Sampling Rate Impact on Electrical Power Measurements Based on Conservative Power Theory

This article presents a study of the sampling rate effect on electrical power measurements whose definitions are based on the Conservative Power Theory (CPT). The definitions of active power and reactive power of the CPT were applied in the MATLAB® software by varying the sampling rate and using a digital power meter as a reference. The measurements were performed in scenarios with linear and non-linear loads. Due to the usage of an integral in the CPT calculus, an error was verified associated with the reactive power being inversely proportional to the sampling rate. From the present study, it is possible to conclude that depending on the sample rate, the errors associated with the reactive power measurements are unacceptable and make the CPT implementation unfeasible. The results also presented effective information about the minimal sampling rate needed to make these errors neglected and to assist in choosing suitable microprocessors for the digital implementation of the CPT. It is worth mentioning that this paper was limited to assess how accurate the measurements of active and reactive powers were and important to highlight that the CPT has the additional contribution of dealing with distortion currents and consequently new portions of powers. For the latter, the influence of sampling rate may be crucial and new lines of investigation are motivated.

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.

Predictive Direct Power Control for Dual-Active-Bridge Multilevel Inverter Based on Conservative Power Theory

This paper explores the feasibility of multilevel dual-active bridge-inverter (DABMI) applications for grid-connected applications of a modern Model of Predictive Direct Power Control (MPDPC) based on the conservative power theory (CPT). In the case of unbalanced grid voltages, the objective of the study is to promote continued active and reactive energy in MPDPC without reducing efficiency such as transient response and current harmonics. The nature of the instantaneous p-q theory permits only one out of three control targets to be fulfilled. The proposed control approached directly regulates the instantaneous active and reactive power to achieve three particular control objectives namely sinusoidal and symmetrical grid current, cancelling twice of fundamental grid frequency reactive power ripples, and removing twice grid frequency active power ripple. The techniques of complicated Grid part sequence extraction are unnecessary and improved at no extra expense, as is the case with current MPDPC fault-tolerant approaches. The instantaneous power at the next sampling instant is predicted with the newly developed discrete-time model. Each possible switching state will then be evaluated in the cost function defined until the optimal state which lead to the minimum power errors is determined. In MATLAB/Simulink simulation, the proposed CPT-based MPDPC measures reliability and performance at balanced and unbalanced grid voltages then compared with the conventional and existing MPDPC The proposed method manages to achieve all of three control targets which generates sinusoidal grid currents and attenuates active and reactive power ripple of twice the grid frequency exactly at the same time without losing its critical efficiency including transient reaction and current harmonics.