Analysis and Evaluation of Leakage Inductance in Power

Analysis and Evaluation of Leakage

Inductance in Power System

Transmission Lines

1M.Nithyavelam,

2Dr.Joseph Henry

1Department of Electronics & Communication

Engineering 2Department of Electrical & Electronics Engineering

Veltech University, Avadi

Abstract

Precise prediction of faults are vital in power system

transmission lines and distribution in order to refurbish the

power supply with least disruption rapidly. The vital

parameter that separates the delivery of ideal current and

voltage from the transmission lines to the load is the leakage

inductance due to the magnetic flux linkage present in the

conductors used in the transmission lines. Moreover, the

energy stored in the leakage inductance become the cause for

the formation of voltage spikes which will in turn create

harmonic problems as a result efficiency will be decreased. In

this paper, a 10m, 230kv, 50Hz power transmission line model

was created and then simulated in MATLAB to get fault

current waveforms with the help of synchro-phasor. Fast

Fourier Transform has been extensively used in the analysis of

fault due to the presence of leakage inductance in various types

of conductor arrangements utilized in the transmission lines

and distribution. Employment of FFT makes the fault analysis

especially, for complicated conductor arrangements as feasible.

As a final point the experimental results will endorse the

simulation.

Keywords: Transmission lines, Fast Fourier Transform,

synchro-phasors.

Introduction

International Journal of Pure and Applied MathematicsVolume 114 No. 12 2017, 699-713ISSN: 1311-8080 (printed version); ISSN: 1314-3395 (on-line version)url: http://www.ijpam.euSpecial Issue ijpam.eu

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Transmission lines are the essential parts of power systems. Transmission line series reactance and the shunt susceptance are vital inputs to various power system analysis functions. Exactness of transmission line parameters is therefore vital in guaranteeing the accurateness of acquired analysis results. Exclusively in case of power system protection, various distance relaying algorithms involve line parameters for defining suitable relay settings, manipulating fault distance, and producing a sound tripping decision [1-3].

Electrical energy from power generation unit transfers to domestic distribution system with the help of transmission lines. Different configurations of transmission lines having different phase conductors with shield wires and kilo volt ratings. Every single transmission line revealsvarious electrical properties, where the most prevalent property is inductance. The inductance present in a transmission line depends upon the line configuration itself. Inductance is vital in the making of transmission line models highly present in the power system analysis [4]. Formerly, for the different kinds of transmission line configurations, in order to calculate the inductance, theanalytical method has been habituallyused. The benefits of analytical method isthat it have the ability to clearly define the physical interpretation of inductance in transmission line. But, analytical method is not practical in general, exclusively for complicated conductor. Thus, the utilization of finite element analysis (FEA) method came into existence in order to calculate the inductance of transmission lines in general, deprived of the necessity of various complex calculations [5]. designed within that two different kinds of layers ofdielectric material, same dielectriclayers in which two conductorsare present and three different dielectriclayers in which three conductors are present. The inductance per unit conductorlength of multi-conductor transmission lines are associated whicheach other. Aninverse matrix of a transmission line isobtained from the FEA model is used to calculate the inductance of the line. The resultsobtained for the inductance per unitconductor length by means of this schemeadopt well with valuesintended in the references. Earlier works has considered the flux-linkage methods to determineinductance values of electrical machines from a twodimensional(2D) FEA model [7,8]. The numericalcharacteristics and equivalence of the flux-linkage methods have been established throughscheming of the time-varying inductances of thefield windings of a turbine generator underthe transient conditions. It was found that both methods yieldinductance values that will be acceptable with each other. However, theflux-linkage method utilizes very few computation spaces and thus becomesmore robust than the FEA.Therefore, the flux-linkage method has been suggested asthe preferred method for calculation of 2D inductance ofelectrical machines. Non-uniform transmission line has

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been generally utilized in extraordinary speed circuit systems and exaggerated the circuit performance and also the consistency [9, 10]. Thus the obtained distributed parameter for the non-uniform transmission line is predominantly significant. Lot ofelectromagnetic numerical methods has been widely utilized to resolve this issue such as finite-difference time-domain [11, 12] and moment of method [13, 14]. Though this technique can successfully resolve the inductance matrix of the high voltage transmission line, the analysis method is multifaceted and desires to be resolved a lot of times. Apart from this, anisotropic dielectric have been additionally used for special electromagnetic characteristics [15]. There are many achievements emphasis on the impact on electromagnetic wave radiation, but rare researches emphasis on inductance parameter calculation of non-uniform transmission line in the case of anisotropic dielectric [16].

In this paper, the identification of the leakage inductance due to leakage current present in current carrying conductor arrangements intransmission lines have been experimentedwith the help of magnetic flux.

Designing ofinductance for the multi-conductors transmission lines with the help of finite element analysis method is proposed in the previous work [6]. In this paper, two conductors are

Analysis of Inductance In Various Transmission Lines Configurations

Line inductance plays a dominant role for medium as well as long distance transmission lines. The current that flows along the conductor is completely responsible for the formation of inductance present in the transmission lines. The fact is that the current carrying conductor definitely produce the magnetic field around it. The current that present in the AC transmission line will vary in a sinusoidal manner, such that the magnetic field that is produced by this current will also varysinusoidal. An EMF will be induced in the current carrying conductor due to this time varying magnetic field present in it. Thus the flow of current in the transmission line will be opposed by this produced EMF. Inductance is the parameter that will prominently used to describe this EMF. The comparative arrangement between the magnetic field and the current carrying conductor in transmission lines will predict the inductance value present in it. The description of inductance is shortly given as the total flux linkage divided by the current that flows in that conductor.


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In case of current carrying conductor the flux linkage will occur internally and externally. If the flux linkage will occur on behalf of self-current then it is represented as internal flux linkage and the flux linkage that happens due to external flux is termed as external flux linkage.Thus finally the calculated inductance is represented as total inductance.The term flux linkage is represented by λ. Inductance is represented the symbol L which is measured in Henry(H) Manufactures generally postulate inductance value as per kilometer or mile. Assumptions for the transmission lines inductance calculation is given as follows:

a) The transmission line should have uniform cross-section.

b) The charge densities and current that present along the transmission lines should be uniform throughout the length.

c) Conductivity, permeability andpermittivityshould be constant through the entire length of the conductor.

The single phase transmission line inductance is given as follows:

Where

=Magnetic flux-linkagepresent in between the two points p1 and p2correspondingly.

Fig.1. (a) Current-carrying conductor perpendicular to the plane,

(b) Single-phase transmission lines and

(c) Three phase-transmission line.


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A single phase two-wire conductor having radius r having current, I2

and charge q2 and then the return current –I1and charge –q1, which is separated by thedistance, D is shown in Fig. 1(b). The inductance, L per phase per unit length[17-19]are estimated using

Figure 1(c) shows the three-phase transmission lines. The inductance, L/phase per unit length is calculated as

Where

a, b, c = Three conductors with phases a, b, c respectively.

r = radius of the conductor

Dab, Dac and Dbc= Distance between two conductors

Figure 2 shows the three-phase double circuit lines. Each conductor carriesthe current with relative phase position of a1b1c1-c2b2a2. The inductance, L/phase unit length for this transmission lines are defined as


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Fig.2. Three-phase double-circuit lines; (a) a transmission line tower and (b) model of the conductors

Having flux-linkage as reference, it is concluded that the inductance is maximum when the distance present between two points which is external to the conductor is higher. Since the inductance is completely depending upon the flux linkage that present between two points, it is clear that the distance is directly proportional to the inductance between two points. The High voltage transmission lines, uses two and more current carrying conductors that are bundled together in order to approximate a large diameter conductor, and thus reduce corona loss.

Methodology

A. Synchro-phasors:

The time-synchronized number representation of both magnitude and phase angle of the sine waves that are found in AC transmission lines are term as synchrophasors. It is time synchronized in order to get accuracy.


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Fig.3Synchrophasor Measurements

In electric power system the voltage and current signals are virtually sin waveforms during steady state. A vector that consists of magnitude and angle with respect to a sine waveform at the given frequency is termed as phasor. Fourier transform extracts the phasor of the sinusoidal waveform with the help of data samples of the signal that have been present within a selected time window. The magnitude is constant for a steady state signal. But the value of the angle entirely depends upon the starting point of the samples.Here the relative quantity is the angle and anideal reference needs to be selected. Measurements are taken from different lengths from the transmission lines present in the power grid in order to identify accurate voltage and current waveforms, through which phasors can be easily calculated.Figure 2 illustrates the synchro-phasor measurements.

B. Method to identify leakage inductance through synchrophasors :

Fig.4 Block diagram for identification leakage inductance through synchro-phasors


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For extracting existing voltage and current waveforms form the transmission lines at a specified location, DAQ B-Class Amplifier is utilized.DAQ B-Class Amplifier comprises sensors, a DAQ measurement hardware, and then a computer with programmable software. When comparingwith the old-fashioned measurement systems, PC-based DAQ systems provides low processing power, high productivity, clear display, and accurate connectivity capabilities for industry-standard computers such that it provides highly powerful, supple, and low-cost measurement solution. The current and voltage signals are obtained by DAQ B-Class Amplifier, from the distributed transmission lines. Since the signals from the transmission lines are noisy, the DAQ consists of Signal conditioning circuit that will employ the obtained signals in a form that will be suitable for input to an Analog-to-Digital Converter (ADC). The ADC converts the signals from the DAQ to the appropriate digital signal. After that the obtained digital signal is processed by the computer.

At a pre-defined rate, the Analog-to-Digital converter takes periodic “samples” of the signal from the continuous analog signal which always vary with time. These samples are transferred to a computer, in which the original signal is constructed again from the samples.

Since the digitized current and voltage signals obtained from the DAQ amplifier consists of DC offset, it has to be removed completely in order to get the precise output. DC offset illustrated in figure.5 is a fault that suddenly happens in the current and voltage signals directly obtained from Transmission lines, which is nothing but the sine wave suddenly becomes asymmetrical, and after a few cycles returns to normal (symmetrical). This fault will be reflected in the digitized current and voltage signals obtained from the DAQ amplifier. DC offset removal block, removes the DC offset present in the digitized current and voltage signals obtained from DAQ.

Fig.5 DC Offest Error


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After removal of DC offset, the obtained signals are subjected to an efficient algorithm named Fast FourierTransform(FFT). Since, the frequency of the obtained current and voltage signals can be recognized and categorized with the help of Fast Fourier transform (FFT). Thus the phase of the obtained current and voltage signals can be calculated precisely.Thus the phase of the ideal signal will be calculated precisely and then it is compared with the phase of the signal in which inductance fault is induced. This is done for various types of inductance values and the results are obtained. From the results it is clear that the minimum and the maximum phase angle for the inductance fault present in the transmission lines can be calculated precisely.

Dentification of Leakage Inductance In Transmission Lines

To identify the presence of leakage inductance in transmission lines the experimental setup of transmission lines having 10m length connecting 230Kv, 50Hz source with the load which is connected at the other end. At the receiving end, the load should get the ideal signal having 230Kv, 50Hz signal. Figure 6 shows the 230Kv, 50Hz ideal signal. The signal with induced inductance fault is shown in figure 7. From fig.6 and fig.7 it is clear that during inductance fault condition there will be no useful signal at the center.

Fig.6230Kv,50HzIdeal Signal


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Fig.7 1mH Leakage Inductance induced in the 230Kv,50HzIdeal Signal of Transmission lines

During ideal condition, the signal generated in the source (230Kv) must be delivered to the load. While comparing the flux produced by the two ideal signal, the obtained flux phase difference between the two ideal signal is 0 deg. Figure 8 illustrates that the flux phase difference between two ideal signal as 0 deg.

When an induced 1mH inductance is present in the transmission lines then in that case the phase shift between the ideal signal and the 1mH induced inductance fault is given in the figure 9.

Fig.8Phase shift between two ideal sgnals

Fig.9 Flux Phase shift between ideal signal and the signal with induced 1mH inductance fault

The normalized FFT for the ideal signal 230Kv,50Hz signal is given in the figure 10 and the normalized FFT for the 10m current


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carrying conductor having 1mH induced inductance fault is given in the figure 11.

Fig.10 FFT for 230Kv,50Hz ideal signal

Fig.11 FFT forsignal with induced 1mH Inductance Fault

The differentiated ideal signal 230Kv,50Hz is given in the figure 12 and the differentiated 1mH induced inductance fault is given in the

figure 13. TABLE I

Results of fault location technique using phase difference between the signals

Type of fault

Leakage Inductance

Calculated faulty flux difference

Percentage Error

for 10 m Transmission Line within 60

sec

Leakage Inductance

1mH 141.26930 11.20

3mH 147.4320 11.76

6mH 154.9060 12.47

9mH 159.3320 12.94

12mH 162.2010 13.34

15mH 160.2210 13.07

18mH 174.3250 13.44


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21mH 177.3350 13.91

27mH 181.9540 14.34

30mH 187.1460 14.782

The inductance fault is created in the transmission lines prototype from the minimum of 1 mH per 60 sec to the maximum threshold of 30mH per sec. From the table I it is clear that when the leakage inductance rate is as 1 per 2 seconds, then the percentage error is increased. This shows that the fault due to leakage inductance present in transmission line conductorswill be clearly identified, and also initial state of fault is also can easily be detected using this flux phase difference method.141 When the flux phase difference between the ideal signal which is 230V, 50Hz signal, and the signal consists of leakage inductance faults is varied between 1410 to 1870. The presence of leakage inductance will create approximately 13.125% error in the transmission line conductors.

TABLE III

Signal Parameters

Ideal Signal (230v,50hz)

Signal With 1mH Leakage

Inductance/10m

Signal With 30mH Leakage Inductance/10

m SNR 37.636 db 46.2636 db 49.5956 db Mean 0.869734 474.769 489.358 Crest factor 228.618 1.026 1.0215 Skewness -48.8447 -0.0635 -0.06324 Kurtosis 10349.2 5.1588 0.5452827 THD 7.06142% 40.7197 % 27.3562% Weighted Mean

5(at 20.182sec)

32740 (at 30.287sec)

32767(at 30.018sec)

Zero-crossing rate

1050.69 148.299 100.083

TABLE IV

Harmonics present in the voltage due to 1mH leakage inductance in 10m transmission lines from distributor to the load

No. Frequency(Hz) Harmonics

1 1000 5.6486 2 2000 -8.1691 3 3000 -12.709 4 4000 7.8267 5 5000 -9.0509


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6 6000 17.863 7 7000 -1.7485 8 8000 -15.662 9 9000 -1.687

10 10000 -3.833

This could be tested for every 1-meter distance in the 10m long transmission lines connected from the distributor to the load. If at any point the flux phase difference between the transmission lines distribution and the actual flux present in the lines are between 1410 to 1870, then the fault present in the particular location is identified as theinductance fault and the value of flux phase difference will provide the intensity of leakage inductance present in the given transmission lines. Once the obtained fault is decided as a inductance fault with the help of the flux phase difference then it is necessary to locate the position as well as eradication is also a vital progress in the development of error-free transmission lines. It is achieved by obtaining the detailed characteristics of the fault present in the transmission lines. Thus the complete characteristics of 1 mH leakage inductance per second are given with the comparison of an ideal signal is given in table II. The harmonics present in the transmission lines are illustrated in the table IV.

Conclusion

The emerging route in transmission line's quality monitoring lies in real-time detection and management. Researchers have paid supplementary consideration on researching detection and management of Transmission lines quality. This article remarks a method for finding transient faults in transmission lines based on fast Fourier transformation. It can be active on de-noise, the recognition of disturbance's start time, amplitude, and frequency. A widely suitable, low-cost, as well as an exact procedure for transmission-line checking was estimated and established in this paper. This technique takes the ideal signal as the reference and compared it with the induced transient faults present in the transmission lines. It is tested for various cases and finally comes to a conclusion that if the flux phase difference is nearly 164.64deg in average then the error present in transmission lines are due to leakage inductance. The phase comparison is achieved with the help of fast Fourier transform. The DAQ B-Class Amplifier utilized in this method makes this technique as achievable and practical. With the help of DC offset removalblock, DC offset problem in more complicated situations with multiple transmission lines are solved successfully. As such, this witnessing


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skill has the excessive perspective to augment situational consciousness, authorize dynamic line evaluation, and understand advanced system measurement of the future smart grid.

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Analysis and Evaluation of Leakage Inductance in Power