Averaging-Based Method for Real-Time Estimation of Voltage Effective Value in Grid-Connected Inverters

Accurate and timely estimation of the root-mean-square (RMS) voltage is essential for grid-connected inverter systems, where it underpins reference generation, synchronization, and protection functions. Conventional RMS estimation methods, based on squaring, averaging, and taking the square root of values over full-cycle windows, achieve high accuracy but incur significant latency and computational overhead, thereby limiting their suitability for real-time control. Frequency-domain approaches, such as the FFT or wavelet analysis offer harmonic decomposition but are too complex for cost-sensitive embedded controllers. To address these challenges, this paper proposes an averaging-based RMS estimation method that exploits the proportionality between the mean absolute value of a sinusoidal waveform and its RMS. The method computes a moving average of the absolute voltage over a half-cycle window synchronized to the phase-locked loop (PLL) frequency, followed by a fixed scaling factor. This recursive implementation reduces the computational burden to a few arithmetic operations per sample while maintaining synchronization with off-nominal frequencies. Time-domain simulations under nominal (60 Hz) and deviated frequencies (57 Hz and 63 Hz) demonstrate that the proposed estimator achieves steady-state accuracy comparable to that of conventional and adaptive methods but with convergence within a half-cycle, thereby reducing latency by nearly 50%. These results confirm the method’s suitability for fast, reliable, and resource-efficient real-time inverter control in modern distribution grids. To provide a comprehensive evaluation, the paper first reviews conventional RMS estimation methods and their inherent limitations, followed by a detailed presentation of the proposed averaging-based approach. Simulation results under both nominal and off-nominal frequency conditions are then presented, along with a comparative analysis highlighting the advantages of the proposed method.