Research on Noise Suppression Strategies for High-Frequency Harmonic Noise in Automotive Electronic Water Pumps

Abstract

In this paper, in order to effectively reduce the electromagnetic noise of automotive electronic water pumps, a Hybrid Random Carrier Space Vector Pulse Width Modulation Hybrid Random Carrier Space Vector Pulse Width Modulation, (HRCSVPWM) technique based on linear congruential generator (LCG) algorithm is proposed to study the suppression effect of current harmonics and acoustic vibration response with an automotive electronic water pump as the research object. Firstly, the HRCSVPWM based technique is proposed on the basis of SVPWM and pulse width modulation strategies. Secondly, the performance of random numbers generated for HRCSVPWM is analyzed, and it is proposed to use an LCG random number generator to generate excellent random numbers combined with a genetic algorithm to quickly determine the optimal values of three random parameters, namely, random number Ri, mixing degree coefficient Ki, and spreading width Ti, which enhances the stochasticity and spatial traversal of random sequences and ensures the effect of the HRSVPWM control method. Finally, simulation analysis is carried out, and a noise experimental platform is built for experimental verification. The results show that using the improved HRCSVPWM control strategy, compared with the SVPWM control strategy, the total harmonic content decreased by close to 21.81%, and the sound pressure level amplitude decreased by an average of approximately 6 dB.

1. Introduction

Noise has become an important indicator of automobile performance [1,2,3,4]. Electronic water pumps have become an indispensable key component in the thermal management systems of modern automobiles. Electronic water pumps are typically used as the main pump for battery and motor cooling circuits, cabin fans, coolant circulation systems, and turbocharger cooling, among other critical automotive applications. These systems operate in close proximity to passengers and sensitive electronic equipment and must therefore meet stringent Noise, Vibration, and Harshness (NVH) and electromagnetic interference (EMI) requirements. Currently, Permanent magnet synchronous motors (PMSM) [5,6,7] have become the dominant topology for automotive electric coolant pumps due to their excellent power density and efficiency characteristics. However, fixed-frequency PWM modulation results in spectral aliasing, where 80% of the harmonic energy is concentrated at the carrier frequency and integer multiples thereof. This phenomenon can cause the total harmonic distortion (THD) of the current to exceed 25%, which generates anomalous flux harmonics in the stator windings, destroying the symmetry of the air-gap magnetic field and triggering a risk of structural resonance in the rotor assembly, resulting in audible noise. The human ear can perceive the noise frequency range of 20 Hz~20 kHz. When the electromagnetic noise frequency is about 700 Hz~5000 Hz, it will make people experience a strong sense of noise, and in serious cases, it can manifest as a shrill whistling.

There are two main approaches to suppressing high-frequency noise. The first is to add filters to remove high-frequency harmonics. The second is to use spread spectrum modulation technology to suppress high-frequency harmonics at the switching frequency and its multiples. Since adding hardware not only increases costs but also takes up a lot of space, the second method is the most economical and effective way to suppress high-frequency harmonics. In [8], DHDRC-SVPWM is proposed for high-frequency vibration suppression through double discrete random variables, reducing the switching frequency harmonic peak by 20.3–44.9% while maintaining efficiency. However, the number of discrete sequences must be balanced between the computational burden and spectral spreading effects, and although improving the random number generation algorithm increases control accuracy, it also increases computation time. Ref. [9] presents a hybrid periodic carrier frequency modulation (HPCFM) technique based on improved SVPWM. By combining improved SVPWM and periodic carrier frequency modulation (PCFM) [10,11], this method can effectively eliminate PWM noise, achieve a 12.5% reduction in switching loss in the 3.2–4.8 kHz range, and significantly suppress PWM noise, especially odd harmonic noise, while reducing switching loss and frequency range. Ref. [12] proposes a multi-state Markov chain [13] random pulse width modulation MRA-SVPWM technique, which utilizes Markov chains to generate multi-state random numbers to optimize harmonic suppression. It also discusses several mainstream methods in detail for comparison, reducing the harmonic suppression from 56 dB to 40 dB at a 6 kHz carrier frequency, but lacks verification of noise.

This paper first introduces the HRCSVPWM algorithm [14,15,16], While traditional Random Pulse Width Modulation RPWM can disperse discrete spectral lines, it may leave residual peaks near the carrier, and pure PCFM may be insufficient for suppressing even-order harmonics and sensitive to the selected waveform. HRCSVPWM combines the advantages of both: The periodic component can deterministically shape the spectrum to avoid residual peak accumulation, while the random component fills the spectrum to break coherence. The mixing coefficient provides a single adjustment parameter that balances spectrum flatness and switching regularity. Second, a random number generation strategy model for the LCG algorithm is established and combined with genetic algorithms [17,18] to optimize three important random numbers, thereby achieving the optimal carrier frequency, effectively reducing harmonic content and suppressing high-frequency noise.

2. Hybrid Random Carrier Space Vector Pulse Width Modulation

2.1. Theoretical Analysis of SVPWM Harmonics

In order to maximize the utilization of DC bus voltage and optimize the output harmonic performance, SVPWM [19,20] is often used in motor control, but high-frequency harmonics will appear at the integer multiple of the carrier frequency. The root is that PWM modulation itself is a discrete sampling process of an ideal continuous signal, which will inevitably produce spectrum mirror and sideband harmonic clusters at the sampling frequency (carrier frequency) and its multiple frequency. Using MATLAB/Simulink version 2024a, an SVPWM simulation diagram for an automotive electric coolant pump was established [21]. The simulation parameters were configured to match the experimental prototype: the carrier frequency was set to 6 kHz, the DC bus voltage to 12 V, and the fundamental frequency output to 40 Hz. The simulation results are presented in Section 4.

2.2. Hybrid Random Switching Frequency Modulation Strategy

Aiming at the problem of high-frequency noise generated by PMSM in frequency conversion drive power supply mode, an HRCSVPWM strategy was proposed. The proposed method combines Random Carrier Space Vector Pulse Width (RCSVPWM) Modulation techniques and Periodic Carrier Space Vector Pulse Width Modulation (PCSVPWM) techniques based on SVPWM. The aim is to discuss the two most important parameters of the two approaches separately, as well as the relationship between the two strategies and their impact on the carrier frequency.

In recent years, RCSVPWM technology has been outstanding for harmonic suppression. Ref. [22] analyzes the generation mechanism of PWM harmonics and establishes a mathematical model of power spectral density. Through accurate calculation of this model, it is concluded that the power spectral density of random pulse position PWM technology is composed of continuous and discrete spectra, and the existence of discrete spectra leads to the consistent presence of PWM harmonics near the carrier frequency. This indicates that the PWM harmonic suppression can only be improved by increasing the random degrees of freedom of the random pulse position PWM technique, and the experimental results verify this conclusion. The classical SVPWM switching frequency is a fixed value, which can be made to vary randomly within a certain range by combining the switching frequency with a random number with the following expression [23]:

$$f_c=f_{c0}+R_i\Delta f$$

(1)

where $f_c$ is the frequency of the triangular carrier, $f_{c0}$ is the center frequency of the randomly varying triangular carrier, $R_i$ is a random number varying between −1 and 1, and $\Delta f$ is the bandwidth. The range of the random switching frequency $\Delta f$ is determined by the bandwidth value.

The signal used to drive the PWM in the SVPWM technique is generated by comparing the modulating waveform with a carrier waveform, which is generally selected as a triangular waveform. Figure 1 shows a schematic diagram of the PWM output waveform.

The PCSVPWM control strategy is to vary the frequency of the carrier waveform periodically over a certain frequency range with some periodic function, which is expressed as follows [24]:

$$f_c(t)=f_0(t)+\Delta f_c(t)$$

(2)

where $f_c(t)$ is the carrier frequency, $f_0(t)$ is the center frequency of the periodic carrier frequency modulation, and $\Delta f_c(t)$ is the time-varying bandwidth. The range of variation of $\Delta f_c(t)$ is also very important for the carrier frequency.

The periodic function carrier frequency is continuously adjusted according to the change of the periodic function and compared with the modulating wave to get the changing three-phase on-time of the motor, realizing the periodic change of the switching frequency. The periodic change of the carrier frequency should be limited to a certain range to prevent the phenomenon of superposition with random changes or repeated within a short time. According to the regular periodic variation of carrier frequency, periodic spread spectrum modulation techniques can be categorized into sine wave periodic frequency modulation, triangle wave periodic frequency modulation, and sawtooth wave periodic frequency modulation. Among the two-level periodic frequency modulation techniques, one of the modulation methods with the strongest ability to suppress harmonic amplitude is sawtooth wave periodic frequency modulation.

The HRCSVPWM technique uses a periodic function instead of the center frequency of the random switching frequency modulation technique to spread the spectrum more efficiently and reduce the computational burden. This approach provides a better spectral distribution over the same random range. The formula for this is as follows:

$$f_c=f_{c0}+\left[kS(t)+R_{LCG}(1-k)\right]\Delta f$$

(3)

where $f_c$ is the frequency of the carrier, $f_{c0}$ is the fixed carrier center frequency, $\Delta f$ is the bandwidth, $V\left(t\right)$ refers to the RCSVPWM algorithm function whose triangular carrier amplitude varies between [−1, 1], $k$ is the coefficients of the random carrier frequency modulation [0, 1], and $R_{LCG}$ is a random number varying between [−1, 1], generated by the LCG algorithm random sequence generator. The signal flow diagram of the HRCSVPWM control strategy is shown in Figure 2, where the center frequency of the carrier, 6 kHz, is fixed. $S\left(t\right)$ Represents the sawtooth wave function period modulation strategy and $R$ is a random number varying between −1 and 1. The range of variation of the switching frequency is determined by $\Delta f$. Figure 2 clearly shows the effect of bandwidth and random numbers on the carrier frequency, and the weight of the effect is reflected in the mixing coefficient K.

3. Random Number Generation

The key to the HRCSVPWM technique is the acquisition of random numbers, which determines the distribution of harmonic spectral lines in the stochastic PWM power spectrum. Random numbers can be divided into three categories: true random numbers, quasi-random numbers, and pseudo-random numbers. Pseudo-random number generators are the most widely used in RPWM technology because they are easy to realize digitally and generate fast.

The pseudo-random sequence generated by an excellent pseudo-random number generator should not only have a sufficiently large and unpredictable period, but also take up little memory and be fast. In current research into RPWM technology, the spreading effect of uniform distribution is obvious, and it is usually chosen as the probability law for constructing the pseudo-random number generator; therefore, in this paper, we choose the LCG algorithm, which obeys discrete uniform distribution to generate the random number sequence.

3.1. LCG Algorithm

In random PWM technology, the generation of random numbers and spreading width is its core link. In a digital system, the random number is mainly generated by the microprocessor through the assembly language, so the generation of the random number cycle is long, and there will be no statistical repetition in the system for a long time; the generation of the algorithm is as simple as possible to reduce the burden of the microprocessor and the occupation of the memory space; the linear congruence method generates the sequence of random numbers through simple mathematical recursive formulas, and this process is very fast to implement on the computer. The core of the linear congruence method lies in a linear recursive formula that is simple in structure and easy to implement in various programming languages.

The linear congruence method is given by [25] as follows:

$$R_{n+1}=\mathrm{mod}{2}^{N_S}[(R_N\times a+b)]$$

(4)

The $N_S$ in the formula indicates the word length of the random number related to the number of microprocessor bits; the more the number of bits, the longer the period of the random number; a and b are two prime numbers in order to make a cycle of 0, 1, 2, …, $2^{N_S}$ all appear, then a should be a 4k + 1 form, and b should be a mutual prime with 2. Each random number $R_{n+1}$ is generated iteratively from the previous random number, and the initial value can be any positive integer in 0~$2^{N_S}$ − 1.

Figure 3a verifies the randomness performance of the sequence over a short period of time by plotting the generated pseudo-random numbers by samples to visualize the fluctuation of the values in the time domain. This confirms that the normalized random numbers cover the target interval [−1, 1] uniformly to avoid overflow or uneven distribution of values due to parameter errors. Ideally, the random sequence should show irregular fluctuations in the time domain with no obvious pattern. The blue dots in the figure are uniformly scattered, indicating that the generator has good surface randomness in the short period. Figure 3b shows statistics of the frequency of random numbers in different subintervals, quantitatively verifying whether they are close to the theoretical probability density of uniform distribution by comparing the height of the histogram bar of 0.5. Superimposing the theoretical probability density curves, the black dashed line in the figure visualizes the degree of deviation of the actual distribution from the ideal distribution. The frequency of the bins is close to the theoretical value, indicating that the generator meets the requirement of uniform distribution. The effectiveness of the LCG algorithm is analyzed through the dual perspective of the “time domain-frequency domain”. Compared with ref. [13], it can be seen that the LCG algorithm is simpler to implement than the Markov chain. In the specific task of generating basic, independent, and uniformly distributed pseudo-random numbers, the LCG algorithm has advantages over the Markov chain in terms of speed, simplicity of implementation, and low resource consumption.

3.2. Improvement of LCG-Based Algorithm for Random Number Optimization

3.2.1. Genetic Algorithm

A genetic algorithm has a strong global search ability in optimization, applicable to continuous, discrete, multimodal and other types of problems. The search space covers a wide range and can effectively avoid falling into the local optimum, and the genetic algorithm is able to find the global optimal solution for complex problems with multiple local optimal solutions. These advantages make genetic algorithms show great potential and application value in the optimization of complex problems. Let the bandwidth $\Delta f$ be variable T. The correspondence between a genetic algorithm and HRCSVPWM is shown in

Table 1. Relationship between genetic counting and HRCSVPWM.

Genetic Algorithm	HRCSVPWM
Gene	R, K, T
Chromosome	Random carrier sequence
Population	Multiple random carrier sequences
Fitness function	Fitness function harmonic distortion rate: the performance of random numbers generated for HRCSVPWM is analyzed
Cross over	Swapping two genes produces new individuals
Mutation	Mutations create new individuals

:

3.2.2. Genetic Algorithm-Based Optimization of HRCSVPWM

The output voltage of the pump motor control system after the mixed random carrier is as follows [26]:

$${\displaystyle \frac{u_a}{E_d/2}}={\displaystyle \frac{a_0^{*}}{2}}+{\displaystyle \sum _{n=1}^{\infty }{a}_n^{*}}\cos n\left({\omega }_{s}t+\Delta f\sin \left({\omega }_{m}t\right)\right)$$

(5)

where ${\omega }_m$ is the signal angular frequency, $U_a$ is the instantaneous value of the output voltage, $U_d$ is the DC voltage, $a_0^{*}$ and $E_d$ are the constant terms, and $a_n^{*}$ is the coefficient in the Fourier series, which represents the amplitude of different frequency components. These coefficients are usually obtained from the original signal through the Fourier transform. N is the number of harmonics, ${\omega }_s$ is the fundamental angular frequency, $\Delta f$ is the frequency deviation, and ${\omega }_m$ is the angular frequency of the modulating signal.

Discrete random signals can be combined with SVPWM technology to randomize the PWM output pulse width, so that the originally concentrated sideband harmonic energy can be extended to a wider frequency range, thus achieving the effect of suppressing sideband harmonics and the amplitude of the acoustic oscillation response. Compared with the traditional PWM and SVPWM, RPWM can effectively reduce THD, which mainly reflects the size of the harmonic components in the output voltage and current of the power supply or inverter, and a high THD will lead to increased vibration and noise.

THD is introduced as the evaluation index of its harmonic negative effect, where $U_i$ represents the harmonic amplitude of the PWM harmonic and $U_0$ represents the fundamental amplitude [27]:

$$U_{THD}=\sqrt{{{\displaystyle \sum _{i=2,3,4,\dots }^{\infty }\left(\frac{U_i}{U_0}\right)}}^2}\times 100\%$$

(6)

Figure 4 depicts the operational framework of the genetic algorithm optimization, where the random carrier waveforms serve as the genetic information units, and the sequential arrangement of these carriers constitutes the algorithm chromosome. The evolutionary selection criterion uses the THD as a quantitative evaluation metric to optimize the system by iterative population. The specific procedure for screening the optimal R, K, and T is as follows:

(1) Initial calibration of the system: according to the phase voltage data collected from the experiment, the angular frequency of the signal modulated by the simulation model, the d-axis inductance, winding resistance, and other parameters are calibrated to ensure the accuracy of the simulation results.

(2) Limit the value range of R, K and T: the range of R is set to [−1, 1] with two decimal places, the range of K is [0, 1] with two decimal places, the range of T is {0, 600, 1200, 1800, …, 6000}, and discrete mapping is applied to T. The following parameters are used for the simulation of T. Crossover probability: pc = 0.8, mutation probability: pm = 0.1, which means that 80% of the chromosomes will undergo crossover operations to increase diversity. The mutation probability is 0.1, and proper mutation can prevent the algorithm from falling into a local optimum.

(3) Initialize chromosomes: Each chromosome contains three basic pieces of information, random gain R, coefficient K of random carrier frequency modulation, and spreading width T. During each iteration, the THD value of each chromosome will be calculated and updated. Considering the amount of computation, the number of chromosomes is set to 50 in this paper.

(4) Run the steady state condition Simulink simulation program and generate the phase voltage harmonic amplitude database in the MATLAB/Simulink version 2024a workspace. The values of R, K, and T are generated by the LCG algorithm, the THD value of each chromosome is calculated by the genetic algorithm, and optimization is sought.

(5) If the number of iterations is not reached, the genes K, R, and T of each chromosome can be obtained by mutation and a crossover operation to get a new chromosome and calculate its THD value, and the optimization search operation is performed again.

(6) Termination condition setting: in this paper, the number of iterations is 100 times as the termination condition. This number of iterations is too easy to be redundant, increases the calculation time, and occupies too much memory.

Figure 5 shows the results of a random parameter optimization based on the GA algorithm. As the iteration proceeds, the closer to the set number of iteration steps of 100, the value of the objective function gradually tends to stabilize, and the suppression effect of the noise level reaches the optimization. At this time, the value of the mixing degree Figure 5a K tends to be 0.7; the value of the random number Figure 5b R tends to be 0.48, and the spreading width Figure 5c T tends to be 1800, which is 30% of the carrier frequency. From Figure 5d, it can be seen that as the number of iterative steps increases, the THD value tends to saturation and finally tends to 7%, and the suppression effect on vibration and noise sound pressure level tends to saturation.

K = 0.7 shows that bandwidth T has a greater impact on the carrier frequency than the random number R, accounting for 70% of the weight. Therefore, selecting an appropriate bandwidth is crucial. Additionally, it can be seen that the optimal mixing effect is achieved when the periodic frequency and random frequency account for 0.7 and 0.3, respectively. With the bandwidth is set to 1500 and the mixing coefficient to 0.7, the random number R is generated within the range [0.28, 0.68], achieving a good carrier frequency effect. This suppresses high-frequency harmonics concentrated at the switching frequency, ultimately reducing noise. In ref. [17], a genetic algorithm is also used to optimize random numbers to reduce harmonics, but there is no optimization of the spread spectrum width T. Instead, it is discussed separately later, which not only increases the workload but also leads to greater errors. This paper adds optimization of the spread spectrum width T to achieve better harmonic suppression.

4. Simulation Analysis

Based on the MATLAB/Simulink environment, a simulation control system for water pump motors was constructed with the following parameter settings: the modulation ratio was 1.0, the number of pole pairs was 2, the fundamental frequency was 40 Hz, the weighting coefficient was 0.5, the rated power was 60 W, the rated rotational speed was 5000 rpm, the stator resistance was 0.146 Ω, the inductance was 0.49 mH, and the rotational inertia was 4.7 × 10⁻⁶ kg·m², The pump motor parameters used in the experimental tests were the same as those used in the simulation tests to ensure consistency between the simulation and the experiment. The hybrid random strategy that uses LCG to generate random numbers is named LCG-HRCSVPWM, while the control strategy that uses genetic algorithms to find the optimal random numbers generated by LCG is named GACG-HRCSVPWM. A schematic diagram of the GACG-HRCSVPWM control system implementation is shown in Figure 6.

Figure 7 shows the phase current diagram. Figure 7b,c exhibit good sinusoidal characteristics compared to Figure 7a, with Figure 7c demonstrating superior sinusoidal performance than Figure 7b. Figure 8 shows the spectral analysis of the phase current. Compared with Figure 8a, the harmonic peaks in Figure 8b,c are greatly reduced at the carrier frequency of 6 kHz and its integer multiple frequencies of 12 kHz and 18 kHz. The energy tends to disperse to the surrounding frequency bands, so as to achieve the effect of frequency diffusion. Figure 8b has poor propagation and mixing results due to a too large or too small range of K and T, while Figure 8c has good results after optimization by GA. In order to better characterize the signal characteristics before and after the application of the suppression strategy, voltage power spectral density analysis was performed, which can accurately locate the noise source and quantify the noise characteristics, and the results are shown in Figure 9. It can be seen from Figure 9b,c that the current power spectral density has a very obvious decrease compared with Figure 9a on the whole, and the spikes at integer multiples of the carrier frequency also become flat.

Table 2. Comparison of THD and power spectral density for three control strategies.

	THD	Current Power Spectral Density Peak at 6K (dB)	Current Power Spectral Density Peak at 12K (dB)	Current Power Spectral Density Peak at 18K (dB)
SVPWM	29.96	31.5	17.7	5.4
LCG—HRCSVPWM	13.54	−8.9	−11.5	−18.0
GACG—HRCSVPWM	8.15	−24.8	−24.7	−26.9

shows the average values of three simulation tests for the SVPWM control strategy and the two strategies GACG-HRCSVPM and LCG-HRCSVPWM. As can be seen from the table, the THD value has decreased by 21.81%. Compared to the SVPWM strategy, the GACG-HRCSVPM strategy and LCG-HRCSVPWM strategy reduced the peak current power spectral density near 6 kHz, 12 kHz, and 18 kHz by 40.4 dBm/Hz, 29.2 dBm/Hz, 23.4 dBm/Hz, 56.3 dBm/Hz, 42.4 dBm/Hz, and 32.3 dBm/Hz, respectively.

5. Experimental Verification

In this study, the electronic water pump of a brand of pure electric vehicle was taken as the research object, and the noise characterization test experiment was carried out in a semi-anechoic chamber environment. The noise data acquisition adopted the Siemens Test Lab test and analysis system, and according to the performance test specification of SAIC Group’s e-water pump, the system recorded the acoustic characteristic parameters under different working conditions and synchronously carried out the analysis of phase current waveform characteristics. The hardware control unit was developed by choosing a Mega Innovation The GD32A503 32-bit automotive-grade master controller chip, is manufactured by GigaDevice Semiconductor Inc, headquartered in Beijing, China. constructing three kinds of control algorithm models based on the Simulink platform, realizing the automated integration of the application layer code and underlying driver through the Embedded Coder tool and deploying it to the electronic water pump controller after compilation. The experiment was conducted in the semi-anechoic chamber of the Shanghai New Energy Vehicle Vibration and Noise Testing and Control Professional Technical Service Platform. The internal dimensions of the semi-anechoic chamber are as follows: 9.76 m × 8.6 m × 3.5 m; cutoff frequency ≤ 63 Hz; and background noise < 20 dB. The test rig was designed and constructed in accordance with industry standards to simulate a vehicle cooling system, with a flow rate range of 0.57–11.3 m³/h, and the coolant type was water: ethylene glycol = 1:1. The experiment utilized a 378B02 capacitive acoustic sensor manufactured by PCB Corporation of the United States. The microphone arrangement is shown in Figure 10: three measurement points (one each in the axial, radial, and tangential directions) are set 20 cm away from the surface of the water pump housing.

In the experimental setup, the DC bus operating voltage is stabilized at 12 V, and the inverter dead zone parameter is configured as 3 μs. The constant speed condition is responsible for collecting data signals from the electronic water pump during stable operation, with a duty cycle set at 80% and a collection time of 10 s. The bandwidth is set to 1500, the mixing coefficient is set to 0.7, and the LCG optimization range is set between [0.28 and 0.68] to achieve the optimal experimental results. Figure 11a–c show the noise map. The horizontal axis represents the noise frequency distribution, and the vertical axis represents the sound pressure amplitude, which is the most basic and direct information about sound wave intensity. It directly quantifies the noise energy intensity through linear scaling. The three colors represent the three acoustic test points. As shown in Figure 11a, the noise at 6 kHz is particularly prominent under the SVPWM control strategy. During the experiment, high-frequency noise showed sharp characteristics and easily caused auditory discomfort. The improved control strategies Figure 11b,c have outstanding noise suppression effects in the 6 kHz band, distributing the energy of the original high-energy bands of 6 kHz and 12 kHz more evenly across wider frequency range, realizing the noise spectrum reshaping and sound pressure level attenuation. Further analysis shows that the noise reduction performance of the GACG-HRCSVPWM strategy is better than that of the LCG-HRCSVPWM. It effectively reduces electromagnetic noise interference to laboratory personnel; motor noise can be ignored when standing two meters away.

Figure 12 shows the flow rates of the three control methods at different duty cycles in offline conditions. It can be seen that different control strategies have little effect on the flow rate, except for a certain delay during startup. This indicates that different control methods do not affect the operation of the electronic water pump. Figure 13 shows the A-weighted sound pressure level (SPL) spectra of three different duty cycle strategies in an offline scenario. Both the LCG-HRCSVPWM strategy and the GACG-HRCSVPWM strategy can significantly reduce the sound pressure level of the electronic water pump. However, the noise changes under the LCG-HRCSVPWM strategy are unstable, while the noise reduction effect under the GACG-HRCSVPWM strategy is more stable, with the sound pressure level maintained around 30 dB, far below the psychoacoustic threshold of the typical electric vehicle (EV) cabin background, indicating that it will not cause perceptible discomfort. Compared to the SVPWM strategy, the GACG-HRCSVPWM strategy achieves an average reduction in sound pressure level amplitude of approximately 6 dB, effectively reducing noise. The noise reduction is approximately 16.7%. Refs. [9,12] provide detailed comparisons of the harmonic noise suppression effects of various strategies at different switching frequencies. Ref. [12] indicates that vibration noise is reduced by approximately 15%. This further validates the effectiveness and practicality of the proposed method.

6. Conclusions and Outlook

This paper addresses the issue of high-frequency electromagnetic noise generated near the switching frequency and its multiples when using an SVPWM control in variable frequency drive-powered automotive electronic water pumps. It proposes a GACG-HRCSVPWM control method, this method employs a random sequence generator based on the LCG algorithm to effectively optimize random number performance. Building upon the RCSVPWM strategy, it combines the excellent spread spectrum effects of periodic functions to propose the HRCSVPWM strategy and utilizes the GA algorithm to optimize three key random parameters. Finally, its control performance is validated through simulation and experimental verification, with the following conclusions:

(1) The proposed LCG-HRCSVPWM strategy focuses on spreading at the carrier frequency and its integer multiples. Combined with the GA-optimized GACG-HRCSVPWM strategy, it achieves an average power spectral density reduction of approximately 43.7 dBm/Hz, an average sound pressure level reduction of about 6 dB, and a THD reduction of 21.81%.

(2) The proposed GA optimization algorithm can effectively optimize the mixing ratFio K, random number R, and spread width T, identifying the optimal bandwidth, mixing ratio of random and periodic strategies, and the range of random numbers in the random strategy that yields the optimal carrier frequency. From the proportion of the mixing ratio, it can be seen that the periodic strategy outperforms the random strategy in suppressing high-frequency harmonics. Optimizing these parameters reduces the coupling between them, providing a clearer understanding of each parameter’s role and minimizing the need for extensive case-by-case analysis. The research conducted in this paper can also be applied to other PMSM systems, providing theoretical and experimental support for future studies on PMSM control of electromagnetic noise.

(3) The electronic water pump test bench simulates the automotive cooling system, but there are still differences from the actual vehicle operating environment. To verify the stability of the algorithm, further real-vehicle loading experiments are required. Additionally, verification can be conducted on other electric vehicle auxiliary equipment, such as interior fans and battery cooling pumps, to assess the impact of spectrum shaping on the long-term reliability of inverter components.