clearer description of embodiments of the invention or of the solutions of the prior art, the drawings that are required to be used in the description of the embodiments or of the prior art are briefly described below, from which, without the inventive effort, the person skilled in the art can obtain further drawings:
FIG. 1 is a diagram of a long secondary linear motor model of the present invention;
FIG. 2 is a diagram of the present invention's set of reference numbers for windings;
FIG. 3 is a schematic diagram of the distribution of magnetic lines without auxiliary slots and magnetic lines with auxiliary slots according to the present invention;
FIG. 4 is a schematic illustration of a linear motor model with auxiliary grooves in accordance with the present invention;
FIG. 5 is a waveform diagram of the positioning thrust of the present invention;
FIG. 6 is a waveform diagram of the no-load induced electromotive force experiment of the present invention;
FIG. 7 is a diagram of experimental waveforms of resistive load induced electromotive force according to the present invention;
FIG. 8 is a waveform diagram of an experimental no-load induced electromotive force at sinusoidal velocity according to the present invention;
FIG. 9 is a graph of velocity and position experiments for a patent of the present invention;
The present invention will be described in further detail with reference to specific examples according to practical circumstances. But not as a basis for any limitation of the invention. All other embodiments, based on the embodiments of the invention, which a person skilled in the art would obtain without making any inventive operation, are within the scope of the invention.
The invention provides a motor optimization control method applied to a single-degree-of-freedom direct-drive wave power generation system, which comprises the following steps:
s1, establishing mathematical model of permanent magnet linear generator
S2, establishing a mathematical model of maximum wave energy capturing conditions
S3, parameter setting and optimal control experimental method for permanent magnet linear generator
Further, according to fig. 1, the establishment of the mathematical model of the permanent magnet linear generator includes the following steps:
The permanent magnet synchronous linear motor (PMSLG) may be modeled mathematically as a permanent magnet synchronous motor (PMSG). The stator windings are symmetrically distributed in three phases, and the axial lines of the windings are different by 120 degrees in electrical angle; the generated air gap magnetomotive force and magnetic flux density are distributed in a sine wave manner; neglecting the influence of the ventilation grooves and the winding grooves, and assuming that the stator and rotor surfaces are smooth; neglecting the influence of magnetic circuit saturation, hysteresis loss and eddy current loss;
The park transformation is performed to transform the electromagnetic quantities represented by stationary three-phase coordinate systems a, b, c into electromagnetic quantities represented by two-phase rectangular coordinate systems d, q rotating with the rotor and a stationary 0-axis coordinate system (collectively referred to as dq0 coordinate system). The coordinate transformation does not change the electromagnetic relationship inside the generator.
The park transformation changes a variable coefficient differential equation into a constant coefficient differential equation, adopts the park transformation with equal power, and has the functions of:
Under a three-phase static coordinate system, the voltage function of the PMSG stator three-phase loop is as follows:
Wherein R a、Rb、Rc is a three-phase resistor, and R a＝Rb＝Rc＝Rs;ia、ib、ic is stator three-phase current because of the symmetry of three-phase windings; phi a、φb、φc is a three-phase stator flux linkage, and the corresponding flux linkage function is:
Wherein L is self-inductance and equal; m is mutual inductance and equal; phi f is the permanent magnet flux linkage; θ is the angle between d-axis and a-axis, θ=ω et;ωe is the electrical angular velocity, N p is the motor pole pair number and τ is the motor pole pitch. After the transformation of the equal power park, the voltage function under the dq axis rotation coordinate system is as follows:
u d、uq、id、iq is dq axis stator voltage and current, respectively; l d、Lq is dq axis equivalent inductance, and L d＝Lq＝Ls;Ψd、Ψq is equivalent flux linkage of the stator flux linkage under dq axis. The equivalent flux linkage function is:
the complete expression of the voltage function of the permanent magnet synchronous generator under d and q coordinate axes is obtained by the formula:
SVPWM control of the generator based on i d =0 can be achieved by the above formula.
The generator electromagnetic force F pto can be obtained in analogy to the electromagnetic force under the motor, and its functional form is:
Also because of i d＝0,Ld＝Lq＝Ls, the reduced function is:
the induced electromotive force E of the PTO device is as follows:
the voltage difference between the stator voltage U and the induced electromotive force E of the PTO device is:
further, the establishing of the mathematical model of the maximum wave energy capturing condition comprises the following steps:
Float kinetic function:
z b is the displacement of the float relative to the hydrological zero; Acceleration of the float
M b is the total mass of the float body and the linear generator rotor
F e is wave force
F hs is hydrostatic recovery: f hs＝-Khs·Zb
K hs is the equivalent elastic coefficient of seawater and is related to the geometric structure of the floater
F pto is the thrust of the PTO device, namely the electromagnetic thrust of the linear motor
F rad is the radiation force to which the float body is subjected
According to the research on wave force, under irregular waves, a convolution integral formula of a Cummins equation is introduced to describe the fluid memory effect, and the corresponding radiation force function is as follows:
after the above formula is finished, the kinetic equation of the single-degree-of-freedom direct-drive wave power generation device can be obtained:
further, a frequency domain equation of the direct-drive wave power generation system is obtained:
Wherein F g is a counter electromagnetic force, and is the interaction force of electromagnetic thrust F pto; b 0 is the radiation force damping coefficient, which is obtained by the formula:
when the back electromagnetic force of the direct-drive wave energy power generation system is only in a linear relation with the speed of the floater, the back electromagnetic force can be expressed as follows:
wherein R e is the optimal damping coefficient of the direct-drive wave energy power generation system.
The wave and float velocity phase difference angles θ, R e, ω can be expressed as:
The method can be obtained after Lawster transformation:
The maximum wave energy capture condition is derived when the damping Z e of the energy output system is equal to the conjugate of the impedance Z 1 within the wave energy conversion system:
The optimal speed for obtaining the float body is:
the system dynamics model can be equivalent to a second-order resonance circuit, and the response form of the system can be compared with series resonance.
Under the condition that the device achieves maximum wave energy capture, resonance can be achieved under any wave energy environment as long as the motion stroke, acting force and output power of the permanent magnet linear generator of the wave energy power generation device are within the allowable range, so that the device captures the maximum wave energy, and the application area is wide. PMLG in operation, energy is often transferred bi-directionally, and the electric machine outputs electrical energy as a generator when energy is flowing in a forward direction, whereas the input electrical energy is input as an electric motor to the PTO.
Further, according to fig. 2, the permanent magnet linear generator parameter setting includes the following steps:
Furthermore, the primary pole structure is selected, and the long secondary pole structure uses more permanent magnet materials, but the whole stator winding is an effective winding, so that the energy conversion efficiency is high. Long secondary structure studies were chosen herein from the perspective of high energy conversion.
Further, parameters are selected, the direct-drive type PTO device float body is connected with a rotor of the linear motor through a connecting rod, and the float body is driven by wave force to move so as to drive the linear motor rotor to do up-down heave motion. In an ideal case, the equation of motion of a wave can be described as:
H is the wave height and lambda is the wavelength. When the sea wave level is 4, h=2.5m, λ=30m, and under ideal conditions (neglecting factors such as motor friction and wave reflection, Φ=0), the motion velocity equation of the wave can be expressed as:
v＝0.26sin0.21t
The maximum wave motion speed is 0.26m/s, and the motor performance is verified for the convenience of data processing, so that the rotor is provided with a constant speed of 0.26m/s, and the linear generator is subjected to optimal control experimental analysis.
Further, the experimental analysis process for optimizing control of the permanent magnet linear generator comprises the following steps:
the permanent magnet linear motor is a 9-pole 12-slot, m=3, the modeling linear generator is the same as the long secondary model, and only the right side is modeled for convenience in analysis because the linear generator model is completely symmetrical left and right. The designed motor is a three-phase permanent magnet linear motor, and the label groups of A, B, C three-phase windings are arranged
According to fig. 3 and 4, the existence of the auxiliary slot structure makes the magnetic flux distribution at the side end of the stator generate a larger difference, and the existence of the auxiliary slot can convert a part of leakage magnetic flux into effective magnetic flux, so that the change rate of air gap magnetic resistance is greatly reduced, and the positioning force applied to the rotor can be reduced theoretically. In order to reduce the positioning force applied to the rotor, the stator structure is improved, and the tooth grooves at the edge are widened, which is equivalent to the function of an auxiliary groove.
According to fig. 5, the positioning pushing force applied to the mover with the auxiliary slot motor during the movement is larger except for the individual position, and the rest positions are below 70N and frequently fluctuated near the value 0. Compared with the positioning driving force of the motor without the auxiliary groove, the positioning driving force is reduced by about 30N, and the correctness of the theoretical analysis is proved.
According to fig. 6, the amplitude of the no-load induced electromotive force of the linear motor without auxiliary slots is increased compared with that before the motor is improved; the difference in induced electromotive force between the C phase and A, B phase is reduced. After the auxiliary groove is added, the electromechanical energy conversion efficiency of the linear motor is enhanced under the same condition, the working efficiency and performance of the motor are improved, and the correctness and rationality of the improvement of the stator tooth slot structure of the linear motor are verified.
According to fig. 7, when the linear motor is loaded, the three phases of load induced electromotive forces are different from each other and smaller than when no load is applied, which is caused by the longitudinal side effect inherent to the linear motor and the armature reaction when loaded. The phases of the phases are shifted from those of the no-load induced electromotive force, because the phase of the no-load induced electromotive force is determined only by the magnetic field generated by the permanent magnet, and the phase of the no-load induced electromotive force is determined by the magnetic field which reacts and acts together with the permanent magnet and the armature when the load is applied.
According to fig. 8 and 9, the initial movement direction of the rotor is downward, the rotor of the linear motor is at the highest position at the moment 0, then the rotor starts to move downward, the speed is faster and faster, and the maximum speed of the rotor reaches 0.26m/s at the moment 0.5 s. At this time, no-load induced electromotive force generated around the stator is also maximized. Thereafter, the mover continues to move down while the speed is gradually reduced, and the magnitude of the induced electromotive force is also gradually reduced. When 1s, the mover moves to the lowest point, the speed of the mover is 0, and the induced electromotive force is also 0. The mover then follows the wave upward, which induces an electromotive force and changes in speed similar to when the mover moves downward.
In conclusion, the rotor of the linear motor with the improved stator tooth slot can be subjected to smaller positioning force during movement. Under no-load and load, the three-phase winding can generate induced electromotive force at the constant speed and the sinusoidal speed at the rotor speed of the linear motor, and the amplitude and the phase change of the induced electromotive force are consistent with the normal theory, so that the correctness and rationality of the structural design of the linear motor are proved, and the high-efficiency conversion from wave energy to electric energy can be further realized.
Claims (4)
1. The permanent magnet linear generator optimal control method applied to the single-degree-of-freedom direct-drive wave energy power generation system is characterized by comprising the following steps of:
s1, establishing a mathematical model of a permanent magnet linear generator;
s2, establishing a mathematical model of the maximum wave energy capturing condition;
s3, setting parameters of the permanent magnet linear generator and optimizing the control method;
2. The construction of a mathematical model of a permanent magnet linear generator according to claim 1, wherein: the stator windings are symmetrically distributed in three phases, and the axial lines of the windings are different by 120 degrees in electrical angle; the generated air gap magnetomotive force and magnetic flux density are distributed in a sine wave manner; neglecting the influence of the ventilation grooves and the winding grooves, and assuming that the stator and rotor surfaces are smooth; neglecting the influence of magnetic circuit saturation, hysteresis loss and eddy current loss;
performing park transformation, namely transforming electromagnetic quantities represented by stationary three-phase coordinate systems a, b and c into electromagnetic quantities represented by two-phase rectangular coordinate systems d and q rotating along with a rotor and a stationary 0-axis coordinate system (collectively referred to as dq0 coordinate system); the coordinate transformation does not change the electromagnetic relationship inside the generator;
the park transformation changes a variable coefficient differential equation into a constant coefficient differential equation, adopts the park transformation with equal power, and has the functions of:
Under a three-phase static coordinate system, the voltage function of the PMSG stator three-phase loop is as follows:
Wherein R a、Rb、Rc is a three-phase resistor, and R a＝Rb＝Rc＝Rs;ia、ib、ic is stator three-phase current because of the symmetry of three-phase windings; phi a、φb、φc is a three-phase stator flux linkage, and the corresponding flux linkage function is:
Wherein L is self-inductance and equal; m is mutual inductance and equal; phi f is the permanent magnet flux linkage; θ is the angle between d-axis and a-axis, θ=ω et;ωe is the electrical angular velocity, N p is the motor pole pair number, τ is the motor pole pitch; after the transformation of the equal power park, the voltage function under the dq axis rotation coordinate system is as follows:
u d、uq、id、iq is dq axis stator voltage and current, respectively; l d、Lq is dq axis equivalent inductance, and L d＝Lq＝Ls;Ψd、Ψq is equivalent flux linkage of the stator flux linkage under dq axis. The equivalent flux linkage function is:
the complete expression of the voltage function of the permanent magnet synchronous generator under d and q coordinate axes can be obtained by the formula:
SVPWM control of the generator based on i d =0 can be realized through the formula;
The generator electromagnetic force F pto can be obtained in analogy to the electromagnetic force under the motor, and its functional form is:
Because of i d＝0,Ld＝Lq＝Ls, the reduced function is:
the induced electromotive force E of the PTO device is as follows:
the voltage difference between the stator voltage U and the induced electromotive force E of the PTO device is:
3. The creation of a mathematical model of maximum wave energy capture conditions according to claim 2, comprising the steps of:
Float kinetic function:
z b is the displacement of the float relative to the hydrological zero; acceleration as a float body;
M b is the total mass of the float body and the linear generator mover;
F e is wave force;
F hs is hydrostatic recovery: f hs＝-Khs·Zb
K hs is the equivalent elastic coefficient of the seawater and is related to the geometric structure of the floater;
F pto is the thrust of the PTO device, namely the electromagnetic thrust of the linear motor;
f rad is the radiation force to which the float body is subjected;
According to the research on wave force, under irregular waves, a convolution integral formula of a Cummins equation is introduced to describe the fluid memory effect, and the corresponding radiation force function is as follows:
after the above formula is finished, the kinetic equation of the single-degree-of-freedom direct-drive wave power generation device can be obtained:
further, a frequency domain equation of the direct-drive wave power generation system is obtained:
Wherein F g is a counter electromagnetic force, and is the interaction force of electromagnetic thrust F pto; b 0 is the radiation force damping coefficient, which is obtained by the formula:
when the back electromagnetic force of the direct-drive wave energy power generation system is only in a linear relation with the speed of the floater, the back electromagnetic force can be expressed as follows:
Wherein R e is the optimal damping coefficient of the direct-drive wave energy power generation system;
the wave and float velocity phase difference angles θ, R e, ω can be expressed as:
The method can be obtained after Lawster transformation:
The maximum wave energy capture condition is derived when the damping Z e of the energy output system is equal to the conjugate of the impedance Z 1 within the wave energy conversion system:
The optimal speed for obtaining the float body is:
The system dynamics model can be equivalent to a second-order resonance circuit, and the response form of the system can be compared with series resonance;
Under the condition that the device achieves maximum wave energy capture, resonance can be achieved under any wave energy environment as long as the motion stroke, acting force and output power of the permanent magnet linear generator of the wave energy power generation device are within the allowable range, so that the device captures the maximum wave energy, and the application area is wide. PMLG in operation, energy is often transferred bi-directionally, and the electric machine outputs electrical energy as a generator when energy is flowing in a forward direction, whereas the input electrical energy is input as an electric motor to the PTO.
4. The permanent magnet linear generator parameter setting and optimizing control method according to claim 3, comprising the steps of:
the primary pole structure is selected, the permanent magnet with a long secondary structure is longer than the stator winding, and the whole stator winding is an effective winding although the permanent magnet is made of more materials, so that the energy conversion efficiency is high; long secondary structure studies are selected herein from the perspective of high energy conversion;
The parameters are selected, the direct-drive type PTO device float body is connected with a rotor of the linear motor through a connecting rod, and the float body is driven by wave force to move so as to drive the linear motor rotor to do up-down heave motion; in an ideal case, the equation of motion of a wave can be described as:
h is wave height, lambda is wavelength; when the sea wave level is 4, h=2.5m, λ=30m, and under ideal conditions (neglecting factors such as motor friction and wave reflection, Φ=0), the motion velocity equation of the wave can be expressed as:
v＝0.26sin 0.21t
The maximum motion speed of the wave obtained by the method is 0.26m/s, so that the rotor is provided with a constant speed of 0.26m/s for the convenience of data processing and the verification of the motor performance, and the linear generator is subjected to optimal control experimental analysis;
The permanent magnet linear motor is a 9-pole 12-slot, m=3, the modeling linear generator is the same as the long secondary model, and for the convenience of analysis, only the right side is modeled; the motor is designed as a three-phase permanent magnet linear motor, and the label groups of A, B, C three-phase windings are arranged;
The auxiliary groove structure is optimized, the existence of the auxiliary groove structure enables the magnetic flux distribution at the side end of the stator to generate larger difference, and the existence of the auxiliary groove can convert part of leakage magnetic flux into effective magnetic flux, so that the change rate of air gap magnetic resistance is greatly reduced, and the positioning force born by the rotor can be reduced theoretically; in order to reduce the positioning force of the rotor, the stator structure is improved, and the tooth grooves at the edge are widened, which is equivalent to the function of an auxiliary groove;
Compared with the prior art of motor improvement, the amplitude of no-load induced electromotive force of the linear motor without the auxiliary groove is increased; the difference of the induced electromotive force of the C phase and the A, B phase is reduced; after the auxiliary groove is added, the electromechanical energy conversion efficiency of the linear motor is enhanced under the same condition, the working efficiency and performance of the motor are improved, and the correctness and rationality of the improvement of the stator tooth slot structure of the linear motor are verified;
When the linear motor is loaded, the three phases of load induction electromotive forces are different and smaller than the situation of no load, which is caused by the inherent longitudinal side end effect of the linear motor and the armature reaction under the load situation; the phases of the phases are shifted compared with the no-load induced electromotive force, because the phase of the no-load induced electromotive force is only determined by the magnetic field generated by the permanent magnet, and the phase of the no-load induced electromotive force is determined by the magnetic field which is reacted and acted together by the permanent magnet and the armature when the load is loaded;
The initial movement direction of the test rotor is downward, the rotor of the linear motor is at the highest position at the moment 0, then the rotor starts to move downward, the speed is faster and faster, the maximum speed of the rotor reaches 0.26m/s at the moment 0.5s, and at the moment, the no-load induced electromotive force generated by the stator winding is also maximum; thereafter, the mover continues to move down while the speed is gradually reduced, the magnitude of the induced electromotive force is also gradually reduced, and when 1s, the mover moves to the lowest point, the speed of the mover is 0, and the induced electromotive force is also 0; then, the mover moves upwards along with the waves, and the induced electromotive force and the speed change of the mover are similar to those of the mover moving downwards;
The linear motor with the improved stator tooth slot has the advantages that the rotor can receive smaller positioning force during movement, under no-load and load conditions, the three-phase winding can generate induced electromotive force at the constant speed and the sinusoidal speed at the rotor speed of the linear motor, and the amplitude and the phase change of the induced electromotive force are consistent with normal principles, so that the correctness and rationality of the structural design and the control method of the linear motor are demonstrated, and the high-efficiency conversion from wave energy to electric energy can be further realized.
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