Geometric Algebra-Based Harmonic Analysis and Adaptive Virtual Resistance Control for Electric Vehicle Charging Converters

The output voltage harmonics of electric vehicle (EV) charging converters directly affect grid power quality. This paper proposes a harmonic analysis method based on geometric algebra (GA), which employs a multivector representation of signals and least squares estimation to accurately extract fundamental, integer-order, and inter-harmonics. A coupling coefficient is defined to quantify the phase correlation between frequency components. Based on measured data, harmonic characteristics under four typical operating conditions are analyzed, and an adaptive PID controller is designed to dynamically adjust the virtual resistance for harmonic suppression. The results show that the GA method significantly reduces spectral leakage under non-integer-period sampling conditions, with amplitude estimation errors below ±2%. The total harmonic distortion (THD) decreases with increasing active power and increases with reactive power injection. The droop coefficient exhibits a non-monotonic effect, while reducing the proportional gain raises the THD. Adaptive control reduces the average THD by 14.0–28.5% with a total response time of less than 0.05 s. The coupling coefficient C13 is strongly positively correlated with THD and negatively correlated with the maximum Lyapunov exponent computed using the Rosenstein small-data method (correlation coefficient −0.85), confirming the intrinsic relationship between coupling and stability. Compared with fast Fourier transform (FFT) and other methods, GA achieves higher accuracy under short data records and non-integer-period sampling. This paper provides a complete theoretical framework and engineering solution for harmonic suppression in charging converters.