A controlled switching methodology for transformer inrush current

A controlled switching methodology for transformer inrush current elimination: theory and experimental validation Alex Reis, José C. de Oliveira

Roberto Apolonio

Herivelto S. Bronzeado

Faculty of Electrical Engineering Federal University of Uberlândia Uberlândia, Brazil

Electrical Engineering Department Federal University of Mato Grosso Cuiabá, Brazil

Ministry of National Integration Brasília, Brazil

Abstract—Transformers are generally energized by closing the circuit breakers at random times. Consequently, this operation generates high transient inrush currents as a result of the asymmetrical magnetic flux produced in the windings. In light of these facts, this paper presents a strategy to control the switching phenomena which occurs during power transformer inrush. The general idea consists of calculating the pre-existing magnetic fluxes left on the core limbs as a function of operating voltage previously applied to the transformer, just prior to the moment in which de-energization has happened. By using these data and the equations to predict the most suitable closing moments, it is shown the proposal effectiveness at accomplishing the main target here pointed out. Experimental investigations are carried out in order to demonstrate the application method and its validation. The results show the feasibility of building hardware and software structures to drastically reduce the transformer inrush currents. Keywords-Controlled switching; Inrush current; Power quality; Residual flux; Transformer energization; Transient mitigation.

I.

INTRODUCTION

It is well known that uncontrolled energization of power transformers can result in dynamic phenomena in magnetic cores, causing transformers to operate with high saturation levels under transient conditions. As a direct consequence, the values of the three-phase magnetization currents will frequently show very high values during the energization. These asymmetrical high-magnitude currents, named inrush currents, have an ample harmonic spectrum, including odd and even components, and may cause a variety of undesirable effects such as improper operation of protective relays and fuses, harmonic resonance, mechanical damage to the transformer windings, deterioration of the insulation and voltage sags. The values reached by the magnetization current depend basically on two factors: the point on the voltage waveform in which the switches are closed and the actual residual flux in the transformer magnetic core. In fact, when the transformer is energized, at the point in which zero crosses the voltage wave, for instance, the core transient flux, produced by the integral of the supply voltage and the magnetization current, may achieve their maximum values and, consequently, high inrush The authors would like to thank CAPES, CHESF and FAPEMIG for providing postgraduate scholarships and financial support to this research project.

currents may be observed. On the other hand, it is possible to start the operation directly with rated steady state magnetic flux in the core. Under these circumstances, the steady state magnetizing current will be promptly assumed. To achieve this, it is necessary that, at the switches closing moments, the instantaneous voltages produce equal fluxes than the preenergizing ones in the transformer core magnetic columns [1]. By using this approach, no transient magnetizing should occur and the transformers will be driven directly to the final steadystate condition. Reference [2] presents a theoretical and experimental pattern to inrush current that establishes a relationship between current peak and the moments of transformer connection and disconnection. A technique to mitigate the energization current is proposed, which uses a three-phase simultaneous closing with the moment of switch, dependent on the moment of disconnection. This strategy has proved to limit inrush current to 2.5 of the nominal current without the need of residual fluxes calculations. Nevertheless, the authors recommend further investigations to determine the general applicability of this approach. Another method to obtain low inrush current consists in using pre-inserting neutral to ground resistors during the transformer energization stage as given by [3]. Computational and laboratory investigations reveal that this approach may result in 80% to 90% of inrush reduction [4], [5]. This technique, however, is restricted to star grounded connected transformers and some specific non earthed star connections. The approach is not applicable to delta arrangements. Aimed at achieving the control of transformers inrush current in more general terms, this paper establishes a proposal to calculate the residual flux that remains in the transformer core by the end of a previous de-energization operation. Then, prior to the next transformer energization, a mathematical strategy is developed to define the optimal moments, based in the applied voltage waveforms, for the closing off the switches so as to eliminate the undesirable high level of inrush currents. The theory concerning the methodology to control the transient current is fully validated throughout laboratory experiments.

II.

INRUSH CURRENT MITIGATION – THE STRATEGY

The basic principle for the elimination of over flux, or the asymmetrical flux appearing in the transformer core during its energization, is to guarantee that the residual flux must be equal to the presumable (or prospective) flux. The presumable flux corresponds to that created in the core when the supply source is connected to the transformer and the steady-state condition is reached. For a single-phase transformer with null residual flux, the optimal moments for closing off the switches occur when the supply voltage waveforms show their maximum values at the closing moment. This would be enough to suppress the transient behavior due to the energization. However, a threephase core type transformer has inherent interaction with the fluxes of the phases or the core structure limbs. Keeping this in mind, after that first phase (or two phases, depending on the winding connections) is energized, new operating fluxes are established through the other columns/legs. These variables are referred to as dynamic fluxes in the core. Starting from initial stored and arbitrary residual fluxes, the optimal instant for the first switch to be closed coincides with the point on the voltage waveform at which the instantaneous voltage assumes the value v defined by (1).
=  ∙  

(1)

In (1), Vmax represents the peak of the sinusoidal voltage as applied to the transformer winding terminals. The angle α defines the exact instant to switch the breaker pole so as to meet the above optimal point on wave and it can be calculated by (2):  = sin 

 

 + 90°

imposed with no transient. The reason for selecting phase C to be first closed is based in the fact that it has the highest absolute residual value of flux. After the first switch closing, the flux generated for it will modify the other transformer columns/legs magnetization state, eliminating the residual fluxes previously existing. This creates the so-called dynamic fluxes. Thus, two periodic fluxes will occur as illustrated later. By adding both waveforms the result must be equaled to the flux generated by the phase that was first energized. The optimal instant for the energization of the two remaining phases still opened is, sequentially, derived from the results of the simulations [6]. This approach uses the presumable fluxes and the dynamic fluxes that are established in the cores after the first phase energization. Fig. 2 illustrates a typical result where phase C, as previously stated, was energized first. In that figure, the presumable flux (Flxp) and the dynamic fluxes (Flxd) related to A and B phases are shown. The comparison between the presumable flux and the dynamic flux generated in the transformer core, as result of the energization only of the phase C, produces repetitive instants of time where, simultaneously, the presumable and the dynamic fluxes in the core are equals for the two phases. These points are optimal moments for the simultaneous switch of the two phases that still meet in open. Table 1 summarizes the general equations to determine the optimal instants for closing (toptimal_closing) the two phases which are still open, as a function of which phase was first energized. The reference for counting off the time 2+,*34 is the phase showing zero-crossing voltage waveform with positive

(2)

As for the maximum value for the flux, this can be readily calculated in accordance with classical relationship as given by (3). # =

$

%,%%'(('∙)∙*

(3)

where: #+,-./01 – residual flux found in the transformer legs; Vrms – RMS voltage applied to the transformer winding; n – number turns for the winding being energized; f – supply fundamental power frequency.

Figure 1. Core flux after phase C is first switched on

The previous equations aiming at defining the optimal closing point for the first phase to be connected yield to two theoretically moments. For positive residual flux, the switching angle will be situated between 90° and 180°, i.e. positive voltage with negative derivative. The second angle will be situated between 180° and 270°, i.e. negative voltage with negative derivative. In this work, only the first angle will be used for control purposes. Fig. 1 shows the dynamic fluxes in the transformer core after the closing of phase C in first place. It is shown that as soon as phase C presumable flux is equal to the corresponding residual value, a steady state condition is immediately

Figure 2. Optimal points for closing the remaining phases: A and B phases

derivative. These equations are applied to optimal switching of Y-grounded/Y-grounded transformers. Reference [6] presents the same methodology while considering other transformer winding connections. TABLE I. OPTIMAL POINT TO CLOSE THE TWO PHASES STILL OPEN (PRIMARY: Y-GROUNDED; SECONDARY: Y-GROUNDED) First Phase energized

567589:;_=;6>8?@ B + 7.7 ∙ 10G 2 B 2 = 2+,*34 + 3 ′ + 14 ∙ + 5.6 ∙ 10G 2 B 2 = 2+,*() + ( ′ + 2) ∙ + 3.45 ∙ 10G 2 2 = 2+,*34 + ′ ∙

(A) (B) (C)

where: T – voltage waveform period; ′ – number of semicycles the optimal instants are repeated; III.

Figure 4. Voltage waveform during transformer de-energization

In accordance with the procedures given in Fig.3, the core transformer residual flux calculation is carried out using the following sequence: •

First, two voltage integrations are sequentially performed (path 1) to estimate the flux mean value. This step uses only the first cycle of the voltage waveform as presented in Fig. 5;

•

The second stage utilizes the single path integration (path 2) over the entire period of measurement given by the region starting from the red line and ending at the point of transformer disconnection from the mains. The blue line is related to the moment the trip signal is sent to the breaker operation. The result of this step is presented in Fig. 6;

•

The residual flux associated with the focused phase is obtained by the difference between the results of the previous steps, as previously illustrated in Fig. 3. This is how the residual flux is determined, as presented in Fig. 7.

RESIDUAL FLUX DETERMINATION

One of the most challenging topics associated with the procedure for controlled switching consists of finding the residual fluxes as required by the control strategy. This is defined by the conditions imposed on the transformer at the moment that precedes its interruption. The correct estimation of the residual flux is extremely important for the success of the controlled switching strategy [7], as it defines the point on the voltage waveform at which the switches are to be closed next. The previous AC flux was established in the core before the transformer is switched off, and consequently, the residual flux can be found throughout the integration of the voltage applied to the transformer winding terminals. Fig. 3 presents the block diagram of the procedure used to calculate this remaining flux in the transformer core. A data acquisition system continuously stores the voltage waveform at the winding terminals during de-energization. Fig 4 makes it clear that the calculation of the residual flux is initiated at first zero crossing of voltage waveform with positive derivate counted from the breaker trip occurrence.

Figure 5. Core transformer flux calculation – stage 1

∫

∫ ∫

Figure 3. Core flux calculation – block diagram

Figure 6. Core transformer flux calculation – stage 2

Figure 7. Core flux before the transformer de-energization

The previously procedure to calculate the residual flux could also be performed using the voltage waveform when zero crosses with negative derivate. In this case, the final flux mean value must be taken with an opposite signal. IV.

EXPERIMENTAL RESULTS

Once the methodology to calculate the residual flux and to determine the optimal switching points have been established, some energization tests were carried out in a laboratory environment in order to verify the effectiveness of the overall controlled switching. These experiments utilized a threephase, three-limb core type transformer with the main parameters given in Table 2. It must be emphasized that, in accordance with previous equations and information, a Ygrounded/Y-grounded winding connections have been used. However, the approach is capable of dealing with other configurations. As for the additional devices required to measure, calculate, and switch on the transformer, they have been omitted due to the lack of space, but they only represent experimental resources that are detailed in [6]. The case studies described here are: •

Case 1: Uncontrolled closing of the switches;

•

Case 2: Controlled switching using the strategy previously defined.

three-phase

simultaneous

Fig. 8 shows the voltage waveforms during transformer deenergization, for case 1. Using the methodology proposed, the residual fluxes were calculated and are presented in Fig. 9. Although the values of the residual fluxes are not used for the uncontrolled switching, they are given here to show that there is no relationship between transformer core pre-existing residual flux and those imposed at the new transformer energization. TABLE II.

Figure 8. Voltage waveforms at the transformer input terminals during deenergization conditions (Case 1)

Figure 9. Calculated residual fluxes (Case 1)

Fig.10 represents the measured voltage waveforms applied to transformer terminals at the subsequent energization procedure with no control. As a direct and expected consequence of this operation, and in agreement with traditional results, the corresponding inrush current waveforms obtained are presented in Fig. 11 and Fig. 12. It can be seen that, under uncontrolled energization conditions, line A has led to the highest peak for the transient current peak. It has reached 92.82 A, which corresponds to about 5 times the rated transformer peak current. To make clear the current waveforms the results related to line A, B and C have been divided in two different figures.

TRANSFORMER PARAMETERS

Rated Power (kVA)

5

Primary and secondary voltage (V)

220

Rated current (A)

13

Primary and secondary windings turns

150

Primary and secondary resistance (Ω)

1.2 Figure 10. Applied voltage waveforms at the transformer input terminals at the re-inergization (Case 1)

0.12

Figure 11. Inrush line A and B currents (Case 1) Figure 13. Block diagram of the controlled switching structure

Figure 12. Inrush line C current (Case 1)

To perform the controlled switching investigation, the experimental arrangement was set up in accordance with the physical structure given in Fig. 13. The following steps have being utilized: •

The monitoring of the voltages at the transformer primary windings over three distinct regions: before, during and after de-energization. Fig. 14 shows the waveforms obtained;

•

Then, utilizing the given measurement and calculation structure, the residual fluxes associated with the previous operating conditions were found as given in Fig. 15. To complement the information, Table 3 summarizes the results obtained in this step and gives the optimum switching angle for line A to be first inserted due the the highest value found for the residual flux;

•

Using the previous angle, the line A switching point is calculated at 3.20 ms after the positive derivate is crossed at zero. It must be stressed that the reference for counting off the time is the phase A zero crossing moment;

•

Finally, the optimal moments to close the two phases which are still open are performed in accordance with the expressions given in Table 1 resulted in the following: T = 16.667 ms and n’ = 8. This implies that a final point of 74.40 ms is to be simultaneously applied to phases B and C switches, counted from phase A connection.

Figure 14. Voltage waveforms at the transformer input terminals during deenergization conditions (Case 2)

Figure 15. Calculated residual fluxes (Case 2)

TABLE III.

PARAMETERS TO DEFINE PHASE A SWITCHING ON INSTANT Phase A

Phase B

Phase C

+- (V)

129

128

128

#+,-./01 (Wb)

-1.122x10-3

2.912 x10-5

1.097 x10-3

α

69º

Fig. 16 gives the measured voltage waveforms at the transformer input windings terminals. As already stated, phase A is the first to be connected, followed by the two others after nearly four cycles. Between these two closing points it is possible to notice that the transformer magnetically behaves on the basis of an induced phenomenon due to phase A operation. This shows a magnetic unbalance functioning as far as magnetic limb flux is concerned. Once the second switch occurs, the balanced operation takes place. On other hand, the corresponding effect of controlling the transformer inrush magnetization currents can be readily seen in Fig. 17 and Fig. 18. The current waveforms are clear enough to emphasize the strategic effectiveness of reducing the transient current peaks. As a matter of fact, the values reached for the peak values are far below the ones with no switch control action. The non-load steady state magnetization currents are directly achieved and absorbed by the equipment.

V. CONCLUSIONS This work presented a methodology to mitigate the power transformer inrush current based on controlled switching. Therefore, optimal points of independent closing can be determined as a function of the residual magnetic flux remaining at the transformer core after the last de-energizing. A proposal to calculate the residual flux was discussed. The method is based on the integration of the applied transformer input three-phase voltages over the last periods before the disconnection of the transformer. It should be noted that this technique provides a simple way of determining the residual fluxes left at the three legs of the transformer core. As previously stated, the first phase closing instant is calculated as a function of the highest absolute residual magnetic flux remaining on the transformer core. The points at which the remaining two phases should be turned on are defined as those when the corresponding presumable flux, related to the supply voltages, are equal to the dynamic ones existing in the transformer. The equations that allow for the corresponding time evaluations for specific Y-grounded/ Ygrounded winding connection were given. Nevertheless, it must be pointed out that other arrangements can be readily taken into account for the present studies. The energization tests carried out without inrush control, as expected, have produced the classical high level of transient currents. These have been nearly eliminated when the control strategy was utilized. Thus, the experimental results obtained by controlling the transformer operation entrance were proved to be effective.

Figure 16. Applied and induced voltage waveforms at transformer terminals (Case 2)

REFERENCES [1]

[2]

[3]

[4] Figure 17. Magnetizing currents on A and B phases (Case 2) [5]

[6]

[7]

Figure 18. Magnetizing currents on C phase (Case 2)

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