Three-phase induction motors (IMs) are widely utilized in modern industry such as water pumps, draught fans, grinding millers and so on. Large starting currents will damage IM if it is directly started with power supply. So three-phase anti-parallel thyristor circuits based on voltage-regulation technology are often adopted for the soft start of IM [1], which have small starting current. However, using this way, electromagnetic torque of IM has more sacrifice than the decline of its starting current. Though many papers have proposed several methods to enhance start torque of IM, but they are based on constant-current control or closed-torque control [2–3]. [4] and [5] propose a novel control strategy of soft start for IM using pulse width modulation(PWM) AC chopper, which uses four insulated gate bipolar transistors(IGBT) to regulate three-phase voltages of IM. This control method is simple and flexible, but the frequency of the three-phase voltages maintains a constant value. The promotion of IM starting torque in papers [2,3,4,5] is limited, because these methods all belong to the voltage-regulation control theory of IM.
Based on the three-phase thyristor circuits, Ginart and his cooperators propose a discrete variable frequency (DVF) theory, which can enhance electromagnetic torque of IM with the same starting current [6]. So, DVF theory is welcomed and further investigated in worldwide. In [7], phase control method of DVF optimal switching is studied, which has a favorable effect on solving switch disturbance but don’t compare with other methods. In [8–10], one triggering scheme of output equivalent sinusoid voltages based on DVF is proposed, which analyzes the voltage symmetry and acquired available frequency dividing coefficients. It is insufficient that the control method can’t consider the flux of IM when two-phase thyristor circuits are triggered. In [10–11], the cause of torque pulsation is studied and the proposed DVF control strategy is based on space voltage vectors, which can decrease the torque pulsation. However, the working principle of space voltage vectors and stator flux of IM isn’t analyzed adequately in these papers. In [12] and [13], the causes of electromagnetic torque shocking and rotor speed shocking are analyzed with torque functions and simulation, and the technique used to suppress electromagnetic torque shocking is based on the closed control strategy of power factor angle compensating. While, there are large harmonic components and torque pulses for these DVF control methods proposed in above papers, which are based on periodic wave control theory. So torque increments of these methods are limited. There are other control methods in [14]–[16] based on AC chopper technology for soft-starting of IM, but they are mainly based on regulation voltage theory which can’t increase starting torque of IM thoroughly.
In context to insufficient information existing in above the papers, based on [10–11], this paper proposes one novel DVF control strategy of IM based on space voltage vectors, which is realized with three-phase thyristor circuits. This novel control strategy is built on hexagon space voltage vectors and the stator flux linkage loci are controlled directly. Because the frequency of three-phase voltages is reduced with the decline of the effective value of the voltages. So the stator flux and the starting torque of IM driven by the proposed strategy are larger than the ramp voltage control.
According to the principle of space voltage vectors, stator voltage vectors of IM can be written as follows [17].
Where
Thyristor control circuits of IM have three working states, which are two-phase circuits conducting, three-phase circuits conducting and three-phase circuits non-conducting. Space voltage vector will generate when two-phase windings of the IM are supplied with a power source, which are shown as fig. 1.
Because stator current of IM will generate when at least two-phase circuits of thyristor control circuits are triggered. So when T1 and T6 are triggered, voltage space vector defined as
Where Um is the peak value of phase voltage, ω1 is the angular frequency of power sources. Meanwhile, the voltage vector that three-phase thyristor circuits are all triggered is defined as
If the voltage of stator resistance of IM is ignored, the stator flux of IM can be shown as the following [18].
Where
Depending on the demand of voltage symmetry, the coefficient dividing the frequency of power voltage should be one, four and seven and so on. In case of starting torque of IM, the frequency f/7 can be chosen as the starting frequency of a heavy load IM. Although, the frequency f/3 of voltage doesn’t meet the symmetry demand, but its third-harmonic component is a power frequency voltage. So the frequency f/3 of voltage has a good effect on the IM in fact. Therefore, voltage with frequency f/3 can also be utilized to drive an IM. Hence frequency division coefficient of power voltage of DVF would be seven, four, three, and one.
Control methods of DVF frequency f/7 based on space voltage vectors can be realized in following way:
First, based on the zero passage of rising edge of phase-A voltage, T1 and T2 are triggered in order to generate
Voltages with frequency f/4 based on three-phase power frequency sinusoid voltages are positive voltages. And control methods of DVF frequency f/4 are also based on hexagonal stator flux linkage loci. But the difference with the control methods of DVF frequency f/7 is that number of working vectors of the former is half of the latter. So voltage with frequency f/4 can be acquired by selectively reducing voltage vectors of frequency f/7 voltage vectors. The sequences of effective voltage vectors are
Sequences of effective space voltage vectors of frequency f/3 are
Based on above control methods and space voltage vectors, soft start control of IM is operated in following methods.
Frequency f/7 is selected as the starting frequency of IM. Before soft start, IM is be excited with one voltage vector in several power frequency periods. In order to acquire suitable stator flux, the pre-excited voltage vector will be the previous of the initial voltage vector of frequency f/7, according to the order of hexagon space voltage vectors. For example, if
After pre-excitation, IM is driven with the method of DVF having frequency f/7, then frequency f/4, frequency f/3 and frequency f/1 as shown in fig. 3 to 5. Frequency f/1 is the traditional ramp voltage control.
When the working frequency of IM is changed, the previous voltage vector and the next voltage space vector accord with the sequence of hexagon space voltage vectors as shown in fig. 2. For example, when the working frequency changes from frequency f/7 to frequency f/4, so if
Space voltage vectors of frequency f/3 for IM is used for the stator flux analysis. Stator windings of IM controlled by three-phase thyristor circuits are shown in fig. 6. When initial conducting circuits are phase-A and phase-B, and stator windings of IM are star connection, then the current in phase-C stator winding is equal to zero. So phase-C stator winding can be located on
Where
Where
Based on the model of IM and from (4) to (7) equations, the following equations are acquired by using Laplace transform.
Where
Where
Based on the stator flux model of IM:
Equation (11) can be rewritten by using Laplace inverse transformation as the following.
Where
The stator flux function is acquired by the same method, when
When
Where,
Using the same method, stator flux can be calculated when IM is also driven by frequency f/7 control method or frequency f/4 control method of DVF.
The simulation model is built by Matlab software. Parameters of IM used in the model are shown as the following:
When IM is driven by control method of DVF with frequency f/7, its line voltage and phase current are shown in fig. 7. The simulation results in fig. 7 show that the period of the line voltage is 0.14ms, and phase current has four continuous conducting sections in time of 0.14ms. So the simulation results in fig. 7 verify the principle of control method of DVF with frequency f/7.
Line voltage and phase current of the IM driven by control method of DVF with frequency f/4 are shown in fig 8(a) and fig 8(b) respectively. Fig 8(a) shows that the period of the line voltage is 0.08ms and fig 8(b) shows that phase current has three continuous conducting sections in one frequency f/4 period. The simulation results in fig. 8 verify the principle of control method of DVF with frequency f/4.
Similarly, line voltage and phase current for frequency f/3 of DVF are shown in fig. 9. Fig. 9(a) shows that the period of the line voltage is 0.06ms and fig. 9(b) shows that phase current has two continuous conducting sections in time of 0.06ms. The simulation results in fig. 9 verify the principle of frequency f/3 control method of DVF.
Stator flux of IM driven by the proposed strategy and the ramp voltage control are shown in fig. 10. The results show that the stator flux amplitude of IM driven by the proposed strategy is larger than the flux under the traditional ramp voltage control. The reason is that the frequency of voltage of DVF decreases, but the frequency of voltage of ramp voltage control is a constant value, in the process of soft starting of IM.
Stator current and rotor speed of IM based on the proposed strategy are shown in fig. 11. The result in fig. 11(a) shows that the currents includes four sections which successively corresponded to frequency f/7 current, frequency f/4 current, frequency f/3 current and ramp voltage regulation current. Meanwhile, rotor speed of IM, shown in fig. 11(b), increases accordingly to the proposed control strategy. The simulation results verify the principle of space voltage vectors control of DVF.
Contrary to this, stator current and rotor speed of IM driven by ramp voltage control are shown in fig. 12. The results show that rotor speed increases quickly and the value of starting current is very large, which all conform to the principle of ramp voltage soft-starting of IM.
Comparing fig. 11 and 12, the current in fig. 11 is smaller than the current in fig. 12, and the rotor speed increases softly. So, the proposed control strategy can acquire better starting performance than ramp voltage control for IM.
For further verifying the performance of the proposed strategy, one experimental set of IM based on three-phase thyristor circuits and STM32F103RC microcontroller is designed as shown in fig. 13. The parameters of IM are same to the parameters used in the simulation model. The experimental results are shown in figs. 14–17.
Fig. 14 shows the experimental results of IM driven by frequency f/7 of the proposed control strategy. Fig. 14(a) shows the voltage of phase-A to phase-B, while fig. 14(b) shows the current in phase A of IM. They correspond to fig. 7 (a) and fig. 7(b) respectively. The experimental results show that the period of the voltage is 0.14ms, and the current has four conducting sections in the period. The experimental results in fig. 14 are in accordance with the simulation results in fig. 7.
Fig. 15 shows the experimental results of IM driven by frequency f/4 of the proposed control strategy. The experimental results in fig. 15 correspond to the simulation results in fig. 8. Fig. 15(a) is the voltage of phase-A to phase-B and fig. 15(b) is the current in phase-A of IM. The experimental results show that the period of the voltage is 0.08ms, and the current has three conducting sections in the period. The experimental results in fig. 15 are in accordance with the simulation results in fig. 8.
Fig. 16 shows the experimental results of IM driven by frequency f/3 of the proposed control strategy. The experimental results in fig. 16 correspond to the simulation results in fig. 9. Fig. 16(a) is the voltage of phase-A to phase-B and the fig. 16 (b) is the current in phase-A of IM. The experimental results show that the period of the voltage is 0. 06ms, and the current has two conducting sections in the period. The experimental results in fig. 16 are in accordance with the simulation results in fig. 9.
Fig. 17 demonstrates the rotor speeds of IM driven by the proposed strategy and the traditional ramp voltage. Fig. 17 (a) shows that the rotor speed responds to the proposed strategy. Fig. 17 (b) also shows that rotor speed responds to the ramp voltage control. Meanwhile, fig. 17(a) corresponds to the simulation result in fig. 11 (b), and fig. 17(b) corresponds to the simulation result in fig.12 (b).
Another experimental results show that the effective value of starting current of IM driven by the proposed strategy with sixty percent load is one hundred and twenty four amperes (124 amps). Whereas when the motor is driven by the ramp voltage control with the same load, the effective value of starting current is one hundred and fifty four amperes (154 amps). The starting current with the proposed strategy decreases by nineteen percent comparing with the traditional strategy.
This paper studies the principle of space voltage vectors based on three-phase thyristor circuits, and proposes the control strategy of DVF based on hexagon space voltage vectors. The study results show that frequency f/7, frequency f/4 and frequency f/3 of power sources can be used to drive IM. The experimental results also show that starting current of a fifteen kilowatt IM driven by the proposed strategy decreases by nineteen percent as comparing to the traditional ramp voltage control with the same load, and rotor speed accurately changes according to the proposed strategy. So, the proposed control strategy of DVF based space voltage vectors is effective for soft starting of IM.