Dual three-phase permanent magnet synchronous generator rectification system and direct current voltage stabilization control method thereof

Abstract

The invention relates to a dual three-phase permanent magnet synchronous generator rectification system and a direct current voltage stabilization control method thereof. Comprising a dual three-phase permanent magnet synchronous generator, a VSD decoupling converter, a load current observer, a dynamic load feed-forward compensator, a voltage closed-loop controller, a dead-beat predictive current controller, a maximum four-vector SVPWM modulation module and a six-phase rectifier. The double-three-phase topological structure adopted by the invention has the advantages of multiple control degrees of freedom, high reliability and the like. A dynamic load feed-forward compensator is constructed to perform dynamic feed-forward compensation on quadrature-axis current of the motor, so that the recovery time of bus voltage is shortened, and the voltage fluctuation amplitude is reduced; the designed dead-beat predictive current controller optimizes the dynamic characteristics of a current loop, improves the torque tracking performance of the motor, and further improves the voltage stabilization regulation capability of the system. The designed load current observer realizes the analysis redundancy of current detection and improves the reliability of the system.

Description

Technical Field

[0001] This invention belongs to the field of motor control technology and relates to a dual three-phase permanent magnet synchronous generator rectification system and a DC voltage stabilization control method. This system and method are suitable for DC power generation systems for various high-end equipment, featuring high reliability, high stability, high load factor, and a wide load range. Background Art

[0002] Compared to traditional three-phase permanent magnet synchronous motors, dual three-phase permanent magnet synchronous motors offer advantages such as increased control freedom and improved fault tolerance, making them a research hotspot and development trend in motor system technology. In rectifier systems employing dual three-phase permanent magnet synchronous generators, large power fluctuations can directly impact the stability of the power system when loads are switched on and off across a wide range, leading to grid voltage fluctuations and severely impacting the operational safety of power equipment. Existing voltage stabilization control methods employ a dual-loop PI control scheme that uses error feedback to regulate the DC bus voltage. However, under these operating conditions, these methods suffer from long voltage recovery times and large voltage fluctuations. Furthermore, the generator current loop utilizes pure error feedback control, which struggles to rapidly track large load variations, limiting the DC bus voltage's ability to recover quickly. Furthermore, under complex and volatile operating environments, the failure probability of bus current sensors increases significantly. As critical sensors for voltage stabilization control, failure of these sensors can severely impact the stability and reliability of the voltage stabilization control system. Summary of the Invention

[0003] To address the above series of problems, the present invention proposes a dual three-phase permanent magnet synchronous generator rectifier system, which is characterized by including: a dual three-phase permanent magnet synchronous generator, a VSD decoupling converter, a load current observer, a dynamic load feedforward compensator, a voltage closed-loop controller, a deadbeat predictive current controller, a maximum four-vector SVPWM modulation module, and a six-phase rectifier. The control system structure block diagram is shown in the following figure. Figure 1 shown.

[0004] The dual three-phase permanent magnet synchronous generator comprises two sets of three-phase windings, the phases of the two sets of three-phase windings are 30 degrees apart from each other, and the neutral points are isolated. Figure 2 shown.

[0005] The VSD decoupling converter is used to convert the six-phase current of the motor into the orthogonal axis current in the fundamental wave space rotating coordinate and the xy axis current in the harmonic wave space stationary coordinate. The input is the six-phase current i of the dual three-phase permanent magnet synchronous generator. a 、i b 、i c 、i d 、i e 、i f , the output is the quadrature axis current i under the fundamental wave space rotating coordinateq , direct axis current i d , and the x-axis current i in the harmonic space stationary coordinate x , y-axis current i y .

[0006] The load current observer is used to estimate the load current and achieve the resolution margin of current detection. Its input is the quadrature axis current i q , the direct axis current i d , DC bus voltage U dc and the generator rotor electrical angular velocity ω e , the rotor electrical angular velocity is given by the rotor electrical angle θ e The output of the load current observer is the load current estimate

[0007] The dynamic load feedforward compensator accurately calculates and outputs the quadrature axis current fast adjustment component i through the motor model and the capacitor energy storage model. q1 * Its input is the bus voltage reference given value U dc * , the DC bus voltage U obtained by sampling dc , load current estimation Generator rotor electrical angular velocity ω e .U dc * Given input from the outside.

[0008] The voltage closed-loop controller is used to achieve error-free tracking of the bus voltage reference given value, and obtain and output the quadrature-axis current error compensation component i q2 * Its input is the bus voltage reference given value U dc * And the DC bus voltage U obtained by sampling dc .

[0009] The above-mentioned quadrature axis current fast adjustment component i q1 * and the quadrature axis current error compensation component i q2 * The algebraic sum is calculated by the adder, and then the quadrature axis current reference value i is obtained by the inverter link. q * .

[0010] The deadbeat predictive current controller is used to achieve fast and accurate tracking of the generator quadrature axis current. Its input includes the k-time fundamental subspace direct axis and quadrature axis current i obtained by VSD coordinate transformation. d (k) and i q (k), harmonic subspace x-axis and y-axis current ix (k) and i y (k), direct-axis and quadrature-axis current reference given quantity i d * and i q * , the x-axis and y-axis current reference given quantity i x * 、i y * The output of the deadbeat predictive current controller is the reference voltage u of the α-axis and β-axis of the orthogonal stationary coordinate system at time k+1. α * (k+1),u β * (k+1), x-axis and y-axis reference voltage u x * (k+1),u y * (k+1).

[0011] The maximum four-vector SVPWM module is used to modulate the reference voltage into a six-phase PWM signal to generate a centrally symmetric switching sequence. Its input is the reference voltage u of the α-axis and β-axis at time k+1. α * (k+1),u β * (k+1), x-axis and y-axis reference voltage u x * (k+1),u y * (k+1), the output is six switch signals S1, S2, S3, S4, S5, and S6.

[0012] The six-phase rectifier is used to rectify the six-phase PWM voltage into a DC voltage. Its input is six switch signals S1, S2, S3, S4, S5, and S6. By controlling the on and off of the power tubes of the six half-bridges, the PWM rectification control of the dual three-phase permanent magnet synchronous generator is realized. Figure 2 shown.

[0013] The DC voltage stabilization control method based on the dual three-phase permanent magnet synchronous generator rectification system of the present invention is characterized by comprising the following steps:

[0014] S1. Build a dual three-phase permanent magnet synchronous generator rectifier system, including: a dual three-phase permanent magnet synchronous generator, a load current observer, a dynamic load feedforward compensator, a voltage closed-loop controller, a deadbeat predictive current controller, a maximum four-vector SVPWM modulation module, a VSD decoupling converter, and a six-phase rectifier.

[0015] S2. Build a dual three-phase permanent magnet synchronous generator with two sets of three-phase windings, with a phase shift of 30° and neutral point isolation. With phase A as the reference, phase B lags phase A by 120°, phase C lags phase A by 240°, phase D lags phase A by 30°, phase E lags phase A by 150°, and phase F lags phase A by 270°.

[0016] S3. Build a six-phase rectifier, with one end of each phase winding connected to a half-bridge in the six-phase rectifier. The output of the six-phase rectifier is connected in parallel with several bus capacitors to supply power to subsequent loads.

[0017] S4. Construct a load current observer, which mainly includes: a load current estimation module, an electromagnetic power estimation module, a motor loss estimation module and a capacitor energy storage model.

[0018] S5. Construct a dynamic load feedforward compensator, which mainly includes: a derivative link, a proportional link, an adder, a multiplier, and an electromagnetic power solution model.

[0019] S6. Build a voltage closed-loop controller, which mainly includes: a subtractor and a voltage regulator AVR.

[0020] S7. Construct a deadbeat prediction current controller, which mainly includes: a one-step prediction model, a deadbeat prediction model and a Park -1 converter.

[0021] S8. Construct a maximum four-vector SVPWM module, which mainly includes: a dual three-phase motor maximum four-vector control set, a duty cycle calculation module, and a switching sequence generation module.

[0022] The VSD decoupling converter in the present invention has six-phase current i of the dual three-phase permanent magnet synchronous generator as input. a 、i b 、i c 、i d 、i e 、i f , the output is the quadrature axis current i under the fundamental subspace rotation coordinate q , direct axis current i d , and the x-axis current i in the stationary coordinates of the harmonic subspace x , y-axis current i y The VSD coordinate transformation maps the above six-phase stator currents to the above fundamental subspace and harmonic subspace, satisfying the following expression:

[0023]

[0024] The mathematical expression of the stator winding voltage equation of the dual three-phase permanent magnet synchronous generator in the present invention is:

[0025]

[0026] Among them, u d 、i d and L d are the voltage, current and inductance of the d-axis respectively, u q 、i q and L q are the voltage, current and inductance of the q axis respectively, u x 、i x 、L x They are the voltage, current, and inductance of the x-axis, u y 、i y 、L y They are the voltage, current, and inductance of the y-axis, R s is the motor winding resistance, ωe is the rotor electrical angular velocity, ψ f is the fundamental magnetic flux.

[0027] The load current observer in the present invention is as follows Figure 3 As shown, it has the following structure: (1) The load current estimation module contains a subtractor and a hyperbolic tangent function link; the subtractor is used to realize the DC bus voltage U dc and bus voltage estimates The subtraction operation of the bus voltage estimation error e is obtained. u The above error is passed through the hyperbolic tangent function link to obtain the load current estimate Among them, the expression of the hyperbolic tangent function link is: (2) The electromagnetic power estimation module contains a multiplier and a proportional link; the multiplier is used to realize the rotor electrical angular velocity ω e and q-axis current i q The product term is multiplied by the proportional link to obtain the estimated value of the electromagnetic power of the generator Among them, the gain of the proportional link is determined by the motor flux, and the gain expression is: 3ψ f (3) The motor loss estimation module contains two square links, an adder, and a proportional link; the square links are used to calculate the quadrature axis current i q and the direct axis current i d The square operation is performed, and the square terms obtained are summed by the adder and then passed through the proportional link to obtain the estimated value of the generator power loss Among them, the gain of the proportional link is determined by the motor winding resistance, and the gain expression is: 3R s (4) Estimated value of the electromagnetic power of the above generator and estimated generator power loss Subtract and get the estimated value of generator output power Then, through a proportional link, the estimated value of the rectifier output bus current is obtained. The gain of the proportional link is determined by the bus voltage reference given value U dc * Determine, the gain expression is:

[0028] The above bus current estimate and load current estimate The estimated value of the capacitor current is obtained through the subtractor (5) The capacitor energy storage model contains a proportional link and an integral link; the input of the proportional link is the estimated value of the capacitor current The proportional gain is expressed as: Where C is determined by the total DC bus capacitance; the output of the proportional link passes through the integral link to obtain the above bus voltage estimate

[0029] The dynamic load feedforward compensator of the present invention has the following structure: DC bus voltage U dc The derivative of the bus voltage is obtained through the derivation link, and then the calculated value of the capacitor current i is obtained through the proportional link. C * The calculated value of the capacitor current i C * and load current estimate Calculate the algebraic sum to get the bus current calculated value i dc * . Bus current calculation value i dc * With the bus voltage reference given value U dc * After multiplication by the multiplier, the calculated value of the electromagnetic power of the generator P is obtained. e * . Generator electromagnetic power calculation value P e * According to the electromagnetic power solution model, the quadrature axis current fast adjustment component i is obtained q1 * , where the analytical expression of the electromagnetic power solution model is as follows:

[0030]

[0031] Where ωe is the rotor electrical angular velocity, ψ f It is the fundamental flux of dual three-phase permanent magnet generator.

[0032] The voltage closed-loop controller in the present invention has the following structure: The subtractor is used to realize the bus voltage reference given value U dc * and DC bus voltage U dcThe subtraction operation is performed to obtain the bus voltage error, which is passed through the voltage regulator AVR to obtain the quadrature axis current error compensation component i q2 * .

[0033] The deadbeat prediction current controller of the present invention has the following structure: (1) The input of the one-step prediction model includes the direct axis and quadrature axis currents i of the fundamental subspace at time k obtained by VSD coordinate transformation. d (k) and i q (k), harmonic subspace x-axis and y-axis current i x (k) and i y (k), the direct-axis and quadrature-axis voltages u of the fundamental subspace at time k d (k) and u q (k), harmonic subspace x-axis and y-axis voltage u x (k) and u y (k). The direct-axis and quadrature-axis currents i in the fundamental subspace at time k+1 are obtained by solving the one-step prediction model. d (k+1) and i q (k+1), and the harmonic subspace x-axis and y-axis current i x (k+1) and i y (k+1). (2) The input of the deadbeat prediction model includes the direct-axis and quadrature-axis currents i of the fundamental subspace at time k+1 obtained by the one-step prediction model. d (k+1) and i q (k+1), harmonic subspace x-axis and y-axis current i x (k+1) and i y (k+1), and the direct-axis and quadrature-axis current reference given quantity i d * and i q * , the x-axis and y-axis current reference given quantity i x * 、i y * The reference voltage u of the direct axis and quadrature axis of the fundamental subspace rotating coordinate system at time k+1 is obtained by solving the deadbeat prediction model. d * (k+1),u q * (k+1), the x-axis and y-axis reference voltage u of the harmonic subspace stationary coordinate system x * (k+1),u y * (k+1). (3)Park -1 The input of the converter includes the reference voltage u of the direct axis and quadrature axis of the fundamental subspace rotating coordinate system at time k+1 output by the deadbeat prediction modeld * (k+1),u q * (k+1), through the coordinate transformation matrix, solve and output the reference voltage u of the α-axis and β-axis of the fundamental subspace stationary coordinate system at time k+1 α * (k+1),u β * (k+1).

[0034] The solution expression of the above one-step prediction model is:

[0035]

[0036] The solution expression of the above deadbeat prediction model is:

[0037]

[0038] Where, T s is the PWM control period.

[0039] The maximum four-vector SVPWM module in the present invention obtains a center-symmetric switching sequence by the following steps:

[0040] S1. Construct a set of basic voltage vectors for the dual three-phase motor based on the switching state combinations of the rectifier bridge arms. The voltage vectors output by the rectifiers can be obtained in the fundamental subspace α-β plane and the harmonic subspace xy plane as follows:

[0041]

[0042] Among them, {v k} αβ and {v k} xy Corresponding to the basic voltage vector set in the α-β plane and the xy plane respectively. i Characterizes the conduction state of the power device of the i-th phase bridge arm, S i =1 means that the upper tube of the bridge arm of this phase is in the forward conduction state, and the lower bridge arm switch tube is turned off; S i =0 means that the upper switch of the bridge arm of this phase is in the off state, while the lower switch arm is on. The subscript k represents the octal code sequence (ABC, DEF) consisting of the six phases A, B, C, D, E, and F in order, with the on phase being 1 and the off phase being 0. Figure 4 shown.

[0043] S2. The non-zero voltage vectors in the basic voltage vector set of the dual three-phase motor are divided into four groups according to their amplitudes. The amplitudes of the voltage vectors in each group in the α-β plane satisfy the following relationship:

[0044]

[0045] Among them, |u max | represents the 12 voltage vector amplitudes of the outermost layer of the α-β plane; |u midL |12 voltage vector amplitudes representing the sub-outer layer of the α-β plane; |u mids |12 voltage vector magnitudes representing the sub-inner layer of the α-β plane;

[0046] |u min |Corresponding to the 12 voltage vector amplitudes in the innermost layer of the α-β plane. In each of the above vector sets, the voltage vectors in the outermost layer of the α-β plane are mapped to the innermost layer in the xy plane, the voltage vectors in the innermost layer of the α-β plane are mapped to the outermost layer in the xy plane, and the voltage vectors in the second outermost and second innermost layers of the α-β plane are mapped to the second outermost and second innermost layers, respectively, in the xy plane.

[0047] S3. Select the amplitude in the α-β plane as |u max | a set of non-zero voltage vector sets, generate the maximum four-vector control set of the dual three-phase motor, and divide the above control set into 12 sectors according to the phase angle of each vector, such as Figure 5 (a). The distribution of the voltage vector set in the xy plane is shown as Figure 5 (b) shown.

[0048] S4. The reference voltage u of the α-axis and β-axis inputted by the maximum four-vector SVPWM module α * 、u β * , according to the expression: The phase angle of the fundamental subspace reference voltage vector in the α-β plane is calculated, and four voltage vectors corresponding to the sector where the reference voltage vector is located and two adjacent sectors are selected according to the phase angle.

[0049] S5. Project the four selected voltage vectors u1, u2, u3, and u4 onto the α-axis and β-axis of the fundamental subspace and the x-axis and y-axis of the harmonic subspace, respectively, to obtain the component matrices of the four voltage vectors on each axis:

[0050]

[0051] S6. According to the vector decomposition principle, the reference voltage u of the α-axis and β-axis input of the maximum four-vector SVPWM module α * 、u β * , x-axis and y-axis reference voltage u x * 、uy * The duty cycle calculation module obtains the action times T1, T2, T3, and T4 of the four voltage vectors, and the calculation method is as follows:

[0052]

[0053] S7. Determine whether T1, T2, T3, and T4 obtained by the above calculation exceed T1 of a PWM cycle. s If T1+T2+T3+T4≤T s , then execute S8; if T1+T2+T3+T4>T s , then execute S9.

[0054] S8. When T1+T2+T3+T4≤T s Calculate the action time of zero vector: t0=T s -T1+T2+T3+T4; calculate the action time of the four voltage vectors: t i =T i , where (i=1,2,3,4).

[0055] S9. When T1+T2+T3+T4>T s When , calculate the action time of the zero vector: t0 = 0; calculate the action time of the four voltage vectors: Where (i=1, 2, 3, 4).

[0056] S10. According to the volt-second balance principle, the t0, t1, t2, t3, and t4 obtained by the above calculation are passed through the switch sequence generation module to generate a six-way center-symmetric switch sequence S1, S2, S3, S4, S5, and S6, and output it to the six-phase rectifier.

[0057] The technical solution of the present invention has the following beneficial effects:

[0058] 1. The present invention is applicable to the control system of dual three-phase permanent magnet synchronous generators. The motor system has multiple control degrees of freedom, flexible control, high fault tolerance and other characteristics.

[0059] 2. The dynamic load feedforward compensator constructed in the present invention takes into account the dynamic behavior of the capacitor. Based on the change in capacitor energy storage, the strong coupling characteristics between the load current and the generator quadrature-axis current, it dynamically feedforwards the quadrature-axis current of the motor, shortens the recovery time of the bus voltage, and reduces the voltage fluctuation amplitude.

[0060] 3. The voltage closed-loop controller designed in the present invention makes up for the voltage regulation error caused by inaccurate modeling in pure feedforward control, and ensures the steady-state performance of voltage stabilization control.

[0061] 4. The deadbeat predictive current controller designed in this invention improves the dynamic characteristics of the current loop. This further enhances the torque tracking characteristics of the motor system during sudden load changes, thereby improving the voltage regulation capability of the rectifier system. It also suppresses the fifth and seventh harmonic currents of the dual three-phase permanent magnet synchronous motor, thereby increasing the motor's operating efficiency.

[0062] 5. The load current observer designed in the present invention takes into account capacitor energy storage, motor electromagnetic power and loss as the analytical margin of current detection, and realizes load current estimation by constructing a sliding mode observer, thereby improving system reliability.

[0063] 6. This invention implements a maximum four-vector SVPWM scheme, improving the THD of a dual three-phase permanent magnet synchronous generator by implementing four-dimensional coupled modulation of the fundamental and harmonics in the α-β and xy planes. The use of a centrally symmetric switching sequence helps reduce the switching frequency of the switching devices, minimizing switching losses and further improving system efficiency. BRIEF DESCRIPTION OF THE DRAWINGS

[0064] Figure 1 This is a control structure diagram of the method of the present invention.

[0065] Figure 2 This is the topology diagram of the dual three-phase permanent magnet synchronous generator control system.

[0066] Figure 3 Schematic diagram of the load current observer designed for the present invention.

[0067] Figure 4 is the spatial voltage vector distribution diagram of the dual three-phase permanent magnet synchronous generator; among them, (a) is the voltage vector set of the fundamental subspace α-β plane, and (b) is the voltage vector set of the harmonic subspace xy plane.

[0068] Figure 5 This is the maximum four-vector SVPWM space voltage vector distribution diagram constructed by the present invention; among them, (a) is the fundamental subspace α-β plane voltage vector set, and (b) is the harmonic subspace xy plane voltage vector set. DETAILED DESCRIPTION

[0069] The present invention will be further described below using embodiments. The accompanying drawings described herein are used to provide a further understanding of the present invention, constitute a part of this application, and do not constitute a limitation of the present invention.

[0070] The control structure diagram of the method of the present invention is as follows Figure 1As shown, this embodiment takes a dual three-phase permanent magnet synchronous generator with two sets of three-phase windings that are 30° apart as an example. Taking phase A as the reference, phase B lags phase A by 120°, phase C lags phase A by 240°, phase D lags phase A by 30°, phase E lags phase A by 150°, and phase F lags phase A by 270°. A six-phase rectifier is built. The six-phase rectifier adopts a 12-tube full-bridge topology structure and consists of 6 groups of half-bridges. Each group of half-bridges contains two power tubes connected in series. Each phase line is connected to a half-bridge in the six-phase rectifier; the output of the six-phase rectifier is connected in parallel with several bus capacitors and supplies power to the subsequent load. The generator speed / position information is collected by the photoelectric encoder, the bus voltage is obtained by the voltage sensor, and the voltage given signal U dc * The currents are transmitted to the controller via an external digital bus. High-precision sampling resistors are used to obtain the six-phase currents in the stator windings. The controller uses a Texas Instruments (TI) TMS320F28377S series digital signal processing chip, which includes an internal timer interrupt source and is combined with a Lattice CPLD chip for hardware protection. Motor control is achieved using the following scheme:

[0071] (1) Establish the stator winding voltage equation in the rotating coordinate system, and its mathematical expression is:

[0072]

[0073] Among them, u d 、i d and L d are the voltage, current and inductance of the d-axis respectively, u q 、i q and L q are the voltage, current and inductance of the q axis respectively, u x 、i x , L x They are the voltage, current, and inductance of the x-axis, u y 、i y , L y They are the voltage, current, and inductance of the y-axis, R s is the motor winding resistance, ω e is the rotor electrical angular velocity, ψ f is the fundamental magnetic flux.

[0074] (2) The present invention uses VSD decoupling transformation to convert the six-phase stator current i a 、i b 、i c 、i d 、i e 、i f , respectively mapped to obtain the quadrature axis current i under the fundamental subspace rotation coordinate q, direct axis current i d , and the x-axis current i in the stationary coordinates of the harmonic subspace x , y-axis current i y The VSD coordinate transformation satisfies the following expression:

[0075]

[0076] (3) The controller internal timing interrupt service program is based on the sampling period T s Regularly sample the current sensor signal to obtain the six-phase current i a 、i b 、i c 、i d 、i e 、i f , the rotor position electrical angle θ and rotor electrical angular velocity ω are obtained through the photoelectric encoder e , and obtain the DC bus voltage U through the voltage sensor dc The interrupt service routine obtains the preset direct axis current reference given quantity i d * , when using i d =0 control strategy, the direct axis current reference given quantity i d * When considering suppressing motor harmonic current, the reference given value i of the x-axis and y-axis currents in the harmonic subspace is x * 、i y * At the same time, the DC bus voltage reference instruction U is obtained from the external communication bus in real time. dc * .

[0077] (4) Construct a load current observer for load current estimation to achieve analytical margin of current detection. It mainly includes: a load current estimation module, an electromagnetic power estimation module, a motor loss estimation module and a capacitor energy storage model. Its structure is as follows: Figure 3 shown.

[0078] (5) Construct the load current estimation module, which contains a subtractor and a hyperbolic tangent function link. The subtractor is used to realize the DC bus voltage U dc and bus voltage estimates The subtraction operation of the bus voltage estimation error e is obtained. u The above error is passed through the hyperbolic tangent function link to obtain the load current estimate Among them, the expression of the hyperbolic tangent function link is:

[0079] (6) Construct the electromagnetic power estimation module, which contains a multiplier and a proportional link. The multiplier is used to realize the rotor electrical angular velocity ω e and q-axis current i q The product term is multiplied by the proportional link to obtain the estimated value of the electromagnetic power of the generator Among them, the gain of the proportional link is determined by the motor flux, and the gain expression is: 3ψ f .

[0080] (7) Construct the motor loss estimation module, which contains two square links, an adder, and a proportional link. The square links are used to calculate the quadrature axis current i q and the direct axis current i d The square operation is performed, and the square terms obtained are summed by the adder and then passed through the proportional link to obtain the estimated value of the generator power loss

[0081] Among them, the gain of the proportional link is determined by the motor winding resistance, and the gain expression is: 3R s .

[0082] (8) The above generator electromagnetic power estimate and estimated generator power loss Subtract and get the estimated value of generator output power Then, through a proportional link, the estimated value of the rectifier output bus current is obtained. The gain of the proportional link is determined by the bus voltage reference given value U dc * Determine, the gain expression is: The above bus current estimate and load current estimate The estimated value of the capacitor current is obtained through the subtractor

[0083] (9) Construct the capacitor energy storage model, which contains a proportional link and an integral link. The input of the proportional link is the estimated value of the capacitor current The proportional gain is expressed as: Where C is determined by the total DC bus capacitance; the output of the proportional link passes through the integral link to obtain the above bus voltage estimate

[0084]

[0085] (10) Construct a dynamic load feedforward compensator, accurately calculate and output the quadrature axis current fast adjustment component i through the motor model and capacitor energy storage model q1 *It mainly includes: a derivative link, a proportional link, an adder, a multiplier and an electromagnetic power solution model. Among them, the DC bus voltage U dc The derivative of the bus voltage is obtained through the derivation link, and then the calculated value of the capacitor current i is obtained through the proportional link. C * The calculated value of the capacitor current i C * and load current estimate Calculate the algebraic sum to get the bus current calculated value i dc * . Bus current calculation value i dc * With the bus voltage reference given value U dc * After multiplication by the multiplier, the calculated value of the electromagnetic power of the generator P is obtained. e * . Generator electromagnetic power calculation value P e * According to the electromagnetic power solution model, the quadrature axis current fast adjustment component i is obtained q1 * , where the analytical expression of the electromagnetic power solution model is as follows:

[0086]

[0087] Where, ω e is the rotor electrical angular velocity, ψ f It is the fundamental flux of dual three-phase permanent magnet generator.

[0088] (11) Construct a voltage closed-loop controller to achieve error-free tracking of the bus voltage reference given value, and obtain and output the quadrature-axis current error compensation component i q2 * It mainly includes: a subtractor and a voltage regulator AVR. Among them, the subtractor is used to realize the bus voltage reference given value U dc * and DC bus voltage U dc The subtraction operation is performed to obtain the bus voltage error, which is passed through the voltage regulator AVR to obtain the quadrature axis current error compensation component i q2 * .

[0089] (12) The above-mentioned quadrature axis current rapid adjustment component i q1 * and the quadrature axis current error compensation component i q2 * The algebraic sum is calculated by the adder, and then the quadrature axis current reference value i is obtained by the inverter link. q * .

[0090] (13) Construct a deadbeat prediction current controller to achieve fast and accurate tracking of the generator quadrature axis current. It mainly includes: a one-step prediction model, a deadbeat prediction model and a Park -1 converter.

[0091] (14) Construct the one-step prediction model, whose input includes the direct axis and quadrature axis current i of the fundamental subspace at time k obtained by VSD coordinate transformation d (k) and i q (k), harmonic subspace x-axis and y-axis current i x (k) and i y (k), the direct-axis and quadrature-axis voltages u of the fundamental subspace at time k d (k) and u q (k), harmonic subspace x-axis and y-axis voltage u x (k) and u y (k). The direct-axis and quadrature-axis currents i in the fundamental subspace at time k+1 are obtained by solving the one-step prediction model. d (k+1) and i q (k+1), and the harmonic subspace x-axis and y-axis current i x (k+1) and i y (k+1). The solution expression of the one-step prediction model is:

[0092]

[0093] (15) Construct the deadbeat prediction model, whose input includes the direct axis and quadrature axis current i of the fundamental subspace at time k+1 obtained by the one-step prediction model d (k+1) and i q (k+1), harmonic subspace x-axis and y-axis current i x (k+1) and i y (k+1), and the direct-axis and quadrature-axis current reference given quantity i d * and i q * , the x-axis and y-axis current reference given quantity i x * 、i y * The reference voltage u of the direct axis and quadrature axis of the fundamental subspace rotating coordinate system at time k+1 is obtained by solving the deadbeat prediction model. d * (k+1),u q * (k+1), the x-axis and y-axis reference voltage u of the harmonic subspace stationary coordinate system x * (k+1),u y* (k+1). The solution expression of the deadbeat prediction model is:

[0094]

[0095] (16) Construct the Park -1 The converter input includes the reference voltage u of the direct axis and quadrature axis of the fundamental subspace rotating coordinate system at time k+1 output by the deadbeat prediction model. d * (k+1),u q * (k+1), through the coordinate transformation matrix, solve and output the reference voltage u of the α-axis and β-axis of the fundamental subspace stationary coordinate system at time k+1 α * (k+1),u β * (k+1).

[0096] (17) Construct a maximum four-vector SVPWM module to modulate the reference voltage into a six-phase PWM signal and generate a center-symmetric switching sequence. It mainly includes: a dual three-phase motor maximum four-vector control set, a duty cycle calculation module, and a switching sequence generation module. The maximum four-vector SVPWM module obtains the center-symmetric switching sequence through the following steps:

[0097] S1. Construct a set of basic voltage vectors for the dual three-phase motor based on the switching state combinations of the rectifier bridge arms. The voltage vectors output by the rectifiers can be obtained in the fundamental subspace α-β plane and the harmonic subspace xy plane as follows:

[0098]

[0099] Among them, {v k} αβ and {v k} xy Corresponding to the basic voltage vector set in the α-β plane and the xy plane respectively. i Characterizes the conduction state of the power device of the i-th phase bridge arm, S i =1 means that the upper switch of the bridge arm of this phase is in the forward conduction state, and the lower switch arm is turned off; S i =0 means that the upper switch of the bridge arm of this phase is in the off state, while the lower switch arm is on. The subscript k represents the octal code sequence (ABC, DEF) consisting of the six phases A, B, C, D, E, and F in order, with the on phase being 1 and the off phase being 0. Figure 4 shown.

[0100] S2. The non-zero voltage vectors in the basic voltage vector set of the dual three-phase motor are divided into four groups according to their amplitudes. The amplitudes of the voltage vectors in each group in the α-β plane satisfy the following relationship:

[0101]

[0102] Among them, |u max | represents the 12 voltage vector amplitudes of the outermost layer of the α-β plane; |u midL |12 voltage vector amplitudes representing the sub-outer layer of the α-β plane; |u mids |12 voltage vector magnitudes representing the sub-inner layer of the α-β plane;

[0103] |u min |Corresponding to the 12 voltage vector amplitudes in the innermost layer of the α-β plane. In each of the above vector sets, the voltage vectors in the outermost layer of the α-β plane are mapped to the innermost layer in the xy plane, the voltage vectors in the innermost layer of the α-β plane are mapped to the outermost layer in the xy plane, and the voltage vectors in the second outermost and second innermost layers of the α-β plane are mapped to the second outermost and second innermost layers, respectively, in the xy plane.

[0104] S3. Select the amplitude in the α-β plane as |u max | a set of non-zero voltage vector sets, generate the maximum four-vector control set of the dual three-phase motor, and divide the above control set into 12 sectors according to the phase angle of each vector, such as Figure 5 (a). The distribution of the voltage vector set in the xy plane is shown as Figure 5 (b) shown.

[0105] S4. The reference voltage u of the α-axis and β-axis inputted by the maximum four-vector SVPWM module α * 、u β * , according to the expression: The phase angle of the fundamental subspace reference voltage vector in the α-β plane is calculated, and four voltage vectors corresponding to the sector where the reference voltage vector is located and two adjacent sectors are selected according to the phase angle.

[0106] S5. Project the four selected voltage vectors u1, u2, u3, and u4 onto the α-axis and β-axis of the fundamental subspace and the x-axis and y-axis of the harmonic subspace, respectively, to obtain the component matrices of the four voltage vectors on each axis:

[0107]

[0108] S6. According to the vector decomposition principle, the reference voltage u of the α-axis and β-axis input of the maximum four-vector SVPWM module α *、u β * , x-axis and y-axis reference voltage u x * 、u y * The duty cycle calculation module obtains the action times T1, T2, T3, and T4 of the four voltage vectors, and the calculation method is as follows:

[0109]

[0110] S7. Determine whether T1, T2, T3, and T4 obtained by the above calculation exceed T1 of a PWM cycle. s If T1+T2+T3+T4≤T s , then execute S8; if T1+T2+T3+T4>T s , then execute S9.

[0111] S8. When T1+T2+T3+T4≤T s Calculate the action time of zero vector: t0=T s -T1+T2+T3+T4; calculate the action time of the four voltage vectors: t i =T i , where (i=1,2,3,4).

[0112] S9. When T1+T2+T3+T4>T s When , calculate the action time of the zero vector: t0 = 0; calculate the action time of the four voltage vectors: Where (i=1, 2, 3, 4).

[0113] S10. According to the volt-second balance principle, the t0, t1, t2, t3, and t4 obtained by the above calculation are passed through the switch sequence generation module to generate a six-way center-symmetric switch sequence S1, S2, S3, S4, S5, and S6, and output it to the six-phase rectifier.

[0114] (18) The six-phase rectifier is used to rectify the six-phase PWM voltage into a DC voltage. Its input is the six-way switch signal S1, S2, S3, S4, S5, S6. By controlling the on and off of the power tubes of the six half-bridges, the PWM rectification control of the dual three-phase permanent magnet synchronous generator is realized, as shown in Figure 2 shown.

Claims

1. A dual three-phase permanent magnet synchronous generator rectification system, characterized in that: include: A dual three-phase permanent magnet synchronous generator, a VSD decoupling converter, a load current observer, a dynamic load feedforward compensator, a voltage closed-loop controller, a deadbeat prediction current controller, a maximum four-vector SVPWM modulation module, and a six-phase rectifier; wherein the input of the VSD decoupling converter is connected to the six-phase rectifier, and the output is connected to the deadbeat prediction current controller and the load current observer; the input of the load current observer is connected to the VSD decoupling converter and the six-phase rectifier; the output is connected to the dynamic load feedforward compensator; the input of the dynamic load feedforward compensator is connected to the load current observer. , a six-phase rectifier is connected to an external given, and outputs to an adder; the input of the voltage closed-loop controller is connected to the six-phase rectifier and the external given, and outputs to the adder; the output signals of the dynamic load feedforward compensator and the voltage closed-loop controller are summed by the adder, and then output to the deadbeat prediction current controller through the inverter link; the input of the deadbeat prediction current controller is connected to the inverter link, the VSD decoupling converter and the external given, and the output is connected to the maximum four-vector SVPWM modulation module; the input of the maximum four-vector SVPWM modulation module is connected to the deadbeat prediction current controller, and the output is connected to the six-phase rectifier; The dual three-phase permanent magnet synchronous generator comprises two sets of three-phase windings, the phases of the two sets of three-phase windings are 30° apart from each other, and the neutral points are isolated; The VSD decoupling converter is used to convert the six-phase current of the motor into the orthogonal axis current in the fundamental wave space rotating coordinate and the xy axis current in the harmonic wave space stationary coordinate; The load current observer is used to estimate the load current and achieve resolution margin of current detection; The dynamic load feedforward compensator accurately calculates and outputs the quadrature axis current fast adjustment component i through the motor model and the capacitor energy storage model. q1 * ; The voltage closed-loop controller is used to achieve error-free tracking of the bus voltage reference given value, and obtain and output the quadrature-axis current error compensation component i q2 * ; The deadbeat predictive current controller is used to achieve fast and accurate tracking of the generator quadrature axis current; The maximum four-vector SVPWM module is used to modulate the reference voltage into a six-phase PWM signal to generate a center-symmetric switching sequence; The six-phase rectifier is used to rectify the six-phase PWM voltage into a DC voltage, and the input is a six-way switch sequence S1, S2, S3, S4, S5, and S6. By controlling the on and off of the power tubes of the six half-bridges, PWM rectification control of the dual three-phase permanent magnet synchronous generator is realized.

2. A dual three-phase permanent magnet synchronous generator rectification system according to claim 1, characterized in that: The input of the VSD decoupling converter is the six-phase current i of the dual three-phase permanent magnet synchronous generator. a 、i b 、i c 、i d 、i e 、i f , after VSD decoupling transformation, the quadrature axis current i in the fundamental wave space rotating coordinate is output q , direct axis current i d , and the x-axis current i in the harmonic space stationary coordinate x , y-axis current i y ; The input of the load current observer is the quadrature axis current i q , the direct axis current i d , DC bus voltage U dc and the generator rotor electrical angular velocity ω e , the rotor electrical angular velocity is given by the rotor electrical angle θ e The load current observer outputs the load current estimate The input of the dynamic load feedforward compensator is the bus voltage reference given value U dc * , DC bus voltage U dc , load current estimation Generator rotor electrical angular velocity ω e The dynamic load feedforward compensator outputs the quadrature axis current rapid adjustment component i q1 * ; The input of the voltage closed-loop controller is the bus voltage reference given value U dc * and DC bus voltage U dc The voltage closed-loop controller outputs the quadrature-axis current error compensation component i q2 * ; The input of the deadbeat predictive current controller includes the direct axis and quadrature axis current i of the fundamental subspace at time k obtained by VSD coordinate transformation. d (k) and i q (k), harmonic subspace x-axis and y-axis current i x (k) and i y (k), direct-axis and quadrature-axis current reference given quantity i d * and i q * , the x-axis and y-axis current reference given quantity i x * 、i y * ; The deadbeat predictive current controller outputs the reference voltage u of the α-axis and β-axis of the orthogonal stationary coordinate system at time k+1. α * (k+1),u β * (k+1), x-axis and y-axis reference voltage u x * (k+1),u y * (k+1); The input of the maximum four-vector SVPWM module is the reference voltage u of the α-axis and β-axis at time k+1 α * (k+1),u β * (k+1), x-axis and y-axis reference voltage u x * (k+1),u y * (k+1); output six switch sequences S1, S2, S3, S4, S5, and S6 through the maximum four-vector SVPWM module.

3. A DC voltage stabilization control method for a dual three-phase permanent magnet synchronous generator rectifier system according to claim 1, characterized in that: The following steps are involved: S1. Build a dual three-phase permanent magnet synchronous generator rectifier system, including: a dual three-phase permanent magnet synchronous generator, a load current observer, a dynamic load feedforward compensator, a voltage closed-loop controller, a deadbeat predictive current controller, a maximum four-vector SVPWM modulation module, a VSD decoupling converter, and a six-phase rectifier. S2. Build a dual three-phase permanent magnet synchronous generator with two sets of three-phase windings. The phases of the two sets of three-phase windings are 30° apart and the neutral points are isolated. With phase A as the reference, phase B lags phase A by 120°, phase C lags phase A by 240°, phase D lags phase A by 30°, phase E lags phase A by 150°, and phase F lags phase A by 270°. S3 build a six-phase rectifier, one end of each phase winding is connected to a half-bridge in the six-phase rectifier; the output of the six-phase rectifier is connected in parallel with several bus capacitors and supplies power to the subsequent load; S4. Construct a load current observer; the load current observer comprises: a load current estimation module, an electromagnetic power estimation module, a motor loss estimation module and a capacitor energy storage model; S5. Constructing a dynamic load feedforward compensator; the dynamic load feedforward compensator comprises: a derivative link, a proportional link, an adder, a multiplier and an electromagnetic power solution model; S6. Constructing a voltage closed-loop controller; the voltage closed-loop controller comprises: a subtractor and a voltage regulator AVR; S7. Constructing a deadbeat prediction current controller; the deadbeat prediction current controller comprises: a one-step prediction model, a deadbeat prediction model and a Park -1 converter; S8. Construct a maximum four-vector SVPWM module; the maximum four-vector SVPWM module includes: a dual three-phase motor maximum four-vector control set, a duty cycle calculation module and a switching sequence generation module.

4. The method according to claim 3, characterized in that The input of the VSD decoupling converter is the six-phase current i of the dual three-phase permanent magnet synchronous generator. a 、i b 、i c 、i d 、i e 、i f , the output is the quadrature axis current i under the fundamental subspace rotation coordinate q , direct axis current i d , and the x-axis current i in the stationary coordinates of the harmonic subspace x , y-axis current i y The VSD coordinate transformation maps the six-phase stator current to the fundamental subspace and harmonic subspace, satisfying the following expression: The mathematical expression of the stator winding voltage equation of the dual three-phase permanent magnet synchronous generator is: Where u d 、i d and L d are the voltage, current and inductance of the d-axis respectively, u q 、i q and L q are the voltage, current and inductance of the q axis respectively, u x 、i x 、L x They are the voltage, current, and inductance of the x-axis, u y 、i y 、L y They are the voltage, current, and inductance of the y-axis, R s is the motor winding resistance, ω e is the rotor electrical angular velocity, ψ f is the fundamental magnetic flux.

5. The method according to claim 3, characterized in that The load current observer has the following structure: The load current estimation module includes a subtractor and a hyperbolic tangent function link; the subtractor is used to realize the DC bus voltage U dc and bus voltage estimates The subtraction operation of the bus voltage estimation error e is obtained. u The above error is passed through the hyperbolic tangent function link to obtain the load current estimate Among them, the expression of the hyperbolic tangent function link is: The electromagnetic power estimation module contains a multiplier and a proportional link; the multiplier is used to realize the rotor electrical angular velocity ω e and q-axis current i q The product term is passed through the proportional link to obtain the estimated value of the electromagnetic power of the generator Among them, the gain of the proportional link is determined by the motor flux, and the gain expression is: 3ψ f ; The motor loss estimation module contains two square links, an adder, and a proportional link; the square links are used to calculate the quadrature axis current i q and the direct axis current i d The square operation is performed, and the square terms obtained are summed through the adder and then passed through the proportional link to obtain the estimated value of the generator power loss The gain of the proportional link is determined by the motor winding resistance, and the gain expression is: 3R s ; The estimated electromagnetic power of the above generator and estimated generator power loss Subtract and get the estimated value of generator output power Then, through a proportional link, the estimated value of the rectifier output bus current is obtained. The gain of the proportional link is determined by the bus voltage reference given value U dc * Determine, the gain expression is: The above bus current estimate and load current estimate The estimated value of the capacitor current is obtained through the subtractor The capacitor energy storage model contains a proportional link and an integral link; the input of the proportional link is the estimated value of the capacitor current The proportional gain is expressed as: Where C is determined by the total DC bus capacitance; the output of the proportional link passes through the integral link to obtain the above bus voltage estimate 6. The method according to claim 3, characterized in that The dynamic load feedforward compensator has the following structure: DC bus voltage U dc The derivative of the bus voltage is obtained through the derivation link, and then the calculated value of the capacitor current i is obtained through the proportional link. C * The adder realizes the calculated value of the capacitor current i C * and load current estimate The sum operation is performed to obtain the bus current calculation value i dc * ; The bus current calculated value i dc * With the bus voltage reference given value U dc * After multiplication by the multiplier, the calculated value of the electromagnetic power of the generator P is obtained. e * ; The calculated value of the generator electromagnetic power P e * Through the electromagnetic power solution model, the quadrature axis current rapid adjustment component i is obtained q1 * , where the analytical expression of the electromagnetic power solution model is as follows: Where, ω e is the rotor electrical angular velocity, ψ f It is the fundamental flux of dual three-phase permanent magnet generator.

7. The method according to claim 3, characterized in that The voltage closed-loop controller has the following structure: The subtractor is used to realize the bus voltage reference given value U dc * and DC bus voltage U dc The subtraction operation is performed to obtain the bus voltage error, which is passed through the voltage regulator AVR to obtain the quadrature axis current error compensation component i q2 * .

8. The method according to claim 3, characterized in that The deadbeat prediction current controller has the following structure: The one-step prediction model has the following inputs: the direct-axis and quadrature-axis currents i of the fundamental subspace at time k obtained by VSD coordinate transformation. d (k) and i q (k), harmonic subspace x-axis and y-axis current i x (k) and i y (k), the direct-axis and quadrature-axis voltages u of the fundamental subspace at time k d (k) and u q (k), harmonic subspace x-axis and y-axis voltage u x (k) and u y (k); The direct-axis and quadrature-axis currents i of the fundamental subspace at time k+1 are obtained by solving the model d (k+1) and i q (k+1), and the harmonic subspace x-axis and y-axis current i x (k+1) and i y (k+1); The deadbeat prediction model, whose input includes the k+1 moment fundamental subspace direct axis and quadrature axis current i obtained by the one-step prediction model d (k+1) and i q (k+1), harmonic subspace x-axis and y-axis current i x (k+1) and i y (k+1), and the direct-axis and quadrature-axis current reference given quantity i d * and i q * , the x-axis and y-axis current reference given quantity i x * 、i y * ; The reference voltage u of the direct axis and quadrature axis of the fundamental subspace rotating coordinate system at time k+1 is obtained by model solution output d * (k+1),u q * (k+1), the x-axis and y-axis reference voltage u of the harmonic subspace stationary coordinate system x * (k+1),u y * (k+1); Park -1 The converter has an input including the reference voltage u of the direct axis and quadrature axis of the fundamental subspace rotating coordinate system at time k+1 output by the deadbeat prediction model. d * (k+1),u q * (k+1), through the coordinate transformation matrix, solve and output the reference voltage u of the α-axis and β-axis of the fundamental subspace stationary coordinate system at time k+1 α * (k+1),u β * (k+1).

9. The method according to claim 3, characterized in that The solution expression of the one-step prediction model is: The solution expression of the deadbeat prediction model is: Where, T s is the PWM control period.

10. The method according to claim 3, characterized in that The maximum four-vector SVPWM module obtains a centrally symmetric switching sequence by the following steps: S1. Based on the switching state combination of each rectifier bridge arm, the basic voltage vector set of the dual three-phase motor is constructed. The voltage vectors output by the rectifier can be obtained in the fundamental subspace α-β plane and the harmonic subspace xy plane according to the following expressions: Among them, {v k } αβ and {v k } xy Corresponding to the basic voltage vector sets in the α-β plane and the xy plane respectively; S i Characterizes the conduction state of the power device of the i-th phase bridge arm, S i =1 means that the upper switch of the bridge arm of this phase is in the forward conduction state, and the lower switch arm is turned off; S i =0 means that the upper switch of the bridge arm of this phase is in the off state, while the lower switch of the bridge arm is on. The subscript k represents the octal code sequence (ABC, DEF) consisting of the six phases A, B, C, D, E, and F in order, with the on phase being 1 and the off phase being 0. S2. The non-zero voltage vectors in the basic voltage vector set of the dual three-phase motor are divided into four groups according to their amplitudes; the amplitudes of the voltage vectors in each group in the α-β plane satisfy the following relationship: Among them, |u max | represents the 12 voltage vector amplitudes of the outermost layer of the α-β plane; |u midL |12 voltage vector amplitudes representing the sub-outer layer of the α-β plane; |u mids |12 voltage vector magnitudes representing the sub-inner layer of the α-β plane; |u min |Corresponding to the 12 voltage vector amplitudes in the innermost layer of the α-β plane; in each of the above vector sets, the voltage vector in the outermost layer of the α-β plane is mapped to the voltage vector in the innermost layer in the xy plane, the voltage vector in the innermost layer of the α-β plane is mapped to the voltage vector in the outermost layer in the xy plane, and the voltage vectors in the second outermost and second innermost layers of the α-β plane are mapped to the second outermost and second innermost layers, respectively, in the xy plane; S3. Select the amplitude in the α-β plane as |u max | a set of non-zero voltage vector sets, generating a maximum four-vector control set for the dual three-phase motor, and dividing the control set into 12 sectors according to the phase angles of the vectors; S4. The reference voltage u of the α-axis and β-axis inputted by the maximum four-vector SVPWM module α * 、u β * , according to the expression: Calculate the phase angle of the fundamental subspace reference voltage vector in the α-β plane, and select four voltage vectors corresponding to the sector where the reference voltage vector is located and the two adjacent sectors based on the phase angle; S5. Project the four selected voltage vectors u1, u2, u3, and u4 onto the α-axis and β-axis of the fundamental subspace and the x-axis and y-axis of the harmonic subspace, respectively, to obtain the component matrices of the four voltage vectors on each axis: S6. According to the vector decomposition principle, the reference voltage u of the α-axis and β-axis input of the maximum four-vector SVPWM module α * 、u β * , x-axis and y-axis reference voltage u x * 、u y * The duty cycle calculation module obtains the action times T1, T2, T3, and T4 of the four voltage vectors, and the calculation method is as follows: S7. Determine whether T1, T2, T3, and T4 obtained by the above calculation exceed T1 of a PWM cycle. s ; If T1+T2+T3+T4≤T s , then execute S8; if T1+T2+T3+T4>T s , then execute S9; S8. When T1+T2+T3+T4≤T s Calculate the action time of zero vector: t0=T s -T1+T2+T3+T4; calculate the action time of the four voltage vectors: t i =T i , where (i=1,2,3,4); S9. When T1+T2+T3+T4>T s When , calculate the action time of the zero vector: t0 = 0; calculate the action time of the four voltage vectors: Where (i=1,2,3,4); S10. According to the volt-second balance principle, the t0, t1, t2, t3, and t4 obtained by the above calculation are passed through the switch sequence generation module to generate a six-way center-symmetric switch sequence S1, S2, S3, S4, S5, and S6, and output it to the six-phase rectifier.

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