On Adaptive Moving Average Algorithms for the Application of the Conservative Power Theory in Systems with Variable Frequency

The Conservative Power Theory (CPT) emerged in recent decades as a theoretical framework for coping with harmonically distorted and unbalanced electric networks of ac power systems with a high participation of converter interfaced loads and generation. The CPT measurements are intrinsically linked to moving averages (MA) over one period of the grid. If the CPT is to be used in a low-inertia isolated-grid scenario, which is subjected to frequency variations, adaptive moving averages (AMA) are necessary. This paper reviews an efficient way of computing MAs and turns it into an adaptive one. It shows that an easily available variable time delay block, from MATLAB, causes steady-state errors in the measurements when the grid frequency varies. A new variable time delay block is, thus, proposed. Nonetheless, natural pulsations in the instantaneous power slip through MAs when the discrete moving average window does not fit perfectly the continuously varying period of the grid. A method consisting of weighing two MAs is reviewed and a new and effective hybrid AMA is proposed. The CPT transducers with the different choices of AMAs are compared via computer simulations of a single-phase voltage source feeding either a linear or a nonlinear load.