1 Introduction
As shown in Figure 1, the rectifier section of a typical cascaded high-voltage frequency converter uses uncontrolled diodes, resulting in irreversible energy transfer. When the motor is in regenerative braking mode, the feedback energy is transferred to the DC bus capacitor, generating a pump-up voltage that causes voltage instability. Excessively high pump-up voltage may damage the switching devices, thereby threatening the safe operation of the frequency converter.
Therefore, this paper adopts mature three-phase PWM rectification technology, using controllable switching devices to form the rectifier circuit of a single power unit to achieve bidirectional energy transfer. Simultaneously, closed-loop control is applied to the DC bus capacitor voltage to stabilize it. This method also achieves unity power factor on the grid side, making the cascaded high-voltage frequency converter a truly green frequency converter. Simulation results demonstrate that this method is simple and effective.
2. Mathematical Modeling and Working Principle of the Rectifier Section of a Single Power Unit
As can be seen from the topology in Figure 1(a), the cascaded high-voltage frequency converter is composed of multiple cascaded power units. Therefore, a mathematical model can be established and its working principle analyzed by taking a single power unit as the research object.
As shown in Figure 1(b), the rectifier section of the power unit is composed of uncontrollable diodes. To achieve energy feedback and stabilize the DC bus capacitor voltage, controllable IGBTs are needed to replace the diodes for PWM rectification control. Figure 2 shows the modified power unit topology.
In Figure 2, lx (x=a, b, c) is the AC side filter inductor, and the resistor rx (x=a, b, c) is the combination of the equivalent resistance of the filter inductor lx and the equivalent resistance of the power switch loss.
Let the three-phase power supply voltage be:
In the formula: ed, eq, id, and iq are the components of the power supply voltage vector and input current vector of the rectifier section of the power unit on the dq axis, respectively.
As can be seen from equation (3), the d-axis and q-axis variables are coupled to each other, making it impossible to control the currents of the d-axis and q-axis independently. Therefore, feedforward decoupling control of id and iq is introduced, and a pi regulator is used as the current loop controller, resulting in the following equation:
In the formula: ud* and uq* are the voltage inputs for the d and q axes; kdp and kdi are the proportional and integral coefficients of the d-axis pi regulator, respectively; kqp and kqi are the proportional and integral coefficients of the q-axis pi regulator, respectively.
As can be seen from equation (4), the voltage command has achieved complete decoupling control, and its system control block diagram is shown in Figure 3. In Figure 3, a voltage-current dual closed-loop structure composed of a pi regulator is adopted. The external voltage loop is used to stabilize the output voltage, and the internal current loop controls the AC input current to be in phase with the input voltage. Its working principle is as follows: The output voltage Vdc is compared with the given reference voltage Vdc* and then sent to the voltage PI controller. The output signal of the voltage controller is used as the given value id* of the active component of the grid-side current. Its magnitude is adjusted according to the active output of the rectifier. In order to achieve unity power factor rectification or inversion, the given value iq* of the reactive component is set to 0. In steady state, the current given signals of the dq axis are both DC. The two given values are compared with the grid-side feedback values id and iq after transformation and then sent to the current PI regulator. After decoupling and dq→αβ transformation, the control signal of the three-phase grid-side voltage in the two-phase stationary coordinate system is obtained. After passing through the voltage space vector pulse width modulation module, six SVPWM control signals are output, thereby realizing the control of the power unit rectifier.
Simulation system of 3 power units cascaded
The simulation model of the power unit, built according to the mathematical model introduced in Section 2, is shown in Figure 4.
The simulation model of the rectifier controller is shown in Figure 5.
Simulation system of 4 power units cascaded
Figure 6 is a system simulation model of a high-voltage frequency converter with three power units connected in series in each phase.
5. Simulation Experiment
The experimental parameters used in the system simulation are as follows: voltage loop sampling frequency: 2.5kHz; current loop sampling frequency: 2.5kHz; effective input voltage of the three-phase PWM rectifier: Vm = 380V; inductor parasitic resistance: r = 0.5ω; DC bus voltage setpoint: Vdc* = 750V, initial voltage: Vdc = 550V; three-phase input power supply frequency: f = 50Hz; triangular wave carrier frequency: fs = 2.5kHz; DC bus terminal capacitance: c = 3200μF; grid-side filter inductance: l = 0.8MH. The load power is 1MW. Switching losses are not considered in the simulation.
In this simulation experiment, from 0 to 0.25s, the rectifier of the cascaded frequency converter is in an uncontrolled rectification state, with uncontrolled rectification performed by the anti-parallel diodes within the IGBTs of the rectifier; from 0.25s to 0.55s, the rectifier of the cascaded frequency converter is in a controlled rectification state, and the IGBTs in the rectifier begin to work; at 0.55s, the frequency converter suddenly switches to a load; at 0.8s, the current direction of the controlled current source of the frequency converter is changed, the energy of the frequency converter begins to be fed back, and the rectifier of the cascaded frequency converter changes from the rectification state to the inversion state.
Figure 7 shows the simulated waveforms of the phase current, phase voltage, and DC bus voltage of the power unit on the grid side of the cascaded frequency converter. As can be seen from Figure 7(b), when the rectifier of the cascaded frequency converter starts working at 0.25s, VDC rapidly rises from its initial value of 550V to the given value VDC*, and then quickly stabilizes. At 0.55s, the frequency converter suddenly switches on a load, causing VDC to drop momentarily, but it quickly regains stability at the given value. After stabilization, the voltage fluctuation is very small. At 0.8s, due to the change in the current direction of the controlled current source, the frequency converter begins to regenerate energy, and the rectifier begins to switch from rectification to inversion. The regenerated energy causes VDC to spike momentarily at 0.8s, but because the rectifier of the cascaded frequency converter responds very quickly, VDC quickly regains stability at the given value. Simultaneously, because the rectifier's response speed is fast, the rise in VDC at 0.8s is minimal, ensuring the safe operation of the system.
As shown in Figure 7(a), when the rectifier of the cascaded frequency converter starts working at 0.25s, the grid-side current fluctuates slightly but quickly stabilizes. When the frequency converter suddenly connects to the load at 0.55s, the grid-side current fluctuates very little and quickly stabilizes. Comparing the phases of the grid-side voltage and current, it can be seen that their phases almost overlap, and the power factor is close to 1. At 0.8s, the cascaded frequency converter enters the energy feedback state, and the rectifier is in the inverter state. The rectifier makes the phase angle of the grid-side current and the phase difference of the grid-side voltage close to 180°, and the power factor is close to -1. The waveforms of the three-phase output voltage, current, and single-phase output voltage of the cascaded frequency converter inverter are shown in Figure 8.
6. Conclusion
The waveforms from the simulation experiments show that the improved cascaded high-voltage frequency converter can not only perform bidirectional energy transmission and achieve energy feedback, but also has a very fast control system response speed, giving the frequency converter good dynamic performance. Therefore, this improvement scheme is correct and feasible.
