Electricity supplies harmonized with

Abstract. Functional data appear in a multitude of industrial applications and processes. However, in many cases at present, such data continue to be studied from the conventional standpoint based on Statistical Process Control (SPC), losing the capacity of analyzing different aspects over the time. In this study is presented a Statistical Control Process based on functional data analysis to identify outliers or special causes of variability of harmonics appearing in power systems which can negatively impact on quality of electricity supply. The results obtained from the functional approach are compared with those obtained with conventional Statistical Process Control that has been done firstly. 

In Europe the main motor is usually an AC motor, using a star-delta starter. An inverter for the main motor is becoming more common, particularly with the smaller decanters. The inverter enables a soft start, and allows speed adjustment for different process requirements. Inverter motors can cause unwanted electrical interference, and harmonic wave forms, on the main electrical supply lines. These problems can be minimised by using electrical filters and the latest advanced electrical technology. 

Many electrical problems, or problems associated with the quality of the incoming power and internal to the motor, can be isolated by monitoring the line frequency. Line frequency refers to the frequency of the alternating current being supplied to the motor. In the case of 60-cycle power, monitoring of the fundamental or first harmonic (60 Hertz), second harmonic (120 Hz), and third harmonic (180 Hz) should be performed. 

Here, instead of the usual delta function d(Eg, — Eg — ftv), which supplies only discontinuous spectral lines, a Lorentz function with a line width 29(normalized to one) is introduced for all vibrational levels labeled by n and m of electronic states j and k which contribute to the transition rate of Eq. (9) [58]. M is the transition operator, in general, pertinent to an electric dipole transition. The nuclear wavefunctions are approximated by products of harmonic oscillator functions... 

Arc furnaces are operated in conjunction with large capacitor banks and harmonic filters to improve the power factor and also to filter the harmonic frequency currents so they do not unduly affect other power users sharing the same power fines. It is not uncommon to see arc furnaces supplied from dedicated utility power fines to minimize their impact on other power users. The presence of large capacitance in an electrical system can result in voltage rise due to the leading reactive power demands of the capacitors, unless they are adequately canceled by the lagging reactive power required by the loads. This is why capacitor banks, whether for power factor correction or harmonic current filtration, are switched on when the furnace is brought on line and switched off when the arc furnace is off line. 

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