1. Introduction
Number and variety of non-linear devices and installations used by residential and commercial customers are increasing continuously. Therefore the effect of harmonics in the network is more and more considered in both the planning and the operation of distribution systems. This analysis is not always easy, because multiple factors influence the emission and propagation of harmonics through the network, like the network impedance, the voltage distortion and the time-variation of number and type of connected equipment.
One of the key aspects of a realistic harmonic analysis is a correct representation of summation of harmonic currents. The presence of different devices with different topologies at one connection point can cause a diversity of current harmonic phase angles and subsequently may lead to a lower magnitude of vector sum than the arithmetical sum of the harmonic currents [1]. This is known as diversity effect (or cancellation effect) and has a high influence on the total harmonic distortion emitted by larger groups of non-linear loads into the grid. Different indices like summation exponent and diversity factor exist to quantify the effect.
Most of the papers that address the summation of harmonic currents consider only the effect of few devices in a single moment of time or a perfect steady state of harmonics [e.g. [2-5]). If variation of system, load and generation are considered, the problem becomes time-varying and an additional statistical post-processing is required in order to calculate aggregated diversity indices. The parameters and methods used for the post-processing can have a considerable impact on the calculated diversity index. Furthermore, the accuracy of these indices depends also on t...
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...l (3) covers always the whole dataset and is therefore also fix for the study.
In the case of aggregation interval (1), three different cases were selected: No aggregation (10 period values), 1min aggregation and 10min aggregation. For the aggregation of harmonic angles, the vector sum of the corresponding currents inside the aggregation interval was calculated, and the resulting angle of this sum was used as the aggregated value. As assessment quantile (4) the impact of 95th vs. 99th quantile are analyzed. Finally different statistical calculation methods (5) can be applied to find those quantiles. In this study the following two methods will be compared:
• Method 1: and are calculated as quantiles based on the instantaneous calculated diversity factors and summation exponents.
• Method 2: and are calculated based on harmonic magnitudes and angle quantiles.
Wikipedia Contributors (2014, March 19). Electrical engineering - Wikipedia, the free encyclopedia. March 19, 2014, from
I then put these results into a graph which you can find in the plastic wallet this was handed in with.
In some low power densities areas, utilities are connected to an existing transmission line using a tapped line because of economic advantages. Such a configuration of transmission lines presents great difficulty in the task of fault location when the fault resistance is not negligible due to the infeed currents from different sources.
times, when there's peak demand of electricity that interacted nature of the grid makes the
[2]. Rehtanz, C. (2001). Wide Area Protection System and Online Stability Assessment based on Phasor Measurements. Bulk Power System Dynamics and Control - V, Onomichi City, Japan, (Augest 2001).
The emergence of the Microgrids came after realizing that the architecture of the electricity grid existing nowadays (Figure 1) is getting obsolete, since it is based on the idea of a top-down system, which is predicated on unidirectional energy flows. [ASMUS09]
The first table was titled Other Measures. It provided information on the sample size, minimum, maximum, first quartile, third quartile, given percentage, and value of percentile. These values are used to compute range and interquartile range in the measures of dispersion. The last table shows the mean plus or minus 1, 2, or 3 times the standard deviation and offers details on how many values fall within the ranges created by those calculations.
of which will be used to find the mean, median, mode, range as well as
Gaussian elimination avoids the need of matrix inversion while solving the nodal equation of large power systems. Moreover it also leads to reduced order network equivalents. This is used to analyze power system with special focus on voltages at some selected buses. For this purpose selective numbering of s...
the rating tables of the six parameters, then by the use of fuzzy membership functions, we can
Based on the calculations that were generated using the molwt macros program I was then able to select the peaks of interest and compute a numerical value for them
In this paper, I will talk about how AC circuits can be described by considering voltage and current using complex numbers. An AC circuit requires two separate numbers to be able to completely describe it. This is because it takes into account the amplitude and the phase of the current. The fact that complex numbers can be easily added, subtracted, multiplied or divided with each other makes them ideal for this operation where both amplitude and phase have to work together.
Given the power consumption at all buses of a known electric power system configuration and the power production at each generator, load flow analysis program, PowerLFA calculates the power flow in each line and transformer of the interconnecting network and the voltage magnitude and angle at each bus.
It is rather difficult to determine Vmax directly from plot of r against [S]. It is however, possible to rearrange the Michaelis-Menten equation (4) so to permit some alternative plots for easy determination of Vmax. Two of the best known methods which make use of rearranged equations are as follows:
Alternating current is always changing in direction and amplitude. The current flow in alternating current changes in even intervals. Ac usually changes in power and direction. The vast majority of power supplied for households and big business is alternating current. This is because of the ease of generating alternating current in alternators. The main concept of alternators is moving a conductor through magnetic lines. The change in the magnetic field around the conductor or vice versa makes electrons move. When you have physically moved either the conductor or magnet in a complete 306-degree circle you have produced one sine wave or one complete cycle. The amount of time it takes to complete one cycle is referred to as a period. The frequency of an alternating sine wave is the amount of cycles per second. Frequency is measured in hertz. One hertz is equivalent to one cycle per second. The frequency coming out of your electrical plug at home is 60 Hz. The peak value in a sine wave is the top voltage level away from zero. The peak-to-peak voltage value is referring to difference between the positive peaks value to the negative peak value. The effective or rms value of a sine wave is the actual amount you would use or measure using a multi-meter. In three-phase alternating current there are three different coils or conductors that produce three different sine waves.