# Evaluation of Flicker of Light Generated by Arc Furnaces

^{*}

## Abstract

**:**

## 1. Introduction

_{st}and long-term flicker severity P

_{lt}.

_{lt}is determined on the basis of the following twelve short-term flicker P

_{st}indicators from Formula (1):

_{st}is determined in a ten-minute period. From the twelve P

_{st}values, the long-term flicker rate P

_{lt}for a period of 2 h can be calculated.

_{lt}are compared with the permissible levels given in the relevant standards and regulations [31,32,33,34].

## 2. Measurement of Flicker of Light Indicators

_{n}-110 kV/S

_{SC}-5000 MVA)—the main line supplying the smelter, Point B (U

_{n}-30 kV/S

_{SC}-750 MVA)—supply line for the arc furnace (EAF), Point C (U

_{n}-6 kV/S

_{SC}-500 MVA)—supplying the ladle furnace (LF), Point D (U

_{n}-230 V)—circuits supplying lighting receivers. Measurements were made both in long measurement periods (including one week of recording) and short measurement periods for individual melts in the arc furnace. Ten-minute measurement intervals were used for the weekly recording cycle and five-second intervals for the recording of individual melts. Conducting the tests with shortened time intervals (5 s and 10 s) was aimed at more precise determination of changes in the light flicker indicators during the smelting. Parallel to the measurements of light flicker indicators, other parameters characterizing the quality of electricity were recorded.

_{n}= 400 kV line with a short-circuit power of S

_{SC}= 8774 MVA. The steel plant is powered by a line with a voltage of U = 110 kV and a short-circuit power S

_{SC}= 1512 MVA.

_{N}coefficient determining the increase in voltage fluctuations with a different number of arc devices working in parallel.

## 3. Propagation of Disturbances Generated by the Arc Furnace

_{PstAB}is defined [39].

_{st}measured during one week at point A (110 kV line supplying the steelworks) and point B (30 kV line supplying EAF)—Figure 3.

_{st}recorded at the voltage level: 110 kV and 30 kV is 0.86. Based on Formula (2), the following were determined: TC

_{PstABmax}= 0.18 and TC

_{PstAB 95%}= 0.17.

_{st}waveforms measured during one smelting process at point A (110 kV line supplying the steel plant) and point B (30 kV line supplying EAF).

_{st}recorded at the voltage level: 110 kV and 30 kV is 0.98. Based on Formula (2), the following were determined: TC

_{PstABmax}= 0.20 and TC

_{PstAB95%}= 0.19.

_{SC}(A), S

_{SC}(B) and P

_{st}(B)—indicators of short-term flicker of light measured at the reference point. The TC

_{AB}propagation coefficient can be calculated from the Formula (3):

_{SC}(A) = 5000 MVA and B; S

_{SC}(B) = 750 MVA—we get:

_{st}short-term flicker severity recorded simultaneously during one week of measurements at three points: steelworks supply line—point A, EAF supply line—point B, LF supply line—point C.

_{st}_Point B and the supply network of the steelworks P

_{st}_Point A-cal were presented, as well as the theoretically determined by the Formula (5)—P

_{st}_Point A-cal. Only the P

_{st}_Point-meas and P

_{st}_110 kV-cal indicators are compared.

_{st}short-term flicker severity recorded simultaneously during one week of measurements at two points: steelworks supply line (P

_{st}_Point A_meas), EAF supply line (P

_{st}_Point B_meas) and determined by Formula (5) (P

_{st}_Point B_cal).

_{SC}= 8774 MVA. The steel plant is powered by a line with a voltage of U = 110 kV and a short-circuit power S

_{SC}= 1512 MVA. There are three arc furnaces and two ladle furnaces operating in the steelworks.

_{AB}= 0.17 propagation coefficient.

- -
- from extra high voltage (EHV) networks to high voltage (HV) networks propagation factor equals C = 0.8;
- -
- propagation factor from high voltage (HV) networks to medium voltage (MW) networks equals C = 0.9;
- -
- from medium voltage (MW) networks to low voltage networks (LW) propagation factor equals C = 1.

_{st99%}taking into account the above factors:

_{st}_Point B_calc shown in Figure 8.

_{st}_Point_B_calc light flicker indices determined on the basis of the Formula (5) and P

_{st}_Point B_calc_C corrected for the attenuation factor C = 0.9.

## 4. Statistical Analysis of Flicker of Light Indicators

_{st}in short time intervals covering individual heats in the arc furnace is presented below. The statistical analysis of the short-term flicker severity P

_{st}was based on the data recorded during individual melts (10 s measurement intervals). Figure 11 shows the change of the Pst coefficient measured in the three phases of the steelworks supply network during one melt carried out in the arc furnace. Very high values of the flicker coefficient are visible in particular phases, namely, P

_{stmax(L1)}= 9.81; P

_{stmax(L2)}= 9.60; P

_{stmax(L3)}= 9.69. The high-level flicker of lightresults from the relatively low short-circuit power S

_{SC}= 750 MVA in relation to the power at the short circuit of the electrodes with the approximate charge S

_{SCf}= 40 MVA.

_{st}. As it results from the measurements carried out by the authors, with the asymmetry coefficient below the permissible value, light flicker indicators in all phases change within a similar range.

_{st}measured during one melt in the arc furnace.

_{st}) during one melt (10 s sampling periods) were determined for the flicker index. In the first stage, grouping was performed, i.e., the classification of the measured light flicker indices by dividing the sample into classes. For the measured short-term flicker severity during one smelting, the number of samples is n = 443. The number of class intervals per m = 10 was established with the length of the class interval being 0.97.

_{st}. During one day of measurements, the obtained 144 values of the flicker index varied from P

_{stmin}= 0.25 with the arc furnace off, to P

_{stmax}= 7.69 with the furnace operating in the melting phase. The mean value of the short-term flicker severity was P

_{stmax}= 3.94. and its standard deviation D(P

_{st}) = 1.69. As in the case of the amplitudes of voltage fluctuations and the flicker index of light measured for one smelt, as well as for one-day measurement, the basic statistical parameters of the distribution series created earlier from the measured values were calculated; they are listed in Table 2.

_{stmax}− P

_{stmin)}/m = (7.69 – 0.25)/7 = 1.06.

_{st}.

_{α}

^{2}= 9.49 and since the value determined from the sample is χ

^{2}= 2.24 < χ

_{α}

^{2}= 9.49, there is no reason to reject the hypothesisthat the analyzed distribution is a normal distribution.

## 5. Assessment of The Increase in Flicker of Light with Parallel Operation of Arc Devices

_{N}coefficient. This factor determines the extent to which voltage fluctuations will increase with successively connected arc furnaces in relation to the fluctuations generated during the operation of a single device.

_{N}can be determined from the formula [26]:

_{st}obtained with the use of the light flicker meter is assumed, and it is determined from the relationship [42].

_{stn}corresponds to 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 five categories:

_{st}= 1 curve;

_{s}

_{t}will approach the value given by this coefficient when there are very high occurrences of coincidental voltage changes.

_{N}coefficient was determined from the formula:

_{Pst}

_{ΔU}= 0.906.

_{N}was worked out [45].

_{N}in the following form:

_{st1}= P

_{st2}=… = P

_{stn}), Formula (14) can be transformed to the form:

_{N}:

_{N}coefficient depending on the number of parallel arc furnaces. The curves drawn on the basis of Formula (20) recommended by UIE are marked in red.

_{N}coefficient can be determined depending on the short-circuit power of the S

_{SC}network, the power of the transformer at the short-circuit of the electrodes with the charge S

_{SCf}, and the voltage in the line supplying the steel plant: respectively for the operation of the N furnaces and the operation of a single furnace (furnace with the highest power, reference furnace). Figure 17 also shows the values of the K

_{N}coefficient corresponding to the supply conditions of the steel plant, the supply scheme of which is shown in Figure 3. For point A, the ratio is S

_{SC}/S

_{SCf}= 140, and for point B it is S

_{SC}/S

_{SCf}= 20.

_{N}coefficient is decisively influenced by the short-circuit power on the rails of the steel plant. The higher the short-circuit power, the greater the K

_{N}coefficient, i.e., the arc devices interact to a lesser extent, mitigating the increase in voltage fluctuations. Obviously, the voltage fluctuations and flicker of light at S

_{SC}/S

_{SCf}= 20 are greater than at S

_{SC}/S

_{SCf}= 140.

## 6. Discussion

_{st}and P

_{lt}indicators. The volume measured by the flickermeter (or the power quality parameter analyzer with the flicker index function) is the voltage change. The remaining elements (functions) must be modeled: the reaction of the lamp–eye–brain system. A 60 W bulb was adopted as the reference lamp. With the currently widely used LED lamps, this assumption is debatable. It is therefore appropriate to ask the question: should the algorithm be modified for determining the flicker indicators by introducing a new reference lamp? According to the authors, this may create a problem related to the use of existing flickermeters and the need for further modifications when developing new light sources.

_{lt}≤ 1 for a different registration period, for example, 80% of the time instead of 95% currently used.

_{st}LM ≤ 1 for LED and OLED MLS. The determined value shall not exceed the declared value by more than 10%. Adopting a new P

_{st}LM unit requires the use of specialized photometric equipment that also allows SVM to be measured (stroboscopic visibility measure), as defined in standards SVM = 1, represents the visibility threshold for an average observer. The metric for flicker used in this Regulation is the parameter ‘P

_{st}LM’, where ‘st’ stands for short-term and ‘LM’ for light flickermeter method, as defined in the standards. A value of P

_{st}LM = 1 means that the average observer has a 50% probability of detecting flicker. Measurements are made in a photometric darkroom by placing the meter at a specified distance from the light source. Another method is to use a meter circuit with an integrating ball, which allows the verification of the ripple characteristics when measuring the luminous flux. The measurements proposed by the EU in [46] are designed to test the resistance of light sources to voltage fluctuations. Before obtaining the certificate, individual types of light sources are tested. This means that the P

_{st}LM indicator is completely different from the P

_{st}and P

_{lt}indicators. P

_{st}and P

_{lt}relate directly to supply voltage fluctuations that directly affect the flickering of light. P

_{st}LM is therefore an additional parameter that is taken into account by manufacturers of LED light sources.

_{lt}and short-term severity flicker P

_{st}recorded in the supply line to the ironworks (a)—Point A (Figure 3) and steel plant (b)—Point B (Figure 3), during the weekly measurement cycle.

_{lt95%}≤ 0.8, it was found that the acceptable value was exceeded, although to a small extent. For point A, P

_{lt95%}= 0.89, P

_{ltmax}= 1.03. During several weekly measuring cycles at point A, similar Plt95% values were obtained. The values of P

_{lt95%}varied from 0.76 through 0.81 to 0.89 (referring to the phase with the highest Plt values). At point A (U

_{n}-110 kV), the short-circuit power of the network is S

_{SC}= 5000 MVA. The rated power of the furnace transformer is S

_{n}= 20 MVA. Assuming the operational short-circuit factor k

_{sc}= 2, the ratio of the short-circuit power of the network to the power of the furnace transformer at the short-circuit of the electrodes with the charge is S

_{SC}/S

_{SCT}= S

_{SC}/(k

_{SC}S

_{n}) = 5000/40 = 125.

_{SC}/S

_{SCT}= 80 and in the publication in [49], S

_{SC}/S

_{SCT}= 120. On the basis of the conducted research, the authors concluded that the minimum ratio of the short-circuit power of the network to the short-circuit power of the electrodes with the charge should be greater than 125.

_{st}and P

_{lt}analysis was proposed in the phase in which the highest values were recorded. Comparing the conducted statistical analysis of the P

_{st}light flicker indices recorded at 10 s (one melt) and 10 min (one day of measurements) measurement intervals, a very similar probability density function was found—Figure 12 and Figure 13.

## 7. Summary

_{N}coefficient defining the increase in light flickering with arc furnaces operating in parallel in a steel mill, compared to the method recommended by UIE (Formula (14)), takes into account, among others: different powers of individual furnace transformers, supply conditions of the steel mill represented by short-circuit power, voltage reduction in supply network at successively connected electric arc furnaces and the individual smelting phases in the electric arc furnace. Assuming that the frequency of voltage fluctuations generated by arc furnaces changes within a small range from a few to several changes per second, it was found that the proposed K

_{N}factor determines both the degree of increase in voltage fluctuations and light flicker in the parallel operation of arc furnaces.

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

## Abbreviations

P_{lt} | long-term flicker severity |

P_{st} | short-term flicker severity |

TC_{AB} | transfer coefficient |

C | coefficient of propagation (attenuation coefficient) |

R_{SVC} | factor that limits voltage fluctuations through the compensator |

R_{self} | coefficient limiting voltage fluctuations through the choke |

K_{N} | coefficient determining the increase in flicker of light depending on the number of parallel operating arc furnaces in steel plant |

P_{stN} | value of the short-term light flicker indicator recorded during the operation N of arc furnaces |

P_{st1} | value of the short-term light flicker indicator recorded during the operation of a single arc furnace |

N | number of parallel operating arc furnaces in steel plant |

S_{scf} | short-circuit power capacity when shorting the electrodes with the scrap |

S_{sc} | short-circuit power capacity of the network |

n_{i}* | cumulative amount |

f_{i}* | cumulative periodicity |

S_{ntr} | power of the furnace transformer |

U_{N} | rated voltage |

ΔU | voltage fluctuations |

${\mathrm{k}}_{\mathrm{q}}^{\u2022}$; ${\mathrm{k}}_{\mathrm{q}}^{*}$ | slope coefficients of the power–voltage characteristic calculated at a constant arc voltage and a constant arc resistance, respectively |

${\overline{\mathrm{Q}}}_{\mathrm{j}}$ | mean reactive power drawn by j-th furnace |

${\mathrm{U}}_{\mathrm{SN}}{\text{};\text{}\mathrm{U}}_{\mathrm{S}1}$ | voltage on the bus-bars of the steelwork at the work of N furnaces and the work of a single furnace (the furnace of the highest power, reference furnace), respectively |

K_{st} | coefficient characterizing the emission of fluctuations of the considered furnace, ranging between 48 and 85 with an average value of approx. 60 (K_{st} changes with the change of the probability function of not exceeding P_{st}) |

C | attenuation coefficient between individual voltage levels |

R_{SVC} | a factor that limits voltage fluctuations through the compensator |

R_{self} | coefficient limiting voltage fluctuations through the choke |

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**Figure 2.**RMS value changes (

**a**) and voltage fluctuations (

**b**) recorded in the power supply line lighting receivers.

**Figure 4.**Changes of P

_{st}short-term flicker severity recorded simultaneously during one week of measurements at two points: steelworks supply line—point A, EAF supply line—point B (

**a**); correlation between the flicker P

_{st}Point A and Point B (

**b**).

**Figure 5.**Changes of P

_{st}short-term flicker severity recorded simultaneously during one smelting of measurements at two points: steelworks supply line—point A, EAF supply line—point B (

**a**), correlation between the flicker P

_{st}Point A and Point B (

**b**).

**Figure 6.**Changes of P

_{st}short-term flicker severity recorded simultaneously during one week of measurements at three points: steelworks supply line—point A, EAF supply line—point B, LF supply line—point C.

**Figure 7.**Changes of P

_{st}short-term flicker severity recorded during one week of measurement (P

_{st}_Point A_meas) and determined by Formula (5) (P

_{st}_Point A_cal).

**Figure 8.**Changes of P

_{st}short-term flicker severity recorded simultaneously during one week of measurements at two points: steelworks supply line (P

_{st}_Point A_meas), EAF supply line (P

_{st}_Point B_meas) and determined by the Formula (5) (P

_{st}_Point B_cal).

**Figure 9.**Changes of P

_{st}short-term flicker severity recorded during one week of measurement (P

_{st}_110 kV_meas) and determined by the Formula (5) (P

_{st}_400 kV_cal).

**Figure 10.**Changes of P

_{st}P

_{st}short-term flicker severity determined by Formula (5) (P

_{st}_Point B_cal).

**Figure 11.**Changes in the short-term flicker severity P

_{st}recorded during one melt in the arc furnace.

**Figure 12.**Distribution of the probability density function of short-term flicker severity: theoretical and real.

**Figure 13.**Probability density function for one day of measurements of the short-term severity flicker P

_{st}.

**Figure 16.**Changes of short-term severity flicker P

_{st}, voltage fluctuations ΔU (

**a**) measured during one melt and correlation between P

_{st}—ΔU (

**b**).

**Figure 17.**Changes in coefficient K

_{N}according to the number of parallel operating arc furnaces in steel plant.

**Figure 18.**Changes of long-term severity flicker P

_{lt}and short-term severity flicker P

_{st}measured during one week in the supply line to the ironworks (

**a**) and steel plant (

**b**).

**Table 1.**Statistical parameters of the short-term flicker severity P

_{st}measured during one melt in the arc furnace.

Class Number | Class Range | Center Class | Amount | Periodicity | Cumulative Amount | Cumulative Periodicity |
---|---|---|---|---|---|---|

I | P_{st} | P_{st} | n_{i} | f_{i} | n_{i}* | f_{i}* |

1 | 0.15–1.12 | 0.635 | 52 | 0.107 | 52 | 0.107 |

2 | 1.13–2.09 | 1.61 | 58 | 0.119 | 110 | 0.226 |

3 | 2.10–3.06 | 2.58 | 94 | 0.193 | 204 | 0.420 |

4 | 3.07–4.03 | 3.55 | 103 | 0.212 | 307 | 0.632 |

5 | 4.04–5.00 | 4.52 | 64 | 0.132 | 371 | 0.763 |

6 | 5.01–5.97 | 5.49 | 47 | 0.097 | 418 | 0.860 |

7 | 5.98–6.94 | 6.46 | 37 | 0.076 | 455 | 0.936 |

8 | 6.95–7.91 | 7.43 | 18 | 0.037 | 473 | 0.973 |

9 | 7.92–8.88 | 8.4 | 8 | 0.016 | 481 | 0.990 |

10 | 8.89–9.85 | 8.92 | 5 | 0.010 | 486 | 1.000 |

Class Number | Class Range | Center Class | Amount | Periodicity | Cumulative Amount | Cumulative Periodicity |
---|---|---|---|---|---|---|

i | P_{st} | P_{st} | n_{i} | f_{i} | n_{i}* | f_{i}* |

1 | 0.25–1.31 | 0.780 | 8 | 0.0556 | 8 | 0.0556 |

2 | 1.32–2.37 | 1.845 | 20 | 0.1389 | 28 | 0.1944 |

3 | 2.38–3.43 | 2.905 | 30 | 0.2083 | 58 | 0.4028 |

4 | 3.44–4.49 | 3.965 | 30 | 0.2083 | 88 | 0.6111 |

5 | 4.50–5.55 | 5.025 | 28 | 0.1944 | 116 | 0.8056 |

6 | 5.56–6.61 | 6.085 | 20 | 0.1389 | 136 | 0.9444 |

7 | 6.62–7.67 | 7.145 | 8 | 0.0556 | 144 | 1.0000 |

P_{sti} | n_{i} | z_{i} | F(z_{i}) | p_{i} | np_{i} | (n_{i} − np_{i})^{2}/np_{i} |
---|---|---|---|---|---|---|

1.31 | 8 | −1.56 | 0.0594 | 0.06 | 8.55 | 0.0358 |

2.37 | 20 | −0.93 | 0.1762 | 0.12 | 16.82 | 0.6015 |

3.43 | 30 | −0.30 | 0.3821 | 0.21 | 29.65 | 0.0041 |

4.49 | 30 | 0.32 | 0.6255 | 0.24 | 35.05 | 0.7275 |

5.55 | 28 | 0.95 | 0.8289 | 0.20 | 29.29 | 0.0568 |

6.61 | 20 | 1.58 | 0.9429 | 0.11 | 16.42 | 0.7825 |

7.67 | 8 | 2.21 | 0.9864 | 0.06 | 8.55 | 0.0358 |

Sum | 144 | x | x | 1.00 | 144 | 2.2441 |

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## Share and Cite

**MDPI and ACS Style**

Olczykowski, Z.; Łukasik, Z.
Evaluation of Flicker of Light Generated by Arc Furnaces. *Energies* **2021**, *14*, 3901.
https://doi.org/10.3390/en14133901

**AMA Style**

Olczykowski Z, Łukasik Z.
Evaluation of Flicker of Light Generated by Arc Furnaces. *Energies*. 2021; 14(13):3901.
https://doi.org/10.3390/en14133901

**Chicago/Turabian Style**

Olczykowski, Zbigniew, and Zbigniew Łukasik.
2021. "Evaluation of Flicker of Light Generated by Arc Furnaces" *Energies* 14, no. 13: 3901.
https://doi.org/10.3390/en14133901