**Bank Harmonic Filters Operation in Power Supply System – Cases Studies**

Ryszard Klempka, Zbigniew Hanzelka and Yuri Varetsky

Additional information is available at the end of the chapter

http://dx.doi.org/10.5772/53425

### **1. Introduction**

[5] B. Kekezoğlu, O. Arıkan, C. Kocatepe, R. Yumurtacı, M. Baysal, A. Bozkurt, Elektrikli Ofis Cihazlarında Güç Faktörü ve cosφ'nin İncelenmesi, 3e Electrotech, Sayı: 174,

[6] Wenzel, E., AN1864 Application Note, 22W/120Vac Compact Fluoresant Lamp Driv‐

[7] S. Onaygil, Ö. Güler, Yüksek Frekanslı Elektronik Balastlar, 1. Ulusal Aydınlatma

[8] R. Yumurtacı, O. Arıkan, A. Bozkurt, Kompakt Flourasant Lambaların Harmonik Kaynağı Olarak İncelenmesi, Enerji Verimliliği Kongresi – EVK'05, Kocaeli, 2005. [9] B. Kekezoğlu, O. Arıkan, A. Bozkurt, C. Kocatepe, R. Yumurtacı, Analysis of AC Mo‐ tor Drives as a Harmonic Source, 4th International Conference on Electrical and Pow‐

er Engineering (EPE-2006), pp. 832- 83712-13 October, Iasi, Romania, 2006.

[10] Applied Protective Relaying, Westinghouse Electric Corporation Relay-Instrument

[11] Horowitz, S. H., Phadke, A. G., Power System Relaying. John Wiley & Sons Inc.,

[12] IEEE Standard Inverse-Time Characteristic Equations for Overcurrent Relays, Power

[13] Yumurtacı R., Gulez K., Bozkurt A., Kocatepe C., Uzunoglu M., Analysis of Harmon‐ ic Effects on Electromechanical Instantaneous Overcurrent Relays with Different Neural Networks Models, International Journal of Information Technology, Vol. 11,

[14] K.B. Dalci, R. Yumurtaci, A. Bozkurt, Harmonic Effects on Electromechanical Over‐ current Relays, Dogus University Journal, Vol. 6, pp. 202-209, Istanbul, 2005.

[15] Mason, C.R.: The Art and Science of Protective Relaying. John Wiley Eastern Limited

[16] Yumurtacı, R., Bozkurt, A., Gulez, K., Neural Networks Based Analysis of Harmonic Effects on Electromechanical Instantaneous Overcurrent Relays, SICE, The Society of Instrument and Control Engineers Annual Conference, Okayama/Japan, 1012-1015,

[17] R. Yumurtacı, A. Bozkurt, K. Gulez, Neural Networks Based Analysis of Harmonic Effects on Inverse Time Static Overcurrent Relays, INISTA, International Symposium on Innovations in Intelligent Systems and Applications, Istanbul/Turkey, 108-111,

System Relaying Committee of the IEEE PES, IEEE Std C37112., 1996.

er with VK05CFL, ST Microelectronics Com, Italy, 2004

110-114, Aralık 2008.

200 Power Quality Issues

Kongresi, İstanbul, 1996

Division, Newark, 1976.

No.5, 26-35, Aralık-2005.

New Delhi, 1991.

08-10 August 2005.

15-18 June 2005.

1992.

Continuous technological development facilitates the increase in the number of nonlinear loads that significantly affect the power quality in a power system and, consequently, the quality of the electric power delivered to other customers. DC and AC variable speed drives and arc furnaces are ranked among the most commonly used large power nonlinear loads.

DC drives can be a significant plant load in many industries. They are commonly used in the oil, chemical, metal and mining industries. These drives are still the most common large power type of motor speed control for applications requiring very fine control over wide speed ranges with high torques. Power factor correction is particularly important for this drives because of relatively poor power factor, especially when the motor is at reduced speeds. Additional trans‐ former capacity is required to handle the poor power factor conditions and more utilities are charging a power factor penalty that can significantly impact the total bill for the facility. The DC drives also generate significant harmonic currents. The harmonics make power factor cor‐ rection more complicated. Power factor correction capacitors can cause resonant conditions which magnify the harmonic currents and cause excessive distortion levels. For the same rea‐ sons arc furnaces are very difficult loads for a supplier and for the customer they are very diffi‐ cult objects of reactive power compensation and harmonics filtering.

One of the most common methods to prevent adverse effects of nonlinear loads on the power network is the use of passive filters. However, different configurations should be considered before making the final design decision. Among the performance criteria are current and volt‐ age ratings of the filter components, and the effect of filter and system contingency conditions. Before any filter scheme is specified, a power factor study should be done to determine if any

© 2013 Klempka et al.; licensee InTech. This is an open access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. © 2013 Klempka et al.; licensee InTech. This is a paper distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

reactive compensation requirements are needed. If power factor correction is not necessary, then a minimum power filter can be designed; one that can handle the fundamental and har‐ monic currents and voltages without consideration for reactive power output. Sometimes, more than one tuned filter is needed. The filter design practice requires that the capacitor and the reactor impedance be predetermined. For engineers not knowing the appropriate initial es‐ timates, the process has to be repeated until all the proper values are found. This trialand-error approach can become complex as more filters are included in the systems.

*RF* ≅0

*L <sup>F</sup>CF*

<sup>=</sup> (1)

Bank Harmonic Filters Operation in Power Supply System − Cases Studies

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203

*<sup>ω</sup><sup>r</sup>* <sup>=</sup>*nrω*<sup>1</sup> <sup>=</sup> <sup>1</sup>

*n C* w

*r F*

Where *k* single-tuned filters are operated in parallel in order to eliminate a larger number of harmonics then *k* voltage resonances (series resonances) and *k* current resonances (parallel resonances) occur in the system. These resonance frequencies are placed alternately and the series resonance is always the preceding one. In other words, each branch has its own reso‐

The schematic diagram of an example group of filters in a large industrial installation and characteristics illustrating the line current variations and the 5th harmonic voltage varia‐ tions in result of connecting ONLY the 5th harmonic filter are shown in Fig. 2. The figure also shows the 7th harmonic voltage variations prior to and after connecting the 5th har‐ monic filter. The 5th harmonic filter selectivity is evident ― its connection has practically no

Relations (2) allow determining parameters of a group of single-tuned filters taking into ac‐ count their interaction, as well as choosing the frequencies for which the impedance fre‐ quency characteristic of the filter bank attains maxima, where (the filters' resistances Ri

ders of filter tuning harmonics; *m*<sup>i</sup> - orders of harmonics for which the impedance character‐


0): Ci

<sup>2</sup> <sup>⋅</sup> *QF <sup>ω</sup>*1*<sup>U</sup>* <sup>2</sup>

*F*

*CF* = *nr* <sup>2</sup> −1 *nr*

**Figure 1.** Single branch filter and the frequency characteristic

influence on the 7th harmonic value.


nance frequency.

*L*

While the effectiveness of a filter installation depends on the degree of harmonic suppres‐ sion, it also involves consideration of alternate system configurations. As the supplying util‐ ity reconfigures its system, the impedance, looking back to the source from the plant's standpoint, will change. Similar effects will be seen with the plant running under light ver‐ sus heavy loading conditions, with split-bus operation, etc. Therefore, the filtering scheme must be tested under all reasonable operating configurations.

The general procedure in analyzing any harmonic problem is to identify the worst harmonic condition, design a suppression scheme and recheck for other conditions. Analysis of impe‐ dance vs frequency dependencies for all reasonable operating contingencies is commonly used practice. A frequency scan should be made at each problem node in the system, with harmonic injection at each point where harmonic sources exist. This allows easy evaluation of the effects of system changes on the effective tuning. Of particular importance is the vari‐ ability of parallel resonance points with regard to changing system parameters. This prob‐ lem is illustrated by the practical example.

In a most classic cases all filter considerations are carried out under the following simplify‐ ing assumptions: (i) the harmonic source is an ideal current source; (ii) the filter inductance *LF* and capacitance *CF* are lumped elements and their values are constant in the considered frequency interval; (iii) the filter resistance can be sometime neglected and the filter is main‐ ly loaded with the fundamental harmonic and the harmonic to which it is tuned e.g. [1]. The above assumptions allow designing simple filter-compensating structures. However, if a more complex filter structures or a larger number of filters connected in parallel are de‐ signed or their mutual interaction and co-operation with the power system (the network im‐ pedance), or non-zero filter resistances should be taken into account, these may impede or even prevent an effective analysis. An example of the new approach is the use of artificial intelligence methods, among them the genetic algorithm (AG) [2 - 4]. The usefulness of this new method is illustrated by examples of designing selected filters' structures: (a) a group of single-tuned filters; (b) double-tuned filter and (c) C-type filter.

### **2. Single-tuned single branch filter**

Many passive *LC* filter systems, of various structures and different operating characteristics have been already developed [4 - 9]. Nevertheless, the single-tuned single branch filter (Fig. 1) still is the dominant solution for industrial applications, and it certainly is the basis for understanding more advanced filtering structures.

Bank Harmonic Filters Operation in Power Supply System − Cases Studies http://dx.doi.org/10.5772/53425 203

**Figure 1.** Single branch filter and the frequency characteristic

reactive compensation requirements are needed. If power factor correction is not necessary, then a minimum power filter can be designed; one that can handle the fundamental and har‐ monic currents and voltages without consideration for reactive power output. Sometimes, more than one tuned filter is needed. The filter design practice requires that the capacitor and the reactor impedance be predetermined. For engineers not knowing the appropriate initial es‐ timates, the process has to be repeated until all the proper values are found. This trialand-error

While the effectiveness of a filter installation depends on the degree of harmonic suppres‐ sion, it also involves consideration of alternate system configurations. As the supplying util‐ ity reconfigures its system, the impedance, looking back to the source from the plant's standpoint, will change. Similar effects will be seen with the plant running under light ver‐ sus heavy loading conditions, with split-bus operation, etc. Therefore, the filtering scheme

The general procedure in analyzing any harmonic problem is to identify the worst harmonic condition, design a suppression scheme and recheck for other conditions. Analysis of impe‐ dance vs frequency dependencies for all reasonable operating contingencies is commonly used practice. A frequency scan should be made at each problem node in the system, with harmonic injection at each point where harmonic sources exist. This allows easy evaluation of the effects of system changes on the effective tuning. Of particular importance is the vari‐ ability of parallel resonance points with regard to changing system parameters. This prob‐

In a most classic cases all filter considerations are carried out under the following simplify‐ ing assumptions: (i) the harmonic source is an ideal current source; (ii) the filter inductance *LF* and capacitance *CF* are lumped elements and their values are constant in the considered frequency interval; (iii) the filter resistance can be sometime neglected and the filter is main‐ ly loaded with the fundamental harmonic and the harmonic to which it is tuned e.g. [1]. The above assumptions allow designing simple filter-compensating structures. However, if a more complex filter structures or a larger number of filters connected in parallel are de‐ signed or their mutual interaction and co-operation with the power system (the network im‐ pedance), or non-zero filter resistances should be taken into account, these may impede or even prevent an effective analysis. An example of the new approach is the use of artificial intelligence methods, among them the genetic algorithm (AG) [2 - 4]. The usefulness of this new method is illustrated by examples of designing selected filters' structures: (a) a group of

Many passive *LC* filter systems, of various structures and different operating characteristics have been already developed [4 - 9]. Nevertheless, the single-tuned single branch filter (Fig. 1) still is the dominant solution for industrial applications, and it certainly is the basis for

approach can become complex as more filters are included in the systems.

must be tested under all reasonable operating configurations.

single-tuned filters; (b) double-tuned filter and (c) C-type filter.

lem is illustrated by the practical example.

202 Power Quality Issues

**2. Single-tuned single branch filter**

understanding more advanced filtering structures.

Where *k* single-tuned filters are operated in parallel in order to eliminate a larger number of harmonics then *k* voltage resonances (series resonances) and *k* current resonances (parallel resonances) occur in the system. These resonance frequencies are placed alternately and the series resonance is always the preceding one. In other words, each branch has its own reso‐ nance frequency.

The schematic diagram of an example group of filters in a large industrial installation and characteristics illustrating the line current variations and the 5th harmonic voltage varia‐ tions in result of connecting ONLY the 5th harmonic filter are shown in Fig. 2. The figure also shows the 7th harmonic voltage variations prior to and after connecting the 5th har‐ monic filter. The 5th harmonic filter selectivity is evident ― its connection has practically no influence on the 7th harmonic value.

Relations (2) allow determining parameters of a group of single-tuned filters taking into ac‐ count their interaction, as well as choosing the frequencies for which the impedance fre‐ quency characteristic of the filter bank attains maxima, where (the filters' resistances Ri 0): Ci - the filters' capacitances; *L*<sup>i</sup> - the filters' inductances; ωri - tuned angular frequency; *n*ri - or‐ ders of filter tuning harmonics; *m*<sup>i</sup> - orders of harmonics for which the impedance character‐

**2.1. Example 1**

1500 r/min, *k* = 2,62

will be achieved.

shuffling crossover (APPENDIX A).

An example application of the method will be the design of single-tuned filters (two singletuned filters) for DC motor (Fig. 3). The basis for design is modelling of the whole supplying system. The system may comprise nonlinear components and analysis of the filters can take into account their own resistance, which depends on the selected components values. Gener‐

control

**Figure 3.** Diagram of the power system with the designed group of single-tuned filters for system with DC drive sup‐ plied by 6-pulse controlled rectifier:*P*N = 22kW, *U*N = 440V, *I*N = 56,2A, *J* = 2,7kgm2, *R*t = 0,465Ω, *L*<sup>t</sup> = 15,345mH, *nN* =

Parameters of the single-tuned filters group were determined by means of the Genetic Algo‐ rithm minimising the voltage harmonic distortion factor with limitation of the phase shift angle between fundamental harmonics of the current and voltage*ϕ*(1)>0. Parameters of the applied Genetic Algorithm: (a) each parameter (*C*F5, *C*F7) is encoded into a 15-bit string; (b) range of variability from 1μF to 100μF; (c) population size 100 individuals; (d) crossover probability *p*k = 0.7; (e) mutation probability *p*m = 0.01; (f) Genetic Algorithm termination condition – 100 generations; (g) selection method Stochastic Universal Sampling (SUS); (h)

The genetic algorithm objective is to find the capacitance values of two single-tuned filters tuned to harmonics *n*r5 = 4.9 and *n*r7 = 6.9. It is worth pointing out that the genetic algorithm itself solves the problem of reactive power distribution between the filters. The voltage total harmonic distortion will be minimized and therefore power distribution between the filters

Basic characteristics of the power system, before and after connecting the filters, are tabulated in Fig. 4 (*C*F5 = 30.14μF; *C*F7 = 4.11μF; the phase shift angle between the voltage and current fun‐

In industry many of the supply systems consist of a combination of tuned filters and a ca‐ pacitor bank. Depending on the system configuration the capacitor bank can lead to magni‐

damental harmonics: prior to connection of filters – 11º, after connection of filters 0.2º).

*C*F5 *L*F5 *R*F5

Sz = 500kVA

6kV

400V

*C*F7 *L*F7 *R*F7

Bank Harmonic Filters Operation in Power Supply System − Cases Studies

http://dx.doi.org/10.5772/53425

205

ally speaking, the model can be detailed without simplifications.

**Figure 2.** Groups of single branch filters: (a) schematic diagram; (b) current (*I*); characteristics of (c) 5th and (d) 7th volt‐ age harmonic. The vertical line indicates the instance of the 5th harmonic filter connection

istic should attain maxima; *Q*<sup>F</sup> - reactive power of the basic harmonic of the filter or group of filters and U – RMS operating voltage.

$$
\begin{bmatrix}
\frac{n\_1^2 m\_1}{n\_1^2 - m\_1^2} & \frac{n\_2^2 m\_1}{n\_2^2 - m\_1^2} & \cdots & \frac{n\_k^2 m\_1}{n\_k^2 - m\_1^2} \\
\frac{n\_1^2 m\_2}{n\_1^2 - m\_2^2} & \cdots & \frac{n\_k^2 m\_2}{n\_k^2 - m\_2^2} \\
\vdots & & \ddots & \vdots \\
\frac{n\_1^2 m\_{k-1}}{n\_5^2 - m\_{k-1}^2} & \cdots & \frac{n\_k^2 m\_{k-1}}{n\_k^2 - m\_{k-1}^2} \\
\frac{n\_1^2 m\_1}{n\_1^2 - 1} & \frac{n\_1^2 m\_1}{n\_2^2 - 1} & \cdots & \frac{n\_k^2 m\_1}{n\_k^2 - 1}
\end{bmatrix} \begin{bmatrix} 0 \\ \vdots \\ \vdots \\ 0 \\ \vdots \\ 0 \\ \frac{Q\_F}{\mathcal{U}^2} \end{bmatrix} \tag{2}
$$

$$L\_i = \frac{1}{n\_{ri}^2 \alpha\_1^2 C\_i} \qquad i = 1...k$$

### **2.1. Example 1**

istic should attain maxima; *Q*<sup>F</sup> - reactive power of the basic harmonic of the filter or group of

**Figure 2.** Groups of single branch filters: (a) schematic diagram; (b) current (*I*); characteristics of (c) 5th and (d) 7th volt‐

1 *n*1 *m*<sup>1</sup>

*n n*2 *m n*<sup>k</sup> 2 *m*k-1

(d)


*C*k *L*k *R*k

(a)

*C*1 *L*1 *R*<sup>1</sup> *C*2 *L*2 *R*<sup>2</sup>

current (I)

*...* 

2 2 2 11 21 1

(b)

(c)

age harmonic. The vertical line indicates the instance of the 5th harmonic filter connection

*r r rk r r rk r rk r rk*

*nm nm n m*

é ù ê úé -- - <sup>ê</sup>

2 2 1 2 2 2 2 2 2 1 2 2

*n m n m n m n m*

2 2 1 1 1 2 2 2 2 5 1 1 2 2 2 11 21 1 2 2 2 1 2 11 1

*n m n m n m n m*

*r r rk*

*nn n*

ww

<sup>1</sup> 1...

*L ik n C* w

= =

2 2 1

*ri i*

*i*

*r k rk k r k rk k*




<sup>2222</sup> 2 2 <sup>1</sup> 11 21 <sup>1</sup>

L

<sup>ê</sup> - - <sup>ê</sup>

L

M O <sup>M</sup>

*C nm nm nm*

*r r rk k*

 w

L <sup>2</sup>

ê

0

M

0

(2)

M

é ù ù ê ú ú ê ú ú ê ú ú ê ú ú ê ú ú ê ú ú ê ú ú = ê ú ê ú ê ú ê ú ê ú ê ú ê ú ê ú ê ú ê ú ê ú ê ú ê ú ê ú ê ú û ê ú ë û

*F*

*Q U*

ê ê ê

ë

*nn n C*

L

filters and U – RMS operating voltage.

IRMS

204 Power Quality Issues

An example application of the method will be the design of single-tuned filters (two singletuned filters) for DC motor (Fig. 3). The basis for design is modelling of the whole supplying system. The system may comprise nonlinear components and analysis of the filters can take into account their own resistance, which depends on the selected components values. Gener‐ ally speaking, the model can be detailed without simplifications.

**Figure 3.** Diagram of the power system with the designed group of single-tuned filters for system with DC drive sup‐ plied by 6-pulse controlled rectifier:*P*N = 22kW, *U*N = 440V, *I*N = 56,2A, *J* = 2,7kgm2, *R*t = 0,465Ω, *L*<sup>t</sup> = 15,345mH, *nN* = 1500 r/min, *k* = 2,62

Parameters of the single-tuned filters group were determined by means of the Genetic Algo‐ rithm minimising the voltage harmonic distortion factor with limitation of the phase shift angle between fundamental harmonics of the current and voltage*ϕ*(1)>0. Parameters of the applied Genetic Algorithm: (a) each parameter (*C*F5, *C*F7) is encoded into a 15-bit string; (b) range of variability from 1μF to 100μF; (c) population size 100 individuals; (d) crossover probability *p*k = 0.7; (e) mutation probability *p*m = 0.01; (f) Genetic Algorithm termination condition – 100 generations; (g) selection method Stochastic Universal Sampling (SUS); (h) shuffling crossover (APPENDIX A).

The genetic algorithm objective is to find the capacitance values of two single-tuned filters tuned to harmonics *n*r5 = 4.9 and *n*r7 = 6.9. It is worth pointing out that the genetic algorithm itself solves the problem of reactive power distribution between the filters. The voltage total harmonic distortion will be minimized and therefore power distribution between the filters will be achieved.

Basic characteristics of the power system, before and after connecting the filters, are tabulated in Fig. 4 (*C*F5 = 30.14μF; *C*F7 = 4.11μF; the phase shift angle between the voltage and current fun‐ damental harmonics: prior to connection of filters – 11º, after connection of filters 0.2º).

In industry many of the supply systems consist of a combination of tuned filters and a ca‐ pacitor bank. Depending on the system configuration the capacitor bank can lead to magni‐ 2

fication or attenuation of the filters loading. Filter detuning significantly affects this phenomenon. Therefore, specifying harmonic filters requires considerable care under analy‐ sis of possible system configurations for avoidance of harmonic problems. 6 Book Title 1

including power factor correction capacitor banks. System contains two sets of powerful DC skip drives as harmonic loads connected to sections A and B. The drives are fed from sixpulse converters. As a result, there is significant harmonic current generation and the plant

M M

Shunt capacitors 2×1.5 MVA connected to main sections 1 and 2 to partially correct the pow‐ er factor but this can cause harmonic problems due to resonance conditions. The sections A and B can be supplying from the main section 1 or 2. Four single-tuned filters (5th, 7th, 11th, and 13th harmonic order) have been added to the sections A and B to limit harmonic prob‐ lems and improve reactive compensation. Specifications of the harmonic filters are shown in

2900 kW 2900 kW

73.1μF, 6.0 mH

58.5μF, 3.54 mH

73.1μF, 1.16 mH

73.1μF, 0.82 mH

5 7 11 13 5 7 11 13

3´ 240 / 30m

2´3´240 / 400m

110 V, 430 MVA

Bank Harmonic Filters Operation in Power Supply System − Cases Studies

20 20 13

40 MVA

6 V

55 Ohm 55 Ohm

200 μH 200 μH

1500 A, 0.139Ohm

830 A, 6.3% 830 A, 6.3%

1 3 4 5 62

3´120 / 20m 3´ 120 / 45m

Section A Section B

4 MVA, 7% 4 MVA, 7%

750 V 750 V

Section 2

http://dx.doi.org/10.5772/53425

207

2´1.5 MVA

power factor without compensation is quite low.

40 MVA

73.1μF, 6.0 mH

**Figure 5.** One-line diagram of a mining power supply system

the Table 1.

58.5μF, 3.54 mH

73.1μF, 1.16 mH

73.1μF, 0.82 mH

13

Section 1

2´1.5 MVA

4 filters **Figure 4.** The voltage-current waveforms and spectrum before and after connecting the filters (*U*1/*I*<sup>1</sup> – basic voltage/ current harmonic; *U*h/*I*h – h. order voltage/current component

3 **Figure 4.** The voltage-current waveforms and spectrum before and after connecting the

### **3. Parallel operation of filters**

### **3.1. Example 2 – description of the system**

Fig. 5 shows a one-line diagram of a mining power supply system which will be used to an‐ alyze operation characteristics of the single tuned harmonic filters in a power supply system including power factor correction capacitor banks. System contains two sets of powerful DC skip drives as harmonic loads connected to sections A and B. The drives are fed from sixpulse converters. As a result, there is significant harmonic current generation and the plant power factor without compensation is quite low.

**Figure 5.** One-line diagram of a mining power supply system

fication or attenuation of the filters loading. Filter detuning significantly affects this phenomenon. Therefore, specifying harmonic filters requires considerable care under analy‐

6 Book Title

sis of possible system configurations for avoidance of harmonic problems.

[%]

*U*<sup>5</sup> [%]

*U*<sup>7</sup> [%]

> 1 *I I* [%]


before connecting the filters

Ih [%]

1 *I I* [%]

after connecting the filters

**Figure 4.** The voltage-current waveforms and spectrum before and after connecting the filters (*U*1/*I*<sup>1</sup> – basic voltage/

Fig. 5 shows a one-line diagram of a mining power supply system which will be used to an‐ alyze operation characteristics of the single tuned harmonic filters in a power supply system

Ih [%]

3 **Figure 4.** The voltage-current waveforms and spectrum before and after connecting the

<sup>t</sup> -150

Current THDI

9.30 5.23 3.94 24.75 20.4 11

t

0 5 10 15 20 25 30 35 40 45 50 0

n

6.3 1.2 0.9 9.6 4.8 2.4

<sup>0</sup> <sup>5</sup> <sup>10</sup> <sup>15</sup> <sup>20</sup> <sup>25</sup> <sup>30</sup> <sup>35</sup> <sup>40</sup> <sup>45</sup> <sup>50</sup> <sup>0</sup>

n

t

[%]

*I*5 [%] *I*7 [%]

Voltage THDU

t

<sup>0</sup> <sup>5</sup> <sup>10</sup> <sup>15</sup> <sup>20</sup> <sup>25</sup> <sup>30</sup> <sup>35</sup> <sup>40</sup> <sup>45</sup> <sup>50</sup> <sup>0</sup>

n

0 5 10 15 20 25 30 35 40 45 50 0

**3. Parallel operation of filters**

**3.1. Example 2 – description of the system**

n

current harmonic; *U*h/*I*h – h. order voltage/current component

1 2

206 Power Quality Issues


Uh [%]

*U*1 *U* [%]

4 filters

Uh [%]


*U*1 *U* [%]

> Shunt capacitors 2×1.5 MVA connected to main sections 1 and 2 to partially correct the pow‐ er factor but this can cause harmonic problems due to resonance conditions. The sections A and B can be supplying from the main section 1 or 2. Four single-tuned filters (5th, 7th, 11th, and 13th harmonic order) have been added to the sections A and B to limit harmonic prob‐ lems and improve reactive compensation. Specifications of the harmonic filters are shown in the Table 1.

Allowable current limit for filter capacitors is 130% of nominal RMS value and voltage limit -110%. The iron-core reactors take up less space comparatively to air-core reactor and make use of a three-phase core. Reactors built on these cores weigh less, take up less space, have lower losses, and cost less than three single-phase reactors of equal capability. Reactors are manufactured with multi-gap cores of cold laminated steel to ensure low tuning tolerance. The primary draw back to iron-core reactors is that they saturate.

cant difference between these two design criteria. For evaluation purposes, reactor weight and temperature rise are a primary indication of the amount of iron that is used. The second feature of the reactors is considerable frequency dependency of eddy currents loss in the

Equation (1) shows that the relative resonant frequency *nr* depends on the power system fre‐ quency and filter inductance and capacitance. Any variation of these parameters causes de‐ viation of the resonant frequency. So, possible deviation from the designed value can be

> \* \*\* \* \*\* (1 ) (1 )(1 ) (1 ) (1 )(1 ) *d d r n n n f LC f LC* £ £

Assuming *Δ f* <sup>∗</sup> ≈ 0, the possible deviation of relative resonant frequency *nr* from the de‐ signed value for the investigated filter circuits can be defined using values of *ΔL* \*

This means that the analysed filter circuits have the following possible ranges of relative res‐

It is obvious that the detuning of higher order filter is more sensitive for the same filter ca‐ pacitance or inductance drift than detuning of lower order filter, as value of resonant fre‐

> *<sup>d</sup> C C dC C*

2 *r r*

 w

*r*

w

w

D » D =- D

tance variations, p.u.; *nd* - designed relative resonant frequency (*d* = 5, 7, 11, 13).

where: *Δ f* <sup>∗</sup>- power system frequency variation, p.u.; *ΔL* \*

+D +D +D -D -D -D (3)

, *ΔC*\*

Bank Harmonic Filters Operation in Power Supply System − Cases Studies

0.93 1.05 *dr d nn n* £ £ (4)

7-thorder filter 6.5- . ; 7 4 *<sup>r</sup>* £ £ *n* (5)

(6)


http://dx.doi.org/10.5772/53425

209

, *ΔC*\*

winding.

from the Table 1:

onant frequency *nr* :

5-thorder filter - 4.3≤ *nr* ≤ 5.1;

11-th order filter - 10.2≤ *nr* ≤ 11.5;

13-th order filter - 12.1≤ *nr* ≤ 13.7.

quency*ωr* defines its deviation:

obtained using (1) by the equation:


**Table 1.** Filter specifications

The saturation level is dependent upon the fundamental current and the harmonic currents that the reactor will carry. There is not standard for rating harmonic filter reactors and there‐ fore, it is difficult to evaluate reactors from different manufacturers. For example, some reac‐ tor manufacturers base their core designs (cross sectional area of core) on RMS flux, while other will based it on peak flux (with the harmonic flux directly adding). There is a signifi‐ cant difference between these two design criteria. For evaluation purposes, reactor weight and temperature rise are a primary indication of the amount of iron that is used. The second feature of the reactors is considerable frequency dependency of eddy currents loss in the winding.

Equation (1) shows that the relative resonant frequency *nr* depends on the power system fre‐ quency and filter inductance and capacitance. Any variation of these parameters causes de‐ viation of the resonant frequency. So, possible deviation from the designed value can be obtained using (1) by the equation:

$$\frac{n\_d}{(1+\Delta f\_\*)\sqrt{(1+\Delta L\_\*)(1+\Delta C\_\*)}} \le n\_r \le \frac{n\_d}{(1-\Delta f\_\*)\sqrt{(1-\Delta L\_\*)(1-\Delta C\_\*)}}\tag{3}$$

where: *Δ f* <sup>∗</sup>- power system frequency variation, p.u.; *ΔL* \* , *ΔC*\* -filter inductance and capaci‐ tance variations, p.u.; *nd* - designed relative resonant frequency (*d* = 5, 7, 11, 13).

Assuming *Δ f* <sup>∗</sup> ≈ 0, the possible deviation of relative resonant frequency *nr* from the de‐ signed value for the investigated filter circuits can be defined using values of *ΔL* \* , *ΔC*\* from the Table 1:

$$0.93\mathfrak{n}\_d \le \mathfrak{n}\_r \le 1.05\mathfrak{n}\_d \tag{4}$$

This means that the analysed filter circuits have the following possible ranges of relative res‐ onant frequency *nr* :

5-thorder filter - 4.3≤ *nr* ≤ 5.1;

Allowable current limit for filter capacitors is 130% of nominal RMS value and voltage limit -110%. The iron-core reactors take up less space comparatively to air-core reactor and make use of a three-phase core. Reactors built on these cores weigh less, take up less space, have lower losses, and cost less than three single-phase reactors of equal capability. Reactors are manufactured with multi-gap cores of cold laminated steel to ensure low tuning tolerance.

**Filter, tuning Capacitor bank Reactor bank (three phase, iron-core)**

Bank rating 2×500 kvar Nominal voltage 7.2 kV Nominal voltage 6.6 kV Nominal current 120.0 A Nominal current 87.4 A S.c. current 14.0 kA Capacitance 73.1 μF Inductance 6.0 mH Cap. tolerance -5…+10 % Inductance tolerance ± 5 %

Bank rating 2×400 kvar Nominal voltage 7.2 kV Nominal voltage 6.6 kV Nominal current 100.0 A Nominal current 70.0 A S.c. current 14.0 kA Capacitance 58.4 μF Inductance 3.54 mH Cap. tolerance -5…+10 % Inductance tolerance ± 5 %

Bank rating 2×500 kvar Nominal voltage 7.2 kV Nominal voltage 6.6 kV Nominal current 130.0 A Nominal current 87.4 A S.c. current 14.0 kA Capacitance 73.1 μF Inductance 1.16 mH Cap. tolerance -5…+10 % Inductance tolerance ± 5 %

Bank rating 2×500 kvar Nominal voltage 7.2 kV Nominal voltage 6.6 kV Nominal current 130.0 A Nominal current 87.4 A S.c. current 14.0 kA Capacitance 73.1 μF Inductance 0.82 mH Cap. tolerance -5…+10 % Inductance tolerance ± 5 %

The saturation level is dependent upon the fundamental current and the harmonic currents that the reactor will carry. There is not standard for rating harmonic filter reactors and there‐ fore, it is difficult to evaluate reactors from different manufacturers. For example, some reac‐ tor manufacturers base their core designs (cross sectional area of core) on RMS flux, while other will based it on peak flux (with the harmonic flux directly adding). There is a signifi‐

The primary draw back to iron-core reactors is that they saturate.

F5 *n* r5 = 4.81

208 Power Quality Issues

F7 *n* r7 = 6.98

F11 *n* r11 = 10.94

F13 *n* r13 = 13.02

**Table 1.** Filter specifications

$$\text{7-thorder filter - 6.5} \le n\_r \le \text{7.4};\tag{5}$$

11-th order filter - 10.2≤ *nr* ≤ 11.5;

13-th order filter - 12.1≤ *nr* ≤ 13.7.

It is obvious that the detuning of higher order filter is more sensitive for the same filter ca‐ pacitance or inductance drift than detuning of lower order filter, as value of resonant fre‐ quency*ωr* defines its deviation:

$$
\Delta\alpha o\_r \approx \frac{d\,\alpha o\_r}{d\,\text{C}} \Delta\text{C} = -\frac{\alpha o\_r}{2\,\text{C}} \Delta\text{C} \tag{6}
$$

### **3.2. Filter characteristics analysis**

In order to demonstrate filter circuits behavior under all reasonable operating configura‐ tions and get numerical results for comparison purposes, computer simulations have been performed using frequency and time domain software.

**Harmonic order**

monic filters

**Feeder current,** *IS*

**Table 2.** Harmonic currents for the system consisting of 5th harmonic filter

**Drive current,** *ID*

Bank Harmonic Filters Operation in Power Supply System − Cases Studies

**A % A % A %** 241,49 100,0 309,68 100,0 157,87 100,0 8,49 3,5 8,04 2,6 0,61 0,4 9,75 4,0 8,03 2,6 1,77 1,1 41,62 17,2 7,51 2,4 39 24,7 27,02 11,2 68,09 22,0 42,54 26,9 4,31 1,8 6,75 2,2 2,42 1,5 25,43 10,5 30,21 9,8 5,28 3,3 0,74 0,3 0,85 0,3 0,28 0,2 2,81 1,2 3,36 1,1 0,57 0,4 2,92 1,2 3,49 1,1 0,57 0,4 22,09 9,1 26,36 8,5 4,33 2,7 4,16 1,7 5,04 1,6 0,89 0,6 12,7 5,3 15,43 5,0 2,77 1,8 1,21 0,5 1,49 0,5 0,27 0,2 2,79 1,2 3,37 1,1 0,59 0,4 2,84 1,2 3,41 1,1 0,59 0,4 12,14 5,0 14,57 4,7 2,48 1,6 3,52 1,5 4,28 1,4 0,73 0,5 7,35 3,0 8,74 2,8 1,38 0,9

**Figure 7.** Frequency scans for the system impedance with 5th (a), (5+7)-th (b), (5+7+11)-th (c), (5+7+11+13)-th (d) har‐

**5-th filter current,** *IF5*

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211

**Figure 6.** Current and voltage waveforms of the fully loaded DC drive (a) and the current harmonic spectrum (b)

Measurements performed at the facility were used to characterize the DC drive load and ob‐ tain true source data for computer analysis of the filter characteristics. For example, Fig. 6 shows the DC drive current and its harmonic spectrum in the supply system consisting of 5th order filter under isolated operation of the section A.

Harmonic currents in the supply system components are listed in Table 2. There are obvious important findings from these measurements: 1) noncharacteristics current harmonics are present due to irregularities in the conduction of the converter devices, unbalanced phase voltages and other reasons; 2) there is resonance condition near 4th harmonic in the system configuration with 5th filter connected. Similar measurements also provided for the system with other filter sets.

Analysis of the system response is important because the system impedance vs frequency characteristics determine the voltage distortion that will result from the DC drive harmonic currents. For the purposes of harmonic analysis, the DC drive loads can be represented as sources of harmonic currents. The system looks stiff to these loads and the current wave‐ form is relatively independent of the voltage distortion at the drive location. This assump‐ tion of a harmonic current source permits the system response characteristics to be evaluated separately from the DC drive characteristics.

In Fig. 7 are depicted the worst case of frequency scan for system impedance looking from the section A with several filters connected as concerns 5th harmonic filter loading. These conditions occur with upper limit (see (3)) of filter reactor and capacitor rating variations. Proximity of the frequency response resonance peaks to 4th and 5th harmonics produces sig‐ nificant magnification the harmonic currents in the 5th filter and feeder circuits.

Bank Harmonic Filters Operation in Power Supply System − Cases Studies http://dx.doi.org/10.5772/53425 211


**Table 2.** Harmonic currents for the system consisting of 5th harmonic filter

**3.2. Filter characteristics analysis**

210 Power Quality Issues

performed using frequency and time domain software.

order filter under isolated operation of the section A.

evaluated separately from the DC drive characteristics.

with other filter sets.

In order to demonstrate filter circuits behavior under all reasonable operating configura‐ tions and get numerical results for comparison purposes, computer simulations have been

**Figure 6.** Current and voltage waveforms of the fully loaded DC drive (a) and the current harmonic spectrum (b)

Measurements performed at the facility were used to characterize the DC drive load and ob‐ tain true source data for computer analysis of the filter characteristics. For example, Fig. 6 shows the DC drive current and its harmonic spectrum in the supply system consisting of 5th

Harmonic currents in the supply system components are listed in Table 2. There are obvious important findings from these measurements: 1) noncharacteristics current harmonics are present due to irregularities in the conduction of the converter devices, unbalanced phase voltages and other reasons; 2) there is resonance condition near 4th harmonic in the system configuration with 5th filter connected. Similar measurements also provided for the system

Analysis of the system response is important because the system impedance vs frequency characteristics determine the voltage distortion that will result from the DC drive harmonic currents. For the purposes of harmonic analysis, the DC drive loads can be represented as sources of harmonic currents. The system looks stiff to these loads and the current wave‐ form is relatively independent of the voltage distortion at the drive location. This assump‐ tion of a harmonic current source permits the system response characteristics to be

In Fig. 7 are depicted the worst case of frequency scan for system impedance looking from the section A with several filters connected as concerns 5th harmonic filter loading. These conditions occur with upper limit (see (3)) of filter reactor and capacitor rating variations. Proximity of the frequency response resonance peaks to 4th and 5th harmonics produces sig‐

nificant magnification the harmonic currents in the 5th filter and feeder circuits.

**Figure 7.** Frequency scans for the system impedance with 5th (a), (5+7)-th (b), (5+7+11)-th (c), (5+7+11+13)-th (d) har‐ monic filters

Harmonic current magnification in a filter circuit can be defined by the following factor:

$$\beta\_{\rm Fn} = \frac{\left| I\_{\rm Fn} \right|}{\left| I\_{\rm Du} \right|} = \frac{\left| Z\_n \right|}{\left| Z\_{\rm Fn} \right|} \tag{7}$$

The calculated harmonic current magnification factors in filter circuits in the possible filter configurations are depicted in the Table 4. It is here noted that harmonic loading of the fil‐ ters in the system without 2×1.5 Mvar capacitors depends on the filter configuration and fil‐ ter detuning. It is well known that the series L-C circuit has the lowest impedance at its resonant frequency. Below the resonant frequency the circuit behaves as a capacitor and above the resonant frequency as a reactor. When a filter is slightly undertuned to desired harmonic frequency it has lower harmonic absorbing as a result of the harmonic current di‐ viding between the filter and system inductances. If the filter is slightly overtuned than par‐ allel resonant circuit created of the filter capacitance and system inductance will magnify the source harmonic current. Regularity of the phenomena for the analyzed system with multi‐ ply filter circuits one can see in the bottom part of the Table 4 for the system configuration

Switching in capacitors 2×1.5 Mvar to the bus section changes the filters loading due to par‐ allel resonant circuit created of the capacitors and system impedances. The resonant fre‐ quency of the system looking from the section A with several connected filters depends on

With cap. 2×1.5 Mvar Up Lo Up Lo Up Lo Up Lo

F5 0.8 1.1 - - - - - -

F5+F7 1.4 1.0 0.1 0.1 - - - -

F5+F7+F11 2.8 0.9 0.1 0.1 0.6 1.9 - -

F5+F7+F11+F13 18.6 0.8 0.1 0.1 1.3 1.3 0.6 3.2

F5 0.3 1.6 - - - - - -

F5+F7 0.4 1.5 0.5 3.0 - - - -

F5+F7+F11 0.5 1.4 0.7 1.9 0.7 1.3 - -

F5+F7+F11+F13 0.6 1.3 0.8 1.5 2.5 1.0 0.7 2.1

**Deviation limits 5th filter 7th filter 11th filter 13th filter**

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213

without capacitors 2×1.5 Mvar.

**System configuration**

Without cap. 2×1.5 Mvar

the number of the filters and specifies the filter loading.

**Table 4.** Harmonic current magnification factors βFn in the filter circuits

and for the feeder circuit similarly:

$$\beta\_{Sn} = \frac{\left| I\_{Sn} \right|}{\left| I\_{Dn} \right|} = \frac{\left| Z\_n \right|}{\left| Z\_{Sn} \right|} \tag{8}$$

where: *IDn*, *ISn*, *IFn* - the *n*th harmonic current of the harmonic source, feeder and filter, cor‐ respondingly; *Zn*, *ZSn*, *ZFn*- the *n*-th harmonic impedances of the system, feeder and filter at the point of common connection, correspondingly.

The harmonic magnification factor allows estimating harmonic current in a filter or feeder circuit for several system configurations relative to source harmonic current. A value less than 1.0 means that only a part of the source harmonic current flows in the circuit branch.

Calculated values of harmonic magnification factors for analyse 5-th filter loading in the several system configurations are listed in Table 3. Column "Upper deviation limits" with 2×1.5 Mvar capacitors corresponds to the Fig. 7. The significant 4-th and 5-th harmonics magnification can be observed from the Table 3 in the 5-th filter and feeder circuits in the case of 2×1.5 Mvar capacitors connected. It can cause the filter overload and allowable sys‐ tem voltage distortion exceeding. On the other hand when lower deviation of the filter pa‐ rameters the magnification factors are considerably less. Switching off the 2×1.5 Mvar capacitors reduces 5-th harmonic magnification in the circuits to acceptable levels, but 4-th harmonic is magnificated considerably more due to close to resonant peak.


**Table 3.** Harmonic current magnification factors β in the system

The calculated harmonic current magnification factors in filter circuits in the possible filter configurations are depicted in the Table 4. It is here noted that harmonic loading of the fil‐ ters in the system without 2×1.5 Mvar capacitors depends on the filter configuration and fil‐ ter detuning. It is well known that the series L-C circuit has the lowest impedance at its resonant frequency. Below the resonant frequency the circuit behaves as a capacitor and above the resonant frequency as a reactor. When a filter is slightly undertuned to desired harmonic frequency it has lower harmonic absorbing as a result of the harmonic current di‐ viding between the filter and system inductances. If the filter is slightly overtuned than par‐ allel resonant circuit created of the filter capacitance and system inductance will magnify the source harmonic current. Regularity of the phenomena for the analyzed system with multi‐ ply filter circuits one can see in the bottom part of the Table 4 for the system configuration without capacitors 2×1.5 Mvar.

Harmonic current magnification in a filter circuit can be defined by the following factor:

*Fn*

*Sn*

harmonic is magnificated considerably more due to close to resonant peak.

b

at the point of common connection, correspondingly.

b

and for the feeder circuit similarly:

212 Power Quality Issues

**System configuration**

**Table 3.** Harmonic current magnification factors β in the system

Without cap. 2×1.5 Mvar

*Fn n*

= = (7)

= = (8)

**Upper deviation limits Lower deviation limits 5th filter Feeder 5th filter Feeder**

*Dn Fn I Z I Z*

*Sn n*

*Dn Sn I Z I Z*

where: *IDn*, *ISn*, *IFn* - the *n*th harmonic current of the harmonic source, feeder and filter, cor‐ respondingly; *Zn*, *ZSn*, *ZFn*- the *n*-th harmonic impedances of the system, feeder and filter

The harmonic magnification factor allows estimating harmonic current in a filter or feeder circuit for several system configurations relative to source harmonic current. A value less than 1.0 means that only a part of the source harmonic current flows in the circuit branch.

Calculated values of harmonic magnification factors for analyse 5-th filter loading in the several system configurations are listed in Table 3. Column "Upper deviation limits" with 2×1.5 Mvar capacitors corresponds to the Fig. 7. The significant 4-th and 5-th harmonics magnification can be observed from the Table 3 in the 5-th filter and feeder circuits in the case of 2×1.5 Mvar capacitors connected. It can cause the filter overload and allowable sys‐ tem voltage distortion exceeding. On the other hand when lower deviation of the filter pa‐ rameters the magnification factors are considerably less. Switching off the 2×1.5 Mvar capacitors reduces 5-th harmonic magnification in the circuits to acceptable levels, but 4-th

With cap. 2×1.5 Mvar βF4 βF5 βS4 βS5 βF4 βF5 βS4 βS5 F5 4.2 0.8 9.3 1.7 0.5 1.1 2.6 0.4 F5+F7 14.4 1.4 32.2 2.8 0.6 1.0 3.3 0.4 F5+F7+F11 4.8 2.8 10.2 5.5 0.8 0.9 4.5 0.4 F5+F7+F11+F13 2.4 18.6 5.2 36.7 1.4 0.8 7.4 0.3

F5 0.8 0.3 1.9 0.7 0.2 1.6 1.3 0.6 F5+F7 1.1 0.4 2.4 0.8 0.3 1.5 1.4 0.6 F5+F7+F11 1.5 0.5 3.2 1.0 0.3 1.4 1.6 0.5 F5+F7+F11+F13 2.1 0.6 4.5 1.1 0.3 1.3 1.8 0.5 Switching in capacitors 2×1.5 Mvar to the bus section changes the filters loading due to par‐ allel resonant circuit created of the capacitors and system impedances. The resonant fre‐ quency of the system looking from the section A with several connected filters depends on the number of the filters and specifies the filter loading.


**Table 4.** Harmonic current magnification factors βFn in the filter circuits

Figure 8 shows current waveforms and its harmonic spectrums for parallel 11th and 13th har‐ monic filters in the analyzed system obtain from time domain computer simulation of the system. The first observation of these two cases is significant harmonic overloading of the filters. In the case in question of filter iron-core reactor the phenomenon can cause the reac‐ tor temperature rise and its failure.

**System configuration**

Without cap. 2×1.5 Mvar

**Deviation limits**

With cap. 2×1.5 Mvar Up Lo Up Lo Up Lo Up Lo 2×(F5+F7)\* 0.55 0.55 0.50 0.50 - - - - 2×(F5+F7) 0.15 0.91 0.10 0.21 - - - -

2×(F5+F7+F11+F13) 0.18 1.05 0.10 0.16 0.57 1.42 2.92 4.82 (F5+F7)+2×(F11+F13) 18.34 - 0.11 - 0.55 1.44 3.02 5.01

2×(F5+F7)\* 0.41 0.41 0.50 0.50 - - - -

2×(F5+F7+F11+F13) 0.15 0.86 1.21 2.11 0.50 1.23 3.12 5.13 (F5+F7)+2×(F11+F13) 0.84 - 1.23 - 0.48 1.20 3.11 5.04

Double-tuned resonant filters are sometimes used for harmonic elimination of very high power converter systems (e.g. HVDC systems). Just like any other technical solution they al‐ so have their disadvantages (e.g. more difficult tuning process, higher sensitivity of frequen‐ cy characteristic to changes in components values) and advantages (e.g. lower power losses at fundamental frequency, reduced number of reactors across which the line voltage is maintained, compact structure, single breaker) versus single-tuned filters. Such filters prove economically feasible exclusively for very large power installations and therefore they are not commonly used for industrial applications. There are, however, rare cases in which the use of such filter is justified. The double-tuned filter structure and its frequency characteris‐

tics are shown in Fig. 9. There are also the relations used to determine its parameters.

As an example let us design a double-tuned filter (consider alternative configurations pre‐ sented in Fig. 10) with parameters: *Q*F = 1Mvar, *U* = 6kV, *n*1 = 5, *n*2 = 7, *n*R = 6. Locations of the filter frequency characteristic extrema are determined using relations as in Fig. 9, whereas the genetic algorithm (APPENDIX A) determines the values of *C*1 and *C*<sup>2</sup> for which the im‐ pedance-frequency characteristic attains the least value (at chosen harmonic frequencies) for the given filter power (*R*C1, *R*C2, *R*L1,*R*L2 –equivalent capacitor and reactor resistances; Fig. 9).

2×(F5+F7) 0.13 0.77 5.40 9.44

**Table 5.** Harmonic current magnification factors βFn in the filter circuits (parallel operation)

Note. \*Both of 5th filters and 7th filters are fine-tuned.

**4. Double-tuned filter**

**4.1. Example 3**

**5th filters 7th filters 11th filters 13th filters**

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215

**Figure 8.** Current waveforms and its harmonic spectrums for parallel 11th (a) and 13th (b) filters

The most representative cases of the parallel filter configurations (e.g. when feeding sections A and B from section 1) are depicted in the Table 5. Two parallel the same order filters have opposite resonance detuning with upper and lower parameter deviation limits. From analy‐ sis of the Table 5 it is seen that opposite resonance detuning of the same order filters can cause considerable filter overload. As it has been noted earlier the higher order harmonic fil‐ ters are more sensitive to filter component parameter variations from the detuning point of view. Furthermore, resonance detuning of the same order filters in the some system configu‐ rations can cause parallel system resonance peaks close to characteristic harmonic.

It should be quite clear from the above presented example that specifying harmonic filters and power factor correction requires considerable care and attention to detail. Main results of the investigation are follows:



**Table 5.** Harmonic current magnification factors βFn in the filter circuits (parallel operation)

### **4. Double-tuned filter**

Figure 8 shows current waveforms and its harmonic spectrums for parallel 11th and 13th har‐ monic filters in the analyzed system obtain from time domain computer simulation of the system. The first observation of these two cases is significant harmonic overloading of the filters. In the case in question of filter iron-core reactor the phenomenon can cause the reac‐

**Figure 8.** Current waveforms and its harmonic spectrums for parallel 11th (a) and 13th (b) filters

The most representative cases of the parallel filter configurations (e.g. when feeding sections A and B from section 1) are depicted in the Table 5. Two parallel the same order filters have opposite resonance detuning with upper and lower parameter deviation limits. From analy‐ sis of the Table 5 it is seen that opposite resonance detuning of the same order filters can cause considerable filter overload. As it has been noted earlier the higher order harmonic fil‐ ters are more sensitive to filter component parameter variations from the detuning point of view. Furthermore, resonance detuning of the same order filters in the some system configu‐

It should be quite clear from the above presented example that specifying harmonic filters and power factor correction requires considerable care and attention to detail. Main results

**•** improper design of the filter resonant point considering capacitor and reactor manufac‐ turing tolerance and operation conditions can cause significant harmonic overloading of

**•** it is a bad practice to add filter circuits to existing power factor correction capacitors,

**•** it is desirable to avoid the parallel operation of the same order filters in the system.

rations can cause parallel system resonance peaks close to characteristic harmonic.

tor temperature rise and its failure.

214 Power Quality Issues

of the investigation are follows:

the filter,

Double-tuned resonant filters are sometimes used for harmonic elimination of very high power converter systems (e.g. HVDC systems). Just like any other technical solution they al‐ so have their disadvantages (e.g. more difficult tuning process, higher sensitivity of frequen‐ cy characteristic to changes in components values) and advantages (e.g. lower power losses at fundamental frequency, reduced number of reactors across which the line voltage is maintained, compact structure, single breaker) versus single-tuned filters. Such filters prove economically feasible exclusively for very large power installations and therefore they are not commonly used for industrial applications. There are, however, rare cases in which the use of such filter is justified. The double-tuned filter structure and its frequency characteris‐ tics are shown in Fig. 9. There are also the relations used to determine its parameters.

### **4.1. Example 3**

As an example let us design a double-tuned filter (consider alternative configurations pre‐ sented in Fig. 10) with parameters: *Q*F = 1Mvar, *U* = 6kV, *n*1 = 5, *n*2 = 7, *n*R = 6. Locations of the filter frequency characteristic extrema are determined using relations as in Fig. 9, whereas the genetic algorithm (APPENDIX A) determines the values of *C*1 and *C*<sup>2</sup> for which the im‐ pedance-frequency characteristic attains the least value (at chosen harmonic frequencies) for the given filter power (*R*C1, *R*C2, *R*L1,*R*L2 –equivalent capacitor and reactor resistances; Fig. 9).

$$\begin{aligned} \rho o\_R &= \frac{1}{\sqrt{L\_2 C\_2}} \quad \Rightarrow \quad L\_2 = \frac{1}{o\_R^2 C\_2} \\ \rho o\_S &= \frac{1}{\sqrt{L\_1 C\_1}} \quad \Rightarrow \quad L\_1 = \frac{1}{o\_S^2 C\_1} \\ \rho o\_S &= \frac{o\_{n1} o\_{n2}}{o\_R} \\ \mathbf{C}\_2 &= \frac{o\_S^2}{o\_{n1}^2 + o\_{n2}^2 - o\_R^2 - o\_S^2} \mathbf{C}\_1 \\ \mathbf{C}\_1 &= \left[ o\_1 \left( \frac{o\_R}{o\_{n1} o\_{n2}} \right)^2 - \frac{1}{o\_1} + \frac{o\_1 \left[ \left( o\_{n1}^2 + o\_{n2}^2 - o\_R^2 \right) o\_R^2 - o\_{n1}^2 o\_{n2}^2 \right]}{o\_{n1}^2 o\_{n2}^2 \left( o\_R^2 - o\_1^2 \right)} \right] \frac{\mathbf{U}^2}{\mathbf{Q}\_F} \end{aligned} \tag{9}$$

a) C1 L1

L2 R2 C2

C1 L1

L C2 2

**Figure 10.** Alternative configurations of a double-tuned filter

NIEC = STOP)

C1 L1

R1

e)

R2

d) C1

L2 C2

L1

L2 R2

**Figure 11.** Graphic window of the program determining parameters one of the double-tuned filter in Fig. 10a (KO‐

R1 b) C1

C2

L1

Bank Harmonic Filters Operation in Power Supply System − Cases Studies

c)

R1

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217

R2

R1

C2 L2

C1 L1

f)

L C2 2

**Figure 9.** The double-tuned filter and its essential frequency characteristics;the basic configuration and frequency characteristics of: the series part, parallel part, and the whole filter (ωR – angular resonance frequency of the parallel part; ωS – angular resonance frequency of the series part; ωn1, ωn2 – tuned angular frequencies of the double-tuned filter; equation 9 R 0).

Figure 11 shows graphic window of the programme developed by authors in the Matlab en‐ vironment for optimisation of double-tuned filter. Ranges of filter parameters seeking are visible in the upper part of the widow, below the found characteristic is displayed, and basic parameters of the found solution are shown in the lowest part.

Bank Harmonic Filters Operation in Power Supply System − Cases Studies http://dx.doi.org/10.5772/53425 217

**Figure 10.** Alternative configurations of a double-tuned filter

2 2

*R*

w

*S*

w

1 2

1 1 22 2 2

 w

Parallel part (*ZR*)

wn1 wn2 *f* [Hz] *f* [Hz]

wS

**Figure 9.** The double-tuned filter and its essential frequency characteristics;the basic configuration and frequency characteristics of: the series part, parallel part, and the whole filter (ωR – angular resonance frequency of the parallel part; ωS – angular resonance frequency of the series part; ωn1, ωn2 – tuned angular frequencies of the double-tuned

Figure 11 shows graphic window of the programme developed by authors in the Matlab en‐ vironment for optimisation of double-tuned filter. Ranges of filter parameters seeking are visible in the upper part of the widow, below the found characteristic is displayed, and basic


parameters of the found solution are shown in the lowest part.

]

Series part (*ZS*)

w w w w w ww

12 1 12 1

*<sup>U</sup> <sup>C</sup>*

ì ü æ ö é ù +- - ï ï ë û = -+ í ý ç ÷ ï ï è ø - î þ

( ) 1

*n n R R nn <sup>R</sup> n n nn R F*

ww

<sup>2</sup> 2 2 2 2 22 <sup>2</sup> 11 2 1 2

 w w

( )


]

*Q*

w<sup>R</sup> *f*[Hz]

(9)

2 2 2

*L L C C*

*L L C C*

1 1

= Þ=

= Þ=

1 1 1

1 1

2 2 1 2 2 22 1 2

*S n n RS*

w

*C C*

<sup>=</sup> + --

w

ww

C1 L1

RC1+RL1

RC2 C2


filter; equation 9 R 0).

]

RL2

L2

1 2

*R*

*n n*

w

w w

w w ww

w

*R*

w

216 Power Quality Issues

*S*

w

*S*

=

w

**Figure 11.** Graphic window of the program determining parameters one of the double-tuned filter in Fig. 10a (KO‐ NIEC = STOP)

The range of variability of decision variables: *C*1 = (10-6 – 10-3), *C*2 = (10-6 – 10-3). The Genetic Algorithm parameters: (a) each parameter is encoded into a 30-bit string, thus the chromo‐ some length is 60 bits; (b) population size 1000 individuals; (c) crossover probability *pk* = 0.7; (d) mutation probability *pm* = 0.01; (e) Genetic Algorithm termination condition – 100 genera‐ tions; (f) ranking coefficients *C*min = 0, *C*max = 2; (g) inverse ranking was applied in order to minimize the objective function; (h) selection method SUS and (i) shuffling crossover. The Genetic Algorithm goal was to minimize impedances for selected harmonics (*n*1 and *n*2) and maximize the impedance for the *n*R harmonic.

**5. C-type filter**

large power losses.

**Figure 12.** The C-type filter circuit

*5.1.1. Traditional approach*

slight increase in the voltage 2nd harmonic.

The filter impedance is given by (Fig. 12) [1]:

**5.1. Example 4**

The principal disadvantage of the majority of filter-compensating device structures is the poor filtering of high frequencies. To eliminate this disadvantage are usually used broad‐ band (damped) filters of the first, second or third order; the C-type filter is included in the category of broadband filters [1, 2, 10]. Broadband filters have one more advantage, substan‐ tial for their co-operation with power electronic converters: they damp commutation notch‐ es more effectively than single branch filters - they have a much broader bandwidth. They also more effectively eliminate interharmonic components (in sidebands adjacent to charac‐ teristic harmonics) generated by static frequency converters. In the C-type filter in which the *L*2*C*2 branch (Fig. 12) is tuned to the fundamental harmonic frequency can be also achieved a significantly better reduction of active power losses compared to single branch filters. Thus the fundamental harmonic current is not passing through the resistor *R*T, avoiding therefore

*R*<sup>T</sup>

*U*

*L*2

*C*<sup>2</sup>

**Load**

Bank Harmonic Filters Operation in Power Supply System − Cases Studies

http://dx.doi.org/10.5772/53425

219

*C*<sup>1</sup>

*I*S *I*F *I*load

In result of the arc furnace modernization (Fig. 13.) its power and consequently the level of load-generated harmonics have increased. It was, therefore, decided to expand the existing reactive power compensation and harmonic mitigation system. Prior to the modernization the system comprised two parallel, single-tuned 3rd harmonic filters that were the cause of a

Considering the system expansion the designed C-type filter should be tuned to the 2nd harmonic. Although currently the 2nd harmonic level in the existing system does not exceed the limit, connection of new loads may increase the 2nd harmonic to an unacceptable level.

Table 6 provides results of a double-tuned filter (Fig. 9 and 10) optimisation. The solutions are similar to each other (in terms of their values). It is noticeable that genetic algorithm is aiming to minimize the influence of additional resistances, that is to make the filter struc‐ tures similar to the basic structure from Fig. 9. It means that additional resistances worsen the quality of filtering. The obtained result ensues from the applied optimisation method, i.e. optimisation of the frequency characteristic shape.


**Table 6.** Basic parameters of filters from Fig. 10, designed using the genetic algorithm

### **5. C-type filter**

The range of variability of decision variables: *C*1 = (10-6 – 10-3), *C*2 = (10-6 – 10-3). The Genetic Algorithm parameters: (a) each parameter is encoded into a 30-bit string, thus the chromo‐ some length is 60 bits; (b) population size 1000 individuals; (c) crossover probability *pk* = 0.7; (d) mutation probability *pm* = 0.01; (e) Genetic Algorithm termination condition – 100 genera‐ tions; (f) ranking coefficients *C*min = 0, *C*max = 2; (g) inverse ranking was applied in order to minimize the objective function; (h) selection method SUS and (i) shuffling crossover. The Genetic Algorithm goal was to minimize impedances for selected harmonics (*n*1 and *n*2) and

Table 6 provides results of a double-tuned filter (Fig. 9 and 10) optimisation. The solutions are similar to each other (in terms of their values). It is noticeable that genetic algorithm is aiming to minimize the influence of additional resistances, that is to make the filter struc‐ tures similar to the basic structure from Fig. 9. It means that additional resistances worsen the quality of filtering. The obtained result ensues from the applied optimisation method,

*C*1 [μF] 85.52 85.52 85.52 85.53 85.53 85.53 85.53 *C*2[μF] 732.21 732.73 732.72 732.71 732.71 732.72 731.90 *L*1[mH] 3.481 3.481 3.482 3.482 3.482 3.482 3.482 *L*2 [mH] 0.384 0.384 0.384 0.384 0.384 0.384 0.385 *R*L1 [mΩ] 10.93 10.94 10.94 10.93 10.94 10.94 10.94 *R*L2 [mΩ] 1.207 1.207 1.207 1.207 1.207 1.207 1.208 *R*C1 [mΩ] 7.44 7.44 7.44 7.44 7.44 7.44 7.44 *R*C2 [mΩ] 0.869 0.868 0.868 0.868 0.868 0.868 0.870 *Z*50 [Ω] 36 36 36 36 36 36 36 *Z*250 [mΩ] 35.82 35.8 35.83 35.85 35.79 35,85 35.86 *Z*300 [Ω] 252.76 252.58 252.53 252.47 252.59 252.53 252.87 *Z*350 [mΩ] 40 40 40.04 40.01 40 40.01 40 *Q*F[MVAr] 1 1 1 1 1 1 1 *P*50 [W] 546.09 546.06 546.10 546,11 546.07 546.11 546.11 *R*1 [MΩ] - 1 1 1 - 1 - *R*2 [MΩ] 1 - 1 1 0 - -

**Filter configuration Fig. 10a Fig. 10b Fig. 10c Fig. 10d Fig. 10e Fig. 10f Fig. 9**

maximize the impedance for the *n*R harmonic.

i.e. optimisation of the frequency characteristic shape.

**Table 6.** Basic parameters of filters from Fig. 10, designed using the genetic algorithm

**Parameter**

218 Power Quality Issues

The principal disadvantage of the majority of filter-compensating device structures is the poor filtering of high frequencies. To eliminate this disadvantage are usually used broad‐ band (damped) filters of the first, second or third order; the C-type filter is included in the category of broadband filters [1, 2, 10]. Broadband filters have one more advantage, substan‐ tial for their co-operation with power electronic converters: they damp commutation notch‐ es more effectively than single branch filters - they have a much broader bandwidth. They also more effectively eliminate interharmonic components (in sidebands adjacent to charac‐ teristic harmonics) generated by static frequency converters. In the C-type filter in which the *L*2*C*2 branch (Fig. 12) is tuned to the fundamental harmonic frequency can be also achieved a significantly better reduction of active power losses compared to single branch filters. Thus the fundamental harmonic current is not passing through the resistor *R*T, avoiding therefore large power losses.

**Figure 12.** The C-type filter circuit

### **5.1. Example 4**

In result of the arc furnace modernization (Fig. 13.) its power and consequently the level of load-generated harmonics have increased. It was, therefore, decided to expand the existing reactive power compensation and harmonic mitigation system. Prior to the modernization the system comprised two parallel, single-tuned 3rd harmonic filters that were the cause of a slight increase in the voltage 2nd harmonic.

Considering the system expansion the designed C-type filter should be tuned to the 2nd harmonic. Although currently the 2nd harmonic level in the existing system does not exceed the limit, connection of new loads may increase the 2nd harmonic to an unacceptable level.

### *5.1.1. Traditional approach*

The filter impedance is given by (Fig. 12) [1]:

**Figure 13.** Single line diagram of the arc furnace power supply system

$$Z\_F = \frac{\left(joL\_2 - j\frac{1}{o\mathcal{C}\_2}\right)R\_T}{R\_T + joL\_2 - j\frac{1}{o\mathcal{C}\_2}} - j\frac{1}{o\mathcal{C}\_1} \tag{10}$$

1000

1500

The *L*2 and *C*2 components are tuned to the fundamental frequency 1: 6 *q*F2=20 *q*F2=20

*q*F2=15

(a)

*n*/*n*<sup>r</sup>

<sup>0</sup> <sup>1</sup> <sup>2</sup> <sup>3</sup> <sup>4</sup> <sup>5</sup> <sup>6</sup> <sup>0</sup>

**Figure 13.** Single line diagram of the arc furnace power supply system

$$L\_2 = \frac{1}{\alpha\_1^2 C\_2} \tag{11}$$

*k* =0.33 *R* = 840

> (b) 1 *k*

0 0.2 0.4 0.6 0.8 1.2 1.4 1.6

hence

vs. the coefficient *k*

*r F X Z*

2

4

8

10

12

$$Z\_F = \frac{jR\_T\left(\alpha^2 - \alpha\_1^2\right)}{R\_T\alpha\alpha\_1^2C\_2 + j\left(\alpha^2 - \alpha\_1^2\right)} - j\frac{1}{\alpha C\_1} \tag{12}$$

**Figure 15.** a) The C-type filter frequency characteristics for various quality factors *q*F = *R*T/*X*r, b) the resistance *R*<sup>T</sup>

*q*F2=15

The C-type filter is tuned to the resonance angular frequency *ω<sup>r</sup>* =*nrω*<sup>1</sup>

$$\alpha\_r \equiv \frac{1}{\sqrt{L\_2 \frac{C\_1 C\_2}{C\_1 + C\_2}}} \Longrightarrow C\_2 = C\_1 \left(n\_r^2 - 1\right) \tag{13}$$

10

hence

that is:

( )


1

The filter reactive power (QF) for the fundamental harmonic is given by the relation:

( ( )) 2

*F <sup>U</sup> <sup>Q</sup> Q C <sup>Z</sup>* w

*T*

<sup>1</sup> <sup>1</sup> Im

( )


*jR U <sup>U</sup> Z j R Q n jU Q*

*In Zn <sup>U</sup> <sup>k</sup> <sup>R</sup> U nQ k L I n Zn nQ k L*

w w

( ) ( )

*T Fr F*


2 22 2 1 1 1

Distribution of the load-generated harmonic current between the filter tuned to that har‐

2

Summarizing, the C-type filter parameters can be determined from above formulas. For the

3rd harmonic filters *Q*<sup>F</sup> = 20 Mvar *L*<sup>3</sup> = 18.48 mH *C*<sup>3</sup> = 63 F *R*<sup>3</sup> = 30.0 m *n*<sup>r</sup> = 2.95

(supply network) *k* = 1

The C-type filter parameters are: *C*1 =70.736μF, *C*2 =198.24μF, *L*2 =51.11mH, *R*T =276.86 Ω.

Figure 14a shows frequency-impedance characteristics of: the power network, the resultant impedance of two single-tuned 3rd harmonic filters, and the C-type filter impedance. Fig. 14b shows frequency-impedance characteristics of: the network, the resultant impedance of the network and two 3rd harmonic filters, and the resultant impedance of the network, two 3rd

1

(supply network) (filter quality factor)

w

w w

*T*

*jR Z j*

*T r*

ww

*F*

ww

> ( ) ( )

*Fr Sr rF S*

arc furnace power supply system (Fig. 13) and the design requirements:

*F*

*F*

*Sr Fr*

monic and the system is:

( ) ( )

Network *U* = 30 kV *S*sc= 1500 MVA *L*<sup>S</sup> = 3.129 mH *R*<sup>S</sup> = 30.0 m

harmonic filters and the C-type filter.

2 2 1 2 2 22 1 1 1 1

( ) ( )


w w

1 2

w*U*

22 2 <sup>2</sup> <sup>1</sup> <sup>1</sup>

w w *F*

*R Cn j C*

1

Bank Harmonic Filters Operation in Power Supply System − Cases Studies

=- Þ = (15)

w

w

4 4 22 22

C-type filter *Q*<sup>F</sup> = 20 Mvar *n*<sup>r</sup> = 1.9 *q*F2 = 10

w

3 2 1

== Þ = - (17)

*T rF S*

(14)

221

http://dx.doi.org/10.5772/53425

(16)

w

hence

$$Z\_F = \frac{jR\_T\left(\alpha^2 - \alpha\_1^2\right)}{R\_T\alpha\alpha\_1^2C\_1\left(n\_r^2 - 1\right) + j\left(\alpha^2 - \alpha\_1^2\right)} - j\frac{1}{\alpha C\_1} \tag{14}$$

The filter reactive power (QF) for the fundamental harmonic is given by the relation:

$$Q\_F = -\frac{\mathcal{U}^2}{\text{Im}\left(Z\_F\left(o\_1\right)\right)} \Longrightarrow \mathcal{C}\_1 = \frac{Q\_F}{o\_1\mathcal{U}^2} \tag{15}$$

that is:

2

*T*

The *L*2 and *C*2 components are tuned to the fundamental frequency 1:

w

**Figure 13.** Single line diagram of the arc furnace power supply system

*F*

*q*F2=20

*q*F2=10 *q*F2=15

**FC** 

**Figure 13.** Single line diagram of the arc furnace power supply system

Ssc = 75 MVA 110/30kV

**Q1**

30/1.2kV 115MVA

*F*

w

*T*

*jR Z j*

ww

(a)

*n*/*n*<sup>r</sup>

<sup>0</sup> <sup>1</sup> <sup>2</sup> <sup>3</sup> <sup>4</sup> <sup>5</sup> <sup>6</sup> <sup>0</sup>

The C-type filter is tuned to the resonance angular frequency *ω<sup>r</sup>* =*nrω*<sup>1</sup>

2

*C C <sup>L</sup> C C*

1 2

1 2

+

hence

vs. the coefficient *k*

*r F X Z*

220 Power Quality Issues

2

4

6

8

10

12

2

1

2

*C C C C <sup>L</sup> <sup>X</sup>*

*q*F2=10

*q*F2=15

1 *T*

30 kV

110 kV

**P5**

**Q3**

**F3** 

w

*q*F2=20

2

2 2 1 2

( )


w w

2 2 1 2 22 1 1 2 1 *<sup>T</sup>* 1

*R Cj C*

 w w

<sup>1</sup> <sup>1</sup> *r r C Cn*

@ Þ= -

( )

2 1

<sup>1</sup> *<sup>L</sup>* w

w

*Z j <sup>C</sup> R jL j <sup>C</sup>*

<sup>r</sup>

*jL j R <sup>C</sup>*

æ ö ç ÷ è ø <sup>=</sup> - + -

**F3** 

**XC3 XC3**

**Q3**

**P2 P P4 <sup>3</sup> P1**

Ssc = 1500 MVA

**XL3 XL3 XL2**

w

1

*R*T

**F2**

**Q2**

**RT**

w

**Figure 15.** a) The C-type filter frequency characteristics for various quality factors *q*F = *R*T/*X*r, b) the resistance *R*<sup>T</sup>

( ) <sup>2</sup>

*<sup>C</sup>* <sup>=</sup> (11)

*k* =0.33 *R* = 840

0 500

1000

1500

2000

2500

3000

Ssc = 75 MVA 110/30kV

(10)

(12)

(b) 1 *k*

*k* = 1 *R* = 276.86

0 0.2 0.4 0.6 0.8 1.2 1.4 1.6

(13)

10

1

w

**XC2 XC1**

$$Z\_F = \frac{jR\_T \mathcal{U}^2 \left(\alpha^2 - \alpha\_1^2\right)}{R\_T \alpha o o\_1 \mathcal{Q}\_F \left(n\_r^2 - 1\right) + j \mathcal{U}^2 \left(\alpha^2 - \alpha\_1^2\right)} - j \frac{o\_1 \mathcal{U}^2}{o \mathcal{Q}\_F} \tag{16}$$

Distribution of the load-generated harmonic current between the filter tuned to that har‐ monic and the system is:

$$\frac{\left|I\_{\rm S}\left(n\_{r}\right)\right|}{\left|I\_{\rm F}\left(n\_{r}\right)\right|} = k = \frac{\left|Z\_{\rm F}\left(n\_{r}\right)\right|}{\left|Z\_{\rm S}\left(n\_{r}\right)\right|} \Longrightarrow R\_{\rm T} = \frac{\mathcal{U}^{2}}{n\_{r}^{3}\mathbb{Q}\_{\rm F}{}^{2}k o\_{1}L\_{\rm S}}\sqrt{\mathcal{U}^{4} - n\_{r}^{4}\mathcal{Q}\_{\rm F}{}^{2}k^{2}o\_{1}^{2}L\_{\rm S}^{2}}\tag{17}$$

Summarizing, the C-type filter parameters can be determined from above formulas. For the arc furnace power supply system (Fig. 13) and the design requirements:


The C-type filter parameters are: *C*1 =70.736μF, *C*2 =198.24μF, *L*2 =51.11mH, *R*T =276.86 Ω.

Figure 14a shows frequency-impedance characteristics of: the power network, the resultant impedance of two single-tuned 3rd harmonic filters, and the C-type filter impedance. Fig. 14b shows frequency-impedance characteristics of: the network, the resultant impedance of the network and two 3rd harmonic filters, and the resultant impedance of the network, two 3rd harmonic filters and the C-type filter.

**Figure 14.** Frequency-impedance characteristics of: a) the power network equivalent impedance (ZS), the resultant impe‐ dance of two 3rd harmonic filters (Z2x3h), the C-type filter impedance (ZCfilter), the resultant impedance of two 3rd harmonic filters and the C-type filter (ZF); b) the impedance seen from the load terminals: without filters (ZS), the network equivalent impedance and two 3rd harmonic filters impedance connected in parallel (*Z*s||Z2x3h), and parallel connection of the net‐ work equivalent impedance, two 3rd harmonic filters and the C-type filter impedances (Zs||Z2x3h||ZCfilter)

Data listed in Table 7 demonstrate that connecting the C-type filter results in the expected re‐ duction of the 2nd voltage harmonic in the supply system, whereas other harmonics are re‐ duced to a small extent. Further reduction of the second harmonic can be achieved by improving the C-type filter quality factor *qF2* and, consequently, reduction of the filter impe‐ dance for the filter resonant frequency and increasing the impedance for higher harmonics.


instead of the supply network. But the increase in the resistance will reduce high harmonic currents through the filter. Thus a compromise between the filter ability to take over the har‐ monic the filter is tuned to, and its capability to mitigate other harmonics should found. In‐ creasing the *R*<sup>T</sup> resistance makes the C-type filter frequency characteristic similar to that of a

**Figure 15.** a) The C-type filter frequency characteristics for various quality factors *q*F = *R*T/*X*r, b) the resistance *R*<sup>T</sup>

*IF [%]* 38.5 44.4 50.0 51.9 57.1 66.6 75.0 83.3 91.0

*IS [%]* 61.5 55.6 50.0 48.1 42.9 33.3 25.0 16.7 9.0

*k* 1.60 1.25 1.00 0.93 0.75 0.50 0.33 0.25 0.10

*RT* **[Ω]** 172 221 276.86 300 350 555 840 1111 2778

**Table 8.** The percentage distribution of the harmonic current between the filter tuned to that harmonic and the

**Figure 15.** a) The C-type filter frequency characteristics for various quality factors *q*F = *R*T/*X*r, b) the resistance *R*T vs. the

> (b) 1 *k*

*k* = 1 *R* = 276.86

http://dx.doi.org/10.5772/53425

223

0 0.2 0.4 0.6 0.8 1.2 1.4 1.6

Bank Harmonic Filters Operation in Power Supply System − Cases Studies

*k* =0.33 *R* = 840

Ssc = 75 MVA 110/30kV

**F2**

*R*T

**Q2**

**RT**

30 kV

110 kV

**P5**

**Q3**

**XC2 XC1**

**F3** 

*q*F2=20

<sup>r</sup>

*q*F2=10 *q*F2=15

1 2 1 2 2 *C C C C <sup>L</sup> <sup>X</sup>*

The goal of genetic algorithm is to seek the C-type filter capacitance (*C*1) in order to compen‐ sate the system's reactive power, and determine the resistance value (*R*T) to ensure a re‐ quired distribution of the 2nd harmonic current. The filter parameters were computed by means of the Genetic Algorithm using the model from Fig. 13 in the Matlab environment. The arc furnace is regarded as an ideal harmonic current source and as a load for the funda‐

10

The range of variability of decision variables: *C*1 = (10-6 – 10-4F), *R*<sup>T</sup> = (1 – 10000) . The Genetic Algorithm parameters: (a) parameter *C*1 is encoded into 8-bit strings, and parameter *R*<sup>T</sup> into a 12-bit string; (b) population size 200 individuals; (c) crossover probability *p*<sup>k</sup> = 0.8; (d) mu‐ tation probability *p*<sup>m</sup> = 0,01; (e) Genetic Algorithm termination condition – 30 generations; (f) ranking coefficients *C*min = 0, *C*max = 2; (g) inverse ranking was applied in order to minimize the objective function; (h) selection method SUS and (i) shuffling crossover. The optimiza‐

mental harmonic with given active power (*P*) and reactive power (*Q*).

**Figure 13.** Single line diagram of the arc furnace power supply system

*q*F2=10 *q*F2=15 *q*F2=20

(a)

supply network; the corresponding *R*T values and the designed filter quality factor.

*n*/*n*<sup>r</sup>

<sup>0</sup> <sup>1</sup> <sup>2</sup> <sup>3</sup> <sup>4</sup> <sup>5</sup> <sup>6</sup> <sup>0</sup>

**FC** 

Ssc = 75 MVA 110/30kV

**Q1**

30/1.2kV 115MVA

**F3** 

**XC3 XC3**

**Q3**

**P2 P P4 <sup>3</sup> P1**

Ssc = 1500 MVA

**XL3 XL3 XL2**

single-branch filter.

vs. the coefficient *k*

coefficient *k*

*r F X Z*

*5.1.2. Genetic approach*

\*Total harmonic voltage distortion factor THDu determined from components up to 15th order.

**Table 7.** Voltage harmonics (at the 30kV side) without filters, with two 3rd harmonic filters, and with two 3rd harmonic filters and the C-type filter

Figure 15a shows the C-type filter frequency characteristics for different filter quality fac‐ tors, figure 15b illustrates the relation between the resistance *R*<sup>T</sup> and the coefficient *k* that in‐ dicates the distribution of the current harmonic to which the filter is tuned (Table 8).

Seemingly, the most advantageous solution is to increase the filter resistance *R*T in order to ensure the largest possible part of the eliminated harmonic current flow through the filter

Ssc = 75 MVA 110/30kV

10

**F2**

**Q2**

**RT**

30 kV

110 kV

**P5**

**Q3**

**XC2 XC1**

**F3** 

**Figure 13.** Single line diagram of the arc furnace power supply system

**FC** 

Ssc = 75 MVA 110/30kV

**Q1**

30/1.2kV 115MVA

**F3** 

**XC3 XC3**

**Q3**

**P2 P P4 <sup>3</sup> P1**

Ssc = 1500 MVA

**XL3 XL3 XL2**

vs. the coefficient *k* **Figure 15.** a) The C-type filter frequency characteristics for various quality factors *q*F = *R*T/*X*r, b) the resistance *R*T vs. the coefficient *k*

**Figure 15.** a) The C-type filter frequency characteristics for various quality factors *q*F = *R*T/*X*r, b) the resistance *R*<sup>T</sup>


**Table 8.** The percentage distribution of the harmonic current between the filter tuned to that harmonic and the supply network; the corresponding *R*T values and the designed filter quality factor.

instead of the supply network. But the increase in the resistance will reduce high harmonic currents through the filter. Thus a compromise between the filter ability to take over the har‐ monic the filter is tuned to, and its capability to mitigate other harmonics should found. In‐ creasing the *R*<sup>T</sup> resistance makes the C-type filter frequency characteristic similar to that of a single-branch filter.

### *5.1.2. Genetic approach*

**Figure 14.** Frequency-impedance characteristics of: a) the power network equivalent impedance (ZS), the resultant impe‐ dance of two 3rd harmonic filters (Z2x3h), the C-type filter impedance (ZCfilter), the resultant impedance of two 3rd harmonic filters and the C-type filter (ZF); b) the impedance seen from the load terminals: without filters (ZS), the network equivalent impedance and two 3rd harmonic filters impedance connected in parallel (*Z*s||Z2x3h), and parallel connection of the net‐

Data listed in Table 7 demonstrate that connecting the C-type filter results in the expected re‐ duction of the 2nd voltage harmonic in the supply system, whereas other harmonics are re‐ duced to a small extent. Further reduction of the second harmonic can be achieved by improving the C-type filter quality factor *qF2* and, consequently, reduction of the filter impe‐ dance for the filter resonant frequency and increasing the impedance for higher harmonics.

**% U2 U3 U4 U5 U6 U7 U8 U9 THDU \***

without filters 1,76 3.01 1.66 2.88 1.12 1.75 1.00 1,12 5.87

\*Total harmonic voltage distortion factor THDu determined from components up to 15th order.

**Table 7.** Voltage harmonics (at the 30kV side) without filters, with two 3rd harmonic filters, and with two 3rd

dicates the distribution of the current harmonic to which the filter is tuned (Table 8).

Figure 15a shows the C-type filter frequency characteristics for different filter quality fac‐ tors, figure 15b illustrates the relation between the resistance *R*<sup>T</sup> and the coefficient *k* that in‐

Seemingly, the most advantageous solution is to increase the filter resistance *R*T in order to ensure the largest possible part of the eliminated harmonic current flow through the filter

2.47 0,27 0.95 1.87 0.78 1.24 0.72 0.81 4.07

1.32 0.27 0.91 1.78 0.74 1.18 0.69 0.78 3.37

work equivalent impedance, two 3rd harmonic filters and the C-type filter impedances (Zs||Z2x3h||ZCfilter)

Busbars voltage harmonics

Busbars voltage harmonics with two 3rd harmonic filters

Busbars voltage harmonics with two 3rd harmonic filters and the

harmonic filters and the C-type filter

C-type filter

222 Power Quality Issues

The goal of genetic algorithm is to seek the C-type filter capacitance (*C*1) in order to compen‐ sate the system's reactive power, and determine the resistance value (*R*T) to ensure a re‐ quired distribution of the 2nd harmonic current. The filter parameters were computed by means of the Genetic Algorithm using the model from Fig. 13 in the Matlab environment. The arc furnace is regarded as an ideal harmonic current source and as a load for the funda‐ mental harmonic with given active power (*P*) and reactive power (*Q*).

The range of variability of decision variables: *C*1 = (10-6 – 10-4F), *R*<sup>T</sup> = (1 – 10000) . The Genetic Algorithm parameters: (a) parameter *C*1 is encoded into 8-bit strings, and parameter *R*<sup>T</sup> into a 12-bit string; (b) population size 200 individuals; (c) crossover probability *p*<sup>k</sup> = 0.8; (d) mu‐ tation probability *p*<sup>m</sup> = 0,01; (e) Genetic Algorithm termination condition – 30 generations; (f) ranking coefficients *C*min = 0, *C*max = 2; (g) inverse ranking was applied in order to minimize the objective function; (h) selection method SUS and (i) shuffling crossover. The optimiza‐ tion goal was to minimize total harmonic distortion of the supply network current THDI and reduce the angle between fundamental voltage and current harmonics *φ*(*I*(1),*U*(1)) - (18).

$$F\_{g\text{out}} = \begin{cases} THD\_I + \sin\left(\wp\left(I\_{\text{(1)}}, U\_{\text{(1)}}\right)\right) & Q\_F \le 20 \text{Mvar} \\ 100 \cdot \left( THD\_I + \sin\left(\wp\left(I\_{\text{(1)}}, U\_{\text{(1)}}\right)\right)\right) & Q\_F > 20 \text{Mvar} \end{cases} \tag{18}$$

According with the achieved results the total capacitance *C*1 = 70.75μF and total capacitance *C*<sup>2</sup> = 196.8μF. The reactor *L*2 inductance is 51.48mH. The resistor resistance is *R*T= 300Ω ± 10%.

Measurements in the power system, configured according to the above specification, were carried out in order to check the correctness of the system operation. The instruments loca‐ tions were (fig. 13): *P*1 – arc furnace, *P*2 – C-type filter, *P*3 – first filter of the 3rd harmonic, *P*<sup>4</sup> – second filter of the 3rd harmonic, and *P*5 – at the 110kV side. Essential results of measure‐ ments are provided in Table 9.

Figures 16 – 18 illustrate voltage and current waveforms recorded at the 110kV side, the arc furnace supply voltage the arc furnace and the C-type filter currents and total harmonic voltage distortion factor THDU at both: the 30kV and 110kV side. The measurements have demonstrated that the C-type filter performance has met the requirements, i.e. it attains the expected reduction of reactive power, ensures the second harmonic reduction in the power system and harmonic distortion THDU reduction by means of high harmonics mitigation. The measurements verified the proposed method and the C-type filter designed using this method operates according to the requirements.

### **6. Conclusion**

This chapter presents several selected cases of power electronic systems analysis with re‐ spect to high harmonics occurrence and reactive power compensation. For these cases are proposed classical solutions, i.e. power passive filters which still are a basic and the simplest method for high harmonics mitigation. Analytical formulas that enable to determine basic parameters of various filters' structures and a group of single-tuned filters are provided.

Also a method for passive filters' design employing artificial intelligence, which incorpo‐ rates genetic algorithms, is presented. It has been proved that this method can be the attrac‐ tive tool to solve some kinds of power quality problems. The results obtained using GA are very close to those obtained with the analytical method. Hence the conclusion that genetic algorithms can be an efficient tool for passive filters design. The advantage of the method employing genetic algorithms is the possibility of multi-criterial optimisation and taking in‐ to account at the design stage different (e.g. voltage or current) constraints. It also can be ap‐ plied to filters of various structures and degrees of complexity and can account for filters' resistance that may influence the filter resonance frequency. In other words, genetic algo‐ rithm can be a useful design tool in cases where the system analysis is too complex or even not possible.

**Figure 16.** Voltage and current characteristics, spectrums and THD factors at 110 kV side. The graphs show two time

Bank Harmonic Filters Operation in Power Supply System − Cases Studies

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225

characteristics: 10 min. averaged values (blue) and 10 ms maximum values (yellow)

tion goal was to minimize total harmonic distortion of the supply network current THDI and reduce the angle between fundamental voltage and current harmonics *φ*(*I*(1),*U*(1)) - (18).

( ( ( ) ( ) ))

1 1

*I F*

According with the achieved results the total capacitance *C*1 = 70.75μF and total capacitance *C*<sup>2</sup> = 196.8μF. The reactor *L*2 inductance is 51.48mH. The resistor resistance is *R*T= 300Ω ± 10%.

Measurements in the power system, configured according to the above specification, were carried out in order to check the correctness of the system operation. The instruments loca‐ tions were (fig. 13): *P*1 – arc furnace, *P*2 – C-type filter, *P*3 – first filter of the 3rd harmonic, *P*<sup>4</sup> – second filter of the 3rd harmonic, and *P*5 – at the 110kV side. Essential results of measure‐

Figures 16 – 18 illustrate voltage and current waveforms recorded at the 110kV side, the arc furnace supply voltage the arc furnace and the C-type filter currents and total harmonic voltage distortion factor THDU at both: the 30kV and 110kV side. The measurements have demonstrated that the C-type filter performance has met the requirements, i.e. it attains the expected reduction of reactive power, ensures the second harmonic reduction in the power system and harmonic distortion THDU reduction by means of high harmonics mitigation. The measurements verified the proposed method and the C-type filter designed using this

This chapter presents several selected cases of power electronic systems analysis with re‐ spect to high harmonics occurrence and reactive power compensation. For these cases are proposed classical solutions, i.e. power passive filters which still are a basic and the simplest method for high harmonics mitigation. Analytical formulas that enable to determine basic parameters of various filters' structures and a group of single-tuned filters are provided.

Also a method for passive filters' design employing artificial intelligence, which incorpo‐ rates genetic algorithms, is presented. It has been proved that this method can be the attrac‐ tive tool to solve some kinds of power quality problems. The results obtained using GA are very close to those obtained with the analytical method. Hence the conclusion that genetic algorithms can be an efficient tool for passive filters design. The advantage of the method employing genetic algorithms is the possibility of multi-criterial optimisation and taking in‐ to account at the design stage different (e.g. voltage or current) constraints. It also can be ap‐ plied to filters of various structures and degrees of complexity and can account for filters' resistance that may influence the filter resonance frequency. In other words, genetic algo‐ rithm can be a useful design tool in cases where the system analysis is too complex or even

100 sin , 20Mvar

sin , 20Mvar

(18)

( ( ( ) ( ) ))

j

*goal*

*F*

224 Power Quality Issues

ments are provided in Table 9.

**6. Conclusion**

not possible.

method operates according to the requirements.

1 1

*THD I U Q*

j

<sup>ì</sup> + £ ïï <sup>=</sup> <sup>í</sup> æ ö <sup>ï</sup> × + ç ÷ <sup>&</sup>gt; ïî è ø

*I F*

*THD I U Q*

**Figure 16.** Voltage and current characteristics, spectrums and THD factors at 110 kV side. The graphs show two time characteristics: 10 min. averaged values (blue) and 10 ms maximum values (yellow)

**Figure 18.** Current characteristics, spectrums and THDU factors at 30 kV side. The graphs show two time characteris‐

URMS [kV] 18.29 17.59 65.04 66.58 IRMS [A] - 2383 391 398 385 602 86.5 P [MW] - 93.75 0.083 0.234 0.198 105 12.14 Q [MVAr] - 71.19 19.55 19.84 19.68 28.2 6.52 S [MVA] - 125.7 20.65 21.0 20.34 117.5 17.25 PF - 0.744 0.0043 0.011 0.001 0.89 0.57 THDU [%] 1.56 2.45 1.92 1.58

 [%] - 6.44 8.04 12.04 10.62 4.64 6.61 I(1)RMS [A] - 2357 387 376 373 594 85.46 U(1)RMS [kV] 18.29 17.57 65.0 66.57 U(2)RMS [%] 0.06 0.73 0.42 0.07 U(3)RMS [%] 0.57 0.61 0.43 0.43 U(4)RMS [%] 0.04 0.34 0.19 0.04 U(5)RMS [%] 1.15 1.51 1.22 1.25 I(2)RMS [A] - 58.7 32 10.8 9.8 15 2.21 I(3)RMS [A] - 97.3 3.5 44.3 38.8 9 4.8 I(4)RMS [A] - 23.1 1.5 5.1 4.5 3.7 0.6 I(5)RMS [A] - 71.2 3.7 11.9 11.2 12.5 3.5 Pst [%] 1 16.66 9.17 1.02

**P3 (3rd harm. Filter)**

off on on on on on off

**P4 (3rd harm. Filter)**

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227

**P5(110kV)**

**P5 (110kV)**

**P2 (Filter C)**

tics: 10 min. averaged values (blue) and 10 ms maximum values (yellow)

**P1 (Furnace) P1 (Furnace)**

**Table 9.** The Measurement results obtained over a period of 7 days

**Measurement point**

Furnace and filters in operation

THDI

**Figure 17.** Current characteristics, spectrums and THDI factors of Arc-furnace and C-type filter. The graphs show two time characteristics: 10 min. averaged values (blue) and 10 ms maximum values (yellow)

**Figure 18.** Current characteristics, spectrums and THDU factors at 30 kV side. The graphs show two time characteris‐ tics: 10 min. averaged values (blue) and 10 ms maximum values (yellow)


**Table 9.** The Measurement results obtained over a period of 7 days

**Figure 17.** Current characteristics, spectrums and THDI

226 Power Quality Issues

time characteristics: 10 min. averaged values (blue) and 10 ms maximum values (yellow)

factors of Arc-furnace and C-type filter. The graphs show two

### **Appendix A - Genetic Algorithms**

Genetic Algorithms (GA) are stochastic global search method, mimicking the natural biolog‐ ical evolution. It has been noted that natural evolution is done at the chromosome level, and not directly to individuals. In order to find the best individual, genetic operators apply to the population of potential solutions, the principle of survival of the fittest individual. In ev‐ ery generation, new solutions arise in the selection process in conjunction with the operators of crossover and mutation. This process leads to the evolution of individuals that are better suited to be the existing environment in which they live.

**Author details**

**References**

ly 2009

March/April 2011

Ryszard Klempka, Zbigniew Hanzelka\*

\*Address all correspondence to: hanzel@agh.edu.pl

Computer Science and Electronic, Krakow, Poland

design, EPE01, Graz 27-29 VIII 2001

Computation, vol. 10, No. 1, February 2006

Industrial Electronics, vol. 50, no. 1, February 2003

of transverse filters, Electrical Review 10/2004, 963-966

for economic load dispatch, Electrical Review 10/2011, 369-372

Utilisation, EPQU'03, September 17-19 2003, Krakow, Poland

designed using genetic algorithm, EPE-PEMC 2002, Dubrownik

and Yuri Varetsky

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229

AGH-University of Science & Technology, Faculty of Electrical Engineering, Automatics,

[1] Dugan R., McGranaghan M., Electrical power systems quality, McGraw-Hill, 2002

[2] Yaow-Ming Ch., Passive filter design using genetic algorithms, IEEE Transactions on

[3] Younes M., Benhamida, Genetic algorithm-particle swarm optimization (GA-PSO)

[4] Zajczyk R., Nadarzyński M., Elimination of the higher current harmonics by means

[5] Hanzelka Z., Klempka R., Application of genetic algorithm in double tuned filters

[6] Klempka R., Designing a group of single-branch filters, Electrical Power Quality and

[7] Klempka R., Filtering properties of the selected double tuned passive filter structures

[8] Nassif A. B., Xu W., Freitas W., An investigation on the selection of filter topologies for passive filter applications, IEEE Transactions on Power Delivery, vol. 24, no. 3, Ju‐

[9] Pasko M., Lange A., Influence of arc and induction furnaces on the electric energy quality and possibilities of its improvement, Electrical Review 06/2009, 67-74

[10] Badrzadeh B., Smith K. S., Wilson R. C., Designing passive harmonic filters for alu‐ minium smelting plant, IEEE Transactions on Industry Applications, vol. 47, no. 2,

[12] Chang S.-J., Hou H.-S., Su Y.-K., Automated passive filter synthesis using a novel tree representation and genetic programming, IEEE Transactions on Evolutionary

[11] Arillaga J., Watson N. R., Power system harmonics, John Wiley and Sons, 2003

GA popularity is due to its features. They: (i) don't process the parameters of the problem directly but they use their coded form; (ii) start searching not in a single point but in a group of points; (iii) they use only the goal function and not the derivatives or other auxiliary in‐ formation; (iv) use probabilistic and not deterministic rules of choice. These features consists in effect on the usability of Genetic Algorithms and hence their advantages over other com‐ monly used techniques for searching for the optimal solution. There is a high probability that the AG does not get bogged in a local optimum.

An important term in genetic algorithms is the objective function. It is on the basis of all the individuals in the population are evaluated and on the basis of a new generation of solu‐ tions is created. Each iteration of the genetic algorithm creates a new generation. Figure 20. shows the basic block diagram of a Genetic Algorithm.

**Figure 19.** Block diagram of the basic Genetic Algorithm (GA)

### **Author details**

**Appendix A - Genetic Algorithms**

228 Power Quality Issues

suited to be the existing environment in which they live.

that the AG does not get bogged in a local optimum.

shows the basic block diagram of a Genetic Algorithm.

**Figure 19.** Block diagram of the basic Genetic Algorithm (GA)

Genetic Algorithms (GA) are stochastic global search method, mimicking the natural biolog‐ ical evolution. It has been noted that natural evolution is done at the chromosome level, and not directly to individuals. In order to find the best individual, genetic operators apply to the population of potential solutions, the principle of survival of the fittest individual. In ev‐ ery generation, new solutions arise in the selection process in conjunction with the operators of crossover and mutation. This process leads to the evolution of individuals that are better

GA popularity is due to its features. They: (i) don't process the parameters of the problem directly but they use their coded form; (ii) start searching not in a single point but in a group of points; (iii) they use only the goal function and not the derivatives or other auxiliary in‐ formation; (iv) use probabilistic and not deterministic rules of choice. These features consists in effect on the usability of Genetic Algorithms and hence their advantages over other com‐ monly used techniques for searching for the optimal solution. There is a high probability

An important term in genetic algorithms is the objective function. It is on the basis of all the individuals in the population are evaluated and on the basis of a new generation of solu‐ tions is created. Each iteration of the genetic algorithm creates a new generation. Figure 20.

Ryszard Klempka, Zbigniew Hanzelka\* and Yuri Varetsky

\*Address all correspondence to: hanzel@agh.edu.pl

AGH-University of Science & Technology, Faculty of Electrical Engineering, Automatics, Computer Science and Electronic, Krakow, Poland

### **References**


[13] Eslami M., Shareef H., Mohamed A., Khajehzadeh M., Particle swarm optimization for simultaneous tuning of static var compensator and power system stabilizer, Elec‐ trical Review 09a/2011, 343-347

**Chapter 9**

**Parameters Estimation of Time-Varying Harmonics**

The increasing use of power electronic devices in power systems has been producing significant harmonic distortions, what can cause problems to computers and microproces‐ sor based devices, thermal stresses to electric equipments, harmonic resonances, as well as aging and derating to electrical machines and power transformers [1–3]. The most impor‐ tant problems that have been reported in the literature concerns to the difficulty of the frequency control within the micro-grids and the increase of the total harmonic distortion. These two factors may negatively impact on the protection system, power quality analysis and intelligent electronic devices (IEDs), in which digital algorithms assume that the fundamental frequency is constant. Based on this fact, there has been an increasing interest in signal processing techniques for detecting and estimating harmonic components of timevarying frequencies. Their correct estimation has become an important issue in measure‐ ment equipment and compensating devices. Although many methods have been proposed in the literature, it still remains difficult to detect and estimate harmonics of time-varying frequencies [4, 5]. The harmonic components (voltage or current) can change its frequen‐ cies due to continuous changes in the system configuration and load conditions, to the rapid proliferation of distributed resources, and to possibilities of new operational scenarios (e.g., islanded microgrids). Also the need for massive monitoring of networks is unquestionable within the concept of *smart grids*. An important line of research in the *smart grids* context is to identify and estimate time-varying harmonics that may appear in the current and voltage signals, and from this information, correct and adjust the digital algorithms that are part of

The concept of time-varying harmonics came recently to the vocabulary of power systems engineers, because more and more nonlinear loads, with dynamic behavior, are being

> © 2013 Marques et al.; licensee InTech. This is an open access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

© 2013 Marques et al.; licensee InTech. This is a paper distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Cristiano A. G. Marques, Moisés V. Ribeiro, Carlos A. Duque and Eduardo A. B. da Silva

Additional information is available at the end of the chapter

protection equipments, power quality monitors and IEDs.

http://dx.doi.org/10.5772/53816

**1. Introduction**

