Investigating Partial Discharge UHF Electromagnetic Waves Propagation in Transformers Using FDTD

Technique and 3D Simulation

M. Zanjani, A. Akbari, H. R. , N. Shirdel Department of electrical and computer engineering

K. N. Toosi University of Technology Tehran, Iran

Mojtaba.Zanjani@ee.kntu.ac.ir

E. Gockenbach, H. Borsi

Institute of Electric Power Systems, Schering-Institute, University of Hannover, German

Abstract—On-line partial discharge (PD) measurement in power transformers has become increasingly popular in recent years. Measuring PD signals at ultra high frequency (UHF) range have many advantages. So, numerical methods have been implemented to model the propagation of electromagnetic (EM) wave in power transformers. Utilizing conventional softwares, such as CST to simulate EM wave propagation in power transformers need tremendous amount of time and memory. So such packages are difficult to be used in these fields of study. In this paper we will verify the program written in C++ environment to simulate UHF wave propagation using the results obtained from CST package in small scale. Using the proposed FDTD code, it is possible to simulate EM wave propagation inside large power transformer. This task cannot be accomplished by CST software in a simple PC. To ensure the validity of the proposed codes, results of simulating EM wave propagation in small volumes such as distribution transformer is compared with CST software package results. After validation, these codes are used to model larger transformers. Finally, the characteristics of PD source are investigated using simulated PD signals detected at different sensor locations.

Keywords-partial discharge, transformer, FDTD modeling, UHF propgation,

I. INTRODUCTION Partial Discharge (PD) is a main pre-cursor to arcing and

eventual transformer failure. Detecting PD is an established means of verifying insulation condition. Locating the source of PD would be an important tool for the repair of faulty transformers. UHF EM waves radiated from the PD can be detected by sensors positioned on the transformer tank. [1]

It is really meaningful of knowing the propagation characteristics of the electromagnetic (EM) waves generated by PD in transformers to facilitate insulation diagnosis and PD location. Finite Differential Method of Time Domain (FDTD) is an effective transient EM wave simulation method with extensive applicability and easy to realize [2]. But the investigation of the attenuation and distortion of EM wave signals brought by transformer components are far insufficient now, which relate greatly to insulation diagnosis and PD location. Transformers are key components of the transmission network and the state of their insulation is of considerable interest to utilities for monetary and safety reasons. We

illustrate how the UHF method for PD detection might form the basis of a real-time monitoring system. This approach would be suitable for transformer testing or on-line monitoring of units that are of particular concern [3].

One of the advantages of working in ultra-high frequency range is its insensitivity against on-site external noises. According to the arrival times of detected signals with sensors that are positioned on the transformer tank, it is possible to determine the PD location.

Investigation of PD EM wave propagation has been done in recent researches, but in this paper we will verify the program results written in C++ environment by results obtained from CST in small scale. Inability of CST software to simulate the propagation of EM wave in power transformer with large size in personal computer is the main reason of implementation of FDTD in C++ environment. CST software for parallel processing needs many computers to simulate EM wave propagation. In large scale simulation environments, it is suitable to solve the problem using FDTD method. Required computer memory estimation in many cases is simple. The number of cells in FDTD that is used for solving the problem is the main factor determining the amount of computer memory usage. To solve the problem of an electromagnetic wave propagation problem using FDTD, it is needed to determine six field values for each FDTD cell. Three field values are for x, y and z components of electric fields and three field values are for x, y and z components of magnetic fields. Six flags associated with each cell have to indicate the material type present at each of the six field locations. The time needed to simulate a power transformer by FDTD method depends on performance of computer processors.

II. FDTD METHOD Computer Simulation Technology (CST) is the first

company to publically market an FDTD software package. So, in this paper the results obtained from C++ code is compared with CST results in small scale which is possible using CST.

In 1966 Yee proposed a technique to solve Maxwell's curl equations using FDTD technique. Yee's method has been used to solve numerous scattering problems on microwave circuits, dielectrics, and etc. Initially there was little interest in the

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FDTD method, probably due to a lack of sufficient computing resources. However, with the advent of low cost, powerful computers and advances to the method itself, the FDTD technique has become a popular method for solving electromagnetic problems [4].

(1) α + β = χ. (1) (1)

(2) α + β = χ. (1) (1)

Where H is the magnetic field, E is the electric field, is the permittivity, μ is the permeability and is the conductivity. To yield accurate results, the grid spacing d in the finite difference simulation must be less than the wavelength, usually less than 1/10. The stability condition relating to the spatial and time step size is:

(3) α + β = χ. (1) (1)

Where is the maximum velocity of the EM wave. Having derived the FDTD updating equations, a time marching algorithm can be constructed as illustrated in [5],[6].

Figure 1. Yee cell demonstrating the arrangement of fieldComponents

within a cubical grid.[7]

III. SIMULATION RESULTS According to the electric and magnetic fields equations and

the algorithm reported by authors in [5], a program was written in C++ environment to consider EM wave propagation inside transformers. At first, a distribution transformer is simulated with both FDTD codes and CST software. Due to the small size of simulation environment, CST software is able to run the simulation. Comparing the obtained results, the accuracy of the FDTD codes could be verified. Afterwards, the EM wave propagation inside a real large power transformer is simulated by FDTD codes.

A dipole antenna is used for PD source modeling and a Gaussian pulse is chosen as an excitation signal in both FDTD

codes and CST Software (Fig. 2). The excitation signal and its parameters are as follows:

(4)

Figure 2. The Gaussian pulse excitaion pulse used in CST and C++.

A. Distribution transformer EM wave propagation in a distribution transformer with

tank size of (360×840×750) mm3 volume is simulated using proposed FDTD codes and CST software. Transformer configuration is shown in Fig.3.

Figure 3. The top view of the transformer configuration in CST simulation.

The PD location is set at the point with coordinates (120,280,270) mm. Sensors are located on the inner surface of the tank to receive the propagated EM wave in the volume of tank (Table 1).

TABLE I. SENSORS LOCATIONS ON THE DISTRIBUTION TRANSFORMER

Sensors X(mm) Y(mm) Z(mm)S1 180 30 375S2 180 420 720S3 180 810 375S4 30 420 375S5 320 420 375

TABLE II. THE ARRIVAL TIMES FOR C++ , CST

Sensors C++ Arrival Time(ns)

CST Arrival Time(ns)

S1 2.2 2 S2 2.5 2.6S3 3.25 3.25S4 1.1 1.2S5 1.45 1.55

Results for both CST and C++ show good agreements. As an example, the y component of the electrical field of sensor No.3 in CST and C++ are shown in Fig. 4.

0 0.2 0.4 0.6 0.8 1 1.2

x 10-9

0

5x 10

-3

Time (s)

Cur

rent

(A)

498

Figure 4. Demonstration of y component ofthe electric field for sensor No. 3

in CST software and proposed C++ FDTD codes.

In FDTD code, an observation plane is set at z=265mm to observe the amplitude of electric field intensity at different time steps. Fig. 5 shows the results of amplitude distribution.

The propagation of the EM wave inside the transformer is shown in Fig. 5. The first time step shows the propagated wave before it meets any obstacle, but in the other time steps diffraction and refraction of wave due to the reflection from tank or the active part of the transformer can be observed.

Figure 5. The snapshots from propagation of PD EM wave in side a transformer at times a) 9.5 ns, b) 47.6 ns , c) 71.5 ns and d) 95.3 ns.

B. Power transformer A real power transformer with the tank size of 4×2×3m3 and

its active part is simulated by using FDTD codes. The CST software is unable to solve this problem in a PC computer because of the large simulation environment. The positions of sensors are given in Table 2. A PD source is located at coordination (2310, 308, 2268) mm.

TABLE III. SENSORS LOCATIONS ON THE POWER TRANSFORMER

Sensors X(mm) Y(mm) Z(mm)S1 50 50 2950S2 3950 50 2950S3 3950 1950 2950S4 50 1950 2950

The x, y and z components of electrical field for sensors positioned on transformer tank are demonstrated in Fig. 6, 7, and 8. Required time for each sensor to detect EM signal due to PD depends on sensor locations as well the PD source location in transformer. As it can be clearly observed in Fig. 6, the arrival times for sensors are discriminative features for each sensor. In table III, the arrival times for sensors obtained from C++ program are given and compared with results obtained from analytical calculations.

Figure 6. The X components of electrical field for sensor No. 1, 2, 3 and 4 in

a real power transformer.

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x 10-9

-0.2

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0.2

Time (ns)

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Figure 7. The Y components of electrical field for sensor No. 1, 2, 3 and 4 in a real power transformer.

Figure 8. The x components of electrical field for sensor No. 1, 2, 3 and 4 in

a real power transformer.

TABLE IV. THE ARRIVAL TIMES FOR C++ AND ANALYTICAL CALCULATIONS

Sensors C++ Arrival Time(ns

Analytical calculations(ns difference

S1 12.1 11.9 0.2S2 9.2 9 0.2S3 13 12.6 0.4S4 15.3 14.9 0.4

IV. CONCLUSION FDTD codes are proposed to simulate the propagation of

PD EM waves inside transformers. The validity of proposed codes is checked with CST software in simulating a small distribution transformer. Also the EM wave propagation inside a real power transformer was done with proposed codes, which was impossible by CST.

REFERENCES [1] L. Yang, M. D. Judd and C.J. Bennoch, “Time Delay Estimation for

UHF Signals in PD location of Transformers,” 2004 Annual Report Conference on Electrical Insulation and Dielectric Phenomena.

[2] Wang Maoguang, Geometrical theory of Diffraction, Northwest Dianxun Engineering Press. 1985

[3] M.D. Judd, G.P. Cleary, CJ. Bennoch, “Applying UHF Partial Discharge Detection to Power Transformers,” IEEE Power Engineering Review, August 2002

[4] Xu Bin, Li Junhao, Si Wenrong, and Li Yanming, “Simulating Propagation Characteristic of UHF Signal for PD monitoring in Transformers by FDTD Technique”, Power and Energy Engineering Conference, 2009. APPEEC 2009. Asia-Pacific

[5] Nader Shirdel, Asghar Akbari, Hassan Reza Mirzaei and Mohammad Sadeg Abrishamian, “Three-Dimensional Simulation of UHF Signal Propagation in Transformer using FDTD Method,” International Conference on Power Engineering, Energy and Electrical Drives, Torremolinos (Málaga), Spain. May 2011

[6] Atef Z.Elsherbeni and Veysel Demir, “The Finite Difference Time Domain Method For Electromagnetics With MATLAB Simulations”,SCITECH, pp.1-32,2009.

[7] K.S.Yee, “Numerical solution of Initial Boundary value problem Involving Maxwell's Equation in Isotropic Media, IEEE Transactionson Antennas and Propagation, vol. AP-17, pp. 585-589, Jan. 1966.

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