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Optimal gang-operated switching for transformer inrush current reduction
Electric Power Systems Research 131 (2016) 80–86
Contents lists available at ScienceDirect
Electric Power Systems Research journal homepage: www.elsevier.com/locate/epsr
Optimal gang-operated switching for transformer inrush current reduction Ramón Cano-González a,∗ , Alfonso Bachiller-Soler a , José Antonio Rosendo-Macías a , Gabriel Álvarez-Cordero b a b
Department of Electrical Engineering, University of Sevilla, Escuela Superior de Ingenieros, Camino de los Descubrimientos s/n, 41092 Sevilla, Spain Red Eléctrica de Espa˜ na (Spanish TSO), Paseo del Conde de los Gaitanes 177, 28109 Alcobendas, Madrid, Spain
a r t i c l e
i n f o
Article history: Received 11 January 2015 Received in revised form 13 May 2015 Accepted 5 October 2015 Keywords: Controlled switching Inrush current Power transformer Gang-operated circuit breaker Simultaneous closing ATP–EMTP
a b s t r a c t Controlled switching technology with independent-pole-operated circuit breakers is an effective way to eliminate transient transformer inrush currents. This technique cannot usually be applied at lower voltage levels where three-pole-operated circuit breakers are more frequent. In this paper, the optimal instant for a simultaneous closing is obtained as a solution of a min–max problem. The proposed strategy has been evaluated in a test system using EMTP/ATP and has presented highly satisfactory results, even when actual characteristics of circuit breakers are taken into account. © 2015 Elsevier B.V. All rights reserved.
1. Introduction Power transformers are among the most important devices in power networks. Transformer energization may result in a high magnetization current, also known as inrush current, due to the saturation of magnetic flux in the core. The inrush current is asymmetric and unbalanced between the phases and can reach a value that is several times higher than the rated current of the transformer. These transient currents have many unfavorable effects including: malfunction of protective relays or fuses [1,2], reduction of transformer lifecycle due to large current forces in windings [3,4], and temporary voltage drop due to impedance of the network between the sources and the energized transformer [5,6], thereby affecting the power quality of the network. Various methods have been proposed to eliminate or at least reduce the inrush current, such as series compensator [7,8], sequential phase energization with a grounding resistor [9,10] and controlled switching [11–13].
∗ Corresponding author. Tel.: +34 954 455 2814. E-mail addresses: [email protected] (R. Cano-González), [email protected] (A. Bachiller-Soler), [email protected] (J.A. Rosendo-Macías), [email protected] (G. Álvarez-Cordero). http://dx.doi.org/10.1016/j.epsr.2015.10.009 0378-7796/© 2015 Elsevier B.V. All rights reserved.
Controlled switching systems have become a technically and economically suitable way to mitigate switching transients. In particular, in [11,13], this method has been applied to three-phase transformers. The fundamental aim is to energize the transformer windings at appropriate instants resulting in flux symmetry in consideration to the residual flux. An optimal energization, without core saturation or inrush transients, can be achieved following this method. Since each phase needs to be switched separately, independent-pole-operated circuit breakers are required. While this is normal practice above about 245 kV, additional mechanisms, and hence costs, may be incurred at lower voltage levels where gang operation is common [14]. Furthermore, this method can only be used in transformers whose primary winding has a wye connection and grounded neutral. To achieve the total elimination of the inrush current using circuit breakers with one operating mechanism, it is necessary that the residual fluxes present a particular pattern [11], where the residual flux is equal to zero in one phase and is high in the other two with opposite polarity. Two different ways have been proposed to attain the desired pattern. In [15], DC auxiliary power supply is used to force the core magnetization to the desired pattern before simultaneous closing transformer energization. The DC supply must be disconnected during the transformer switch-on. The method requires a precise knowledge of the magnetization curve of the transformer core and the use of additional equipment. On the other hand, a synchronized switching method for a three-pole
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circuit breaker with fixed delay between poles (mechanically staggered) is presented in [16]. Optimal energization is obtained by setting the residual flux with controlled de-energization. The residual flux pattern is a function of many factors, such as the chopping-current value of the circuit breaker, the magnetic characteristic of the transformer core, and mainly of the capacitance of the winding and other capacitances connected to the transformer. For this reason, precisely controlling deenergization is a difficult task. Furthermore, in the case where there is an unplanned de-energization, for example when a fault occurs, any non-desired pattern can be found in the magnetic core. In this paper, a simpler approach of controlled switching is used to avoid the drawbacks of the above methods and, particularly, to reduce the costs. As in commercial controlled switching devices for three-pole breakers, during uncontrolled de-energization, residual flux is computed by integrating the corresponding phase voltage, in accordance with Faraday’s law. Considering the residual flux, a simultaneous closing instant can be chosen to reduce the inrush current. In [17], a non-optimal heuristic closing instant has been proposed. In this work, an optimal closing instant that results in the lowest possible inrush current is obtained by solving a min–max problem. The advantages of this approach are: three phases are closed simultaneously and hence no independent pole control is required, de-energization does not need to be controlled, and no additional device is required because the corresponding voltage signals needed by the controller for the residual flux calculation process may be taken from Voltage Transformers (VTs) or Capacitor Voltage Transformers (CVTs) which are commonly installed near to the transformer. This method cannot guarantee the complete elimination of the inrush current in all cases, but for its simplicity and low cost, this approach may be the most appropriate solution, especially at lower voltage levels where gang-operated circuit breakers are common. Section 2 focuses on the principles of controlled switching to reduce the inrush current. Section 3 describes the proposed controlled energization strategy, while Section 4 presents the simulation results which verify that a higher reduction of inrush is obtained compared to uncontrolled energization. Practical considerations on how the characteristics of a real circuit breaker affect the proposed strategy are analyzed in Section 5. The results of this paper are summarized in Section 6.
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Fig. 1. Large flux asymmetry created by energization at zero crossing of voltage.
the flux is higher than twice the normal maximum (Fig. 1). The prospective flux is the steady-state flux if the supply source was already connected to the transformer. Fig. 2 illustrates the influence of the maximum flux on the inrush current. Power transformers are designed to operate at a rated voltage and flux close to the saturation knee point (Fig. 2a). The core enters deep saturation as soon as the core flux exceeds the rated value, resulting in a large magnetizing current (Fig. 2b). The basic principle for the elimination of the core flux asymmetry in single-phase transformers is shown in Fig. 3. The optimal instant for transformer energization is when prospective and residual fluxes are equal. This is equivalent to selecting the switching instant t0 such that r = o sin(ωt0 ), in accordance with (2).
2. Controlled switching principles 3. Proposed strategy When a voltage u(t) is applied on the primary winding of an unloaded transformer a flux (t) is established in the magnetic core. Neglecting winding resistance, the relationship between the applied voltage and flux is u(t) = N
d(t) dt
(1)
Suppose a sinusoidal voltage u(t) = Uo cos(ωt) is applied at instant t0 , then the core flux can be calculated analytically as (t) = r +
1 N
t
u()d = r − o sin(ωt0 ) + o sin(ωt)
(2)
t0
where o =Uo /(Nω) is the normal flux peak and r is the residual flux prior to instant t0 . r is a magnetic flux that remains after the transformer is de-energized. From (2), the maximum possible value of the flux (t) upon energization is 2o + r . In the worst case, when the transformer is energized at zero crossing of the voltage and prospective flux is of the opposite polarity as residual flux, then the peak value of
In this section, an optimal strategy for three-phase transformer energization using simultaneous closing is described. The method can be applied to three-phase transformers energized from any winding connection where the sum of the three winding fluxes is equal to zero, that is, for three-legged-core transformers or transformers with a delta connection in another winding. This is not the case for five-leg or shell-type core transformers without delta connected winding. In order to describe the energization process more clearly, it is assumed that the residual fluxes are Ar = R1 , Br = R2 , Cr = R3 with |R1 |, |R2 | ≥ |R3 |, and R1 > 0. As already mentioned, in single-phase transformers, the inrush current can be eliminated by selecting the energization instant when the prospective flux is equal to the residual flux. However, except when the remanent fluxes have certain patterns, this condition cannot be fulfilled simultaneously in each of the three windings of a three-phase transformer. Fig. 4 illustrates the residual fluxes (solid line) R1 , R2 and R3 and prospective fluxes (dashed lines) Ap (t), Bp (t) and Cp (t), as well
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Fig. 3. Optimal energization to eliminate core flux asymmetry in single-phase transformers.
Fig. 4. Remanent fluxes (solid line) do not match simultaneously prospective fluxes (dashed lines) at any instant.
when this difference is as small as possible in the three phases. Hence, there is an optimal instant t0 that can be found as the solution of the following min–max problem: min
ωt ∈ [0,2]
max{|Ap (t) − R1 |, |Bp (t) − R2 |, |Cp (t) − R3 |}
(4)
where residual fluxes, R1 , R2 and R3 satisfy |Ri | < o ,
Fig. 2. Relationship between inrush current and core flux.
i = 1, 2, 3
R1 + R2 + R3 = 0 as the phase-A-to-ground voltage, uAG , used as a time reference defined by uAG (t)
= Uo sin(ωt)
Ap (t)
= o sin(ωt − /2)
Bp (t)
= o sin(ωt + 5/6)
Cp (t)
= o sin(ωt + /6)
(3)
Typically, as Fig. 4 shows, residual fluxes do not simultaneously match prospective fluxes at any instant. Therefore, there is no closing instant that allows the complete elimination of the core flux asymmetry after switching. Since the magnitude of the inrush current depends on the difference between the residual and prospective fluxes, the best instant to energize the transformer is
(5)
As Fig. 5 shows, the min–max problem in (4) has one solution per period, instant t0 , where the greatest difference between the residual and prospective fluxes of the three phases is at its minimum. Graphically, it can be observed that the solution occurs when |Cp (t0 ) − R3 | = 0, sign(Ap (t)) = sign(R1 ) and sign(Bp (t)) = sign(R2 ). By using the zero crossing of voltage uAG with positive derivative as a reference, the instant t0 can be analytically found by means of
arcsin t0 =
R3 o
2f
−
6
(6)
Fig. 6 shows actual (solid lines) and prospective fluxes (dashed lines) during the energization process if simultaneous closing is made at the optimal instant. As can be observed, at t = t0 the residual fluxes of phases A and B are not equal to the corresponding
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Fig. 7. ATPDraw circuit for system simulation.
Fig. 5. Optimal simultaneous closing instant as solution of min–max problem.
Fig. 8. Large core fluxes during uncontrolled energization.
Fig. 6. Actual (solid lines) and prospective (dashed lines) core fluxes for the switching of three phases at optimal time instant t0 .
prospective fluxes and therefore magnetic fluxes of these phases have a DC component after instant t0 . However, if the simultaneous closing of the three phases took place at another instant other than t0 , then the DC component value of the flux in some phase would be greater, resulting in higher saturation of the core and greater inrush current. The optimal energization strategy proposed can be summarized as: (a) Measure phase voltages on the primary side during the deenergization process of the transformer. (b) Compute residual fluxes by integrating the corresponding phase voltages during de-energization. (c) Determine the optimal closing instant based on (6), i.e., the instant at which residual flux and prospective flux match for the phase with lowest absolute value of the residual flux, and the polarities of the residual flux and the prospective flux coincide in the other two phases. (d) Close the three phases simultaneously at the time instant calculated in (c). 4. Simulation of simultaneous closing strategy A number of simulations were conducted using the Alternative Transient Program (ATP) version of Electromagnetic Transients
Fig. 9. High inrush current during uncontrolled energization.
Program (EMTP) to verify the proposed strategy. The test system employed to carry out the simulations, shown in Fig. 7, is composed of a 220 kV, 50 Hz voltage source and a 160 MVA, 220/70.9/24 kV, three-legged-core transformer with YNynd connections. The transformer has been modeled using the hybrid transformer model in ATP/EMTP, whose parameters have been obtained from standard test data provided by the manufacturer. The hybrid transformer model can give an accurate representation of the transformer cores [18–20]. Random energization of this transformer may produce core saturation and large dynamic fluxes (Fig. 8). This saturation results in high magnitude currents (Fig. 9).
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Fig. 10. Core fluxes during controlled energization at the optimal time instant proposed in this paper.
Fig. 12. Residual flux as a function of the disconnection time.
Fig. 11. Inrush current during controlled energization at the optimal time instant proposed in this paper.
Fig. 13. Comparative of results using the proposed strategy, the heuristic strategy and the worst-case uncontrolled energization scenario.
During de-energization, the residual fluxes were calculated by integrating the corresponding phase voltages, yielding, in this case, Ar = 0.56 pu, Br = −0.38 pu, and Cr = −0.18 pu (Fig. 10). Fig. 10 shows core flux evolution during energization following the strategy described in the previous section. The three phases are closed at instant t0 , given by (6) when the prospective flux is equal to the residual flux in the phase in which residual flux is the lowest: phase C in this case. After instant t0 , the phase-C flux does not exceed its nominal amplitude but magnetic fluxes in the other phases have a DC component. As a result of this, no inrush current appears in phase C (Fig. 11), and a significant reduction of this current is obtained in the remaining two phases with respect to random energization. In order to verify the feasibility and performance of the proposed method under any residual flux pattern, a total of 1000 simulations have been carried out according to the following methodology: the transformer is energized and, in steady state, the circuit breaker is randomly opened to generate residual flux conditions. Fig. 12 shows residual fluxes as a function of the disconnection instant using the zero crossing of phase-A voltage as a reference. Related results can be found in [21,22]. The three poles of the breaker are then closed simultaneously at the calculated optimal instant and
the maximum absolute value of inrush current is recorded. The maximum absolute values of inrush current have been plotted as a function of the disconnection instant (Fig. 13). The latter values have been compared to those of the heuristic strategy proposed in [17], and also compared to the values of the worst-case uncontrolled scenario. An important reduction of inrush current has been achieved by the proposed method. 5. Practical considerations Assuming ideal circuit breakers, the currents begin to flow in three poles of circuit breakers at the same instant. In a HVAC circuit breaker, the currents do not start at the same time due to the phenomenon of pre-arcing even when the three phases are mechanically closed simultaneously [23]. During the closing operation, the moving contact approaches the fixed contact and the withstand voltage of the gap decreases from its maximum value to zero when the two contacts touch each other at a rate called the Rate of Decrease of Dielectric Strength (RDDS). At a certain instant, when the momentary voltage across the contact gap exceeds dielectric strength, an electric arc is established and the current flows through it before contacts touch (Fig. 14).
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Fig. 16. Prospective (dashed lines) and actual core fluxes (solid lines) during simultaneous closing operation considering pre-arcing. Fig. 14. Pre-arcing curve. Dielectric strength and voltage across circuit breaker during closing operation.
Fig. 17. Inrush current during controlled energization considering pre-arcing and dynamic flux. Fig. 15. Dielectric strength and voltage across 3-phase circuit breaker during simultaneous closing operation.
In a three-phase system, pre-arcing occurs in one phase earlier than the other two since the three voltages across the circuit breaker are 120◦ out-of-phase from each other. After the first phase has been energized, the flux in the other phases is not a static residual flux and new fluxes, called dynamic fluxes, are established throughout the interaction among the phases [11,13]. This interaction is inherent in most transformers on power systems (transformers with three-phase core type or a delta winding). The simulations performed in the previous section are now revisited while considering the effects of the pre-arcing and the dynamic flux. The dielectric strength and absolute value of voltages across three poles during the closing operation is shown in Fig. 15. Pre-arcing occurs in the first phase (phase C) at instant t0 and in the other two phases at a slightly later time, instant t1 . The dynamic fluxes in the transformer core, after phase C is energized, can be observed in Fig. 16. It is shown that as soon as phase C is energized, the fluxes in the other phases (not yet connected) change in accordance with the magnetic interaction in the transformer. In this case, the dynamic flux has a beneficial effect on reducing the inrush current, because when phases A and B are energized (instant
t1 ), the difference between the prospective and actual fluxes is less than the difference at instant t0 . Inrush current reduction can be observed by comparing Fig. 11 in Section 4 where a circuit-breaker ideal model was used on simulations and Fig. 17 where pre-arcing and dynamic flux has been considered. The simulations considering pre-arcing and dynamic flux have been extended to include any possible flux pattern. The resulting inrush current has been plotted as a function of the disconnection instant in Fig. 18. It is shown that the dynamic flux causes a higher reduction on inrush current due to its contribution to the decrease in the difference between residual and prospective fluxes during the energization process. The performance of a controlled switching strategy can be affected by other factors in addition to the effect of pre-arcing. These factors include mechanical closing time deviations, and errors in the measurement of residual flux [12]. However, this is not a particular problem of the proposed method; it is common to all controlled switching devices that take into account the residual flux. In order to ensure the success of these systems, it is considered that the deviation in the closing time of the circuit breaker must be less than 1ms and that the error in the measurement of
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Fig. 18. Comparative of results using the proposed method with pre-arcing and dynamic flux, and the worst-case uncontrolled energization scenario.
residual flow must not exceed 20% [22]. These requirements are easily achievable with current technology. 6. Conclusions Controlled switching using simultaneous closing strategy allows the use of a three-pole-operated circuit breaker, which represent a significant reduction in costs compared to that of an independentpole-operated circuit breaker. In this work, the optimal instant for simultaneous closing is obtained as a function of the lowest absolute residual magnetic flux remaining on the transformer core. Simulation results, using an ideal circuit-breaker, have demonstrated that the inrush current can be drastically reduced if the transformer is energized at the calculated optimal instant. Subsequent simulations considering the effects of circuit breaker pre-arcing and dynamic flux in the transformer core have shown that these effects provide a higher reduction of the inrush current. Complete elimination of the inrush current cannot be achieved by simultaneous closing strategy. However, this approach may be the most appropriate solution at lower voltage levels where gangoperated circuit breakers are common. Acknowledgement The authors would like to acknowledge the financial support of ˜ (Spanish TSO) under grant PI-0939/2012. Red Eléctrica de Espana References [1] R.J.N. Alencar, U.H. Bezerra, A.M.D. Ferreira, A method to identify inrush currents in power transformers protection based on the differential current gradient, Electric Power Syst. Res. 111 (2014) 78–84, http://dx.doi.org/10.1016/ j.epsr.2014.02.009. [2] R. Hamilton, Analysis of transformer inrush current and comparison of harmonic restraint methods in transformer protection, IEEE Trans. Ind. Appl. 49 (4) (2013) 1890–1899, http://dx.doi.org/10.1109/TIA.2013.2257155.
[3] M. Steurer, K. Frohlich, The impact of inrush currents on the mechanical stress of high voltage power transformer coils, IEEE Trans. Power Deliv. 17 (1) (2002) 155–160, http://dx.doi.org/10.1109/61.974203. [4] M. Abdul Rahman, T. Lie, K. Prasad, The effects of short-circuit and inrush currents on HTS transformer windings, IEEE Trans. Appl. Supercond. 22 (2) (2012) 5500108, http://dx.doi.org/10.1109/TASC.2011.2173571. [5] M. Nagpal, T. Martinich, A. Moshref, K. Morison, P. Kundur, Assessing and limiting impact of transformer inrush current on power quality, IEEE Trans. Power Deliv. 21 (2) (2006) 890–896, http://dx.doi.org/10.1109/TPWRD.2005. 858782. [6] L.F. Blume, G. Camilli, S.B. Farnham, H.A. Peterson, Transformer magnetizing inrush currents and influence on system operation, Trans. Am. Inst. Electr. Eng. 63 (6) (1944) 366–375. [7] H.-T. Tseng, J.-F. Chen, Bidirectional impedance-type transformer inrush current limiter, Electr. Power Syst. Res. 104 (2013) 193–206, http://dx.doi.org/10. 1016/j.epsr.2013.06.007. [8] A. Ketabi, A. Hadidi Zavareh, New method for inrush current mitigation using series voltage-source PWM converter for three phase transformer, in: 2011 2nd Power Electronics, Drive Systems and Technologies Conference (PEDSTC), 2011, pp. 501–506, http://dx.doi.org/10.1109/PEDSTC.2011.5742470. [9] Y. Cui, S. Abdulsalam, S. Chen, W. Xu, A sequential phase energization technique for transformer inrush current reduction – Part I: Simulation and experimental results, IEEE Trans. Power Deliv. 20 (2) (2005) 943–949, http://dx.doi.org/10. 1109/TPWRD.2004.843467. [10] G. Hajivar, S. Mortazavi, M. Saniei, The neutral grounding resistor sizing using an analytical method based on nonlinear transformer model for inrush current mitigation, in: 2010 45th International Universities Power Engineering Conference (UPEC), 2010, pp. 1–5. [11] J. Brunke, K. Frohlich, Elimination of transformer inrush currents by controlled switching. I. Theoretical considerations, IEEE Trans. Power Deliv. 16 (2) (2001) 276–280, http://dx.doi.org/10.1109/61.915495. [12] J. Brunke, K. Frohlich, Elimination of transformer inrush currents by controlled switching. II. Application and performance considerations, IEEE Trans. Power Deliv. 16 (2) (2001) 281–285, http://dx.doi.org/10.1109/61.915496. [13] J. Oliveira, C. Tavares, R. Apolonio, A. Vasconcellos, H. Bronzeado, Transformer controlled switching to eliminate inrush current – Part I: Theory and laboratory validation, in: TDC ’06. IEEE/PES Transmission Distribution Conference and Exposition: Latin America 2006, 2006, pp. 1–5, http://dx.doi.org/10.1109/ TDCLA.2006.311523. [14] CIGRÉ Working Group A3.07, Controlled Switching of HVAC Circuit Breakers, Benefits and Economic Aspects, CIGRÉ Broschure No. 262. [15] M. Novak, Elimination of three-phase transformer inrush current through core forced magnetization and simultaneous closing, in: 2010 International Conference on Applied Electronics (AE), 2010, pp. 1–4. [16] L. Prikler, G. Bánfai, G. Bán, P. Becker, Reducing the magnetizing inrush current by means of controlled energization and de-energization of large power transformers, Electric Power Syst. Res. 76 (8) (2006) 642–649, http://dx.doi.org/10. 1016/j.epsr.2005.12.022 (Selected Topics in Power System Transients). [17] T. Koshizuka, H. Kusuyama, M. Saito, H. Maehara, Y. Sato, H. Toda, Controlled switching for energizing 3-phase transformers in isolated neutral system, in: 2009 Transmission Distribution Conference Exposition: Asia and Pacific, 2009, pp. 1–4, http://dx.doi.org/10.1109/TD-ASIA.2009.5357024. [18] B. Mork, F. Gonzalez, D. Ishchenko, D. Stuehm, J. Mitra, Hybrid transformer model for transient simulation; Part I: Development and parameters, IEEE Trans. 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Contents lists available at ScienceDirect
Electric Power Systems Research journal homepage: www.elsevier.com/locate/epsr
Optimal gang-operated switching for transformer inrush current reduction Ramón Cano-González a,∗ , Alfonso Bachiller-Soler a , José Antonio Rosendo-Macías a , Gabriel Álvarez-Cordero b a b
Department of Electrical Engineering, University of Sevilla, Escuela Superior de Ingenieros, Camino de los Descubrimientos s/n, 41092 Sevilla, Spain Red Eléctrica de Espa˜ na (Spanish TSO), Paseo del Conde de los Gaitanes 177, 28109 Alcobendas, Madrid, Spain
a r t i c l e
i n f o
Article history: Received 11 January 2015 Received in revised form 13 May 2015 Accepted 5 October 2015 Keywords: Controlled switching Inrush current Power transformer Gang-operated circuit breaker Simultaneous closing ATP–EMTP
a b s t r a c t Controlled switching technology with independent-pole-operated circuit breakers is an effective way to eliminate transient transformer inrush currents. This technique cannot usually be applied at lower voltage levels where three-pole-operated circuit breakers are more frequent. In this paper, the optimal instant for a simultaneous closing is obtained as a solution of a min–max problem. The proposed strategy has been evaluated in a test system using EMTP/ATP and has presented highly satisfactory results, even when actual characteristics of circuit breakers are taken into account. © 2015 Elsevier B.V. All rights reserved.
1. Introduction Power transformers are among the most important devices in power networks. Transformer energization may result in a high magnetization current, also known as inrush current, due to the saturation of magnetic flux in the core. The inrush current is asymmetric and unbalanced between the phases and can reach a value that is several times higher than the rated current of the transformer. These transient currents have many unfavorable effects including: malfunction of protective relays or fuses [1,2], reduction of transformer lifecycle due to large current forces in windings [3,4], and temporary voltage drop due to impedance of the network between the sources and the energized transformer [5,6], thereby affecting the power quality of the network. Various methods have been proposed to eliminate or at least reduce the inrush current, such as series compensator [7,8], sequential phase energization with a grounding resistor [9,10] and controlled switching [11–13].
∗ Corresponding author. Tel.: +34 954 455 2814. E-mail addresses: [email protected] (R. Cano-González), [email protected] (A. Bachiller-Soler), [email protected] (J.A. Rosendo-Macías), [email protected] (G. Álvarez-Cordero). http://dx.doi.org/10.1016/j.epsr.2015.10.009 0378-7796/© 2015 Elsevier B.V. All rights reserved.
Controlled switching systems have become a technically and economically suitable way to mitigate switching transients. In particular, in [11,13], this method has been applied to three-phase transformers. The fundamental aim is to energize the transformer windings at appropriate instants resulting in flux symmetry in consideration to the residual flux. An optimal energization, without core saturation or inrush transients, can be achieved following this method. Since each phase needs to be switched separately, independent-pole-operated circuit breakers are required. While this is normal practice above about 245 kV, additional mechanisms, and hence costs, may be incurred at lower voltage levels where gang operation is common [14]. Furthermore, this method can only be used in transformers whose primary winding has a wye connection and grounded neutral. To achieve the total elimination of the inrush current using circuit breakers with one operating mechanism, it is necessary that the residual fluxes present a particular pattern [11], where the residual flux is equal to zero in one phase and is high in the other two with opposite polarity. Two different ways have been proposed to attain the desired pattern. In [15], DC auxiliary power supply is used to force the core magnetization to the desired pattern before simultaneous closing transformer energization. The DC supply must be disconnected during the transformer switch-on. The method requires a precise knowledge of the magnetization curve of the transformer core and the use of additional equipment. On the other hand, a synchronized switching method for a three-pole
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circuit breaker with fixed delay between poles (mechanically staggered) is presented in [16]. Optimal energization is obtained by setting the residual flux with controlled de-energization. The residual flux pattern is a function of many factors, such as the chopping-current value of the circuit breaker, the magnetic characteristic of the transformer core, and mainly of the capacitance of the winding and other capacitances connected to the transformer. For this reason, precisely controlling deenergization is a difficult task. Furthermore, in the case where there is an unplanned de-energization, for example when a fault occurs, any non-desired pattern can be found in the magnetic core. In this paper, a simpler approach of controlled switching is used to avoid the drawbacks of the above methods and, particularly, to reduce the costs. As in commercial controlled switching devices for three-pole breakers, during uncontrolled de-energization, residual flux is computed by integrating the corresponding phase voltage, in accordance with Faraday’s law. Considering the residual flux, a simultaneous closing instant can be chosen to reduce the inrush current. In [17], a non-optimal heuristic closing instant has been proposed. In this work, an optimal closing instant that results in the lowest possible inrush current is obtained by solving a min–max problem. The advantages of this approach are: three phases are closed simultaneously and hence no independent pole control is required, de-energization does not need to be controlled, and no additional device is required because the corresponding voltage signals needed by the controller for the residual flux calculation process may be taken from Voltage Transformers (VTs) or Capacitor Voltage Transformers (CVTs) which are commonly installed near to the transformer. This method cannot guarantee the complete elimination of the inrush current in all cases, but for its simplicity and low cost, this approach may be the most appropriate solution, especially at lower voltage levels where gang-operated circuit breakers are common. Section 2 focuses on the principles of controlled switching to reduce the inrush current. Section 3 describes the proposed controlled energization strategy, while Section 4 presents the simulation results which verify that a higher reduction of inrush is obtained compared to uncontrolled energization. Practical considerations on how the characteristics of a real circuit breaker affect the proposed strategy are analyzed in Section 5. The results of this paper are summarized in Section 6.
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Fig. 1. Large flux asymmetry created by energization at zero crossing of voltage.
the flux is higher than twice the normal maximum (Fig. 1). The prospective flux is the steady-state flux if the supply source was already connected to the transformer. Fig. 2 illustrates the influence of the maximum flux on the inrush current. Power transformers are designed to operate at a rated voltage and flux close to the saturation knee point (Fig. 2a). The core enters deep saturation as soon as the core flux exceeds the rated value, resulting in a large magnetizing current (Fig. 2b). The basic principle for the elimination of the core flux asymmetry in single-phase transformers is shown in Fig. 3. The optimal instant for transformer energization is when prospective and residual fluxes are equal. This is equivalent to selecting the switching instant t0 such that r = o sin(ωt0 ), in accordance with (2).
2. Controlled switching principles 3. Proposed strategy When a voltage u(t) is applied on the primary winding of an unloaded transformer a flux (t) is established in the magnetic core. Neglecting winding resistance, the relationship between the applied voltage and flux is u(t) = N
d(t) dt
(1)
Suppose a sinusoidal voltage u(t) = Uo cos(ωt) is applied at instant t0 , then the core flux can be calculated analytically as (t) = r +
1 N
t
u()d = r − o sin(ωt0 ) + o sin(ωt)
(2)
t0
where o =Uo /(Nω) is the normal flux peak and r is the residual flux prior to instant t0 . r is a magnetic flux that remains after the transformer is de-energized. From (2), the maximum possible value of the flux (t) upon energization is 2o + r . In the worst case, when the transformer is energized at zero crossing of the voltage and prospective flux is of the opposite polarity as residual flux, then the peak value of
In this section, an optimal strategy for three-phase transformer energization using simultaneous closing is described. The method can be applied to three-phase transformers energized from any winding connection where the sum of the three winding fluxes is equal to zero, that is, for three-legged-core transformers or transformers with a delta connection in another winding. This is not the case for five-leg or shell-type core transformers without delta connected winding. In order to describe the energization process more clearly, it is assumed that the residual fluxes are Ar = R1 , Br = R2 , Cr = R3 with |R1 |, |R2 | ≥ |R3 |, and R1 > 0. As already mentioned, in single-phase transformers, the inrush current can be eliminated by selecting the energization instant when the prospective flux is equal to the residual flux. However, except when the remanent fluxes have certain patterns, this condition cannot be fulfilled simultaneously in each of the three windings of a three-phase transformer. Fig. 4 illustrates the residual fluxes (solid line) R1 , R2 and R3 and prospective fluxes (dashed lines) Ap (t), Bp (t) and Cp (t), as well
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Fig. 3. Optimal energization to eliminate core flux asymmetry in single-phase transformers.
Fig. 4. Remanent fluxes (solid line) do not match simultaneously prospective fluxes (dashed lines) at any instant.
when this difference is as small as possible in the three phases. Hence, there is an optimal instant t0 that can be found as the solution of the following min–max problem: min
ωt ∈ [0,2]
max{|Ap (t) − R1 |, |Bp (t) − R2 |, |Cp (t) − R3 |}
(4)
where residual fluxes, R1 , R2 and R3 satisfy |Ri | < o ,
Fig. 2. Relationship between inrush current and core flux.
i = 1, 2, 3
R1 + R2 + R3 = 0 as the phase-A-to-ground voltage, uAG , used as a time reference defined by uAG (t)
= Uo sin(ωt)
Ap (t)
= o sin(ωt − /2)
Bp (t)
= o sin(ωt + 5/6)
Cp (t)
= o sin(ωt + /6)
(3)
Typically, as Fig. 4 shows, residual fluxes do not simultaneously match prospective fluxes at any instant. Therefore, there is no closing instant that allows the complete elimination of the core flux asymmetry after switching. Since the magnitude of the inrush current depends on the difference between the residual and prospective fluxes, the best instant to energize the transformer is
(5)
As Fig. 5 shows, the min–max problem in (4) has one solution per period, instant t0 , where the greatest difference between the residual and prospective fluxes of the three phases is at its minimum. Graphically, it can be observed that the solution occurs when |Cp (t0 ) − R3 | = 0, sign(Ap (t)) = sign(R1 ) and sign(Bp (t)) = sign(R2 ). By using the zero crossing of voltage uAG with positive derivative as a reference, the instant t0 can be analytically found by means of
arcsin t0 =
R3 o
2f
−
6
(6)
Fig. 6 shows actual (solid lines) and prospective fluxes (dashed lines) during the energization process if simultaneous closing is made at the optimal instant. As can be observed, at t = t0 the residual fluxes of phases A and B are not equal to the corresponding
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Fig. 7. ATPDraw circuit for system simulation.
Fig. 5. Optimal simultaneous closing instant as solution of min–max problem.
Fig. 8. Large core fluxes during uncontrolled energization.
Fig. 6. Actual (solid lines) and prospective (dashed lines) core fluxes for the switching of three phases at optimal time instant t0 .
prospective fluxes and therefore magnetic fluxes of these phases have a DC component after instant t0 . However, if the simultaneous closing of the three phases took place at another instant other than t0 , then the DC component value of the flux in some phase would be greater, resulting in higher saturation of the core and greater inrush current. The optimal energization strategy proposed can be summarized as: (a) Measure phase voltages on the primary side during the deenergization process of the transformer. (b) Compute residual fluxes by integrating the corresponding phase voltages during de-energization. (c) Determine the optimal closing instant based on (6), i.e., the instant at which residual flux and prospective flux match for the phase with lowest absolute value of the residual flux, and the polarities of the residual flux and the prospective flux coincide in the other two phases. (d) Close the three phases simultaneously at the time instant calculated in (c). 4. Simulation of simultaneous closing strategy A number of simulations were conducted using the Alternative Transient Program (ATP) version of Electromagnetic Transients
Fig. 9. High inrush current during uncontrolled energization.
Program (EMTP) to verify the proposed strategy. The test system employed to carry out the simulations, shown in Fig. 7, is composed of a 220 kV, 50 Hz voltage source and a 160 MVA, 220/70.9/24 kV, three-legged-core transformer with YNynd connections. The transformer has been modeled using the hybrid transformer model in ATP/EMTP, whose parameters have been obtained from standard test data provided by the manufacturer. The hybrid transformer model can give an accurate representation of the transformer cores [18–20]. Random energization of this transformer may produce core saturation and large dynamic fluxes (Fig. 8). This saturation results in high magnitude currents (Fig. 9).
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Fig. 10. Core fluxes during controlled energization at the optimal time instant proposed in this paper.
Fig. 12. Residual flux as a function of the disconnection time.
Fig. 11. Inrush current during controlled energization at the optimal time instant proposed in this paper.
Fig. 13. Comparative of results using the proposed strategy, the heuristic strategy and the worst-case uncontrolled energization scenario.
During de-energization, the residual fluxes were calculated by integrating the corresponding phase voltages, yielding, in this case, Ar = 0.56 pu, Br = −0.38 pu, and Cr = −0.18 pu (Fig. 10). Fig. 10 shows core flux evolution during energization following the strategy described in the previous section. The three phases are closed at instant t0 , given by (6) when the prospective flux is equal to the residual flux in the phase in which residual flux is the lowest: phase C in this case. After instant t0 , the phase-C flux does not exceed its nominal amplitude but magnetic fluxes in the other phases have a DC component. As a result of this, no inrush current appears in phase C (Fig. 11), and a significant reduction of this current is obtained in the remaining two phases with respect to random energization. In order to verify the feasibility and performance of the proposed method under any residual flux pattern, a total of 1000 simulations have been carried out according to the following methodology: the transformer is energized and, in steady state, the circuit breaker is randomly opened to generate residual flux conditions. Fig. 12 shows residual fluxes as a function of the disconnection instant using the zero crossing of phase-A voltage as a reference. Related results can be found in [21,22]. The three poles of the breaker are then closed simultaneously at the calculated optimal instant and
the maximum absolute value of inrush current is recorded. The maximum absolute values of inrush current have been plotted as a function of the disconnection instant (Fig. 13). The latter values have been compared to those of the heuristic strategy proposed in [17], and also compared to the values of the worst-case uncontrolled scenario. An important reduction of inrush current has been achieved by the proposed method. 5. Practical considerations Assuming ideal circuit breakers, the currents begin to flow in three poles of circuit breakers at the same instant. In a HVAC circuit breaker, the currents do not start at the same time due to the phenomenon of pre-arcing even when the three phases are mechanically closed simultaneously [23]. During the closing operation, the moving contact approaches the fixed contact and the withstand voltage of the gap decreases from its maximum value to zero when the two contacts touch each other at a rate called the Rate of Decrease of Dielectric Strength (RDDS). At a certain instant, when the momentary voltage across the contact gap exceeds dielectric strength, an electric arc is established and the current flows through it before contacts touch (Fig. 14).
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Fig. 16. Prospective (dashed lines) and actual core fluxes (solid lines) during simultaneous closing operation considering pre-arcing. Fig. 14. Pre-arcing curve. Dielectric strength and voltage across circuit breaker during closing operation.
Fig. 17. Inrush current during controlled energization considering pre-arcing and dynamic flux. Fig. 15. Dielectric strength and voltage across 3-phase circuit breaker during simultaneous closing operation.
In a three-phase system, pre-arcing occurs in one phase earlier than the other two since the three voltages across the circuit breaker are 120◦ out-of-phase from each other. After the first phase has been energized, the flux in the other phases is not a static residual flux and new fluxes, called dynamic fluxes, are established throughout the interaction among the phases [11,13]. This interaction is inherent in most transformers on power systems (transformers with three-phase core type or a delta winding). The simulations performed in the previous section are now revisited while considering the effects of the pre-arcing and the dynamic flux. The dielectric strength and absolute value of voltages across three poles during the closing operation is shown in Fig. 15. Pre-arcing occurs in the first phase (phase C) at instant t0 and in the other two phases at a slightly later time, instant t1 . The dynamic fluxes in the transformer core, after phase C is energized, can be observed in Fig. 16. It is shown that as soon as phase C is energized, the fluxes in the other phases (not yet connected) change in accordance with the magnetic interaction in the transformer. In this case, the dynamic flux has a beneficial effect on reducing the inrush current, because when phases A and B are energized (instant
t1 ), the difference between the prospective and actual fluxes is less than the difference at instant t0 . Inrush current reduction can be observed by comparing Fig. 11 in Section 4 where a circuit-breaker ideal model was used on simulations and Fig. 17 where pre-arcing and dynamic flux has been considered. The simulations considering pre-arcing and dynamic flux have been extended to include any possible flux pattern. The resulting inrush current has been plotted as a function of the disconnection instant in Fig. 18. It is shown that the dynamic flux causes a higher reduction on inrush current due to its contribution to the decrease in the difference between residual and prospective fluxes during the energization process. The performance of a controlled switching strategy can be affected by other factors in addition to the effect of pre-arcing. These factors include mechanical closing time deviations, and errors in the measurement of residual flux [12]. However, this is not a particular problem of the proposed method; it is common to all controlled switching devices that take into account the residual flux. In order to ensure the success of these systems, it is considered that the deviation in the closing time of the circuit breaker must be less than 1ms and that the error in the measurement of
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Fig. 18. Comparative of results using the proposed method with pre-arcing and dynamic flux, and the worst-case uncontrolled energization scenario.
residual flow must not exceed 20% [22]. These requirements are easily achievable with current technology. 6. Conclusions Controlled switching using simultaneous closing strategy allows the use of a three-pole-operated circuit breaker, which represent a significant reduction in costs compared to that of an independentpole-operated circuit breaker. In this work, the optimal instant for simultaneous closing is obtained as a function of the lowest absolute residual magnetic flux remaining on the transformer core. Simulation results, using an ideal circuit-breaker, have demonstrated that the inrush current can be drastically reduced if the transformer is energized at the calculated optimal instant. Subsequent simulations considering the effects of circuit breaker pre-arcing and dynamic flux in the transformer core have shown that these effects provide a higher reduction of the inrush current. Complete elimination of the inrush current cannot be achieved by simultaneous closing strategy. However, this approach may be the most appropriate solution at lower voltage levels where gangoperated circuit breakers are common. Acknowledgement The authors would like to acknowledge the financial support of ˜ (Spanish TSO) under grant PI-0939/2012. Red Eléctrica de Espana References [1] R.J.N. Alencar, U.H. Bezerra, A.M.D. Ferreira, A method to identify inrush currents in power transformers protection based on the differential current gradient, Electric Power Syst. Res. 111 (2014) 78–84, http://dx.doi.org/10.1016/ j.epsr.2014.02.009. [2] R. Hamilton, Analysis of transformer inrush current and comparison of harmonic restraint methods in transformer protection, IEEE Trans. Ind. Appl. 49 (4) (2013) 1890–1899, http://dx.doi.org/10.1109/TIA.2013.2257155.
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