The Impact of Post-Furnace Steel Processing Equipment on Reducing Voltage Fluctuations Caused by Arc Furnaces

Abstract

Arc devices are among the receivers with the highest power connected to power systems. Due to dynamic load changes, these receivers generate a number of disturbances that affect the quality of electric power. The most important disturbances include voltage fluctuations. It is also worth mentioning the asymmetry and deformation of the supply voltage curve. This article discusses the mutual interaction of receivers operating in parallel, operating stably, and devices with dynamic current consumption. Calculations based on model tests and the results of parameters characterizing the quality of energy, which were recorded in the line supplying the steelworks, are presented. The power supply conditions (power of the short-circuit network) were assessed to influence the degree of suppression of voltage fluctuations by loads with stable current consumption.

1. Introduction

In recent decades, there has been a continuous increase in steel production [1,2], with the most dynamic development being the process based on electric arc steelmaking furnaces [3,4]. Arc furnaces are among the largest receivers supplied by the power system. The unit power of these devices reaches over 300 MW and a capacity of over 350 tons [5,6,7]. Additionally, arc furnaces are characterized by dynamically changing loads resulting from the unstable operation of the electric arc [8,9].

Arc furnaces are a source of disturbances affecting the quality of power in the power system. The main disturbance generated by arc furnaces is fast-changing voltage fluctuations [10,11,12,13,14,15,16,17]. These devices are also a source of asymmetry [18,19,20] and voltage curve distortion [20,21,22,23,24,25,26].

Along with the development of steel melting technologies in arc furnaces, there has been a continuous reduction in the operating time of these devices, limited mainly to melting scrap. Further technological processes take place in devices for post-furnace steel processing. Devices used for post-furnace steel processing (LF, VAD, and VOD), in comparison to arc furnaces, are characterized by stable operation (constant current consumption). The introduction of LF, VAD, and VOD devices also contributed to reducing the impact of the steel production process on the natural environment [27,28,29].

In the previous works on the impact of arc devices, mainly issues related to the increase in voltage fluctuations during parallel operation of arc furnaces (operating mainly in the scrap melting phase) were dealt with. Arc devices operating in a stable manner (LF, VOD, VAD and arc furnaces in the final phase of scrap melting) were not taken into account. The article indicates that devices with stable power consumption affect the reduction in voltage fluctuations generated by restless receivers (arc furnaces in the initial phase of scrap melting).

In large steelworks, several arc furnaces are usually installed, which melt scrap at the same time. The increase in voltage fluctuations resulting from the parallel operation of arc furnaces is described, among others, in [30]. Figure 1 shows the power supply diagram of a steelworks with an installed arc furnace and a device for post-furnace steel processing LF. Figure 1 also shows the places where power quality analyzers are connected.

The analysis of the recorded power quality indicators is presented later in this article.

In most publications, the increase in voltage fluctuations caused by switching on subsequent furnaces is mainly estimated. For example, in [31], the degree of increase in voltage fluctuations and, consequently, the flicker coefficient is determined from Formula (1):

$$P_{st}=\sqrt[m]{P_{st1}^m+P_{st2}^m+\cdots +P_{stn}^m}$$

(1)

where

• P_stn corresponds to the flicker level induced by the n-th disrupting receiver.

The value of the coefficient m, occurring in the above formula, depends upon the characteristics of unquiet receivers, and can be categorized into the following five categories:

• m = 4: Used only for the summation of voltage changes due to arc furnaces specifically run to avoid coincident melts;
• m = 3.2: This choice matches the slope of the straight part of the P_st = 1 curve;
• m = 3: This is used for most types of voltage changes where the risk of coincident voltage occurring is small. The vast majority of studies combining unrelated disturbances will fall into this category, and it should be used where there is any doubt over the magnitude of the risk of coincident voltage changes occurring;
• m = 2: This is used where coincident stochastic noise is likely to occur, e.g., coincident melts on arc furnaces;
• m = 1: The resultant P_st will approach the value given by this coefficient when there are very high occurrences of coincident voltage changes.

The article presents issues related to limiting voltage fluctuations in the network supplying the steelworks resulting from the simultaneous operation of arc furnaces and devices used for non-furnace steel processing. The results of model tests are presented, which were related to data recorded in the power network supplying the steelworks.

In the European Standard [32] and the provisions of the Polish legal regulations [33], the permissible ranges of voltage changes are expressed in percentages and referred to as the rated voltage. For this reason, the results of measurements and model tests of voltage fluctuations are expressed in percentages, in relation to the supply voltage U_L = 100%.

2. Voltage Fluctuations Generated by an Arc Device During Scrap Melting

Voltage fluctuations are defined as cyclic changes in the voltage envelope or a series of random changes in the effective voltage value around the nominal value. Figure 2 shows the changes in the effective voltage value (expressed as a percentage of the nominal voltage) recorded in the arc furnace supply line (Figure 1—Point P).

The effective voltage value was determined for one period (20 ms). The course of changes in the effective voltage value presented in Figure 2 covers one second of measurements.

Figure 3 shows the changes in the voltage fluctuation amplitudes determined based on the measured effective voltage values ΔU (Figure 2). Additionally, Figure 3 shows the value of the standard deviation DS(ΔU) determined from Formula (4).

Figure 4 shows a pie chart of the arc furnace determined based on measurements recorded in the line supplying the furnace transformer–arc furnace. The voltage of the line supplying the steelworks U_S is expressed as a percentage of the rated voltage U_N.

The arc furnace current is expressed as a percentage of the rated current, where 100% corresponds to the I_N current. The current change from I_A to I_B causes voltage change between U_A and U_B values. Voltage fluctuations between U_A and U_B values can be determined from Formula (2):

$$∆U=U_A-U_B$$

(2)

Referring to the rated voltage U_N, voltage fluctuations w can be calculated using Formula (3):

$$∆U={\displaystyle \frac{U_A-U_B}{U_N}}100[\mathrm{\%}]$$

(3)

The voltage standard deviation SD(U) was used as a reliable source to evaluate randomly changing voltage fluctuations (3):

$$SD\left(U\right)=\sqrt{{\displaystyle \frac{1}{n}}{\sum }_{i=1}^n{(U_i-U_{mean})}^2}$$

(4)

where

• SD(U)—standard deviation of voltage
• U_i—value for the i-th rms voltage sample
• U_mean—RMS voltage mean for n samples
• n—number of voltage samples.

The ΔU waveform shown in Figure 3 shows that arc furnaces generate voltage fluctuations with a frequency of several changes per second. The effect of fluctuations of such frequency is the occurrence of the phenomenon of light flicker generated by lighting receivers, mainly incandescent ones.

The value of voltage fluctuations caused by the operation of arc furnaces depends on many factors, including the following: furnace transformer power, power supply conditions of the steel mill (short-circuit power in PCC), melting period, and type and quality of melted scrap, adopted technological process (for example, melting with foamed slag). Figure 5 shows changes in voltage fluctuations recorded during one of the melting cycles in the arc furnace at the supply point of the furnace transformer (Point B) and at the supply point of the steel mill (Point P).

3. Voltage Fluctuations Generated by a Single Arc Furnace—Modeling Studies

Based on measurement data recorded in the networks supplying arc devices of the actual parameters of the supply lines, high-current circuits, and furnace transformers, the assumptions adopted in the model tests were developed. The considered arc supply system was replaced with a single-phase equivalent circuit of the supply line and the high-current circuit of the arc device, as shown in Figure 6.

The supply network voltage (substitute source voltage) was assumed as a reference value with an effective value of U_RMS marked U_L = 100%. The assumption was made of two-state current variation from I_A to I_B (circular chart Figure 7), which corresponds to changes in the arc voltage from U_ArcA to U_ArcB and changes in the voltage on the steelworks rails from U_SA to U_SB, i.e., fluctuations of this voltage ΔU_SAB.

The arc voltage (in single furnace operation) is determined from Formula (5) as follows:

$$U_{Arc}=\sqrt{U_L^2-I^2{(X_L+X_T)}^2}-\left(R_L+R_T\right)I$$

(5)

The voltage on the steelworks rails from Formula (6) is as follows:

$$U_S=\sqrt{{(U_L+R_{T}I)}^2+I^2{X}_T^2}$$

(6)

For the variation of currents I_A and I_B, we obtain the value of the arc voltages, as follows:

$$U_{ArcA}=\sqrt{U_L^2-I_A^2{(X_L+X_T)}^2}-\left(R_L+R_T\right)I_A$$

(7)

$$U_{ArcB}=\sqrt{U_L^2-I_B^2{(X_L+X_T)}^2}-\left(R_L+R_T\right)I_B$$

(8)

The voltages supplying the furnace transformer are as follows:

$$U_{SA}=\sqrt{{(U_L+R_T{I}_A)}^2+I_A^2{X}_T^2}$$

(9)

$$U_{SB}=\sqrt{{(U_L+R_T{I}_B)}^2+I_B^2{X}_T^2}$$

(10)

These correspond to the voltage fluctuations, as follows:

$${∆U}_S=U_{SA}-U_{SB}$$

(11)

The voltage fluctuations are expressed as a percentage, as follows:

$${∆U}_S={\displaystyle \frac{U_{SA}-U_{SB}}{U_L}}100\%$$

(12)

The standard deviation of the voltage at the point supplying the steelworks is as follows:

$${SD(U}_S)={\displaystyle \frac{U_{SA}-U_{SB}}{2}}={\displaystyle \frac{{∆U}_S}{2}}$$

(13)

4. Model of the Power Supply System for Devices with Stable Power Consumption

The power supply diagram of an arc device for post-furnace steel processing (LF) is shown in Figure 8.

It was assumed that the LF steel treatment device operates stably. This means that the LF does not generate voltage fluctuations. The pie chart is shown in Figure 9.

The arc voltage of a stably operating LF device is determined by Formula (14) as follows:

$$U_{LF}=\sqrt{U_L^2-I^2{(X_L+X_{TLF})}^2}-\left(R_L+R_{TLF}\right)I$$

(14)

The supply voltage of the LF transformer at Point C is given by Formula (15) as follows:

$$U_C=\sqrt{{(U_L+R_{TLF}I)}^2+I^2{X}_{TLF}^2}$$

(15)

For the I_LF (steady operating) arc device current, the arc voltage is U_LF—Point R on the pie chart in Figure 9.

5. Modeling of Voltage Fluctuations in Parallel Operation of Arc Furnace and LF

This article presents the results of model tests and measurements of voltage fluctuations in the networks supplying steelworks during the parallel operation of an arc furnace (in the initial phase of scrap melting—unstable operation) and a device used for post-furnace steel processing (stable operation of the device—the arc between the electrodes and the molten charge does not change its length).

Figure 10a shows the power supply diagram of the arc furnace, the ladle furnace LF (operating in the steelworks), and the substitute arc device, as shown in Figure 10b,c.

The voltage on the “replacement arc device—Figure 10c” for each of these states can be determined by Formula (16), as follows:

$$U_{AFL}={\displaystyle \frac{\frac{U_{Arc}}{X_{TArc}}+\frac{U_{LF}}{X_{TLF}}}{\frac{1}{X_{TArc}}+\frac{1}{X_{TLF}}}}={\displaystyle \frac{U_{Arc}+U_{LF}}{2}}$$

(16)

Its substitute reactance is as follows:

$$X_{TAFL}={\displaystyle \frac{1}{\frac{1}{X_{TArc}}+\frac{1}{X_{TLF}}}}$$

(17)

The supply voltage of the steelworks U_S, taking into account the parallel operation of arc devices, can be determined using the iterative method by solving Equation (18):

$$U_L^2=U_s^2+2U_S^2{\displaystyle \frac{X_L}{X_{TAFL}}} (2-\frac{{U_{Arc}^2+U}_{LF}^2}{U_S^2})+U_S^2{\displaystyle \frac{X_L^2}{X_{TAFL}^2}}\left[{{\left({\displaystyle \frac{{U_{Arc}^2+U}_{LF}^2}{U_S^2}}\right)}^2+\left({\displaystyle \frac{U_{Arc}}{U_S}}\sqrt{1-{\left({\displaystyle \frac{U_{Arc}}{U_S}}\right)}^2}\right)+\left({\displaystyle \frac{U_{LF}}{U_S}}\sqrt{1-{\left({\displaystyle \frac{U_{LF}}{U_S}}\right)}^2}\right)}^2\right]$$

(18)

Leaving aside the expressions (19):

$${\left({\displaystyle \frac{X_L}{X_{TAFL}}}\right)}^2$$

(19)

Formula (18) is simplified to the Formula (20) as follows:

$$U_L^2=U_s^2+4U_S^2{\displaystyle \frac{X_L}{X_{TAFL}}}-2{\displaystyle \frac{X_L}{X_{TAFL}}}(U_{Arc}^2+U_{LF}^2)$$

(20)

From the above formula, the first approximation of the U_S voltage can be determined as follows:

$$U_{s\prime }^2={\displaystyle \frac{U_L^2+2\frac{X_L}{X_{TAFL}}(U_{Arc}^2+U_{LF}^2)}{1+4\frac{X_L}{X_{TAFL}}}}$$

(21)

$$U_{s\prime }=\sqrt{{\displaystyle \frac{U_L^2+2\frac{X_L}{X_{TAFL}}(U_{Arc}^2+U_{LF}^2)}{1+4\frac{X_L}{X_{TAFL}}}}}$$

(22)

The next approximations of U_S are obtained by substituting into Formula (22) until satisfactory accuracy is obtained, i.e., when voltage UL = 100%. For the same arc voltages in both furnaces, the equivalent source voltage is as follows:

$$U_{ALF}=U_{ALFA} \mathrm{lub} U_{ALF}=U_{ALFB}$$

(23)

In the case of different arc voltages in each furnace (e.g., U_ArcA in one furnace and U_ArcB in the other), the matter is more complicated. The changes in the phase angles of the U_ArcA and U_ArcB voltages must be adjusted to the unchanged value of the source voltage of the supply network (U_L = 100%) and maintaining the same values of the U_S modules on each of the furnaces operating in parallel and on the “substitute” furnace, i.e.,

$$U_{ALFA}^2+{I\prime }_A^2{X}_{TAFL}^2=U_{ALF}^2+{I\prime }_B^2{X}_{TAFL}^2=U_{AFL}^2+{I\prime }^2{\left({\displaystyle \frac{X_{TAFL}}{2}}\right)}^2={U\prime }_S$$

(24)

Then, the supply voltage U_L for the first approximation U_S is determined by the correction U_S according to Formula (25):

$$U_S^{\prime \prime }=U_S^{\prime }{\displaystyle \frac{U_L}{{U\prime }_L}}$$

(25)

Based on the calculated U_SAA and U_SBB voltages, the average USAFL voltage value is as follows (26):

$${\overline{U}}_{SAFL}={\displaystyle \frac{U_{SAFL}+U_{SBFL}}{2}}$$

(26)

The mean square of the U_SAFL voltages is as follows:

$${\overline{U}}_{SAFL}^2={\displaystyle \frac{U_{SAFL}^2+U_{SBFL}^2}{2}}$$

(27)

The standard deviation SD (U_SAFL) is as follows:

$${SD(U}_{SAFL})=\sqrt{{\overline{U}}_{SAFL}^2-{\left({\overline{U}}_{SAFL}\right)}^2}$$

(28)

Based on the knowledge of the standard deviation of the voltage during the operation of one SD(U_SArc) furnace and the standard deviation of the voltage during parallel operation of an arc furnace and an LF ladle furnace SD(U_SAFL) (29) is as follows:

$$K_{AFL}={\displaystyle \frac{{SD(U}_{SAFL})}{{SD(U}_{SArc})}}$$

(29)

6. Discussion

The supply network with the power transformer (X_L) and the furnace transformer, the high-current track consisting of the flexible part, busbars, and electrodes (X_T) were replaced only with reactance. The reactance of the supply network was marked as X_L and three of its values were assumed for calculations: X_S = 0.1–0.2–0.5. This is to take into account the changes in the short-circuit power of the supply network in relation to the short-circuit power of the arc furnace electrodes with the charge, amounting to S_CC/S_CArc=100–50–20, respectively.

The arc was modeled as a source of sinusoidal voltage with a constant effective value, depending on the arc length. When the arc length changes, the voltage between the electrolytes and the charge also changes. This results in a change in the value of the current drawn by the furnace. In the model tests, the current drawn by the arc furnace changes between the value I_A = 0.9I_N and the value I_B = 1.5I_N. This corresponds to the voltage changes between U_A and the value U_B, i.e., voltage fluctuations ΔU_AB.

Table 1. Sample data and model test results.

Arc	Arc + Arc	Arc + LF
Parameters of the power supply network and the arc furnace
UL = 100	UL = 100	UL = 100
RL = 0.04	RL = 0.04	RL = 0.04
XL = 0.2	XL = 0.2	XL = 0.2
RT = 1.5	RT = 1.5	RT = 1.5
XT = 5	XT = 5	XT = 5
IA = 0.9IN	IA = 0.9IN	IA = IN
IB = 1.5IN	IB = 1.5IN	IB = IN
Calculation results
USArc(mean) = 98.10	US2Arc(mean) = 96.29	USAFL(mean) = 96.35
DS(USArc) = 0.775	DS(US2Arc) = 1.06	DS(USAFL) = 0.748
-	K2ARC = 1.367	KAFL = 0.965

presents the data adopted for the model tests and the calculation results in the case of operation in a steelworks: a single arc furnace (Arc), two arc furnaces (Arc + Arc), and an arc furnace and a device for post-furnace steel processing FL (Arc + LF).

After switching on the arc furnace, in the initial phase of melting scrap, we are dealing with a decrease in the average voltage value in the line supplying the furnace transformer to the level of U_SArc(mean) = 98.10% of the supply voltage U_L. This is caused by a voltage drop in the impedance of the supply line. Additionally, as a result of sudden changes in the current consumption by the arc furnace, voltage fluctuations are generated. The size of the voltage fluctuations determines the standard deviation from the mean value U_SArc(mean), which in the analyzed case is as follows:

DS(U_SArc) = 0.775

After switching on the second, identical arc furnace (operating in the initial phase of scrap melting), there is a further decrease in the average voltage value in the line supplying the steelworks U_S2Arc(mean) = 96.29 and an increase in voltage fluctuations characterized by the standard deviation of voltage D_S(US2Arc) = 1.06. The coefficient K_2ARC = 1.367, therefore, determines how much the voltage fluctuations increased during the parallel operation of two furnaces in relation to the voltage fluctuations generated by a single furnace. In the analyzed case, this is an increase of 36.7%.

From the analysis of the model tests, the sample results of which are presented in Table 1, it turns out that the parallel operation of the arc furnace melting scrap in the initial phase and the arc device operating stably (with a constant current value) limits the voltage fluctuations, in relation to the arc furnace operating alone. In this case, the average voltage value in the line supplying the steelworks is also reduced to U_SAFL(mean) = 96.35. The voltage fluctuations estimated on the basis of the standard deviation DS(U_SAFL) = 0.748 and the coefficient KAFL = 0.965 are lower by 3.5%, in relation to the fluctuations caused by the arc furnace operating alone.

One of the most important factors influencing the degree of voltage fluctuation damping is the impedance of the supply network. The impedance (mainly reactance) of the network supplying the steelworks (steel mill) determines the short-circuit power of the network at the point of connection of arc devices.

Table 2. Voltage fluctuation damping degree depending on the reactance X_L.

XL	Us	DS(UArc)	DS(UAFL)	KAFL
0.1	97.80	0.4	0.39	0.98
0.2	96.35	0.77	0.74	0.96
0.3	94.90	1.16	1.10	0.94
0.4	93.44	1.57	1.46	0.93
0.5	91.98	1.99	1.82	0.91

and Figure 11 show how the average voltage U_S changes and to what extent voltage fluctuations decrease when the reactance of the supply network X_L changes.

Based on the data presented in Table 2 and the waveforms from Figure 11, it can be concluded that the network with high reactance X_L reduces voltage fluctuations caused by the arc furnace to a greater extent. However, the voltage supplying the furnace transformer U_S is reduced. This results in a change in the furnace operating point, which reduces its active power and extends the melting time. The furnace operating point is corrected by regulating the voltage of the electric arc using the furnace transformer tap changer. Another factor influencing the reduction in voltage fluctuations generated by the arc furnace is the power of the arc device or the device for post-furnace steel processing LF operating in parallel.

Figure 12 shows the changes in the voltage supplying the steelworks when the I_LF current drawn by the LF device changes.

Additionally, the U_S voltage changes are presented for two reactances of the line supplying the steelworks (two short-circuit powers of the supply networks). Due to the nonlinear nature of the electric arc of the arc furnace, the relationship between the voltage supplying the steelworks U_S and the current of the LF arc device is also nonlinear. The nonlinear nature of the electric arc also affects the amount of voltage fluctuation attenuation.

Figure 13 shows the relationship between the K_AFL coefficient and the value of the I_FL current drawn by the LF device.

Figure 13 also shows the characteristics of two short-circuit powers of the line supplying the steelworks, represented by the reactances of the supply line X_L = 0.2 and X_L = 0.4.

7. Conclusions

The measurement results and model tests presented in this article were aimed at estimating the extent to which stably operating devices in steelworks affect the reduction in voltage fluctuations generated by arc furnaces. Due to the nonlinear nature of the electric arc, the superposition principle could not be applied. Using the iteration method, the voltage supplying the arc devices and the standard deviation of the voltage from the average value were determined. The standard deviation is representative of voltage fluctuations. However, the standard deviation does not take into account the frequency of changes in the voltage fluctuation amplitude.

Previous works have presented an analysis of the increase in voltage fluctuations when connecting subsequent devices. The author proposed his method for calculating the increase in voltage fluctuations during parallel operation of arc devices. Details of the proposed method are presented, among others, in Olczykowski Z., “Superposition of Voltage Fluctuations During the Operation of Arc Receivers”, doctoral dissertation, Warsaw University of Technology, Poland, 2001 [34]. The proposed method is related to other methods presented in [31,35,36,37,38,39]. According to the author, extending the method to voltage fluctuation suppression may be justified.

The example presented in this article can be extended to other receivers connected to the power system. Due to the increasing number of nonlinear receivers, the importance of receivers stabilizing the power system is increasing.