The first wavelet, the Haar wavelet, is the simplest and earliest wavelet documented. It obeys all of the criteria discussed above except differentiability, i. This implies that choosing a suitable set of Haar wavelets to represent a smooth waveform becomes difficult and not economical. Other exa. The Daubechies wavelet has rigorous mathematical support and has served in many applications outside the power systems area, such as signal and image processing.
The wavelets in Figure 5 were generated using WaveLab, software that is publicly available on the Internet from Stanford University [lo]. Wavelab was written in Matlab and uses filter bank theory to generate most of the wavelet waveforms. This was usedl as the "mother" wavelet for the Discrete Wavelet Transform in the comparison with the Discrete Fourier Transform to be discussed later. Note the similarity with the Fourier functions if alpha is zero.
The mother wavelet refers to the example function 3 based on which a set of member functions is generated. The family, or set of functions is built by dilating, or translating the mother wavelet. This family is expressed as: where a controls the dilation of the wavelet and b the translation. Figure :2 shows a Morlet mother wavelet and its family members. If a and b are taken as continuous numbers, the wavelet transform produces redundant information.
To avoid this problem, a and b are usually taken as discrete numbers that vary logarithmically with a base of 2. This will be discussed further in the next section. A Figure 1. While the Fourier Transform can be plotted on a 2 dimensional plot whose axes are frequency and magnitude or phase , the Wavelet Transform requires a three dimensional plot whose horizontal axes represent dilation and translation and the vertical axis may represent magnitude or phase.
In order to avoid the redundancy that results from using a continuous set of values for a and b, these are usually taken as follows: The Wavelet Transform then becomes: where m and k are taken as discrete numbers. As m increases, the wavelets dilate and as k increases the wavelets are translated farther away from the origin. When ao is taken as 2, we have what is referred to as dyadic translation and binary dilation.
As an example of a Wavelet Transform plot, a sinusoid containing two discrete frequencies was used as an input to the Morlet Wavelet Transform. The resulting three dimensional plot is shown below. The transform was done using Matlab. For example, an SVC may cause, upon switching, frequencies around a kHz that superimpose on the 60 Hz fundamental. In order to accurately identify this transient, we could look at the spectrum of the data record.
An accurate spectrum needs to resolve both the 60 Hz and the high frequencies. The discussion that follows shows why this a difficult task for a Fourier analysis but readily feasible in terms of the Wavelet Transform. One of the most restrictive factors that comes with any useful application of the Fourier Transform is the periodicity condition that the input function or the data record has to assume.
A way around this is to assume periodicity for the length of the data record. The result is an increase in the sidebands of the frequencies of interest because the: input function or data record becomes the unintended product of a square window function a.
In order to limit the increase of the sidebands, windowing techniques, such as Hamming, Hanning, and the Short Time Fourier Transform Gibbons Transform were developed. This resulted in an improvement for the frequency of interest but not for all the frequencies present in, for example, a broadband signal.
A broadband signal requires a window thiit is long for low frequencies and short for high frequencies. This is exactly what the Wavelet Transform provides. If the mother wavelet is chosen appropriately, the low frequencies are analyzed with wavelets that are dilated in shape, and the high frequencies are analyzed using ,wavelets that are compressed in shape. Before we move on to a numerical example, it is worth noting one more difference between Fourier and wavelet analysis. This relationship between transform and series is not possible with the Fourier analysis.
This allows Wavelets to be an efficient medium of storage for nonperiodic functions. The following numerical example illustrates the above discussion, first in terms of a broadband steady state input datarecord, then a characteristic transient, found in capacitive switching. The resulting waveform is used as an input function for the DWT and the D m.
In this example, the spectrum command in Matlab was used to accomplish the FlT,While the Wavelet Transform was accomplished using a Morlet mother wavelet implemented in a short Matlab file that is given in the appendix. The results from the FlT show that there are two prominent peaks, but it is difficult to determine where the lower frequency actually occurs. The Wavelet Transform also shows two prominent peaks.
In this case however, the two peaks are easily identifiable. Note that there is a direct relationship between dilation factors and the frequencies of the wavelets. In the next example, we examine similar results for a transient case. The spectrum from the FFT is now very difficult to use in accurately identifying the frequencies present in the input waveform. The sidebands present around one kHz are high enough to produce considerable error. The frequency of the fundamental is not obvious either.
The Wavelet transform however, still produces two prominent peaks. The above examples illustrate briefly the DWT capability in accurately identifying transients. The next section will discuss more general applications for power system transients. As was shown in the previous section, Wavelet Transforms can be used in identification of transients more accurately than Fourier analysis. Once a transient is identified, it can be efficiently stored using similar techniques. This will allow easy c1assific;ationof transients and the source of the disturbances.
Transient categories such as high and low impedance faults, capacitor switching, transformer inrush current, large motor starts, voltage flicker, and nonsimultaneous pole closure can be easily formed. Then a decision can be made on which transients to keep and which to discard. A recognition system [9] can be trained to detect incipient modes of failure in transformer windings or other on-line equipment.
Also, identification of the source cause of transients can aid in resolving power quality conflicts in utility-industrial interfaces. Analysis of transients and propagation in power systems is one of the most recently proposed applications for wavelets [ 5 ].
The attempt in this area is to reduce transient analysis to an analysis similar to the harmonic analysis. Harmonic analysis decomposes the forcing current or voltage into harmonics which can be used in conventional circuit theory.
The result is then obtained from the superposition of the effects of the individual harmonics. In a similar manner, a forcing transient current or voltage , as in lightening surges, could be decomposed into wavelets with suitable characteristics.
To extend the analogy further, in harmonic analysis the time domain system model is mapped into a frequency domain model. Likewise, in wavelet analysis of transients, the time domain of the system model will have to be mapped into a dilation-translation model, i.
The choice of an appropriiate set of wavelets will preferably represent the largest possible number of different classes of power transients and result in convenient wavelet impedances that lend themselves to conventional circuit analysis. At this stage a full analysis including the above properties has not been realized yet. It is only in the past couple years that wavelet analysis has been introduced for power system transients. The effort in this area has been very recent and seems to be moving in two main directions.
One is concerned with the accurate identification and classification of transients. The other is more concerned with the development of an analysis tool to study the effects of transients on power systr:ms. July Pure Appl. Heydt, A. Lafayette, IN Bologna, Italy. Robertson, Octavia I.
Camps, Jeffrey S. Mayer, and William El. One major source of flicker is the electric arc furnaces used at steel production facilities. An increasing percentage of steel mills, including the aggressive mini-mills, are: using electric arc furnaces[l]. The popularity of DC furnaces has also contributed to the: evaluation of their effects on power systems compared to traditional AC furnaces. Electric utilities are faced with the challenge of providing high quality power to all customers as well as high short circuit capabilities to minimize the effects of large arc furnace loads.
One main concern in operating an arc furnace, which is a rapidly varying load, is voltage flicker on the power system. In the planning stage, various methods are utilized to estimate the capacity of the power system required to operate the furnace and avoid voltage flicker problems. As a general rule of thumb, the ratio of the arc furnace MVA to the utility available short circuit MVA can yield some insight into the likelihood of potential problems.
In general, the higher the ratio the better, but a ratio of 80 or larger is sometimes used as a guideline to determine if serious study efforts are required.
Voltage flicker is expressed as the RMS value of the modulating waveform divided by the RMS value of the fundamental waveform. This is equivalent to expressing voltage flicker as the change in voltage divided by the voltage.
A general. Impression of fluctuating brightness or color, occurring when the frequency of the observed variation lies between a few hertz and the fusion frequencies of the images.
When exposed to the same voltage modulation, different types of lighting may produce different variations in output light intensity. For this reason the terms voltizgeflicker and lightflicker or lampflicker are not interchangeable.
The scaling difference between the voltage flicker and the light flicker for a given light has been called the gain factor for that type of light. When the ternflicker is used alone in a power engineering context it is most commonly referring to voltage flicker.
Some organizations have defined flicker as the peak-to-peak value of the modulating waveform divided by the peak value of the fundamental waveform.
This definition will produce flicker values that are double those obtained using the conventional definition. There is nothing inherently wrong with such a definition as long as the flicker limit curves are adjusted to match this definition.
The definition of flicker can be checked by generating flicker in a laboratory and comparing it to both the commonly accepted flicker curves and human observation. The modulating waveform is also shown. Figure II. In most cases it is not possible to visually identify the multiple flicker frequencies and corresponding magnitudes present in a voltage waveforrrk. The human eye is most sensitive to flicker modulation frequencies in the 6 to 10 Hz range. Flicker levels of 0.
The liuman eye is progressively less sensitive to frequencies below this range. This is why it is important to measure both the magnitude and the frequency of any modulation of the voltage waveform. In actual power system voltage waveforms, multiple flicker modulation frequencies are present. The flicker produced by these multiple frequency components can be calculated by means of analog or digital filtering techniques or by means of a Fast Fourier Transform FFT algorithm.
An advantage of performing an FFT is the fact that the frequency spectrum information is easily obtained. This is useful irkformation for analyzing a flicker problem or the effects of flicker reduction equipment such as static var compensators or furnace electrode position control systems.
Cyclical flicker is caused by fluctuating loads such as electric arc furnaces, arc welders, and reciprocating pumps and compressors. The load fluctuations must be quite large to cause flicker on a power system. Common household appliances may cause flicker in one persons house, but does not normally cause a large enough variation in load current to affect the neighbors.
For a fixed load size, a strong, or stiff, source high short circuit MVA will tend to reduce voltage flicker as compared to a weak source.
This is due to the fact that flicker is caused by variations in load current and the voltage drop across the source impedance caused by the load current. When the load current varies, the voltage throughout the system will vary as well. A stiff source means a lower source impedance which means less voltage drop for a given change in load current.
Loads which do not usually cause flicker may be a source of background flicker on a power system. The flicker generated by these loads is of a very low level and is predominantly in the low frequency regions of a flicker spectrum. This can be explained by changes in load. Whenever a large load is disconnected or connected the voltage will rise or fall slightly, respectively.
A flicker meter will sense these voltage changes and report flicker in the low frequency range. This is consistent with observation. If a large load is started people notice the light intensity drop for a moment. The establishment of a tolerance threshold is subjective, since it is influenced by many variables. Factors affecting the determination of a 1i:mitfor flicker can include ambient lighting levels, size and type of lamp, room decor, duiration, and the abruptness of the voltage variation, and the intensity and immediate occupation or interest of the observer.
Incandescent light bulbs produce a slightly higher change in light intensity for a given amount of voltage flicker than do most fluorescent bulbs.
For this reason most flicker curves are based on how much voltage flicker causes a majority of viewers to observe light flicker from an incandescent bulb. Curves have been developed to express the magnitude and frequency of flicker that is visible to the human eye.
Because there are so many variables in the perception of flicker, many flicker curves have been developed to represent visible flicker. Some researchers distinguish between perceptible flicker and objectionable flicker levels.
For the purposes of analysis, however, the perceptible flicker curves are used as a more conservative way to evaluate the effects of voltage flicker. Using a perceptible flicker curve should keep the flicker levels below the objectionable level. Unlike harmonics, which cause well-known problems in a power system, the final determination of whether there is a flicker problem is whether the utility receives cornplaints fiom customers who observe flicker.
Frequency Hz Figure System planning can help in determining the available short circuit duty at a point of common coupling between the flicker load and system to keep the voltage flicker within acceptable limits. Perceptible flicker limit curves are useful in determining the amount o:f flicker in a system. When applicable, on-site field tests with equipment that will accurately capture multiple frequencies can aid in measuring the existing voltage flicker.
At that point a determination can be made whether the problem is severe enough to further study or pursue corrective measures to remedy the problem. Some common corrective measures that are effective in providing economical reactive power support for electric furnace supply systems are: capacitor banks andlor harmonic filters. Power factor penalties and demand charges can also be reduced or eliminated. The design of the power factor correction system must be carefully engineered so as not to itself create voltage flicker problems themselves.
Harmonic analysis studies are helpful to insure a proper system design. Field measurements are desirable to eliminate the number of assumptions that are required in performing the studies. The ultimate determination whether acceptable voltage flicker exists in a system will be complaints from customers served by the utility system actually experiencing objectionable or noticeable flicker.
Bishop, A. Do, and S. Mendis, M. Bishop, and J. The main advantages of using shunt capacitors are their low cost and their flexibility of installation and operation. These capacitors are implemented in the system in order to control system voltage, to increase power transfer capability, to reduce equipment loading, and to reduce energy costs by improving power factor of the system.
It can be said that by far the most economic means of providing reactive power and voltage support is the use of shunt capacitors[l]. However, energizing these shunt capacitors produces a transient oscillation in the power systems.
Due to the fact that the operation of switching shunt capacitors happens frequently, shunt capacitor switching is regarded as the main source of generating transient voltages on many utility systems. These transients can cause damages on both utility systems and customer systems, depending on the system parameters such as switched shunt capacitol-size, transformer size, and the type of customer loads connected to the system.
In this paper, transient characteristics resulting fiom shunt capacitor switching are studied, impacts of varying system parameters on transient voltages are examined, and methods used to control transient overvoltages are discussed. I Single line diagram for example power system. To simplify the ideas, the system is divided into two parts of different 1,C circuits as shown in Fig. The circuit in part one consists of L l and C1, which can be viewed as system inductance fiom source and step-up transformer and switched shunt capacitance, respectively.
Likewise, the circuit in part two consists of L2 and C2, which represents step-down transformer inductance inductance in distribution lines may also be included and capacitance appearing at the low voltage bus. The source of the capacitance C2 founded in customer systems can be power factor correction capacitors or capacitors used as a filter in adjustable speed drives.
Figure Simpl8ed equivalent circuit for the example power system. Energizing a shunt capacitor bank fiom a predominately inductive source can cause an oscillatory transient voltage which can be as high as 2. The theoretical analysis in detail of shunt capacitor switching has been done in the reference paper[3], using simplified equivalent circuit as shown in Fig.
Figure Simple equivalent circuit for three-phme shunt capacitor switching. Diagram in Fig. It is worth noting that the maximunl voltage appearing across the switching contacts of circuit breaker at this point can be as high as 2. These voltages may induce restrikes or reignitions in the circuit breaker, which in turn can lead to much higher transient voltages that can result in serious damages on the utility system.
For further analysis of transients due to restrikes, we refer the reader to the reference paper[3]. Figure Voltage trapped on the capacitor after the switch is opened. Transients due to shunt capacitor switching in the LC circuit in part one L1 and C1 can excite an LC circuit in part two L2 and C2 , resulting in transient magnification at the low voltage bus where C2 is connected.
This happens when the resonant frequencies of these two LC circuits are in the same range. The resonant frequencies of these two LC circuits are equal; i.. The switched shunt capacitor C1 is much larger than the low voltage capacitor C2; i.
The connected loads at the low voltage bus provide little darnping for the system. To illustrate transient characteristics analyzed above, the case study performed by using Electromagnetic Transients Program EMTP and the simulation results from thle reference paper[2] are presented here. According to Fig. Notice that transient voltages in high side are in the range of 1. Figure Figure III. Practically, the magnitude of these transient voltages is decreased by damping provided by system loads and losses.
In addition, the characteristics of customer loads at the low voltage bus play an essential part in this magnification, for they provide damping required to reduce the magnitude of transients. The effects of these parameters are illustrated, using the results of the simulation obtained from the reference paper[2]. It's obvious that the higher the differences between the size of switched shunt capacitor and the size of low voltage capaci.
Moreover, as the size of the switched shm: capacitor gets larger, the potential for magnification occurs over a wide range of low voltage capacitor sizes.
The peak transient magnitude at the low voltage bus as a function of low voltage capacitor size for three different sizes of step down transformer is shown in Fig. Furthermore, magnification can occur over a wide range of the low voltage capacitor sizes. Unfortunately, it is inevitable for many industrial customers to have their loads dominated by motors. Other factors that can affect transient magnification include the source strength at the switched shunt capacitor, the connection of shunt capacitor bank to the system, and the capacitor placement.
Basically, the stronger the source the lower the source impedance , the lower the transient voltages[5]. The study also shows that switched shunt capacitor bank! Additionally, if the capacitors are more distributed on the distribution feeder, transients can be lowered. The case study done in the reference paper[5] reveals that already energized capacitors on the line tend to reduce transient voltages caused by shunt capacitor switching.
However, in the peculiar conditions when prestrikes or restrikes in the switching device occur, relatively high transients produced by these two conditions can result in severe damages on both the switching device and an overall system. Prestrike during capacitor energizing can occur when there is an arc forming across switching contacts and contracting before the contacts are completely closed.
This arc is extinguished by the switch being able to clear the current zeroes and causing the contacts to close completely. Restrike during deenergizing capacitor can occur when the switch is unable to handle the voltages across the contacts when the switch is opened and therefore, causes the contacts to reclose momentarily.
It is essential for utility system suppliers that they use switching devices which have mechanism to minimize the occurrence of both prestrikes and restrikes.
Transients due to shunt capacitor switching may result in failure of transformer. The study shows that energizing a transformer and shunt capacitors at the same time can cause transient voltages that affect the transformer provided that the transients product:d have the resonant frequency near one of the harmonics in the transformer inrush current.
This will in turn produce substantial overvoltages that last for many cycles at the harmonic frequency. Details of the analysis of capacitor switching and transformer transients are presented in the reference paperL Unlike utility systems, customer systems are significantly affected by transients due to shunt capacitor switching because of magnification that occurs in LC circuit in :part two.
Usually, magnified transient voltages at the low voltage bus are in the range of These transients have substantial energy that can cause damages on protective devices, electronic equipment, capacitors and other devices connected to the low voltage bus.
Some types of power electronic equipment are exclusively sensitive to these transients. For example, adjustable speed drives ASDs are likely to have serious clamages when experiencing transients due to shunt capacitor switching even without magnification involved. This is because typically ASDs consists of relatively low peak inverse voltage PIV rating semiconductor devices and low energy rating metal oxide varistors M0Vs used to protect the power electronic equipment[7].
These methods are as follows[2]: -Synchronous closing control This method is to control closing instants of the capacitor switching device so that each phase of the capacitor bank is energized at the time when the voltage across switching contacts is zero. In practice, a vacuum breaker is the only switching device that can be implemented with this concept.
It has been proven that synchronous closing control is efficient for large substation banks and transmission system capacitors. This method has not typically been employed for feeder capacitors. The problem of this method is that normally the optinium size of these resistors are not available for distribution switching devices.
Nonetheless, this method is regarded cs an effective way in reducing capacitor switching transients in power systems. I I Transients due to shunt capacitor switching as afinction of resistor size used in the capacitor switching device. The coordination among these MOVs in the system has to be done properly. I2 Low voItage harmonic filter configuration. However, this method will be effective only if all of the low voltage power factor correction is applied as harmonic filters.
These transient voltages can be magnified at the low voltage bus due to inductance-capacitance characteristics formed by customer step down transformer and low voltage capacitors connected to the bus on the purposes of power factor correction or being a part of electronic circuit load , causing significant interruption and damages on customer systems. The main parameters that have an impact on transients and transient magnification produced by shunt capacitor switching include switched shunt capacitor size, step down transformer size, low voltage capacitor size, and customer load characteristics.
The analysis of these parameters gives both utility suppliers and customers an idea of how to solve transient problems which occur in their systr:ms. Methods currently used to control these transient voltages are synchronous closing control on switching devices, optimum closinglopening resistor insertion, the use of metal oxide varistor arresters, and the use of harmonic filters instead of pure capacitor as power factor correction.
McGranaghan, R. Zavadil, G. Hensley, T. Singh, and M. Schultz, J. Johnson, and N. Shankland, J. Feltes, and J. Burke, "The Effect of Switching Surges on Bayless, J. Selman, D. Truax, and W. McGranaghan, T. Grebe, G. McGranaghan, W. Reid, S. Law, and D. Their effects can be felt not only in the same site where the furnace is operating but also by other customers of the same utility company connect'ed to the system, even at remote locations.
In the last twenty years the number of electric arc furnaces has increased considerably in the steel producing countries.
The increased number of mini-mills has generated a renewed awareness of the impact of electric furnaces on the power system. Disturbances produced in electrical networks by arc furnaces may be able to significantly affect the quality of energy distributed by electrical companies. An arc furnace is a non- linear, time-varying load, which gives rise to both voltage fluctuations and h. The former phenomenon causes luminosity variations of lamps, the flicker effect, which may give trouble to the human visual system.
Melting cycles of arc furnace are characterized by strongly time-varying electrical behavior. Quick variations of current and reactive power, which cause flickler, as well as generation of harmonic currents with almost continuous spectrum, whose aimplitude changes with time and phase, are associated to normal furnace operation. Time variations of electrical quantities are due to arc-length fluctuations, which can be cause:d by electromagnetic forces, collapses of metal scraps and electrodes movement activated by regulators.
Where voltage flicker is a problem, or the likelihood of a problem caused by an electric arc furnace addition is high, the solutions are normally difficult andlor expensive. Since the arc furnace constitutes a highly unbalanced load it was better represented in a three phase model contrarily to previous models who worked only with single phase models. Rf I Fig.
Bus 1 is the point of common coupling PCC. T1 is the high voltage-mediu:mvoltage transformer, T2 is the medium voltage-low voltage transformer, with secondary adjustable voltage.
Xlsc is the short-circuit reactance at the PCC, Xp the series reactance inserted for flicker compensation, Xcf, Xlf and Rf are the equivalent capacitance, reactance and resistance of the harmonic filters for distortion compensation, Xc and Rc are reactance and resistance of the connection line between furnace electrodes and T2. The maximum power absorbed by the furnace is 60 MVA. In the first case the arc-length variations are assumed to be sinusoidal, and hence k t is a sinusoid of frequency between 0.
Include is the range where maximum sensitivity of human eye to luminous fluctuations occurs. The second case is a probabilistic model that represents the arc-length variations as band limited white noise. Comparing the results with actual field measurements in steel plants in Northern Italy, the deterministic model sinusoidal variation law provides worst case approlximations which enable determination of maximum flicker sensation [I].
The results of the white noise variation law model, according to the authors, seemed more realistic and closer to the average field measurements. It is also expressed as the change in voltage divide by the voltage AVN. Mathematical relations for Fig. I objectionable i Each utility has its own standard or guideline based on their individual experiences with the voltage flicker phenomena. Factors affecting the determination of a limit for flicker can includle ambient lighting levels, size and type of lamp, room decor, length in time and the abruptness of the voltage variation, and the intensity and immediate occupation of interest of the observer.
Revised and updated curves should be available by For example, incandescent illumination changes more than fluorescent, but fluorescent illumination changes faster than incandescent. It can be noticed that the maximum sensitivity occurs between Hertz. This issue was analyzed by a study that Southern California Edison Company performed in a steel plant from one of their customers. A thorough description of the study and its results and an interesting discussion on the subject are available in reference 7.
Fig IV. Esr are taken fiom experimental data. Ssc: apparent power at bus 2 when furnace is in short circuit conditions. Pst: short term flicker severity AVN. However, to increase the system short-circuit capacity usually is very difficult and expensive. Besides, the Ssc of a an electrical distribution system is not constant, it varies throughout the day depending on the numbers of generating units on line and transmission lines in use.
Nevertheless some viable options can be grouped in this category, for example to feed the arc furnace directly fiom a high voltage line, without an intermediate transformer. Also using a DC arc furnace will reduce the flicker severity for the same given capacity.
It is generally accepted that the voltage fluctuations for DC arc furnaces are approximately one half to one third of that of equivalent AC arc furnaces. However, a DC furnace will be more expensive since it requires an additional high power rectifier circuit. SVCs provide an effective voltage regulation with very quick response times.
Nonetheless they are among the most expensive systems for flicker control and generate the so called pole frequencies that can interact with the system adding another power quality problem, specially if the added signals are near the resonant frequency of the network. The latter can be overcome by means of a filter tuned at the offending frequency. In some cases, depending; on the configuration, the SVC may generate less amount of pole frequencies or frequencies of a higher range that need less filtering.
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Start by pressing the button below! Author: Allan Greenwood. Transients in Power Systems. Read more. Power Systems Electromagnetic Transients Simulation. Power Quality in Electrical Systems. Automation In Electrical Power Systems. Electrical Power Systems. Electrical Power Systems Quality.
Voltage Quality in Electrical Power Systems. Electrical Power Systems and Computers, Volume 3. Computer Modelling of Electrical Power Systems. Fundamentals of Electrical Drives Power Systems. Schaum's Outline of Electrical Power Systems.
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