A Novel Method for Ultra-HighFrequency Pd Loc in Power Tf Using Particle Swarm Opt Algo

26 IEEE Electrical Insulation Magazine

F E A T U R E A R T I C L E

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This article describes a method of lo-cating a PD source within a power transformer by measurement of ul-tra-high-frequency electromagnetic waves with receiving antennas in the transformer and using a localization method based on the particle swarm optimization algorithm.

A Novel Method for Ultra-High-Frequency Partial Discharge Localization in Power Transformers Using the Particle Swarm Optimization AlgorithmKey words: transformer, partial discharge, ultra-high frequency, localization

Hasan Reza MirzaeiK. N. Toosi University of Technology, Tehran, Iran

Asghar AkbariK. N. Toosi University of Technology, Tehran, Iran, and Leibniz Universität Hannover, Hanover, Germany

Ernst GockenbachLeibniz Universität Hannover, Hanover, Germany

Mojtaba ZanjaniK. N. Toosi University of Technology, Tehran, Iran

Karim MiralikhaniIran Transfo Co., Zanjan, Iran

IntroductionNowadays, the localization of partial discharge (PD) in pow-

er transformers by measurement of ultra-high-frequency (UHF) electromagnetic (EM) waves from a PD source is receiving more attention. This method is based on comparing the differences in the arrival times, to antennas in the transformer, of EM waves emitted from the PD source. From the measured UHF signal, and factoring in the influence of the transformer active part on the EM wave propagation, the correct determination of an EM wave arrival time in the localization algorithm is a critical task that influences the accuracy of the UHF PD localization method.

Nearly all weak points in the dielectric system of power transformers generate PD. These discharges gradually degrade the insulation, leading to transformer failure. It is possible to detect these defects in the early stages of PD generation by mea-suring and analyzing the PD data. Suitable maintenance and re-pair strategies can then be implemented.

Accurate PD localization is very important for both power grid management companies and transformer manufacturers. In this way, they can recognize the severity of the damages and reduce the time and cost of the reparation. Several methods have been used for PD localization, including electrical modeling

March/April — Vol. 29, No. 2 27

of the transformer winding, acoustic method, and the UHF de-tection method. The electrical method is sensitive to weak PD activities, but it can only predict the turn number in which PD occurs and perform 1-D localization [1]–[5]. Using the acous-tic method, 3-D localization is possible; however, this method has less sensitivity to weak PDs and those that occur inside the winding [6]–[8]. However, the UHF PD detection method is sen-sitive to weak PDs and those that are inside the winding. It also helps to predict the PD location in 3-D coordinates [6], [9]–[12]. These advantages have directed many research projects to im-prove the UHF PD detection and localization in power trans-formers [13]–[21].

In the UHF localization method, the differences between the delay times of the EM wave reaching antennas within the trans-former are used to locate the source of the PD [7], [9], [19]. But one must take into account the effects of the physical size and position of the active part of the transformer in the EM wave propagation. Because of the different characteristics of the vari-ous materials used in the transformer, such as dielectric constant and losses, EM waves will suffer different time delays and atten-uation while propagating through these materials. In [19], none of these effects was used in the method adopted for UHF PD localization. In [9], only the effects of the materials in the time delay of the EM wave were considered in the PD localization.

In this article, a new method is introduced to calculate the time delay in the transmission of the EM wave from the PD lo-cation to the detecting antennas. Here, the different velocities and attenuations of the various materials inside the transformer are taken into account. The resultant time delays are utilized in a localization method that is based on the particle swarm opti-mization (PSO) algorithm. Furthermore, a new method for auto-matically calculating the arrival time of the EM waves measured by UHF antennas is introduced.

The Effects of the Active Part on the EM Wave Propagation

To study the effects of the winding and insulation materials within a transformer, or the active part, a simplified model of a power transformer was simulated by the CST Microwave Studio software (Figure 1). This software package uses the finite in-tegration technique, which can numerically simulate EM wave propagation. Because of computer memory and processor limi-tations, and for the purpose of simplifying the simulation, only one phase of a transformer and its related core and winding was included in the model.

The simulated HV winding consists of 80 disks, each disk is 10-mm high and there are 5-mm gaps between the disks for radial oil ventilating, and is positioned within a transformer tank filled with oil of relative permittivity 2.33. A short dipole antenna with a Gaussian excitation current signal in the UHF frequency range (0.3 to 3 GHz) was used to simulate the PD source. At the inner surface of the transformer tank, probes to monitor electric fields in various positions were considered in the analysis.

The UHF EM waves radiated from the PD source are trans-mitted through the radial oil gaps of the HV winding. To illus-

trate the technique, consider a PD source within the winding as shown in Figure 2. The shortest path for an EM wave from the source to reach probe #3 may be the one shown in Figure 2. Simulations of the arrival times of the EM waves reaching probe #3, with the winding in place and without the winding, show that the difference is equal to the difference between the transmis-sion times calculated using the lengths of the direct path and the path shown in Figure 2, both divided by the velocity of the EM waves in the oil.

Figure 1. Simulation of the active part of the transformer in CST Microwave Studio software.

Figure 2. The shortest transmission route of the electromagnetic wave from partial discharge (PD) source to probe #3.


For PDs within the winding, the peak signal value, the en-ergy, and the arrival time of the decoupled UHF waves depend on the spacing of the radial oil gaps, the thickness of the paper around the conductors, the distance between the PD source and the probes, and their relative positions.

In actual power transformers, the thickness of the turn insula-tion is usually negligible compared to the conductor height and the radial gaps between HV winding disks. To investigate the effect of the paper, simulations were performed with no paper and with paper of 1- and 2-mm thicknesses, and these results are shown in Figure 3. It is seen that the paper insulation shows insignificant effects on the arrival times and on the peak values of the UHF EM waves. Therefore, the paper insulation in the HV winding can be eliminated in the simulation without influencing the accuracy. In this way, the computational time for the simula-tions is reduced.

Because the energy of the radiated wave from an aperture in a metallic object depends on its wavelength, a large gap will less attenuate the low frequency (short wavelength) waves trans-mitted through the winding. Figure 4 shows the peak values of the electric field at the probes for various gap sizes in an actual transformer winding. One can see that by increasing the gap size, the peak values of the signals also increase. Figure 4 also shows the peak values of the electric fields at the probes when no winding is included in the model. These values, shown by horizontal lines, can be used to calculate the attenuation of the EM waves while propagating through the HV winding.

Although the attenuation of the UHF waves depends on the relative positions of the PD source and the detecting antennas, the polarization of the PD current, the polarization of the detect-ing antennas, and the gap size, as a rule of thumb, the attenuation in a disk-type HV winding is nearly one-half of its value when

Figure 3. The electric field measured by probe #3 in Figure 2 for 2-mm-thick paper insulation (blue), 1-mm-thick paper insulation (red), and without paper insulation (black).

Figure 4. Peak values of the electric field at the probes as a function of radial oil gap size, with and without the winding.


no winding is present. Similar experimentally obtained results are reported in [10].

Layer-type windings are very common in low-voltage and regulating windings of the transformers. In windings of this type, usually there are no radial oil gaps, and the only way for EM waves to propagate through the winding is through the apertures between adjacent layers created by the thickness of the paper insulation on adjacent turns. Because of the small dimensions of these apertures, the magnitude of the transmitted EM energy is very low compared with EM energy from the HV winding. The simulations indicate that the peak value of the EM wave propagating through a layer winding is reduced to an average of 1/15th of the peak value when no winding is present in the EM wave propagation path.

The cylindrical presspahn paper insulation sheets that are used between the windings present another obstacle to UHF wave propagation within the transformer. Simulation results for various sheet thicknesses indicate a very low attenuation and time delay for EM waves propagating through them. Therefore, the presence of these sheets can be neglected.

Calculation of the Arrival TimeEstimating the arrival time of the EM waves detected by the

antennas plays a very crucial role in the UHF localization meth-od, and the accurate estimation of the arrival times determines the accuracy of the localization. Up to now, different methods such as the cumulative energy method [9], the energy criterion method [8], and the threshold method [20], [21] have been used to measure the arrival times.

Cumulative Energy MethodIn the cumulative energy method, the voltage signal is con-

verted into the energy signal using Equation (1), whereby the start of its knee point is assumed to be the start point of the PD signal:

E m vi

i

m

( ) ,==∑ 2

1 (1)

where vi is the ith sample of the UHF signal. As illustrated in Figure 5, the knee point of the energy signal (red in the figure) is considered to be the time epoch when the background noise gives way to the signal. However, in cases where the delayed transmitted EM energy from the reflections or other longer par-allel routes is higher than the energy transmitted by the short-est route in the beginning of the signal, the cumulative energy method may not result in a clearly recognizable knee point. An example of such a case is shown in Figure 6.

Energy Criterion MethodIn the energy criterion method, the time point related to the

minimum of the signal defined by Equations (2) and (3) is taken as the starting point of the UHF signal.

S m v mi

i

m

( ) = −=∑ 2

1

δ

(2)

δ = =∑vN

ii

N2

1

(3)

Here, N is the total number of samples. A successful case of applying this method is shown in Figure 7. But as illustrated in Figure 8, in cases where the transmitted EM energy due to reflections is higher than the energy transmitted by the shortest route, this method may fail to correctly determine the beginning of the UHF signal.

Average Time Window Threshold MethodIn the threshold method, the first point that the absolute or

squared value of the UHF signal exceeds a predefined thresh-

Figure 5. Determining the arrival time of the ultra-high-frequency signal (blue) using the cumula-tive energy signal (red).


old level is assumed to be the start of the signal. This method is easily automated, but precautions must be taken to assign a proper threshold level. In the case of background noise having a magnitude above the threshold level, this method will yield er-roneous results; thus, before applying this method, the UHF sig-nal must be denoised. Denoising methods might be complicated and might introduce errors into the calculated arrival times [20], [21]. To overcome this problem, here a new method called the average time window threshold method is used. In this method, the average of the signal v over a shifting window on the time axis is used to generate a signal as follows:

T m w v m wi

i m w

m

( ) , ,= ≥= − +∑1

1 (4)

where w is the width of the time window. The value of w is determined by the frequency spectrum of the UHF signal using Equations (5) and (6):

w fd=12 ,

(5)

ff V f

V fd

i ii

N

ii

N=⋅

=

=

∑

∑

( )

( )

,1

1

(6)

Figure 6. Cumulative energy method (red) clearly does not show a recognizable knee point for the determination of the ultra-high-frequency signal (blue) arrival time.

Figure 7. Determining the arrival time of the ultra-high-frequency signal (blue) using the energy criterion signal (red).


where fd is the average frequency of the UHF signal calculated using its frequency spectrum V(f). Figure 9 is used to explain the method whereby a single frequency sine wave signal of pe-riod 1/fd is converted into a step-like signal using the average time window threshold method. The method eliminates the os-cillations, and thus the start time of the signal is clearly recog-nizable. In the case of a pure sine wave, a wide window width will result in less slope of the resultant step signal, which is not desirable and will cause errors in finding the start of the UHF signal. But, if the window width is selected to be less than the value defined by Equation (5), the oscillations will not be elimi-nated effectively.

Figure 10 illustrates the determination of the beginning of a sine wave, with a low signal-to-noise ratio, using the average time window threshold method. Although the start time of the

sine wave is not easy to determine, using its average time win-dow signal helps in the accurate accomplishment of the task. Under noisy conditions, averaging removes the zero mean white noise from the UHF signal. Although a wider window width will remove white background noises more effectively, it may impair the slope of the resultant step-like signal. Figure 11 depicts the calculation of the arrival time of a UHF PD signal using the method.

PD Localization MethodTo obtain accurate localization of the PD source using arrival

time of EM waves, the effects of the active part of the trans-former, i.e., the winding, core, and so on, on the propagation of EM waves within the transformer must be factored into the

Figure 8. An incorrect case of determining the arrival time of the ultra-high-frequency signal (blue) using the energy criterion signal (red).

Figure 9. Determining the arrival time of a sine wave (blue) using the average time window thresh-old signal (red).


PD localization method. It is well known that EM waves can-not penetrate metallic conductors such as iron core and copper. Likewise, the velocities of EM waves in different materials have to be considered while computing the time delays. Because the arrival times of the EM waves at the antennas are utilized for the estimation of the PD location, it is sufficient to find the shortest route from the PD source to the antenna location in which suf-ficient energy is transmitted to be detected effectively.

The attenuation of the EM waves of the materials must be considered while finding the shortest route. The short routes, which cannot transmit EM energy greater than the energy of the background noise, cannot be considered as the valid answers. Such short routes will give too low signal-to-noise ratio at the

beginning of the UHF signal to be detectable by the antenna and used for calculating the arrival time of the EM wave.

To create a numerical model of the transformer, its inner vol-ume is meshed with dl = 10 mm. Therefore, each point in the transformer with coordinates x = i × dl, y = j × dl, and z = k × dl can be represented by a node that is presented by discrete numbers (i, j, k). For each node, two parameters, the velocity factor and the relative propagation factor, are defined, which depend on the material used at that location inside the trans-former. Including the velocity and relative propagation factors of all nodes in two separate 3-D matrices, the internal structure of the transformer could be fully represented concerning EM wave propagation. The velocity factor of node (i, j, k) is computed by

Figure 10. Determining the arrival time of a sine wave (blue) with very low signal-to-noise ratio using the average time window signal (red).

Figure 11. Determining the arrival time of the ultra-high-frequency partial discarge signal (blue) using the average time window signal (red).


dividing the velocity of the EM wave in the material used at that node by its velocity in the oil.

The relative propagation factor, which is an index of the abil-ity of the materials in transmitting EM wave energy, is defined as inversely proportional to the attenuation of the material used at node (i, j, k). Because oil occupies most of the transformer tank volume and the great portion of the EM wave propagation path is in the oil, it is assumed that the relative propagation factor of the oil is one. As was shown in previous sections, if obstacles such as winding or presspahn paper insulation sheets do exist in the EM wave propagation path, the attenuation of the EM wave will be more than the case in which the whole of the propaga-tion path is in the oil. This suggests that the relative propagation factors of the other materials must be less than one. Due to the fact that EM waves cannot be transmitted through conductors, the relative propagation factors of the iron core and copper disks are set to zero. Also as indicated previously, the radial oil gaps and apertures allow the EM energy to be transmitted through the windings. Therefore, if w is the oil gap width (also the width of the winding), the relative propagation factor of the nodes situ-ated at the oil gaps are calculated as follows:

gappropagation factor

winding attenuation=

1w dl .

(7)

Finding the Shortest RouteA route is a sequence of nodes with a previously determined

start node, that is a PD position represented by node (iPD, jPD, kPD), and the end node where the antenna is installed and is rep-resented by node (iant, jant, kant). The principle of finding the valid shortest route is to move from the start node to the end node regarding the limitations stated above. Thus, starting from the first node, the nodes of the route must be selected one by one in a sequence to reach to the end node. During the movement from one node to the next, one of its suitable neighbor nodes must be selected. As stated in [9], to reduce the space discretization error, searches for a suitable node to move to are performed up to two nodes away. So, there will be 124 neighbor nodes as illustrated in Figure 12 in which, regarding the symmetry, only one-eighth of the search space is shown. The motion from one node to the next is allowed to be in diagonal directions as well as directions parallel to the axis coordinates.

The probability of neighbor nodes of the node (im, jm, km) within a route to be chosen as the (m + 1)th node is calculated as follows:

p n c n n n( ) ( ) ( ), ,= × ≤ ≤desireα 1 124 (8)

c ni j ki j kn n n

n n n( )

( , , )( , , )

,=≠=

1 00 0

propprop

(9)

where prop is the 3-D relative propagation matrix, (in, jn, kn) is the nth neighbor node, desire(n) is the nth neighbor node desir-ability, and α is the emphasis power of desirability. The desir-ability of the nth node is defined as follows:

desire

ant

antn

dir n dirdir n dir

( ) =

⋅

⋅+

� ��

� �� ( )( )

,

1

200 1≤ ( ) ≤desire n

(10)

where

dir ni i a j j a k k ai in m x n m y n m z

n m

� ��

( )( ) ( ) ( )( ) (

=− + − + −− +2 jj j k kn m n m− + −) ( )2 2

(11)

and

diri i a j j a k k am x m y m z

antant ant ant

� ��

=− + − + −( ) ( ) ( )(ii i j j k km m mant ant ant− + − + −) ( ) ( )

.2 2 2

(12)

The dir(n) is the unit vector from the mth node in the route to its nth neighbor and dirant is the unit vector from mth node to-ward the antenna. In (8), c(n) does not allow the motion through core and conductors and desireα(n) makes the overall direction of the motion toward the antenna position.

In this way, by selecting the nodes one by one, an initial route will be formed. The red route in Figure 13 demonstrates an ex-ample of a route in its initial stage. Because of the probabilistic selection of the nodes, the route has a zigzag form and does not represent the shortest possible route. This results from the flex-ibility taken to search the space for better routes. Choosing large values for α makes the route straighter, whereas smaller values

Figure 12. The schematic of one-eighth of the neighbor nodes (blue dots) to be selected as the next node in completing a route [9].


give the opportunity to explore the ambient more flexibly. At first, the value of α is chosen to be one and then, during the opti-mization of the route, it is increased.

Optimizing a route will make it shorter and straighter and si-multaneously, provides the ability to transfer sufficient amounts of the EM energy. To do this, the cost function of a route is defined as follows:

route_cost

time_delaypropagation_index

= β ,

(13)

where

time_delay

vel

=

− + − + −− − −

=

( ) ( ) ( )( , , )

i i j j k ki j k

m m m m m m

m m mm

12

12

12

22

l

∑

(14)

and

propagation_index prop

propagation_index

=

< ≤=∏ ( , , ),i j km m mm

l

1

0 11.

(15)

In the above equations, time_delay is the total time delay for the EM wave to propagate along the route, propagation_index is the ultimate propagation factor of the route, l is the length of the route, vel is the 3-D velocity matrix, and the (im, jm, km) are the coordinates of the route nodes. Minimizing the route_cost during the optimization will decrease the time delay of the route (decrease route length) and increase its ultimate propagation fac-tor. The positive parameter β is the power of ultimate propaga-tion factor, and its value, which is less than one, depends on the background noise level and the threshold factor in the automatic arrival time determination. Because the ultimate propagation factor of the route determines the energy of the initial part of the EM waves reaching the antenna, and because this part is used to calculate the arrival time of the wave, the less the background noise and the threshold levels are, the greater the value of β will be. An increase in the value of β will intensify the influence of ultimate propagation factor in route_cost.

In the optimization process, two nodes of the route are se-lected at random, and a new subroute between these two nodes is calculated with the help of the above-mentioned process, with larger α in (8). This subroute will be replaced with the relevant subroute of the original route to make a new one. Then, the cost of the new route will be calculated again. If it is decreased, the adjustment will be accepted; otherwise it will be discarded. This

Figure 13. Route from a possible partial discharge location to the antenna in its initial stage (red route) and after optimization (blue route).


procedure is iterated until the variation of the route cost falls below a predefined value. The blue route shown in Figure 13 is the optimization result of the red route.

This procedure will be performed for each antenna to obtain the routes with the lowest time delays and the greatest ultimate propagation factor (Figure 14). Afterward, the differences of arrival times of EM waves at the antennas are computed. For example, if antenna #1 is assigned as the reference antenna, the time differences of Δt12, Δt13, and Δt14 are time delay characteris-tics of that possible PD location.

PSO Algorithm for PD LocalizationTo find the PD location, the global best particle swarm opti-

mization algorithm is used. In the PSO localization algorithm, particles that are possible PD locations move in the inner space of the transformer to find the real PD location. In this work, so-cial-only model PSO is adopted in which particles update their locations toward the best particle of the entire swarm with mini-mum cost [22]. The cost function of each particle is the Euclide-an distance between the measured time delays and the calculated time delay characteristics assigned to each particle:

cost( )

( ) ( ) ( ) ,

P

t t t t t tim P m P m Pi i i

=

− + − + −∆ ∆ ∆ ∆ ∆ ∆12 122

13 132

14 142

(16)

where the superscripts Pi and m refer to the ith particle and the measured time differences, respectively. The initial positions of particles in the search space are important in decreasing the time needed to solve the problem. To have a more effective initial guess, the inner space of the transformer is divided into cubes with side lengths equal to, for example, 50 cm. A point inside each cube that is not in the core or windings space is selected and treated as a possible PD location. Then, to reduce the time of the analysis, a rough estimate of the related time delay char-acteristics of these points is made by dividing their distances to the antennas to the velocity of the EM wave in the oil, ignoring the presence of core and windings. Next, the cost of each point is computed, and only the top Np points are kept as the initial particles, where Np is the swarm size. After that, the exact time delay characteristics of the initial particles are calculated using the algorithm described in previous section, and then the particle with the lowest cost is selected as the global best particle.

The velocity equation to adjust the location of the ith particle is computed as follows:

v Pi i a j j a k k a

iP x P y P zi i i

��

( )( ) ( ) ( )

=− + − + −gbest gbest gbest

��

( ) ( ) ( ),

i i j j k kP P Pi i igbest gbest gbest− + − + −2 2 2

(17)

Figure 14. The shortest routes from a possible partial discharge location to the detecting antennas.


Figure 15. The electric field at probes for a possible partial discharge source at x, y, z coordinates 391 cm, 247 cm, 248 cm; (a) probe #1, (b) probe #2, (c) probe # 3, and (d) probe #4.


where (igbest, jgbest, kgbest) are the coordinates of the global best

particle and ( , , )i j kP P Pi i i are the coordinates of ith particle. The

particle moves from its current position according to (8), (10), (11), and (17). The motion length of the ith particle is:

l P KP

P

i i

ii

i

Pi

( )( ) ( )

( )

( )

=−

−

cost cost gbestcost

gbest× 22 2 2+ − + −( ) ( ) ,j j k kP Pi igbest gbest

(18)

where cost(Pi) and cost(gbest) are the costs of the ith particle and global best particle, respectively, and K is a positive factor with a value less than one. To prevent the very fast or very slow motion of the particle, its motion length is limited to a maximum and minimum range. These limits are imposed because of the fact that, on one hand, a very long motion length of the particle impairs the effective search of the space, and on the other, a very short motion length slows down the convergence of the particles.

While the other particles change their locations toward the best particle, the points around the global best particle are exam-ined for better solutions to force the algorithm to explore a wider area. The best particle will be replaced if a point with a lower cost is found. After adjusting the particle positions, their cost is computed again and the best particle is selected. This process is iterated either until the cost function of the best particle falls be-low a predefined error criterion or until the number of iterations exceeds the maximum allowed.

ResultsIn this section, the accuracy of the proposed method in locat-

ing the PD site is validated. For this study, the finite difference time domain algorithm is used on a three-phase 420/15.75-kV, 200-MVA power transformer with a 710 cm × 268 cm × 414 cm tank. A short dipole antenna with a UHF Gaussian excitation signal is placed in a supposed PD location. Then, the EM wave propagation inside the transformer is simulated and recorded at four probe positions, which are placed at the positions of the detecting antennas. Typical positions for the antennas are listed in Table 1. Figure 15 shows the electric field signals recorded by probes for a supposed PD location at x, y, z coordinates 391 cm, 247 cm, 248 cm.

After calculating the arrival times of the signals at the probes using the average time window threshold method, the resultant time differences are applied to the PSO localization method. In

this way, the accuracy of the time window threshold method in determining the arrival times of the UHF signals and the accura-cy of the PSO localization algorithm are investigated simultane-ously. This validation process is repeated for three other potential PD locations inside the transformer. Table 2 shows the results of the proposed PD localization method for four potential PD sites. These results demonstrate a highly accurate PD localization. The maximum error is 17.2 cm, which is considered a favorable result considering the size of the simulated transformer.

ConclusionsSimulation results show that EM waves can penetrate through

windings, pressboards, and other insulations inside a transform-er, ensuing extra attenuation and time delays with respect to propagation in the oil. The amount of the time delay and the attenuation of the various materials are extracted by the applica-tion of the simulation results in the CST Microwave Studio soft-ware. These effects are included in a newly developed method for computing the arrival time of EM waves from a PD source to the antennas. Furthermore, a PSO algorithm is introduced for PD localization in which the computed arrival times of possible PD positions are compared with measured ones. A new method for the automatic calculation of the arrival times of the measured UHF signals by the antennas is also developed.

The validity of the localization method is investigated by us-ing the finite difference time domain simulations of EM wave’s propagation inside an actual power transformer. The obtained results confirm the reasonable and convenient accuracy of the proposed localization method.

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Table 2. Coordinates of the Potential Partial Discharge (PD) Locations and the Estimated Locations Using the Proposed Localization Method.

Potential PD site

PD x, y, z coordinates (cm)

Estimated x, y, z coordinates (cm)

Error (cm)

PD #1 (231, 31, 227) (230, 36, 226) 5.2

PD #2 (391, 247, 342) (389, 239, 345) 8.8

PD #3 (391, 247, 248) (391, 252, 261) 13.9

PD #4 (580, 31, 87) (582, 33, 104) 17.2

Table 1. Coordinates of the Antenna Positions.

Probe index x, y, z Probe coordinates (cm)

Probe #1 (5, 5, 410)

Probe #2 (705, 5, 50)

Probe #3 (705, 263, 410)

Probe #4 (5, 263, 50)


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Hasan Reza Mirzaei was born in Zanjan, Iran, in 1983. He received his BSc degree in electrical engineering in 2005 from Za-njan University, Zanjan, Iran, and MSc de-gree in 2008 from K.N. Toosi University of Technology, Tehran, Iran. Since September 2008, he has been studying for the PhD de-gree at K.N. Toosi University of Technol-ogy. His research interests include power

transformers monitoring such as PD localization, PD classifica-tion, and frequency response analysis.

Asghar Akbari was born in 1962 in Iran. He received his BSc degree in 1988 from Tehran University, his MSc degree in 1991 from Amirkabir University, and PhD de-gree in 1998 from Tarbiat Modarres Uni-versity, Tehran, Iran, all in electrical en-gineering. Since 1998, he has worked as a lecturer and a member of the academic staff of K.N. Toosi University of Technol-

ogy, Tehran, Iran. From April 2000 to February 2002, he worked as a guest scientist (postdoctoral fellow of the Alexander von Humboldt Foundation of Germany) for the Schering Institute of High Voltage Techniques and Engineering at the Leibniz Uni-versity of Hanover, Germany. His main research interests are monitoring and diagnostics of HV apparatus, partial discharges, modeling, and computer applications in power systems. While he is an associate professor for HV engineering and power sys-tems at K.N. Toosi University of Technology, Tehran, Iran, pres-ently he is a guest scientist at the Leibniz Universität Hannover, Germany.

Ernst Gockenbach is professor of HV en-gineering and director of the Schering-In-stitute at the Leibniz Universität Hannover. From 1979 to 1982 he worked at the High Voltage Test Laboratory of the Switchgear Factory, Siemens AG, Berlin, Germany, and was responsible for the High Voltage Outdoor Test Field. From 1982 to 1990, he worked with E. Haefely AG in Basel,

Switzerland, as chief engineer for HV test equipment. He is a member of VDE, CIGRE, and IEEE (Fellow), former chairman of CIGRE Study Committee D1 Materials and Emerging Test Techniques, chairman of IEC TC 42 High voltage and high cur-rent test technique, and a member of national and international Working Groups (IEC, CIGRE) for Standardization of High Voltage Test and Measuring Procedures.


Mojtaba Zanjani was born in 1987 in Iran. He received the BSc degrees in electrical engineering in 2010 from Birjand Univer-sity, Birjand, Iran. He has been studying for the MSc degree from September 2011 at K.N. Toosi University of Technology. His research interests include monitoring and diagnostics of transformers, PD local-ization in power transformers and HVDC

apparatus, and modeling of electro hydrodynamic flows and micro-bubbles generation in dielectric liquid.

Karim Miralikhani was born in Abhar, Iran, in 1967. He received his BSc degree in electronic engineering in 1991 from Iran University of Science & Technology and MSc degree in 1997 from K.N. Toosi Uni-versity of Technology, Tehran, Iran. Since May 1997, he has been working on trans-former field. His research interests include transient analysis, power transformers

monitoring, PD localization, PD classification, electrical insula-tion analysis, and HV testing and diagnostics.

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