**3. Measured signals in electrical installation of the induction furnace**

The measurements have been made both in the secondary (Low Voltage Line - LV Line) and in the primary (Medium Voltage Line - MV Line) of the furnace transformer, using the CA8334 three-phase power quality analyzer. CA8334 gave an instantaneous image of the main characteristics of power quality for the analyzed induction furnace. The main parameters measured by the CA8334 analyser were: TRMS AC phase voltages and TRMS AC line currents; peak voltage and current; active, reactive and apparent power per phase; harmonics for voltages and currents up to the 50th order (CA8334, technical handbook, 2007).

CA8334 analyser provide numerous calculated values and processing functions in compliance with EMC standards in use (EN 50160, IEC 61000-4-15, IEC 61000-4-30, IEC 61000-4-7, IEC 61000-3-4).

The most significant moments during the induction melting process of the cast-iron charge were considered:


Further are presented the waveforms and harmonic spectra of the phase voltages and line currents measured during the heating of the charge (Iagăr et al, 2009).

The analyzed coreless induction furnace has 12.5 t capacity of cast-iron; the furnace is supplied from the three-phase medium-voltage network (6 kV) through a transformer in / connection, with step-variable voltage. Load balancing of the three-phase network is currently achieved by a Steinmetz circuit, and the power factor correction is achieved by

In the electric scheme from fig. 1: Q1 is an indoor three-poles disconnector, type STIm–10– 1250 (10 kV, 1250 A), Q2 is an automatic circuit-breaker OROMAX (6 kV, 2500 A), T is the furnace transformer (2625 kVA; 6/1.2 kV), K1 is a contactor (1600 A), (1) is the Steinmetz circuit used to balance the line currents, (2) is the power factor compensation installation, TC1m, TC2m, TC3m (300/5 A) and TC1, TC2, TC3 (1600/5 A) are current transformers, TT1m (6000/100 V), TT1 (1320/110 V) are voltage transformers, and M is the flexible connection of



As consequence, will be present the influence of the following factors upon the energetic parameters of the installation: furnace charge, furnace supply voltage, load balancing

The measurements have been made both in the secondary (Low Voltage Line - LV Line) and in the primary (Medium Voltage Line - MV Line) of the furnace transformer, using the CA8334 three-phase power quality analyzer. CA8334 gave an instantaneous image of the main characteristics of power quality for the analyzed induction furnace. The main parameters measured by the CA8334 analyser were: TRMS AC phase voltages and TRMS AC line currents; peak voltage and current; active, reactive and apparent power per phase; harmonics for voltages and currents up to the 50th order (CA8334, technical handbook,

CA8334 analyser provide numerous calculated values and processing functions in compliance with EMC standards in use (EN 50160, IEC 61000-4-15, IEC 61000-4-30, IEC

The most significant moments during the induction melting process of the cast-iron charge

Further are presented the waveforms and harmonic spectra of the phase voltages and line



currents measured during the heating of the charge (Iagăr et al, 2009).

**3. Measured signals in electrical installation of the induction furnace** 

**2. Electrical installation of the induction-melt furnace** 

Within the study the following physical aspects were taken into account:

means of some step-switching capacitor banks (fig.1).

mechanical stress of the processed material); - the resistivity of cast-iron increases with temperature;

installation and the one of power factor compensation.

the induction furnace CI.

paramagnetic).

61000-4-7, IEC 61000-3-4).

were considered:

process);

2007).

Fig. 1. Electric scheme of the analyzed furnace

Power Quality Problems Generated by Line Frequency Coreless Induction Furnaces 239

Fig. 4. Waveforms and harmonic spectra of the line currents in the cold state of the charge

Fig. 5. Waveforms and harmonic spectra of the line currents in the cold state of the charge

Fig. 6. Waveforms and harmonic spectra of the phase voltages in the intermediate state (LV

(LV Line)

(MV Line)

Line)

 Fig. 2. Waveforms and harmonic spectra of the phase voltages in the cold state of the charge (LV Line)

Fig. 3. Waveforms and harmonic spectra of the phase voltages in the cold state of the charge (MV Line)

In the first heating stage, the electromagnetic disturbances of the phase voltages on LV Line and on MV Line are very small. The 5th harmonic does not exceed the compatibility limit, but the voltage interharmonics exceed the compatibility limits (IEC 61000-3-4, 1998; IEC/TR 61000-3-6, 2005).

On MV Line the current I2 was impossible to be measured because the CA8334 three-phase power quality analyser was connected to the watt-hour meter input. The watt-hour meter had three voltages (U12, U23, U31) and two currents (I1 and I3).

Waveform distortion of the currents in cold state is large (fig. 4, 5). At the beginning of the cast-iron heating the 3rd, 5th, 7th, 9th, 11th, 13th, 15th harmonics and even harmonics (2nd, 4th, 6th, 8th) are present in the currents on the LV Line. The 5th and 15th harmonics exceed the compatibility limits (IEC 61000-3-4, 1998).

In the cold state the 2nd, 3rd, 5th, 7th, 9th, 11th, 13th and 15th harmonics are present in the currents absorbed from the MV Line. The 5th harmonic exceeds the compatibility limits (IEC/TR 61000-3-6, 2005).

In the intermediate state, part of the charge is heated above the Curie temperature and becomes paramagnetic, and the rest of the charge still has ferromagnetic properties. The furnace charge is partially melted.

 Fig. 2. Waveforms and harmonic spectra of the phase voltages in the cold state of the charge

 Fig. 3. Waveforms and harmonic spectra of the phase voltages in the cold state of the charge

In the first heating stage, the electromagnetic disturbances of the phase voltages on LV Line and on MV Line are very small. The 5th harmonic does not exceed the compatibility limit, but the voltage interharmonics exceed the compatibility limits (IEC 61000-3-4, 1998; IEC/TR

On MV Line the current I2 was impossible to be measured because the CA8334 three-phase power quality analyser was connected to the watt-hour meter input. The watt-hour meter

Waveform distortion of the currents in cold state is large (fig. 4, 5). At the beginning of the cast-iron heating the 3rd, 5th, 7th, 9th, 11th, 13th, 15th harmonics and even harmonics (2nd, 4th, 6th, 8th) are present in the currents on the LV Line. The 5th and 15th harmonics exceed the

In the cold state the 2nd, 3rd, 5th, 7th, 9th, 11th, 13th and 15th harmonics are present in the currents absorbed from the MV Line. The 5th harmonic exceeds the compatibility limits

In the intermediate state, part of the charge is heated above the Curie temperature and becomes paramagnetic, and the rest of the charge still has ferromagnetic properties. The

had three voltages (U12, U23, U31) and two currents (I1 and I3).

compatibility limits (IEC 61000-3-4, 1998).

(IEC/TR 61000-3-6, 2005).

furnace charge is partially melted.

(LV Line)

(MV Line)

61000-3-6, 2005).

Fig. 4. Waveforms and harmonic spectra of the line currents in the cold state of the charge (LV Line)

Fig. 5. Waveforms and harmonic spectra of the line currents in the cold state of the charge (MV Line)

Fig. 6. Waveforms and harmonic spectra of the phase voltages in the intermediate state (LV Line)

Power Quality Problems Generated by Line Frequency Coreless Induction Furnaces 241

Fig. 10. Waveforms and harmonic spectra of the phase voltages at the end of the melting

 Fig. 11. Waveforms and harmonic spectra of the phase voltages at the end of the melting

At the end of the melting process, the electromagnetic disturbances of the phase voltages are very small. Voltage interharmonics exceed the compatibility limits. The 5th harmonic is

 Fig. 12. Waveforms and harmonic spectra of the line currents at the end of the melting

Waveform distortion of the currents at the end of the melting process is smaller than in cold state, or intermediate state. On LV Line, harmonic spectra of the currents show the presence of 3rd, 5th, 7th, 9th, 11th, 13th, 15th, 17th, 25th harmonics and even harmonics (2nd, 4th, 6th). The

5th, 15th and 25th harmonics exceed the compatibility limits (IEC 61000-3-4, 1998).

within compatibility limits (IEC 61000-3-4, 1998; IEC/TR 61000-3-6, 2005).

process (LV Line)

process (MV Line)

process (LV Line)

Fig. 7. Waveforms and harmonic spectra of the voltages in the intermediate state (MV Line)

In the intermediate state of the charge, the voltage interharmonics exceed the compatibility limits. The 5th harmonic do not exceeds the compatibility limits.

Fig. 8. Waveforms and harmonic spectra of the currents in the intermediate state (LV Line)

Fig. 9. Waveforms and harmonic spectra of the currents in the intermediate state (MV Line)

In the intermediate state, harmonic spectra of the currents absorbed from the LV Line present the 3rd, 5th, 7th, 11th, 13th, 15th, 17th, 25th harmonics and even harmonics (2nd, 4th, 8th). The 5th, 15th, 17th and 25th harmonics exceed the compatibility limits (IEC 61000-3-4, 1998).

On MV Line, harmonic spectra of the currents present the 3rd, 5th, 7th, 9th, 11th, 13th, 15th, 17th, 25th harmonics and even harmonics (2nd, 4th, 6th, 8th). The 5th and 25th harmonics exceed the compatibility limits (IEC/TR 61000-3-6, 2005).

After 8 hours from the beginning of the heating process the furnace charge is totally melted, being paramagnetic.

 Fig. 7. Waveforms and harmonic spectra of the voltages in the intermediate state (MV Line) In the intermediate state of the charge, the voltage interharmonics exceed the compatibility

Fig. 8. Waveforms and harmonic spectra of the currents in the intermediate state (LV Line)

 Fig. 9. Waveforms and harmonic spectra of the currents in the intermediate state (MV Line) In the intermediate state, harmonic spectra of the currents absorbed from the LV Line present the 3rd, 5th, 7th, 11th, 13th, 15th, 17th, 25th harmonics and even harmonics (2nd, 4th, 8th). The 5th, 15th, 17th and 25th harmonics exceed the compatibility limits (IEC 61000-3-4, 1998). On MV Line, harmonic spectra of the currents present the 3rd, 5th, 7th, 9th, 11th, 13th, 15th, 17th, 25th harmonics and even harmonics (2nd, 4th, 6th, 8th). The 5th and 25th harmonics exceed the

After 8 hours from the beginning of the heating process the furnace charge is totally melted,

limits. The 5th harmonic do not exceeds the compatibility limits.

compatibility limits (IEC/TR 61000-3-6, 2005).

being paramagnetic.

 Fig. 10. Waveforms and harmonic spectra of the phase voltages at the end of the melting process (LV Line)

Fig. 11. Waveforms and harmonic spectra of the phase voltages at the end of the melting process (MV Line)

At the end of the melting process, the electromagnetic disturbances of the phase voltages are very small. Voltage interharmonics exceed the compatibility limits. The 5th harmonic is within compatibility limits (IEC 61000-3-4, 1998; IEC/TR 61000-3-6, 2005).

Fig. 12. Waveforms and harmonic spectra of the line currents at the end of the melting process (LV Line)

Waveform distortion of the currents at the end of the melting process is smaller than in cold state, or intermediate state. On LV Line, harmonic spectra of the currents show the presence of 3rd, 5th, 7th, 9th, 11th, 13th, 15th, 17th, 25th harmonics and even harmonics (2nd, 4th, 6th). The 5th, 15th and 25th harmonics exceed the compatibility limits (IEC 61000-3-4, 1998).

Power Quality Problems Generated by Line Frequency Coreless Induction Furnaces 243

 Fig. 16. Unbalance of the phase voltages and line currents at the end of the melting process

Voltage unbalance exceeds the permitted values in intermediate state. Current unbalance is

The values computed by the CA8334 analyser are: total harmonic distortion of voltages and currents, distortion factor of voltages and currents, K factor for current, voltage and current unbalance, power factor and displacement factor, extreme and average values for voltage and current, peak factors for current and voltage (CA8334, technical handbook, 2007). Mathematical formulae used to compute the total harmonic distortion (THD) of voltages

50

50

2

*I* 

50

2 <sup>1</sup> ( ) <sup>2</sup>

*V*

*VRMS* 

*n*

*I*

V represents the phase voltage, I represents the line current, i represents the phase (i = 1, 2,

*n*

2

*V* 

*V*

*n*

*i*

*i*

Distortion factor (DF) of voltages and currents are computed by the formulae:

*i*

*VDF*

*VTHD*

*ITHD*

3) and n represents the order of harmonics.

2

2

2

*harm ni*

*i*

100

100

100

(1)

(2)

(3)

1

1

*harm i*

( )

*harm ni*

*harm i*

( )

*harm ni*

very large in the cold state and decreases as the furnace charge is melting down.

**4. The values computed by the CA8334 analyser** 

(LV Line)

and currents are:

Fig. 13. Waveforms and harmonic spectra of the line currents at the end of the melting process (MV Line)

On MV Line, harmonic spectra of the currents show the presence of 3rd, 4th, 5th, 7th, 9th, 11th, 13th harmonics at the end of the melting. The 5th harmonic exceeds the compatibility limits (IEC/TR 61000-3-6, 2005).

Fig.14-16 show the values of voltage and current unbalance on LV Line, in all the heating stages.

Fig. 14. Unbalance of the phase voltages and line currents in the cold state of the charge (LV Line)

Fig. 15. Unbalance of the phase voltages and line currents in the intermediate state of the charge (LV Line)

 Fig. 13. Waveforms and harmonic spectra of the line currents at the end of the melting

On MV Line, harmonic spectra of the currents show the presence of 3rd, 4th, 5th, 7th, 9th, 11th, 13th harmonics at the end of the melting. The 5th harmonic exceeds the compatibility limits

Fig.14-16 show the values of voltage and current unbalance on LV Line, in all the heating

Fig. 14. Unbalance of the phase voltages and line currents in the cold state of the charge (LV

Fig. 15. Unbalance of the phase voltages and line currents in the intermediate state of the

process (MV Line)

stages.

Line)

charge (LV Line)

(IEC/TR 61000-3-6, 2005).

Fig. 16. Unbalance of the phase voltages and line currents at the end of the melting process (LV Line)

Voltage unbalance exceeds the permitted values in intermediate state. Current unbalance is very large in the cold state and decreases as the furnace charge is melting down.

#### **4. The values computed by the CA8334 analyser**

The values computed by the CA8334 analyser are: total harmonic distortion of voltages and currents, distortion factor of voltages and currents, K factor for current, voltage and current unbalance, power factor and displacement factor, extreme and average values for voltage and current, peak factors for current and voltage (CA8334, technical handbook, 2007). Mathematical formulae used to compute the total harmonic distortion (THD) of voltages and currents are:

$$\sqrt{VTHD\_i} = \frac{\sqrt{\sum\_{n=2}^{50} (V\_{harm\\_ni})^2}}{V\_{harm\\_1 i}} \cdot 100\tag{1}$$

$$ITHD\_i = \frac{\sqrt{\sum\_{n=2}^{50} \left(I\_{harm\\_ni}\right)^2}}{I\_{harm\\_1 i}} \cdot 100\tag{2}$$

V represents the phase voltage, I represents the line current, i represents the phase (i = 1, 2, 3) and n represents the order of harmonics.

Distortion factor (DF) of voltages and currents are computed by the formulae:

$$VDF\_i = \frac{\sqrt{\frac{1}{2}\sum\_{n=2}^{50} (V\_{harm\\_ni})^2}}{VRMS\_i} \cdot 100\tag{3}$$

Power Quality Problems Generated by Line Frequency Coreless Induction Furnaces 245

100 *unb IRMS*

> *i i i*

0

0

*k*

In the relations (14), (15): Vpp is the PEAK+ of the phase voltage; Vpm is the PEAK- of the phase voltage; Ipp is the PEAK+ of the line current; Ipm is the PEAK- of the line current; i represents the phase (i = 1, 2, 3); N represents the number of the samples per period

Peak values (PEAK+/PEAK-) for voltage (or current) represent the maximum/minimum values of the voltage (or current) for all the samples between two consecutive zeros. For a sinusoidal signal, the peak factor is equal to 2 (1.41). For a non-sinusoidal signal, the peak factor can be either greater than or less than 2 . In the latter case, the peak factor signals

MIN/MAX values for voltage (or current) represent the minimum/maximum values of the half-period RMS voltage (or current). Average values (AVG) for voltage and current are

Tables 1-25 show the values computed by the CA8334 analyser on LV Line and on MV Line.

Table 1. Total harmonic distortion THD [%] for phase voltages (LV Line)

Heating moment VTHD1[%] VTHD2[%] VTHD3[%] Cold state 0 4 5.4 Intermediate state 0 3.8 3.8 End of melting process 0 0 6.3

<sup>1</sup> ( )

*n*

max ,

*Ipp Ipm ICF*

<sup>1</sup> ( )

<sup>1</sup> <sup>2</sup>

*V n*

<sup>1</sup> <sup>2</sup>

*I k*

*i*

*i i*

*i*

*i i*

(11)

*<sup>S</sup>* (12)

(13)

(14)

(15)

*IRMS* 

*<sup>P</sup> PF*

cos *DPFi i*

Pi [W] and Si [VA] represent the active power and the apparent power per phase (i = 1, 2, 3);

Mathematical formulae used to compute the **peak factors (CF) for current and phase** 

max ,

*Vpp Vpm VCF*

*<sup>i</sup> <sup>N</sup>*

*N*

*<sup>i</sup> <sup>N</sup>*

*N*

*<sup>i</sup>* is the phase difference between the fundamental current and voltage, and i represents

*I*

**Power factor (PF) and displacement factor (DPF)** are computed by relations:

the phase.

**voltage** are:

(between two consecutive zeros).

computed over 1 second.

divergent peak values with respect to the RMS value.

$$IDF\_i = \frac{\sqrt{\frac{1}{2} \sum\_{n=2}^{50} (I\_{harm\\_ni})^2}}{IRMS\_i} \cdot 100\tag{4}$$

VRMS and IRMS represent the root mean square values (RMS values or effective values) for phase voltage and line current, computed over 1 second, and i represents the phase (i = 1, 2, 3). **K factor (KF)** is a weighting of the harmonic load currents according to their effects on transformer heating. **K factor** for current is computed by relation:

$$\begin{aligned} \sum\_{i=1}^{50} n^2 \cdot \underbrace{\left(I\_{harm\\_ni}\right)^2}\_{\begin{array}{c} \sum\_{i=1}^{50} \left(I\_{harm\\_ni}\right)^2 \\ \sum\_{n=1}^{50} \left(I\_{harm\\_ni}\right)^2 \end{array}} \tag{5} \end{aligned} \tag{5}$$

In the above relation I represents the line current, i represents the phase (i = 1, 2, 3) and n represents the order of harmonics. A K factor of 1 indicates a linear load (no harmonics); a higher K factor indicates the greater harmonic heating effects.

The unbalanced three-phase systems of voltages (or currents) can be reduce into three balanced systems: the positive (+), negative (-) and zero (0) sequence components.

The positive voltage True RMS and the negative voltage True RMS are given by the relations:

$$VRMSS\_{+} = \frac{V\_1 + aV\_2 + a^2V\_3}{3} \tag{6}$$

$$VRMS\_{-}=\frac{V\_1 + a^2V\_2 + aV\_3}{3} \tag{7}$$

where 123 *VVV* , , represent the phase voltages (using simplified complex) and 2 3 *j a e* is the complex operator.

The positive current True RMS and the negative current True RMS are given by the relations:

$$IRMS\_{+} = \frac{I\_1 + aI\_2 + a^2I\_3}{3} \tag{8}$$

$$IRMS\_{-} = \frac{I\_1 + a^2 I\_2 + a I\_3}{3} \tag{9}$$

where 123 *III* , , represent the line currents (using simplified complex). Voltage and current unbalances (unb) are:

$$V\_{\mu nb} = \frac{\left|VRMS\_{-}\right|}{\left|VRMS\_{+}\right|} \cdot 100\tag{10}$$

*I*

*IRMS* 

VRMS and IRMS represent the root mean square values (RMS values or effective values) for phase voltage and line current, computed over 1 second, and i represents the phase (i = 1, 2, 3). **K factor (KF)** is a weighting of the harmonic load currents according to their effects on

2

*harm ni*

*i*

2 2

( )

*harm ni*

( )

*harm ni*

2

2 12 3 3

2 12 3 3

(6)

(7)

(8)

(9)

(10)

2 3 *j a e*

is

100

(4)

(5)

50

2 <sup>1</sup> ( ) <sup>2</sup>

*n*

50

*<sup>n</sup> <sup>i</sup>*

 

*IKF*

1 50

*n*

balanced systems: the positive (+), negative (-) and zero (0) sequence components.

1

*n I*

*I*

In the above relation I represents the line current, i represents the phase (i = 1, 2, 3) and n represents the order of harmonics. A K factor of 1 indicates a linear load (no harmonics); a

The unbalanced three-phase systems of voltages (or currents) can be reduce into three

The positive voltage True RMS and the negative voltage True RMS are given by the

*V aV a V VRMS*

*V a V aV VRMS*

The positive current True RMS and the negative current True RMS are given by the

*I aI a I IRMS*

*I a I aI IRMS*

100 *unb VRMS*

 

*VRMS*

where 123 *III* , , represent the line currents (using simplified complex).

*V*

Voltage and current unbalances (unb) are:

2 1 23 3

where 123 *VVV* , , represent the phase voltages (using simplified complex) and

2 1 23 3

*i*

*IDF*

transformer heating. **K factor** for current is computed by relation:

higher K factor indicates the greater harmonic heating effects.

relations:

relations:

the complex operator.

$$I\_{unb} = \frac{\left| IRMS\_{-}\right|}{\left| IRMS\_{+}\right|} \cdot 100\tag{11}$$

**Power factor (PF) and displacement factor (DPF)** are computed by relations:

$$PF\_i = \frac{P\_i}{S\_i} \tag{12}$$

$$DPF\_i = \cos\varphi\_i \tag{13}$$

Pi [W] and Si [VA] represent the active power and the apparent power per phase (i = 1, 2, 3); *<sup>i</sup>* is the phase difference between the fundamental current and voltage, and i represents the phase.

Mathematical formulae used to compute the **peak factors (CF) for current and phase voltage** are:

$$\begin{aligned} VCF\_i &= \frac{\max\left(Vpp\ \, \_i\prime \, \_V\prime pnn\ \_i\right)}{\sqrt{\frac{1}{N}\cdot \sum\_{n=0}^{N-1} \left(V\{n\}\, \_i\right)^2}} \end{aligned} \tag{14}$$

$$ICF\_i = \frac{\max\left(lpp\_{i\cdot\nu} \left| lpm\_i \right|\right)}{\sqrt{\frac{1}{N} \cdot \sum\_{k=0}^{N-1} \left(l(k)\_i\right)^2}}\tag{15}$$

In the relations (14), (15): Vpp is the PEAK+ of the phase voltage; Vpm is the PEAK- of the phase voltage; Ipp is the PEAK+ of the line current; Ipm is the PEAK- of the line current; i represents the phase (i = 1, 2, 3); N represents the number of the samples per period (between two consecutive zeros).

Peak values (PEAK+/PEAK-) for voltage (or current) represent the maximum/minimum values of the voltage (or current) for all the samples between two consecutive zeros. For a sinusoidal signal, the peak factor is equal to 2 (1.41). For a non-sinusoidal signal, the peak factor can be either greater than or less than 2 . In the latter case, the peak factor signals divergent peak values with respect to the RMS value.

MIN/MAX values for voltage (or current) represent the minimum/maximum values of the half-period RMS voltage (or current). Average values (AVG) for voltage and current are computed over 1 second.

Tables 1-25 show the values computed by the CA8334 analyser on LV Line and on MV Line.


Table 1. Total harmonic distortion THD [%] for phase voltages (LV Line)

Power Quality Problems Generated by Line Frequency Coreless Induction Furnaces 247

Heating moment IDF1[%] IDF2 [%] IDF3[%] Cold state 21.7 46.2 32 Intermediate state 19.3 38.1 33.4 End of melting process 15.6 14.8 27.9

Heating moment IDF1[%] IDF3[%] Cold state 23.9 43.2 Intermediate state 32.2 61.8 End of melting process 22.7 23.4

The values of distortion factor of line currents are very high during the heating process

Heating moment IKF1 IKF2 IKF3 Cold state 2.02 6.07 3.52 Intermediate state 1.88 4.8 4.02 End of melting process 1.59 1.58 2.93

Heating moment IKF1 IKF3 Cold state 2.51 5.59 Intermediate state 3.54 8.7 End of melting process 2.21 2.27

K factor is greater than unity in all the heating stages. The values of K factor in the cold state and in the intermediate state are very high. This indicates the significant harmonic current content. K factor decrease at the end of the melting. Harmonics generate additional heat in the furnace transformer. If the transformer is non-K-rated, overheat possibly causing a fire,

Cold state 0.96 0.84 0.93 0.98 0.93 0.99 Intermediate state 0.93 0.88 0.92 0.95 0.97 0.98 End of melting process 0.97 0.97 0.96 0.99 0.99 0.99

PF DPF 1 2 3 1 2 3

(Table 7 and Table 8). The values of IDF are higher on MV Line versus LV Line.

Table 7. Distortion factor DF [%] of line currents (LV Line)

Table 8. Distortion factor DF [%] of line currents (MV Line)

Table 9. K factor KF [-] of line currents (LV Line)

Table 10. K factor KF [-] of line currents (MV Line)

Table 11. PF [-] and DPF [-] per phase (1, 2, 3) on LV line

also reducing the life of the transformer.

Heating moment


Table 2. Total harmonic distortion THD [%] for phase voltages (MV Line)

THD of the phase voltages do not exceed the compatibility limits in all the heating stages. The values of VTHD on MV Line are higher than the values of VTHD on LV Line.


Table 3. Total harmonic distortion THD [%] for line currents (LV Line)


Table 4. Total harmonic distortion THD [%] for line currents (MV Line)

ITHD exceed the limits permitted by norms in all the analyzed situations. The values of ITHD are higher on MV Line versus LV Line. Because THD of line currents exceed 20%, this indicates a significant electromagnetic pollution produced by the furnace in MV network.


Table 5. Distortion factor DF [%] of phase voltages (LV Line)


Table 6. Distortion factor DF [%] of phase voltages (MV Line)

Distortion factor of phase voltages is very small during the heating process of cast-iron charge. In all situations, distortion factor of phase voltages is smaller than total harmonic distortion.


Table 7. Distortion factor DF [%] of line currents (LV Line)

246 Power Quality Harmonics Analysis and Real Measurements Data

THD of the phase voltages do not exceed the compatibility limits in all the heating stages.

Heating moment ITHD1[%] ITHD2[%] ITHD3[%] Cold state 26.5 43 42 Intermediate state 20.1 39 35.5 End of melting process 14.9 16.7 30.3

Heating moment ITHD1[%] ITHD3[%] Cold state 31 57.5 Intermediate state 34.3 68.7 End of melting process 22.7 24.3

ITHD exceed the limits permitted by norms in all the analyzed situations. The values of ITHD are higher on MV Line versus LV Line. Because THD of line currents exceed 20%, this indicates a significant electromagnetic pollution produced by the furnace in MV network.

> Heating moment VDF1[%] VDF2[%] VDF3[%] Cold state 0 0 0 Intermediate state 0 0 0 End of melting process 0 0 5.5

> Heating moment VDF1[%] VDF2[%] VDF3[%] Cold state 1.9 0 1.4 Intermediate state 3.4 0 3 End of melting process 1.9 0 1.4

Distortion factor of phase voltages is very small during the heating process of cast-iron charge. In all situations, distortion factor of phase voltages is smaller than total harmonic distortion.

Table 2. Total harmonic distortion THD [%] for phase voltages (MV Line)

Table 3. Total harmonic distortion THD [%] for line currents (LV Line)

Table 4. Total harmonic distortion THD [%] for line currents (MV Line)

Table 5. Distortion factor DF [%] of phase voltages (LV Line)

Table 6. Distortion factor DF [%] of phase voltages (MV Line)

The values of VTHD on MV Line are higher than the values of VTHD on LV Line.

Heating moment VTHD1[%] VTHD2[%] VTHD3[%] Cold state 2.2 0 1.7 Intermediate state 3.4 0 3.1 End of melting process 1.9 0 1.7


Table 8. Distortion factor DF [%] of line currents (MV Line)

The values of distortion factor of line currents are very high during the heating process (Table 7 and Table 8). The values of IDF are higher on MV Line versus LV Line.


Table 9. K factor KF [-] of line currents (LV Line)


Table 10. K factor KF [-] of line currents (MV Line)

K factor is greater than unity in all the heating stages. The values of K factor in the cold state and in the intermediate state are very high. This indicates the significant harmonic current content. K factor decrease at the end of the melting. Harmonics generate additional heat in the furnace transformer. If the transformer is non-K-rated, overheat possibly causing a fire, also reducing the life of the transformer.


Table 11. PF [-] and DPF [-] per phase (1, 2, 3) on LV line

Power Quality Problems Generated by Line Frequency Coreless Induction Furnaces 249

Values i1 i2 i3 MAX [A] 1150 732 1665 AVG [A] 416 224 544 MIN [A] 0 0 0 PEAK+ [A] 608 384 928 PEAK- [A] -608 -384 -928

Values i1 i3 MAX [A] 96 60 AVG [A] 84 48 MIN [A] 0 0 PEAK+ [A] 138 90 PEAK- [A] -138 -90

Values i1 i2 i3 MAX [A] 1267 976 1713 AVG [A] 480 288 544 MIN [A] 0 0 0 PEAK+ [A] 704 512 992 PEAK- [A] -704 -512 -992

Table 18. Extreme and average values for line currents in the intermediate state (LV line)

Values i1 i3 MAX [A] 324 240 AVG [A] 96 60 MIN [A] 0 0 PEAK+ [A] 162 108 PEAK- [A] -162 -102 Table 19. Extreme and average values for line currents in the intermediate state (MV line)

> Values i1 i2 i3 MAX [A] 672 672 672 AVG [A] 608 640 672 MIN [A] 544 544 608 PEAK+ [A] 896 992 1088 PEAK- [A] -896 -992 -1056

Table 20. Extreme and average values for line currents at the end of melting (LV line)

Table 16. Extreme and average values for line currents in the cold state (LV line)

Table 17. Extreme and average values for line currents in the cold state (MV line)


PF is less than unity in all the analyzed situations on LV Line. In the cold state and in the intermediate state, PF is less than neutral value (0.92) per phase 2.

Table 12. Extreme and average values for phase voltages in the cold state (LV line)


Table 13. Extreme and average values for phase voltages in the cold state (MV Line)


Table 14. Extreme and average values for phase voltages at the end of melting (LV line)


Table 15. Extreme and average values for phase voltages at the end of melting (MV Line)

Tables 12-15 indicate a small unbalance of phase voltages in all the analyzed situations, on LV Line and on MV Line.

PF is less than unity in all the analyzed situations on LV Line. In the cold state and in the

Values u1 u2 u3 MAX [V] 552 624 558 AVG [V] 456 540 468 MIN [V] 0 0 0 PEAK+ [V] 660 786 678 PEAK- [V] -672 -786 -726

Table 12. Extreme and average values for phase voltages in the cold state (LV line)

Table 13. Extreme and average values for phase voltages in the cold state (MV Line)

Values u1 u2 u3 MAX [V] 498 570 516 AVG [V] 486 564 504 MIN [V] 456 540 474 PEAK+ [V] 708 828 732 PEAK- [V] -732 -810 -768

Table 14. Extreme and average values for phase voltages at the end of melting (LV line)

Values u1 u2 u3 MAX [V] 4140 4068 4146 AVG [V] 3594 3606 3600 MIN [V] 3558 3522 3480 PEAK+ [V] 5052 5118 5028 PEAK- [V] -5094 -5136 -5046

Table 15. Extreme and average values for phase voltages at the end of melting (MV Line)

LV Line and on MV Line.

Tables 12-15 indicate a small unbalance of phase voltages in all the analyzed situations, on

Values u1 u2 u3 MAX [V] 4176 4182 4158 AVG [V] 3558 3564 3600 MIN [V] 0 2862 2796 PEAK+ [V] 5034 5058 5028 PEAK- [V] -5076 -5076 -5046

intermediate state, PF is less than neutral value (0.92) per phase 2.


Table 16. Extreme and average values for line currents in the cold state (LV line)


Table 17. Extreme and average values for line currents in the cold state (MV line)


Table 18. Extreme and average values for line currents in the intermediate state (LV line)


Table 19. Extreme and average values for line currents in the intermediate state (MV line)


Table 20. Extreme and average values for line currents at the end of melting (LV line)

Power Quality Problems Generated by Line Frequency Coreless Induction Furnaces 251

Peak factors of line currents are between 1.48 and 1.88. This indicates that the analyzed furnace is a non-linear load. A high peak factor characterizes high transient overcurrents

**5. Recorded parameters in the electrical installation of the induction furnace**  The recorded parameters in the electrical installation of analyzed furnace are: RMS values of phase voltages and currents, total harmonic distortion of phase voltages and currents, power factor and displacement factor per phase 1, active power, reactive power and

Fig.17-21 show the recorded parameters on MV Line, in the first stage of the heating. In the

RMS values of phase voltages in the cold state indicate a small unbalance of the load. THD of phase voltages are within compatibility limits in the first stage of the heating process. The RMS values of line currents show a poor balance between the phases. The Steinmetz

THD of line currents have values of 20%...70%, and exceed very much the compatibility limits during the recording period. This indicates a significant harmonic pollution with a

which, when detected by protection devices, can cause nuisance tripping.

recording period (11:20-12:18), the furnace charge was ferromagnetic.

Fig. 17. RMS values of the phase voltages in the cold state (MV Line)

Fig. 18. THD of phase voltages in the cold state (MV Line)

circuit is not efficient for load balancing in this stage of the melting process.

apparent power per phase 1.

risk of temperature rise.


Table 21. Extreme and average values for line currents at the end of melting (MV line)

The extreme and average values of line currents indicate a large unbalance in the cold state and in intermediate state. At the end of the melting the unbalance of currents is small.


Table 22. Peak factors CF [-] of phase voltages (LV Line)


Table 23. Peak factors CF [-] of phase voltages (MV Line)

Peak factors of phase voltages do not exceed very much the peak factor for sinusoidal signals (1.41) in all the heating stages. This indicates a small distortion of phase voltages.


Table 24. Peak factors CF [-] of line currents (LV Line)


Table 25. Peak factors CF [-] of line currents (MV Line)

Values i1 i3 MAX [A] 102 102 AVG [A] 90 90 MIN [A] 90 84 PEAK+ [A] 150 150 PEAK- [A] -150 -150

Table 21. Extreme and average values for line currents at the end of melting (MV line)

The extreme and average values of line currents indicate a large unbalance in the cold state and in intermediate state. At the end of the melting the unbalance of currents is small.

> Heating moment VCF1 VCF2 VCF3 Cold state 1.47 1.46 1.53 Intermediate state 1.48 1.44 1.56

Heating moment VCF1 VCF2 VCF3 Cold state 1.42 1.42 1.39 Intermediate state 1.44 1.42 1.39

Peak factors of phase voltages do not exceed very much the peak factor for sinusoidal signals (1.41) in all the heating stages. This indicates a small distortion of phase voltages.

> Heating moment ICF1 ICF2 ICF3 Cold state 1.59 1.83 1.81 Intermediate state 1.51 1.88 1.83

Heating moment ICF1 ICF3 Cold state 1.68 1.82 Intermediate state 1.72 1.79 End of melting process 1.68 1.68

1.45 1.47 1.49

1.45 1.47 1.49

1.48 1.64 1.66

End of melting process

End of melting process

End of melting process

Table 24. Peak factors CF [-] of line currents (LV Line)

Table 25. Peak factors CF [-] of line currents (MV Line)

Table 22. Peak factors CF [-] of phase voltages (LV Line)

Table 23. Peak factors CF [-] of phase voltages (MV Line)

Peak factors of line currents are between 1.48 and 1.88. This indicates that the analyzed furnace is a non-linear load. A high peak factor characterizes high transient overcurrents which, when detected by protection devices, can cause nuisance tripping.

## **5. Recorded parameters in the electrical installation of the induction furnace**

The recorded parameters in the electrical installation of analyzed furnace are: RMS values of phase voltages and currents, total harmonic distortion of phase voltages and currents, power factor and displacement factor per phase 1, active power, reactive power and apparent power per phase 1.

Fig.17-21 show the recorded parameters on MV Line, in the first stage of the heating. In the recording period (11:20-12:18), the furnace charge was ferromagnetic.

Fig. 17. RMS values of the phase voltages in the cold state (MV Line)

RMS values of phase voltages in the cold state indicate a small unbalance of the load. THD of phase voltages are within compatibility limits in the first stage of the heating process.

The RMS values of line currents show a poor balance between the phases. The Steinmetz circuit is not efficient for load balancing in this stage of the melting process.

THD of line currents have values of 20%...70%, and exceed very much the compatibility limits during the recording period. This indicates a significant harmonic pollution with a risk of temperature rise.

Fig. 18. THD of phase voltages in the cold state (MV Line)

Power Quality Problems Generated by Line Frequency Coreless Induction Furnaces 253

Fig.22-29 show the recorded parameters in the intermediate state of the heating. The furnace

charge was partially melted in the recording period, 13:20-14:18.

Fig. 22. RMS values of phase voltages in the intermediate state (MV Line)

Fig. 23. THD of phase voltages in the intermediate state (MV Line)

Fig. 24. RMS values of line currents in the intermediate state (MV Line)

are bigger comparatively with the cold state.

In the intermediate state, THD of phase voltages do not exceed the compatibility limits, but

Fig. 19. RMS values of the currents in the cold state (MV Line)

Fig. 20. THD of line currents in the cold state (MV Line)

Fig. 21. DPF and PF per phase 1 in the cold state (MV Line)

In the recorded period of the cold state, power factor (PF) per phase 1 and displacement factor (DPF) per phase 1 are less than unity; in the time period 12:00 - 12:18 PF is less than neutral value (0.92). PF is smaller than DPF because PF includes fundamental reactive power and harmonic power, while DPF only includes the fundamental reactive power caused by a phase shift between voltage and fundamental current.

Fig. 19. RMS values of the currents in the cold state (MV Line)

Fig. 20. THD of line currents in the cold state (MV Line)

Fig. 21. DPF and PF per phase 1 in the cold state (MV Line)

caused by a phase shift between voltage and fundamental current.

In the recorded period of the cold state, power factor (PF) per phase 1 and displacement factor (DPF) per phase 1 are less than unity; in the time period 12:00 - 12:18 PF is less than neutral value (0.92). PF is smaller than DPF because PF includes fundamental reactive power and harmonic power, while DPF only includes the fundamental reactive power Fig.22-29 show the recorded parameters in the intermediate state of the heating. The furnace charge was partially melted in the recording period, 13:20-14:18.

Fig. 22. RMS values of phase voltages in the intermediate state (MV Line)

Fig. 23. THD of phase voltages in the intermediate state (MV Line)

In the intermediate state, THD of phase voltages do not exceed the compatibility limits, but are bigger comparatively with the cold state.

Fig. 24. RMS values of line currents in the intermediate state (MV Line)

Power Quality Problems Generated by Line Frequency Coreless Induction Furnaces 255

In the time period 13:20 - 13:35, the values of reactive power per phase 1 are almost equal to the values of active power. As a result, the power factor per phase 1 is very poor in the time

Fig.30-37 show the recorded parameters in the last stage of the heating. The furnace charge

Fig. 30. RMS values of phase voltages in the last stage of the melting process (MV Line)

limits, being smaller comparatively with the cold state or the intermediate state.

In the last stage of the melting process, THD of phase voltages are within compatibility

Fig. 28. Reactive power per phase 1 in the intermediate state (MV Line)

Fig. 29. Apparent power per phase 1 in the intermediate state (MV Line)

was totally melted in the recording period, 18:02-18:12.

period 13:20 - 13:35 (fig.26).

Fig. 25. THD of line currents in the intermediate state (MV Line)

In the intermediate state, the RMS values of the line currents show a poor balance between the phases. THD of line currents are remarkably high and exceed the compatibility limits.

Fig. 26. DPF and PF per phase 1 in the intermediate state (MV Line)

The difference between the power factor and the displacement factor is significant in the intermediate state. This indicates the significant harmonic pollution and reactive power consumption.

PF per phase 1 is less than neutral value (0.92) almost all the time during the intermediate state. In the time period 13:20-13:35, PF is very small.

Fig. 27. Active power per phase 1 in the intermediate state (MV Line)

In the intermediate state, the RMS values of the line currents show a poor balance between the phases. THD of line currents are remarkably high and exceed the compatibility limits.

The difference between the power factor and the displacement factor is significant in the intermediate state. This indicates the significant harmonic pollution and reactive power

PF per phase 1 is less than neutral value (0.92) almost all the time during the intermediate

Fig. 25. THD of line currents in the intermediate state (MV Line)

Fig. 26. DPF and PF per phase 1 in the intermediate state (MV Line)

Fig. 27. Active power per phase 1 in the intermediate state (MV Line)

state. In the time period 13:20-13:35, PF is very small.

consumption.

Fig. 28. Reactive power per phase 1 in the intermediate state (MV Line)

In the time period 13:20 - 13:35, the values of reactive power per phase 1 are almost equal to the values of active power. As a result, the power factor per phase 1 is very poor in the time period 13:20 - 13:35 (fig.26).

Fig. 29. Apparent power per phase 1 in the intermediate state (MV Line)

Fig.30-37 show the recorded parameters in the last stage of the heating. The furnace charge was totally melted in the recording period, 18:02-18:12.

Fig. 30. RMS values of phase voltages in the last stage of the melting process (MV Line)

In the last stage of the melting process, THD of phase voltages are within compatibility limits, being smaller comparatively with the cold state or the intermediate state.

Power Quality Problems Generated by Line Frequency Coreless Induction Furnaces 257

In the time period 18:07 - 18:12, the values of reactive power per phase 1 increase;

consequently, the power factor and the displacement factor per phase 1 decrease. Recorded values of active power per phase 1 are close to the apparent power values.

Fig. 34. DPF and PF per phase 1 in the last stage of the melting process (MV Line)

Fig. 35. Active power per phase 1 in the last stage of the melting process (MV Line)

Fig. 36. Reactive power per phase 1 in the last stage of the melting process (MV Line)

Fig. 31. THD of phase voltages in the last stage of the melting process (MV Line)

Fig. 32. RMS values of line currents in the last stage of the melting process (MV Line)

Fig. 33. THD of line currents in the last stage of the melting process (MV Line)

At the end of the melting process, the RMS values of line currents are much closer comparatively with cold state or intermediate state. THD of line currents exceed the compatibility limits, being of 20%…50% during this recording period.

The difference between the power factor and the displacement factor is small in the last stage of the melting process (fig.34). This indicates a decrease of harmonic disturbances and reactive power consumption (fig.36), comparatively with the cold state or the intermediate state.

Fig. 31. THD of phase voltages in the last stage of the melting process (MV Line)

Fig. 32. RMS values of line currents in the last stage of the melting process (MV Line)

Fig. 33. THD of line currents in the last stage of the melting process (MV Line)

compatibility limits, being of 20%…50% during this recording period.

At the end of the melting process, the RMS values of line currents are much closer comparatively with cold state or intermediate state. THD of line currents exceed the

The difference between the power factor and the displacement factor is small in the last stage of the melting process (fig.34). This indicates a decrease of harmonic disturbances and reactive power consumption (fig.36), comparatively with the cold state or the intermediate state.

In the time period 18:07 - 18:12, the values of reactive power per phase 1 increase; consequently, the power factor and the displacement factor per phase 1 decrease. Recorded values of active power per phase 1 are close to the apparent power values.

Fig. 34. DPF and PF per phase 1 in the last stage of the melting process (MV Line)

Fig. 35. Active power per phase 1 in the last stage of the melting process (MV Line)

Fig. 36. Reactive power per phase 1 in the last stage of the melting process (MV Line)

Power Quality Problems Generated by Line Frequency Coreless Induction Furnaces 259

The capacitors for power factor correction and the ones from Steinmetz circuit amplify in

PF is less than unity in all the analyzed situations. But, Steinmetz circuit is efficient only for

Under nonsinusoidal conditions, any attempt to achieve unity PF does not result in harmonic-

For optimizing the operation of analyzed induction furnace, it's imposing the simultaneous adoption of three technical measures: harmonics filtering, reactive power compensation and load balancing. That is the reason to introduce harmonic filters in the primary of furnace transformer to solve the power interface problems. In order to eliminate the unbalance, it is necessary to add another load balancing system in the connection point of the furnace to the

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free current. Similarly, compensation for current harmonics does not yield unity PF.

fact the harmonic problems.

power supply network.

8977.

**7. References** 

unity PF, under sinusoidal conditions.

Fig. 37. Apparent power per phase 1 in the last stage of the melting process (MV Line)
