# Variable Switching Frequency Deadbeat Predictive Current Control for PMSM with High-Speed and Low-Carrier Ratio

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## Abstract

**:**

## 1. Introduction

## 2. Deadbeat Predictive Current Control Principle and Error Analysis

_{e}is the electric rotor speed, and L

_{s}and R

_{s}are the stator inductance and resistance, respectively. ψ

_{f}is the rotor permanent magnet flux linkage. (1) can be calculated and obtained as the current equation on the d-q axis by Laplace:

_{0}is the start time of the calculation.

_{e}, the control voltage u, and the back EMF phase C are generally considered as constant between the two adjacent sampling moments kT and (k + 1)T. At this point, the predictive current equation can be approximated as:

_{e}*T will be very small. According to the mathematical limit approximate principle, the current equation can be approximated, as shown in (4):

_{e}T, and this value can reach dozens of degrees when the motor is running at high speed and low carrier ratio conditions. In the end, when the traditional deadbeat predictive control operates at low carrier ratio conditions, the stator current tracking has a large static difference, leading to very serious control errors and current fluctuations [18].

## 3. Variable Switching Frequency Deadbeat Predictive Current Control

#### 3.1. Improved Prediction Model Suits Low Carrier Ratio Condition

#### 3.2. Clamping PWM Modulation Strategy

_{A}is the instantaneous voltage and the u

_{Af}is the fundamental voltage.

_{Af}can be represented by u

_{α}. u

_{A}can be synthesized by calculating the basic voltage vector [21]. Therefore, the calculation formula of A phase current harmonic is shown in (19):

_{A0}and u

_{A7}are zero vectors and T

_{0}and T

_{7}are their duration. u

_{A1}represents the first effective voltage vector synthesized by the three-phase switching action of the inverter in the first half of the carrier cycle, T

_{1}is its duration, u

_{A2}represents the first effective voltage vector in the second half of the carrier cycle, and T

_{2}is its duration. The effective voltage vector combined with its action time can generate control voltage applied to the motor.

_{A1}and u

_{A2}, it can be considered to split their action times, which can theoretically halve the amplitude of the current fluctuation. The two parts of a carrier cycle can be regarded as two independent control cycles. Therefore, this paper sets the control algorithm to be executed twice in a carrier cycle so that the voltage vectors can be synthesized twice in each carrier cycle [22]. Sampling and control are carried out at both the beginning and middle of a carrier cycle to further reduce the delay error and improve the accuracy of the algorithm, as shown in Figure 6.

_{a}, T

_{b}, and T

_{c}(T

_{a}, T

_{b}, T

_{c}∈(0,1)) can be analyzed and adjusted, which are denoted as T

_{max}, T

_{med}, and T

_{min}in Figure 7. As shown in Figure 7, the formation process of the improved clamping modulation strategy is demonstrated, as shown in Figure 7a for the traditional modulation strategy, the c-phase bridge leg acts once in the unit carrier cycle, but when the motor is running at high speed, the modulation degree is high, and the c-phase bridge leg action time is very short, so the modulation strategy shown in Figure 7b was used to clamp this bridge leg. According to (21) and (22), the duty cycle was recalculated, and T

_{med}was readjusted to obtain the improved clamping modulation strategy proposed in this paper, as shown in Figure 7c. At this time, the middle phase bridge leg operates twice in the unit carrier cycle, reducing the continuous action time of the active vector, which will facilitate the reduction of current fluctuations. Thus, the variable switching frequency control of the power devices within a unit stator current cycle was realized without increasing the switching frequency, and the improved strategy reduces the current ripple and improves the current quality.

_{med1}was divided into two segments, respectively: t

_{m1}and t

_{m2}, as shown in Figure 7c, which realizes the splitting of the intermediate active vector and effectively reduces the A phase current fluctuation.

_{k}moment, and the duty ratio is updated once; sampling once at T

_{k+0.5}moment, and the duty ratio was updated once. That is the double sampling and double updating control strategy. Combined with the proposed clamping modulation strategy, the dynamic and steady performance of the motor system was improved, and the output current fluctuation was reduced on the premise that the switching frequency was not increased.

## 4. Simulation and Experimental Results

#### 4.1. Simulation Results

_{d}and i

_{q}show a large tracking error when the traditional prediction model is used for the simulation. It can be found that the i

_{d}and i

_{q}tracking accuracy is improved when the prediction model proposed in this paper is used. The effectiveness of the improved prediction model proposed in this paper was verified.

#### 4.2. Experimantal Results

_{q}steps from 0A to 2A, the d-q axis current starts to show tracking errors, and there is a tracking error of about 1A between i

_{q}and i

_{q}

^{ref}, as when i

_{q}changes to 4A, the error between i

_{q}and i

_{q}

^{ref}increases, and there is a tracking error of about 1.4A. Meanwhile, the tracking error of i

_{d}increases with the increase of i

_{q}. However, i

_{q}can always track i

_{q}

^{ref}when using the improved prediction model considering the change of rotor position angle, and the i

_{d}basically has no tracking error. The reason for the above experimental results is that when the carrier ratio is reduced, the traditional prediction model obtained by the approximation cannot meet the accuracy required by the model under this working condition. Meanwhile, the current harmonic content is increased under the low carrier ratio condition, which also amplifies the tracking error of the d-q axis current. The improved prediction model established in this paper fully considers the error of the prediction model under low carrier ratio conditions.

_{d}, i

_{q}, and i

_{a}when the motor is running at 8000 r/min. At this time, since the advantages of the improved prediction model proposed in this paper have been proved by the experiment in Figure 13, the improved prediction model was adopted in subsequent experiments. By comparing the current waveforms in Figure 14a,b, it can be seen that the i

_{d}and i

_{q}can track the reference value well. Therefore, the improved modulation strategy added to the control algorithm does not affect the current control.

## 5. Conclusions

## Author Contributions

## Funding

## Data Availability Statement

## Conflicts of Interest

## References

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**Figure 3.**Schematic diagram of three-phase switching state and A-phase current fluctuation in sector II.

**Figure 7.**Comparison diagram of three-phase switching state and A-phase current fluctuation with different modulation strategy in sector II. (

**a**) represents double-sampling and double-updating non-clamping modulation, (

**b**) represents double-sampling and double-updating clamping modulation, and (

**c**) represents the improved clamping modulation used in this paper.

**Figure 11.**d-q axis current and A-phase current waveform at 13,000 r/min. (

**a**) represents traditional PWM modulation, (

**b**) represents improved PWM modulation.

**Figure 13.**d-q axis current and A-phase current waveform at 8000 r/min and carrier ratio about 18. (

**a**) represents traditional prediction model, (

**b**) represents improved prediction model.

**Figure 14.**d-q axis current and A-phase current waveform at 8000 r/min and carrier ratio about 18. (

**a**) represents traditional PWM modulation, (

**b**) represents improved PWM modulation.

**Figure 15.**THD analysis of the phase current at 8000 r/min and carrier ratio about 18. (

**a**) represents the current THD analysis of traditional PWM modulation, (

**b**) represents current THD analysis of improved PWM modulation.

**Figure 16.**d-q axis current and A-phase current waveform at 13,000 r/min and carrier ratio about 11. (

**a**) represents traditional PWM modulation, (

**b**) represents improved PWM modulation.

**Figure 17.**THD analysis of the phase current at 13,000 r/min and carrier ratio about 11. (

**a**) represents the current THD analysis of traditional PWM modulation, (

**b**) represents the current THD analysis of improved PWM modulation.

**Figure 18.**Three-phase switch state and current waveform on improved PWM modulation strategy at 13,000 r/min and carrier ratio at about 11.

U_{N}/V | I_{N}/A | P_{N}/kW | T_{N}/N·m | ω_{N}/r/min | P_{n} | L_{s}/mH | R_{s}/Ω | ψ_{f}/Wb |
---|---|---|---|---|---|---|---|---|

540 | 19.3 | 3.7 | 11.8 | 3000 | 2 | 3.2 | 0.38 | 0.145 |

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## Share and Cite

**MDPI and ACS Style**

Wang, Z.; Wang, C.; Liang, H.; Han, Z.; Jin, X.; Zhang, G.
Variable Switching Frequency Deadbeat Predictive Current Control for PMSM with High-Speed and Low-Carrier Ratio. *World Electr. Veh. J.* **2023**, *14*, 64.
https://doi.org/10.3390/wevj14030064

**AMA Style**

Wang Z, Wang C, Liang H, Han Z, Jin X, Zhang G.
Variable Switching Frequency Deadbeat Predictive Current Control for PMSM with High-Speed and Low-Carrier Ratio. *World Electric Vehicle Journal*. 2023; 14(3):64.
https://doi.org/10.3390/wevj14030064

**Chicago/Turabian Style**

Wang, Zhiqiang, Chenyu Wang, Haishen Liang, Zhuangzhuang Han, Xuefeng Jin, and Guozheng Zhang.
2023. "Variable Switching Frequency Deadbeat Predictive Current Control for PMSM with High-Speed and Low-Carrier Ratio" *World Electric Vehicle Journal* 14, no. 3: 64.
https://doi.org/10.3390/wevj14030064