**Active Power Conditioners to Mitigate Power Quality Problems in Industrial Facilities**

João L. Afonso, J. G. Pinto and Henrique Gonçalves

Additional information is available at the end of the chapter

http://dx.doi.org/10.5772/53189

### **1. Introduction**

[11] G. Chicco, J. Schlabbach, F. Spertino, Characterisation and Assessment of the Har‐ monic Emission of Grid-Connected Photovoltaic Systems, in Proc. IEEE Power Tech

2005, St. Petersburg, Russia, June 27-30, 2005, pp.7

104 Power Quality Issues

Non-linear loads are commonly present in industrial facilities, service facilities, office build‐ ings, and even in our homes. They are the source of several Power Quality problems such as harmonics, reactive power, flicker and resonance [1-3]. Therefore, it can be observed an in‐ creasing deterioration of the electrical power grid voltage and current waveforms, mainly due to the contamination of the system currents with harmonics of various orders, including inter-harmonics. Harmonic currents circulating through the line impedance produces distor‐ tion in the system voltages (see Figure 1). Moreover, since many of the loads connected to the electrical systems are single-phase ones, voltage unbalance is also very common in threephase power systems [2]. The distortion and unbalance of the system voltages causes several power quality problems, including the incorrect operation of some sensitive loads [4,5]. Fig‐ ure 1 presents a power system with sinusoidal source voltage (*vS* ) operating with a linear and a non-linear load. The current of the non-linear load (*i* L1) contains harmonics. The har‐ monics in the line-current (*i <sup>S</sup>* ) produce a non-linear voltage drop (∆*v*) in the line impedance, which distorts the load voltage (*vL* ). Since the load voltage is distorted, even the current at the linear load (*i* L2) becomes non-sinusoidal.

The problems caused by the presence of harmonics in the power lines can be classified into two kinds: instantaneous effects and long-term effects. The instantaneous effects problems are associated with interference problems in communication systems, malfunction or per‐ formance degradation of more sensitive equipment and devices. Long-term effects are of

© 2013 Afonso 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 Afonso 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.

thermal nature and are related to additional losses in distribution and overheating, causing a reduction of the mean lifetime of capacitors, rotating machines and transformers. Because of these problems, the issue of the power quality delivered to the end consumers is, more than ever, an object of great concern. International standards concerning electrical power quality (IEEE-519, IEC 61000, EN 50160) impose that electrical equipments and facilities should not produce harmonic contents greater than specified values, and also indicate dis‐ tortion limits to the supply voltage. According to the European COPPER Institute – Leonard Energy Initiative, costs related to power quality problems in Europe are estimated in more than €150.000.000 per year. Therefore, it is evident the necessity to develop solutions that are able to mitigate such disturbances in the electrical systems, improving their power quality.

by its recovery after a brief interval) and flicker (cyclic variation of light intensity of lamps caused by fluctuation of the supply voltage). Three-phase Series Active Power Filters can al‐ so compensate unbalances in the phase voltages [12]. If the DC link of the Series Active Power Filter inverter is connected to a power supply, its compensation capabilities increas‐ es, allowing also the compensation of long term undervoltages and overvoltages [10,11].

Active Power Conditioners to Mitigate Power Quality Problems in Industrial Facilities

http://dx.doi.org/10.5772/53189

107

The Unified Power Quality Conditioner (UPQC) is composed by two power converters shar‐ ing the DC Link. One of these power converters is connected in series with the electrical power grid and the other is connected in parallel with the electrical power grid. This condi‐ tioner offers many compensation options in function of the type of control used. Some of the power quality problems that the UPQC can compensate are: voltage harmonics, voltage un‐ balance, voltage sags, voltage swells, current harmonics, current unbalance, undervoltages, overvoltages, reactive power, and neutral wire current in three-phase four wire systems.

The utilization of equipment like Shunt Active Power Filters, Series Active Power Filters and UPQCs presents significant advantages to the power system. In this way, the research of new topologies and new control algorithms to improve the performance and capabilities of

The aforementioned Active Power Conditioners are the most suited for industrial applica‐

The Shunt Active Power Filter is a device which is able to compensate for both current har‐ monics and power factor. Furthermore, in three-phase four wire systems it allows to balance the currents in the three phases, and to eliminate the current in the neutral wire [15-17]. Fig‐ ure 2 presents the electrical scheme of a Shunt Active Power Filter for a three-phase power

The power stage is, basically, a voltage-source inverter with a capacitor in the DC side (the Shunt Active Filter does not require any internal power supply), controlled in a way that it acts like a current-source. From the measured values of the phase voltages (*va*, *vb*, *vc*) and

*<sup>c</sup>*), the controller calculates the reference currents (*i*

closed-loop current control of the inverter (in both cases the fourth current, the neutral wire

also requires 4 voltage sensors: 3 to measure the phase voltages (*va*, *vb*, *vc*) and another for the closed-loop control of the DC link voltage (*Vdc*). For three-phase balanced loads (threephase motors, three-phase adjustable speed drives, three-phase controlled or non-controlled

*a*, *i b*, *i* *ca*, *i cb*, *i cc*, *i*

*cn*, are calculated by adding the three measured currents of phases *a*, *b*, *c*). It

*ca \**, *i cb \**, *i cc \**, *i cn \**) used

*<sup>c</sup>*) for the control system and 3 for the

*cn*). This solution requires 6

tions, so they will be presented with more detail in the following topics.

these equipments is object of great interest [13,14].

**2. Shunt Active Power Filter**

system with neutral wire.

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

*a*, *i b*, *i*

by the inverter to produce the compensation currents (*i*

current sensors: 3 to measure the load currents (*i*

load currents (*i*

currents, *i*

**Figure 1.** Single line block diagram of a system with non-linear loads.

Passive filters have been used as a solution to solve harmonic current problems, but they present several disadvantages, namely: they only filter the frequencies they were previously tuned for; their operation cannot be limited to a certain load; the interaction between the passive filters and other loads may result in resonances with unpredictable results [6]. To cope with these disadvantages, in the last years, research engineers have presented various solutions based in power electronics to compensate power quality problems [6-12]. These equipments are usually designated as Active Power Conditioners. Examples of such devices are the Shunt Active Power Filter, the Series Active Power Filter, and the Unified Power Quality Conditioner (UPQC).

Active Power Filters are conditioners connected in parallel or in series with the electrical power grid. When connected in parallel is called Shunt Active Power Filter, and when con‐ nected in series is named Series Active Power Filter. The Shunt Active Power Filter behaves as a controlled current-source draining the undesired components from the load currents, such that the currents in the electrical power grid become sinusoidal, balanced, and in phase with fundamental positive sequence component of the system voltages. On the other hand, the Series Active Power Filter works as a voltage-source connected in series with the electri‐ cal power grid, compensating voltage harmonics, sags (sudden reduction of the voltage fol‐ lowed by its recovery after a brief interval), swells (sudden increase of the voltage followed by its recovery after a brief interval) and flicker (cyclic variation of light intensity of lamps caused by fluctuation of the supply voltage). Three-phase Series Active Power Filters can al‐ so compensate unbalances in the phase voltages [12]. If the DC link of the Series Active Power Filter inverter is connected to a power supply, its compensation capabilities increas‐ es, allowing also the compensation of long term undervoltages and overvoltages [10,11].

The Unified Power Quality Conditioner (UPQC) is composed by two power converters shar‐ ing the DC Link. One of these power converters is connected in series with the electrical power grid and the other is connected in parallel with the electrical power grid. This condi‐ tioner offers many compensation options in function of the type of control used. Some of the power quality problems that the UPQC can compensate are: voltage harmonics, voltage un‐ balance, voltage sags, voltage swells, current harmonics, current unbalance, undervoltages, overvoltages, reactive power, and neutral wire current in three-phase four wire systems.

The utilization of equipment like Shunt Active Power Filters, Series Active Power Filters and UPQCs presents significant advantages to the power system. In this way, the research of new topologies and new control algorithms to improve the performance and capabilities of these equipments is object of great interest [13,14].

The aforementioned Active Power Conditioners are the most suited for industrial applica‐ tions, so they will be presented with more detail in the following topics.

### **2. Shunt Active Power Filter**

thermal nature and are related to additional losses in distribution and overheating, causing a reduction of the mean lifetime of capacitors, rotating machines and transformers. Because of these problems, the issue of the power quality delivered to the end consumers is, more than ever, an object of great concern. International standards concerning electrical power quality (IEEE-519, IEC 61000, EN 50160) impose that electrical equipments and facilities should not produce harmonic contents greater than specified values, and also indicate dis‐ tortion limits to the supply voltage. According to the European COPPER Institute – Leonard Energy Initiative, costs related to power quality problems in Europe are estimated in more than €150.000.000 per year. Therefore, it is evident the necessity to develop solutions that are able to mitigate such disturbances in the electrical systems, improving their power quality.

> *Si* LR *<sup>S</sup> <sup>v</sup>* <sup>D</sup>*<sup>v</sup> <sup>L</sup> <sup>v</sup>*

Passive filters have been used as a solution to solve harmonic current problems, but they present several disadvantages, namely: they only filter the frequencies they were previously tuned for; their operation cannot be limited to a certain load; the interaction between the passive filters and other loads may result in resonances with unpredictable results [6]. To cope with these disadvantages, in the last years, research engineers have presented various solutions based in power electronics to compensate power quality problems [6-12]. These equipments are usually designated as Active Power Conditioners. Examples of such devices are the Shunt Active Power Filter, the Series Active Power Filter, and the Unified Power

Active Power Filters are conditioners connected in parallel or in series with the electrical power grid. When connected in parallel is called Shunt Active Power Filter, and when con‐ nected in series is named Series Active Power Filter. The Shunt Active Power Filter behaves as a controlled current-source draining the undesired components from the load currents, such that the currents in the electrical power grid become sinusoidal, balanced, and in phase with fundamental positive sequence component of the system voltages. On the other hand, the Series Active Power Filter works as a voltage-source connected in series with the electri‐ cal power grid, compensating voltage harmonics, sags (sudden reduction of the voltage fol‐ lowed by its recovery after a brief interval), swells (sudden increase of the voltage followed

**Figure 1.** Single line block diagram of a system with non-linear loads.

**Electrical Power Grid** 

106 Power Quality Issues

Quality Conditioner (UPQC).

**Non-linear Load** 

*L*1 *i*

*L*2 *i*

**Linear Load** 

> The Shunt Active Power Filter is a device which is able to compensate for both current har‐ monics and power factor. Furthermore, in three-phase four wire systems it allows to balance the currents in the three phases, and to eliminate the current in the neutral wire [15-17]. Fig‐ ure 2 presents the electrical scheme of a Shunt Active Power Filter for a three-phase power system with neutral wire.

> The power stage is, basically, a voltage-source inverter with a capacitor in the DC side (the Shunt Active Filter does not require any internal power supply), controlled in a way that it acts like a current-source. From the measured values of the phase voltages (*va*, *vb*, *vc*) and load currents (*i a*, *i b*, *i <sup>c</sup>*), the controller calculates the reference currents (*i ca \**, *i cb \**, *i cc \**, *i cn \**) used by the inverter to produce the compensation currents (*i ca*, *i cb*, *i cc*, *i cn*). This solution requires 6 current sensors: 3 to measure the load currents (*i a*, *i b*, *i <sup>c</sup>*) for the control system and 3 for the closed-loop current control of the inverter (in both cases the fourth current, the neutral wire currents, *i <sup>n</sup>*and *i cn*, are calculated by adding the three measured currents of phases *a*, *b*, *c*). It also requires 4 voltage sensors: 3 to measure the phase voltages (*va*, *vb*, *vc*) and another for the closed-loop control of the DC link voltage (*Vdc*). For three-phase balanced loads (threephase motors, three-phase adjustable speed drives, three-phase controlled or non-controlled

rectifiers, etc) there is no need to compensate for the current in neutral wire, so the forth wire of the inverter is not required, simplifying the Shunt Active Power Filter hardware. Since they compensate the power quality problems upstream to its coupling point they should be installed as near as possible of the non-liner loads, avoiding the circulation of cur‐ rent harmonics, reactive currents and neutral wire currents through the facility power lines. Therefore it is advantageous to use various small units, spread along the electrical installa‐ tion, instead of using a single high power Shunt Active Power Filter at the input of the in‐ dustry, at the PCC (Point of Common Coupling – where the electrical installation of the industry is connected to the electrical power distribution system).

**Figure 2.** Shunt Active Power Filter for a three-phase power system with neutral wire.

### **2.1. Typical Waveforms**

Typical waveforms of an electrical installation equipped with a Shunt Active Power Filter are presented in Figure 3. It can be seen that the currents in the load present high harmonic content (THD% of 58%, in average, see Figure 4), and are also unbalanced, which results in a considerable neutral wire current (Figure 3 (d)). The Shunt Active Power Filter makes the currents in the source sinusoidal and balanced (see Figure 3 (b)). The THD% of the source currents is only of about 1% (Figure 4).

In Figure 4 is presented the THD% of the different currents in the system (at the load, source and active filter). The THD% was, in all the cases, calculated in relation to the fundamental frequency of the power grid source (50 Hz). That is why the values of THD% presented for the compensation currents injected by the active filter are so high.

**Figure 3.** Typical waveforms of an installation with a Shunt Active Power Filter: (a) Load currents; (b) Source currents;

Active Power Conditioners to Mitigate Power Quality Problems in Industrial Facilities

http://dx.doi.org/10.5772/53189

109

(c) Active filter compensation currents; (d) Neutral wire currents.

rectifiers, etc) there is no need to compensate for the current in neutral wire, so the forth wire of the inverter is not required, simplifying the Shunt Active Power Filter hardware. Since they compensate the power quality problems upstream to its coupling point they should be installed as near as possible of the non-liner loads, avoiding the circulation of cur‐ rent harmonics, reactive currents and neutral wire currents through the facility power lines. Therefore it is advantageous to use various small units, spread along the electrical installa‐ tion, instead of using a single high power Shunt Active Power Filter at the input of the in‐ dustry, at the PCC (Point of Common Coupling – where the electrical installation of the

**Inverter** 

*Vdc*

*ica\* icb\* icc\* icn\**

*isa isb isc isn*

**Shunt Active Power Filter** 

Typical waveforms of an electrical installation equipped with a Shunt Active Power Filter are presented in Figure 3. It can be seen that the currents in the load present high harmonic content (THD% of 58%, in average, see Figure 4), and are also unbalanced, which results in a considerable neutral wire current (Figure 3 (d)). The Shunt Active Power Filter makes the currents in the source sinusoidal and balanced (see Figure 3 (b)). The THD% of the source

In Figure 4 is presented the THD% of the different currents in the system (at the load, source and active filter). The THD% was, in all the cases, calculated in relation to the fundamental frequency of the power grid source (50 Hz). That is why the values of THD% presented for

**+**


**Load**

*ia ib ic i n*

*ica icb icc icn*

industry is connected to the electrical power distribution system).

*vb*

*vc*

*va*

**Controller**

*Vdc*

**Figure 2.** Shunt Active Power Filter for a three-phase power system with neutral wire.

the compensation currents injected by the active filter are so high.

*ia ib ic*

*va vb vc*

**a b c n**

**Electrical Power Grid** 

108 Power Quality Issues

**2.1. Typical Waveforms**

currents is only of about 1% (Figure 4).

**Figure 3.** Typical waveforms of an installation with a Shunt Active Power Filter: (a) Load currents; (b) Source currents; (c) Active filter compensation currents; (d) Neutral wire currents.

The Series Active Power Filter consists of a voltage-source inverter (behaving as a controlled voltage-source) and requires 3 single-phase transformers to interface with the power system. However, some authors have presented research results of Series Active Power Filter topol‐ ogies without the use of line transformers [21,22]. From the measured values of the phase

> *\**, *vcb \**, *vcc*

compensation voltages (*vca*, *vcb*, *vcc*). The Series Active Power Filter does not compensate for load current harmonics but it acts as high-impedance to the current harmonics coming from the electrical power grid side. Therefore, it guarantees that passive filters eventually placed at the load side will work appropriately and not drain harmonic currents from the rest of the

Typical waveforms of an installation equipped with a Series Active Power Filter are present‐

**Figure 6.** Typical waveforms of an installation with a Series Active Power Filter: (a) Load voltages; (b) Source voltages;

*a*, *i b*, *i*

Active Power Conditioners to Mitigate Power Quality Problems in Industrial Facilities

*\**), used by the inverter to produce the

*<sup>c</sup>*), the controller calcu‐

http://dx.doi.org/10.5772/53189

111

voltages at the source side (*vsa*, *vsb*, *vsc*) and of the load currents (*i*

lates the reference compensation voltages (*vca*

power system.

ed in Figure 6.

**3.1. Typical Waveforms**

(c) Active filter compensation voltages.

**Figure 4.** Harmonic spectrum and THD% of the currents in an installation with a Shunt Active Power Filter: (a) Load currents; (b) Source currents; (c) Compensation currents.

### **3. Series Active Power Filter**

The Series Active Power Filter is the dual of the Shunt Active Power Filter, and is able to compensate for voltage harmonics, voltage sags, voltage swells and flicker, making the vol‐ tages applied to the load almost sinusoidal (compensating for voltage harmonics) [18,19]. The three-phase Series Active Filter can also balance the load voltages [20]. Figure 5 shows the electrical scheme of a Series Active Power Filter for a three-phase power system.

**Figure 5.** Series Active Power Filter for a three-phase power system.

The Series Active Power Filter consists of a voltage-source inverter (behaving as a controlled voltage-source) and requires 3 single-phase transformers to interface with the power system. However, some authors have presented research results of Series Active Power Filter topol‐ ogies without the use of line transformers [21,22]. From the measured values of the phase voltages at the source side (*vsa*, *vsb*, *vsc*) and of the load currents (*i a*, *i b*, *i <sup>c</sup>*), the controller calcu‐ lates the reference compensation voltages (*vca \**, *vcb \**, *vcc \**), used by the inverter to produce the compensation voltages (*vca*, *vcb*, *vcc*). The Series Active Power Filter does not compensate for load current harmonics but it acts as high-impedance to the current harmonics coming from the electrical power grid side. Therefore, it guarantees that passive filters eventually placed at the load side will work appropriately and not drain harmonic currents from the rest of the power system.

### **3.1. Typical Waveforms**

**Figure 4.** Harmonic spectrum and THD% of the currents in an installation with a Shunt Active Power Filter: (a) Load

The Series Active Power Filter is the dual of the Shunt Active Power Filter, and is able to compensate for voltage harmonics, voltage sags, voltage swells and flicker, making the vol‐ tages applied to the load almost sinusoidal (compensating for voltage harmonics) [18,19]. The three-phase Series Active Filter can also balance the load voltages [20]. Figure 5 shows

the electrical scheme of a Series Active Power Filter for a three-phase power system.

**Series Active Power Filter**

**Figure 5.** Series Active Power Filter for a three-phase power system.

currents; (b) Source currents; (c) Compensation currents.

**3. Series Active Power Filter**

110 Power Quality Issues

**Electrical Power Grid** Typical waveforms of an installation equipped with a Series Active Power Filter are present‐ ed in Figure 6.

**Figure 6.** Typical waveforms of an installation with a Series Active Power Filter: (a) Load voltages; (b) Source voltages; (c) Active filter compensation voltages.

In Figure 7 is presented the THD% of the different voltages in the system (load, source and series active filter). It can be seen that the voltages in the source present some harmonic con‐ tent (THD% between 2.5% and 4%). The Series Active Power Filter makes the voltages in the load practically sinusoidal, with almost none distortion (see Figure 6 (a)). The THD% of the load voltages is below or equal to 0.4%. The THD% was, in all the cases, calculated in rela‐ tion to the fundamental frequency of the power grid source (50 Hz). That is the motive way the values presented for the compensation voltages produced by the active filter are so high.

**Electrical Power Grid**

**4.1. Typical Waveforms**

shown in Figure 10 (e)).

0.4% (Figure 10 (d)).

**Unified Power Quality Conditioner** 

Active Power Conditioners to Mitigate Power Quality Problems in Industrial Facilities

http://dx.doi.org/10.5772/53189

113

Typical waveforms of an installation equipped with a Unified Power Quality Conditioner are presented next. In Figure 9 are shown the load currents, source currents, compensa‐ tion currents, neutral wire currents, load voltages, and source voltages. It can be seen that the currents in the load present a high harmonic content (THD% between 32% and 41%, see Figure 10 (a)), and are also unbalanced, which results in a considerable neutral wire current (*in* in Figure 9 (d)). The THD% of the source voltages is also high (about 6%, as

By the action of the Unified Power Quality Conditioner the currents in the source become sinusoidal, in phase with the voltages, and balanced (Figure 6 (b)). The THD% of the source currents is reduced to about 1% (Figure 10 (b)). Also, the load voltages become sinusoidal with almost none distortion (Figure 6 (e)). The THD% of the load voltages is reduced to only

In Figure 10 is presented the THD% of the different currents and voltages in the electrical system (at the load, source and UPQC). The THD% was, in all the cases, calculated in rela‐ tion to the fundamental frequency of the power grid source (50 Hz). That is way the values

presented for the compensation currents injected by the UPQC are so high.

**Figure 8.** Unified Power Quality Conditioner for a three-phase power system.

**Figure 7.** Harmonic spectrum and THD% of the voltages in an installation with a Series Active Power Filter: (a) Load voltages; (b) Source voltages; (c) Compensation voltages.

### **4. Unified Power Quality Conditioner**

The Unified Power Quality Conditioner (UPQC) combines the Shunt Active Power Filter with the Series Active Power Filter, sharing the same DC Link, in order to compensate both voltages and currents, so that the load voltages become sinusoidal and at nominal value, and the source currents become sinusoidal and in phase with the source voltages [23,24]. In the case of three-phase systems, a three-phase UPQC can also balance the load voltages and the source currents, and eliminate the source neutral current. Figure 8 shows the electrical scheme of a Unified Power Quality Conditioner for a three-phase power system.

From the measured values of the source phase voltages (*vsa*, *vsb*, *vsc*) and load currents (*i a*, *i b*, *i c*), the controller calculates the reference compensation currents (*i ca \**, *i cb \**, *i cc \**, *i cn \**) used by the in‐ verter of the shunt converter to produce the compensation currents (*i ca*, *i cb*, *i cc*, *i cn*). Using the measured values of the source phase voltages, and source currents (*i sa*, *i sb*, *i sc*), the control‐ ler calculates the reference compensation voltages (*vca \**, *vcb \**, *vcc \**) used by the inverter of the series converter to produce the compensation voltages (*vca*, *vcb*, *vcc*).

**Figure 8.** Unified Power Quality Conditioner for a three-phase power system.

### **4.1. Typical Waveforms**

In Figure 7 is presented the THD% of the different voltages in the system (load, source and series active filter). It can be seen that the voltages in the source present some harmonic con‐ tent (THD% between 2.5% and 4%). The Series Active Power Filter makes the voltages in the load practically sinusoidal, with almost none distortion (see Figure 6 (a)). The THD% of the load voltages is below or equal to 0.4%. The THD% was, in all the cases, calculated in rela‐ tion to the fundamental frequency of the power grid source (50 Hz). That is the motive way the values presented for the compensation voltages produced by the active filter are so high.

**Figure 7.** Harmonic spectrum and THD% of the voltages in an installation with a Series Active Power Filter: (a) Load

The Unified Power Quality Conditioner (UPQC) combines the Shunt Active Power Filter with the Series Active Power Filter, sharing the same DC Link, in order to compensate both voltages and currents, so that the load voltages become sinusoidal and at nominal value, and the source currents become sinusoidal and in phase with the source voltages [23,24]. In the case of three-phase systems, a three-phase UPQC can also balance the load voltages and the source currents, and eliminate the source neutral current. Figure 8 shows the electrical

scheme of a Unified Power Quality Conditioner for a three-phase power system.

the controller calculates the reference compensation currents (*i*

ler calculates the reference compensation voltages (*vca*

verter of the shunt converter to produce the compensation currents (*i*

series converter to produce the compensation voltages (*vca*, *vcb*, *vcc*).

measured values of the source phase voltages, and source currents (*i*

From the measured values of the source phase voltages (*vsa*, *vsb*, *vsc*) and load currents (*i*

*ca \**, *i cb \**, *i cc \**, *i cn*

*\**, *vcb \**, *vcc* *ca*, *i cb*, *i cc*, *i*

> *sa*, *i sb*, *i*

*\**) used by the inverter of the

*a*, *i b*, *i c*),

*cn*). Using the

*sc*), the control‐

*\**) used by the in‐

voltages; (b) Source voltages; (c) Compensation voltages.

112 Power Quality Issues

**4. Unified Power Quality Conditioner**

Typical waveforms of an installation equipped with a Unified Power Quality Conditioner are presented next. In Figure 9 are shown the load currents, source currents, compensa‐ tion currents, neutral wire currents, load voltages, and source voltages. It can be seen that the currents in the load present a high harmonic content (THD% between 32% and 41%, see Figure 10 (a)), and are also unbalanced, which results in a considerable neutral wire current (*in* in Figure 9 (d)). The THD% of the source voltages is also high (about 6%, as shown in Figure 10 (e)).

By the action of the Unified Power Quality Conditioner the currents in the source become sinusoidal, in phase with the voltages, and balanced (Figure 6 (b)). The THD% of the source currents is reduced to about 1% (Figure 10 (b)). Also, the load voltages become sinusoidal with almost none distortion (Figure 6 (e)). The THD% of the load voltages is reduced to only 0.4% (Figure 10 (d)).

In Figure 10 is presented the THD% of the different currents and voltages in the electrical system (at the load, source and UPQC). The THD% was, in all the cases, calculated in rela‐ tion to the fundamental frequency of the power grid source (50 Hz). That is way the values presented for the compensation currents injected by the UPQC are so high.

**Figure 10.** Harmonic spectrum and THD% of the currents and voltages in an installation with an UPQC: (a) Load cur‐

Active Power Conditioners to Mitigate Power Quality Problems in Industrial Facilities

http://dx.doi.org/10.5772/53189

115

The control methods applied to Active Power Filters and Unified Power Quality Condition‐ ers are decisive in achieving the goals of compensation, in the determination of the condi‐ tioner power rate, and in theirs dynamic and steady-state performances. Basically, the different approaches regarding the calculation of the compensation currents and voltages from the measured distorted quantities can be grouped into two classes: frequency-domain

rents; (b) Source currents; (c) Compensation currents; (d) Load voltages; (e) Source voltages.

**5. Control Methods for Active Power Filters**

and time-domain.

**Figure 9.** Typical waveforms of an installation with a UPQC: (a) Load currents; (b) Source currents; (c) Compensation currents; (d) Neutral wire currents; (e) Load voltages; (f) Source voltages.

**Figure 10.** Harmonic spectrum and THD% of the currents and voltages in an installation with an UPQC: (a) Load cur‐ rents; (b) Source currents; (c) Compensation currents; (d) Load voltages; (e) Source voltages.

### **5. Control Methods for Active Power Filters**

**Figure 9.** Typical waveforms of an installation with a UPQC: (a) Load currents; (b) Source currents; (c) Compensation

currents; (d) Neutral wire currents; (e) Load voltages; (f) Source voltages.

114 Power Quality Issues

The control methods applied to Active Power Filters and Unified Power Quality Condition‐ ers are decisive in achieving the goals of compensation, in the determination of the condi‐ tioner power rate, and in theirs dynamic and steady-state performances. Basically, the different approaches regarding the calculation of the compensation currents and voltages from the measured distorted quantities can be grouped into two classes: frequency-domain and time-domain.

The frequency-domain approach implies the analysis of the Fourier transform, which leads to a huge amount of calculations, making the control method very heavy in terms of proc‐ essing time and required computational capacity. The time-domain approach uses the tradi‐ tional concepts of circuit analysis and algebraic transformations associated with changes of reference frames, which greatly simplify the control task. In general, power definitions in the time domain offer a more appropriate basis for the design of controllers for power elec‐ tronic devices, because they are also valid during transients. This is especially true for appli‐ cations in three-phase electrical power systems if the definitions are done already considering a three-phase circuit, instead of considering a single-phase circuit and then summing up to have a three-phase system [14].

In a three-phase electrical power system the three-phase power delivered to a load by the source has the well-known expression:

$$
\psi\_3(t) = \upsilon\_a(t)i\_a(t) + \upsilon\_b(t)i\_b(t) + \upsilon\_c(t)i\_c(t) \tag{1}
$$

vantage of the p-q Theory is the simplicity of its calculations, which consists only in algebra‐ ic operations, being the only exception the extraction of the average and alternating

The p-q Theory was initially developed for three-phase electrical power systems without neutral wire, with a short reference to three-phase systems with neutral wire. Later, Wata‐ nabe et al. [35] and Aredes et al. [36] extended it to three-phase electrical power systems

This theory consists in an algebraic transformation (the Clarke transformation) of the threephase voltages and currents in the *a-b-c* coordinates to the *α-β-0* coordinates, where *α-β* are orthogonal, and the *0* coordinate corresponds to the zero-sequence component. The p-q Theo‐ ry transformation applied to the electrical power grid voltages and load currents is given by:

> 1 / 2 1 / 2 1 / 2 1 -1 / 2 -1 / 2 0 3 / 2 - 3 / 2

> 1 / 2 1 / 2 1 / 2 1 -1 / 2 -1 / 2 0 3 / 2 - 3 / 2

> > *<sup>a</sup>* + *vbi*

*<sup>α</sup>* + *vβi*

*<sup>b</sup>* + *vci*

*<sup>β</sup>* + *v*0*i*

*<sup>β</sup>* Instantaneous real power (5)

<sup>0</sup> Instantaneous zero−sequence power (6)

*<sup>c</sup>* (3)

<sup>0</sup> (4)

*<sup>β</sup>* (7)

The instantaneous three-phase electrical power, in the *a-b-c* coordinates is defined as:

In the *α-β-0* coordinates the instantaneous three-phase electrical power is defined as:

*p*<sup>3</sup> = *p*<sup>a</sup> + *p*<sup>b</sup> + *p*c=*vai*

*p*<sup>3</sup> = *p* + *p*<sup>0</sup> =*vαi*

*q* =*vβi*

*<sup>α</sup>* - *vαi*

*va vb vc*

Active Power Conditioners to Mitigate Power Quality Problems in Industrial Facilities

http://dx.doi.org/10.5772/53189

117

*i a i b i c* (2)

components of the calculated powers.

with neutral wire.

*5.1.1. Clarke for Three-Phase Four-Wire Electrical Power Systems*

*v*0 *vα vβ*

> *i* 0 *i α i β*

The two components of *p*3 are defined as follow:

*p* =*vαi*

The instantaneous imaginary power is defined as:

*p*<sup>0</sup> =*v*0*i*

*<sup>α</sup>* + *vβi*

= 2 / 3

= 2 / 3

where *va* (*t*), *vb* (*t*), and *vc* (*t*) represents the instantaneous load voltages referred to the neu‐ tral point, and *i a* (*t*), *i b* (*t*), and *i c* (*t*) are the load instantaneous currents. However, for the given voltages, there is more than one set of currents producing the same instantaneous power. So, what is the optimal set of currents for a given power? One possible answer is the set of currents that minimizes power loss in the lines. On the other hand, it is known that for a balanced sinusoidal system, in voltage and current, the instantaneous power is constant, and equal to the active power, since this value corresponds to the average value of the in‐ stantaneous power. Therefore, the best set of currents can be the one that leads to a constant instantaneous power.

Different time-domain power definitions can be found in the literature. The most important are: the p-q Theory (Instantaneous Power Theory) proposed by Akagi et al. [25,26]; FBD (Fryze - Buchholz - Depenbrock) proposed by Depenbrock [27]; the CPT (Conservative Pow‐ er Theory) proposed by Tenti [28]; and the CPC (Current's Physical Components) proposed by Czarnecki [29,30]. It can be also found in the literature p-q Theory inspired control algo‐ rithms for switching compensators, as for example, the p-q-r Theory [31-33]. A comparison involving the p-q-r and the p-q theories is provided in [33]. The control algorithm denomi‐ nated as Synchronous Reference Frame (SRF) [34] also presents similar aspects related with the p-q-r and the p-q theories. The SRF control algorithm is defined in the *d-q-0* reference frame. All of these control algorithms can be applied to control switching compensators con‐ nected in three-phase systems, with or without neutral wire.

### **5.1. The p-q Theory Fundamentals**

In 1983, Akagi et al. [25,26] have proposed "The Generalized Theory of the Instantaneous Reactive Power in Three-Phase Circuits", also known as Instantaneous Power Theory, or p-q Theory, for the control of Active Power Filters. The fact of being a time-domain theory makes it viable for operation in steady state or transient state, as well as for generic voltage and current waveforms, allowing a real time control of the Active Power Filters. Another ad‐ vantage of the p-q Theory is the simplicity of its calculations, which consists only in algebra‐ ic operations, being the only exception the extraction of the average and alternating components of the calculated powers.

### *5.1.1. Clarke for Three-Phase Four-Wire Electrical Power Systems*

The frequency-domain approach implies the analysis of the Fourier transform, which leads to a huge amount of calculations, making the control method very heavy in terms of proc‐ essing time and required computational capacity. The time-domain approach uses the tradi‐ tional concepts of circuit analysis and algebraic transformations associated with changes of reference frames, which greatly simplify the control task. In general, power definitions in the time domain offer a more appropriate basis for the design of controllers for power elec‐ tronic devices, because they are also valid during transients. This is especially true for appli‐ cations in three-phase electrical power systems if the definitions are done already considering a three-phase circuit, instead of considering a single-phase circuit and then

In a three-phase electrical power system the three-phase power delivered to a load by the

(*t*)*i b* (*t*) + *vc*

given voltages, there is more than one set of currents producing the same instantaneous power. So, what is the optimal set of currents for a given power? One possible answer is the set of currents that minimizes power loss in the lines. On the other hand, it is known that for a balanced sinusoidal system, in voltage and current, the instantaneous power is constant, and equal to the active power, since this value corresponds to the average value of the in‐ stantaneous power. Therefore, the best set of currents can be the one that leads to a constant

Different time-domain power definitions can be found in the literature. The most important are: the p-q Theory (Instantaneous Power Theory) proposed by Akagi et al. [25,26]; FBD (Fryze - Buchholz - Depenbrock) proposed by Depenbrock [27]; the CPT (Conservative Pow‐ er Theory) proposed by Tenti [28]; and the CPC (Current's Physical Components) proposed by Czarnecki [29,30]. It can be also found in the literature p-q Theory inspired control algo‐ rithms for switching compensators, as for example, the p-q-r Theory [31-33]. A comparison involving the p-q-r and the p-q theories is provided in [33]. The control algorithm denomi‐ nated as Synchronous Reference Frame (SRF) [34] also presents similar aspects related with the p-q-r and the p-q theories. The SRF control algorithm is defined in the *d-q-0* reference frame. All of these control algorithms can be applied to control switching compensators con‐

In 1983, Akagi et al. [25,26] have proposed "The Generalized Theory of the Instantaneous Reactive Power in Three-Phase Circuits", also known as Instantaneous Power Theory, or p-q Theory, for the control of Active Power Filters. The fact of being a time-domain theory makes it viable for operation in steady state or transient state, as well as for generic voltage and current waveforms, allowing a real time control of the Active Power Filters. Another ad‐

(*t*)*i c*

(*t*) represents the instantaneous load voltages referred to the neu‐

(*t*) are the load instantaneous currents. However, for the

(*t*) (1)

summing up to have a three-phase system [14].

*p*3 (*t*)=*va* (*t*)*i a* (*t*) + *vb*

(*t*), and *i*

nected in three-phase systems, with or without neutral wire.

*c*

source has the well-known expression:

(*t*), and *vc*

where *va*

116 Power Quality Issues

tral point, and *i*

(*t*), *vb*

instantaneous power.

*a* (*t*), *i b*

**5.1. The p-q Theory Fundamentals**

The p-q Theory was initially developed for three-phase electrical power systems without neutral wire, with a short reference to three-phase systems with neutral wire. Later, Wata‐ nabe et al. [35] and Aredes et al. [36] extended it to three-phase electrical power systems with neutral wire.

This theory consists in an algebraic transformation (the Clarke transformation) of the threephase voltages and currents in the *a-b-c* coordinates to the *α-β-0* coordinates, where *α-β* are orthogonal, and the *0* coordinate corresponds to the zero-sequence component. The p-q Theo‐ ry transformation applied to the electrical power grid voltages and load currents is given by:

$$
\begin{bmatrix} v\_0 \\ v\_\alpha \\ v\_\beta \end{bmatrix} = \sqrt{2/3} \begin{bmatrix} 1/\sqrt{2} & 1/\sqrt{2} & 1/\sqrt{2} \\ 1 & -1/2 & -1/2 \\ 0 & \sqrt{3}/2 & -\sqrt{3}/2 \end{bmatrix} \begin{bmatrix} v\_a \\ v\_b \\ v\_c \end{bmatrix}
$$

$$
\begin{bmatrix} i\_0 \\ i\_\alpha \\ i\_\beta \end{bmatrix} = \sqrt{2/3} \begin{bmatrix} 1/\sqrt{2} & 1/\sqrt{2} & 1/\sqrt{2} \\ 1 & -1/2 & -1/2 \\ 0 & \sqrt{3}/2 & -\sqrt{3}/2 \end{bmatrix} \begin{bmatrix} i\_a \\ i\_b \\ i\_c \end{bmatrix}
$$

The instantaneous three-phase electrical power, in the *a-b-c* coordinates is defined as:

$$p\_3 = p\_a + p\_b + p\_c = \upsilon\_a i\_a + \upsilon\_b i\_b + \upsilon\_c i\_c \tag{3}$$

In the *α-β-0* coordinates the instantaneous three-phase electrical power is defined as:

$$p\_3 = p + p\_0 = \upsilon\_\alpha i\_\alpha + \upsilon\_\beta i\_\beta + \upsilon\_0 i\_0 \tag{4}$$

The two components of *p*3 are defined as follow:

$$
\mathbf{v} = v\_a \mathbf{i}\_a + v\_\beta \mathbf{i}\_\beta \qquad \text{Instantaneous real power} \tag{5}
$$

$$p\_0 = v\_0 i\_0 \qquad \text{Instantaneous zero-sequence power} \tag{6}$$

The instantaneous imaginary power is defined as:

$$
\mathbf{q} = \boldsymbol{\upsilon}\_{\beta} \mathbf{i}\_{\alpha} - \boldsymbol{\upsilon}\_{\alpha} \mathbf{i}\_{\beta} \tag{7}
$$

The *q*power difers form the conventional reactive three-phase electrical power, since it also takes into consideration all the voltage and current harmonics.

Since the *p*and *q*powers do not depend on the zero-sequence components of the voltages and currents, but only on the same *α-β* components, they can be written together:

$$
\begin{bmatrix} p \\ q \end{bmatrix} = \begin{bmatrix} \upsilon\_{\alpha} & \upsilon\_{\beta} \\ \upsilon\_{\beta} & -\upsilon\_{\alpha} \end{bmatrix} \begin{bmatrix} i\_{\alpha} \\ i\_{\beta} \end{bmatrix} \tag{8}
$$

**Figure 11.** Power components of the p-q Theory in α-β-0 coordinates.

**Figure 12.** Power components of the p-q Theory in a-b-c coordinates.

**Figure 13.** Compensation of power components˜*p*, *<sup>q</sup>*, ˜*p*0, and *<sup>p</sup>*

¯ and *p* ¯

components that the source must supply. The other power components can be compensated using a Shunt Active Power Filter. Figure 13 shows the Shunt Active Power Filter for an electrical power system represented in *a-b-c* coordinates, and Figure 14 shows the Shunt Ac‐

¯

<sup>0</sup> in a-b-c coordinates.

tive Power Filter for an electrical power system represented in *α-β-0* coordinates.

0 are usually the only desirable p-q Theory power

Active Power Conditioners to Mitigate Power Quality Problems in Industrial Facilities

http://dx.doi.org/10.5772/53189

119

*5.1.3. The p-q Theory Powers Compensation*

From the concepts seen before, *p*

### *5.1.2. Physical Meaning of the p-q Theory Electrical Powers*

The different p-q Theory electrical powers are illustrated in Figure 11, for an electrical pow‐ er system represented in *α-β-0* and in Figure 12 for an electrical power system represented in *a-b-c* coordinates, and have the following physical meaning:

*p* ¯ : mean value of the instantaneous real power – corresponds to the energy per time unity that is transferred from the power supply to the load, through the *α-β* coordinates, or through the *a-b-c* coordinates, in a balanced way (it is the desired power component).

*p*˜: alternated value of the instantaneous real power – It is the energy per time unity that is exchanged between the power supply and the load, through the *α-β* coordinates, or through the *a-b-c* coordinates.

*q*: instantaneous imaginary power – corresponds to the power that is exchanged between the *α-β* coordinates, or between the *a-b-c* coordinates. This power does not imply any trans‐ ference or exchange of energy between the power supply and the load, but is responsible for the existence of undesirable currents, which circulate between the system phases. In the case of a balanced sinusoidal voltage supply and a balanced load, with or without harmonics, q ¯ (the mean value of the instantaneous imaginary power) is equal to the conventional reactive power (q ¯ =3V*I*1sin *ϕ*1).

*p* ¯ 0: mean value of the instantaneous zero-sequence power – corresponds to the energy per time unity which is transferred from the power supply to the load through the zero-se‐ quence components of voltage and current.

*<sup>p</sup>*˜ 0:alternated value of the instantaneous zero-sequence power – it means the energy per time unity that is exchanged between the power supply and the load through the zero-sequence components.

The zero-sequence power, *p*0, only exists in three-phase systems with neutral wire. Further‐ more, the systems must have unbalanced voltages and currents and/or 3rd harmonics in both voltage and current of at least one phase.

**Figure 11.** Power components of the p-q Theory in α-β-0 coordinates.

The *q*power difers form the conventional reactive three-phase electrical power, since it also

Since the *p*and *q*powers do not depend on the zero-sequence components of the voltages

The different p-q Theory electrical powers are illustrated in Figure 11, for an electrical pow‐ er system represented in *α-β-0* and in Figure 12 for an electrical power system represented in

: mean value of the instantaneous real power – corresponds to the energy per time unity that is transferred from the power supply to the load, through the *α-β* coordinates, or

*p*˜: alternated value of the instantaneous real power – It is the energy per time unity that is exchanged between the power supply and the load, through the *α-β* coordinates, or through

*q*: instantaneous imaginary power – corresponds to the power that is exchanged between the *α-β* coordinates, or between the *a-b-c* coordinates. This power does not imply any trans‐ ference or exchange of energy between the power supply and the load, but is responsible for the existence of undesirable currents, which circulate between the system phases. In the case of a balanced sinusoidal voltage supply and a balanced load, with or without harmonics, q

(the mean value of the instantaneous imaginary power) is equal to the conventional reactive

0: mean value of the instantaneous zero-sequence power – corresponds to the energy per time unity which is transferred from the power supply to the load through the zero-se‐

*<sup>p</sup>*˜ 0:alternated value of the instantaneous zero-sequence power – it means the energy per time unity that is exchanged between the power supply and the load through the zero-sequence

The zero-sequence power, *p*0, only exists in three-phase systems with neutral wire. Further‐ more, the systems must have unbalanced voltages and currents and/or 3rd harmonics in

through the *a-b-c* coordinates, in a balanced way (it is the desired power component).

*i α i β*

(8)

¯

and currents, but only on the same *α-β* components, they can be written together:

*v<sup>α</sup> v<sup>β</sup> v<sup>β</sup>* -*v<sup>α</sup>*

*p q* =

takes into consideration all the voltage and current harmonics.

*5.1.2. Physical Meaning of the p-q Theory Electrical Powers*

*a-b-c* coordinates, and have the following physical meaning:

*p* ¯

118 Power Quality Issues

the *a-b-c* coordinates.

=3V*I*1sin *ϕ*1).

quence components of voltage and current.

both voltage and current of at least one phase.

power (q ¯

components.

*p* ¯

**Figure 12.** Power components of the p-q Theory in a-b-c coordinates.

### *5.1.3. The p-q Theory Powers Compensation*

From the concepts seen before, *p* ¯ and *p* ¯ 0 are usually the only desirable p-q Theory power components that the source must supply. The other power components can be compensated using a Shunt Active Power Filter. Figure 13 shows the Shunt Active Power Filter for an electrical power system represented in *a-b-c* coordinates, and Figure 14 shows the Shunt Ac‐ tive Power Filter for an electrical power system represented in *α-β-0* coordinates.

**Figure 13.** Compensation of power components˜*p*, *<sup>q</sup>*, ˜*p*0, and *<sup>p</sup>* ¯ <sup>0</sup> in a-b-c coordinates.

sary to compensate *p*˜ and*p*˜ 0, since these quantities must be stored in this component at one moment to be later delivered back to the load. The instantaneous imaginary power (*q*), which includes the conventional reactive power, is compensated without the contribution of this capacitor. This means that, the size of the DC link capacitor does not depend on the

Active Power Conditioners to Mitigate Power Quality Problems in Industrial Facilities

http://dx.doi.org/10.5772/53189

121

The p-q Theory presents some interesting features when applied to the control of Active

**•** It can be applied to any three-phase system (balanced or unbalanced, with or without har‐

**•** Its calculations are relatively simple (it only includes algebraic expressions that can be im‐

**•** It allows two control strategies: "constant instantaneous real power at source"and "sinus‐

As can be seen in Figure 15, the inputs of the control system are the instantaneous values of the voltages and currents in the phases that feed the load to be compensated

**Figure 15.** Control system structure for the control strategy "constant instantaneous real power at source".

amount of reactive power to be compensated.

**5.2. Calculations for theShunt Active Power Filter Control**

monics, for compensation of both voltages and/or currents);

**•** It is based in instantaneous values, allowing excellent dynamic response;

Power Filters for three-phase power systems, namely:

**•** It is inherently a three-phase system theory;

plemented using a simple controller);

*<sup>a</sup>*, *i <sup>b</sup>*, *i c*).

oidal current at source".

(*va*, *vb*, *vc* and *i*

**Figure 14.** Compensation of power components˜*p*, *<sup>q</sup>*, ˜*p*0, and *<sup>p</sup>* ¯ <sup>0</sup>in α-β-0 coordinates.

With the Shunt Active Power Filter in operation, the *p*˜ and *p*˜ 0 power components cease to be exchanged between the load and the electrical power source and start to be exchanged be‐ tween the load and the Shunt Active Power Filter DC link capacitor, which continuously stores and delivers energy, to compensate these pulsating electrical powers.

The power component*q* is not associated with any energy transference, so the currents asso‐ ciated with this electrical power component start to circulate only between the Shunt Active Power Filter and the load, and not anymore through the electrical power grid.

The power component *p*0only can exist in three-phase four-wire systems with voltage and current distortions or/and unbalances (when simultaneously *i* <sup>0</sup> ≠0 and *v*<sup>0</sup> ≠0, at the same fre‐ quencies), in these conditions it is necessary to compensate the electrical power component *p*0to allow the balancing of the currents, and to make the current in the neutral wire assume a null value upstream of the Shunt Active Power Filter, or in other words, to make that the zero-sequence component of the current between the electrical power source and the Shunt Active Power Filter is eliminated.

The compensation of *p* ¯ 0, requires that the Shunt Active Power Filter delivers energy to the load. To do this there are two possibilities:


The second possibility, was proposed by Aredes et al. [36], and is implicit in Figure 13. It is also possible to conclude that the Shunt Active Power Filter DC link capacitor is only neces‐ sary to compensate *p*˜ and*p*˜ 0, since these quantities must be stored in this component at one moment to be later delivered back to the load. The instantaneous imaginary power (*q*), which includes the conventional reactive power, is compensated without the contribution of this capacitor. This means that, the size of the DC link capacitor does not depend on the amount of reactive power to be compensated.

### **5.2. Calculations for theShunt Active Power Filter Control**

The p-q Theory presents some interesting features when applied to the control of Active Power Filters for three-phase power systems, namely:

**•** It is inherently a three-phase system theory;

**Figure 14.** Compensation of power components˜*p*, *<sup>q</sup>*, ˜*p*0, and *<sup>p</sup>*

¯

With the Shunt Active Power Filter in operation, the *p*˜ and *p*˜ 0 power components cease to be exchanged between the load and the electrical power source and start to be exchanged be‐ tween the load and the Shunt Active Power Filter DC link capacitor, which continuously

The power component*q* is not associated with any energy transference, so the currents asso‐ ciated with this electrical power component start to circulate only between the Shunt Active

The power component *p*0only can exist in three-phase four-wire systems with voltage and

quencies), in these conditions it is necessary to compensate the electrical power component *p*0to allow the balancing of the currents, and to make the current in the neutral wire assume a null value upstream of the Shunt Active Power Filter, or in other words, to make that the zero-sequence component of the current between the electrical power source and the Shunt

**•** Include a power supply on the Shunt Active Power Filter inverter DC link to deliver this

The second possibility, was proposed by Aredes et al. [36], and is implicit in Figure 13. It is also possible to conclude that the Shunt Active Power Filter DC link capacitor is only neces‐

¯

stores and delivers energy, to compensate these pulsating electrical powers.

Power Filter and the load, and not anymore through the electrical power grid.

current distortions or/and unbalances (when simultaneously *i*

Active Power Filter is eliminated.

¯

load. To do this there are two possibilities:

**•** Drain the energy required for the *p*

a balanced way by the three-phases.

The compensation of *p*

energy.

120 Power Quality Issues

<sup>0</sup>in α-β-0 coordinates.

0, requires that the Shunt Active Power Filter delivers energy to the

<sup>0</sup> compensation from the electrical power grid itself, in

<sup>0</sup> ≠0 and *v*<sup>0</sup> ≠0, at the same fre‐


As can be seen in Figure 15, the inputs of the control system are the instantaneous values of the voltages and currents in the phases that feed the load to be compensated (*va*, *vb*, *vc* and *i <sup>a</sup>*, *i <sup>b</sup>*, *i c*).

**Figure 15.** Control system structure for the control strategy "constant instantaneous real power at source".

These currents and voltages are calculated in the *α-β-0* coordinates through the equations given in (2). Using the equations (5), (6) and (7) are calculated the instantaneous powers *p*, *p*<sup>0</sup> and *q*, respectively. The separation of the p-q Theory power components in their aver‐ age and alternating values can be obtained using analog or digital filters, according to the type of control system.

To calculate the reference compensation currents in the *α-β-0* coordinates is used the equa‐ tion (9):

$$
\begin{bmatrix} i\_{c\alpha} \\ i\_{c\beta} \end{bmatrix} = \frac{1}{v\_a \,^2 + v\_\beta \,^2} \begin{bmatrix} v\_\alpha & \text{-} v\_\beta \\ v\_\beta & v\_\alpha \end{bmatrix} \begin{bmatrix} p\_x \\ q\_x \end{bmatrix} \tag{9}
$$

where *K* is a proportional gain1

So:

**•** If Vdc>Vref

**•** If Vdc<Vref

and Vdc decreases.

and Vdc increases.

ces the following results:

sated);

the steady-state error.

and *Vdc* is the average voltage in the DC link.

formation given in equation (15) and equation (16):

*i ca \**

*i cb \**

= 2 / 3

*i cn* \*= - (*i ca* \* + *i cb* \* + *i cc* \*

*i cc \**

with unbalanced and/or distorted voltages.

, *Vref* is the reference of the desired voltage in the DC link,

http://dx.doi.org/10.5772/53189

Active Power Conditioners to Mitigate Power Quality Problems in Industrial Facilities

– the Shunt Active Power Filter delivers energy to the electrical power grid

– the Shunt Active Power Filter absorbs energy from the electrical power grid

*i c*0 *\**

*i cα \**

(15)

123

*i cβ \**

) (16)

*sc* (17)

The reference compensation currents in the *a-b-c* coordinates can be obtained by the trans‐

1 / 2 1 0 1 / 2 -1 / 2 3 / 2 1 / 2 -1 / 2 - 3 / 2

The calculations presented so far are synthesized in Figure 15, and correspond to a Shunt Active Power Filter control strategy for "constant instantaneous real power at source". This approach, when applied to a three-phase system with balanced sinusoidal voltages, produ‐

**•** The phase supply currents become sinusoidal, balanced, and in phase with the voltages (in other words, the power supply "sees" the load as a purely resistive symmetrical load);

**•** The neutral current is made equal to zero (even 3rd order current harmonics are compen‐

*sb* + *vci*

The p-q Theory is also a valid control strategy for the Shunt Active Power Filter when the voltages are distorted and/or unbalanced, and sinusoidal supply currents are desired. How‐ ever, with this strategy the total instantaneous power supplied will not be constant, since it is not physically possible to achieve both sinusoidal currents and constant power in systems

1 Is also possible to use a PI controller to regulate de DC link voltage. Whit the PI controller it is possible to eliminate

**•** The three-phase instantaneous power supplied, equation (17), is made constant.

*sa* + *vbi*

*p*3s=*vai*

In the previous equation, *px* and *qx*are the values of the power components to be provided by the Shunt Active Power Filter. Always that the Shunt Active Power Filter compensates the zero-sequence power (*p*0) , *px*must be subtracted of the average value of the zero-se‐ quence power,*p* ¯ 0, as presented in equation (10). In this way the energy per time unit, which *p* ¯ <sup>0</sup> represents, can be delivered to the load by the electrical power grid. The *qx*power compo‐ nent usually assumes the value of*q*, as shown in equation (11).

$$p\_x = \tilde{p} - \bar{p}\_0 \tag{10}$$

$$
\mathfrak{q}\_{\mathfrak{x}} = \mathfrak{q} \tag{11}
$$

Since the zero-sequence current must be compensated, the reference compensation current in the *0* coordinate is *i* <sup>0</sup> itself:

$$\mathbf{i}\_{c0} \mathbf{^\*} = \mathbf{i}\_0 \tag{12}$$

For a proper operation of the inverter of the Shunt Active Power Filter, the DC link voltage (*Vdc*), which corresponds to the capacitor voltage, should be regulated to be kept within ap‐ propriate levels. The p-q Theory calculations allow a simple method to regulate that voltage: if the Shunt Active Power Filter receives energy from the electrical power grid, it is stored in the capacitor and its voltage (*V dc*) will increase, otherwise, *Vdc*will decrease. It is set a regu‐ lation power (*preg*), that is included in the value of*px*:

$$p\_{\mathbf{x}} = \tilde{p} \cdot \bar{p}\_0 \cdot p\_{reg} \tag{13}$$

And the regulation power,*preg*, can be calculated according to:

$$p\_{reg} = \mathcal{K} \left( V\_{ref} - V\_{dc} \right) \tag{14}$$

where *K* is a proportional gain1 , *Vref* is the reference of the desired voltage in the DC link, and *Vdc* is the average voltage in the DC link.

So:

(9)

These currents and voltages are calculated in the *α-β-0* coordinates through the equations given in (2). Using the equations (5), (6) and (7) are calculated the instantaneous powers *p*, *p*<sup>0</sup> and *q*, respectively. The separation of the p-q Theory power components in their aver‐ age and alternating values can be obtained using analog or digital filters, according to the

To calculate the reference compensation currents in the *α-β-0* coordinates is used the equa‐

*v<sup>α</sup>* -*v<sup>β</sup> v<sup>β</sup> v<sup>α</sup>*

In the previous equation, *px* and *qx*are the values of the power components to be provided by the Shunt Active Power Filter. Always that the Shunt Active Power Filter compensates the zero-sequence power (*p*0) , *px*must be subtracted of the average value of the zero-se‐

<sup>0</sup> represents, can be delivered to the load by the electrical power grid. The *qx*power compo‐

Since the zero-sequence current must be compensated, the reference compensation current

For a proper operation of the inverter of the Shunt Active Power Filter, the DC link voltage (*Vdc*), which corresponds to the capacitor voltage, should be regulated to be kept within ap‐ propriate levels. The p-q Theory calculations allow a simple method to regulate that voltage: if the Shunt Active Power Filter receives energy from the electrical power grid, it is stored in the capacitor and its voltage (*V dc*) will increase, otherwise, *Vdc*will decrease. It is set a regu‐

*px* <sup>=</sup> ˜ *p* - *p* ¯

> *i c*0 \*=*i*

*px* <sup>=</sup> ˜ *p* - *p* ¯

*px qx*

0, as presented in equation (10). In this way the energy per time unit, which

<sup>0</sup> (10)

<sup>0</sup> (12)

<sup>0</sup> - *preg* (13)

*preg* = *K*(*Vref* - *Vdc*) (14)

*qx* =*q* (11)

*i cα* \*

*i cβ*

nent usually assumes the value of*q*, as shown in equation (11).

<sup>0</sup> itself:

lation power (*preg*), that is included in the value of*px*:

And the regulation power,*preg*, can be calculated according to:

\* <sup>=</sup> <sup>1</sup> *vα* <sup>2</sup> + *v<sup>β</sup>* 2

type of control system.

tion (9):

122 Power Quality Issues

quence power,*p*

in the *0* coordinate is *i*

*p* ¯

¯


The reference compensation currents in the *a-b-c* coordinates can be obtained by the trans‐ formation given in equation (15) and equation (16):

$$
\begin{bmatrix} i\_{ca}^\* \\ i\_{cb}^\* \\ i\_{c\alpha}^\* \end{bmatrix} = \sqrt{2/3} \begin{bmatrix} 1/\sqrt{2} & 1 & 0 \\ 1/\sqrt{2} & -1/2 & \sqrt{3}/2 \\ 1/\sqrt{2} & -1/2 & \sqrt{3}/2 \end{bmatrix} \begin{bmatrix} i\_{c0}^\* \\ i\_{c\alpha}^\* \\ i\_{c\beta}^\* \end{bmatrix} \tag{15}
$$

$$\dot{\mathbf{i}}\_{cn} \stackrel{\*}{=} - \left(\dot{\mathbf{i}}\_{ca} \stackrel{\*}{} + \dot{\mathbf{i}}\_{cb} \stackrel{\*}{} + \dot{\mathbf{i}}\_{cc} \stackrel{\*}{}\right) \tag{16}$$

The calculations presented so far are synthesized in Figure 15, and correspond to a Shunt Active Power Filter control strategy for "constant instantaneous real power at source". This approach, when applied to a three-phase system with balanced sinusoidal voltages, produ‐ ces the following results:


$$
\boldsymbol{\nu}\_{3\text{s}} = \boldsymbol{\upsilon}\_{a}\mathbf{i}\_{\text{sa}} + \boldsymbol{\upsilon}\_{b}\mathbf{i}\_{\text{sb}} + \boldsymbol{\upsilon}\_{c}\mathbf{i}\_{\text{sc}} \tag{17}
$$

The p-q Theory is also a valid control strategy for the Shunt Active Power Filter when the voltages are distorted and/or unbalanced, and sinusoidal supply currents are desired. How‐ ever, with this strategy the total instantaneous power supplied will not be constant, since it is not physically possible to achieve both sinusoidal currents and constant power in systems with unbalanced and/or distorted voltages.

<sup>1</sup> Is also possible to use a PI controller to regulate de DC link voltage. Whit the PI controller it is possible to eliminate the steady-state error.

In the case of a non-sinusoidal or unbalanced supply voltage, with the control strategy "con‐ stant instantaneous real power at source", the compensated supply currents will include harmonics, but in practical cases, when the voltage distortion and the voltage unbalance are within the limits established by the standards for the supply voltage at industries, the distor‐ tion in the source currents will be negligible after the compensation made by the Shunt Ac‐ tive Power Filter.

In terms of hardware the main components that were used are:

**•** Hall effect sensors (used to measure the voltages and currents);

**Figure 16.** Two of the four final prototypes of Shunt Active Power Filters.

execution time);

one for each leg of the inverter).

**•** A DSP (Digital Signal Processor) from Texas Instruments (the control system was imple‐ mented using only fixed point calculations in order to enhance performance in terms of

Active Power Conditioners to Mitigate Power Quality Problems in Industrial Facilities

http://dx.doi.org/10.5772/53189

125

**•** Semikron IGBTs (the inverter stage was implemented using 4 Semikron IGBT modules -

Two of the most important aspects when an equipment prototype is installed in field envi‐ ronment are security and reliability. The security of the human operators, the security of the industry plant, and the integrity of the equipment are factors that must be evaluated careful‐ ly. Therefore, it is very important to protect the Shunt Active Power Filter prototype against phenomena that usually do not exist in a laboratory environment, but that may occur in real industry installations. To accomplish these constraints, the laboratory prototypes were de‐ signed to be assembled in an electric switchboard (Figure 16). To prevent that anomalous operations could damage the Shunt Active Power Filter components, or other equipment connected to the electrical installation, various protections schemes were implemented.

A supervision and protection system was developed to permanently monitor the Shunt Ac‐ tive Power Filter operation parameters, and to disconnect the device if any anomalous val‐ ues are detected. Some of the implemented protections have two levels of actuation, in a first level the problem can be detected through software algorithms, and the Shunt Active Power Filter is softly turned off if the problem persists. More extreme malfunctions will acti‐ vate implemented hardware protections that instantaneously disconnect the Shunt Active Power Filter from the electrical power grid and also discharge the DC link capacitors. The supervision and protection system also has the responsibility to correctly operate the Shunt Active Power Filter. It is responsible for the soft connection of the Shunt Active Power Filter

With the control strategy "sinusoidal current at source", even with highly distorted and/or unbalanced source voltages, are obtained sinusoidal supply currents with the compensation made by the Shunt Active Power Filter. When this approach is used the results are:


The only difference of the control strategy "sinusoidal current at source" in relation to the control strategy "constant instantaneous real power at source" is that its control system uses the fundamental positive sequence component of the system voltages, instead of using the real measured system voltages. It is usually accomplished using a PLL (Phase Locked Loop) algorithm, as described in [37-39].

### **6. Shunt Active Power Filter Implementation and Field Results**

The Shunt Active Power Filter previously described in this chapter was implemented in the form of prototypes in order to validate the topology and control algorithms. To strength this validation it is advisable to test the active filter in different operation conditions, so it were developed four prototypes to be tested in real operation conditions in four different electri‐ cal installations, with different load profiles.

The target installations were previously monitorized, and simulation models of each instal‐ lation were developed using a simulation tool. The simulation models were used to foresee the Shunt Active Power Filter behavior and to help sizing the hardware components and the protection systems.

According to the performed measurements and studies, the four Shunt Active Power Filters were constructed within three different compensation ranges: two 20 kVA prototypes to be used in a computation center and in an hospital, a 35 kVA prototype to be used in a textile industry installation, and a 55 kVA prototype to be applied in a medical drugs distribution warehouse.

In terms of hardware the main components that were used are:

In the case of a non-sinusoidal or unbalanced supply voltage, with the control strategy "con‐ stant instantaneous real power at source", the compensated supply currents will include harmonics, but in practical cases, when the voltage distortion and the voltage unbalance are within the limits established by the standards for the supply voltage at industries, the distor‐ tion in the source currents will be negligible after the compensation made by the Shunt Ac‐

With the control strategy "sinusoidal current at source", even with highly distorted and/or unbalanced source voltages, are obtained sinusoidal supply currents with the compensation

**•** The phase supply currents become sinusoidal, balanced, and in phase with the funda‐

**•** The neutral current is made equal to zero (even 3rd order current harmonics are compen‐

**•** The total instantaneous power supplied (p3s) is not made constant, but in real cases when voltages and unbalance are within normal limits, it will present a small ripple (much

The only difference of the control strategy "sinusoidal current at source" in relation to the control strategy "constant instantaneous real power at source" is that its control system uses the fundamental positive sequence component of the system voltages, instead of using the real measured system voltages. It is usually accomplished using a PLL (Phase Locked Loop)

The Shunt Active Power Filter previously described in this chapter was implemented in the form of prototypes in order to validate the topology and control algorithms. To strength this validation it is advisable to test the active filter in different operation conditions, so it were developed four prototypes to be tested in real operation conditions in four different electri‐

The target installations were previously monitorized, and simulation models of each instal‐ lation were developed using a simulation tool. The simulation models were used to foresee the Shunt Active Power Filter behavior and to help sizing the hardware components and the

According to the performed measurements and studies, the four Shunt Active Power Filters were constructed within three different compensation ranges: two 20 kVA prototypes to be used in a computation center and in an hospital, a 35 kVA prototype to be used in a textile industry installation, and a 55 kVA prototype to be applied in a medical drugs distribution

**6. Shunt Active Power Filter Implementation and Field Results**

made by the Shunt Active Power Filter. When this approach is used the results are:

tive Power Filter.

124 Power Quality Issues

mental voltages;

smaller than before the compensation).

cal installations, with different load profiles.

protection systems.

warehouse.

algorithm, as described in [37-39].

sated);


Two of the most important aspects when an equipment prototype is installed in field envi‐ ronment are security and reliability. The security of the human operators, the security of the industry plant, and the integrity of the equipment are factors that must be evaluated careful‐ ly. Therefore, it is very important to protect the Shunt Active Power Filter prototype against phenomena that usually do not exist in a laboratory environment, but that may occur in real industry installations. To accomplish these constraints, the laboratory prototypes were de‐ signed to be assembled in an electric switchboard (Figure 16). To prevent that anomalous operations could damage the Shunt Active Power Filter components, or other equipment connected to the electrical installation, various protections schemes were implemented.

**Figure 16.** Two of the four final prototypes of Shunt Active Power Filters.

A supervision and protection system was developed to permanently monitor the Shunt Ac‐ tive Power Filter operation parameters, and to disconnect the device if any anomalous val‐ ues are detected. Some of the implemented protections have two levels of actuation, in a first level the problem can be detected through software algorithms, and the Shunt Active Power Filter is softly turned off if the problem persists. More extreme malfunctions will acti‐ vate implemented hardware protections that instantaneously disconnect the Shunt Active Power Filter from the electrical power grid and also discharge the DC link capacitors. The supervision and protection system also has the responsibility to correctly operate the Shunt Active Power Filter. It is responsible for the soft connection of the Shunt Active Power Filter to the electrical power grid, performing the pre-charge of the DC capacitor. Some of the im‐ plemented protections are:

of current in red color) the three phase currents are distorted, and at the source side (blue waveforms) the three phase currents become almost sinusoidal, and in phase with the sys‐

Active Power Conditioners to Mitigate Power Quality Problems in Industrial Facilities

http://dx.doi.org/10.5772/53189

127

**Figure 18.** System voltages (black) and currents waveforms at Load (red) and Source (blue) sides of the Shunt Active

**Figure 19.** Current harmonics and THD% at Load and Source sides of the Shunt Active Power Filter, registered in in‐

Power Filter, registered in installation 1 (Textile Industry).

stallation 1 (Textile Industry).

tem voltages (black waveforms). The total power factor increased from 0.82 to 1.


In Figure 17 is presented the generic electrical diagram of the case studies installations with the Shunt Active Power Filter. It shows the main electrical signals that were measured to validate the installation's power quality improvement achieved with the active filter. In blue are the source currents that are expected to become sinusoidal and balanced by the action of the active filter. In red are the non-sinusoidal currents of the load. In green are represented the compensation currents produced by the Shunt Active Power Filter.

The experimental results achieved in the four demonstration installations are presented in the following topics.

**Figure 17.** Generic electrical diagram of the case studies installations with the Shunt Active Power Filter.

### **6.1. Results at the Textile Industry**

The first place selected to test the Shunt Active Power Filters consisted in an electrical switchboard that feeds a cloth whitening machine, in a large textile industry. In this place, the load is composed by eight variable speed drives with different power rates. Figure 18 shows the voltage and current waveforms and RMS values measured with the Shunt Active Power Filter in operation. In this figure it is possible to see that at the load side (waveforms of current in red color) the three phase currents are distorted, and at the source side (blue waveforms) the three phase currents become almost sinusoidal, and in phase with the sys‐ tem voltages (black waveforms). The total power factor increased from 0.82 to 1.

to the electrical power grid, performing the pre-charge of the DC capacitor. Some of the im‐

**•** Protection against abnormal system voltages (protections for different values of transitory

**•** Protection against overcurrents produced by the Shunt Active Power Filter (the maxi‐ mum compensation currents are limited by software, but several malfunctions can origin

**•** Protections against high temperature are also implemented through temperature sensors assembled in various representative points. Temperature sensors also allow the ON/OFF control of the electric board ventilation fans, which are responsible for cooling the heat‐ sinks of the IGBTs modules, and the inductors (that connect the inverter to the electrical‐

In Figure 17 is presented the generic electrical diagram of the case studies installations with the Shunt Active Power Filter. It shows the main electrical signals that were measured to validate the installation's power quality improvement achieved with the active filter. In blue are the source currents that are expected to become sinusoidal and balanced by the action of the active filter. In red are the non-sinusoidal currents of the load. In green are represented

The experimental results achieved in the four demonstration installations are presented in

**Figure 17.** Generic electrical diagram of the case studies installations with the Shunt Active Power Filter.

The first place selected to test the Shunt Active Power Filters consisted in an electrical switchboard that feeds a cloth whitening machine, in a large textile industry. In this place, the load is composed by eight variable speed drives with different power rates. Figure 18 shows the voltage and current waveforms and RMS values measured with the Shunt Active Power Filter in operation. In this figure it is possible to see that at the load side (waveforms

a current higher than the parameterized limit, triggering the protection).

the compensation currents produced by the Shunt Active Power Filter.

plemented protections are:

126 Power Quality Issues

power grid).

the following topics.

**6.1. Results at the Textile Industry**

and RMS values are implemented).

**Figure 18.** System voltages (black) and currents waveforms at Load (red) and Source (blue) sides of the Shunt Active Power Filter, registered in installation 1 (Textile Industry).

**Figure 19.** Current harmonics and THD% at Load and Source sides of the Shunt Active Power Filter, registered in in‐ stallation 1 (Textile Industry).

The load currents presented a Total Harmonic Distortion (THD%) greater than 60% in all the three phases, the fifth and seventh harmonics are the highest ones, but other harmonics are also present (see Figure 19 - Load). In this load the neutral wire current was nearly zero. Ac‐ cording to the measurements presented in Figure 19, the source current THD% of all the three phases decreased to values smaller than 3%.

### **6.2. Results at the Computational Center**

The second test installation consisted in the main electrical switchboard of a computational center, at the University of Minho, where the main loads are computers, deskJet and laser printers, lighting and air-conditioning circuits.

At this electrical installation the load current presented a THD% near to 50%, the third har‐ monic was especially high, although other harmonics were present (Figure 21). The load presented significant unbalances at certain periods of the day, and the neutral current was high, not only due to the unbalance, but specially due to the third order harmonics at the phase currents, resulting in a neutral wire current with a higher value at the frequency of 150 Hz. As result of the Shunt Active Power Filter operation, the three phase currents were enhanced, the waveforms became approximately sinusoidal (Figure 20), with a THD% around 6%. At the source side the three phase currents became balanced, the neutral wire current was reduced from 16.5 A to 1 A, and the total power factor was increased from 0.88 to 0.99.

**Figure 21.** Current harmonics and THD% at Load and Source sides of the Shunt Active Power Filter, registered in in‐

Active Power Conditioners to Mitigate Power Quality Problems in Industrial Facilities

http://dx.doi.org/10.5772/53189

129

The third test site was the electrical switchboard of the clinical analyses laboratory of a hos‐ pital. Here, the loads were composed by some computers, diverse medical equipments, and

**Figure 22.** System voltages (black) and currents waveforms at Load (red) and Source (blue) sides of the Shunt Active

**6.3. Results at the Clinical Analysis Laboratory of an Hospital**

Power Filter, registered in installation 3 (Clinical Analysis Laboratory).

stallation 2 (Computational Center).

lighting and air-conditioning circuits.

**Figure 20.** System voltages (black) and currents waveforms at Load (red) and Source (blue) sides of the Shunt Active Power Filter, registered in installation 2 (Computational Center)

**Figure 21.** Current harmonics and THD% at Load and Source sides of the Shunt Active Power Filter, registered in in‐ stallation 2 (Computational Center).

### **6.3. Results at the Clinical Analysis Laboratory of an Hospital**

The load currents presented a Total Harmonic Distortion (THD%) greater than 60% in all the three phases, the fifth and seventh harmonics are the highest ones, but other harmonics are also present (see Figure 19 - Load). In this load the neutral wire current was nearly zero. Ac‐ cording to the measurements presented in Figure 19, the source current THD% of all the

The second test installation consisted in the main electrical switchboard of a computational center, at the University of Minho, where the main loads are computers, deskJet and laser

At this electrical installation the load current presented a THD% near to 50%, the third har‐ monic was especially high, although other harmonics were present (Figure 21). The load presented significant unbalances at certain periods of the day, and the neutral current was high, not only due to the unbalance, but specially due to the third order harmonics at the phase currents, resulting in a neutral wire current with a higher value at the frequency of 150 Hz. As result of the Shunt Active Power Filter operation, the three phase currents were enhanced, the waveforms became approximately sinusoidal (Figure 20), with a THD% around 6%. At the source side the three phase currents became balanced, the neutral wire current was reduced from 16.5 A to 1 A, and the total power factor was increased from

**Figure 20.** System voltages (black) and currents waveforms at Load (red) and Source (blue) sides of the Shunt Active

three phases decreased to values smaller than 3%.

**6.2. Results at the Computational Center**

0.88 to 0.99.

128 Power Quality Issues

printers, lighting and air-conditioning circuits.

Power Filter, registered in installation 2 (Computational Center)

The third test site was the electrical switchboard of the clinical analyses laboratory of a hos‐ pital. Here, the loads were composed by some computers, diverse medical equipments, and lighting and air-conditioning circuits.

**Figure 22.** System voltages (black) and currents waveforms at Load (red) and Source (blue) sides of the Shunt Active Power Filter, registered in installation 3 (Clinical Analysis Laboratory).

**Figure 23.** Current harmonics and THD% at Load and Source sides of the Shunt Active Power Filter, registered in in‐ stallation 3 (Clinical Analysis Laboratory).

**Figure 24.** System voltages (black) and currents waveforms at Load (red) and Source (blue) sides of the Shunt Active

Active Power Conditioners to Mitigate Power Quality Problems in Industrial Facilities

http://dx.doi.org/10.5772/53189

131

**Figure 25.** Current harmonics and THD% at Load and Source sides of the Shunt Active Power Filter, registered in in‐

The presented results confirm the ability of the Shunt Active Power Filters to compensate problems like current harmonics, current unbalance and power factor. The developed proto‐

types presented a good performance in all the four demonstration installations.

Power Filter, registered in installation 4 (Medical Drugs Distribution Warehouse).

stallation 4 (Medical Drugs Distribution Warehouse).

The load currents presented low harmonic distortion (the worst case was phase *A* with a THD% near to 11%), but the unbalance was very significant during certain periods of the day (see Figure 21 and Figure 23). In Figure 22 it is possible to see that the phase *A* current was almost 29 A, while the phase *B* current was smaller than 9 A. The phases *B* and *C* also presented low power factor (less than 0.78). When the Shunt Active Power Filter was operat‐ ing, the current THD% at the source side decreased in all the three phases, reaching values near to 3%, and became balanced with unitary power factor. The current in the neutral wire decreased from 16 A to approximately 1 A.

### **6.4. Results at the Medical Drugs Distribution Warehouse**

The fourth test site consisted in a medical drugs distribution warehouse. Here, the Shunt Ac‐ tive Power Filter was installed at the main switchboard of the warehouse. The principal loads of this installation were illumination circuits (composed by a large number of fluorescent tube lamps with magnetic ballasts), chest refrigerators, conveyor belt systems, and a central air-con‐ ditioning unit. The load current presented low distortion (the worst case was in phase *A* with a THD% near to 5%), as it can be seen in Figure 25. The current unbalance was also small, re‐ sulting in a neutral wire current of around only 8 A (also there were not large values of third order harmonics). The major problem of this installation was the power factor. According to the Portuguese legislation, if an installation presents a *tan φ* higher than 0.4 (equivalent to a *cos φ* lower than 0.93), the Reactive Energy is taxed. It is possible to see in Figure 24 that the total power factor of the installation was lower than 0.7. When the Shunt Active Power Fil‐ ter was connected, the current THD% at the electrical power grid side decreased in all the three phases, reaching values of less than 2%. The three phase currents became sinusoidal, in phase with the system voltages, and perfectly balanced. The power factor increased from 0.69 to 1, and the current in the neutral wire decreased from 8 A to 3 A.

Active Power Conditioners to Mitigate Power Quality Problems in Industrial Facilities http://dx.doi.org/10.5772/53189 131

**Figure 24.** System voltages (black) and currents waveforms at Load (red) and Source (blue) sides of the Shunt Active Power Filter, registered in installation 4 (Medical Drugs Distribution Warehouse).

**Figure 23.** Current harmonics and THD% at Load and Source sides of the Shunt Active Power Filter, registered in in‐

The load currents presented low harmonic distortion (the worst case was phase *A* with a THD% near to 11%), but the unbalance was very significant during certain periods of the day (see Figure 21 and Figure 23). In Figure 22 it is possible to see that the phase *A* current was almost 29 A, while the phase *B* current was smaller than 9 A. The phases *B* and *C* also presented low power factor (less than 0.78). When the Shunt Active Power Filter was operat‐ ing, the current THD% at the source side decreased in all the three phases, reaching values near to 3%, and became balanced with unitary power factor. The current in the neutral wire

The fourth test site consisted in a medical drugs distribution warehouse. Here, the Shunt Ac‐ tive Power Filter was installed at the main switchboard of the warehouse. The principal loads of this installation were illumination circuits (composed by a large number of fluorescent tube lamps with magnetic ballasts), chest refrigerators, conveyor belt systems, and a central air-con‐ ditioning unit. The load current presented low distortion (the worst case was in phase *A* with a THD% near to 5%), as it can be seen in Figure 25. The current unbalance was also small, re‐ sulting in a neutral wire current of around only 8 A (also there were not large values of third order harmonics). The major problem of this installation was the power factor. According to the Portuguese legislation, if an installation presents a *tan φ* higher than 0.4 (equivalent to a *cos φ* lower than 0.93), the Reactive Energy is taxed. It is possible to see in Figure 24 that the total power factor of the installation was lower than 0.7. When the Shunt Active Power Fil‐ ter was connected, the current THD% at the electrical power grid side decreased in all the three phases, reaching values of less than 2%. The three phase currents became sinusoidal, in phase with the system voltages, and perfectly balanced. The power factor increased from 0.69

stallation 3 (Clinical Analysis Laboratory).

130 Power Quality Issues

decreased from 16 A to approximately 1 A.

**6.4. Results at the Medical Drugs Distribution Warehouse**

to 1, and the current in the neutral wire decreased from 8 A to 3 A.

**Figure 25.** Current harmonics and THD% at Load and Source sides of the Shunt Active Power Filter, registered in in‐ stallation 4 (Medical Drugs Distribution Warehouse).

The presented results confirm the ability of the Shunt Active Power Filters to compensate problems like current harmonics, current unbalance and power factor. The developed proto‐ types presented a good performance in all the four demonstration installations.

### **7. Conclusions**

The growing use of non-linear loads in industrial facilities is the source of several power quality problems, such as harmonics, reactive power, flicker and resonance. These problems affect not only the facility but also the electrical power system by distorting the voltage and current waveforms with harmonics of various orders, including inter-harmonics. Active Power Conditioners are an up-to-date solution to mitigate these power quality problems. It can be found conditioners to mitigate current problems, others to mitigate voltage problems, and others that mitigate both current and voltage problems, both in power systems and in industrial facilities. In this chapter were presented the Active Power Conditioners more suit‐ able for use in industrial facilities, explaining in detail their concepts, presenting their power electronics topologies and typical waveforms.

compensate for load current unbalance, and almost eliminate the current in the neutral wire at the source side. Therefore, the Shunt Active Power Filters allow the power source to see an unbalanced and non-linear load, with reactive power consumption, as if the load is a symmetrical linear resistive load. By the action of the Shunt Active Power Filters, the cur‐ rents at the three phases of the source side become almost sinusoidal and in phase with the voltages, and the neutral wire current become almost null. Since all the source currents are

Active Power Conditioners to Mitigate Power Quality Problems in Industrial Facilities

http://dx.doi.org/10.5772/53189

133

reduced in relation to the load currents, the electrical installation losses also decrease.

, J. G. Pinto and Henrique Gonçalves

Centro Algoritmi, Universityof Minho, Guimarães, Portugal

\*Address all correspondence to: jla@dei.uminho.pt

This work is financed by FEDER Funds, through the Operational Program for Competitive‐ ness Factors – COMPETE, and by National Funds through FCT – Foundation for Science and Technology, under the projects: DEMTEC/020/1/03, PTDC/EEA-EEL/104569/2008, and

[1] IEEE Working Group on Power System Harmonics, "The Effects of Power System Harmonics on Power System Equipment and Loads," Power Apparatus and Sys‐

[2] A. Bachry; Z. A. Styczynski, "An Analysisof Distribution System Power Quality Problems Resulting from Load Unbalance and Harmonics," IEEE PES – Transm. and

[3] V.E. Wagner, J.C. Balda, D.C. Griffith, A. McEachern, T.M. Barnes, D.P. Hartmann, D.J. Phileggi, A.E. Emannuel, W.F. Horton, W.E. Reid, R.J. Ferraro, and W.T. Jewell, "Effects of harmonics on equipment," Power Delivery, IEEE Transactions on, vol.8,

[4] E.F. Fuchs, D.J. Roesler, and F.S. Alashhab, "Sensitivity of Electrical Appliances to Harmonics and Fractional Harmonics of the Power SYSTEM's Voltage. Part I: Trans‐ formers and Induction Machines," Power Delivery, IEEE Transactions on, vol. 2,

tems, IEEE Transactions on, vol. PAS-104, 1985, pp. 2555-2563.

Dist. Conf. and Exp., Vol 2, 7-12 Sept. 2003 pp.763–766.

**Acknowledgements**

**Author details**

João L. Afonso\*

**References**

FCOMP-01-0124-FEDER-022674.

1993, pp. 672-680.

1987, pp. 437-444.

Shunt Active Power Filters allow the compensation of problems related to the consumed currents, like current harmonics and current unbalance, together with power factor correc‐ tion, and can be a much better solution than the conventional approach (capacitors for pow‐ er factor correction and passive filters to compensate for current harmonics). They are most suitable for facilities with a high level of distortion and/or unbalance of the consumed cur‐ rents. There are some situations in which the use of Shunt Active Power Filters to compen‐ sate the current problems also improves the power grid voltage waveforms due to the reduction of the current harmonics flowing through the line impedances.

Series Active Power Filters permit the compensation of problems related to the supplied vol‐ tages, like voltage harmonics, voltage unbalance, sags, swells and flicker. They are most suitable for facilities with loads sensitive to voltage problems. In installations that use shunt passive filters to mitigate current harmonics they also improve the behavior of those passive filters and the overall installation power quality.

Unified Power Quality Conditioners (UPQCs) can compensate both and simultaneously problems related to the consumed currents and to the supplied voltages. So, it is suitable for facilities that have problems in the consumed currents and that also have loads which are sensitive to voltage problems. The UPQC topology allows the power flow between the shunt and series conditioners, so it is able to compensate undervoltages and overvoltages in steady-state. This is a great advantage comparing to the use of shunt and series active power filters operating independently.

The control of the conditioners is also a matter of great importance, and different control theories can be found. The p-q Theory is a suitable tool to the analysis of three-phase electri‐ cal systems with non-linear loads and for the control of Active Power Conditioners. Based on this theory, two control strategies for Shunt Active Power Filters were described in this chapter, one leading to constant instantaneous real power at source and the other leading to sinusoidal currents at source.

The experimental results obtained in four different test facilities, and presented in this chap‐ ter, show that the developed Shunt Active Power Filters have a good performance.They dy‐ namically compensate for harmonic currents, and correct power factor. They also compensate for load current unbalance, and almost eliminate the current in the neutral wire at the source side. Therefore, the Shunt Active Power Filters allow the power source to see an unbalanced and non-linear load, with reactive power consumption, as if the load is a symmetrical linear resistive load. By the action of the Shunt Active Power Filters, the cur‐ rents at the three phases of the source side become almost sinusoidal and in phase with the voltages, and the neutral wire current become almost null. Since all the source currents are reduced in relation to the load currents, the electrical installation losses also decrease.

### **Acknowledgements**

**7. Conclusions**

132 Power Quality Issues

electronics topologies and typical waveforms.

filters and the overall installation power quality.

filters operating independently.

sinusoidal currents at source.

The growing use of non-linear loads in industrial facilities is the source of several power quality problems, such as harmonics, reactive power, flicker and resonance. These problems affect not only the facility but also the electrical power system by distorting the voltage and current waveforms with harmonics of various orders, including inter-harmonics. Active Power Conditioners are an up-to-date solution to mitigate these power quality problems. It can be found conditioners to mitigate current problems, others to mitigate voltage problems, and others that mitigate both current and voltage problems, both in power systems and in industrial facilities. In this chapter were presented the Active Power Conditioners more suit‐ able for use in industrial facilities, explaining in detail their concepts, presenting their power

Shunt Active Power Filters allow the compensation of problems related to the consumed currents, like current harmonics and current unbalance, together with power factor correc‐ tion, and can be a much better solution than the conventional approach (capacitors for pow‐ er factor correction and passive filters to compensate for current harmonics). They are most suitable for facilities with a high level of distortion and/or unbalance of the consumed cur‐ rents. There are some situations in which the use of Shunt Active Power Filters to compen‐ sate the current problems also improves the power grid voltage waveforms due to the

Series Active Power Filters permit the compensation of problems related to the supplied vol‐ tages, like voltage harmonics, voltage unbalance, sags, swells and flicker. They are most suitable for facilities with loads sensitive to voltage problems. In installations that use shunt passive filters to mitigate current harmonics they also improve the behavior of those passive

Unified Power Quality Conditioners (UPQCs) can compensate both and simultaneously problems related to the consumed currents and to the supplied voltages. So, it is suitable for facilities that have problems in the consumed currents and that also have loads which are sensitive to voltage problems. The UPQC topology allows the power flow between the shunt and series conditioners, so it is able to compensate undervoltages and overvoltages in steady-state. This is a great advantage comparing to the use of shunt and series active power

The control of the conditioners is also a matter of great importance, and different control theories can be found. The p-q Theory is a suitable tool to the analysis of three-phase electri‐ cal systems with non-linear loads and for the control of Active Power Conditioners. Based on this theory, two control strategies for Shunt Active Power Filters were described in this chapter, one leading to constant instantaneous real power at source and the other leading to

The experimental results obtained in four different test facilities, and presented in this chap‐ ter, show that the developed Shunt Active Power Filters have a good performance.They dy‐ namically compensate for harmonic currents, and correct power factor. They also

reduction of the current harmonics flowing through the line impedances.

This work is financed by FEDER Funds, through the Operational Program for Competitive‐ ness Factors – COMPETE, and by National Funds through FCT – Foundation for Science and Technology, under the projects: DEMTEC/020/1/03, PTDC/EEA-EEL/104569/2008, and FCOMP-01-0124-FEDER-022674.

### **Author details**

João L. Afonso\* , J. G. Pinto and Henrique Gonçalves

\*Address all correspondence to: jla@dei.uminho.pt

Centro Algoritmi, Universityof Minho, Guimarães, Portugal

### **References**


[5] E.F. Fuchs, D.J. Roesler, and K.P. Kovacs, "Sensitivity of Electrical Appliances to Har‐ monics and Fractional Harmonics of the Power System's Voltage. Part II: Television Sets, Induction Watthour Meters and Universal Machines," Power Delivery, IEEE Transactions on, vol. 2, 1987, pp. 445-453.

[15] R. Pregitzer, J. G. Pinto, Luís F.C. Monteiro, João L. Afonso," Shunt Active Power Fil‐ ter with Dynamic Output Current Limitation" , Proceedings of ISIE 2007- 2007 IEEE International Symposium on Industrial Electronics, 4-7 June, 2007, Vigo, Spain. [16] Pedro Neves, Gabriel Pinto, Ricardo Pregitzer, Luís Monteiro, João L. Afonso," Ex‐ perimental Results of a Single-Phase Shunt Active Filter Prototype with Different Switching Techniques", Proceedings of ISIE 2007- 2007 IEEE International Symposi‐

Active Power Conditioners to Mitigate Power Quality Problems in Industrial Facilities

http://dx.doi.org/10.5772/53189

135

[17] Filipe Ferreira, Luís Monteiro, João L. Afonso, Carlos Couto, "A Control Strategy for a Three-Phase Four-Wire Shunt Active Filter", IECON'08 - The 34th Annual Confer‐ ence of the IEEE Industrial Electronics Society, Orlando, Florida, USA, 10-13 Nov.

[18] J. G. Pinto, Pedro Neves, Ricardo Pregitzer, Luís F. C. Monteiro, João L. Afonso, "Sin‐ gle-Phase Shunt Active Filter with Digital Control", Proceedings of ICREPQ'07- In‐ ternational Conference on Renewable Energies and Power Quality, 28-30 March

[19] H. Carneiro, J. G. Pinto, J. L. Afonso, "Single-Phase Series Active Conditioner for the Compensation of Voltage Harmonics, Sags, Swell and Flicker", ISIE 2011 - 20th IEEE International Symposium on Industrial Electronics, pp. 384-389, 27-30 June 2011,

[20] J. G. Pinto, R. Pregitzer, Luís. F. C. Monteiro, Carlos Couto, João. L. Afonso, "A Com‐ bined Series Active Filter and Passive Filters for Harmonics, Unbalances and Flicker Compensation", Proceedings of POWERENG - First International Conference on Power Engineering, Energy and Electrical Drives, 12 14 April, 2007, Setubal, Portu‐

[21] J. G. Pinto; Helder Carneiro, Bruno Exposto, Carlos Couto, João L. Afonso, "Transfor‐ merless Series Active Power Filter to Compensate Voltage Disturbances", Proceed‐ ings of the 14th European Conference on Power Electronics and Applications (EPE

[22] A. J. Visser, J. H. R. Enslin, H. du T. Mouton, "Transformerless Series Sag Compensa‐ tion With a Cascaded Multilevel Inverter," IEEE Transactions on Industrial Electron‐

[23] Carneiro, H.; Exposto, B.; Gonçalves, H.; Pinto, J.G.; Afonso, J.L. , "Single-phase Ser‐ ies Active Conditioner Active Power Flow in a Harmonic Free Electrical System Dur‐ ing Sag and Swell Events", Proceedings of the 14th European Conference on Power Electronics and Applications (EPE 2011), pp. 1-10, Aug. 30 - Sept. 2011, Birmingham,

[24] Luís F. C. Monteiro, José C. C. Costa, Maurício Aredes, João L. Afonso, "A Control‐ Strategy for a Three-LevelUnifiedPowerQualityConditioner," Proceedings (CD-ROM) 8th COBEP - Congresso Brasileiro de Eletrônica de Potência, Recife, PE, Brasil,

2011), pp. 1-6, Birmingham, United Kingdom, Aug. 30 - Sept. 1 2011.

ics, vol. 49, nº 4, August 2002, pp. 824-831.

um on Industrial Electronics, 4-7 June, 2007, Vigo, Spain.

2008, pp.411-416.

Seville, Spain.

Gdansk, Poland.

United Kingdom.

14 17 Julho 2005.

gal.


[15] R. Pregitzer, J. G. Pinto, Luís F.C. Monteiro, João L. Afonso," Shunt Active Power Fil‐ ter with Dynamic Output Current Limitation" , Proceedings of ISIE 2007- 2007 IEEE International Symposium on Industrial Electronics, 4-7 June, 2007, Vigo, Spain.

[5] E.F. Fuchs, D.J. Roesler, and K.P. Kovacs, "Sensitivity of Electrical Appliances to Har‐ monics and Fractional Harmonics of the Power System's Voltage. Part II: Television Sets, Induction Watthour Meters and Universal Machines," Power Delivery, IEEE

[6] João L. Afonso, Carlos Couto, Júlio Martins, "Active Filters with Control Based on the p-q Theory," IEEE Industrial Electronics Society Newsletter, vol. 47, nº 3, Sept.

[7] J. G. Pinto, Pedro Neves, D. Gonçalves, João L. Afonso, "Field Results on Developed Three-Phase Four-Wire Shunt Active Power Filters," IECON 2009 - The 35th Annual Conference of the IEEE Industrial Electronics Society, 3 5 November, Porto, Portugal.

[8] Pedro Neves, Gabriel Pinto, Ricardo Pregitzer, Luís Monteiro, João L. Afonso, "Ex‐ perimental Results of a Single-Phase Shunt Active Filter Prototype with Different Switching Techniques," Proceedings of ISIE 2007- 2007 IEEE International Symposi‐

[9] J. G. Pinto, Pedro Neves, Ricardo Pregitzer, Luís F. C. Monteiro, João L. Afonso, "Sin‐ gle-Phase Shunt Active Filter with Digital Control," Proceedings of ICREPQ'07- In‐ ternational Conference on Renewable Energies and Power Quality, 28-30 March

[10] M. Aredes, J. Häffner and K. Heumman, "A combined series and shunt active power filters," IEEE/KTH– Stockholm Power Tech. Conf., SPT PE 07-05-0643, vol. Power

[11] H. Fujita, H. Akagi,"The Unified Power Quality Conditioner:The Integration of Ser‐ ies and Shunt Active Filters," IEEE Trans. On Power Electronics, vol.13, No.2, March

[12] J. G. Pinto, R. Pregitzer, Luís. F. C. Monteiro, Carlos Couto, João. L. Afonso, "A Com‐ bined Series Active Filter and Passive Filters for Harmonics, Unbalances and Flicker Compensation," Proceedings of POWERENG - First International Conference on Power Engineering, Energy and Electrical Drives, 12 14 April, 2007, Setubal, Portu‐

[13] L. F. C. Monteiro, João L. Afonso, J. G.Pinto, E. H. Watanabe, M. Aredes, H. Akagi, "CompensationAlgorithmsbasedonthe p-q andCPCTheories for SwitchingCompen‐ sators in Micro-Grids," Revista Eletrônica de Potência – Associação Brasileira de Ele‐ trônica de Potência – SOBRAEP, ISSN 1414-8862, Vol. 14, no. 4, Novembro de 2009,

[14] E. H. Watanabe, J. L. Afonso, J. G. Pinto, L. F. C. Monteiro, M. Aredes, H. Akagi, "In‐ stantaneous p-q Power Theory for Control of Compensators in Micro-Grids," IEEE ISNCC - International School on Nonsinusoidal Currents and Compensation, 15-18

um on Industrial Electronics, 4-7 June, 2007, Vigo, Spain.

Transactions on, vol. 2, 1987, pp. 445-453.

Elect., Sweden, June 1995, pp. 237–242.

gal, pp 54-59 ISBN: 1-4244-0895-4.

2000, pp. 5-10.

134 Power Quality Issues

Seville, Spain.

1998, pp. 315-322.

pp. 259-268.

June 2010, àagów, Poland.


[25] H. Akagi, Y. Kanazawa, A. Nabae, "Generalized Theory of the Instantaneous Reac‐ tive Power in Three-Phase Circuits," IPEC'83 - Int. Power Electronics Conf., Tokyo, Japan, 1983, pp. 1375-1386.


Active Power Conditioners to Mitigate Power Quality Problems in Industrial Facilities

http://dx.doi.org/10.5772/53189

137

[38] Helder Carneiro; Bruno Exposto; João L. Afonso, "Evaluation of Two Fundamental Positive-Sequence Detectors for Highly Distorted and Unbalanced Systems", IEEE EPQU 2011 - Electrical Power Quality and Utilization Conference, Lisbon, Portugal,

[39] L. G. Barbosa Rolim, D. Rodrigues da CostaJr., and M. Aredes, "Analysis and Soft‐ ware Implementation of a Robust Synchronizing PLL Circuit Based on the pq Theo‐ ry," IEEE Transactions on Industrial Electronics, vol. 53, no. 6, pp. 1919-1926, Dec.

ber 2009, Porto, Portugal.

17-19 Oct. 2011.

2006.



[38] Helder Carneiro; Bruno Exposto; João L. Afonso, "Evaluation of Two Fundamental Positive-Sequence Detectors for Highly Distorted and Unbalanced Systems", IEEE EPQU 2011 - Electrical Power Quality and Utilization Conference, Lisbon, Portugal, 17-19 Oct. 2011.

[25] H. Akagi, Y. Kanazawa, A. Nabae, "Generalized Theory of the Instantaneous Reac‐ tive Power in Three-Phase Circuits," IPEC'83 - Int. Power Electronics Conf., Tokyo,

[26] H. Akagi, Y. Kanazawa, A. Nabae, "Instanataneous Reactive Power Compensator Comprising Switching Devices without Energy Storage Compenents," IEEE Trans.

[27] M. Depenbrock, "The FBD-Method, a Generally Applicable Tool for Analysing Pow‐ er Relations," IEEE Transactions on Power Systems, vol. 8, no. 2, pp. 381-387, May

[28] P. Tenti, E. Tedeschi, P. Mattavelli, "Cooperative Operation of Active Power Filters by Instantaneous Complex Power Control," 7th International Conference on Power

[29] L. S. Czarnecki, "On some misinterpretations of the instantaneous reactive power p– q theory," IEEE Transactions on Power Electronics, vol. 19, no. 3, pp. 828–836, May

[30] L. S. Czarnecki, "Instantaneous reactive power p–q theory and power properties of three-phase systems," IEEE Transactions on Power Delivery, vol. 21, no. 1, pp. 362–

[31] H. S. Kim, H. Akagi, "The instantaneous power theory on the rotating p-q-r reference

[32] M. Depenbrock, V. Staudt, H. Wrede, "Concerning instantaneous power compensa‐ tion in three-phase systems by using p–q–r theory," IEEE Transactions on Power

[33] M. Aredes, H. Akagi, E. H. Watanabe, E. V. Salgado, L. F. Encarnação, "Comparisons Between the p–q and p–q–r Theories in Three-Phase Four-Wire Systems," IEEE

[34] R. I. Bojoi, G. Griva, V. Bostan, M. Guerreiro, F. Farina, F. Profumo, "Current Control Strategy for Power Conditioners Using Sinusoidal Signal Integrators in Synchronous Reference Frame," IEEE Transactions on Power Electronics, vol. 20, no. 6, pp. 1402–

[35] E. H. Watanabe, R. M. Stephan, M. Aredes, "New Concepts of Instantaneous Active and Reactive Powers in Electrical Systems with Generic Loads," IEEE Trans. Power

[36] M. Aredes, E. H. Watanabe, "New Control Algorithms for Series and Shunt Three-Phase Four-Wire Active Power Filters," IEEE Trans. Power Delivery, vol 10, no. 3, Ju‐

[37] H. Carneiro, L. F. C. Monteiro, João L. Afonso, "Comparisons between Synchroniz‐ ing Circuits to Control Algorithms for Single-Phase Active Converters", IECON 2009

Transactions on Power Electronics, , vol. 24, no. 4, pp. 924-933, April 2009.

frames," in Proc. IEEE/PEDS 1999 Conf., Hong Kong, Jul., pp. 422–427.

Electronics, vol. 19, no. 4, pp. 1151–1152, Jul. 2004.

Delivery, vol. 8, no. 2, April 1993, pp. 697-703.

Electronics and Drive Systems, 2007 (PEDS '07), pp. 555-561, November 2007.

Japan, 1983, pp. 1375-1386.

1993.

136 Power Quality Issues

2004.

367, January 2006.

1412, November 2005.

ly 1995, pp. 1649-1656.

Industry Applic., vol. 20, May/June 1984.

[39] L. G. Barbosa Rolim, D. Rodrigues da CostaJr., and M. Aredes, "Analysis and Soft‐ ware Implementation of a Robust Synchronizing PLL Circuit Based on the pq Theo‐ ry," IEEE Transactions on Industrial Electronics, vol. 53, no. 6, pp. 1919-1926, Dec. 2006.


$$J\_i\left(\mathbf{x},\boldsymbol{\mu}\right) \quad i=1,..., \ N\_{\boldsymbol{\phi}\circ i} \tag{1}$$

$$\log\left(\mathbf{x},\boldsymbol{\mu}\right) = \mathbf{0} \tag{2}$$

$$h(x,u) \le 0\tag{3}$$

$$f = \sum\_{i=1}^{N\_{\mathcal{S}}} \left( a\_i + b\_i P\_{\mathcal{S}^i} + c\_i P\_{\mathcal{S}^i}^2 \right) \tag{4}$$

$$f\_e = \sum\_{i=1}^{Ng} 10^{-2} \times \left(\alpha\_i + \beta\_i P\_{gi} + \gamma\_i P\_{gi}^2 + \alpha\_i \exp\left(\mu\_i P\_{gi}\right)\right) \text{Ton } / \text{ h} \tag{5}$$

$$f\_{cc} = o \imath f\_c \\$/\,\text{h} \tag{6}$$

$$F\_T = af + (1 - a)f\_{\alpha} \tag{7}$$

$$f\_T = \sum\_{i=1}^{NG} \left( a\_i + b\_i P\_{\bar{g}^j} + c\_i P\_{\bar{g}^i}^2 \right) + \left| d\_i \sin \left( e\_i \left( P\_{\bar{g}^i}^{\min} - P\_{\bar{g}^j} \right) \right) \right| \tag{8}$$

$$P\_{\rm loss} = \sum\_{k=1}^{N\_l} g\_k \left[ \left( t\_k V\_i \right)^2 + V\_j^2 - 2t\_k V\_i V\_j \cos \delta\_{ij} \right] \tag{9}$$

$$
\Delta V = \sum\_{k=1}^{N\_{PQ}} \left| V\_k - V\_k^{\text{des}} \right| \tag{10}
$$

$$P\_{gj} - P\_{di} = V\_i \sum\_{j=1}^{N} V\_j \left( g\_{i\bar{j}} \cos \delta\_{i\bar{j}} + b\_{i\bar{j}} \sin \delta\_{i\bar{j}} \right) \tag{11}$$

$$Q\_{gi} - Q\_{di} = V\_i \sum\_{j=1}^{N} V\_j \left( g\_{ij} \sin \delta\_{ij} - b\_{ij} \cos \delta\_{ij} \right) \tag{12}$$


$$V\_{g^i}^{\min} \le V\_{g^i} \le V\_{g^i}^{\max}, \ i = 1, 2, \dots, NPV \tag{13}$$

$$S\_{li} \le S\_{li}^{\max}, \ i = 1, 2, \dots, NPQ \tag{14}$$

$$V\_{Ii}^{\min} \le V\_{Ii} \le V\_{Ii}^{\max}, \ i = 1, 2, \dots, NPQ \tag{15}$$

$$t\_i^{\min} \le t\_i \le t\_i^{\max}, i = 1, 2, \dots, NT \tag{16}$$

$$X^{\text{min}} \le X\_{FACTS} \le X^{\text{max}} \tag{17}$$



$$\beta\left(r\right) = \beta\_0 \exp\left(-\gamma r^m\right), \text{ with } m \ge 1,\tag{18}$$

$$\|r\_{ij} = \|\boldsymbol{\pi}\_i - \boldsymbol{\pi}\_j\| = \sqrt{\sum\_{k=1}^d \left(\boldsymbol{\pi}\_{i,k} - \boldsymbol{\pi}\_{j,k}\right)^2} \tag{19}$$

$$\mathbf{x}\_{i} = \mathbf{x}\_{i} + \beta\_{0} \exp\left(-\gamma r\_{\text{ij}}^{2}\right) \mathbf{x}\_{j} - \mathbf{x}\_{i}\tag{20} \\ \text{and} \\ \mathbf{z} = \mathbf{0}.5\text{)}\_{i} \tag{20}$$

$$
\mathcal{B}\_{\; \; 0} = 1 \tag{21}
$$

$$\mathbf{x}\_{i} = rand. \left( \mathbf{x}\_{i}^{\text{max}} - \mathbf{x}\_{i}^{\text{min}} \right) + \mathbf{x}\_{i}^{\text{min}} \tag{22}$$





$$P d1 = \sum\_{i=1}^{M1} P\_{Gi} \tag{23}$$

$$Pd2 = \sum\_{i=1}^{M2} P\_{Gi} = PD - Pd1\tag{24}$$

$$P d1 + P d2 = PD + P \text{loss} \tag{25}$$


$$\sum\_{i=1}^{N\_g} \left( Pg\_i \right) = \sum\_{i=1}^{pvr\_i} \left( Pd\_i \right) + ploss \tag{26}$$

$$P\mathcal{g}\_i^{\min} \le P\mathcal{g}\_i \le P\mathcal{g}\_i^{\max} \tag{27}$$

$$I\_{\rm SVC} = jB\_{\rm SVC}V \tag{28}$$

$$\begin{aligned} B\_{\text{SVC}} &= B\_{\text{C}} - B\_{\text{TCR}} = \frac{1}{X\_{\text{C}} X\_{L}} \left\{ X\_{L} - \frac{X\_{\text{C}}}{\pi} \left[ 2\left(\pi - \alpha\right) + \sin\left(2\alpha\right) \right] \right\}\_{\text{V}} \\ X\_{L} &= \alpha L, X\_{\text{C}} = \frac{1}{\alpha \text{C}}. \end{aligned} \tag{29}$$

$$Q\_i^{\text{SVC}} = B\_i^{\text{SVC}} \cdot V\_i^2 \tag{30}$$










**Chapter 7**

**Harmonic Effects of Power System Loads:**

Celal Kocatepe, Recep Yumurtacı, Oktay Arıkan,

Additional information is available at the end of the chapter

sults were discussed and suggestions were given.

**2. Power system harmonics**

Mustafa Baysal, Bedri Kekezoğlu, Altuğ Bozkurt and

Today, electric power systems is spreading to a large area and wide variety of loads are con‐ nected to energy system. During the planning and management of power systems, accurate determination of load characteristics that connected to power system is very important. Thus, power system problems, that may occur, can be pre-determined and precautions may

Especially with the developing semi-conductor technology, harmonics have become one of the most popular issues in power system. In this study, the measurements for the harmonic effects of the loads in power system were carried out and also contribution of these loads to harmonic distortion was exhibited. Moreover, the effect of harmonics existing in power sys‐ tem on the performance of some equipment was analyzed experimentally. The obtained re‐

Harmonics can be defined as components with periodic waveforms having multiples of fun‐ damental frequency. Harmonics, one of the most important issues of power quality, have re‐ cently come into prominence though they are known since the early time of the ac power systems. In 1893, only eight years after first ac power plant is built, engineers conducted har‐ monic analyses to identify and solve the motor heating problem [1]. A paper written by E.J.

> © 2013 Kocatepe 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 Kocatepe 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.

**An Experimental Study**

C. Fadıl Kumru

**1. Introduction**

be taken against them.

http://dx.doi.org/10.5772/53108

### **Chapter 7**
