Direct power control of dual three-phase permanent magnet synchronous motor based on multiple vectors

In response to the traditional mode of dual three-phase permanent magnet synchronous generator switch form vector direct power control (DPC), the current harmonics are large, the active (P) and reactive (Q) harmonic oscillations are large, and the unstable losses of each phase current are large. A virtual voltage vector direct power control method based on duty cycle modulation is proposed. This method compares and synthesizes the two vectors of the outermost and second layers of the PWM rectifier, as well as three large vector synthesis methods, to obtain 12 new virtual voltage vectors. Then, the combined voltage vector is directly modulated into the deadbeat switching table, and the optimal predicted vector value is calculated based on the principle of the deadbeat formula, further suppressing the problem of large fluctuations in active and reactive power. Results show that the proposed multi-vector composite odd even quadrant DPC can effectively reduce current harmonics and power ripple, make the phase current more stable, reduce motor operating losses, and significantly improve the motor.


Introduction
Compared to the complex structure of DPC generators, direct power control is one of the commonly used mainstream control strategies for permanent magnet generators [1~3] .The traditional direct power control based on switch tables has a similar structure to the direct torque control of electric motors.Usually, two power hysteresis controllers are used, sorted by the magnitude of active power control error.Select the desired voltage vector from the switch table [4] .This method does not require coordinate transformation and has a low dependence on motor parameters.The main pursuit is accuracy and agility in power handling [5~9] .However, because the problem of harmonic sub planes was not considered and harmonic control was carried out, its stator current was too high, which affected the normal operation of the generator.Direct power control based on switch tables usually only uses a non-zero voltage vector throughout the entire control cycle, which is not precise enough for power regulation, resulting in a large output power ripple [5] .
This article introduces a virtual voltage vector, which is achieved by applying αβ selecting the maximum voltage vector and the larger voltage vector in the subspace for synthesis, distinguishing between odd and even intervals, and using three vector synthesis for even quadrants [9] .Synthesize the new voltage vector into a virtual voltage vector to make the voltage vector in the subspace zero.This can further suppress the harmonics current of the generator stator and improve the operational efficiency of the generator [7] .But only virtual voltage is used for control.As the amplitude of the virtual voltage vector is immutable, to solve the problem of a large current ripple, zero beat is introduced to adjust the amplitude.By calculating the duty cycle of the voltage vector within one sampling cycle and inserting a zero vector, the current control accuracy is improved, and the ripple of active and reactive power is further reduced.And the pulsation of phase current.Finally, the effectiveness of this structural method was verified through simulation [10] .

DPC mathematical modeling
The DTP-PMSG is driven by a two-level six-phase PWM rectifier, whose mathematical model and topology are shown in Figure 1.The model and topology of DTP-PMSG are shown in Figure 1, where udc and idc represent the DC bus voltage and load current, respectively, and C and RL represent the DC bus capacitance and load, respectively.Omitting the tedious derivation process, due to space vector decoupling theory [10] , the math model of DTP-PMSG after Clark transformation may be obtained as follows in α subspace: In Equation ( 1), E, U, i, R, and L represent the generator back electromotive force, rectifier side voltage, stator current, winding resistance, and inductance, respectively [10] .
The decomposition of the generator back electromotive force E onto the α axis is: According to the theory of instantaneous power, it can be concluded that: The derivative of Equation 3 yields the following result: The changes in active power P and reactive power Q over time t obtained by combining Equations ( 2), (3), and ( 4) are [9][10] :

Basic voltage vector of rectifier
As shown in Figure 1, it can be seen that it has 6 bridge arms, each with two on and off states.When the upper bridge arm is on, that later bridge arm automatically turns off.Therefore, the entire inverter switch state has a total of 64 states in all cases, Correspondingly, there are 64 voltage vectors determined by Equations ( 6) and ( 7 In the equation, SABCDEF represents the switching status of each phase, and SA ~ SF represents the switching status of each bridge arm.The opening of the upper bridge arm is specified as "1", and the closing of the upper bridge arm is specified as "0".The numbering of traditional single voltage vectors is determined by the order of rectifiers ABC and DEF, and the combination of switch states is represented in octal.To determine the distribution of the voltage vector in the αβ planes, we can see details in Figure 2. The flat surface electric potential vector diagram of DPC PMSG is shown in the following figure.The above figure contains 60 effective voltage vectors, plus 4 zero vectors.These voltage vectors divide the αβ plane and xy plane into four regular dodecagonal shapes with different amplitudes, from inside out: L1 (0.173 Udc), L2 (0.333 Udc), L3 (0.471 Udc), and L4 (0.644 Udc) among αβ.The outermost large vector of the plane maps to the xy plane, becoming the innermost small vector.The innermost small vector of a plane maps to the outermost large vector of the plane.The planes of the middle two layers remain unchanged.

Switch table based on large vectors
Traditional DPC uses the outermost 12 large vectors, which can be achieved by the voltage vector in Figure 2 (a).The expression for both active and passive effects power obtained by substituting the outermost layer into Equation (5): In the equation, i=1, 2, 3… 12, VL =0.644udc.It is the amplitude of a large vector.The positive and negative values of Equation ( 8) respectively reflect the increase and decrease of power, and their absolute values are compared with 0. Its size reflects the magnitude of the power variation generated by the corresponding voltage vector.

Virtual vector control
This article selects a set of data from Figure 2 (a), where vectors in the same direction u56, u65, and u44 have the same direction.Their main difference is that their amplitude sizes are different, so they have the same effect.Mapping these three vectors to the xy subspace, the u56 and u44 directions are consistent with each other and u65 opposite, so the effect is opposite to suppress the flow of current harmonics in the xy subspace as much as possible.This paper selects two vectors u65 and u44 that are opposite in the xy subspace and calculates the time when the voltage vectors act on each other using the following equation: 0.471 (1 )  0.173 0 From the above equation, we can get the answer t ＝ 0.732,1-t=0.268Since the direction is consistent with that in the αβ subspace, the synthesized vector is: 0.471 (1 ) 0.644 0.598 According to the above principles, 12 virtual voltage vectors with uniformly distributed amplitude and phase angles can be constructed, as shown in Figure 5.Even numbered virtual vectors, where V2 is composed of three large vectors: u66, u64, and u44.The amplitude size is consistent with the size of u64 and u46, and can still maintain 0.598 udc, thus changing the new synthesis method.The purpose is to reduce the occurrence of three conduction cycles per cycle, to avoid unnecessary losses.

Simulation verification
The system is simulated by DPC, parameters can be seen in Table 1.  1, the paper simulated the unidirectional DPC of DTP-PMSG.Firstly, Figure 6 (a) shows the simulation waveform of the DC voltage Udc.It is not difficult to find that the harmonic ripple of Udc is relatively large.Figure 6 (b) shows the variation of power.Before 0.1 seconds, the active power stabilized at 400 W. At 0.1 seconds, the load interference was received, and the active power quickly increased to 600 W and remained balanced.The reactive power Q remained at 0 V throughout the entire process but can be seen from the figure that the power ripple fluctuates greatly.As shown in Figure 6 (c), the opposite electromotive force and current of A indicate that the generator is operating at high power, but the current is unstable and current harmonics are large.As shown in Figure 6 (d), the harmonic rate is 36.63%.The above experimental results indicate that using 12 maximum vectors for control can make the system operate at the unit power factor and achieve higher voltage utilization.However, due to the larger stator current harmonics, the motor is greatly consumed.

Multi virtual vector DPC simulation
Based on the parameter, simulation was conducted on DTP vector control.Figure 7 (a) shows the simulation waveform of the Udc in the power generation system, where Udc rises to 80 V and maintains a balanced and stable output.Figure 7 (b) shows the changes in power, with the active power rapidly increasing to 600 W, and the reactive power is set to 0 V throughout the entire process.

Conclusion
This article focuses on the problem of large current harmonics in the single vector DPC of traditional DTP-PMSG, as well as severe power fluctuations and unstable phase currents.A method based on multi-vector control has been proposed, which has been proven through experiments to reduce stator current harmonics to a certain extent, making the phase current more stable, reducing motor operating losses, and significantly improving the steady-state performance of motor operation.

Figure 6 .
Figure 6.Simulation results of single vector DPC.

Figure 7 (Figure 7 .
Figure 7. Simulation results of duty cycle modulation DPC. ): α Switching Vector of Subspace Vα and xy.The subspace switch vector Vxy satisfies the following equations:

Table 1 .
Parameters of the DTP-PMSG system.Simulation analysis of traditional single-vector DPC Finally, based on the parameters in Table