Formulations for the apparent and unbalanced power vectors in three-phase sinusoidal systems

Abstract

The proper operation of the grid-connected power electronics converters usually needs using some kind of synchronization technique in order to estimate the phase of the grid voltage. The performance of this synchronization technique is of a great importance when trying to improve the quality of the consumed or delivered electric power. The synchronous reference frame phase-locked loop (SRF-PLL) synchronization algorithm has been widely used in recent years due to its ease of operation and robust behavior. However, the estimated phase can have a considerable amount of unwanted ripple if the grid voltage disturbances (e.g. harmonic distortion and unbalance) are not properly rejected. The aim of this paper is to propose an adaptive SRF-PLL which is able to strongly reject the aforementioned disturbances even if the fundamental frequency of the grid voltage varies. This synchronization method will allow the designer to easily upgrade an existing SRF-PLL, thus improving the performance of working power converters. This is accomplished by using several adaptive Infinite Impulse Response (IIR) notch filters, implemented by means of an inherently stable Schur-lattice structure. Besides the stability properties, this structure accomplished the most important topics required to be programed into the commonly used fixed point DSPs (i.e. high mapping precision, low round-off accumulation, suppression of quantization limit cycle oscillations). The proposed adaptive SRF-PLL has been tested by programing the algorithm into the fixed-point digital signal processor TI TMS320F2812. The obtained experimental results show up that the proposed synchronization method highly rejects the undesired harmonics, even if the fundamental harmonic frequency of a highly polluted grid voltage abruptly varies.

Decarbonization of Distribution Transformers Based on Current Reduction: Economic and Environmental Impacts

“…These effects could be reduced by equitably distributing the active and reactive loads connected to the secondary of the transformer. For this, the vector unbalanced power [29,30] can be a very useful tool, since the angles (α p and α q ) of the active and reactive components ( → S uip and → S uiq ) of this vector quantity, calculated according to Equations ( 12) and (13), provide information about the phase or phases of the transformer in which the active and reactive powers have greater values. This information can be obtained in real time for dispatch tasks, or it can be represented throughout a measurement period, as Figure 14 represents.…”

“…To determine the value and the phase in which the unbalances are most important, a mathematical tool can be used. This tool is the unbalance power vector ( → S u ), which has been described in detail in [29,30]. This quantity has two components, which determine the unbalanced powers caused by the imbalances of active currents ( → S uip ) and by the imbalances of reactive currents ( → S uiq ), respectively.…”

An Alternate Representation of the Vector of Apparent Power and Unbalanced Power in Three-Phase Electrical Systems

“…In this study, the unbalance power is not proposed by means of a vector expression. In [16], the unbalanced power vectors due to voltage and current are defined. To consider the unbalanced voltages, they use the unbalance factors δ − = V − /V + and δ 0 = V 0 /V + .…”

“…In [18], the phasor of the total unbalance power is defined. It presents the same problem as [16] since they use the unbalance factors δ − and δ 0 to consider the unbalance power caused by the unbalanced voltages. Other authors extend their studies to the analysis of non-linear three-phase systems [19,20].…”

Power Measurement Model Optimization using MATLAB

“…The two-wattmeter method of power measurement can be used to measure the power in a three-phase wye or delta-connected system, regardless if it is balanced or unbalanced [1,2]. In this method, the current coils of the wattmeter are connected with any two lines, while the potential coil of the wattmeter is connected to a third line [3,4].…”