Proper operation of the grid-tie transformerless converters under unbalanced and distorted conditions entails a precise detection of the frequency and fundamental component of the grid voltage. One of the main problems that could arise during the estimation of grid parameters is the existence of a DC offset generated from measurement and A/D conversion. This undesirable induced DC offset could appear as a part of the reference sinusoidal current of grid-tie converters. Although literature has proposed the use of an extended complex Kalman filter (ECKF) for the estimation of positive and negative sequence voltage components as a promising competitor to phase locked loops, mitigating the effect of possible DC offsets when a Kalman filter is employed remains scarce. This paper proposes a new extended complex Kalman filter to improve the filter stability for estimating the frequency and the fundamental positive and negative symmetrical components of the grid voltages, where DC offset, scaling error, and noise can successfully be rejected. The theoretical findings are experimentally validated.

This paper presents a novel hybrid renewable water pumping system (WPS) designed for remote areas, utilizing solar photovoltaic (PV) and wind energy to drive a six-phase induction machine (6PIM). Compared to conventional three-phase machines, the 6PIM offers improved fault tolerance, scalability, and reduced converter ratings. The proposed modular architecture assigns each three-phase winding set a dedicated power converter, enabling independent control and enhancing system reliability. To simplify implementation and reduce cost, a sensorless voltage-to-frequency (V/f) control strategy is adopted. This eliminates the need for current and speed sensors, making the approach especially suitable for off-grid water pumping applications where robustness is more critical than fast dynamic response. A key contribution of this work is the integration of flexible power-sharing control into the V/f framework, marking, to the best of the authors’ knowledge, its first application in multiphase drives. The system is validated through simulations on a 200 HP model under realistic solar and wind profiles, as well as experimental tests on a 1.5 HP prototype with an emulated centrifugal pump load. Results demonstrate the effectiveness of the proposed control scheme in achieving stable operation and efficient energy utilization under varying input and load conditions.

The growing adoption of asymmetrical six-phase machines (A6PM) in electric vehicle (EV) drivetrains necessitates computationally efficient and modulation-accurate carrier-based PWM (CBPWM) techniques. Double zero-sequence injection PWM (DZSPWM) is one of the widely used CBPWM techniques, as it offers optimal dc-link utilization and easier straightforward real-time implementation. However, the need for CBPWM approaches capable of replicating the benchmark four-dimensional (4D) 24-sector SVPWM has emerged, since the latter provides lower current total harmonic distortion (THD) compared to DZSPWM. Recent CBPWM implementations targeting 4D 24-sector SVPWM equivalence, however, continue to impose a relatively high computational burden, primarily due to sector-dependent zero-sequence formulations, multiple case-based expressions, and carrier logic that varies with the sector number. In contrast, DZSPWM employs a single zero-sequence expression and fixed carrier logic independent of the sector, highlighting the practical importance of sector-independent formulations. This paper introduces a computationally efficient and fully sector-independent CBPWM strategy for A6PM-based EV drives that replicates the modulation behavior of the benchmark 4D 24-sector SVPWM while eliminating sector identification, sector-dependent zero-sequence definitions, and virtual vector synthesis. The unified injected zero-sequence signals are generated directly from instantaneous extrema of scaled phase-voltage references using a dynamic saturation mechanism, avoiding piecewise sector-dependent equations, virtual-reference generation, and trigonometric phase-shifting operations employed in prior CBPWM approaches. A gradient-based carrier adjustment mechanism, governed by the core zero-sequence signal, adaptively regulates carrier toggling without explicit sector detection or carrier reconfiguration logic, requiring only two comparisons per sampling cycle. Analytical derivations establish exact equivalence with 4D 24-sector SVPWM in terms of vector synthesis and dc-link utilization under linear modulation. Experimental validation on an asymmetrical six-phase induction motor drive confirms the equivalence with SVPWM, with reductions of 67% in execution time and 68% in memory usage relative to existing CBPWM implementations incorporating carrier adjustment under identical hardware and switching conditions for fair comparison. Additionally, the proposed method exhibits lower CPU load and memory requirements, reinforcing its suitability for real-time implementation in asymmetrical six-phase EV drive systems.