20th Iranian Conference on Electrical Engineering, (ICEE2012), May 15-17,2012, Tehran, Iran

Harmonics Analysis in Autotransformers Ferroresonance Circuit

lHamid Radmanesh,2Hamid Fathi 3Seyed UsefMosazade, 4Hossein Hosseinian Department of Electrical Engineering, Amirkabir University of Technology (Tehran Polytechnic),

Tehran, Iran lhamid.Radmanesh@ aut.ac.ir, 2fathi@aut.ac.ir, 3anijdan@aut.ac.ir , 4hosseinian@aut.ac.ir

Tel: {+98-21)64543335, Fax: (+98-21) 88212072

Abstract: This paper studies the effect of iron core saturation characteristic degree on the occurrence of harmonic modes in an autotransformer. The selected transformer for study has a rating of 50 MVA, 635.1 kV. The magnetization characteristic index of the autotransformer is chosen with q=5, 7, II. The linear core loss is considered for transformer core. The MATLAB software is used for analyzing existence harmonic modes in the proposed power system. it is shown high order harmonics are occurred when degree of core nonlinearity is gone from 5 to 11.

Keywords: Linear core losses, Autotransformers, harmonic modes, nonlinear core degree

1. Introduction A sinusoidal voltage is a conceptual quantity produced

by an ideal AC generator. Since the distribution and winding magnetic field are uniform in a working AC machine, voltage waveform distortions are created, and the voltage-time relationship deviates from the pure sine function. The distortion at the point of generation is very small (about 1 % to 2%). Because this is a deviation from a pure sine wave, the deviation is in the form of a periodic function, and by definition, the voltage distortion contains harmonics. In contrast, some loads cause the current to vary disproportionately with the voltage during each cyclic period. These are classified as nonlinear loads, and the current taken by them has a non-sinusoidal waveform. Waveform distortion can be mathematically analyzed to show that it is equivalent to superimposing additional frequency components onto a pure sine wave. These frequencies are harmonics (integer multiples) of the fundamental frequency, and can sometimes propagate outwards from nonlinear loads, causing problems elsewhere on the power system. One of the harmonic cases in the power system is ferroresonance circuits. Ferroresonance overvoltage is an unwanted electrical phenomenon, which may cause overvoltages and over­currents in the electrical power. Ferroresonance overvoltage in electrical power systems were recognized and studied as early as 1930s. Kieny first suggested applying chaos to the study of ferroresonance in electric power circuits [1]. Ferroresonant behavior of a 275 kV electromagnetic voltage transformer, fed from a

978-1-4673-1148-9/12/$31.00©2012IEEE 354

sinusoidal supply via circuit breaker grading capacitance, has been studied in [2]. Voltage transformer ferroresonance from an energy transfer standpoint is given in [3]. Discussion of modeling and analysis guidelines for ferroresonance slow transients has been addressed in [4]. Fast ferroresonance suppression of coupling capacitor voltage transformers was investigated in [5]. Magnetic core modeling for ferroresonance computations using the harmonic balance method is given in [6]. This paper describes a modeling of the magnetization curve and the core losses appropriate for ferroresonance computations using the harmonic balance method. A harmonic and transient overvoltage analysis in arc furnace power systems has been given in [7]. In this paper, guidelines for analyzing harmonics and transient overvoltages generated by arc furnaces are presented. Computer simulation techniques for creating accurate models for the analysis of arc furnace power systems are discussed. Simulation guidelines are outlined in detail to assist the power systems engineer in performing a complete and accurate study of arc furnace power systems. Identification of problems when using long high voltage ac cable in transmission system based on resonance and harmonic resonance has been studied in [8]. This paper focused on European countries power system which replacing the transmission lines with cables. The project was supplying the power to the greater Copenhagen area in early I990s. Recently, the Danish TSO Energinet.dk has initiated a research project for analyzing the HV underground cable in transmission system. The objective of this paper and the companion paper is to address the most important problems expected in transmission system with relatively larger share of long HV underground cables. Harmonic domain modeling of laminated iron core is given in [9]. Harmonic balance based bifurcation analysis of three-phase ferroresonance with full scale experimental validation has been studied in [10], [11]. The determination of ferroresonant oscillations in circuits with transformers is a highly nonlinear problem due to the possible core saturation. It is achieved with an algorithm based upon the harmonic balance method in the frequency domain which is given

in [10]. In all references sited above, harmonic modes in voltage transformers based on ferroresonance phenomenon have not been studied yet. This paper focused on occurred harmonic modes in the voltage transformer which is connected in the 275kV substation. The proposed power system in this paper is a case of ferroresonance that occurred on 1100 kV system of Bonneville Power Administration as described in [12]. Also, Advantages over a time domain description are discussed. Branches of solutions in relevant parameter planes can be continued beyond bifurcation points and lead to a better understanding of the stability domains of the periodic ferroresonant oscillations.

2. Circuit Descriptions and Modeling

The power system circuit is shown in Fig. 1, while 1100 k V transmission line which is shown in this figure reported in autotransformers. Ferroresonance phenomenon occurred in phase A when this phase was switched off on the low-voltage side of the autotransformer; phase C was not yet connected to the transformer at that time [12]. The autotransformer is modeled by a T-equivalent circuit with all impedances referred to the high voltage side. Iron core saturation characteristic is given by:

C.B la 2a � _:lb 2b c m

�e

�)mn�""

C

-----

2

� : l: 16....-----_0 I

(1)

I ______ ----------- --------------------� Fig. I. System modelling of the power system

The exponent q depends on the degree of the saturation of transformer iron core. In this paper for proper representation of the saturation characteristics of a power transformer the exponent q may take the values 5, 7, and 11 and core losses is modelled by a linear resistance [13].

CB Ls L1

ia

+ Ea ru Vm

635.1<0 kv

Rl L2

iRm

Rm

Fig. 2.Thevenin circuit of the power system

R2 Zth la

Lm 130.1<-120 kv

355

L2

Lm Vm

R2 Zth

la

Fig. 3. Initial circuit of the ferroresonance circuit

+

The circuit in Fig. 1 can be reduced to a simple form by replacing the proposed power system with the the venin final reduced equivalent circuit as shown in Fig. 2. Also, Fig. 3 shows the equivalent circuit of the power system including auto transformer. By using the steady-state solution, Eth and Zth were found to be:

Eth =130.1kv; Zth =-j1.01243E+O.5Q 3. Nonlinear dynamics and equation

The resulting harmonic circuit is shown in Fig. 3 where Zth represents the thevenin impedance. By applying KVL and KCL the behaviour of this power system can be described by the following nonlinear differential equations.

v =L di 1.2 2 dt

dvc =� [aA+bAY +h +_l_dA J dt C O Rm dt

i=(iLm +iRJ= [aA+bA'1 +_l_dA J Rm dt

v = L di = L [a dA qbA,,-l dA +_1_ d2 A J L2 2 dt 2 dt dt R dt2 m

(2)

(3)

(4)

(5)

(6)

(7)

(8)

(9)

The base values of the power system parameters are listed in table I.

Also, the per unit values of the nonlinear index coefficients are listed in table II.

Table (II): Different value of q with its coefficient q/coetlicient a b

5 0.0071 0.0034e( -19)

7 0.000375 7.3824e(-24)

11 0.000375 1.5648e( -37)

4. Simulation Results and Discussion

In this case, fourth order Runge-Kutta method is used for deriving harmonic modes validated against MA TLAB SIMULINK. The effect of changing in the value of nonlinear core index on occurring harmonic modes is investigated in this paper. The values of initial conditions are:

-1 =0,0; vm =1.67 pu; Vc =1.55pu

Simulation has been done in three categories, first: system simulation with linear core losses effect considering degree of core nonlinearity q=5, second, considering degree of core nonlinearity q= 7 and finally investigation of harmonic modes by considering q= 11.

1 •

0.9- I - --------1--- I ---1--------I I I

0.8- - - - - - - - - - - - T - - - -1- ---1--------

:3 0.7 ; 06-

� 0,5-� § 0.4 1\ " � 0,3-

- - - - - - - - - - - + - - - -1- - - -l- --- - ----

__ _ ________ 1.. ____ 1 ____ L ___ _ ___ _

I I I - - - - - - - - - - - T - - - -1- ---1--------

0,2- - - - - - - - - - - - i - - - -1- - - -1 --- - ----

0.1

°0-a� �0�

5--�--

--�

,�5 ----L-

---2�

.5�-- �--�

35 Normalized Frequency (rad/sec)

Fig. 4. Harmonic analysis considering q�5. Eth�lp.u

0.9

0.6

'8 °,7- - - - - - - - - - - - i - - - -1- - - -1 - -- - ----

i 0.6

8 � 0.5

§ 0.4-

g 0.3

H-3 I

Hly ___ � _______ .. l __ _

I H-9

H-l1

:::- - - t� - -� - - +- - �--- -:-� - - � -

-- - ----

o �... 1 •••• _. • •• ___ .l _______ r _______ � _____ � ___ � ____________ � _____________ .;... ________ _ ° 0.5 1 1 .5 2 2.5 3 3.5

Normalized Frequency (rad/sec)

Fig. 5. Harmonic analysis considering q�5, Eth�3p. u

356

Fig. 4 Shows the FFT of voltage of the transformer with q=5, according to this plot, trajectory of the system has a period-l behavior. Corresponding FFT diagram in Fig.6 clearly shows the subharmonic oscillation behavior of the voltage on the transformer. Value of frequency is considered as a normalized value where it is means horizontal axis is based on the normalized frequency. It means each 377 rad/sec is one unit, so when spectrum shows the 0.16, its actual value is 60Hz. In Fig. 4, Eth = I p. u and coefficients of the transformer current are listed in table (2). The degree of nonlinear core index is considered q=5. According to this FFT plot, period-l is obvious and power system works under normal operation condition. By increasing the value of Eth to 3p.u, some odd harmonics are generated in the system behavior as shown in Fig. 5.

1 .--�----�------------------�----� X=Q,15 I

0.9 I

0.6

'8 0,7 - - - ""1 - - - - 1- - - - - - - - - - - - - - - - - I - ----

i 0.6

8 � 0.5

§ 0.4

g 0.3

:: j - - -+ - --- :- - - - - - - - - - - - - - - - - � - ----l I I I 0.... l .. o _____ .L ___________ l. ________________ ____________________________________ 1 _____ _ _ ° 0.5 1 1 .5 2 2.5 3 3.5

Normalized Frequency (rad/sec)

Fig. 6. Harmonic analysis considering q�7, Eth�lp.u

I I I 09 - - - i1illatn rmrrrrnptc - - - - - - - - - - - - - - - - I - ----I I I

0,8 -;:/- I - - - - 1- - - - - - - - - - - - - - - - - I - ----

:3 0.7

� � 06

� 0,5

� § 0.4 1\ " � 0,3

--- �----�--- - -------- - --- �--- �

_ __ ..1 __ _ __ _ ________ _ ___ -.J ____ _

3.5 Normalized Frequency (rad/sec)

Fig. 7. Harmonic analysis considering q�7. Eth�3p.u

In this section, FFT of voltage on transformer with q= 7 is analyzed as shown in Figs. 6 and 7. It is shown when the degree of q increases from 5 to 7, main harmonic value is remained the same as q=5 behavior. Fig. 7 shows the system behavior with some subharmonic resonance in it. It is shown that when q is increased, nonlinear phenomena in the transformer are begun in the low value of the input voltage, so the subharmonic modes begin at a value of Eth = 3p. u, which represents the amplitude of Eth.

1-.--------------�----�--�----------�

09

0.8

0.7- -- - -------- T --- �---- r --- - ----

0.8

0.5

0.4-

0.3

0.2

0.1 - - - - - - - - - - - - + - - - -1- - - - +- - - - - - - - -I I I

° 0-UL-� 05��� ----�, 5�--

-L----�2.� 5----�--�35

Normalized Frequency (rad/sec)

Fig. 8. Harmonic analysis considering q�ll, Eth�lp.u

In Fig. 8, harmonic analysis is done for q= I I. In this plot, value of the input voltage is I p.u, so only main harmonic is obvious. By increasing Eth to 3p.u, some extra sub­harmonics oscillation are take placed as shown in Fig. 9 with text row. As shown in this figure, amplitude of harmonic-3 is so big and can affect on the power system equipments more than other harmonic modes.

0.9-

0.8-

:3 0.7 ; 08-

� 0,5-

§ 0.4

I ---1--------

- - - - - - - - - - - T - - - � - - - - r - - - - - - - -

- - - - - - - - - - - + - - - -1- - - -l- - - - - - - - -H'l

_ 1.. ____ 1 ____ L ___ _ ___ _ I I I

Normalized Frequency (rad/sec)

Fig. 8. Harmonic analysis considering q�ll, Eth�3p.u

In the real system, when the input voltage due to the abnormal switching or other unwanted phenomena reaches to 4p.u, transformer core is heated and can cause transformer core failure. This overvoltage has some harmonics modes which can cause dangerous cases for power system equipments.

5. Conclusions The harmonic modes of an autotransformer are shown by the dynamical tool and graphical tools such as FFT analysis. In this paper, effect of changing the value of degree q on occurring harmonics is studied. It is shown the nonlinear iron core and its degree" q" has a great effect of occurring nonlinear oscillation in the autotransformer. When q is II, occurred harmonics are more nonlinear and amplitude of this case is higher than

357

the other cases. With q= I I, settling down to higher order harmonics is more dangerous and should consider protecting tool on this transformers such as damping resistor, MOSA and other suppressing circuits.

References

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[111 Hamid Radmanesh, G. B. Gharehpetian & Hamid Fathi, "Ferroresonance of Power Transformers Considering Non-linear Core Losses and Metal Oxide Surge Arrester Effects ", Electric Power Components and Systems, Vol. 40, No. 5, 2012.

[12] Radmanesh, Hamid,"controlling ferroresonance in autotransformer considering linear and Nonlinear Core Losses Effect, International Review of electrical engineering (I. R. E. E), Vol. 5 N. 6, Part A,

NOV-DEC 2010. 113J H. Radmanesh, M. Rostami, "Effect of circuit breaker shunt

resistance on chaotic ferroresonance in voltage transformer," Advances in Electrical and Computer Engineering, Vol. 10, No. 3, pp. 71-77,2010.