One Novel Soft-Starting Control Strategy for Induction Motor Based on Space Voltage Vectors

According to the principle of space voltage vectors, stator voltage vectors of IM can be written as follows [17]. (1) us=23(uA0ej0+uB0ej2π/3+uC0ej4π/3) {\boldsymbol{u}_{\rm{s}}} = \sqrt {{2 \over 3}} \left( {{u_{{\rm{A}}0}}{{\rm{e}}^{{\rm{j}}0}} + {u_{{\rm{B}}0}}{{\rm{e}}^{{\rm{j}}2\pi /3}} + {u_{{\rm{C}}0}}{{\rm{e}}^{{\rm{j}}4\pi /3}}} \right)

Where u_A0, u_B0 and u_C0 are three-phase stator winding voltages, respectively, and e^j0, e^j2π/3 and e^j4π/3 are unit space vector at the directions of A-phase, B-phase and C-phase stator winding axis of IM, respectively.

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.

Figure 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 u_AB which is shown in fig. 1(a) will generate in stator winding space of IM. When T1 and T2 are triggered, voltage space vector defined as u_AC in fig. 1(b) will generate. Similarly, u_BC, u_BA, u_CA and u_CB are presented in fig. 1(c) to (f). Expressions of following six space voltage vectors are shown here in equations (2) when the initial phase angle of phase-A voltage is equal to zero. (2) {uAB=23Um(cos ω1t−cos(ω1t−2π3)ej2π3)uAC=23Um(cos ω1t−cos(ω1t−2π3)·ej4π3)uBC=23Um(cos (ω1t−2π3)ej2π3−cos(ω1t+2π3)ej4π3)uBA=23Um(cos (ω1t−2π3)ej2π3−cos(ω1t))uCA=23Um(cos (ω1t+2π3)ej4π3−cos(ω1t))uCB=23Um(cos (ω1t+2π3)ej4π3−cos(ω1t−2π3)ej2π3) \left\{ {\matrix{ {{\boldsymbol{u}_{{\rm{AB}}}} = \sqrt {{2 \over 3}} {U_{\rm{m}}}\left( {\cos \,{\omega _1}t - \cos \left( {{\omega _1}t - {{2\pi } \over 3}} \right){e^{{{{\rm{j}}2\pi } \over 3}}}} \right)} \hfill \cr {{\boldsymbol{u}_{{\rm{AC}}}} = \sqrt {{2 \over 3}} {U_m}\left( {\cos \,{\omega _1}t - \cos \left( {{\omega _1}t - {{2\pi } \over 3}} \right) \cdot {e^{{{{\rm{j}}4\pi } \over 3}}}} \right)} \hfill \cr {{\boldsymbol{u}_{{\rm{BC}}}} = \sqrt {{2 \over 3}} {U_m}\left( {\cos \,\left( {{\omega _1}t - {{2\pi } \over 3}} \right){e^{{{{\rm{j}}2\pi } \over 3}}} - \cos \left( {{\omega _1}t + {{2\pi } \over 3}} \right){e^{{{{\rm{j}}4\pi } \over 3}}}} \right)} \hfill \cr {{\boldsymbol{u}_{{\rm{BA}}}} = \sqrt {{2 \over 3}} {U_{\rm{m}}}\left( {\cos \,\left( {{\omega _1}t - {{2\pi } \over 3}} \right){e^{{{{\rm{j}}2\pi } \over 3}}} - \cos \left( {{\omega _1}t} \right)} \right)} \hfill \cr {{\boldsymbol{u}_{{\rm{CA}}}} = \sqrt {{2 \over 3}} {U_{\rm{m}}}\left( {\cos \,\left( {{\omega _1}t + {{2\pi } \over 3}} \right){e^{{{{\rm{j}}4\pi } \over 3}}} - \cos \left( {{\omega _1}t} \right)} \right)} \hfill \cr {{\boldsymbol{u}_{{\rm{CB}}}} = \sqrt {{2 \over 3}} {U_{\rm{m}}}\left( {\cos \,\left( {{\omega _1}t + {{2\pi } \over 3}} \right){e^{{{{\rm{j}}4\pi } \over 3}}} - \cos \left( {{\omega _1}t - {{2\pi } \over 3}} \right){e^{{{{\rm{j}}2\pi } \over 3}}}} \right)} \hfill \cr } } \right.

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 u_ABC. Similarly, the voltage vector with that three-phase thyristor circuits are all closed is defined as u₀. According to the actual conducting circuits, u_ABC can be compounded with two space voltage vectors in (2).

If the voltage of stator resistance of IM is ignored, the stator flux of IM can be shown as the following [18]. (3) ψ=∫(u+Rs·i)dt≈∫udt \psi = \int {\left( {u + {R_s} \cdot i} \right)dt \approx \int {udt} }

Where ψ is the stator flux of IM, u is the stator voltage and R_s is the stator resistance. If the six space voltage vectors shown in (2) are connected in sequence, then one hexagon space voltage vectors will generate and stator flux linkage loci are also one hexagon as in fig. 2 shown.

Figure 2.

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 u_AC, which will trigger angle θ₁. When current i_AC declines to zero, T1 and T2 will be closed naturally. Then, during next primitive period of power source, based on the zero passage of falling edge of phase-C voltage, T3 and T2 are triggered in order to generate u_BC. Their trigger angles are all θ₂. Circulating this way, after thyristors are closed every time, next vector of hexagonal space voltage vectors will be generated during the next primitive period of the power source. All of hexagonal voltage vectors are generated once during seven primitive periods of the power source. So voltage with frequency f/7 has waves of DVF based on hexagon space voltage vectors is acquired as fig. 3 shown.

Figure 3.

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 u_AC to u_BC to u_BA to u_CA to u_CB to u_AB. The stator flux linkage loci will be three continuous sections which consist of ψ_AC, ψ_BC, ψ_BA, ψ_CA, ψ_CB, and ψ_AB. Frequency f/4 Voltage waveforms are shown in fig. 4.

Figure 4.

Sequences of effective space voltage vectors of frequency f/3 are u_AC, u_BC, u_BA, u_CA, u_CB, and u_AB, which are also based on hexagonal stator flux linkage loci, but they are divided into two sets. The first set is continuously triggered, containing u_AC, u_BC, and u_BA while second set is also continuously triggered, which contain u_CA, u_CB, and u_AB. Voltage waveforms of frequency f/3 are shown in fig. 5.

Figure 5.

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 u_AC is the first working voltage vector of frequency f/7, then u_AB will be the pre-excitation voltage vector. Time for pre-excitation can be calculated by (3) according to the actual IM parameters.

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 u_BC is the final voltage vector of frequency f/7 space voltage vectors, then u_BA will be the first voltage vector of frequency f/4 voltage vectors. Similarly, when working frequency changes from frequency f/4 to frequency f/3, so if u_AB is the final voltage vector of frequency f/4 voltages, then u_AC will be the first voltage vector of frequency f/3 voltage vectors. After frequency f/3, IM is controlled by the ramp voltage control.

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 α axis of the α-β stationary reference frame, and the equations are acquired as the following. (4) isα=0, iA=−iB {i_{{\rm{s}}\alpha }} = 0,\,\,{i_{\rm{A}}} = - {i_{\rm{B}}} (5) isβ=23(32iB−32iA)=−2iA {i_{{\rm{s}}\beta }} = \sqrt {{2 \over 3}} \left( {{{\sqrt 3 } \over 2}{i_{\rm{B}}} - {{\sqrt 3 } \over 2}{i_{\rm{A}}}} \right) = - \sqrt 2 {i_{\rm{A}}} (6) usβ=23(32uA−32uB)=2uAB {u_{{\rm{s}}\beta }} = \sqrt {{2 \over 3}} \left( {{{\sqrt 3 } \over 2}{u_{\rm{A}}} - {{\sqrt 3 } \over 2}{u_{\rm{B}}}} \right) = \sqrt 2 {u_{{\rm{AB}}}}

Figure 6.

Where i_sα and i_sβ are the α-axis stator current and the β-axis stator current respectively under α-β stationary reference frame, and u_sβ is the stator voltage of α-β stationary reference frame. i_A and i_B are respectively the current in phase-A and phase-B of IM under A-B-C three-phase stationary reference frame. u_AB is the line voltage of phase-A to phase-B stator windings. u_AB is shown as the following. (7) uAB(t)=3Umsin(ω1t+α0) {u_{{\rm{AB}}}}\left( t \right) = \sqrt 3 {U_{\rm{m}}}\sin \left( {{\omega _1}t + {\alpha _0}} \right)

Where α₀ is trigger angle of T1 and T6.

Based on the model of IM and from (4) to (7) equations, the following equations are acquired by using Laplace transform. (8) {UAB(s)=−(Rs+sLs)IA(s)+2sLmIrβ(s)/20=(Rr+sLr)Irα(s)+ωrLrLrβ(s)−2ωrLmIA(s)0=(Rr+sLr)Irβ(s)−2sLmIA(s)−ωrLrLrα(s) \left\{ {\matrix{ {{U_{{\rm{AB}}}}\left( s \right) = - \left( {{R_{\rm{s}}} + s{L_{\rm{s}}}} \right){I_{\rm{A}}}\left( s \right) + \sqrt 2 s{L_{\rm{m}}}{I_{{\rm{r}}\beta }}\left( s \right)/2} \hfill \cr {0 = \left( {{R_{\rm{r}}} + s{L_{\rm{r}}}} \right){I_{{\rm{r}}\alpha }}\left( s \right) + {\omega _{\rm{r}}}{L_{\rm{r}}}{L_{{\rm{r}}\beta }}\left( s \right) - \sqrt 2 {\omega _{\rm{r}}}{L_{\rm{m}}}{I_{\rm{A}}}\left( s \right)} \hfill \cr {0 = \left( {{R_{\rm{r}}} + s{L_{\rm{r}}}} \right){I_{{\rm{r}}\beta }}\left( s \right) - \sqrt 2 s{L_{\rm{m}}}{I_{\rm{A}}}\left( s \right) - {\omega _{\rm{r}}}{L_{\rm{r}}}{L_{{\rm{r}}\alpha }}\left( s \right)} \hfill \cr } } \right.

Where L_m is mutual inductance between stator windings and rotor windings, L_s is stator self-inductance, L_r is rotor self-inductance, R_s is stator resistance, R_r is rotor resistance, I_A(s) is the current in phase-A stator winding. I_rα(s) and I_rβ(s) are the α axis current and the β axis current of IM under α-β stationary reference frame respectively. ω_r is angular frequency of IM. In order to simplify the progress of solving I_A(s), ω_r is set to be zero. Then IA(s) is solved by using (8). (9) {IA(s)=P(s)/Q(s)P(s)=3Um(−scos α0+ω1 sin α0) (1+sTr)RsTsTr′Q(s)=(s2+ω12)(s2+s(1Tr′+1Ts′)+1Ts′·Tr′) \left\{ {\matrix{ {{I_{\rm{A}}}\left( s \right) = P\left( s \right)/Q\left( s \right)} \hfill \cr {P\left( s \right) = {{\sqrt 3 {U_{\rm{m}}}\left( { - s\cos \,{\alpha _0} + {\omega _1}\,\sin \,{\alpha _0}} \right)\,\left( {1 + s{T_{\rm{r}}}} \right)} \over {{R_s}{T_s}T_{\rm{r}}^\prime}}} \hfill \cr {Q\left( s \right) = \left( {{s^2} + \omega _1^2} \right)\left( {{s^2} + s\left( {{1 \over {T_{\rm{r}}^\prime}} + {1 \over {T_{\rm{s}}^\prime}}} \right) + {1 \over {T_{\rm{s}}^\prime \cdot T_{\rm{r}}^\prime}}} \right)} \hfill \cr } } \right.

Where σ=1-L²_m/(L_sL_r), T_s=L_s/R_s, T_r=L_r/R_r, T’_s=σT_s, T’_r=σT_r. When Q(s) is equal to zero, then there are four roots that can be acquired from the equation. Two of the four roots are complex conjugate: λ_1,2=±jω₁, which correspond to steady components of I_A(s). Another two roots are signed as λ₃ and λ₄. The real parts of λ₃ and λ₄ are negative, which correspond to transient components of I_A(s). I_rβ(s) are also acquired by using (8). (10) Irβ(s)=6Um(s cos α0−ω1 sin α0)sLmLsLrσ(s2+ω12)(s2+s(1Tr′+1Ts′)+1Ts′·Tr′) {I_{{\rm{r}}\beta }}\left( {\rm{s}} \right) = {{\sqrt 6 {U_m}\left( {s\,\cos \,{\alpha _0} - {\omega _1}\,\sin \,{\alpha _0}} \right)s{L_{\rm{m}}}} \over {{L_{\rm{s}}}{L_r}\sigma \left( {{s^2} + \omega _1^2} \right)\left( {{s^2} + s\left( {{1 \over {T_{\rm{r}}^\prime}} + {1 \over {T_{\rm{s}}^\prime}}} \right) + {1 \over {T_{\rm{s}}^\prime \cdot T_r^\prime}}} \right)}}

Based on the stator flux model of IM: ψ_s=L_si_s+L_mi_r, ψ_s can be calculated by using (4), (5), (8), (9) and (10), (11) ψs(s)=j(LmIrβ(s)−2LsIA(s))=j6Um(s cos α0−ω1 sin α0)((1−σ+1Ls)s+1LsTr)σ(s2+ω12)(s2+s(1Tr′+1Ts′)+1Ts′·Tr′) \matrix{ {{\boldsymbol{\psi }_{\rm{s}}}\left( s \right) = j\left( {{L_{\rm{m}}}{I_{{\rm{r}}\beta }}\left( s \right) - \sqrt 2 {L_{\rm{s}}}{I_{\rm{A}}}\left( s \right)} \right)} \hfill \cr { = j{{\sqrt 6 {U_{\rm{m}}}\left( {s\,\cos \,{\alpha _0} - {\omega _1}\,\sin \,{\alpha _0}} \right)\left( {\left( {1 - \sigma + {1 \over {{L_s}}}} \right)s + {1 \over {{L_s}{T_{\rm{r}}}}}} \right)} \over {\sigma \left( {{s^2} + \omega _1^2} \right)\left( {{s^2} + s\left( {{1 \over {T_{\rm{r}}^\prime}} + {1 \over {T_{\rm{s}}^\prime}}} \right) + {1 \over {T_{\rm{s}}^\prime \cdot T_{\rm{r}}^\prime}}} \right)}}} \hfill \cr }

Equation (11) can be rewritten by using Laplace inverse transformation as the following. (12) ψs(t)=L−1ψs(s)=K1e−jω1t+K2ejω1t+K3eλ3t+K4eλ4t \matrix{ {{\psi _s}\left( t \right)} \hfill & = \hfill & {{L^{ - 1}}{\psi _{\rm{s}}}\left( s \right)} \hfill \cr {} \hfill & = \hfill & {{K_1}{e^{ - j{\omega _1}t}} + {K_2}{e^{j{\omega _1}t}} + {K_3}{e^{{\lambda _3}t}} + {K_4}{e^{{\lambda _4}t}}} \hfill \cr }

Where (13) {K1=6Umω1(−cosα0+jsinα0)(−(1−σ+1Ls)jω1+1LsTr)σ(2jω1)(jω1+λ3)(jω1+λ4)K2=6Umω1(−cosα0−jsinα0)((1−σ+1Ls)jω1+1LsTr)σ(2jω1)(jω1−λ3)(jω1−λ4)K3=j6Um(λ3cosα0−ω1sinα0)((1−σ+1Ls)λ3+1LsTr)σ(λ32+ω12)(λ3−λ4)K4=j6Um(λ4cosα0−ω1sinα0)((1−σ+1Ls)λ4+1LsTr)σ(λ42+ω12)(λ4−λ3) \left\{ {\matrix{ {{K_1} = {{\sqrt 6 {U_{\rm{m}}}{\omega _1}\left( { - \cos {\alpha _0} + j\sin {\alpha _0}} \right)\left( { - \left( {1 - \sigma + {1 \over {{L_s}}}} \right)j{\omega _1} + {1 \over {{L_s}{T_{\rm{r}}}}}} \right)} \over {\sigma \left( {2j{\omega _1}} \right)\left( {j{\omega _1} + {\lambda _3}} \right)\left( {j{\omega _1} + {\lambda _4}} \right)}}} \hfill \cr {{K_2} = {{\sqrt 6 {U_{\rm{m}}}{\omega _1}\left( { - \cos {\alpha _0} - j\sin {\alpha _0}} \right)\left( {\left( {1 - \sigma + {1 \over {{L_s}}}} \right)j{\omega _1} + {1 \over {{L_s}{T_{\rm{r}}}}}} \right)} \over {\sigma \left( {2j{\omega _1}} \right)\left( {j{\omega _1} - {\lambda _3}} \right)\left( {j{\omega _1} - {\lambda _4}} \right)}}} \hfill \cr {{K_3} = {{j\sqrt 6 {U_{\rm{m}}}\left( {{\lambda _3}\cos {\alpha _0} - {\omega _1}\sin {\alpha _0}} \right)\left( {\left( {1 - \sigma + {1 \over {{L_s}}}} \right){\lambda _3} + {1 \over {{L_s}{T_{\rm{r}}}}}} \right)} \over {\sigma \left( {\lambda _3^2 + \omega _1^2} \right)\left( {{\lambda _3} - {\lambda _4}} \right)}}} \hfill \cr {{K_4} = {{j\sqrt 6 {U_{\rm{m}}}\left( {{\lambda _4}\cos {\alpha _0} - {\omega _1}\sin {\alpha _0}} \right)\left( {\left( {1 - \sigma + {1 \over {{L_s}}}} \right){\lambda _4} + {1 \over {{L_s}{T_{\rm{r}}}}}} \right)} \over {\sigma \left( {\lambda _4^2 + \omega _1^2} \right)\left( {{\lambda _4} - {\lambda _3}} \right)}}} \hfill \cr } } \right.

The stator flux function is acquired by the same method, when u_AC and u_BC are working. Similarly, u₀ is working, then stator current of IM is equal to zero, and the rotor current of IM is shown as following. (14) ir(t)=ir0e−t/Tr {i_{\rm{r}}}\left( t \right) = {i_{{\rm{r}}0}}{e^{ - t/{T_{\rm{r}}}}}

When u₀ is working, fig. 5 shows that max value of t₃ is 23.3ms and minimum value of t₃ is 13.3ms. When trigger angle becomes equal to ninety degrees, t₃ is 16.7ms. For a common fifteen kilowatt IM, rotor time constant is approximately equal to 300ms which is much larger than t₃. So, based on these parameters and the stator flux model of IM: ψ_s=L_si_s+L_mi_r, stator flux ψ_s can be calculated by using the following equation. (15) ψs(t)=Lmir0e−t/Tr=ψ0e−t/Tr=0.955ψ0 {\psi _{\rm{s}}}\left( t \right) = {L_{\rm{m}}}{i_{{\rm{r}}0}}{e^{ - t/{T_{\rm{r}}}}} = {\psi _0}{e^{ - t/{T_{\rm{r}}}}} = 0.955{\psi _0}

Where, ψ₀ is the initial value of ψ_s. Equation (15) shows that the decrement of stator flux is very small and can be neglected when u₀ is working.

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: P_N=15kW, U_N=380V, n_N=1460r/min, I_N=29.5A, f_N=50Hz, Lm=64.19mH, Rs=0.2147Ω, Rr=0.2205Ω, J=0.602 kg·m², L_sσ=L_rσ=0.991mH. Load rate of IM is 60 percent. Simulation results are shown in fig. 7 to 12.

Figure 7.

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.

Figure 8.

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.

Figure 9.

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.

Figure 10.

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.

Figure 11.

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.

Figure 12.

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.

Figure 13.

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.

Figure 14.

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.

Figure 15.

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.

Figure 16.

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).

Figure 17.

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.