محاسبه ضریب توان (PF) ساده برای سیستم های قدرت الکتریکی

ABSTRACT A simple power factor calculation for electrical power systems

The rapid developments of the power electronics technology rise the using of controlled AC drives, power converters and nonlinear loads, causing the Power Quality Disturbances (PQD). These disturbances can be defined in terms of waveform distortion at the power signals and increasing of the reactive power consumption. They can cause the power loses, terminal voltage drops and negatively affects the safety, quality and economic efficiency of the electricity service. The new electrical politicizes and strategies are required for the operation and management of the electricity service in order to prevent these negative effects and to maintain the reliability and quality.

The term Power Factor (PF) has emerged with the increasing of the reactive power consumption in the electrical distribution systems recently. This term is used to express how effectively the electrical energy is converted into useful form and simultaneously indicating the quality of the service to the electricity authorized and end-users. PF is the ratio between the active (P) and the apparent (S) powers. It is also defined as the cosine value of the Phase Difference (PD) between the voltage (V) and current (I) of an AC electrical power system. It is given in (1).

PF = cos (φ) = P / S

where u is the angle value of PD between the two sinusoids signals. The industrial companies try to maintain PF of their system close to unity. In other word, an ideal value of PF is 1.0, known as unity power factor. If the value of PF is under 0.95, it is considered to be poor. Then, its correction can be typically achieved by increasing this value to 0.95–1.0. A poor power factor is generally caused by the distorted current and inductive loads, drawing the reactive power from the utility distribution system. This situation results with the increasing of the phase difference between the voltage and current at the load terminals. Hence, the fast and accurately estimation of PD is required to calculate the PF for taking the precautions how effectively the value of PF can be set to the unity. It has also important significance in the engineering area, such as system model identification, intelligent control, industrial automation, and system characteristic analysis and failure diagnosis [1].

In the literature, the need for the estimating of PD between the power signals is justified by numerous papers for the engineering area. In these studies, several types of Zero Crossing [2,3] with their electronic circuit implementations, Discrete Fourier Transform [4– 6], Sine-Wave Fit [7] and Ellipse-Fit Methods [8] are proposed. These estimation methods use some form of interpolation between points by using the correlation function to obtain a better resolution. The other types are based on Quadrature Delay Estimator (QDE) if the source is a real-valued sinusoid. These techniques utilize the in-phase and quadrature-phase components of one of the receiver outputs and provide a high-resolution phase-shift estimate [9–11]. The applications of QDE based methods are simple according to the other types of PD estimation methods.

The quadrature-phase component is obtained from delayed versions of the input signal such as phase-shifting as the integer number times of π/2 [9] and time-shifting as the integer number samples [10,11]. If the frequency of the signal is known, phaseshifting could be achieved as exactly π/2 by an integer number of sampling periods. However, calculating QDE with a non-integer number of signal periods causes a bias in estimation [11]. The time-shifting methods are not enough for the estimation of PD due to that the additive methods are used for improving their performance [10,11]. Also, these methods are lack of why the quadrature-phase components are used and where the equations of PD estimation are derived.

This paper presents a new and simple method derived by using the trigonometric functions is proposed for PD estimation to calculate the PF of a power system. The much faster and accurate of PD estimation are provided by minimizing the number of mathematical equations. The theoretical explanation is given in detail by – supporting its implementation by using simulation program named as Power System Computer Aided Design (PSCAD). The proposed method is evaluated by performing simulation cases under the various system conditions. The results of case studies are given to demonstrate its effectiveness under the distorted system conditions.

The rest of the paper is organized as follows. Section ‘Mathematical derivation of the proposed method’ presents the mathematical derivation of the proposed method. Section ‘Improvement of the proposed method for Power Quality Disturbances’ describes the improvement of the proposed method for power quality disturbances. Section ‘Case studies’ reports the evaluation of the case studies by comparing the simulation results with their real values. Section ‘Conclusions’ concludes this paper.