Capacitance balance control strategy for three-phase four-switch open-winding permanent magnet synchronous motor

Abstract

The open-winding permanent magnet synchronous motor (OWPMSM) system is a novel high-cost system that uses dual-inverters to control both sides of the stator to improve the performance of the motor. To save the system cost, the three-phase four-switch open-winding permanent magnet synchronous motor (TPFS-OWPMSM) system is proposed to replace the general three-phase six-switch OWPMSM system, but it brings the problem of bridge arm capacitor voltage offset. To solve the instability problem caused by capacitance, this paper carries out the state analysis and offset source analysis of the inverter capacitor voltage, and proposes a dual-inverters capacitor voltage balance control strategy. The capacitor balance control converts unstable capacitor offset voltage into current and injects the currents into the stator current loop through closed-loop correction. And this strategy includes the optimal control of different capacitors under dual-inverters with the goal of system stability. The effectiveness of the balancing strategy is verified by the simulation of various motor working conditions.

Keywords

Three-phase four-switch open-winding permanent magnet synchronous motor capacitor voltage offset capacitance balance control

1. Introduction

Limited to the inverter capacity and voltage level, the performance of the existing permanent magnet synchronous motor (PMSM) system is gradually unable to meet the requirements of large-scale modern equipment [1,2]. Therefore, the open-winding permanent magnet synchronous motor (OWPMSM) system is proposed to increase the output of the motor [3]. As shown in Fig. 1, the topology of the OWPMSM system opens the star connection of the stator and uses dual-inverters on both sides to supply power. This control system can break through the limit speed of the motor powered by the single inverter, and enables the motor to have a wider operating range [4–6].

Since the dual-inverters in the OWPMSM topology increase the overall cost of the system, the three-phase four-switch open-winding permanent magnet synchronous motor (TPFS-OWPMSM) topology in Fig. 2 is proposed to reduce the cost [7]. Under the premise of meeting most of the performance of the three-phase six-switch inverter, replacing the IGBT with a capacitor saves hardware costs, and it is suitable for high-power PMSM in medium-low speed and rated torque operation. However, since the capacitor is used as the power supply bridge arm, there is a problem that the voltage offset of the neutral point of the capacitor destroys the stability of the system, which needs to be solved urgently [8].

Fig. 1.

General OWPMSM control system.

Fig. 2.

TPFS-OWPMSM control system.

To solve the voltage offset caused by capacitance, this paper carries out the capacitance-voltage state analysis and offset source analysis of OWPMSM, and proposes a dual-inverters capacitor voltage balance control strategy. The capacitor balance control converts unstable capacitor offset voltage into current injected into the stator current loop through closed-loop correction. By analyzing and evaluating the impact of the capacitance offset of dual-inverters, the voltage offset evaluation module is added to strategy to select the capacitors to balance. The effectiveness of the strategy is verified by the simulation under different conditions.

2. Capacitance voltage offset analysis of three-phase four-switch in PMSM and OWPMSM

2.1. Capacitance voltage offset analysis of TPFS-PMSM

To further analyze the capacitor voltage offset state of the TPFS-PMSM under dual-inverters, the voltage state of the single-inverter TPFS-PMSM is firstly analyzed.

Fig. 3.

Single-inverter TPFS-PMSM topology.

The single-inverter TPFS-PMSM topology is shown in Fig. 3. V_dc1 is the DC bus voltage, S_b, S_c are the states of upper switch T₁, T₃ in phases B and C, and V_C1, V_C2 are the capacitor voltages of the upper and lower arms of phase A. The line voltage U_BA, U_CA of PMSM are obtained according to Kirchhoff’s law: $\begin{eqnarray}\left[\begin{array}{@{}l@{}}U_{BA}\\ U_{CA}\end{array}\right]=\left[\begin{array}{@{}l@{}}S_{b}V_{c1}-(1-S_{b})V_{c2}\\ S_{c}V_{c1}-(1-S_{c})V_{c2}\end{array}\right].\end{eqnarray}$ (1)

Convert TPFS-PMSM line voltage to phase voltage: $\begin{eqnarray}\displaystyle \left[\begin{array}{@{}l@{}}U_{AN}\\ U_{BN}\\ U_{CN}\end{array}\right] & = & \displaystyle {\displaystyle \frac{1}{3}}\left[\begin{array}{@{}cc@{}}-1 & -1\\ 2 & -1\\ -1 & 2\end{array}\right]\left[\begin{array}{@{}l@{}}U_{BA}\\ U_{CA}\end{array}\right]=\left[\begin{array}{@{}l@{}}\left(-{\displaystyle \frac{1}{3}}V_{c2}-{\displaystyle \frac{1}{3}}V_{c1}\right)S_{b}+\left(-{\displaystyle \frac{1}{3}}V_{c2}-{\displaystyle \frac{1}{3}}V_{c1}\right)S_{c}+{\displaystyle \frac{1}{3}}V_{c2}\\[5.0pt] \left({\displaystyle \frac{2}{3}}V_{c2}+{\displaystyle \frac{2}{3}}V_{c1}\right)S_{b}+\left(-{\displaystyle \frac{1}{3}}V_{c2}-{\displaystyle \frac{1}{3}}V_{c1}\right)S_{c}-{\displaystyle \frac{1}{3}}V_{c2}\\[5.0pt] \left(-{\displaystyle \frac{1}{3}}V_{c2}-{\displaystyle \frac{1}{3}}V_{c1}\right)S_{b}+\left({\displaystyle \frac{2}{3}}V_{c2}+{\displaystyle \frac{2}{3}}V_{c1}\right)S_{c}-{\displaystyle \frac{1}{3}}V_{c2}\end{array}\right]\nonumber\\ \displaystyle & = & \displaystyle {\displaystyle \frac{V_{dc1}}{3}}\left[\begin{array}{@{}ccc@{}}2 & -1 & -1\\ -1 & 2 & -1\\ -1 & -1 & 2\end{array}\right]\left[\begin{array}{@{}l@{}}1/2\\ S_{b}\\ S_{c}\end{array}\right]+\left[\begin{array}{@{}c@{}}-{\displaystyle \frac{2}{3}}\\[5.0pt] {\displaystyle \frac{1}{3}}\\[5.0pt] {\displaystyle \frac{1}{3}}\end{array}\right][V_{c1}-V_{c2}].\end{eqnarray}$ (2)

To further describe voltage offset of the capacitor C₁, C₂, Clark transforms the phase voltage to get: $\begin{eqnarray}\displaystyle \left[\begin{array}{@{}l@{}}U_{{\alpha}}\\ U_{{\beta}}\end{array}\right] & = & \displaystyle {\displaystyle \frac{1}{3}}\left[\begin{array}{@{}cc@{}}-S_{b1}-S_{c1} & 2-S_{b1}-S_{c1}\\[5.0pt] \sqrt{3}(S_{b1}-S_{c1}) & \sqrt{3}(S_{b1}-S_{c1})\end{array}\right]\left[\begin{array}{@{}l@{}}V_{c1}\\ V_{c2}\end{array}\right]\nonumber\\ \displaystyle & = & \displaystyle \left[\begin{array}{@{}c@{}}{\displaystyle \frac{V_{dc1}}{3}}(1-S_{b1}-S_{c1})\\[10.0pt] {\displaystyle \frac{V_{dc1}}{\sqrt{3}}}(S_{b1}-S_{c1})\end{array}\right]+\left[\begin{array}{@{}c@{}}-{\displaystyle \frac{2V_{c1}-2V_{c2}}{3}}\\[7.0pt] 0\end{array}\right].\end{eqnarray}$ (3)

It can be deduced from the (2), (3): the voltage of phase-A where the capacitor is used as the bridge arm is not equal to phase B and phase C. After transformation, it is found that the voltage offset is mainly on the 𝛼 axis, and the offset value is 2∕3(V_c1 − V_c2).

2.2. Capacitance voltage analysis of TPFS-OWPMSM

The topology of TPFS-OWPMSM is shown in Fig. 4. Since the neutral point of the OWPMSM is opened in series with three-phase four-switch inverter, the output state of TPFS-OWPMSM can be regarded as the subtraction of the outputs of the two sets of single-inverter TPFS-PMSM.

Fig. 4.

Dual-inverter TPFS-OWPMSM topology.

According to (2) of TPFS-PMSM, subtract the output of inverter 1 from inverter 2 to obtain the overall output of TPFS-OWPMSM: $\begin{eqnarray}\displaystyle \left[\begin{array}{@{}l@{}}U_{A_{1}A_{2}}\\ U_{B_{1}B_{2}}\\ U_{C_{1}C_{2}}\end{array}\right] & = & \displaystyle {\displaystyle \frac{V_{dc1}}{3}}\left[\begin{array}{@{}ccc@{}}2 & -1 & -1\\ -1 & 2 & -1\\ -1 & -1 & 2\end{array}\right]\left[\begin{array}{@{}l@{}}1/2\\ S_{b1}\\ S_{c1}\end{array}\right]+\left[\begin{array}{@{}c@{}}-2/3\\ 1/3\\ 1/3\end{array}\right]\left[V_{c1}-V_{c2}\right]\nonumber\\ \displaystyle \text{} & \text{} & \displaystyle -∼{\displaystyle \frac{V_{dc2}}{3}}\left[\begin{array}{@{}ccc@{}}2 & -1 & -1\\ -1 & 2 & -1\\ -1 & -1 & 2\end{array}\right]\left[\begin{array}{@{}l@{}}1/2\\ S_{b2}\\ S_{c2}\end{array}\right]-\left[\begin{array}{@{}c@{}}-2/3\\ 1/3\\ 1/3\end{array}\right][V_{c3}-V_{c4}].\end{eqnarray}$ (4) Clark transforms the TPFS-OWPMSM phase voltage into the 𝛼–𝛽 axis to get: $\begin{eqnarray}\displaystyle \left[\begin{array}{@{}l@{}}U_{{\alpha}}\\ U_{{\beta}}\end{array}\right]=\left[\begin{array}{@{}c@{}}{\displaystyle \frac{V_{dc1}}{3}}(1-S_{b1}-S_{c1})-{\displaystyle \frac{V_{dc2}}{3}}(1-S_{b2}-S_{c2})\\[7.0pt] {\displaystyle \frac{V_{dc1}}{\sqrt{3}}}(S_{b1}-S_{c1})-{\displaystyle \frac{V_{dc2}}{\sqrt{3}}}(S_{b2}-S_{c2})\end{array}\right]+\left[\begin{array}{@{}c@{}}-{\displaystyle \frac{2{\rm\Delta}U_{1}}{3}}+{\displaystyle \frac{2{\rm\Delta}U_{2}}{3}}\\[5.0pt] 0\end{array}\right] & & \displaystyle\end{eqnarray}$ (5) where V_dc1, V_dc2 are the DC bus voltage of inverter 1 and 2, S_{b1, c1, b2, c2} are the states of upper switch T_1,3,5,7 in phase B and C, V_C3, V_C4 are the capacitor voltages of the upper and lower arms of phase A in inverter 2. Among them, ΔU₁ = V_c1 − V_c2, ΔU₂ = V_c3 − V_c4. When there is an unbalanced component ΔU₁, ΔU₂ in the voltages at both ends of C₁, C₂, C₃ and C₄, the 𝛼 axial voltage of the motor will be offset by −2∕3(ΔU₁ − ΔU₂). The basic voltage vector output of FPFS-OWPMSM containing the offset voltage is shown in Table 1.

Table 1

The output voltage vector of FPFS-OWPMSM with unbalanced voltage

S _b1	S _c1	S _b2	S _c2	U _𝛼	U _𝛽	S _b1	S _c1	S _b2	S _c2	U _𝛼	U _𝛽
0	0	0	0	[(V_dc1 − V_dc2 ) −2(ΔU₁ − ΔU₂ )]∕3	0	0	0	1	0	[V_dc1 −2(ΔU₁ − U₂ )]∕3	$-V_{dc2}/\sqrt{3}$
0	1	0	0	[−V_dc2 −2(ΔU₁ − ΔU₂ )]∕3	$-V_{dc1}/\sqrt{3}$	0	1	1	0	−2(ΔU₁ − ΔU₂ )∕3	$-(V_{dc1}+V_{dc2})/\sqrt{3}$
1	0	0	0	[−V_dc2 −2(ΔU₁ − ΔU₂ )]∕3	$V_{dc1}/\sqrt{3}$	1	0	1	0	−2(ΔU₁ − ΔU₂ )∕3	$(V_{dc1}-V_{dc2})/\sqrt{3}$
1	1	0	0	[−(V_dc1 + V_dc2 ) −2(ΔU₁ − ΔU₂ )]∕3	0	1	1	1	0	[V_dc1 −2(ΔU₁ − ΔU₂ )]∕3	$-V_{dc2}/\sqrt{3}$
0	0	0	1	[V_dc1 −2(ΔU₁ − ΔU₂ )]∕3	$V_{dc2}/\sqrt{3}$	0	0	1	1	[(V_dc1 + V_dc2 ) −2(ΔU₁ − ΔU₂ )]∕3	0
0	1	0	1	−2(ΔU₁ − ΔU₂ )∕3	$-(V_{dc1}-V_{dc2})/\sqrt{3}$	0	1	1	1	[V_dc2 −2(ΔU₁ − ΔU₂ )]∕3	$-V_{dc1}/\sqrt{3}$
1	0	0	1	−2(ΔU₁ − ΔU₂ )∕3	$(V_{dc1}+V_{dc2})/\sqrt{3}$	1	0	1	1	[V_dc2 −2(ΔU₁ − ΔU₂ )]∕3	$V_{dc1}/\sqrt{3}$
1	1	0	1	[−V_dc1 −2(ΔU₁ − ΔU₂ )]∕3	$V_{dc2}/\sqrt{3}$	1	1	1	1	[(−V_dc1 + V_dc2 ) −2(ΔU₁ − ΔU₂ )]∕3	0

Fig. 5.

Voltage vector diagram with offset voltage ΔU₁, ΔU₂.

The voltage vector diagram of FPFS-OWPMSM with offset voltage is shown in Fig. 5. When the capacitor voltage is unbalanced, the eight basic voltage vectors OA’, OB’, OC’, OD’, OE’, OF’, OH’, and OI’ all shift to the left by −2∕3(ΔU₁ − ΔU₂) compared with the normal state (ΔU₁ − ΔU₂ < 0 is shifted to the right). The voltage vector area E’A’I’D’H’C’F’B’ actually generated by the inverter 1,2 is also shifted to the left by −2∕3(ΔU₁ − ΔU₂). Due to the existence of capacitor offset voltage, the basic voltage vector of the FPFS-OWPMSM is changed with time, which affects the stable operation of the inverters.

3. Capacitor voltage balance control strategy of OWPMSM

3.1. Causes of capacitor voltage offset

To find the cause of the capacitor voltage offset in TPFS-OWPMSM, the transient analysis of capacitor voltage is performed. According to the KCL law, the transient current on capacitors C₁, C₂, C₃, and C₄: $\begin{eqnarray}C_{1}{\displaystyle \frac{dV_{c1}}{dt}}-C_{1}{\displaystyle \frac{dV_{c2}}{dt}}=i_{c1}-i_{c2}=C_{3}{\displaystyle \frac{dV_{c4}}{dt}}-C_{3}{\displaystyle \frac{dV_{c3}}{dt}}=i_{c4}-i_{c3}=i_{a}\end{eqnarray}$ (6)

Furtherly, the voltages of capacitors C₁, C₂, C₃ and C₄ are obtained as: $\begin{eqnarray}\displaystyle \left\{\begin{array}{@{}l@{}}V_{c1}(t)={\displaystyle \frac{1}{2}}V_{dc1}+{\displaystyle \frac{1}{2}}{\displaystyle \frac{1}{C_{1}}}\displaystyle \int _{0}^{t}i_{a}dt+{\displaystyle \frac{1}{2}}(V_{c1}(0)-V_{c2}(0))\quad \\[10.0pt] V_{c2}(t)={\displaystyle \frac{1}{2}}V_{dc1}-{\displaystyle \frac{1}{2}}{\displaystyle \frac{1}{C_{1}}}\displaystyle \int _{0}^{t}i_{a}dt-{\displaystyle \frac{1}{2}}(V_{c1}(0)-V_{c2}(0))\quad \\[10.0pt] V_{c3}(t)={\displaystyle \frac{1}{2}}V_{dc2}+{\displaystyle \frac{1}{2}}{\displaystyle \frac{1}{C_{3}}}\left(-\displaystyle \int _{0}^{t}i_{a}dt\right)-{\displaystyle \frac{1}{2}}(V_{c4}(0)-V_{c3}(0))\quad \\[10.0pt] V_{c4}(t)={\displaystyle \frac{1}{2}}V_{dc2}-{\displaystyle \frac{1}{2}}{\displaystyle \frac{1}{C_{3}}}\left(-\displaystyle \int _{0}^{t}i_{a}dt\right)+{\displaystyle \frac{1}{2}}(V_{c4}(0)-V_{c3}(0)).\quad \end{array}\right. & & \displaystyle\end{eqnarray}$ (7)

According to (7), there are two reasons for the unbalanced capacitor voltage: one is that the initial voltage of the capacitor is offset, and the other is that the offset phase current fluctuates in the dynamic process of the TPFS-OWPMSM, resulting in the unbalanced charging and discharging of the capacitor.

3.2. Principle of capacitor voltage balance control strategy

Since the initial voltage of the capacitor under the same size is usually kept constant, the main reason for the unbalance of the capacitor voltage of the TPFS-OWPMSM is the current fluctuation of the offset phase. According to (4), the motor phase current with offset can be derived as: $\begin{eqnarray}\displaystyle \left\{\begin{array}{@{}l@{}}i_{\text{a}}=I_{\text{s}}\cos ({\theta})-2i_{0}\quad \\ i_{\text{b}}=I_{\text{s}}\cos ({\theta}-2{\pi}/3)+i_{0}\quad \\ i_{\text{c}}=I_{\text{s}}\cos ({\theta}+2{\pi}/3)+i_{0}\quad \end{array}\right. & & \displaystyle\end{eqnarray}$ (8) where I_s is the phase current amplitude, θ is the current phase angle, and i₀ is the offset current caused by the DC voltage offset. The 𝛼–𝛽 axis currents are obtained by Clark transformation: $\begin{eqnarray}\displaystyle \left\{\begin{array}{@{}l@{}}i_{{\alpha}}=I_{s}\cos ({\theta})-2i_{0}\quad \\ i_{{\beta}}=I_{s}\sin ({\theta}).\quad \end{array}\right. & & \displaystyle\end{eqnarray}$ (9) Consistent with the voltage offset, the current offset exists on the 𝛼 axis but not on the 𝛽 axis.

Substituting (8) into (9) gets the transient offset in capacitor voltage: $\begin{eqnarray}\displaystyle {\rm\Delta}V_{1} & = & \displaystyle V_{c1}(t)-V_{c2}(t)={\displaystyle \frac{1}{C_{1}}}\displaystyle \int _{0}^{t}i_{a}dt+V_{c1}(0)-V_{c2}(0)\nonumber\\ \displaystyle & = & \displaystyle {\displaystyle \frac{I_{\text{s}}\sin ({\theta})}{{\omega}\text{C}_{1}}}-{\displaystyle \frac{2i_{0}}{\text{C}_{1}}}t-{\displaystyle \frac{I_{\text{s}}\sin ({\theta}(0))}{{\omega}\text{C}_{1}}}+V_{c1}(0)-V_{c2}(0)\end{eqnarray}$ (10) $\begin{eqnarray}\displaystyle {\rm\Delta}V_{2} & = & \displaystyle V_{c3}(t)-V_{c4}(t)={\displaystyle \frac{1}{C_{3}}}\displaystyle \int _{0}^{t}-i_{a}dt+V_{c3}(0)-V_{c4}(0)\nonumber\\ \displaystyle & = & \displaystyle -{\displaystyle \frac{I_{\text{s}}\sin ({\theta})}{{\omega}\text{C}_{3}}}+{\displaystyle \frac{2i_{0}}{\text{C}_{3}}}+{\displaystyle \frac{I_{\text{s}}\sin ({\theta}(0))}{{\omega}\text{C}_{3}}}+V_{c3}(0)-V_{c4}(0).\end{eqnarray}$ (11) To differentiate between stable and unstable voltage variables, split the total voltage offset: $\begin{eqnarray}\displaystyle \left\{\begin{array}{@{}l@{}}{\rm\Delta}{V_{1}}^{\text{*}}={\displaystyle \frac{I_{\text{s}}\sin ({\theta})}{{\omega}\text{C}_{1}}}={\displaystyle \frac{i_{{\beta}}}{{\omega}\text{C}_{1}}},{\rm\Delta}{V_{1}}^{+}=-{\displaystyle \frac{2i_{0}}{\text{C}_{1}}}t-{\displaystyle \frac{I_{\text{s}}\sin ({\theta}(0))}{{\omega}\text{C}_{1}}}+V_{c1}(0)-V_{c2}(0)\quad \\[11.0pt] {\rm\Delta}V_{2}^{\text{*}}=-{\displaystyle \frac{I_{\text{s}}\sin ({\theta})}{{\omega}\text{C}_{3}}}=-{\displaystyle \frac{i_{{\beta}}}{{\omega}\text{C}_{3}}},{\rm\Delta}{V_{2}}^{+}={\displaystyle \frac{2i_{0}}{\text{C}_{3}}}+{\displaystyle \frac{I_{\text{s}}\sin ({\theta}(0))}{{\omega}\text{C}_{3}}}+V_{c3}(0)-V_{c4}(0)\quad \end{array}\right. & & \displaystyle\end{eqnarray}$ (12)

${\rm\Delta}V_{1}^{\ast }$ , ${\rm\Delta}V_{2}^{\ast }$ are the steady-state voltage offset component, which forms the A-phase current. ${\rm\Delta}V_{1}^{+}$ , ${\rm\Delta}V_{2}^{+}$ are the unstable voltage offset component caused by the unbalanced capacitor voltage, which directly affects the capacitor voltage and system stability. It should be noted that the ${\rm\Delta}V_{1}^{+}$ , ${\rm\Delta}V_{2}^{+}$ are DC voltage offset that does not decay over time.

Fig. 6.

Control structures of capacitor voltage balance.

To maintain the stability of the TPFS-OWPMSM, it is necessary to separate the unstable voltage offset component ${\rm\Delta}V_{1}^{+}$ , ${\rm\Delta}V_{2}^{+}$ from the all offset component and correct the unstable voltage offset. The control structure of capacitor voltage balance control is shown in Fig. 6. G_i(s) is the closed-loop transfer function of the current control loop, and can be approximated as 1 due to its high bandwidth compared with the voltage variation control loop. G_c(s) is the transfer function of offset voltage and offset current.

Since the system uses four capacitors and the voltages of the DC power supplies on both sides are different, the offset voltage evaluation module is proposed to ensure that the system stably balances the voltage offset. The capacitors voltage V_c1, V_c2, V_c3, V_c4 on the four bridge arms is sampled into the voltage offset evaluation module in Fig. 7, and the RMS voltage in time T_s is taken into the flow chart for comparison and output. k_cn is the system evaluation factor, reflecting the influence of capacitor voltage offset on the inverter. k is the balance switch. When k = 1, the capacitor voltage of Inverter 1 is preferentially controlled by capacitor balance, and k = −1 means that the capacitor voltage of Inverter 2 is balanced. The output error voltage is injected into the motor current loop for correction.

Fig. 7.

Voltage offset evaluation module.

Fig. 8.

Overall diagram of the TPFS-OWPMSM strategy.

The overall control strategy of the system is shown in Fig. 8. The offset voltage ΔV is optimized from the four capacitors through the voltage offset evaluation module. The unstable voltage offset component ΔV⁺ is obtained by subtracting the steady-state voltage offset component ΔV^∗ from the offset voltage ΔV . And ΔV⁺ will be regulated by a proportional-integral (PI) controller to generate the desired compensatory current i_𝛼^′′. Then, i_𝛼^′′ will be injected into the stator current control loop to realize voltage balance control.

The power distribution control module samples the motor current i_d, i_q and motor voltage u_d, u_q to calculate the reactive power Q generated during the operation of the motor. Then uses the capacitor voltage PI regulator to obtain the active power P of the Inverter 2, and calculates the voltage component u_cd, u_cq required for the operation of the Inverter 2 by the power distribution module. Finally, the voltage component u_cd𝛼, u_cq𝛽 is modulated by SVPWM to control the switching signal of the Inverter 2 to realize the power distribution of the motor.

4. Simulation of capacitor voltage balance control strategy

4.1. Verification of capacitor balance control

Fig. 9.

Capacitor voltage and TPFS-OWPMSM output before and after voltage balance control.

The simulation results of capacitor balance control are shown in Fig. 9. The initial voltages of the upper and lower capacitors C₁, C₂, C₃, and C₄ are set to be unequal, and the TPFS-OWPMSM applies capacitance balance control at 0.6 s. Figure 9(e) shows the unit power factor operation of inverter 1 under the power distribution strategy. It can be seen that the balance control is compatible with the power distribution control. The results in Fig. 9 show that the capacitor voltage offset of inverters 1 and 2 is eliminated, and the balance strategy does not affect the stable operation of the system.

4.2. Sudden torque and speed under balance control

Fig. 10.

Capacitor voltage and TPFS-OWPMSM output of voltage balance control under sudden torque.

Fig. 11.

Capacitor voltage and TPFS-OWPMSM output characteristics of voltage balance control under sudden torque.

The simulation results of sudden load and speed under capacitor control are shown in Figs 10 and 11. The capacitor voltage balance control system of TPFS-OWPMSM changes the given speed and torque respectively in 1.2 s. It can be seen from the simulation results that the control strategy is not affected by speed regulation and loading.

5. Conclusion

This paper analyzes the capacitor voltage offset of TPFS-OWPMSM and proposes a capacitor-voltage balance control strategy according to the source of the voltage offset. The strategy converts unstable capacitor offset voltage into stator current loop to realize the stable control of the dual-inverters capacitor voltage. This strategy has good compatibility without affecting the stable operation of the motor during the injection. The effectiveness of strategy is verified by the simulation of various working conditions.

Footnotes

Acknowledgements

This work was supported in part by the National Natural Science Foundation of China, under Grant 52077123 and 51737008, in part by the the Natural Science Foundation of Shandong Province of China for Outstanding Young Scholars, under Grant ZR2021YQ35, in part by Open Research Fund of State Key Laboratory of Large Electric Drive System and Equipment Technology in China, under Grant SKLLDJ032020005.

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