Analyzing power quality issues in electric arc furnace by modeling

Energy 115 (2016) 830e839

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Analyzing power quality issues in electric arc furnace by modeling Deepak C. Bhonsle a, *, Ramesh B. Kelkar b a b

Electrical Engineering Department, CKPCET, Gujarat Technological University, Surat, Gujarat, India Electrical Engineering Department, Faculty of Technology, M S University of Baroda, Vadodara, Gujarat, India

a r t i c l e i n f o

a b s t r a c t

Article history: Received 2 January 2016 Received in revised form 21 May 2016 Accepted 6 September 2016

Rapid growth of non-linear loads in distribution network has attracted power system engineers' attention from power quality point of view. Electric arc furnace (EAF) is one of the typical industrial nonlinear loads responsible for deteriorating the power quality in the distribution network by introducing harmonics, propagating voltage flicker and causing unbalance in voltages and currents. Therefore, the EAF model is required to be studied and the power quality required to be analyzed in the distribution network. This paper presents a novel time domain EAF model to study power quality problems. The proposed model is a combination of two previous EAF models called-exponential and hyperbolic modelusing transition functions. The functioning of the proposed model has been validated by comparing its various performance characteristics with the existing Cassie-Mayr's EAF model and with real measured data available. Current harmonics, voltage harmonics along with voltage flickers are considered as power quality problems for study and analysis. Simulation is carried out in SIMULINK/MATLAB environment. © 2016 Elsevier Ltd. All rights reserved.

Keywords: Electric arc furnace Harmonics Harmonic distortion Arcs

1. Introduction An EAF load is inherently non-linear, time-variant in nature which results into power quality problems such as-current harmonic, voltage harmonics and voltage flickers. The EAF operation generates odd and even current harmonics. These current harmonics, when circulated in the electric network, interact with the system impedance and generate voltage harmonics. These current and voltage harmonics together can affect other consumers connected in the distribution network. The EAF is also an inherent large source of voltage flicker. The voltage flicker is defined as the sensation that is experienced by a human eye when subjected to changes in the illumination intensity in the frequency range of 5e15 Hz [1,2]. The voltage flicker can causes large voltage fluctuation in the connected distribution network which in turn affects operation of other connected loads in the distribution network. The institute of Electrical and Electronics Engineers (IEEE) has set limits to the permitted voltage distortion and current distortion at the point of common coupling (PCC) of the utility-plant interface in IEEE 519-2014 [24]. Therefore an EAF is required to be studied and to be analyzed from power quality point of view w. r. t. IEEE 519 regulations. Hence, EAF modeling has attracted power system

* Corresponding author. E-mail address: [email protected] (D.C. Bhonsle). http://dx.doi.org/10.1016/j.energy.2016.09.043 0360-5442/© 2016 Elsevier Ltd. All rights reserved.

engineers to solve these power quality issues. Simulation of an electric arc is an important issue in EAF modeling. Several methods describing the electric arc are available in the literature [1e7]. On the basis of actual measured samples of an electric arc in several functioning cycles of EAF, different operating points are generated in the quantitative form of statistical probability, corresponding to hidden Markov theory in Ref. [3]. This requires actual measurement of an electric arc. The time domain model utilizing differential equations are presented in Ref. [4]. Variation of power transmitted to the load by the arc furnace during the cycle of operation is considered in Ref. [5]. Balanced steady state equations are used in Ref. [6]. Comparisons of the time domain and frequency domain EAF models emphasize use of time domain models [1,7]. Frequency response and voltage current characteristics (VIC) are taken into account to analyze the EAF behavior in Ref. [7]. These methods impose limitations such as prior knowledge of initial conditions in case of the differential equations, consideration of balanced three phase currents, use of complicated mathematics and actual arc measurement for the EAF modeling. This paper presents a novel time domain approach in EAF modeling validated by simulation and by comparing its various performance characteristics with that of existing Cassie-Mayr's EAF model in MATLAB environment and that of available real measured data. The main features of the proposed EAF model are good mathematical approximation, no need of initial conditions, and no need of measurements of arc voltage, arc current, etc. in actual arc and

D.C. Bhonsle, R.B. Kelkar / Energy 115 (2016) 830e839

consideration of unbalanced three phase currents. The proposed model can be used to describe various operating cycles of electric arc furnace and its impact on the connected electric network from power quality point of view. Finally, the proposed method presents a suitable model with a very good approximation for the VIC. In order to increase the accuracy of the load model, a random noise is employed to establish a new model of the furnace load.

Table 1 EAF model 1 and 2 parameters.

Typical VIC of an EAF is found to be exponential and hyperbolic in nature [3]. Complete VIC can be obtained by combining the hyperbolic and the exponential nature of the characteristics. Efforts have been made to combine these characteristics in Refs. [2,6]. These characteristics can also be combined using transition function suggested in Refs. [4,8]. In this paper the same transition function is used for combining the exponential and hyperbolic model characteristics and thus to propose a novel EAF model. A brief detail of exponential and hyperbolic model along with the detailed proposed model is as follows:

¼


Vat  Vat $e


 
i= Io 7 $V þe 1  e 5 at 3

i= Io



!

2

2 i 2 I t

6 $41  e

i= Io

N(t) (Hz) 4e14


 i= Io

 (2)

Exponential and hyperbolic models can be combined into single model by defining a transition functionO(i), which is a function of arc current and is given by:

vcom ðiÞ ¼ ½1  OðiÞ $vexp þ |fflfflfflfflfflffl{zfflfflfflfflfflffl}

I

t




i= Io

i= Io

7 5þe

þ Vat $e

þ Vat $e !

i= Io

2

$Vat þ e

$e

Lower Current

! 2 i2 I t

OðiÞ ¼ e

(4)

In equation (4) It is the transition current. Substituting equations (1), (2) and (4) in equation (3), one can get:


C $ Dþi

!

!

2

I

$e ! I t

t




i 2

þe

2 i 2 I t

$

!

2

i2

2

i2 t

(3)

!




I

$vhyp

In equation (3), vhyp and vexp are the arc voltages given by equations (1) and (2) respectively. A satisfactory form of O(i) used in this combination is given in Refs. [4,5]:

!

2

 Vat $e

Higher Current

OðiÞ |ffl{zffl}


 C $ Vat þ Dþi 2 i 2 I t

i2


 ¼ Vat  Vat $e

uf (Hz) 4

! 2 i2 I t

3

!


 ¼ Vat  Vat $e

m 0.8

In equation (2) Io is a current constant employed to model the steepness of positive and negative phases of arc currents. A typical value of Io is tabulated in Table 1.

(1)




Vat0(V) 200

vexp ðiÞ ¼ Vat 1  e

In equation (1) variable vhyp is arc voltage given by hyperbolic EAF model and variable i is arc current per phase. Variable C is arc power and variable D is arc current. These constants can take different values which depend on the sign of the derivative of the arc current and can be obtained in steady state. It can be easily understood that arc voltage vhyp increases as arc current i decreases. Vat is the voltage threshold magnitude to which the arc voltage vhyp approaches as EAF current increases. This voltage is dependent on the arc length. In equation (1) Table 1 shows typical values of various parameters of EAF models. The values of arc power (C) and maximum arc current (Io) are obtained from M/S Maithan Alloys Limited, Byrnihat, Meghalaya, INDIA by M/S Ohm Encon (P) Limited, whereas Vat and D can be decided arbitrarily.

6 vcom ðiÞ ¼ 41  e

10

2.3. Model 3: proposed model

C Dþi

!

Io(kA)

5






2 i2 I t

D(kA)

23

VIC of exponential EAF model is described as [2,6]:

VIC of hyperbolic EAF model is described as [2,6]:

2

C(kW)

200

2.2. Model 2: exponential model

2.1. Model 1: hyperbolic model

vhyp ðiÞ ¼ Vat þ

Vat(V)

Table 2 Sinusoidal and Random variations Parameters.

2. Modeling of EAF as non-linear load




831

þ Vat $e

C Dþi

I t

i2

þe

I t

 C Dþi




2

i2

$

 (5)

832

D.C. Bhonsle, R.B. Kelkar / Energy 115 (2016) 830e839

When arc current (i) is taking small value (ideally approaching zero), equation (5) results into:


 i= Io

vcom ðiÞ ¼ Vat  Vat $e

!


 i= Io

þ Vat $e

$e

2 i2 I t




C Dþi 

¼ Vat  Vat $e0 þ Vat $e0 $e0 þ e0 $

! 
C $ Dþi

2  i2 I t

þe




C ¼ Vat  Vat $1 þ Vat $1$1 þ 1$ Dþi 
C ¼ Vat Vat þ Vat þ Dþi 
C ¼ Vat þ Dþi ¼ vhyp ðiÞ

(6) Equation (6) implies that when arc current i is approaching zero which yields arc voltage value vcom is dominated by vhyp. Similarly when arc current (i) is taking large value (ideally approaching infinity), equation (5) results into:







i= Io

i= Io

vcom ðiÞ ¼ Vat  Vat $e

þ Vat $e


 i= Io

¼ Vat  Vat $e

¼ Vat  Vat $e

i= Io

2

2

i2 I

$e

i= Io

þ Vat $e


 þ Vat $e


 ¼ Vat  Vat $e

!

t

 i2

i= Io


 þ Vat $e




i= Io

$ e

1 i2 I2 t

I

þe





 i= Io

! t


C $ Dþi


C !$ Dþi 2

1

!þ e

i I2 t

Here, l is arc length in centimeters. A variation in arc length is root cause of typical dynamic behavior of EAF. The arc length can be varied by varying arc voltage directly. In actual practice the variation in arc length is of random in nature. Two types of arc length variations are considered for simulation purpose-sinusoidal and random. Effect of voltage flicker on the power system can be studied by varying Vat as follows: (a) Sinusoidal variation: Mathematically the sinusoidal variation can be expressed as [6,8]:


C $0 þ 0$ Dþi

In equation (10) m and uf are modulation index and flicker frequency respectively.

vat ðtÞ ¼ Vat0 ½1 þ m$NðtÞ

(7) Equation (7) implies that when value of arc current i is approaching large value (ideally approaching infinity) which yields arc voltage value vcom is dominated by vexp. The exponential and hyperbolic functions are mathematically joined to make arc voltage to follow exponential model characteristic during high arc currents and to follow hyperbolic model characteristic during low arc currents. Finally the VIC of the proposed model is thus described by following combined equation:

for higher arc current (8) for lower arc current

(10)

(b) Random variation: Mathematically the random variation can be expressed as [6,8],

¼ vexp ðiÞ

> 
> > C > : Vat þ Dþi

(9)

j  k vat ðtÞ ¼ Vat0 1 þ m$sin uf $t

i= I

vcom ðiÞ ¼

Vat ¼ A þ B$l


1 1 C $ ð∞Þ þ ð∞Þ $ Dþi e e

¼ Vat  Vat $e o þ 0 þ 0
 
i= I ¼ Vat 1  e o


 8   > i= > > > < Vat 1  e Io

It can be seen from equation (8), for the positive current and regarding the hysteresis property of the arc, there are two cases-to increase and decrease the current of the EAF. The hyperbolic equation and exponential-hyperbolic form of the equation are used for the same. Dynamic specifications of EAF at any instant of time are affected by conditions of the furnace at that time and previous instants of the time. The reason for that is when the arc is created, the sudden change in the electrons, ions and gas temperature (that may occur due to sudden change of current) is impossible. Therefore, the sudden change of the current will not lead to sudden change of the arc characteristic. In fact, there is a hysteresis phenomenon in the dynamic of the arc characteristic due to the effects of the rate of change of current in the previous instants of time on the present time. The refining stage contributes harmonics in current and voltage, while scrap meltdown stage yields voltage flicker at PCC. Therefore, real time analysis of power quality demands dynamic model of EAF. In order to bring the stationary arc-model to give rise to voltage fluctuations, cause of flicker, the VIC must undergo time variations which correspond to a time dependence of the arc length as [9,10]:

(11)

In equation (11) N(t) is a band limited white noise. It is expressed with zero. Voltage flicker assessment is also one of the important aspects of power quality analysis. The assessment of voltage flicker involves the derivation of system RMS voltage variation and the frequency at which the variation occurs. The voltage flicker usually expressed as the RMS value of the modulating waveform divided by the RMS value of the fundamental value, as follows [11e13]:

RMS Voltage of Modulating waveform Average RMS Voltage

(12)

DV V  V RMS Voltage of Modulating waveform ¼ pffiffiffi ¼ 2P pffiffiffi 1P 2 2 2

(13)

% Voltage Flickr ¼

where, V1P ¼ lower peak of modulating voltage, V2P ¼ upper peak of modulating voltage

D.C. Bhonsle, R.B. Kelkar / Energy 115 (2016) 830e839

 Average RMS Voltage ¼

V2P

.pffiffiffi 2 2

 þ

V1P

.pffiffiffi 2 2

in Refs. [4,8]:

V þV ¼ 2P pffiffiffi 1P 2 2 (14)

  

i2 v$i i2 i2 dg $ 2 þ exp  $  q$ g ¼ gmin þ 1  exp  dt It It P0 E0 (16)

Substituting equations (13) and (14) in equation (15), we get:

% Voltage Flickr ¼

833

V2P þ V1P V2P  V1P

(15)

Equation (15) is useful for voltage flicker estimation. A variety of perceptible/limit curves are available in published literature which can be used as general guidelines to verify whether the amount of flicker is a problem or not [12,13]. Comparison of data from various sources for perceptible flicker is given in Ref. [10]. By frequency of voltage pulsation and % cyclic voltage pulsation, calculated by equation (12), it is possible to judge whether voltage flicker is perceptible or not [13]. The proposed EAF model is validated by comparing its performance characteristics with the existing CassieMayer EAF model [2] which is described in next section.

2.4. Model 4: Cassie-Mayer EAF model Classical arc models are based on the energy conservation principle describing the arc as an electro-thermal system with an internal source term due to Joule heating and exchanging heat with the surrounding, colder environment. If Joule heating is higher (lower) than energy dissipation to the outer environment, then the arc energetic content increases (decreases). Since the arc electric conductivity is related to the arc energetic content, the electric characterization of the arc as a non-linear resistance of electric component of an electric network is thus produced. In 1939 Cassie proposed a model of arc in which the arc was assumed to have cylindrical column with uniform temperature and current density. That means its virtual cross-sectional area varies to accommodate the change in current. i. e. cross-sectional area is proportional to arc current. The power dissipation was assumed to be proportional to the column cross section [14,15]. The electric current is relatively high (>500A) and the model is thus unsuited for describing arcs in the vicinity of current zero. A few years later, in 1943, Mayr proposed an improved model, in which arc was assumed to be of fixed diameter but of varying temperature and conductivity, the power loss occurred from the surface of the arc only [16,17]. Mayr assumed power losses are caused by thermal conduction at small currents. This means that the conductance is strongly temperature dependent but fairly independent of the cross-section area of the arc. The area is therefore assumed constant. The electric current is relatively low (say <500A) and the model is thus suited for describing arcs in the vicinity of current zero, at least not too close to the current zero. This model is applicable for the analysis of the residual current, which is arisen after current interruption [18,19]. It has been found that Cassie's model describes the period before current zero where as Mayr's model represent better the post arc regime. Thus Cassie's theory was looking at high current arcs with convection as the dominant energy transfer feature while Mayr's paper was looking at low current arcs with thermal conduction transfer as the main feature for current zero behavior. Mathematical model of Cassie-Mayr's EAF model expressed as

Table 3 EAF model 4 (Cassie-Mayr's) parameters. gmin

It(kA)

E0(V)

P0(W)

q0

q1

a

0.08

10

250

100

110e-06

100e-06

0.0005

q ¼ q0 þ q1 $expða$jijÞ v¼

i g

(17) (18)

where, i ¼ Arc current v ¼ Arc voltage g ¼ Arc conductance E0 ¼ Momentarily constant steady state arc voltage q ¼ Arc time constant q0 ¼ Constant q1 ¼ Constant a ¼ Constant P0 ¼ Momentarily power loss It ¼ Transition current gmin ¼ Minimum conductance Typical values ofE0,q0, q1, a, P0, It, and gmin and are tabulated in Table 3. The required data was taken from Refs. [4,8] for reference. Combined Cassie-Mayr's arc model provides a qualitative description of the arc phenomena in the low and high current regions respectively. These models include a differential equation that depends on a set of parameters which should be obtained from experimental data as shown in Table 3. By selecting a suitable set of arc parameters it is possible to obtain a better approximation to the arc dynamics described by experimental data. However, increasing the number of parameters can lead to difficulties for calculating their magnitudes. Such seven parameters are required to be obtained from experimental data to formulate Cassie-Mayr's EAF model, whereas the proposed EAF model require only two parameters (arc power C and maximum value of arc current Io) to be obtained from the experimental data, which is a major advantage. Moreover, the proposed method can describe EAF behavior in time domain using differential equation [8]. In addition, it is able to analyze the behaviors in the frequency domain without solving the sophisticated differential equations. Moreover, the proposed EAF model can describe various operating conditions such as scrap meltdown stage, refining stage from power quality point of view. The results agree with actual conditions of the EAF in the steel industries [20]. 3. Simulation of EAF with power system Fig. 1 shows a single phase equivalent circuit of an EAF supplied by source. It consists of voltage source, source impedance, furnace transformer impedance and an EAF. In Fig. 1, ZS is system impedance and Zft is furnace transformer impedance. Table 4 shows the power system parameters along with proposed EAF Model. The power system data for simulation was taken from Refs. [5] and [7]. Fig. 2 shows complete simulation of three-phase electric network supplying an EAF using Simulink/MATLAB platform. As shown in Fig. 2 (a), three phase power source is simulated by considering three single phase voltage source (VR, VY andVB) shifted by 120 electrical degrees each. System impedance and furnace transformer impedance is represented by three elements for three phases. A non-linear time varying voltage controlled source is used

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Fig. 1. EAF with an electric network (a) single phase network along with EAF (b) simulated three phase network along with EAF.

Table 4 Power system parameters. V (V)

f(Hz)

ZS (mU)

Zft (mU)

415

50

0.0527 þ j0.467

0.3367 þ j3.23

as function to represent EAF model as shown in Fig. 2 (b). As shown in Fig. 2 (a), the arc current acts as an input to this function which results in to non-linear time varying voltage as an output. Such three elements are connected in star to form three phase EAF model. Fig. 2 (c) shows simulation of the proposed EAF model equation. Three phase voltage, current measurements along with active power, reactive power, power factor measurements are done at point of common coupling (PCC). Fig. 3(a) & (b) show MATLAB simulation of sinusoidal and random flicker generation respectively. 4. Comparison and analysis of simulated results and real measured data Comparisons of performance of EAF for model 3 (proposed model) with that of model 4 (Cassie-Mayr) and real measured data are presented in this section. Current harmonics, voltage harmonics and voltage flicker are considered as power quality problems in various EAF operations. The performance of EAF includes various performance characteristics such as arc current, arc voltage, harmonic spectrum, arc conductance variation, arc voltage-current characteristic (VIC), variation in active & reactive power, etc. For better comparison, each performance characteristic of EAF model 4 and model 3 along with real measured data are presented together. 4.1. Steady state characteristics (refining cycle) Steady state characteristic of EAF is exhibited mainly during refining cycle. The level of molted material is constant along with uniform rate of melting in the furnace. Arc length is almost constant during this cycle resulting into uniform VIC. This produces voltage and current harmonics mainly at PCC as shown in Fig. 4e8. 4.1.1. Arc voltage and arc current Fig. 4 shows waveform of arc voltage and arc current at PCC generated by Model 4 and Model 3. It can be noted that the magnitude and the shape of both-the voltage and the current waveform-are nearly identical, which confirms validity of the proposed model i.e. model 3. Simulated results of arc voltage and arc current are typically same as real EAF waveforms [20e23] [20e24]. 4.1.2. V-I characteristic (VIC) Fig. 5 shows VIC produced by EAF Model 4 and model 3, which are identical in shape and in values. The Comparison between the

VIC obtained by the proposed EAF model with that of acquired by real measured data shows that the VICs are identical in nature [22e24], which confirms validity of EAF model 3on practical ground. 4.1.3. Current harmonics @ PCC It can be noted from Fig. 6 that total harmonic distortion (THD) observed in the arc current of both the models is nearly equal (3.40% for model 4 and 3.22% for model 3). This shows validity of model 3 for refining cycle. % Harmonic distortions of individual harmonic orders (5th, 7th, 11th, 13th, 17th, 19th, 23rd and 25th) are tabulated in Table 5. Table 5 shows comparison of current harmonic analysis among EAF Model 4, Model 3 and real measured data [22]. % Error observed in THD of Model 3 (Proposed) with respect to Model 4 is 5.29%, which is less than 10%. It makes Model 3 acceptable. Harmonic distortion of each harmonic order is expressed as % of fundamental as shown in Table 5. % Error for each harmonic order is calculated by taking Model 4 (Cassie-Mayr) to be the reference. Average error observed is 8.07% which is less than 10%, which makes model 3 (Proposed) acceptable. % Error observed in the current magnitude at PCC of Model 3 with respect to Model 4 is 2.13%, which again confirms validity of Model 3. The proposed EAF model produces individual current harmonic components those are very close in magnitude to the real measured data [22]. Average error observed is þ2.35% which is less than 10%, which makes model 3 (Proposed) acceptable. 4.1.4. Voltage harmonics @ PCC Similarly, it can be also being noted from Fig. 7 that the THD observed in the arc voltage of both the models is nearly equal (46.42% for model 4 and 46.67% for model 3). This again confirms validity of model 4 for refining cycle. Voltage waveform is distorted due to superimposition of 3rd, 5th, 7th, 9th, 11th, 13th, 15th, 17th, 19th, 21st, 23rd and 25th order harmonics predominantly on fundamental wave. % harmonic distortions of individual harmonic are tabulated in Table 6. Table 6 shows comparison of voltage harmonic analysis among EAF Model 4, Model 3 and real measured data [23] Total harmonic distortion observed in Model 4 and Model 3 is 46.42% and 46.67% respectively, which is violating IEEE 4192014 [24] Limits of 5%. % Error observed in THD of Model 3 (Proposed) with respect to Model 4 is 0.54%, which is less than 10%. It makes Model 3 acceptable. Harmonic distortion of each harmonic order is expressed as % of fundamental as shown in Table 6. Harmonic distortion observed in almost all harmonic orders (3rd to 25th) is more than IEEE 4191992 Limit of 3% for individual harmonic order. The comparison of each individual harmonic order with that of Model 4 (Cassie-Mayr) and real measured data confirms validity of the proposed EAF model. Maximum error observed in model 3 with respect to model 4 is þ 0.15% (3rd order) and 4.66% (23rd order) on positive and negative side respectively. Average error observed is 1.86% which

D.C. Bhonsle, R.B. Kelkar / Energy 115 (2016) 830e839

835

Fig. 2. Complete Simulink/MATLAB simulation file of the proposed EAF Model (a) Single Phase EAF simulation (b) EAF equation modeling (c) Proposed EAF model.

Fig. 3. Simulink/MATLAB Simulation of (a) Sinusoidal flicker generation (b) Random flicker generation comparison and analysis of simulated results and real measured data.

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Fig. 4. Waveform of arc voltage-current v/s time of (a) Model 4 (Cassie-Mayr) (b) Model 3 (Proposed) during refining cycle.

Fig. 5. VIC during refining cycle of an EAF of (a) Model 4 (Cassie-Mayr) (b) Model 3 (Proposed) during refining cycle.

Fig. 6. Harmonic spectrum of arc current at PCC during refining cycle of (a) Model 4 (Cassie-Mayr) (b) Model 3 (Proposed).

Fig. 7. Harmonic spectrum of arc voltage at PCC during refining cycle of (a) Model 4 (Cassie-Mayr) (b) Model 3 (Proposed).

D.C. Bhonsle, R.B. Kelkar / Energy 115 (2016) 830e839

837

Fig. 8. Active power (P) and reactive power (Q) consumption of (a) Model 4 (Cassie-Mayr) (b) Model 3 (Proposed) during refining cycle.

Table 5 Current harmonic analysis @ PCC.

Model 4 Model 3 Real Measured Data % Errors in Model 3 w. r. t. Model 4 % Errors in Model 3 w. r. t. real data

Ipeak(kA)

THDI

5th

7th

11th

13th

17th

19th

23rd

25th

117.50 120.00 127.05 2.13 5.55

3.4 3.22 2.98 5.29 8.05

2.98 2.79 3.1 6.38 11.11

1.43 1.24 2.33 13.29 7.26

0.58 0.56 0.48 3.45 3.57

0.42 0.39 0.41 7.14 5.13

0.24 0.22 0.49 8.33 4.55

0.19 0.17 0.21 10.53 5.88

0.14 0.13 0.28 7.14 15.38

0.09 0.08 0.05 11.11 25.00

Table 6 Voltage harmonic analysis @ PCC.

Model 4 Model 3 Real Measured Data % Errors in Model 3 w. r. t. Model 4 % Errors in Model 3 w. r. t. Model 4

Vpeak(V)

THDV

3rd

5th

7th

9th

11th

13th

15th

17th

19th

21st

23rd

25th

305 288 316 5.57 8.86

46.42 46.67 44.65 0.54 4.52

33.69 33.64 32.95 0.15 2.09

19.98 20.07 18.76 0.45 6.98

14.12 14.19 13.29 0.50 6.77

10.99 11.05 10.47 0.55 5.54

8.78 8.92 8.47 1.59 5.31

7.3 7.41 7.67 1.51 3.39

6.27 6.39 6.46 1.91 1.08

5.36 5.54 5.69 3.36 2.64

4.67 4.82 4.52 3.21 6.64

4.16 4.29 4.21 3.13 1.90

3.65 3.82 3.85 4.66 0.78

3.26 3.38 3.51 3.68 3.70

Table 7 Power analysis @ PCC. Parameter

Model 4 (Cassie-Mayer)

Model 3 (proposed)

Real measured data

% Errors (w. r. t. Model 4)

% Errors (w. r. t. real measured data)

Active Power P (kW) Reactive Power Q (kVAr) Power Factor (PF)

23280 17250 0.574

25900 16130 0.606

23497 21357 0.74

11.25 6.49 5.57

10.23 24.47 18.11

is less than 10%, which makes model 3 (Proposed) acceptable. % Error observed in the voltage magnitude at PCC of Model 3 with respect to Model 4 is 5.57%, which again confirms validity of Model 3. The proposed EAF model produces individual voltage harmonic components those are very close in magnitude to the real measured data [23]. Average error observed is 4.18% which is less than 10%, which makes model 3 (Proposed) acceptable. 4.1.5. Active and reactive power (PQ) Fig. 8 shows active and reactive power consumption during refining cycle by the proposed model compared to the existing Cassie-Mayr's model which also agrees with the real measured data [20]. Table 7 shows comparison of active power, reactive power and power factor among Model 4, Model 3 and real measured data [24]. % errors calculated for the proposed model w. r. t. Cassie-Mayr model and that of the real measured data are less than 10%. For reactive power and power factor, % errors calculated for the proposed model w. r. t. the actual measured data is less than 24.47% as shown in Table 7, which is little higher.

4.2. Dynamic characteristics Dynamic characteristic represents melting cycle of EAF. In this operation the furnace is charged with scrap, after that the electrodes could be lowered, each of which has its own regulator and mechanical drive. The steel scrap surface is irregular by nature of the scrap, and, as parts of the scrap melt, it moves about, changing the contours of the surface. Thus, random disturbances in the arc length occur continuously. This operation exhibits severe voltage flickers. Voltage variation with reference to time can be utilized to study voltage flicker effect on the power system with EAF. Effects of sinusoidal and random flicker of the EAF are studied in this section. Simulation results are obtained using equations (7) and (8) along with tabulated parameters given in Table 2. 4.2.1. Sinusoidal flicker Fig. 9 shows simulation results for sinusoidal flicker. It indicates variation of arc voltage and arc current with flicker frequency. 4.2.1.1. Arc current & arc voltage. The variation in the voltage and

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D.C. Bhonsle, R.B. Kelkar / Energy 115 (2016) 830e839

Fig. 9. Waveform of arc voltage-current v/s time during melting cycle of (a) Model 4 (Cassie-Mayr) (b) Model 3 (Proposed) for Sinusoidal flicker.

Table 8 Voltage flicker analysis @ PCC. Sinusoidal voltage flicker Model 4 (Cassie-Mayer) Voltage Measurement 65 V1P (V) V2P (V) 390 % Flicker Calculation % Voltage Flicker 1.39

Model 3 (proposed)

Real measured data

64 400 1.38

% Error (w. r. t. model 4)

% Error (w. r. t. real measured data)

1.54 2.56 1.40

þ0.72

þ1.42

Fig. 10. Waveform of arc voltage-current v/s time during melting cycle of (a) Model 4 (Cassie-Mayr) (b) Model 3 (Proposed) for Random flicker.

current waveforms due to sinusoidal flicker is reflected in Fig. 9. It can be observed from Fig. 9(a) and (b) that the variations reflected in Model 4 and Model 3 are identical and are also matching with the real measured data available in Ref. [20]. Table 8 shows voltage flicker analysis at PCC. Voltage flicker is calculated using equation (12) for Model 4 and Model 3 and tabulated in Table 8. Table 8 shows comparison of % voltage flicker generated among Model 4, Model 3 and real measured data [24]. % errors calculated for the proposed model w. r. t. Cassie-Mayr model and that of the real measured data are þ0.72% and þ1.42% respectively. This confirms validity of Model 3 (Proposed).

4.2.2. Random flicker Fig. 10 show simulation results for random flicker. Variation in arc voltage and arc current during melting cycle (considering random variation) of the proposed EAF model is matching with close proximity to that of Cassie-Mayr's. Real measured data in Ref. [23] validates the same fact.

5. Conclusion This paper presents a novel time domain model of EAF to study power quality problems. The proposed model is a combination of two previous EAF models called-Exponential and hyperbolic model-using transition functions. The functioning of the proposed model has been validated by comparing its performance characteristics with the existing Cassie-Mayer EAF model. Simulation carried out in SIMULINK/MATLAB environment validates the proposed EAF model. The main features of the proposed EAF model are good mathematical approximation, no need of initial conditions, and no need of actual arc parameter measurements and consideration of unbalanced three phase currents. The proposed model can be used to describe various operating cycles of electric arc furnace and its impact on the connected electric network from power quality point of view. Finally, the proposed method presents a suitable model with a very good approximation for the VIC. The model is also able to describe the almost all the specifications of EAF. In this paper, a three phase structure of the electric EAF is proposed which includes the power quality aspects-voltage

D.C. Bhonsle, R.B. Kelkar / Energy 115 (2016) 830e839

harmonics, current harmonics, voltage flicker and unbalance loading. Two types of voltage flicker-sinusoidal and random-are carried out. Detailed power quality analysis is presented. The proposed novel EAF model is useful to study power quality issues pertaining to EAF connected distribution network, to design and to validate various power quality improvement techniques.

[9]

[10]

Acknowledgment

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Authors gratefully acknowledge the contributions of Mr. Tarang Thakkar, Director of M/S Ohm Encon (P) Ltd., 991/3B, GIDC, Makarpura, Vadodara, Gujarat, INDIA for their assistance in EAF data measurement at M/S Maithan Alloys Limited, Byrnihat, Meghalaya, INDIA.

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