A Weak Magnetic Field Control Strategy for a Direct-Drive Wave Energy Generation System Based on Model Predictive Control

Abstract

The present invention discloses a field-weakening control strategy for a direct-drive wave power generation system based on model predictive control, belonging to the technical field of renewable energy power generation. The present invention applies the model predictive control algorithm to the direct-drive wave power generation system, takes maximizing power capture as the optimization objective, incorporates the actual physical limitations of the device into the constraints of the algorithm, predicts using the wave force data within a certain future time domain, and obtains the optimal control quantity of the wave power generation system; and adopts a stator current vector control scheme combining i d = 0 and field-weakening control, and incorporates the d-axis current into the control objective of the model predictive control algorithm. The present invention can improve the power capture performance of the direct-drive wave power generation system while satisfying the system constraints, effectively broaden the operating speed range of the permanent magnet linear generator, and improve the stability of system operation.

Description

Technical Field

[0001] The present invention belongs to the technical field of renewable energy power generation, and particularly relates to wave energy power generation technology. Specifically, it relates to a field-weakening control strategy for a direct-drive wave power generation system based on model predictive control. Background Art

[0002] The scientific development and utilization of wave energy are of great significance for alleviating energy crises and environmental pollution problems. Among many types of wave power generation devices, the direct-drive wave power generation system has the advantages of simple system structure and high efficiency, and has become a research hotspot for the development and utilization of wave energy. In order to improve the power generation efficiency of the direct-drive wave power generation system, effective control strategies must be adopted to achieve maximum power capture of wave energy on the premise of meeting the actual constraints of the power generation system state variables. Traditional wave power generation system control strategies include real part control and complex conjugate control. Among them, the power captured by real part control is small, and the power captured by complex conjugate control is large, but the system state variables are easily beyond the actual allowable range, affecting the normal operation of the system. On the other hand, for the stator current vector control of the permanent magnet linear generator in the wave power generation system, in order to reduce losses, the control method of id = 0 is often adopted. However, the actual sea conditions change complexly and fluctuate greatly from time to time, which easily causes the float speed to exceed the allowable value. At this time, if no additional control is taken, it will exceed the generator rated capacity, and the increase in the generator back electromotive force will cause overmodulation of the DC bus voltage, resulting in distortion of the stator current waveform. Summary of the Invention

[0003] Aiming at the defects and deficiencies of the existing technology, the purpose of the present invention is to provide a field-weakening control strategy for a direct-drive wave power generation system based on model predictive control, so that the direct-drive wave power generation system can extract the maximum power under the condition of meeting physical constraints; in addition, the stator current vector control method of field-weakening control is used to effectively broaden the operating speed range of the permanent magnet linear motor.

[0004] According to the present invention, the following technical solutions are adopted to achieve the above invention purpose:

[0005] A field-weakening control strategy for a direct-drive wave power generation system based on model predictive control, comprising the following steps:

[0006] S1: Establish a mechanical motion model of the direct-drive wave power generation system according to the force condition of the float in the direct-drive wave power generation system and Newton's second law;

[0007] S2: Establish a linear permanent magnet motor model of the direct-drive wave power generation system;

[0008] S3: Establish a state space model of the direct-drive wave power generation system based on model predictive control according to the mechanical motion model and the linear permanent magnet motor model of the direct-drive wave power generation system;

[0009] S4: Based on the control objectives of the direct-drive wave power generation system, establish a power optimization objective function, and then augment and transform the state-space model according to the power optimization objective function to the discrete domain to obtain the discrete state-space model of the direct-drive wave power generation system;

[0010] S5: Perform rolling optimization of the state variables of the discrete state-space model until the rolling predictive control is completed to achieve online optimization and solution of the system;

[0011] S6: Set the constraint conditions of the system. When the mover speed of the linear permanent magnet motor is within the normal range, adopt the control method of i d = 0, and when the mover speed exceeds the normal range, adopt the field-weakening control method.

[0012] A further solution of the present invention is that the expression of the mechanical motion model of the direct-drive wave power generation system established in S1 is:

[0013]

[0014] In the formula, M is the mass of the float, m add is the added mass of water, and the two together constitute the equivalent total mass of the float; z(t) is the heave displacement of the float, is the moving speed of the float, is the moving acceleration of the float; the convolution term of the damping coefficient k(t) and the speed corresponds to the radiation force f R (t) received by the float; the product of the float displacement z(t) and the elastic coefficient k s corresponds to the equivalent spring resistance f s (t) received by the float; f wave is the wave excitation force as the input; f PTO is the applied electromagnetic thrust from the system power take-off device (Power Take-Off, PTO).

[0015] A further solution of the present invention is to approximately replace the radiation force f R (t) in the expression of the mechanical motion model with a state-space model.

[0016] A further solution of the present invention is that the expression of the state-space model established in S3 is:

[0017]

[0018] In the formula, v(t) is the scaled wave excitation force; u q (t) is the control quantity of the system.

[0019] A further solution of the present invention is that the power optimization objective function established in S4 includes a PTO force f PTO penalty term, and the expression of this power optimization objective function is:

[0020]

[0021] In the formula, is the change in the speed of the float, and r represents the penalty coefficient.

[0022] A further solution of the present invention is that the constraint conditions in S6 include linear constraints and non-linear constraints, where the linear constraints include the heave displacement z(t) of the float, the motion speed and the PTO force f PTO , and the expressions are as follows:

[0023]

[0024] The non-linear constraints include the stator voltage, stator current and field weakening ratio τ of the linear permanent magnet motor, and the expressions are as follows:

[0025]

[0026] In the formula, u d is the d-axis voltage in the d-q rotating coordinate system, and u q is the q-axis voltage; i d is the d-axis current, and i q is the q-axis current, and I s is the current of the stator winding; L s is the inductance of the stator winding; Ψ PM is the magnetic flux generated by the permanent magnet rotor in the stator.

[0027] Compared with the prior art, the present invention has the following beneficial effects:

[0028] Under the condition of meeting the system constraints, the power capture performance of the direct-drive wave power generation system is improved, the operating speed range of the permanent magnet linear generator is effectively broadened, and the operating stability of the system is improved. BRIEF DESCRIPTION OF THE DRAWINGS

[0029] Figure 1 is the inner and outer loop control block diagram of the direct-drive wave power generation system based on model predictive control;

[0030] Figure 2 is the force diagram of the direct-drive wave power generation system;

[0031] Figure 3 is the schematic diagram of the operating range of the stator current vector of the permanent magnet linear motor. DETAILED DESCRIPTION OF THE INVENTION

[0032] The technical solution of the invention will be described in detail with reference to the accompanying drawings as follows:

[0033] The inner and outer loop control block diagram of the direct-drive wave power generation system based on model predictive control is as Figure 1 shown. In the outer loop model predictive control structure, in order to obtain a higher adjustment speed and control accuracy, the increment of the q-axis current reference value of the linear motor stator, Δi q_ref , and the increment of the d-axis current reference value, Δi d_ref , are used as the control quantity outputs of the control algorithm. The predicted value of the future wave force, Δv, is used as the uncontrollable input, and the displacement z(t), velocity , etc. of the float are used as state variables. The optimal control quantity output through rolling optimization is obtained as the q-axis current reference value i q_ref , and the d-axis current reference value i d_ref after zero-order hold. Then, after decoupling by the current inner loop, a PI controller is used to track the reference signal, and finally, PWM technology is used to modulate the signal to complete the optimization control process of the system.

[0034] The specific steps involved in the present invention are described as follows:

[0035] Step 1: Establish the mechanical motion model of the direct-drive wave power generation system:

[0036] For the mechanical motion equation of the direct-drive wave power generation system, according to the force condition of the float in the direct-drive wave power generation system (as Figure 2 shown) and Newton's second law, a simplified motion equation of the direct-drive wave power generation system is established, and the expression is as follows:

[0037]

[0038] In the formula, M is the mass of the float, m add is the added mass of water, and the two together form the equivalent total mass of the float; z(t) is the heave displacement of the float, is the motion speed of the float, is the motion acceleration of the float; the convolution term of the damping coefficient k(t) and the speed corresponds to the radiation force f R (t) received by the float; the product of the float displacement z(t) and the elastic coefficient k s corresponds to the equivalent spring resistance f s (t) received by the float; the Hydrodynamic parameters involved in the equation (including the float mass M, the float added mass m add , the damping coefficient k(t), and the elastic coefficient k s ) is calculated using WAMIT software; f wave is the wave excitation force as the input; f PTOis the external electromagnetic thrust from the system power take-off (PTO).

[0039] To improve the computational efficiency of the control process, the present invention uses a state-space model to approximately replace the radiation force f in the mechanical motion model expression R (t) convolution term, and the conversion process is as follows:

[0040] First, use the Prony algorithm to fit the k(t) curve to obtain its form of complex exponential weighted sum, then obtain the S-domain expression of the radiation coefficient through Laplace transform, and then use the balanced truncation method to reduce the order of the above formula to obtain the parameters A r ∈R 4×4 and B r ∈R 4 ×1 , C r ∈R 1×4 and D r ∈R 1×1 , and obtain the fourth-order state-space model of f R (t), and the expression form is as follows:

[0041]

[0042] In the formula, x r (t) ∈ R 4×1 , it has no actual physical meaning and only represents the state variable in the state-space model; z(t) represents the displacement of the float, and its differential term is the motion speed of the float,

[0043] Step 2: Establish the linear permanent magnet motor model of the direct drive wave power generation system:

[0044] Establish the stator terminal voltage equation of the linear permanent magnet motor in the a-b-c coordinate system, and the expression is as follows

[0045]

[0046] In the formula, u s_abc is the voltage vector at the stator terminal; R = diag(R s , R s , R s ), R s is the resistance of the stator winding; L is the stator inductance matrix; i abc is the stator winding current vector; Ψ PM_abc is the magnetic flux generated by the permanent magnet rotor in the stator;

[0047] Convert the stationary a-b-c coordinate system to the d-q rotating coordinate system to obtain the dq-axis voltage balance equation as follows:

[0048]

[0049] where ω is the electrical angular velocity of the linear permanent magnet motor, ω = 2πv / λ, λ is the pole pitch of the motor; i d is the stator d-axis current, i q is the stator q-axis current, M is the mutual inductance between the stator windings, L ss is the self-inductance of the stator winding, L s = L ss - M;

[0050] According to the relationship between the parameters of the linear permanent magnet motor, the linear relationship between the q-axis current i qs and the PTO force f PTO is derived as follows:

[0051]

[0052] Step 3: Establish the state space model of the direct-drive wave power generation system based on model predictive control:

[0053] Establish the equivalent expression of the motion equation of the wave power generation system device as follows

[0054]

[0055] where represents the scaled wave excitation force; is used as the control quantity of the system; obtain the relationship between the control quantity u q (t) and the stator q-axis current i qs (t) as follows:

[0056]

[0057] Taking the heave displacement z(t), motion velocity and the intermediate quantity x r (t) of the buoy as the state variables, the continuous state space model of the wave power generation system is obtained as follows:

[0058]

[0059] Among them, the coefficient matrix is:

[0060]

[0061] Step 4: Establish the objective function of model predictive control and build the discrete state space model:

[0062] Based on the control objective of the direct-drive wave power generation system, establish a power optimization objective function including the PTO force f PTO penalty term, in the form as follows:

[0063]

[0064] Based on the objective function and considering the working principle of the direct-drive wave power generation system with field-weakening control, the control variable u q (t), the scaled wave excitation force v(t), the velocity change and the d-axis current i d (t) are taken as newly added state variables, the model is augmented, and then transformed into the discrete domain. Finally, the discrete state-space model of the system is obtained:

[0065]

[0066] where the coefficient matrices are:

[0067]

[0068]

[0069]

[0070] where, Υ = [0 1 0], T l is the sampling interval, and A c , B c , F c are the coefficient matrices of the continuous state-space model obtained in step 3, respectively.

[0071] Step 5. Rolling optimization of state variables:

[0072] The output sequence within the future N-step time domain starting from time instant k is iteratively predicted for the state variables, and the expression is as follows:

[0073]

[0074] where,

[0075]

[0076]

[0077]

[0078]

[0079] x(k) represents the system state variable at time instant k, represents the increment sequence of the scaled wave force within the future N steps starting from time instant k.

[0080] Only the first increment is applied to the system to obtain the control variable at the next time instant:

[0081] U(k) = ΔU(k) + U(k - 1)

[0082] Repeat the above process until the rolling predictive control is completed to achieve the online optimal solution of the system.

[0083] Step 6. Constraint conditions:

[0084] In the control process, incorporate the physical limitations of the direct - drive wave power generation system into the constraints of the algorithm. The linear constraints include the heave displacement z(t) of the buoy, the motion speed and the PTO force f PTO , and the expressions are as follows:

[0085]

[0086] The non - linear constraints include the stator voltage amplitude, the stator current amplitude, and the field - weakening ratio τ. Among them, the limit value U max of the stator voltage depends on the DC - side voltage of the PWM rectifier and is 1 / 2 of the DC - bus voltage U dc under the SPWM pulse - width modulation mode; the limit value I max of the stator current amplitude depends on the motor temperature rise and the limit of the PWM rectifier output capacity. It should also be particularly noted that during the actual field - weakening operation of the permanent - magnet motor, if the direct - axis demagnetizing current is too large, the permanent magnet will face the risk of permanent demagnetization. Therefore, the field - weakening ratio τ should be controlled to be always less than or equal to 1. The definition formula of the field - weakening ratio τ is as follows:

[0087]

[0088] Therefore, the expression of the non - linear constraint can be summarized as follows:

[0089]

[0090] The schematic diagram of the operating range of the stator current subject to non - linear constraints is as Figure 3 shown. When the generator is in the low - speed region, under the i d = 0 control, the stator - current vector is located on the i q axis. At this time, the current reference value i qref corresponding to Fpto1 required for maximum - power capture is always within the current - limit circle and the voltage - limit circle, as shown by point A; as the follower speed increases, the voltage - limit loop shrinks, and the current reference value corresponding to Fpto2 required intersects with the voltage - limit circle, being in a critical state, as shown by point B; as the follower speed further increases, the voltage - limit circle shrinks, and the intersection of the current reference value corresponding to Fpto3 required with the q - axis is outside the limit circle. Therefore, at this time, the direct - axis current reference value i dref, the operating point moves to the right until the limit condition is met, as shown by point C. The current vector control switches from the i d = 0 control to the field-weakening control.

[0091] In summary, the present invention can improve the power capture performance of the direct-drive wave power generation system while meeting the system constraints, and adopts the stator current vector control method combining the i d = 0 control and the field-weakening control, effectively broadening the operating speed range of the permanent magnet linear generator and improving the operating stability of the system.

Claims

1. A field-weakening control strategy for a direct-drive wave power generation system based on model predictive control, characterized in that Including the following steps: S1: Establish a mechanical motion model of the direct-drive wave power generation system according to the force conditions of the float in the direct-drive wave power generation system and Newton's second law; S2: Establish a linear permanent magnet motor model of the direct-drive wave power generation system; S3: Establish a state space model of the direct-drive wave power generation system based on model predictive control according to the mechanical motion model and the linear permanent magnet motor model of the direct-drive wave power generation system; S4: Based on the control objective of the direct-drive wave power generation system, establish a power optimization objective function, and then augment and transform the state space model to the discrete domain according to the power optimization objective function to obtain the discrete state space model of the direct-drive wave power generation system; S5: Perform rolling optimization of the state variables of the discrete state space model until the rolling predictive control is completed to achieve online optimization and solution of the system; S6: Set the constraint conditions of the system. When the mover speed of the linear permanent magnet motor is within the normal range, adopt the control method of i d = 0. When the mover speed exceeds the normal range, adopt the field-weakening control method.

2. The field-weakening control strategy for a direct-drive wave power generation system based on model predictive control according to claim 1, wherein: The expression of the mechanical motion model of the direct-drive wave power generation system established in S1 is: where M is the mass of the float, and m add is the added mass of water, and the two together constitute the equivalent total mass of the float; z(t) is the heave displacement of the float, is the movement speed of the float, is the movement acceleration of the float; the convolution term of the damping coefficient k(t) and the speed corresponds to the radiation force f R (t) acting on the float; the product of the float displacement z(t) and the elastic coefficient k s corresponds to the equivalent spring resistance f s (t) acting on the float; f wave is the wave excitation force as the input; f PTO is the external electromagnetic thrust from the system power take-off (PTO).

3. A field-weakening control strategy for a direct-drive wave power generation system based on model predictive control according to claim 2, characterized in that: The radiation force f R (t) in the expression of the mechanical motion model is approximately replaced by the state space model.

4. A field-weakening control strategy for a direct-drive wave power generation system based on model predictive control according to claim 1, characterized in that: The expression of the state space model established in S3 is: where \(v(t)\) is the scaled wave excitation force; \(u\) q (t) is the control variable of the system.

5. A field-weakening control strategy for a direct-drive wave power generation system based on model predictive control according to claim 1, characterized in that: The power optimization objective function established by S4 includes the PTO force f PTO a penalty term, and the expression of this power optimization objective function is: In the formula, is the change in the speed of the float, and r represents the penalty coefficient.

6. A field-weakening control strategy for a direct-drive wave power generation system based on model predictive control according to claim 1, characterized in that: The constraints of S6 include linear constraints and non-linear constraints, where the linear constraints include the heave displacement z(t) of the buoy and the motion speed and the PTO force f PTO , and the expressions are as follows: The non-linear constraints include the stator voltage, stator current and field weakening ratio τ of the linear permanent magnet motor, and the expressions are as follows: where, u d is the d-axis voltage in the d-q rotating coordinate system, and u q is the q-axis voltage; i d is the d-axis current, and i q is the q-axis current, and I s is the current of the stator winding; L s is the inductance of the stator winding; Ψ PM is the magnetic flux generated by the permanent magnet rotor in the stator.

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