International Conference on Electrical, Control and Comuter Engineering Pahang, Malaysia, June 1-, 011 Study on the Electromagnetic Force Affected by Short-Circuit Current in Vertical and Horizontal Arrangement of Busbar System Farhana Mohamad Yuso, Mohamad Kamarol Mohd Jamil, Dahaman Ishak and Syafrudin Masri School of Electrical & Electronic Engineering Universiti Sains Malaysia Nibong Tebal, Pulau Pinang youth_cambaguz@yahoo.com Abstract Each busbar conductor of a hase is subjected to a force due to the short-circuit currents. In this aer, the electromagnetic forces affected by the short-circuit current in three-hase busbar conductor are calculated in vertical and horizontal arrangement. The short-circuit current densities are calculated mathematically. The calculations are erformed by assuming a eak value of steady-state ac current is equal to the eak value of the short-circuit current. The electromagnetic forces due to the short-circuit current are calculated according to the equation introduced by IEC Standards 865/1993. The electromagnetic force generated in vertical arrangement is comared with the horizontal of busbar. The result deicted that the busbar in vertical arrangement has about times higher electromagnetic force comared with that in horizontal arrangement. The arrangement of the busbar obviously influences the strength of electromagnetic force due to short-circuit current. Furthermore, the electromagnetic force obtained from the simulation by finite element method in vertical arrangement was agree with the calculation obtained using IEC Standard 865/1993. Keywords busbars, busbar short-circuit current, electromagnetic forces, methamatical analysis, simulation. I. INTRODUCTION A short-circuit test is one of the imortant ste to verify the quality of the busbar after the manufacturing rocess. It is erformed to rove that the busbar caability to withstand short-circuits current for a definite time and to withstand the force from the momentary eak of short-circuit current [1]. Mathematical exression is used to redict the erformance of the busbar during short-circuit current. This method can assist to determine the first imression in the erformance of busbar. The occurrence of short-circuit in busbar system roduce a very high current flowing through the busbar conductor. The magnitude of short-circuit current is deended on the voltage source and the total imedance of the oerational equiment [1]. Higher value of current induces electromagnetic force between each arallel busbar conductor. Each busbar of a hase is subjected to an electromagnetic force due to the actions between other hases. The force gives a maximum value at the first half cycle of the short-circuit occurrence which caused by the eak value of short-circuit current. This force need to be identified in order to determine the size of conductors and the structures for suorting them []. The electromagnetic force deends on the strength of the short-circuit currents and the configuration dimension of busbar conductor. This work focus on three-hase short-circuits current since it gives the highest effect on mechanical force. The short-circuit current is calculated according to IEC Standards. The magnitude of electromagnetic force is analyzed between vertical and horizontal arrangement of busbar conductor in order to determine the effect of arrangement on the electromagnetic force. Simulation by finite element method (FEM) is conducted to evaluate the magnitude of maximum electromagnetic force on busbar conductor and the result is comared with the calculated result. II. THREE-PHASE SHORT-CIRCUIT CURRENT A. Arrangement of busbar Fig.1 shows two arrangements of busbars that considered for the basic numerical calculations. It is assumed that [3] - the fault examined is a three-hase symmetrical shortcircuit, because it gives the greatest dynamic stress ; - the central-line distance between busbars is much smaller comared with the length of conductor, so that the busbars can be regarded as being of infinite length; - the ermeability is constant, since coer bars are used in installations; - a steady state, balanced three-hase system is alied to the three-hase busbars, with a eak value is equal to the eak value of the short-circuit current. B. Calculation of three-hase short-circuit current Fig. shows the single-line circuit diagram for short circuit current test on busbar [1]. Basically it consists of transformer as ower source. The circuit shows the assumtion of shortcircuit current occurs at the end terminal of the busbar conductor. In this work, the current flowing through each busbar conductor is analyzed due to the occurrence of shortcircuit. 978-1-6184-8-8/11/$6.00 011 IEEE 196
a) Vertical arrangement Figure : Single-line circuit diagram [1] b) Horizontal arrangement Figure 1: Arrangement of busbar For dimensioning of busbar system, it is necessary to consider three-hase short-circuit current in order to guarantee the mechanical stability of the systems. The requirements for calculating the largest three-hase short circuit current are [1]: - temerature of conductor at 0 o C - network circuitry is mostly resonsible for this current - network feeder deliver the maximum short circuit ower - voltage factor is chosen in accordance with IEC Standard 60909 Fig. 3 shows the equivalent circuit for the calculation of three-hase short-circuits current. Three-hase short circuit current is given by [1] I c U N " k 3 = (1) 3 ZT where U N is the voltage at the nominal system volatge and Z T is the total imedances of oerational equiment. While the value of c in Eq. (1) is the voltage factor which can be comuted from table given in IEC Standard 60909 [1]. At the first half cycle, the current will be at the eak value of three-hase short circuit current. This eak value of short circuit current is taking into account in order to calculate the maximum electromagnetic force between the busbar conductors. The eak short circuit current can be calculated from the equation i = k () I" k 3 where factor k deends on the ratio R/X of the short circuit ath is given by [4] 3R X k = 1.0 + 0.98e (3) where R is the total resistance and X is the total reactance of the system. Figure 3: Equivalent circuit [1] III. SHORT-CIRCUIT ELECTROMAGNETIC FORCES Busbar systems are subjected to mechanical force as a result of short circuits. This maximum electromagnetic force is roduced during short-circuit occurrence by current flowing in adjacent conductors in the busbar structure. This force mainly deendent on the strength of the short circuit current,shae and also the dimensional arrangement of the bubsar conductors. The dimensioning of busbar with resect to stability against mechanical force is described exactly in IEC 60865 [1]. A. Electromagnetic force calculations introduced by IEC Standards 60865/1993 Referring busbar arrangement in Fig.1, the maximum electromagnetic force er unit length acting on the central rectangular conductor (hase B) is given by [4] F μ 3 0 mb = i (4a) πa m While the maximum electromagnetic forces er unit length acting on the outer rectangular conductor (hase A and hase C) are smaller than F mb. These forces can be calculated as follow [4] F ma = F mc μ0 = πa m 3 + 8 3 i (4b) Instead of the centre-line distance a, the effective distance, a m is introduced in this Standard. This introducing is due to skin and roximity effect in low voltage system that cannot be neglected. This effective distance is defined in [4] by a am = (5) k where k 1s is a correction factor that can be comuted from the IEC Standard 865/1993 and shows in Fig. 4. 1s 197
= J Bds F (7) where J is the current density and B is the magnetic flux of the busbar conductor. IV. ANALYSIS OF ELECTROMAGNETIC FORCE The vertical and horizontal arrangement of busbar are assumed to be connected to a 630 kva, 0 kv/ 400 V transformer with rated short-circuit voltage 6% and coer losses of 6930 W. By using Eqs. (1) (3), the eak shortcircuit current is obtained and the result of these two busbar arrangements are shown in Table I. As stated in the assumtion in section II (A), the eak value of steady-state current is equal to the eak value of the shortcircuit current. This value is used in order to calculate the magnitude of maximum electromagnetic force on the busbar. The electromagnetic force between two arrangements is determined by considering the dimension of vertical and horizontal arrangements of the busbar as shown in Table II. V. RESULTS AND DISCUSSIONS µ 0 = ermeability of free sace a = central line distance between two conductor (m) i = eak short circuit current (A) = effective distance (m) a m Figure 4: Variation of k 1s as a function of ratios a/d and b/d [1] B. Simulation of electromagnetic force by finite element method The simulation by (FEM) using Oera-D is alied to notify the magnitude of electromagnetic force for coer busbars with carrying short-circuit current. The steady-state AC analysis has been alied for the vertically adjacent busbar conductors. Two dimensional model as shown in Fig. 1(a) was used to carry out the analysis. Each three busbars are loaded with steady-state balanced 50 Hz currents with the rated value shown in Table I. I A =i cos(ωt) I B =i cos(ωt-10 0 ) I C =i cos(ωt-40 0 ) (6) The simulation is erformed to identify the magnetic flux density of three busbars where the currents are varying sinusoidally in time. This magnetic flux is a rincial arameter for evaluation of electromagnetic forces on the busbar conductor due to the high short-circuits current [5]. The total force on a busbar conductor is determined by integrating the surface of the busbar conductor. The software calculates the total force er unit length, F of conductor by alying Maxwell Stress equation. A. Calculations according to Standards The maximum forces due to the magnitude of eak shortcircuit current acting on the three arallel busbar conductors of vertical and horizontal arrangement are calculated using Eqs.(4a-b). The results of maximum electromagnetic force are shown in Table III. The results revealed that the central conductor (hase B) give a higher value of electromagnetic force comared with outer conductor (hase A and C) for both arrangements. Busbar at the central conductor exerience a greatest electromagnetic force influence by the high current flowing through busbar conductor in hase A and hase C. Furthermore, with the same size of busbar, the vertical arrangement give a higher electromagnetic force effect comared with horizontal arrangement. This result indicates that, the busbar under insection of short-circuit test should be examined in the vertical arrangement in order to determine the level of ability for conductor busbar to withstand the electromagnetic force exists. Besides, it can hel to determine the size for both conductors and the structures for suorting them. The force between the conductor busbar in which shortcircuit current flows also deend on the geometrical arrangement and the rofile of the conductors. This is the reason why effective distance has been introduced by IEC Standard 685/93 in the Eqs. (4a-b). Voltage, U N (V) TABLE I. RATED VALUES OF BUSBARS Three-hase short circuit current, I k3 (ka) Peak short circuit current, i (ka) 400 15.818 34.947 198
Arrangement TABLE II. DIMENSIONS ARRANGEMENT OF BUSBAR Central distance, a (m) Height, b (m) Thickness, d (m) Effective distance, a m (m) vertical 0.0071 0.0750 0.00600 0.0300 horizontal 0.0761 0.0060 0.0750 0.0500 TABLE III. CALCULATED MAXIMUM FORCES ON THE BUSBAR Maximum Force (N/m) vertical horizontal F ma 6578.80 3947.8 F mb 7051.14 430.68 F mc 6578.80 3947.8 Figure 5: Magnetic flux density distribution at ωt = 0 0 B. Simulation of three-hase bubsar The magnitude of maximum force existing between three busbars is determined by simulating three-hase busbar using Oera-D. The three busbar conductors are loaded with current in Eq. (6). The simulation is conducted at first half cycle of short-circuit current. The magnitude of electromagnetic forces is identified at each electrical angle of the short-circuit current. Fig. 5 shows the distribution of magnetic flux density at 0 0. At this time, a stronger magnetic flux density roduced at the region between busbar of hase A and hase B. This result is due to the high current flowing through busbar of hase A. The higher the current carrying by busbar conductor, the higher magnetic flux is roduced around conductor. Fig. 6 shows the electromagnetic force obtained from the simulation versus the electrical angle in three-hase bubsar for vertical arrangement. From the result, the busbar conductor in hase A encounters maximum electromagnetic force at 0 0 while hase B and hase C encounter maximum electromagnetic force at 60 0. These maximum electromagnetic forces occur due to the high short-circuit current carrying by the conductor and adjacent busbar conductor at that moment. From this simulation, the value of maximum electromagnetic force only considered the magnitude in the x-axis by neglecting the direction of force. The maximum electromagnetic force of busbars conductor comuted by Oera-D is comared with those calculated given by Eqs. (4a-b). The comarison results for vertical arrangement of busbar are shown in Table IV. From the both results, the central conductor exeriences the greatest electromagnetic force comared with the outer conductors. As mention in Eq. (7), the electromagnetic force is deends on the current density and magnetic flux density of the conductor. When three conductors carrying currents lace arallel in magnetic field, it exeriences an electromagnetic force between each conductor. Higher electromagnetic force is due to the stronger magnetic flux density roduced by the high shortcircuit current carrying by the busbar conductor and its adjacent busbar. Figure 6: Electromagnetic force er unit length vs. electrical angle in three-hase busbar system for vertical arrangement TABLE IV. CALCULATED MAXIMUM FORCES COMPARED WITH SIMULATION RESULT Maximum Force (N/m) calculation simulation difference F ma 6578.80 7156.60 8.78% F mb 7051.14 766.0 3.05% F mc 6578.80 715.50 8.78% VI. CONCLUSIONS The occurrence of short-circuit in busbar system, roduced higher current flowing through the bubsar conductor. This high current generates electromagnetic forces between each conductor. The electromagnetic force is deended on the configuration arrangement. The busbar in vertical arrangement has about times higher electromagnetic force comared with that in horizontal arrangement. The results from FEM analysis of electromagnetic force for three-hase busbar revealed slightly differences with the calculation using IEC Standards. However, the result is considered well agrees with the calculation which are about 3%-8%. It also roved that the central conductor exerience the highest electromagnetic force comared with the outer conductor. 199
ACKNOWLEDGMENT The authors are highly indebted to School of Electrical & Electronic Engineering, Universiti Sains Malaysia and management of FURUTEC Electrical Sdn. Bhd for technical suort of this roject. REFERENCES [1] I. Kasikci, Short Circuits in Power Systems: Wiley-VCH Verlag-GmbH, 00. [] Jean-Pierre Thierry and Christohe Killindjian, "Electrodynamic Forces on Busbars in LV Systems, " Cahier Technique Merlin Gerin, Oct 1996. [3] D. P. Labridis and P. S. Dokooulos, "Electromagnetic forces in threehase rigid busbars with rectangular cross-sections," IEEE Transactions on Power Delivery, vol. 11, Aril 1996. [4] IEC-Publ. 865/1993, Short-circuit currents-calculation of effects. Part 1: Definitions and calculation methods. Geneve/Suisse: Bureau Central de la CEI. [5] J. Y. Lee, H. M. Ahn and J. K. Kim, "Finite element Analysis of Short Circuit Electromagnetic Force in Power Transformer, " IEEE. [6] IEC-Publ. 865/1986, Calculation of the effects of short-circuit currents, Geneve/Suisse:Bureau Central de la CEI. [7] J. Schlabbach, Short-circuit Current: The Institution of Electrical Engineers, 005. [8] D. G. Triantafyllidis, P. S. Dokooulos, and D. P. Labridis, "Parametric Short-Circuit Force Analysis of Three Phase Busbars - A Fully Automated Finite Element Aroach," IEEE Transactions on Power Delivery, vol. 18, Aril 003. [9] G. Hosemann and D. Tsanakas, Dynamic short-circuit stress of busbar structure with stiff conductors. arametric studies and conclusions for simlified calculation methods, Electra, no.68, 1980,. 37-64. [10] Mona M. Abd-El-Aziz, Maged N.F.Nashed and Amr A. Adly, "Comutation of Busbars Local Electromagnetic Force Densities Connected to 3-Pulse Rectifier Load over a Comlete Cycle, " IEEE, 008. [11] Mona M. Abd-El-Aziz, Amr A. Adly and Essam-El-Din M. Abou-El- Zahab, "Assessment of Electromagnetic Forces Resulting from Arbitrary Geometrical Busbar Configurations, " IEEE, 004 00