Journal of Modern Power Systems and Clean Energy

ISSN 2196-5625 CN 32-1884/TK

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Flexible Power Supply System of AC Electric Arc Furnace  PDF

  • Chongbin Zhao (Student Member, IEEE)
  • Qirong Jiang
  • Dong Liu
the Department of Electrical Engineering, Tsinghua University, Beijing 100084, China; Capital Engineering & Research Incorporation Ltd., Beijing 100176, China

Updated:2023-03-24

DOI:10.35833/MPCE.2021.000414

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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.

NOMENCLATURE

A. Parameters and Variables

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

ωcr, ωc Cut-off angular frequencies of proportional-resonant (PR) controller GPR(s) and low-pass filters

ωn, ξn Natural angular frequency and damping coefficient of the second-order hydraulic cylinder

ω0, ωl Rated and load-side angular frequencies

A, B, C, D Constants of arc volume temperature and thermal inertia of arc resistance Ra

Bdel, fc Bandwidth and cut-off frequency of low-pass filter

Bi, Bo Bandwidth of inner- and outer-loop control

Cdc Capacitor of power module (PM)

D1-D6 Diodes in rectifier circuit of PM

Dc1, Dc Diodes in chopper circuit of PM

F() Function value related to La

fswt Equivalent switching frequency of PM

fPCC Frequency of PCC

f0 Rated frequency of power cycle

i, Ei Harmonic order and amplitude of each harmonic for la

iload Current reference of voltage-controlled current source in hybrid AC/DC equivalence

Ia, Il Phase currents flowing to arc and load sides

IPCC Phase current injected to point of common coupling (PCC)

kp, ki, kr Proportional, integral, and resonant gains

k1, k2 Coefficients of electrode control

kup, kdown Coefficients of automatic control

Ldc, Ltr, Lac, Lc Inductors of DC filter, transformer, AC output of PM, and chopper

Pinv, Prec Components of inverter and rectifier for mixed potential function

Pl, Ql, Sl Active power, reactive power, and apparent power flowing to load side

Ploss, P0 Actual and base values of the maximum power dissipation during one power cycle

PPCC, QPCC, Active power, reactive power, and apparent SPCC 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

Rs, Rtr, Ra, Rc Resistances of short net, transformer, arc, and chopper

RƩ Sum of resistances of load side and equivalent PM

SPM, Str Apparent power consumed by a single PM and transformer

Uref Vector of reference voltage

Ua, Ul Line-to-ground voltage of arc and load side

Udc DC voltage of PM

Uf, Um Feedforward voltage and its amplitude for control loops

Xs, Xtr, Xac Reactances of short net, transformer, and Lac

XƩ Sum of reactances of load side and equivalent PM

Zs, Zr, Ztr Per-unit impedances of short net, reactor, and transformer

B. Subscripts and Superscripts

eq Equivalent value of multiple PMs

pu Per-unit value

rated Rated value

RMS Root mean square (RMS) value

1 Fundamental electrical quantities

^ Estimated value

* Setpoint

I. Introduction

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 [

3]. Such disturbances affect the operation accuracy of the EAF itself, couple to the adjacent renewable energy generation units through harmonic transmission [4], and even induce system-level instability. Therefore, modeling AC EAFs to verify the effect of PQ conditioning has been a popular research topic over the years.

Generally, EAF can be modeled both in the time and the frequency domains [

5]. In the time domain, some representative methods, e.g., the piecewise linear approximation of the voltage-current (v-i) characteristic [6], solving differential equations based on power balancing theory [7]-[10], and the quasi-square voltage amplitude modulation, can all emulate the stochastic short-term variation of electrical quantities. In the frequency domain, the current source model for deterministic harmonic injection using empirical statistical data is more suitable for long-term PQ analysis [11]. The recent trend of EAF modeling is to embody its inherent nonlinearities aided by artificial intelligence [4], [5] or optimization algorithms based on measurement data [12]. However, most of the reported methods merely focus on the external v-i characteristic of the point of common coupling (PCC) or neglect the effect of electrode control, which is unable to reveal the origin of PQ issues. Furthermore, the universality of data-driven models is questionable when any inconsistency exists between the tested systems, especially the power electronics control system investigated in this paper without field experiment data at the design stage.

Conventionally, air-core reactors and inductive short nets are configured for the suppression of reactive power fluctuation and arc stability enhancement [

13], but they inevitably decrease the power factor (PF). To regulate the PF and reduce the harmonics/interharmonics at the PCC, the shunt reactive power compensation by static var compensators (SVCs) or static synchronous compensators (STATCOMs) is mandatory. Even if several predictive methods have been proposed [14], the performance of SVC is still unsatisfactory due to the inherent delays of measurement and thyristor ignition. Reference [2] reports that the capability of flicker suppression by STATCOM can be strengthened if the constant DC voltage reference is released to an acceptable range, which indicates the requirement for not only reactive but active power regulation for EAF. Reference [15] proposes to compensate the typical interharmonics selectively for EAF to decrease the capacity of STATCOM, which meets the standard of instantaneous flicker (IFL) [16], but the effects on other PQ indexes such as the three-phase imbalance are not analyzed or validated.

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 [

17]. By series connecting voltage source inverter (VSI) with the second side of the EAF transformer, the strength of vector current control using insulated gate bipolar transistors (IGBTs) [18] or integrated gate-commutated thyristors (IGCTs) is validated, but the source of the DC side is not explicitly explained. In addition, the existing studies do not fully account for the PQ conditioning, load characteristics, or the effect on electrode control. HITACHI, ABB, and Siemens published their patent topologies in [19], [20] but no follow-up reports are provided. Reference [21] unveiled the patented IGBT-based Q-ONE system in 2017 with the first two sets put into the configuration in 2019, which proves that the active mode can increase the active power availability and system efficiency significantly and meet PQ standards. However, no public literature has discussed the optimal topology or coordinated control strategies.

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) [

22], which suits the hybrid AC/DC system.

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.

II. Basics of Power Supply System for AC EAF

A. Power Circuit of Steelwork

Figure 1 shows a simplified single-line diagram of a steelwork at a typical voltage level, where the EAF is located at the melting shop. Three stages are carried out in turn after power-on: ① arc-striking and bore-down; ② bath expansion with melt collapse; and ③ flat-bath and overheating. Oxidation and refining are executed in the ladle furnace (LF). SVCs or STATCOMs are connected to the same 110 kV bus as EAF in the TPS system.

Fig. 1  Simplified single-line diagram of steelwork at typical voltage level.

B. Limitations of Power Regulation at Load Side

In the TPS system, when the transformer tap is fixed, La regulated by the electrode control is the only independent variable of Pl. However, the irregular fluctuation of the liquid level or melt collapse may lead to stochastic and unbalanced disturbances on La, which are beyond the control bandwidth and thus should be responsible for the imperfect regulation of Pl.

To address the negative incremental attribute of AC EAF [

7], the reactor and the high-impedance short net release their accumulated energy at each current zero-crossing moment for sufficient ignition voltage and continuous combustion of the arc to improve the arc stability. The EAF transformer suffers from the abundant surges in operation, and extra capacity induced by the reactive power loss complicates its manufacture.

C. Various PQ Issues at System Side

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(a), indicates that the smelting period should be first selected to assess the power supply of EAF [

23]. Figure 2(b) reflects the drastic voltage variation at the load side, and countermeasures should be taken to avoid the power variation couples to the grid side.

Fig. 2  Typical waveforms of power supply system for EAF. (a) Sequence of operation. (b) Voltage variation at load side.

D. Novel Technique to Enhance Operation Flexibility

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.

III. Modeling of Power Circuit

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.

A. Overall Configuration

The overall configuration of the power circuit is presented in Fig. 3(a). The symmetry of each phase is realized except for the instantaneous imbalance of the AC EAF.

Fig. 3  Schematic diagram of FPS system. (a) Overall configuration (furnace wall is grounded). (b) Internal structure of PM.

B. Multiwinding Phase-shifting Transformer

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 Pl. Besides, with the elimination of transformer taps, the FPS system owns a higher degree of automation than the TPS system.

C. PM

A single PM shown in Fig. 3(b) can be decomposed by the diode rectifier (no energy feedback command for EAF to save the cost), VSI-based full-bridge inverter, DC chopper, capacitors, and inductors.

The connection of solid-state devices can be observed in Fig. 3. One rectifier is back-to-back connected with multiple two-level inverters considering the low-voltage but ultra-high-current features (typically less than 1 kV but more than tens of kiloamperes) of EAF. All the positive poles P are star-connected with the short net of the same phase to form differential-mode circuits, thus the load-side current Il is equal to the arc current Ia. All the negative poles N are connected to form a common end, which is the source of the common-mode voltage UCM. The negative poles N are recommended not to be grounded to avoid polluting the grounding system.

D. Short Net

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 [

23]. Since the three-phase parameter discrepancies can be omitted by proper layout [9], the short net is modeled as symmetrical impedances based on the technical manual.

E. EAF

Due to the same zero-crossing moment but various amplitude ratios of Ua and Ia 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 [

8]:

Ra(t)=CF(La)La(t)exp[A+B(1-cos(2ωlt+D))]-1La(t)=la(t)+Δla(t) (1)

la can be emulated as:

la(t)=l0+i=150Eisin(iω0t) (2)

la should be limited in the range of Ul and the following linear approximation using the measured data:

Ua,RMS=α0La+β0 (3)

IV. Design of Control System

According to the above discussions, the core target of the FPS system is to regulate Pl 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.

A. Overall Configuration

The overall configuration of FPS system is illustrated in Fig. 4. The control system of each phase is independent but consistent. The necessities, modes, and coordination of the PM control with the electrode control will be discussed as follows.

Fig. 4  Overall control configuration of FPS system.

B. PM Control

PM control acts on the gates of IGBTs/IGCTs of the VSI by Uref 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 Fig. 5(a), in which some variables are expressed as:

kp,v1=Bo/Bdelki,v=2πBo (4)
kp,v2=BiXkr,v=Bi(Ul,1/Il,1)2-X2ωcr=2πBi (5)
Vm=Il,RMS*R2+X2fc=50  Hz (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 Ul* 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 [

17], which is given as:

dRa/dt=Ra(1-UaIl/Ploss)/τPloss=P0Ra-α    α0,1  (7)

Equation (7) suggests that the air gap between the electrode and the scrap is ionized to a quasi-steady state of a balance between thermal accumulation and dissipation in τ. Taking s=ln(Ra) as an intermediate variable, (7) is transformed into:

ds/dt=[1-UaIlexp(αs)/P0]/τs0=ln(P0/(UaIl))/α (8)

Linearizing (8) at the general solution s0 (Δs=s0-s), we have:

dΔsdt=-Δsτα+1Il(s0)Ils+1Ua(s0)Uass=s0 (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:

dΔs/dt>0 (10)

Suppose that the electrode control is coordinated with the VCM of PM to regulate Ua at a constant level or make Ua/s|s=s0=0. Substituting (10) into (9) gives α<1, which is in the physical range of α. When the VCM is replaced by CCM, Il/s|s=s0=0 is achieved, and α<1, which is far away from the approximated α 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 [

17] that an extra increase in dIl/dt at the zero-crossing moment is beneficial for the arc stability but requires a higher Udc. Therefore, Il is set as a sine wave in Fig. 5(b). Both Il,RMS and Pl can be the control objectives, which are for the current limitation and higher power transmission accuracy, respectively. The tuning methods can be learned from the VCM in addition to a phase angle of Uf (Ψ=arctan(XƩ/Rs)).

3) Modulation

The zero common mode (ZCM) modulation [

24] can double fswt, which has the same effect as the well-known interleaving. Besides, it can eliminate UCM to 0 and benefit the insulation of the furnace wall, so it is selected for the FPS system.

C. Electrode Control

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.

Fig. 6  Block diagram of electrode control.

Three functions are focused on the manual setting mode of the proportional valve. As shown in Fig. 6, regarding the inputs of hydraulic cylinder Uin, “max” and “min” represent the maximum rise and fall of the electrode, respectively; and “0” represents the function is blocked, which means the vertical position of the corresponding electrode is fixed.

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 Uin is calculated as:

Uin=k1ΔUl,RMS=k1Il,RMS*RΣ*-Ul,RMS2-(Il,RMS*X)2 (11)

The ideal transfer function Ghc(s) of the hydraulic cylinder is given as:

Ghc(s)=Δla(s)Uin=k2sωn2s2+2ξnωns+ωn2 (12)

A group of parameters of electrod control is listed in Table I, which reflects that the mechanical electrode control cannot cover the wide range of disturbances, as can be observed from ωn.

TABLE I  Parameters of Electrode Control
Parameterk1k2ξnωn (rad/s)Uin (V)
Value 0.5 0.078 0.2 18.5 [-10,10]

The open-loop frequency characteristics of the current loops Gc(s) in CCM and Ghc(s) are compared in Fig. 7.

Fig. 7  Bode diagram of Gc(s) and Ghc(s).

The results show that sufficient stability margins of Gc(s) are achieved when Ra varies from 0.1 to 10 p.u. since the bandwidth of Gc(s) is separated from that of Ghc(s). Note that Gc(s) of Ra=0.1 p.u. is close to that of Ra=1 p.u. and thus overlaps.

D. Operation Condition Classification with Specific Coordinated Control Strategies

The active operation condition (AOC) and passive operation condition (POC) are defined and distinguished according to whether the output of Fig. 8(a) triggers the corresponding control strategies. Considering that the estimated impedances in [

18] are easily disturbed by the coupling of three-phase Il and may lead to errors as the input of hysteresis detection logic, the real-time estimation value of La would replace Il as the input, which is calculated as:

U^a,RMS(t)=t-tdt[Ul,1(t)-Il,1(t)Rs-Il,1(t-td)X]2dtL^a(t)=U^a,RMS(t)-β0α0 (13)

Fig. 8  Diagram of coordinated control strategies. (a) Hysteresis detection logic of POC. (b) Arc-striking process.

where td is set as one quarter of the power supply due to the approximate half-wave odd symmetry of Ua [

8], [10] as well as the improvement in detection speed owing to the use of PMs.

Figure 8(a) indicates that the equivalent open circuit and quasi-short-circuit should be classified as POCs since the nonideal la leads Ra to vary from zero to infinite unpredictably, while the classic topic of arc-striking, two-phase operation, and power upgrade (used to be tap-changing) for EAF belong to AOCs since they can be executed according to the planners of the FPS system users.

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.

Figure 8(b) illustrates the proposed automatic process of arc-striking, which used to depend on the engineering experience in the TPS system. Extra annotations are as follows.

1) The feedforward voltage Uf 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 La is to suppress the second harmonic ripple of Pl.

3) When ascending three electrodes, to guarantee the arc stability, both the outer loop of electrode and PM control regulate Il first with a reasonable increasing rate slightly larger than the speed of the electrode v, and then switch to control Pl once Ul and Il 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 Pl should be examined based on the availability of Ul and Il 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 Il for the double-loop current limitation. For the normal operation phases, the outer loops of control blocks are both set to maintain Pl, while the inner current limiter of the CCM can suppress the impact on fsys.

2) When Il 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 Pl may be more noticeable whereas the overcurrent risk is less than the quasi-short-circuit recovery.

V. Large Disturbance Stability Issue

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 Ul, and a co-optimization of Cdc and LƩ is feasible. Considering that the real-time stability monitoring is valuable for the FPS system, a solution based on MPT [

22] is derived in this section.

A. System Equivalent Model

Supposing a consistent AC voltage amplitude Vin for the input end of PMs, an equivalent model of the investigated AC/DC hybrid FPS system is shown in Fig. 9.

Fig. 9  Hybrid AC/DC equivalent model of FPS system.

According to [

25], Leq, Req, and Veq are nonlinear functions of DC current idc, which are related to the commutation of diodes:

Leq=LD1LD2[(15/π)(LD2-LD1)μ+LD1]-1Req=[(15/π)(RD1/LD1-RD2/LD2)μ+RD2/LD2]LeqVeq=(15/π)Vin{[(1+π/15)LD1-1-LD2-1]sinμ+          [sin(π/15)-sin(μ-π/15)]LD2-1}Leq (14)
μ=arccos[1-ωLacidc(Vinsin(π/15))-1]2ωLacidc[Vinsin(π/15)]-1 (15)
LD1=(3/2)Ltr,eq+Ldc,eqLD2=2Ltr,eq+Ldc,eqRD1=(3/2)Rtr,eq+Rdc,eqRD2=2Rtr,eq+Rdc,eq (16)

where Rdc is neglected for its small value; and LD1, LD2, RD1, and RD2 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 [

22]:

P=Pinv+Prec=iloaddUdc+3Ul*dIl,RMS-32Il,RMS2R+Veq(idc)didc-Req(idc)idcdidc-Udcidc (17)
iload=Pl2+Ql2/Udc=3Il,RMS2R2+(2πf0Ld)2/Udc=Sl/Udc (18)
Ul,RMS*Um+kp(Il,RMS*-Il,RMS)+ki(Il,RMS*-Il,RMS)dt          CCMUm+kp(Pl*-3Il,RMS2R)+ki(Pl*-3Il,RMS2R)dt   DDM (19)

Since the dynamics of the inner loop are neglected, P can reflect the stability issue of the DC voltage time-scale because only the RMS value control is considered.

B. Application

1) Short Net Reduction

When Pl is regulated to a constant, the load side can be equivalent to an apparent power load proportional to L and iload. Therefore, the critical value of Udc, which is denoted as Udc,cr, can be derived by setting λ1+λ2=0:

Udc,cr=SlLeqidcCdc,eq-1(Veq/idc-Req-idcReq/idc)-1 (20)

Substituting (20) into (17)-(19), the stable region can be obtained by projecting P to the corresponding plane, as shown in Fig. 10, which indicates that a larger Cdc,eq and a 20% reduction on the sum of the short net and the series reactor are both beneficial for the system stability, which is adopted in the FPS system. Moreover, it reveals a potential to cancel the component like delta closure or reconfigure the system by shortening power cables in the application, and the possible energy rearrangement needs to be examined based on the engineering experience.

Fig. 10  Feasibility of short net reduction. (a) Two-dimensional stable regions for different parameters. (b) Three-dimensional diagram of Idc, Udc,eq, and P.

2) Stability Monitoring

An analytical criterion H>0 is used to monitor the large disturbance stability in the simulation.

H=min(Veqidc-Req-idcReqidc)Leq-1,i=a,b,cR,i+3kpL-1-i=a,b,cIl,RMS,i2R,i2+(2πf0Ls)2Cdc,eq-1Udc-2 (21)

It offers an extra guideline for the system design. Furthermore, it reveals that an increase in kp is beneficial for the online stability enhancement.

VI. Simulation Results

A. Test Benchmark

The single-line diagram of the test benchmark established in PSCAD is shown in Fig. 11. The following two cases are compared: ① case 1: the TPS system with a transformerless delta-connected STATCOM [

26], in which cases 1-1, 1-2, and 1-3 are corresponding to the operation conditions where the STATCOM is off, only activates its function of reactive power compensation and further negative-sequence compensation, respectively; ② the proposed FPS system, in which cases 2-1 and 2-2 are corresponding to using the VCM and CCM, respectively. The key simulation parameters, including the real technical data from an operating EAF owned by China First Heavy Industries in the TPS system, are listed in Tables II and III. The base values of voltage and power are 35 kV and 75 MW, respectively. Please note that the reactor is configured to be fixed instead of the short net, which is only for validating the feasibility of short net reduction by simulation but not consistent with the real case.

Fig. 11  Single-line diagram of test benchmark.

TABLE II  Parameters of Power Circuit for FPS System
DeviceParameterValue

PM

(Diode: ZPb4600-40

IGBT: FZ1500R33HL3)

SPM, rated (MVA) 5
Udc, rated (kV) 1.35
Cdc (μF) 10000
n 10 (+2)
Lac (μH) 5
Ldc (μH) 5
fswt (Hz) 750
m 3
Multiwinding phase-shifting transformer Str (MVA) 15
Ztr,pu (%) 2
Xtr/Rtr 10
q 5
TABLE III  Parameters at the Second Stage in Smelting Period
Symbolα0(V/mm)β0 (V)

Pl*

(MW)

Il*(kA)Xs/RsZs,pu(%)

Zr,pu

(%)

Value 1 40 36.5 47.95 3.33 30 8

B. Verification on EAF Model

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, which is the basis of the following studies.

Fig. 12  Verification on EAF model. (a) Ua and Il. (b) v-i characteristic.

C. Comparisons of Active Power Regulation

Comparisons of the regulation on Pl are shown in Fig. 13(a) and (b). Before t=3  s, case 2-1 is applied for the power upgrade belonging to AOC. By continuously tuning Il,RMS* of the outer loop, Ul can be increased at a set speed to save the original tap-changing time. The tuning principle should consider both the frequency of the PCC fPCC and the stresses of the devices. However, the discrete tap-changings in case 1-3 make fPCC approximate the lower limit of 49.9 Hz.

Fig. 13  Comparison results of active power regulation in different cases. (a) Pl (t=1-3 s). (b) Pl and fPCC (t=3-6 s). (c) Il. (d) la (phase a). (e) Ul and Il.

At t=3.5 s, the fluctuation of la is backward deduced and limited at 0.5-25 Hz using the data in Fig. 2 and then added to l0 based on (2). It can be observed that for the normal conduction, the regulation on Pl in case 2-1 has no obvious advantages over that in case 1-3, which reflects the defect of the VCM. Comparatively, fewer perturbations on the fPCC are observed when switching case 2-1 to case 2-2 at t=4 s. The second harmonic of Pl is due to the three-phase instantaneous imbalance of the AC EAF.

The extreme POCs represented by a three-phase quasi-short-circuit and a single-phase (phase a) open circuit are emulated at t=4.5 s and t=5 s, respectively. It is validated that the single-phase open circuit results in more serious defects on Pl (actually close to that of the two-phase operation of the TPS system), which leads fPCC to cross the boundaries, while the quasi-short-circuit suffers from the overcurrent potential. As shown in Fig. 13(c), the maximum absolute decreases from 102.6 kA in case 1-3 to 85.8 kA in case 2-2, which means the limitation on Il is realized in case 2-2 with the coordination of control blocks in the FPS system. In Fig. 13(d), the reaction time of less than one power cycle (12.5 ms) is mainly attributed to the interval of operation detection and arc striking, after which the third-order characteristics of Ghc(s) indicated by (13) can be observed. The dead zone effect induced by the proportional valve and the minimum air gap (0.02 m) related to the ignition voltage further verify the effectiveness of modeling.

In Fig. 13(e), the “cut-off” of Il at the zero-crossing point in the TPS system is similar to that of VCM adopted in the FPS system. The “active boost” of Ul at the zero-crossing point for the CCM is consistent with the theoretical analysis, which proves that the CCM is good for arc stability.

D. Comparisons of PQ Conditioning

As shown in Fig. 14(a) and (b), even if the compensation on the negative sequence and the reactive circuit are both executed [

26] in case 1-3, the IFL of which is still around the critical value, while the IFL in case 2-2 is suppressed far below the critical value for the FPS system. Besides, the imbalance or harmonics cannot be observed from the waveform of the IPCC in Fig. 14(c) owing to the asynchronous back-to-back connection of PM, and the comparison of the very-short-time harmonic measurement [16] of the IPCC (phase a) in various cases in Table IV demonstrates the merits of the FPS system. Based on the fast Fourier transform (FFT) results, the maximum individual interharmonics voltage (denoted as percentage of nominal with the resolution of 1 Hz [26]) in case 1-1 and case 2-2 are 2.32% at 72 Hz and 0.56% at 36 Hz, respectively. Even though the values of both two cases are less than 3% and meet the standard for the investigated 35 kV system [27], the FPS system owns obvious advantages, which is also embodied in the flicker assessment shown in Fig. 14(a). The above results prove that the FPS system can solve the PQ issue fundamentally.

Fig. 14  Comparison of PQ conditioning. (a) IFL of PCC voltage. (b) Compensation effect of case 1-3. (c) IPCC.

TABLE IV  Comparison of Harmonics of IPCC in Different Cases
CaseTHD (%)Individual harmonic order h (%)
234567
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 <1 0.2 0.2 <0.1 0.2 <0.1 <0.1

Note:   only typical (the 2nd to 7th) harmonics of AC EAF are listed; and THD refers to the total harmonic distortion [

27
].

E. Validation of Large Disturbance Stability Criterion

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 Ql and potential decrease in Pl, which introduces uncertainties in Sl. Before t=4.5 s, a larger H is obtained by the proper reduction in Xs, which indicates a larger stability margin. In Fig. 15(a), under the extreme operation condition, H monotonically reduces below 0 and a diverging oscillation on Udc is observed when Xs=2π×1.0 p.u.. Correspondingly, H rises before dropping to the critical value, finally suppressing the oscillation on Udc when Xs=2π×0.8 p.u.. The simulation results are in accordance with the comparison of green and red curves in Fig. 10(b). Furthermore, an emergency enhancement of the stability can be realized by boosting kp after detecting the operation, as shown in Fig. 15(b).

Fig. 15  Validation of proposed MPT-based large disturbance stability criterion. (a) Real-time change of H. (b) Real-time change of Udc.

VII. Benefit Analysis

A. Cost and Power Loss Analysis

Table V confirms that the total installation cost for the FPS system is 0.78 times that for the TPS system, which will be welcomed by the steel industry. For the unified analysis, the transformer with diode rectifiers is regarded as an equivalent rectifier transformer in case 2-2, while the IGBT-based full-bridge modules of the STATCOM are selected as inverters in case 1-3. Suppose that the cost of an IGBT is approximately proportional to its capacity, while the cost of capacitors is proportional to peak energy storage. Due to fewer surges and harmonics during the operation, the unit cost of apparent power of the rectifier transformer is regarded as 60%-70% of that of the EAF transformer [

28]. Remind that the capacity of the transformer in case 1-3 is almost 1.5 times that of in case 2-2 due to the requirement for extra reactive power transmission. Furthermore, even if the approaching numbers of IGBTs with higher capacity are used in case 1-3, the capacitance decreases due to the low-voltage feature of AC EAF compared with that in case 2-2.

TABLE V  Comparison of Installation Cost (Case 1-3 as Base Value)
DeviceCost ratio
Base value in case 1-3Per-unit value in case 2-2 (p.u.)
Transformer 0.36 0.6×0.67
PM (IGBT) 0.18 1500/1200
PM (Capacitor) 0.26 (10×1.35)/(12×1.5)
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 σ is expressed as:

σ=1-PlPPCCPPCCSPCC=1-σP·PF (22)

where 1-σP denotes the sum of active power loss including the transformer and inverter.

Table VI indicates that the TPS system theoretically performs better on the power loss, mainly due to its specific countermeasure on PF. Referring to the data of power in the cycle of the smelting stage presented in Fig. 2(a), it is easy to derive that the extra power loss of the FPS system is no more than 700 kWH for a single heat of steel, which counts for merely 2%-2.5% of the total power consumption. However, such a small theoretical advance for the TPS system may be weakened due to the communication or sampling delay in the real test. Additionally, the potential profit of the FPS system by hierarchical consumption of renewable energy through DC buses [

29], executing variable-frequency control to save electrode loss [21], and avoiding tripping by the strategies in Section IV should be considered during the operation. Due to the lack of persuasive field data of the proposed FPS system at present, the complete assessment is going to proceed in the future.

TABLE VI  Comparison of Active Power Loss, PF, AND σ
CaseActive power loss (%)PFσ (%)
TransformerPM
Case 1-3 1.32 2.19 0.992 4.3
Case 2-2 1.04 1.84 0.975 5.4

B. Topology Selection

Extra comments are added on the topology in Fig. 3. In [

19] and [20], PMs are added between the PCC and the primary side of the transformer, which makes its secondary side connected to the short net of the load side. Thus, the EAF transformer must be retained, which may lead the total cost in [19] and [20] is estimated to be between those in cases 1-3 and 2-2. In addition, the negligible sampling delays and errors strengthen the active power regulation of the proposed topology in Fig. 3 compared with those in [19] and [20], which is important for AOCs and POCs.

The replacement of the centralized three-phase half-bridge inverter in [

19] by discrete full-bridge inverters of each phase in Fig. 4 makes it possible for the single-phase maintenance and enhances the system reliability by electrical isolation and modularity. Furthermore, the output ends of PMs of three phases can be delta-connected to match the ultra-high-current AC EAFs, and the selected ZCM modulation in Section IV is necessary for eliminating the high-frequency fswt interphase circulating current Icc due to UCM. However, the proposed independent derivation of Uref by sampling Ul and Il of each phase is challenged, especially for AOCs and POCs, and the third harmonic of Icc cannot be avoided when considering the instantaneous imbalance of the AC EAF. Such issues are worth further investigation for the FPS system.

VIII. Conclusion

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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