# Suppression of the Second Harmonic Subgroup Injected by an AC EAF: Design Considerations and Performance Estimation of a Shunt APF

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## Abstract

**:**

## 1. Introduction

## 2. Problem Definition

## 3. Proposed Hybrid Solution Including APF

_{eq}. More than one APF unit is considered to be used in order to eliminate the need for series operation of power semiconductor switches. The three-phase three-wire bridge converter topology for each APF unit is chosen, as illustrated in Figure 4b.

## 4. Proposed APF Design Methodology

#### 4.1. Determination of the Maximum RMS Value of the Second Harmonic Subgroup

_{A}(t) + I

_{B}(t) + I

_{C}(t) = 0), but asymmetrical, load on the power system for the vast majority of time as reported in [6]. Sample line current waveforms of an AC EAF installation recorded in the field and the corresponding 95-, 100-, and 105-Hz components obtained by the real-time interharmonic and harmonic detection method recommended in [7] are given in Figure 5a–d, respectively. As observed from Figure 5, AC EAF currents contain significant amounts of second harmonic subgroup components (95-, 100-, 105-Hz) and they are highly time-varying. The maximum RMS value of the second harmonic subgroup is determined during the boring phase of the EAF operation in which the currents are more rapidly fluctuating in comparison with those of the consecutive melting and refining periods. Instantaneous current variations in Figure 6a–c are obtained by MSRF analysis in boring phase for 40 s of measurement period. Their sample-by-sample summation is as given in Figure 6d. Their maximum peak values are also marked on Figure 6a–d. The true RMS value of the resultant reference signal by using the maximum RMS values (obtained by dividing the max peak values by √2) is calculated from Equation (1) and is found to be 166.3 A.

- (i)
- for the vast majority of the operating time, the true RMS value is lower than 166.3 A;
- (ii)
- the peak values of the subgroup current harmonic components rarely coincide in time;
- (iii)
- the optimum solution to the preliminary design study is chosen to be the minimization of the second harmonic subgroup currents instead of the elimination of them entirely; and
- (iv)
- the fundamental current component flowing through the coupling transformer compensates only for APF switching and conduction losses and to magnetize the transformer core. Since it is much lower than the true RMS value of the second harmonic subgroup, it is neglected in the preliminary design procedure.

#### 4.2. Estimation of Coupling Transformer MVA Rating

_{l-to-l}is the line-to-line value of the fundamental component of the primary voltage (33.5 kV is the most probable value), and I

_{line}is the true RMS value of the second harmonic subgroup (166.3 A).

_{m}, created in the core, however, minor hysteresis loops arising from 95-, 100-, and 105-Hz components will be superimposed on the major hysteresis loop obtained at 50-Hz. Furthermore, these minor loops will move on the major loop depending upon the frequency and phase differences. Therefore, the variations in B

_{m}should be taken into account in hysteresis loss, P

_{h}, and eddy current loss, P

_{e}, calculations. Their expressions are given in Equations (3) and (4), respectively:

_{h}, K

_{e}, and K

_{f}are constants depending on the core material, and f is the corresponding frequency.

_{m}is usually taken to be 1.8 T. As can be understood from Equations (3) and (4), the increase in P

_{h}and P

_{e}owing to the second harmonic subgroup current components can only be compensated by keeping the design value of B

_{m}much lower than 1.8 T. Our experience shows that B

_{m}should be chosen in the range from 1 T to 1.2 T in order to compensate for the extra core loss components [34]. Total leakage reactance of 6% is implementable for this size of a transformer. These considerations result in an oversized coupling transformer.

#### 4.3. Estimation of Transformer Secondary Voltage

_{dc}, at a value greater than, or equal to, the peak value of the AC voltage appearing at the coupling transformer secondary terminals. For this purpose, peak values of individual harmonic and interharmonic voltages should be superimposed on peak value of the fundamental component of the transformer secondary voltage. Here, it is assumed that all peak voltages should be added algebraically. Single phase equivalent circuit of the overall system on the MV side is as shown in Figure 8a. In this figure, L

_{s}is the equivalent source inductance, L

_{tr}the transformer leakage inductance, L

_{apf}the current sharing inductors, and m the number of parallel APF units. Figure 8a shows the equivalent circuit for the fundamental component. A very small current at the fundamental frequency flows through the APF system, therefore the fundamental voltage component of each APF unit should be nearly equal to the supply voltage V

_{s}. Figure 8b shows the harmonic and interharmonic equivalent circuits of the APF system, in which the supply side provides a short-circuit return path to the harmonic and interharmonic current components changing at 95-, 100-, and 105-Hz. Therefore, in this equivalent circuit, only these particular harmonic and interharmonic components are considered to be injected by the AC EAF, I

_{eaf,h}. V

_{apf}for 95-, 100-, and 105-Hz components, can then be calculated as the potential drop on L

_{apf}/m and L

_{tr}, owing to the amount of harmonic and interharmonic components to be suppressed by the APF system.

_{tr,k}the transformer impedance calculated at the kth interharmonic and harmonic frequency and referred to as the MV side.

_{DRM}the maximum repetitive peak blocking voltage, and V

_{DC}the DC link voltage.

_{DC}, are then calculated from Equation (6) for typical blocking voltage ratings of HV IGBTs as given in Table 3.

_{C}, rating should be considered for the sake of minimum number of parallel APF units. Required transformer line currents in peak amps on the secondary side are than calculated from the peak current in Figure 6d by multiplying it by the required n. These results are given in Table 4 as a function of HV IGBT ratings.

_{DRM}= 4500 V, I

_{C}= 1500 A is the preferred one because it minimizes the number of parallel APF units with the lowest possible semiconductor voltage rating and, hence, the cost.

#### 4.4. Proposed Control Strategy

_{fx}> I

_{fx}* + HB then S

_{X}= 1,

_{fx}< I

_{fx}* − HB then S

_{X}= 0,

_{fx}is the actual current flowing through phase x, I

_{fx}

^{*}is the reference current which should be tracked for phase x, and S

_{X}is the switching state of the converter leg corresponding to phase x.

_{X}= 1 corresponds to the case where upper semiconductor in converter leg of phase x is turned on while lower one is turned off. Likely, state S

_{X}= 0 corresponds to the case where lower semiconductor in converter leg of phase x is turned on while the upper one is turned off. The digital implementation of the hysteresis band modulation technique is as illustrated in Figure 10.

_{ref}− ΔI and I

_{ref}+ ΔI, as illustrated in Figure 10, and according to the fixed hysteresis band current control strategy.

## 5. Performance of Proposed APF System by EMTDC/PSCAD Simulations

_{eafn}, and supply side, I

_{sn}, are simultaneously given in Figure 12. As can be understood from Figure 12:

- (a)
- 100-Hz component is eliminated;
- (b)
- 95- and 105-Hz components are significantly suppressed;
- (c)
- The non-idealities in the performance are attributed to the facts that extraction of interharmonic and harmonic components using MSRF analysis in real-time may lead to small magnitude and phase errors, hence, the APF system cannot suppress the second harmonic subgroup perfectly.
- (d)
- The proposed APF system does not affect interharmonic and harmonic current components other than the second harmonic subgroup; and
- (e)
- Second harmonic subgroup reduction is computed for the harmonic spectrum given in Figure 12 and it is found to be 36.9% without affecting the neighboring interharmonic components by using the proposed APF topology. This is much better than the best cases for passive shunt harmonic filters given in Table 2, which are case-e and -f. Although 56.4 and 48.0% of the second harmonic subgroup of the EAF current are reflected to the supply-side for case-e and –f in Table 2, these topologies still amplify other interharmonic components, as shown in Figure 3.

## 6. Conclusions

## Author Contributions

## Conflicts of Interest

## References

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**Figure 1.**Block diagram illustrating all harmonics and interharmonics of an EAF power system. (I

_{eafn}, I

_{sn}, and I

_{fn}denote the harmonics and interharmonics injected by the EAF, all harmonic and interharmonic components in the supply lines, and harmonic and interharmonic components sunk by the passive shunt harmonic filter bank/s, respectively).

**Figure 2.**Typical second and third harmonic passive filter topologies (

**a**) single-tuned damped second HF; (

**b**) C-type third HF; and (

**c**) single-tuned undamped third HF.

**Figure 3.**Filtering performances of different passive shunt harmonic filter topologies against harmonics and interharmonics with 5 Hz resolution injected by the EAF. Case-(

**a**): single-tuned third HF with f

_{o}= 148.9 Hz, no second HF; Case-(

**b**): single-tuned second HF with f

_{o}= 99.8 Hz and single-tuned third HF with f

_{o}= 148.9 Hz; Case-(

**c**): heavily-damped C-type second HF with R

_{D}= 40 Ω and f

_{o}= 99.8 Hz and single-tuned third HF with f

_{o}= 148.9 Hz; Case-(

**d**): lightly-damped C-type second HF with R

_{D}= 250 Ω and f

_{o}= 99.8 Hz and single-tuned third HF with f

_{o}= 148.9 Hz; Case-(

**e**): lightly-damped C-type second HF with R

_{D}= 250 Ω and f

_{o}= 94.8 Hz and single-tuned third HF with f

_{o}= 148.9 Hz; and Case-(

**f**): lightly-damped C-type second HF with R

_{D}= 250 Ω and f

_{o}= 94.8 Hz, no third HF (ESR/L is assumed to be 10 for all HF reactors; ESR is the equivalent series resistance of all HF reactors).

**Figure 4.**Proposed EAF system (

**a**) block diagram including an APF and an SVC; (

**b**) m APF units operating in parallel and connected to the grid via a coupling transformer; and (

**c**) the three-phase three-wire two-level VSC converter for each APF unit.

**Figure 5.**EAF line currents on MV side (

**a**) a sample line current waveforms collected in the field at a sampling rate of 25.6 kS/s and (

**b**) 95-Hz components (

**c**) 100-Hz components, and (

**d**) 105-Hz components obtained from field data by MSRF analysis in real-time.

**Figure 6.**A sample set of EAF current waveforms obtained by MSRF analysis in real-time (

**a**) 95-Hz, (

**b**) 100-Hz, (

**c**) 105-Hz components, and (

**d**) the reference current signal produced from (

**a**–

**c**).

**Figure 8.**Single-phase equivalent circuit of the proposed system at (

**a**) the fundamental frequency (50 Hz) and (

**b**) any harmonic or interharmonic frequency.

**Figure 10.**Illustration of digital implementation of hysteresis band current control philosophy (— current generated by HAPF unit; T

_{e}= execution time typical values 20–30 µs; T

_{s}= sampling time typical value is nearly 40 µs).

**Figure 11.**A sample reference current signal including 95-, 100-, and 105-Hz (deduced from field data) and corresponding current waveform injected by the APF system (simulation results).

**Figure 12.**Harmonic spectrum of the load (field data) and source current in phase-A (simulation results), referring to the MV side.

**Figure 13.**Ten-cycle DFT expansion of (

**a**) EAF current (deduced from field data) and (

**b**) APF current (deduced from simulation results) on the MV side.

**Figure 14.**Harmonic spectrum of the APF line current showing the effect of hysteresis switching (simulation results).

**Figure 15.**Proposed hybrid filter topology for the suppression of second and third harmonic subgroups, (

**a**) block diagram including APF and third HF and (

**b**) filtering performance of the proposed topology in comparison with APF only and third HF only solutions (EAF current collected in the field and single phase currents are expanded in DFT with 5 Hz resolution).

**Table 1.**EAF and supply-side current components of second harmonic subgroup for the block diagram in Figure 1 for various filter topologies.

Frequency Hz | Case-0 I _{eafn} (%) | Case-(a) I _{sn} (%) | Case-(b) I _{sn} (%) | Case-(c) I _{sn} (%) | Case-(d) I _{sn} (%) | Case-(e) I _{sn} (%) | Case-(f) I _{sn} (%) |
---|---|---|---|---|---|---|---|

95 | 1.16 | 1.50 | 3.34 | 1.99 | 2.90 | 0.34 | 0.33 |

100 | 1.32 | 1.81 | 0.19 | 1.29 | 0.41 | 0.75 | 0.66 |

105 | 1.00 | 1.48 | 0.55 | 0.87 | 0.57 | 0.79 | 0.63 |

_{o}= 148.9 Hz, no second HF; Case-(b): single-tuned second HF with f

_{o}= 99.8 Hz and Single-tuned third HF with f

_{o}= 148.9 Hz; Case-(c): heavily-damped C-type second HF with R

_{D}= 40 Ω and f

_{o}= 99.8 Hz and single-tuned third HF with f

_{o}= 148.9 Hz; Case-(d): lightly-damped C-type second HF with R

_{D}= 250 Ω and f

_{o}= 99.8 Hz and single-tuned third HF with f

_{o}= 148.9 Hz; Case-(e): lightly-damped C-type second HF with R

_{D}= 250 Ω and f

_{o}= 94.8 Hz and single-tuned third HF with f

_{o}= 148.9 Hz; Case-(f): lightly-damped C-type second HF with R

_{D}= 250 Ω and f

_{o}= 94.8 Hz, no third HF; Note: ESR/L = 10 for all HF reactors.

**Table 2.**Second harmonic subgroup content of the supply line current waveform for different passive shunt harmonic filter bank/s as defined in Table 1 (Case-0 is the no filter case, therefore, I

_{sn}= I

_{eafn}).

Source Second Harmonic Subgroup | Case-0 (%) | Case-a (%) | Case-b (%) | Case-c (%) | Case-d (%) | Case-e (%) | Case-f (%) |
---|---|---|---|---|---|---|---|

As a percentage of Fundamental Component | 2.02 | 2.78 | 3.39 | 2.53 | 2.98 | 1.14 | 0.97 |

As a percentage of Furnace Second Harmonic Subgroup | 100 | 137.6 | 167.8 | 125.2 | 147.5 | 56.4 | 48.0 |

**Table 3.**Maximum permissible DC link voltage against blocking voltage capability of commercially available HV IGBTs.

IGBT Blocking Voltage (VDRM) | MAX DC Link Voltage (VDC) |
---|---|

6500 V | 4000 V |

4500 V | 2800 V |

3300 V | 2000 V |

2500 V | 1500 V |

1700 V | 1000 V |

HV IGBT | Optimum DC Link Voltage V_{DC} | Turns Ratio N | Required Transformer Line Current on the Secondary (A) | Minimum Number of APF Units M | |
---|---|---|---|---|---|

V_{DRM} (V) | I_{C} (A) | ||||

6500 | 1000 | 4000 | 13.3 | 4522 | 5 |

4500 | 1500 | 2800 | 19.0 | 6460 | 5 |

3300 | 1700 | 2000 | 26.6 | 9044 | 6 |

2500 | 1700 | 1500 | 35.5 | 12,070 | 8 |

1700 | 3600 | 1000 | 53.2 | 18,088 | 6 |

© 2018 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).

## Share and Cite

**MDPI and ACS Style**

Durna, E.; Gerçek, C.Ö.; Salor, Ö.; Ermiş, M. Suppression of the Second Harmonic Subgroup Injected by an AC EAF: Design Considerations and Performance Estimation of a Shunt APF. *Electronics* **2018**, *7*, 53.
https://doi.org/10.3390/electronics7040053

**AMA Style**

Durna E, Gerçek CÖ, Salor Ö, Ermiş M. Suppression of the Second Harmonic Subgroup Injected by an AC EAF: Design Considerations and Performance Estimation of a Shunt APF. *Electronics*. 2018; 7(4):53.
https://doi.org/10.3390/electronics7040053

**Chicago/Turabian Style**

Durna, Emre, Cem Özgür Gerçek, Özgül Salor, and Muammer Ermiş. 2018. "Suppression of the Second Harmonic Subgroup Injected by an AC EAF: Design Considerations and Performance Estimation of a Shunt APF" *Electronics* 7, no. 4: 53.
https://doi.org/10.3390/electronics7040053