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Transformer Riddle No.36 -ARC furance trafo capacity estimation
I know basic equation for Arc furnace trafo cal Q= m C . delta T
Can anybody explain what the major consideration for Arc furnace trafo calculation is?

Author : ASAD MALIK - From: Saudi Arabia
Tue, January 12th, 2010 - 20:08
The electric circuit specifics are determined first of all by the specifics of the arcs themselves. For simplicity sake, let us discuss first the processes which occur in a direct current (DC) arc; similar processes take place in high-power AC arcs.
DC arc column between a graphitized electrode (cathode) and either scrap lumps or a furnace bath, is high-temperature plasma consisting of neutral molecules and atoms of various gases and vapors present in the furnace freeboard, as well as of electrically charged particles, i.e., of electrons and ions. Current transfer in the arc is conducted mainly by electrons emitted from the heated cathode. According to various estimates, in high-power furnaces, the temperatures in the arc column range within 6000–7000◦C and current density reaches several thousands of A/cm2.
Arc column is compressed by electro-dynamic forces resulting from the interaction of the arc current with its own electromagnetic field surrounding the arc. The resulting pressure affects the liquid bath surface causing the arc to submerge into the melt to a certain degree. If the current increases electro-dynamic forces compressing the arc rise as well as heat energy concentration within the arc space and depth of arc submersion into the liquid bath. Similar to the regular conductors, e.g., metallic ones, arc voltage rises as its length increases. However, contrary to these conductors which obey Ohm’s law stating linear dependence between voltage and current, active resistance of the arc decreases as current increases. Therefore, an increase in current does not require voltage rise. Such a nonlinear volt–ampere characteristic of the arc does not provide conditions required to stabilize arc discharge. The secondary circuit should have a certain resistance for stable arcing, active resistance in DC EAF (Electrical Arc Furnace), as well as inductance for the AC EAF. All the above stated with respect to the DC arc can also be applied to arcs in AC EAFs, considering values of current and voltage within each half cycle, with taking into account inductance in the secondary circuit.
In the AC arc cathode and anode alternate at each voltage direction change. Either electrode or surface of scrap lumps or liquid bath serves as the cathode, by turns. In modern furnaces, the arc discharge does not cease as voltage approaches zero at the end of each half cycle, since high-power arcs have significant inertia regarding both conductivity and temperature condition of the arc column. However, the shape of arc voltage curves can significantly differ from sinusoidal. That difference is getting smoothened as power and current grow.
Arcing stability could vary significantly during the course of the heat.
Immediately after charging a new basket of scrap, arcing takes place on the surface of separate scrap lumps which are continuously moving while the charge settles down. During this period, arcs are not stable, and break rather often as a result of sudden sharp increase of arc length. Arc discharge breaks occur also during short circuit when electrodes get in contact with scrap pieces. After the initial bore-in period, arcing is observed between the electrodes and the surface of molten metal collected at the bottom, and later, between the electrodes and the surface of formed bath. In this case, arc stability increases significantly. As arc current and power are increased their stability grows during all periods of the heat. The same is observed when scrap is preheated to high temperature.
According to the energy conservation law, heat does not appear out of nothing and does not disappear. All other forms of energy can be transformed into heat, for instance, electrical or chemical energy, in strictly equivalent amounts. During heating of any body, a certain quantity of heat transfers to it from the heat source. This process is called heat transfer. The heat assimilated by the body increases its internal energy. The body temperature thus rises. When cooling down, the body gives a part of its internal energy (in a form of heat) to objects surrounding it. Heat transfer processes proceed at a practically constant pressure in EAFs and in other furnaces. In all such cases a change in internal energy of the body is equivalent to a change in what is called enthalpy. This thermodynamic parameter is widely applied in thermo-technical calculations. Enthalpy, like other kinds of energy, can be measured in Joules (J) or in kW-hours (kWh). As a Joule is a very small quantity (3600 kJ = 1 kWh), energy unit of kWh will be used further in most cases. While solving heat engineering problems, knowing absolute body enthalpy values is not necessary. It is sufficient to determine the enthalpy changes ΔE, which are calculated per 1 kg of substance or per 1 m3(for gases). In processes taking place at constant pressure, these changes are calculated by the following formula:

Heat capacity CP is measured by a quantity of heat transferred to a body with 1kg mass or with 1 m3 volume (for gases) to raise its temperature by 1◦C. Correspondingly, we can distinguish between specific mass or volumetric heat capacities. Since only enthalpy differences are determined, they are counted off the
initial temperature equal to 0◦C according to formula. Mean heat capacity values presented in the tables correspond to temperature differences between 0◦C and t ◦C.
In modern steelmaking shops, the required steel qualitative characteristics are achieved in ladle furnaces and other units of secondary metallurgy. Energy (heat) balances give a general quantitative idea of an electric arc furnace as a thermoenergetical unit. These balances are derived from the law of conservation of energy according to which the total input of energy must be equal to energy output.
It is true for the entire unit and for each of its zones. In the EAF the specifics of electrical units are combined with those of thermo-technical ones. Therefore, we can speak about both energy and heat balances. These balances should not be opposed to each other because in the furnaces all forms of energy are utilized or lost ultimately only in the form of heat. Henceforward these terms will be used depending on zone of the EAF under consideration. For instance, with regard to electro-technical zone (b–b) that includes the furnace transformer (1), the secondary electrical circuit (2), and electrodes (3) with electric arcs (4), we will speak about the energy balance, below Fig.

In zone (a-a), which includes the entire EAF excluding the off-gas evacuation system (zone (e-e), different sources of energy are used concurrently. Therefore, it is better to consider the balance of this zone as a heat balance, as well as that of the EAF freeboard, zone (c–c), including the bath, zone (d–d).
Heat (energy) balances are usually written in the form of balance equations, the left side of which is the total sum of the amounts of energy of different kinds coming into the furnace (or zone) while the right side is the total sum of the amounts of all kinds of consumed energy. Heat (energy) balances can be equated for different zones of the EAF, above Fig. , as well as for different time intervals, e.g., for the entire heat, for separate stages of the heat, or for a given moment of time. Equations for the first two cases contain the amounts of electrical and heat energy consumed within a certain time interval. In the last case, the so-called instantaneous balance equations contain the power of the respective energy fluxes. As we did earlier, we will use kWh as a unit of measurement of the amounts of energy. In most cases it is reasonable to examine the specific amounts of energy per ton of liquid steel (kWh/ton) as the weight of liquid steel can be calculated in practice much more precisely than that of the metal charge. Equations of the energy (heat) balance for different zones of the furnace are different.
They can contain different summands corresponding to different kinds of energy both at the input and at the output of a zone. Some of these summands are enthalpies. There are two kinds of enthalpies in balance equations. The first is enthalpies of heated substances (physical heat) E, for instance, the heat of liquid steel, slag, or off-gases. The second is enthalpies of chemical reactions, which are designated as ECH or H. The enthalpies E are estimated using data on substance heat capacity. The enthalpies ECH and H represent the amount of heat emitted or absorbed in a chemical reaction.
Designation ECH is used in the balance equations where different kinds of energy are summed up. The designation H is used for description of separate chemical reactions.
Heat engineering calculations contain not the absolute values of enthalpies, but their changes corresponding to the changes in temperature Δt = t1 − t2 and to the changes in average heat capacity in this temperature range. For enthalpy E and enthalpy H to be comparable, they would be counted off from the same initial temperature
t1. Traditionally, as an initial temperature, the room temperature of 25◦C is used in the tables of H and the temperature of 0◦C is used in tables of average heat capacities used for calculation of E. This difficulty can be overcome by a respective conversion of heat capacities. However, in practice it is not necessary, because the temperatures of steelmaking processes are so high that the initial reference point displacement by 25◦C does not produce noticeable errors in calculations of heat balances of the furnace.

The following standards govern the furnace and rectifier transformers, and their application field:

IEC 60076 series
IEC 61378-1
IEC 60146 IEC 60214
IEEE C57.12.00
IEEE C57.12.90
IEEE C57.18

Electric arc furnace (EAF) transformers are required for many different furnace processes and applications. They are built for:

- Steel furnaces, mainly long arc
- Ladle furnaces
- Ferro-alloy furnaces and similar with short or submerged arc
- Smelting of other materials

Steel arc furnace transformers operate under very severe conditions with regard to frequent overcurrents and overvoltages generated by short-circuits in the furnace and the operation of the HV circuit breaker (“furnace breaker”). The loading is cyclic, while in other applications the loading is more continuous at high utilization.
EAF transformers are rigidly designed to withstand repeated short-circuit conditions and high thermal stresses.
They are also protected against operational overvoltages due to frequent switching.
Design options:
- Direct or indirect regulation
- On-load or no-load tap changer (OLTC or NLTC)
- Built-in reactor for long-arc stability
- Secondary bushing arrangements and designs, air or water cooled
- Internal secondary phase closure (internal delta)
- RC-SA high voltage protection system

Transformers for DC furnace operation are normally provided in a transformer/rectifier package. DC furnaces are typically one of the largest arc furnaces. Most large DC arc furnaces are built for steel production. The use of a thyristor rectifier for the conversion to DC normally reduces the requirement for on-load voltage regulation of the furnace transformer. The step voltages are larger than for an AC furnace transformer, and a no-load tap changer (NLTC) is adequate in many applications. DC furnace transformers are mostly built with two axially displaced LV windings, normally one connected in delta and one in wye, each having a separate high voltage winding. In this double-tier design the transformer is connected to two six-pulse rectifiers, adding up to a 12-pulse system or two parallel 6-pulse systems. The regulation of the LV transformer voltage is normally done by using a NLTC in the primary winding. The location of the 6-pulse rectifiers can be on the same side of the transformer or on opposite sides, as required by the plant layout.

Generally the energy required for melting of metal scrap is:

Q = mc(θ2- θ1) + mL
where, m = mass to be melted (kg),
c = specific heat capacity of metal to be melted (KJ/Kg0C),
θ2 = melting point of the metal (0C),
θ1 = room temperature (0C), and
L = latent heat of fusion of the metal

Table 1 contains some recommendations on transformer power for furnaces of different size, which are based on experiences in many countries.
By analogy with the existing furnaces (using Table 1), the transformer power may be taken as Pap (MVA). Noting the inevitable switching off of the furnace during melting required to push the scrap from the banks, partial operation of the furnace at a reduced voltage when the arcs are open and radiation of much heat onto the walls and roof, the average power consumed during the melting period can be found by using a factor of 0.8 – 0.9:

Pav = 0.8 Pap (KVA)

Useful power consumed during the melting period (power consumed for the melting proper) is represented as:

Pu = Pav cos φηel (KW)

The upper voltage tap of the secondary voltage for small furnaces can be selected by using the following empirical formulae [Edneral, 1979>:
For basic furnaces

Author : Hamid - From: Iran
Mon, February 22nd, 2010 - 18:44
Dear Hamid ,

I would like to estimate the power requirement , Please suggest :

The available data from vender is :

    - consumption of hot metal       :     0.75  
    - Consumption of DRI                 :     0.705
    - Steel Scrap                                   :     0.045  
    - Tapping weight (proposed)             :     112.8 T per heat
    - Average electrical power reqd.       :     47.6 MW (say 50 MW) (@ 280 KWH/T)                
    - Power on time:                             :     27 Min.
    - Blowing time                               :     31 Min.
    - Tap to Tap time                         :     40 Min.   (Considering both the vessels)
    -  Nos. of Heats                           :     36 per day
    - Productivity based on 320 days/yr.
    (320 days x 36 heats x 112.8 T/heat) :     Approx. 1.3 MTPY  

On this given information I calculate the power as below :

- Tapping weight (proposed)
:     112.8 T per heat
Energy units required per T
:     @280 KWH/T
Total Energy units required for 1 Heat
:     112.8 x 280 = 31584 KWH
Power on time:
:     27 Min. = 0.45 H
- In order produce 112.8 T in 27 min Amount of power  required
:     31584 /0.45  =  Approx 70 MW

Please recheck and confirm  the conflic in power estimation i.e 70 MW instead of 50 MW .....

Thnx & Regards
Author : ASAD - From: Saudi Arabia
Mon, March 1st, 2010 - 18:22
I think your calculation is very simple and suitable for electrical consumption estimation not for equipments sizing. As mentioned above the Steel arc furnace transformers operate under very severe conditions with regard to frequent over currents and overvoltages generated by short-circuits in the furnace and the operation of the HV circuit breaker (“furnace breaker”). The loading is cyclic, while in other applications the loading is more continuous at high utilization. EAF transformers are rigidly designed to withstand repeated short-circuit conditions and high thermal stresses. They are also protected against operational overvoltages due to frequent switching. Therefore EAF transformers are special transformer in design and applications. I can just refer you to some recommendation which illustrated in table 1. 
Author : Hamid - From: Iran
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