Modeling and simulation of three-level DC/DC converters of high voltage wide range PI control

The three-level DC/DC converter is widely used in various applications, including electric vehicle charging stations, portable power supplies, and photovoltaic power generation. The mathematical models of input voltage, output voltage, and duty cycle of IGBT switch tube are established by analyzing the different operating modes of IGBT switch tube under PWM control. To validate the accuracy of the mathematical models, a simulation model can be built in MATLAB virtual environment, and a proportional-integral (PI) controller can be utilized to implement a hybrid closed-loop control strategy, where the current serves as the inner loop and the voltage as the outer loop. Such a control scheme will help to verify the feasibility of the mathematical models.


Introduction
With the rapid development of new energy, bidirectional converters play a crucial role in energy conversion [1].Three-level BUCK-BOOST converters have been widely used in many fields such as electric vehicles and photovoltaic energy storage [2] [3].Three-level BUCK-BOOST circuit can generate waveforms with three voltage levels, which significantly reduces harmonic components compared to the two-level inverter circuit [4].Furthermore, as the number of switch devices corresponding to each position increases, the voltage across each switch device is reduced to half, making it more suitable for applications in high-input voltage environments [5] [6].
Compared to the bidirectional full-bridge three-level circuit, the bidirectional three-level DC/DC converter can use low-voltage-rated switch devices in high-voltage and high-power scenarios, enabling higher switching frequencies, increased power density, reduced losses, and improved efficiency [7] [8].

Circuit analysis
By utilizing Pulse Width Modulation (PWM) control, the power converter's output can be regulated.PWM technology compares the modulation wave with a triangular carrier wave to determine the switching state of the IGBT switches.This enables adjustment of the switches' duty cycle, changing the power transmission's magnitude and direction.Models for power transmission need to be established to achieve desired output results and apply appropriate control methods.

Three-level BUCK-BOOST topology
The non-isolated system, compared to the isolated system, offers several advantages such as a simpler structure, reduced cost and weight, and relatively higher efficiency.These benefits come from the absence of a large and bulky transformer in the non-isolated system.
The main circuit of the three-level BUCK-BOOST is shown in Figure 1.It consists of Switches S1-S4 and continuous current diodes D1-D4.Capacitors C1 and C2 act as support capacitors on the highvoltage side, while Capacitor C3 serves as a filter capacitor on the low-voltage side.Additionally, the circuit includes a filter inductor, denoted as L1.

Switching tube driving signal and modulating signal
The driving signals of each IGBT switch tube are shown in Figure 2. The on-off and off-off of the switching tube are represented by high and low levels, and T is the working period value of the switching tube.S1 and S2 as well as S3 and S4 are complementary.When S1 is on, S2 is disconnected; When S3 is connected, S4 is disconnected.

Operation mode and modeling of three-level BUCK circuit
PI control consists of two main components: proportional regulation and integral regulation.The proportional regulation reacts to the system's deviation in proportion, while the integral regulation helps eliminate steady-state errors.
One advantage of PI control is its ability to provide fast dynamic response and ease of use, especially when controlled by a triangular carrier.The Gi (S) current regulator, Gv (s) voltage regulator, and Giv (s) deviation regulator are all composed of PI controllers.Within the current inner loop, Ts represents the sampling period, and the variables "kp" and "ki" represent the proportional coefficient and integral coefficient, respectively, of the PI regulator.
Figure 3 is the working mode diagram of the three-level BUCK circuit.

Mathematical model of three-level BUCK circuit
    (1

Neutral point potential balance
An imbalance in the midpoint voltage of a three-level converter can affect the output waveform of the AC measurement.To address this issue, a voltage-current dual-loop PI control is employed.The input voltage reference value and voltage feedback value are processed by the PI control to generate the input current reference value and feedback value.These, in turn, are utilized by the PI control to regulate the output duty cycle (D), which is further controlled by PWM to control the conduction of the switch in the BUCK circuit.
When UC1 is greater than UC2, Switches S1/S3 are closed, and Capacitor C1 charges the inductor, causing UC1 to decrease.Conversely, when UC2 is greater than UC1, Switches S2/S4 are closed, and Capacitor C2 charges the inductor, leading to a decrease in UC2.

Hybrid control simulation
Figure 4 shows double closed-loop PI control of the voltage and current.In addition to the control circuit, the drive circuit, the protection circuit, the auxiliary power supply, and the sampling circuit are also essential in the actual project.To verify the accuracy of the three-level BUCK circuit model and hybrid control-side strategy, a simulation model is established in the MATLAB virtual environment.Table 1 shows the model parameters used in the three-level BUCK circuit.

Results
The voltage waveform of supporting capacitors C1 and C2 is shown in Figure 5.The voltage rise time is about 0.5 ms, and the response speed is very fast.As can be seen from Figure 7, after the adjustment of PI controller parameters, the voltage rise time on the load side is about 0.02 s, which further improves the response speed, and the steady-state error is 0.

Conclusions
By using PWM control, the duty cycle of the IGBT switch-off is determined by comparing the modulating wave with the triangular carrier.By establishing a simulation model and adjusting the PI parameters, depressurization from 1, 900 V to 900 V is achieved, resulting in faster response speed and lower steady-state error.The correctness of the PI controller's three-level BUCK model under double closed-loop control is verified.

Figure 3 .
Figure 3. Operating mode diagram of a three-level BUCK circuit.

Figure 5 .
Figure 5.The voltage waveform of the supporting capacitor.The amplified waveform of C1 and C2 voltages reaching steady-state midpoint balance is shown in Figure6.It can be seen that the voltage fluctuation range is about 0.5 V, and the effect is good.

Table 1 .
Parameters of the model.