Abstract
The AC electric arc furnace (EAF) is becoming a core apparatus of the modern steel industry. Nevertheless, it used to be a major threat of power quality in the traditional power supply system. In this paper, a flexible power supply system of the AC EAF is proposed, which is expected to completely alter its inherent cognition of impact load in the power grid. The basics of the power supply for EAF are first reviewed and the novel techniques to enhance the operation flexibility of EAF are introduced. The power circuit and the control structure are then presented, followed by the detailed strategies of various operations fully considering the features of EAF. A large disturbance stability criterion based on the mixed potential theory is also established for the practical application. Both electromagnetic transient simulations using PSCAD and benefit analyses verify the feasibility of the proposed system.
Δla, La, la, l0 Closed-loop regulation, real value, objective law, and DC offset of simulated arc length
α Binary variable denoting Cassie or Mayr model
μ Commutation angle of diode rectifier hybrid AC/DC equivalence
τ Typical time constant of low-voltage arc
, Cut-off angular frequencies of proportional-resonant (PR) controller and low-pass filters
, Natural angular frequency and damping coefficient of the second-order hydraulic cylinder
, Rated and load-side angular frequencies
, , , Constants of arc volume temperature and thermal inertia of arc resistance
, Bandwidth and cut-off frequency of low-pass filter
, Bandwidth of inner- and outer-loop control
Capacitor of power module (PM)
Diodes in rectifier circuit of PM
, Diodes in chopper circuit of PM
Function value related to
Equivalent switching frequency of PM
Frequency of PCC
Rated frequency of power cycle
, Harmonic order and amplitude of each harmonic for
Current reference of voltage-controlled current source in hybrid AC/DC equivalence
, Phase currents flowing to arc and load sides
Phase current injected to point of common coupling (PCC)
, , Proportional, integral, and resonant gains
, Coefficients of electrode control
, Coefficients of automatic control
, , , Inductors of DC filter, transformer, AC output of PM, and chopper
, Components of inverter and rectifier for mixed potential function
, , Active power, reactive power, and apparent power flowing to load side
, Actual and base values of the maximum power dissipation during one power cycle
, , Active power, reactive power, and apparent power flows injected to PCC QSTAT Output reactive power of static synchronous compensator (STATCOM)
q, n, m Numbers of secondary windings of transformer, inverters of a single PM, and phases
, , , Resistances of short net, transformer, arc, and chopper
Sum of resistances of load side and equivalent PM
, Apparent power consumed by a single PM and transformer
Vector of reference voltage
, Line-to-ground voltage of arc and load side
DC voltage of PM
, Feedforward voltage and its amplitude for control loops
, , Reactances of short net, transformer, and
Sum of reactances of load side and equivalent PM
, , Per-unit impedances of short net, reactor, and transformer
WITH the accumulation of scrap steel and the banning of induction furnaces, the short steelmaking process by electric arc furnace (EAF) is urgently required to be upgraded. Such a process is a typical energy conversion transferring electrical energy to thermal energy, which aims to melt down the mixture of solid and liquid scrap for useable high-grade steel. The EAF technology is of global significance to reduce the carbon emissions of the steel industry towards a future low-carbon society. To balance the ultra-high power (up to hundreds of megawatts) and the operation reliability of EAF, the three-phase AC power supply replaces the DC power supply to be the mainstream and is in the scope of this paper.
Experience shows that the tap changing of the EAF transformer typically covers over one third of the heat cycle but contributes none to the finished steels in a traditional power supply (TPS) system, which owns the potential to improve the production efficiency. Due to the restricted regulation on arc length by the established electrode control in the TPS system, the AC EAF is well-known for the extensive disturbances on the power quality (PQ), especially harmonics, interharmonics, and flickers [
Generally, EAF can be modeled both in the time and the frequency domains [
Conventionally, air-core reactors and inductive short nets are configured for the suppression of reactive power fluctuation and arc stability enhancement [
With the continuous increasement in EAF capacity, the aforementioned passive mode of shunt compensation for EAF will become less cost-effective in the space occupation, power loss, and manufacture of corollary equipment. Therefore, an active mode embedding power electronics units into the series circuit has attracted much attention. The enhancements of the arc stability using thyristor-based power modules (PMs) in series with the primary side of the EAF transformer are given in [
In this paper, a novel technique to enhance the operation flexibility of EAF is proposed, namely the flexible power supply (FPS) system. It matches the well-known concept of flexible power transmission. The main contributions of this paper are summarized as follows.
1) The power circuit of the FPS system is explicated fully considering the feature of EAF.
2) A coordinated control structure including the electrode control and the PM control is proposed, which adds an extra current control mode (CCM) on the existing voltage control mode (VCM), and the control strategies for various operation conditions are well explained.
3) Both the theoretical basis of the short net reduction and the urgent stability enhancement are derived using a large disturbance stability criterion based on the mixed potential theory (MPT) [
4) The benefit analyses and the simulation results validate the merits of the FPS system compared with the TPS system.
The remainder of this paper is organized as follows. Section II reviews the basics of the power supply system for AC EAF. Sections III and IV focus on the power circuit and the control system of the proposed FPS system, respectively. Section V constructs an MPT-based stability criterion for the stable operation of EAF. Simulations in Section VI verify the theoretical analyses followed by the benefit analyses in Section VII. Finally, conclusions are given in Section VIII.

Fig. 1 Simplified single-line diagram of steelwork at typical voltage level.
In the TPS system, when the transformer tap is fixed, regulated by the electrode control is the only independent variable of . However, the irregular fluctuation of the liquid level or melt collapse may lead to stochastic and unbalanced disturbances on , which are beyond the control bandwidth and thus should be responsible for the imperfect regulation of .
To address the negative incremental attribute of AC EAF [
The PQ issues of EAF can be concluded as frequency impact, low PF, voltage imbalance, harmonic current injection, and IFL. The sequence of operation in each heat cycle, as shown in

Fig. 2 Typical waveforms of power supply system for EAF. (a) Sequence of operation. (b) Voltage variation at load side.
The above shortcomings of the TPS system will be magnified with the capacity increasement of EAF. Compared with the passive mode of power consumption compensation used in the TPS system, the advantages of active mode of power regulation aided by novel techniques for AC EAF are mainly reflected by:
1) In the part of the power circuit, the multiwinding phase-shifting transformer and power electronics based PMs are series-connected to replace the tap-changing transformer and the reactors, which suits the low-voltage and ultra-high-current features of AC EAF, and saves the PQ conditioning devices.
2) In the part of the control system, the adaptivity of the characteristic CCM is proven, and the control strategies focusing on the electromagnetic dynamic performance are given to increase the control bandwidth essentially.
The FPS system is proposed to solve the concerns mentioned in Section II. This section mainly focuses on modeling the power circuit fully considering the features of AC EAF.
The overall configuration of the power circuit is presented in

Fig. 3 Schematic diagram of FPS system. (a) Overall configuration (furnace wall is grounded). (b) Internal structure of PM.
Discrete multiwinding phase-shifting transformers replace the unified EAF transformer in the FPS system, which prevents the typical harmonic current from being injected into the power grid. The PF can be easily kept above 0.95 with the further reactive power support of capacitors in PMs, which also decreases the total capacity of transformers with the same level of . Besides, with the elimination of transformer taps, the FPS system owns a higher degree of automation than the TPS system.
A single PM shown in
The connection of solid-state devices can be observed in
To ensure that the AC EAF has a strong current tolerance, the short net including the delta closure, the conducting arm, and the power cables should be retained in the FPS system [
Due to the same zero-crossing moment but various amplitude ratios of and in each power cycle, an analytical time-varying resistance model introducing the dynamic of La to reflect the mechanism of AC EAF is derived as [
(1) |
la can be emulated as:
(2) |
la should be limited in the range of and the following linear approximation using the measured data:
(3) |
According to the above discussions, the core target of the FPS system is to regulate precisely on the premise of arc stability. An elaborated control system that can make full use of the hardware is the focus of this section.
The overall configuration of FPS system is illustrated in

Fig. 4 Overall control configuration of FPS system.
PM control acts on the gates of IGBTs/IGCTs of the VSI by from the feedback control and the selected modulation.
1) VCM with Feedback Control
VCM is first proposed to imitate the working principle of the TPS system, where the input end of the short net can be regarded as an AC voltage source. The control strategy is shown in
(4) |
(5) |
(6) |

Fig. 5 Control strategies of PM. (a) VCM. (b) CCM.
where the subscript v represents the VCM.
The experienced setpoint of the TPS system can be followed in the VCM of the FPS system. More importantly, a sine-wave real-time modulation of can be automatically realized, which saves the tap-changing time to increase the operation efficiency. Since the low-pass filters (LPFs) are used in both the outer and inner feedback loops of the VCM, the control bandwidth of Pl is still completely attributed to the electrode control, which indicates no improvement over that of the TPS system.
2) CCM with Feedback Control
A heuristic theoretical derivation of the arc stability enhancement of CCM is based on the single-phase hybrid Cassie-Mayr arc model [
(7) |
(8) |
Linearizing (8) at the general solution s0 , we have:
(9) |
If s monotonically increases until the discontinuity moment of Ia, the arc will cool rapidly due to the break of the power balance. Therefore, a necessary condition for the arc instability is given as:
(10) |
Suppose that the electrode control is coordinated with the VCM of PM to regulate Ua at a constant level or make . Substituting (10) into (9) gives , which is in the physical range of . When the VCM is replaced by CCM, is achieved, and , which is far away from the approximated of the ultra-high-current arc. Furthermore, Il can be managed by feedback control to prominently improve the bandwidth of Pl.
Therefore, CCM is an essential improvement for the AC EAF. It is pointed out in [
3) Modulation
The zero common mode (ZCM) modulation [
Even if the control bandwidth is effectively improved by the CCM of PM control, it is still necessary to retain the electrode control, to not only fine-tune the position of the electrode under the normal operation conditions according to (3) but also establish an acceptable ignition voltage based on physical laws. The block diagram of electrode control is illustrated in

Fig. 6 Block diagram of electrode control.
Three functions are focused on the manual setting mode of the proportional valve. As shown in
The constant arc impedance mode, which is widely used in the TPS systems for keeping the power supply at the only stable operation point, is taken as an example of the automatic control mode.
The hydraulic cylinder is calculated as:
(11) |
The ideal transfer function of the hydraulic cylinder is given as:
(12) |
A group of parameters of electrod control is listed in
Parameter | (rad/s) | (V) | |||
---|---|---|---|---|---|
Value | 0.5 | 0.078 | 0.2 | 18.5 | [-10,10] |
The open-loop frequency characteristics of the current loops in CCM and are compared in

Fig. 7 Bode diagram of and .
The results show that sufficient stability margins of are achieved when varies from 0.1 to 10 p.u. since the bandwidth of is separated from that of . Note that of p.u. is close to that of p.u. and thus overlaps.
The active operation condition (AOC) and passive operation condition (POC) are defined and distinguished according to whether the output of
(13) |

Fig. 8 Diagram of coordinated control strategies. (a) Hysteresis detection logic of POC. (b) Arc-striking process.
where is set as one quarter of the power supply due to the approximate half-wave odd symmetry of [
The last one of the aforementioned extreme operation conditions will be explained intuitively with simulation results in Section VII while the others are worth no detailed discussion, and the CCM with direct anti-overcurrent potential and enhanced arc stability is preferred for those four conditions in the FPS system. The control strategy for a certain operation is a coordination of the electrode control and PM control, and the mode of each control can be dynamically switched according to certain rules.
1) The feedforward voltage acts as a “probing voltage” for the ignition and stable combustion once the air gap is small enough, which can be estimated by (3).
2) The arc length synchronization with the phase of the maximum is to suppress the second harmonic ripple of .
3) When ascending three electrodes, to guarantee the arc stability, both the outer loop of electrode and PM control regulate first with a reasonable increasing rate slightly larger than the speed of the electrode , and then switch to control once and are around their set values.
The two-phase operation at a lower power level is unique for the FPS system due to the avoidance of the EAF transformer. It can increase the feasibility of production scheduling and the flexibility of equipment maintenance. However, the defect on should be examined based on the availability of and of the remaining PMs, and the heat cycle should also be adjusted.
The proposed strategy for the quasi-short-circuit recovery is as follows.
1) For the detected quasi-short-circuit phase, the electrode should be locked immediately. The outer loop of CCM is set to control for the double-loop current limitation. For the normal operation phases, the outer loops of control blocks are both set to maintain , while the inner current limiter of the CCM can suppress the impact on .
2) When is stable, follow the rules of arc-striking to ascend the electrodes as soon as possible.
The open circuit recovery can be regarded as a sequence of arc-striking control and quasi-short-circuit recovery for the corresponding phase. Please note that the defect on may be more noticeable whereas the overcurrent risk is less than the quasi-short-circuit recovery.
The FPS system can fully cover the functions of the TPS system without hardware parameter adjustment at the load side. However, with the active control of arc stability by CCM, the major function of the short net turns to filter the harmonics of , and a co-optimization of and is feasible. Considering that the real-time stability monitoring is valuable for the FPS system, a solution based on MPT [
Supposing a consistent AC voltage amplitude for the input end of PMs, an equivalent model of the investigated AC/DC hybrid FPS system is shown in

Fig. 9 Hybrid AC/DC equivalent model of FPS system.
According to [
(14) |
(15) |
(16) |
where is neglected for its small value; and , , , and are intermediate variables.
Under the assumption of average symmetry in each power cycle of the load-side three phases, the basic mixed potential function is expressed as [
(17) |
(18) |
(19) |
Since the dynamics of the inner loop are neglected, can reflect the stability issue of the DC voltage time-scale because only the RMS value control is considered.
1) Short Net Reduction
When is regulated to a constant, the load side can be equivalent to an apparent power load proportional to and . Therefore, the critical value of , which is denoted as , can be derived by setting :
(20) |
Substituting (20) into (17)-(19), the stable region can be obtained by projecting P to the corresponding plane, as shown in

Fig. 10 Feasibility of short net reduction. (a) Two-dimensional stable regions for different parameters. (b) Three-dimensional diagram of and .
2) Stability Monitoring
An analytical criterion is used to monitor the large disturbance stability in the simulation.
(21) |
It offers an extra guideline for the system design. Furthermore, it reveals that an increase in is beneficial for the online stability enhancement.
The single-line diagram of the test benchmark established in PSCAD is shown in

Fig. 11 Single-line diagram of test benchmark.
Device | Parameter | Value |
---|---|---|
PM (Diode: ZPb4600-40 IGBT: FZ1500R33HL3) | (MVA) | 5 |
(kV) | 1.35 | |
(μF) | 10000 | |
10 (+2) | ||
(μH) | 5 | |
(μH) | 5 | |
(Hz) | 750 | |
3 | ||
Multiwinding phase-shifting transformer | (MVA) | 15 |
(%) | 2 | |
10 | ||
5 |
Symbol | (V/mm) | (V) |
(MW) | (kA) | (%) |
(%) | |
---|---|---|---|---|---|---|---|
Value | 1 | 40 | 36.5 | 47.95 | 3.33 | 30 | 8 |
The effectiveness of modeling AC EAF introduced in Section III is first tested in case 1-1. Various operation conditions of the smelting period due to the disturbances on la and the negative incremental v-i characteristic are emulated in

Fig. 12 Verification on EAF model. (a) and . (b) - characteristic.
Comparisons of the regulation on Pl are shown in

Fig. 13 Comparison results of active power regulation in different cases. (a) ( s). (b) and fPCC ( s). (c) . (d) (phase a). (e) and .
At s, the fluctuation of is backward deduced and limited at 0.5-25 Hz using the data in
The extreme POCs represented by a three-phase quasi-short-circuit and a single-phase (phase a) open circuit are emulated at s and s, respectively. It is validated that the single-phase open circuit results in more serious defects on (actually close to that of the two-phase operation of the TPS system), which leads to cross the boundaries, while the quasi-short-circuit suffers from the overcurrent potential. As shown in
In
As shown in

Fig. 14 Comparison of PQ conditioning. (a) IFL of PCC voltage. (b) Compensation effect of case 1-3. (c) .
Case | THD (%) | Individual harmonic order h (%) | |||||
---|---|---|---|---|---|---|---|
2 | 3 | 4 | 5 | 6 | 7 | ||
1-1 | 11.2 | 3.8 | 4.7 | 1.7 | 4.3 | 0.7 | 2.3 |
1-3 | 2.3 | 0.6 | 1.0 | 0.4 | 0.6 | 0.2 | 0.6 |
2-2 | 0.2 | 0.2 | 0.2 |
Note: only typical (the to ) harmonics of AC EAF are listed; and THD refers to the total harmonic distortion [
The applications of the proposed large disturbance stability criterion are tested in case 2-2. The three-phase quasi-short-circuit is selected as an example for its instantaneous dramatic increase in and potential decrease in , which introduces uncertainties in . Before s, a larger is obtained by the proper reduction in , which indicates a larger stability margin. In

Fig. 15 Validation of proposed MPT-based large disturbance stability criterion. (a) Real-time change of H. (b) Real-time change of Udc.
Device | Cost ratio | |
---|---|---|
Base value in case 1-3 | Per-unit value in case 2-2 (p.u.) | |
Transformer | 0.36 | |
PM (IGBT) | 0.18 | |
PM (Capacitor) | 0.26 | |
PM (Others (filters, controllers, etc.)) | 0.13 | 1.2 (with choppers) |
Others (reactor, cooling system, etc.) | 0.07 | 0.85 |
Total | 1.00 | 0.78 |
As the EAF consumes active power for steelmaking, a practical method for calculating the total power loss is expressed as:
(22) |
where denotes the sum of active power loss including the transformer and inverter.
Case | Active power loss (%) | PF | (%) | |
---|---|---|---|---|
Transformer | PM | |||
Case 1-3 | 1.32 | 2.19 | 0.992 | 4.3 |
Case 2-2 | 1.04 | 1.84 | 0.975 | 5.4 |
Extra comments are added on the topology in
The replacement of the centralized three-phase half-bridge inverter in [
To offer a unified solution to the PQ issues at the grid side and operation flexibility at the load side of AC EAF with its irreversible capacity upgrade, a complete FPS system is proposed in this paper. With theoretical analyses and validations, the following conclusions are drawn.
1) The circuit and the control system are designed in detail fully considering the feature of impact EAF load with the support of electromagnetic simulations in PSCAD, which verifies the enhanced operation flexibility, arc stability, and efficiency (one third of the heat cycle for tap-changing can be saved) of the FPS system.
2) It offers an opportunity to avoid various PQ disturbances of EAF on the premise of large-disturbance stability by cooperative parameter design and online monitoring. The test on a 35 kV system shows the IFL is far below 1, the maximum individual interharmonics voltage is far below 3%, and the THD is far below 5% of the IEEE standard without unbalanced components observed.
3) Further comments on at least 20% of the installation cost saving, the optimistic long-term power loss reduction with PF above 0.95, and the optimized topology selection verify the feasibility of the FPS system for the steel industry.
The FPS system is expected to replace the TPS system for AC EAFs in a future low-carbon society. Since only the operation performance of the smelting period is assessed for necessity in the existing work, future studies will reveal the merits of the FPS system during the complete heat cycle with more practical factors in the application considered.
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