Dc Reactor Type Transformer Inrush Current Limiter.pdf

DC reactor type transformer inrush current limiter M. Tarafdar Hagh and M. Abapour Abstract: A new inrush current limiter (ICL) is presented to limit the inrush current of transformers. The proposed ICL consists of three similar sets. Each set includes a diode-bridge and a single DC reactor and is connected in series with the individual phases of transformer. The ICL has almost no effect on normal operation of transformer. It needs no control, measurement and gate driving system and has a simple power circuit topology. The equivalent instantaneous inductance of transformer is used for analysis of circuit operation. The theoretical analysis, design features, power losses and voltage distortion because of using ICL are presented. The proposed method has been tested by simulation and laboratory experiments. Both results show that the proposed ICL successfully limits the inrush current.

List of Symbols

rS

L1d r1 u1 i1 iM w L 20 d r 20 u 20 i 20 LM

LS

Zpr 0 Z sec 0 Z load LNS

LSa Zs Ze re Le rd Ld VDF id

primary leakage inductance primary effective resistance primary terminal voltage primary current magnetising current mutual flux linkage secondary leakage inductance referred to primary secondary resistance referred to primary secondary terminal voltage referred to primary secondary current referred to primary instantaneous magnetising inductance of the transformer primary impedances of transformer secondary impedances of transformer referred to primary load impedance referred to primary side magnetising inductance when the iron core is not saturated magnetising inductance when the iron core is saturated equivalent impedance of source and transmission line equivalent impedance of transformer and load resistance of Ze inductance of Ze resistance of DC reactor inductance of DC reactor forward voltage drop across rectifier diodes DC reactor current

# The Institution of Engineering and Technology 2007 doi:10.1049/iet-epa:20060511 Paper first received 26th December 2006 and in revised form 12th May 2007 The authors are with the Power Electronics and FACTS Laboratory, Faculty of Electrical and Computer Engineering, University of Tabriz, Tabriz, Iran E-mail: [email protected]

808

Xm Rp Rsc Xsc ir IDC Imax PDC PBridge PTotal

1

equivalent resistance of source and transmission line equivalent inductance of source and transmission line magnetising reactance of transformer transformer iron core resistance resistance in the primary and secondary winding the leakage impedance in the primary and secondary winding ripple current in DC reactor average current in DC reactor maximum of utility current DC reactor power loss average power loss of diode-bridge total power loss of ICL

Introduction

The transformer inrush current is a transient current that occurs in an electric circuit when a transformer has been energised. This current depends on different parameters such as the magnitude of voltage, the switching-on angle, the remanent flux, the hysteresis characteristics of core, the resistance in the primary circuit and others [1]. The magnitude of the inrush current may be several times higher than the transformer rated current. This could result in high mechanical and thermal stresses. If the inrush current is suppressed by some methods, these problems may be avoided. There are two basic methods for limiting the inrush current: (a) Interior improvement methods [2, 3], (b) Additional control circuits [4 – 6]. Interior improvement methods usually make use of magnetising characteristics of transformer core. One idea is using a virtual air-gap which its equivalent thickness is controllable [3]. It needs an auxiliary winding inside the magnetic core. A DC current is injected in auxiliary winding to make a local magnetic saturation with the permeability closed to m0 . So the saturated zone is similar to an IET Electr. Power Appl., 2007, 1, (5), pp. 808 –814

air-gap. Inserting the virtual air-gap inside the magnetic core reduces the remanent flux and decreases the peak value of inrush current. However, this idea needs a DC current source and result in complex design of transformer and increasing the cost. In addition, the auxiliary winding is redundant after startup mode of transformer. In [2], another interior improvement method for transformer design with an asymmetric winding configuration is proposed. This method can provide the high inrush equivalent inductance and suitable leakage inductance for a transformer. The transformer designs with the three-layered S-P-S and the four-layered S-P-S-P structures for changing the crosssectional area of the primary winding where P and S stand for primary and secondary windings. It seems that the complex design of multi-layer structure of transformer is the main disadvantage of mentioned method. On the other hand, there are some methods for additional control circuits such as (a) (b) (c) (d)

controlling the switching on angle [5 – 7], resistor insertion, combination of (a) and (b) [5, 6], power-electronic-based methods [4].

In addition, it requires no information of power-on angle of circuit breaker and measurement of residual flux. Theoretical analysis, power losses computations and the effect on voltage quality are presented. Simulation and experimental results are obtained to verify the performance of proposed ICL in transient and steady states. 2

Fig. 1 shows the single-phase power circuit topology of proposed ICL. The source is assumed to be sinusoidal. An R-L load is connected to secondary side of transformer. The ICL consists of a diode bridge and a DC reactor. The rd and Ld stand for resistance and inductance of DC reactor, respectively. By choosing an appropriate value for Ld , it is possible to achieve a nearly DC current in DC reactor at steady-state operation of transformer. Therefore the DC reactor has no significant role in normal operation of system. Unfortunately, because of forward voltage drop across the rectifier diodes VDF , the DC reactor will discharge gradually and there would be a current ripple through it. 3

All of the first three methods require additional control circuitry outside the transformer. These methods suffer from uncertainty factors in circuit breaker (e.g. springs), remanent flux, measurement of instantaneous magnitude of residual flux and direction at the instant of transformer excitation and so on. For power-electronic-based methods, there are two main approaches which are (1) controlling the switching-on angle by using SCR, (2) series compensator. The disadvantages of the former are the on-state voltage, power consumption, and using control, protection measurement and gate driving circuits. As an example for the latter, in [4] an inverter-based series compensator using the current-mode control is proposed. But, it needs controlled semiconductors, a DC capacitor, a series transformer, control, measurement and gate driving circuits. In addition, it needs the short-circuit protection and voltage regulation of DC capacitor. This paper proposes a new series compensator-based circuit for limiting inrush current of transformers. This circuit consists of a diode-bridge type DC reactor that connects in series with each phase of transformer. It does not need any control, measurement and gate driving circuits. The power circuit simplicity, reliable operation and almost no effect on normal operation of transformer are other advantages of proposed inrush current limiter (ICL).

Power circuit topology of proposed ICL

Mathematical model of transformer

The equivalent T circuit for a two-winding transformer with its load referred to primary side is shown in Fig. 2a, where L1d: primary leakage inductance r1: primary effective resistance u1: primary terminal voltage i1: primary current iM: magnetising current w: mutual flux linkage L 20 d: secondary leakage inductance referred to primary r20 : secondary resistance referred to primary u 20 : secondary terminal voltage referred to primary i 20 : secondary current referred to primary Considering Fig. 2a, we have u1 ¼ r1 i1 þ L1d

di1 dw diM þ
dt diM dt

(1)

where iM ¼ i1 2 i 20 . The LM represents the instantaneous magnetising inductance (IMI) of the transformer and is defined by LM ¼

dw diM

(2)

The approximate solution of IMI shown in (3) can be obtained when the voltage drops in r1 and L1d are ignored,

Fig. 1 Power circuit arrangement of proposed system IET Electr. Power Appl., Vol. 1, No. 5, September 2007

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Fig. 2 Transformer and load model during the inrush current

because they are almost negligible for large transformers LM ¼

u1 diM =dt

(3)

Considering (3), it is possible to obtain LM by using the measured instantaneous primary and secondary windings currents and primary winding voltage in the transformer [8]. Considering this fact that the inrush current is a result of the transformer core saturation shows that the iron core alternates between the saturation and non-saturation during the inrush current. This will result in a drastic variation of the IMI, as shown in Fig. 2b. In this figure, LNS is the magnetising inductance when the iron core is not saturated and LSa corresponds to a high degree of saturation in the iron core. Therefore the IMI variation is an inherent feature of the inrush current, which can be used to detect and modelling the inrush current. In Fig. 2a, Zpr stands for 0 0 and Z load stand for the primary side impedance and Z sec the secondary and load impedances referred to primary side, respectively. The equivalent impedance of transformer and load is as follows Ze ¼ re þ jvLe ¼

0 {(Zsec

þ

0 ZLoad )k(jvLM )}

þ Zpr

(4)

where r ¼ rS þ rd þ re , L ¼ LS þ Ld þ Le . rS and LS stand for equivalent resistance and inductance of source and transmission line. From (5), the current equation in charging mode between t0 to t2 is shown by   V 2VDF (r=L)(tt0 )  sin(vt0  u) þ i(t) ¼ e r z (6) V 2VDF þ sin(vt  u)  r z p 2 2 where: z ¼ ðr þ (Lv) Þ, u ¼ tan1 (Lv=r), i(t0) ¼ 0, i(t) ¼ id (t) The discharging mode begins at t ¼ t2 when the inrush current reaches to its maximum value. As shown in Fig. 4a, during this mode the inrush current is less than DC reactor current and all of diodes turn on because of charged current in DC reactor. Indeed, the DC reactor is short circuit by diodes and it has no effect on circuit operation as shown in Fig. 3b. In discharging mode, we have Ld

did (t) þ rd id (t) þ 2VDF ¼ 0 dt

(7)

where re and Le stand for resistance and inductance of Ze , respectively. The equivalent impedance of transformer and load Ze is used for circuit analysis and simulation. 4

Circuit analysis

The proposed ICL has two modes of operation: 1. Charging, 2. Discharging. The single-phase equivalent circuits of mentioned modes are shown in Fig. 3. The utility voltage is assumed to be sinusoidal and the equivalent impedance of source and transmission line is shown with Zs . Fig. 4 shows the inrush and DC reactor currents for a typical transformer. Considering Fig. 4a, the charging mode begins at t0 and continues until t2 . When the transformer energises at t ¼ t0 , the inrush current begins to rise. At t0 the diodes D1 and D3 turn on and DC reactor connects in series with utility as shown in Fig. 3a. In this mode, the voltage across Ld causes the limitation of inrush current of transformer. When t ¼ t1 , the transformer saturates and LM changes its value from LNS to LSa . In charging mode, we have the following equation V sin(vt) ¼ ri(t) þ L 810

di(t) þ 2VDF dt

(5)

Fig. 3 Single-phase equivalent power circuit topology IET Electr. Power Appl., Vol. 1, No. 5, September 2007

Fig. 4 Inrush and DC reactor currents when transformer energised

From (7), the DC reactor current in discharging mode is   2V 2V id (t) ¼ e(rd =Ld )(tt2 ) i2 þ DF  DF rd rd

(8)

where i(t2) ¼ i2 . In this mode for inrush current we have di (t) V sin(vt) ¼ riL (t) þ L L dt

(9)

At t ¼ ta , LM changes its value from LSa to LNS again. So from (9) the inrush current between t2 and ta is iL (t) ¼ e

(r=L)(tt2 )

  V i2  sin(vt2  u) z

(10)

V þ sin(vt  u) z p where r ¼ rS þ re , L ¼ LS þ Le , z ¼ ðr2 þ (Lv)2 Þ, u ¼ 1 tan (Lv=r), i(t2 ) ¼ i2 . After t ¼ t2 and limiting inrush current by DC reactor, the DC reactor discharges because of its resistance and the voltage drops of diodes and at t ¼ t3 the reactor current reaches again to load current as shown in Fig. 4b. Between t2 and t3 , the DC reactor has no effect on circuit operation because there is not any charging mode in its operation. Similarly, after t ¼ t3 , the ICL has almost no effect on circuit operation because the DC reactor carries almost DC current. So, the proposed ICL limits the inrush current without any considerable effect on steady-state circuit operation.

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Using (12), it is possible to calculate the desired value of Ld as follows Ld ¼

rT =4  LS  Le ln (ðri2  VDS þ 2VDF Þ=ðVDS þ 2VDF )Þ (13)

where T stands for period of power frequency. Fig. 5 shows a typical characteristic of maximum inrush current magnitude against DC reactor inductance (using the data of simulation results in next part). This figure shows that increasing of Ld results in decreasing of maximum inrush current. Obviously, the suitable value for Ld depends on electrical parameters of utility and transformer. From practical point of view, to avoid saturation effect and getting the suitable value of Ld , the DC reactor may have a core with an air-gap or a non-saturated iron core. A non-saturated iron core (linear reactor) is used for analytical, simulation and experimental results. Obviously, it is possible to use a single-phase parallel circuit breaker with each phase of proposed ICL to bypass it during steady-state operation of transformer and cancelling any possible voltage distortion and power loss of proposed ICL [10]. However, the following parts describe the voltage distortion and power loss considerations of proposed ICL. Fig. 6a shows the load voltage with proposed ICL. This figure shows a voltage distortion that is because of DC reactor resistance and voltage drop on diodes. Fig. 6b shows the total harmonic distortion (THD) against resistance of ICL for various value of VDF . This figure shows that the THD increases by increasing the resistance of DC reactor and VDF but it is in acceptable ranges for small values of rd . Fig. 6 is obtained by using parameters of ‘simulation results’ part of this article.

Design considerations

By substitute the average of rectified source voltage by (VDS), it is possible to write (11) from (5) [9] i(t) ¼

VDS  2VDF  1  e(r=L)(tt0 ) r  (r=L)(tt ) 0 þ i0 e

(11)

where r ¼ rS þ rd þ re , L ¼ LS þ Ld þ Le , VDS ¼ 2V =p. By choosing the maximum permitted inrush current in Fig. 4a equal to i2 , from (11) we have L ri  VDS þ 2VDF t2  t0 ¼ ln 2 VDS þ 2VDF r IET Electr. Power Appl., Vol. 1, No. 5, September 2007

(12)

Fig. 5 Maximum inrush current against inductance of DC reactor 811

From economical point of view, there are five basic items that should be considered for all power-electronic-based circuits: (a) Control, measurement, protection and gate driver circuits, (b) Engineering costs (designing, laboratory tests etc.) (c) Input and output filters (d) Semiconductor devices (e) Passive components The item (a) is cancelled for proposed ICL. The simple power circuit topology and absence of the circuits mentioned in this item would result in considerable reduction of engineering efforts and cost as item (b), too. For item (c), the result of voltage distortion analysis showed that there is almost no need for input and output filters. For the price of semiconductor devices as item (d), by using only diodes it is reasonable to have lower price compared with other methods based on controlled turn on and turn off switches. For making the DC reactor as item (e), there are well-known technologies with good prices, too. By considering the mentioned items, it seems that the proposed ICL would have reasonable cost for practical applications.

Fig. 6 Distortion of load voltage with proposed ICL in steady state

By considering a DC current with negligible ripple through DC reactor as shown in Fig. 4b during steady state (after t3) we have ir ’ 0 ¼) IDC ’ Imax

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Simulation results

The simulation results are obtained by PSCAD/EMTDC software [11] for three-phase power circuit topology of Fig. 7. The parameters are given in Appendix 1.

(14)

where, ir , IDC and Imax stand for ripple current in DC reactor, the average current in DC reactor and the maximum of utility current in steady state, respectively. In this way, the DC reactor power loss PDC is 2 2 PDC ¼ rd IDC ¼ rd Imax

(15)

For power loss of diodes, Fig. 3a shows that in charging mode two diodes are in series and their current is IDC (neglecting ripple current). In discharging mode all of diodes are on and we have IDC ¼ [iD1 (t) þ iD2 (t)] ¼ [iD3 (t) þ iD4 (t)]

Fig. 7 Simulated power circuit topology

(16)

By assuming a constant VDF , the average power loss of diode-bridge PBridge is PBridge ¼ 2VDF  IDC

(17)

The total power loss of ICL in each phase would be the sum of (15) and (17) and is PTotal ¼ IDC [rd IDC þ 2VDF ]

(18)

For example for a 20/0.4 kV transformer with primary rated current Irms ¼ 50 (A), power factor ¼ 0.9 and installation of ICL in high-voltage side with parameters rd ¼ 0.01 (Ohm) and VDF ¼ 3 (V) we have PTotal ¼ 474W ¼)

3PTotal ¼ 0:0009 PLoad

This shows that the power losses of proposed ICL are very small percentage of overall distribution feeder rated power PLoad and it can be acceptable for most of practical applications. 812

Fig. 8 Primary side current of transformer IET Electr. Power Appl., Vol. 1, No. 5, September 2007

Fig. 8a shows the primary side current without ICL. At t ¼ 0.2 (s), the transformer is energised at no-load condition and at t ¼ 1 (s) induction motor is switched on. Fig. 8b shows the primary side and DC reactor currents with ICL. Comparison of Figs. 8a and b shows that using ICL has resulted in cancelling the transformer inrush current and decreasing the peak of start-up current of induction motor from 4200 to 3400 A, too. This shows that using the ICL is useful in soft-starting induction motors. Fig. 9 shows the mechanical start-up speed of induction motor with and without ICL. This figure shows that using ICL results in a little increase in settling time of motor speed that is not considerable in most of the practical applications.

Fig. 9 Mechanical speed of induction motor at starting mode with and without ICL

Fig. 10 Electrical torque of induction motor

Fig. 11 Primary side current of transformer at no-load condition (Time/Div ¼ 50 ms)

Fig. 12 Primary side current of transformer (Time/Div ¼ 50 ms) IET Electr. Power Appl., Vol. 1, No. 5, September 2007

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Figs. 10a and b show the electrical torque of induction motor with and without ICL, respectively. Comparison of these figures shows a considerable decreasing of oscillating torques of induction motor using the ICL that is important to reduce mechanical stress. 7

Experimental results

An experimental test system is prepared similar to Fig. 7. The parameters are given in Appendix 2. Figs. 11a and b show the primary side current of transformer with and without ICL, respectively. These figures show that using ICL has resulted in cancelling the transformer inrush current. Figs. 12a and b show the primary side current of transformer with and without ICL after starting up of induction motor, respectively. These figures show the effect of proposed ICL on limiting maximum start-up current that result in soft-starting of induction motor. Soft starting induction motor is another advantage of proposed ICL. 8

Conclusion

A new approach for limiting the inrush current of power transformers by using a series connected diode-bridge DC reactor in each phase is proposed. A method is derived to calculate the DC reactor value to reduce the inrush current to a predetermined value. The simulation and experimental results show satisfactory performance of mentioned ICL in limiting inrush current of transformer. Advantages of the proposed ICL transformer are the simple power circuit topology, reliable operation and no need for control, measurement, protection and gate driver circuits. Furthermore, the ability of proposed ICL for fault current limiting and reduction of start-up current of motors would be interesting for further research. 9

References

1 Cheng, C.K., Liang, T.J., Chen, J.F., and Yang, W.H.: ‘Novel approach to reducing the inrush current of a power transformer’, IEE Proc. Electr. Power Appl., 2004, 34, pp. 289– 295 2 Chen, J.F., Liang, T.J., Cheng, C.K., Chen, S.D., Lin, R.L., and Yang, W.H.: ‘Asymmetrical winding configuration to reduce inrush current with appropriate short-circuit current in transformer’, IEE Proc. Electr. Power Appl., 2005, 152, pp. 605– 611 3 Molcrette, V., Kotny, J.L., Swan, J.P., and Brudny, J.F.: ‘Reduction of inrush current in single-phase transformer using virtual air gap technique’, IEEE Trans. Magn., 1998, 34, (4), pp. 1192– 1194 4 Shyu, J.L.: ‘A novel control strategy to reduce transformer inrush currents by series compensator’. Int. Conf. on Power Electronics and Drives Systems, PEDS 2005, vol. 2, pp. 1283–1288 5 Cui, Y., Abdulsalam, S.G., Chen, Sh., and Xu, W.: ‘A sequential phase energization technique for transformer inrush current reduction Part I: simulation and experimental results’, IEEE Trans. Power Deliv., 2005, 20, (2), pp. 943– 949 6 Xu, W., Abdulsalam, S.G., Cui, Y., and Liu, X.: ‘A sequential phase energization technique for transformer inrush current reduction – Part II: theoretical analysis and design guide’, IEEE Trans. Power Deliv., 2005, 20, (2), pp. 950–957 7 Mahgoub, O.A.: ‘Microcontroller-based switch for three-phase minimization’. Proc. of the IEEE Int. power electronics congress, Cuernavaca Mexico, 1996, pp. 107– 112 8 Baoming, G., de Almeida, A.T., Zheng, Q., and Wang, X.: ‘An equivalent instantaneous inductance-based technique for discrimination between inrush current and internal faults in power transformers’, IEEE Trans. Power Deliv., 2005, 20, (4), pp. 2473– 2482 9 Hoshino, T., Salim, K.M., Kawasaki, A., Muta, I., Nakamura, T., and Yamada, M.: ‘Design of 6.6 kV, 100 A saturated DC reactor type

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superconducting fault current limiter’, IEEE Trans. Appl. Superconduct., 2003, 13, (2), pp. 2012– 2015 10 Abapour, M., Taghizadegan, N., and Sharifian, M.B.B.: ‘A novel approach for reducing inrush current in power transformer’. Proc. Int. Conf. on Electrical Machines, Chania, Crete Island, Greece, 2– 5 September 2006, on CD 11 PSCAD/EMTDC V3.0.8, Power System Simulation Software User_Manual, Manitoba HVDC Research Center, Canada 2001

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Appendices

10.1 Appendix 1 The parameters of simulated power circuit are as follows. Source data: Zs ¼ 0.01 þ j0.314 (V) vs(t) ¼ 10 sin(314t) (kV) DC reactor data: rd ¼ 0.01 (V) Ld ¼ 0.2 (H) VDF ¼ 3 (V) Transformer data: Transformer MVA ¼ 10 (MVA) Leakage reactance ¼ 0.1 (p.u.) Air core reactance ¼ 0.1 (p.u.) Inrush decay time ¼ 0.2 (s) Magnetising current ¼ 2% In Transformer ratio ¼ 1 Induction motor general data: Rated voltage ¼ 10 (kV) Rated power ¼ 1.2 (MW) Stator/rotor turns ratio ¼ 2.6376 Mechanical damping ¼ 0.01 (p.u.) 10.2 Appendix 2 The parameters of experimental power circuit are as follows. Source data: Rated voltage (L-L) ¼ 380 (V) Frequency ¼ 50 (Hz) Induction motor data: Rated voltage ¼ 220 (V) Rated power ¼ 180 (W) Rated current ¼ 1.3 (A) DC reactor data: rd ¼ 0.07 (V) Ld ¼ 0.2 (H) VDF ¼ 1.2 (V) Transformer data: Transformer power ¼ 2 (KVA) Voltage ¼ 220/110 (V) Xm ¼ 731 (V) Rp ¼ 1622 (V) Rsc ¼ 1.4544 (V) Xsc ¼ 0.493 (V)

IET Electr. Power Appl., Vol. 1, No. 5, September 2007