Analysis of Electromagnetic Interferences Induced by High Voltage Lines under Normal and Fault Conditions

Transcription

1 Analysis of Electromagnetic Interferences Induced by High Voltage Lines under Normal and Fault Conditions Calin MUNTEANU, Vasile TOPA, Laura GRINDEI Technical University of Cluj-Napoca, Baritiu 8, Cluj-Napoca, Romania, Leslie BORTELS, Johan DECONINCK Vrije Universiteit Brussel, Pleinlaan, 050 Brussel, Belgium Abstract. The paper presents a method for analysis of the electromagnetic interferences created on pipeline networks by the High Voltage (HV) power lines working on normal or fault conditions. In order to perform the numerical computations, a particular 3D numerical code was developed. The code was validated for particular problems by comparison using the CatPro software developed by Elsyca []. In the second part of the paper numerical results for normal and fault examples are outlined. Final conclusions end the paper. Introduction Nowadays there is an increasing concern regarding the hazards resulting from the electromagnetic interferences generated on buried pipe network by the electric power systems working under normal or fault conditions (see Figure ). The safety of the people touching the pipes, the damages of the pipe networks and the cathodic protection equipment to be implemented are only few of the important questions to be answered. Thus, there is an industrial need for development of user-friendly, high-precision computation software applications able to compute the induced voltage values and their effects on the victim pipelines. y z HV Line Fault to Ground Lossy Ground Buried Pipeline Figure : Pipelines in the neighbourhood of HV power lines In this light, the numerical analysis software application proposed to be developed is aimed to compute the values of the AC induced potential and currents on the buried pipelines by the source currents flowing through the HV power line that is placed in closed proximity with the pipeline network. Being a high complexity application, the software package is intended to be an addition of several computation modules, aimed to solve together the global 3D electromagnetic field problem. In this paper will be presented the module that computes the effects of the currents from the HV power line working on normal of fault conditions. The computation of the currents on HV line working on normal or fault situations, in the presence of the lossy conductive ground, is not the object of the present paper.

2 D FEM - 3D BEM electromagnetic field model In order to solve the electromagnetic field problem, a D Finite Element Method (FEM) model for the internal pipe problem coupled with a 3D Boundary Element Method (BEM) model for the external pipe problem has been developed. Dividing the pipe in so-called pipe elements as shown in Figure and assuming an ial symmetry of the problem, the starting equation for the current distribution is: i ( τ ) = i ( τ + dτ) + i ( τ) () rad i rad (τ) i (τ + dτ) i (τ) dτ Figure : Small pipe length and the st theorem of Kirchhoff Equation () will lead to the following current density components [], [3], [4]: Φ σ + jωa J = τ Φ σ + jωa = J = Q r rad rad ( AC ) () Taking into account (), the equation for the pipe internal problem can be written as: A π R + jω Q= 0 (3) τ τ σs Φ Using the weighted residual method [] for minimization of the functional associated to equation (3) one lead to the following system of equations: Q0 Q A + A 0 I = 0 ( Φ Φ 0 ) G + k jωlg Q Q A 0 + A 0 I = ( Φ Φ 0) G k jωlg (4) valid for a pipe element, where R is the pipe radius, l is the length of the pipe element, S is the transversal surface, k = π Rl is the surface of revolution and G = σ Sl is the ial conductance of the pipe element. The above system of equations may be rewritten for each node (i) in the following form suitable for the numerical implementation in accordance with sign convention from Figure 3. k k k k i i i i Q + Q Q G ( G G ) G i + + Φ + + Φ Φ i i j ω l G j l G j lg j lg i i i i i i i i A ω ω i A ω i + A i+ i i i i i i i+ = (5)

3 Q i- Q i Q i+ Ф i- Z i- Ф i Z i Ф i+ (i-) (i) (i+) I i- I i- I i I i I i+ I i+ Figure 3: The D FEM model for the pipe internal problem The 3D boundary integral equation for the pipe external problem can be formulated starting from the diffusion equation and using the Lorentz gauge condition A =μσφ []: Ω() i G Q Φ () i + Φ d Γ= G + j ω A d Γ 4π Γ n Γ σ rad (6) where ne r is the normal unit vector in the positive sense considered (from interior to exterior of the pipe) and G is the fundamental solution (Green s function) associated to the governing equation and given by []: r jkr δ e e r r G = = cos jsin 4π r 4πr δ δ (7) where r is the position vector and δ is the skin depth. In order to solve the coupled FEM BEM problem, a global matrix system has been set-up. The final global matrix system implemented is presented in the equation below: HR + HI + σ GR σ GI Φ R + ωgi + ωgr 0 0 ARR HI HR σ GI σ GR I ωgi ωgi 0 0 ARI + + Φ + = + G 0 + K 0 QR G3 AZR 0 + G 0 + K QI 0 0 G3 0 AZI (8) where: ФR, ФI are the real and the imaginary parts of the potential on the pipe boundary nodes; QR, QI are the real and the imaginary parts of the radial current density on the pipe boundary nodes (see Figure 3); ARR, ARI are the real and the imaginary radial components of the vector magnetic potential values on the pipe boundary nodes; AZR, AZI are the real and the imaginary ial components of the vector magnetic potential values on the pipe boundary nodes; The sources are therefore the values of the vector magnetic potential produced by the HV power line on the pipe nodes. These values are computed using the relation: jkr μ e A= I S S 4π dl (9) r Conductor 3

4 3 Numerical examples In order to test the computation accuracy of the software module developed the numerical results for particular cases have been compared with the results obtained with CatPro.4 [],[3] that uses the Transmission Lines Method (TLM). This software was developed by Elsyca []. The results in the case of a km long pipe placed parallel with a km straight HV power line working under normal condition (balanced three-phased line currents) are shown below. 5 PIPE HV Tline PIPE HV Tline x [km] x [km] (a) (b) Figure 4: Test cases for software computation accuracy (a) FEM-BEM software module developed (b) CatPro-Elsyca results Figure 5: Computation accuracy numerical results As it can be noticed from Figure 5, there is a very good agreement between the two results. Moreover, if the mimum potential values at the ends of the pipe are compared, one gets a relative error of 0.07% which means a very good agreement between the computation methods. In addition to the CatPro software that may be used only for normal working conditions on HV line and for straight geometries, the FEM-BEM software module developed is able to compute the potential distribution along the pipe for HV line fault cases and also for more complicated geometries of the pipe and HV line. In the first example presented in Figure 6 one considers a 0 km long pipeline placed parallel with a km long HV line. The potential distribution along the pipeline is computed in three cases: HV line working on normal condition (500 A balanced three-phased current through the line) case, HV line has a fault to ground at km distance from the left end cases. The 0 ka fault is considered fed in two ways: first case from both HV line ends (5 ka each) and second case from left end only (0 ka). Numerical results are presented in Figure 7 and Figure 8. Looking to the results presented in Figure 7 one can notice that the magnitude of the current influences dramatically the potential distribution on the neighbour pipe. 4

5 5 PIPE 0 ka 5 ka 5 ka HV Tline x [km] 0 ka Figure 6: Problem formulation for the first numerical example (a) Normal working condition (b) Fault supplied from one side left side Figure 7: Numerical results for the first example (a) Fault supplied from one side left side (b) Fault supplied from both sides Figure 8: Numerical results for the first example While in the case of normal working conditions (500 A balanced currents) one get mimum 43 V induced potential value along the pipe, for 0 ka fault current an induced potential value of up to 4. kv is obtained, which is a really dangerous value. Also the way the fault is supplied influences essentially the induced potential distribution. This fact is outlined in Figure 8. One can observe that if the fault currents flow along all the HV line the induced potentials are much higher than in the case of a higher current flowing on only one side. In this last case the potential values on the opposite side of the pipe is much lower. The software module implemented can be used for more complicated geometries, as the one presented in Figure 9. The potential distribution computed for normal and fault conditions are presented in Figure 0. 5

6 -5000 Pipe HV Line x [m] ka Figure 9: Problem formulation for the second numerical example 4 Conclusions (a) Normal working condition (b) Fault supplied from one side left side Figure 0: Numerical results for the second example The paper presents a method for computation of induced potential values along pipe networks due to HV line currents working on normal and fault conditions. The influences of the HV line supply method and of the geometry of the problem are outlined in the numerical examples proposed. References [] Web page [] C. Munteanu, L. Bortels, J. Deconinck, V. Topa, E. Simion. Advances on BEM FEM 3D Numerical Modelling of Electromagnetic Interferences between HV Lines and Buried Pipelines, Proceedings of the nd International Workshop on Advances in Numerical Computation Methods in Electromagnetism, ANCME 003, Gent, Belgium, 003, pp [3] L. Bortels, C. Munteanu, J. Deconinck, V. Topa. A User-Friendly Simulation Software for AC Predictive and Mitigation Techniques, 58 th Annual Conference and Exposition, CORROSION NACExpo 003, San Diego, USA, 003. [4] C. Munteanu, V. Topa, E. Simion, L. Bortels, J. Deconinck. 3D Numerical Modelling of the Induced Voltages on Pipelines by Neighbour HV Transmission Lines, Proceedings al Simpozionului National de Electrotehnica Teoretica, SNET 03, Bucharest, 003, pp. 9-6 Acknowledgments - The authors are grateful to the Flemish Government and to the Romanian Minister of Education and Science for the financial support in the frame of the Flemish- Romanian Bilateral Project BWS 0/05. 6