26

Active Filters for Power Conditioning

Hirofumi Akagi

Tokyo Institute of Technology

26.1    Harmonic-Producing Loads

Identified Loads and Unidentified Loads • Harmonic Current Sources and Harmonic Voltage Sources

26.2    Theoretical Approach to Active Filters for Power Conditioning

The Akagi-Nabae Theory • Energy Storage Capacity • Classification of Active Filters • Classification by Objectives: Who Is Responsible for Installing Active Filters? • Classification by System Configuration • Classification by Power Circuit • Classification by Control Strategy

26.3    Integrated Series Active Filters

System Configuration • Operating Principle • Control Circuit • Experimental Results

26.4    Practical Applications of Active Filters for Power Conditioning

Present Status and Future Trends • Shunt Active Filters for Three-Phase Four-Wire Systems • The 48-MVA Shunt Active Filter Hirofumi Akagi for Compensation of Voltage Impact Drop, Variation, and Imbalance

Acknowledgment

References

Much research has been performed on active filters for power conditioning and their practical applications since their basic principles of compensation were proposed around 1970 (Bird et al., 1969; Gyugyi and Strycula, 1976; Kawahira et al., 1983). In particular, recent remarkable progress in the capacity and switching speed of power semiconductor devices such as insulated-gate bipolar transistors (IGBTs) has spurred interest in active filters for power conditioning. In addition, state-of-the-art power electronics technology has enabled active filters to be put into practical use. More than one thousand sets of active filters consisting of voltage-fed pulse-width-modulation (PWM) inverters using IGBTs or gate-turn-off (GTO) thyristors are operating successfully in Japan.

Active filters for power conditioning provide the following functions:

•  Reactive-power compensation

•  Harmonic compensation, harmonic isolation, harmonic damping, and harmonic termination

•  Negative-sequence current/voltage compensation

•  Voltage regulation

The term “active filters” is also used in the field of signal processing. In order to distinguish active filters in power processing from active filters in signal processing, the term “active power filters” often appears in many technical papers or literature. However, the author prefers “active filters for power conditioning” to “active power filters,” because the term “active power filters” is misleading to either “active filters for power” or “filters for active power.” Therefore, this section takes the term “active filters for power conditioning” or simply uses the term “active filters” as long as no confusion occurs.

26.1  Harmonic-Producing Loads

26.1.1  Identified Loads and Unidentified Loads

Nonlinear loads drawing nonsinusoidal currents from utilities are classified into identified and unidentified loads. High-power diode/thyristor rectifiers, cycloconverters, and arc furnaces are typically characterized as identified harmonic-producing loads because utilities identify the individual nonlinear loads installed by high-power consumers on power distribution systems in many cases. The utilities determine the point of common coupling with high-power consumers who install their own harmonic-producing loads on power distribution systems, and also can determine the amount of harmonic current injected from an individual consumer.

A “single” low-power diode rectifier produces a negligible amount of harmonic current. However, multiple low-power diode rectifiers can inject a large amount of harmonics into power distribution systems. A low-power diode rectifier used as a utility interface in an electric appliance is typically considered as an unidentified harmonic-producing load. Attention should be paid to unidentified harmonic-producing loads as well as identified harmonic-producing loads.

26.1.2  Harmonic Current Sources and Harmonic Voltage Sources

In many cases, a harmonic-producing load can be represented by either a harmonic current source or a harmonic voltage source from a practical point of view. Figure 26.1a shows a three-phase diode rectifier with a DC link inductor L_d. When attention is paid to voltage and current harmonics, the rectifier can be considered as a harmonic current source shown in Figure 26.1b. The reason is that the load impedance is much larger than the supply impedance for harmonic frequency ω_h, as follows:

$\sqrt{R_L^2+{\left({\omega }_h{L}_d\right)}^2}\gg {\omega }_h{L}_S.$

Here, L_S is the sum of supply inductance existing upstream of the point of common coupling (PCC) and leakage inductance of a rectifier transformer. Note that the rectifier transformer is disregarded from Figure 26.1a. Figure 26.1b suggests that the supply harmonic current i_Sh is independent of L_S.

FIGURE 26.1  Diode rectifier with inductive load. (a) Power circuit. (b) Equivalent circuit for harmonic on a per-phase base.

FIGURE 26.2  Diode rectifier with capacitive load. (a) Power circuit. (b) Equivalent circuit for harmonic on a per-phase base.

Figure 26.2a shows a three-phase diode rectifier with a DC link capacitor. The rectifier would be characterized as a harmonic voltage source shown in Figure 26.2b if it is seen from its AC terminals. The reason is that the following relation exists:

$\frac{1}{{\omega }_h{C}_d}\ll {\omega }_h{L}_S.$

This implies that i_Sh is strongly influenced by the inductance value of L_S.

26.2  Theoretical Approach to Active Filters for Power Conditioning

26.2.1  The Akagi-Nabae Theory

The theory of instantaneous power in three-phase circuits is referred to as the “Akagi-Nabae theory” (Akagi et al., 1983, 1984). Figure 26.3 shows a three-phase three-wire system on the a-b-c coordinates, where no zero-sequence voltage is included in the three-phase three-wire system. Applying the theory to Figure 26.3 can transform the three-phase voltages and currents on the a-b-c coordinates into the two-phase voltages and currents on the α-β coordinates, as follows:

$\left[\begin{array}{c}{e}_{\alpha }\\ e_{\beta }\end{array}\right]=\sqrt{\begin{array}{c}2\\ 3\end{array}}\left[\begin{array}{lll}1\hfill & -1/2\hfill & -1/2\hfill \\ 0\hfill & \sqrt{3}/2\hfill & -\sqrt{3}/2\hfill \end{array}\right]\left[\begin{array}{c}{e}_a\\ e_b\\ e_c\end{array}\right]$

(26.1)

FIGURE 26.3  Three-phase three-wire system.

$\left[\begin{array}{c}{i}_{\alpha }\\ i_{\beta }\end{array}\right]=\sqrt{\frac{2}{3}}\left[\begin{array}{lll}1\hfill & -1/2\hfill & -1/2\hfill \\ 0\hfill & \sqrt{3}/2\hfill & -\sqrt{3}/2\hfill \end{array}\right]\left[\begin{array}{c}{i}_a\\ i_b\\ i_c\end{array}\right].$

(26.2)

As is well known, the instantaneous real power either on the a-b-c coordinates or on the α-β coordinates is defined by

$p=e_a{i}_a+e_b{i}_b+e_c{i}_c=e_{\alpha }{i}_{\alpha }+e_{\beta }{i}_{\beta }.$

(26.3)

To avoid confusion, p is referred to as three-phase instantaneous real power. According to the theory, the three-phase instantaneous imaginary power, q, is defined by

$q=e_{\alpha }{i}_{\beta }-e_{\beta }{i}_{\alpha }.$

(26.4)

The combination of the above two equations bears the following basic formulation:

$\left[\begin{array}{c}p\\ q\end{array}\right]=\left[\begin{array}{cc}{e}_{\alpha }& e_{\beta }\\ -e_{\beta }& e_{\alpha }\end{array}\right]\left[\begin{array}{c}{i}_{\alpha }\\ i_{\beta }\end{array}\right].$

(26.5)

Here, e_α…i_α or e_β … i_β obviously means instantaneous power in the α-phase or the β-phase because either is defined by the product of the instantaneous voltage in one phase and the instantaneous current in the same phase. Therefore, p has a dimension of [W]. Conversely, neither e_α · i_β nor e_β · i_α means instantaneous power because either is defined by the product of the instantaneous voltage in one phase and the instantaneous current in the other phase. Accordingly, q is quite different from p in dimension and electric property although q looks similar in formulation to p. A common dimension for q should be introduced from both theoretical and practical points of view. A good candidate is [IW], that is, “imaginary watt.”

Equation 26.5 is changed into the following equation:

$\left[\begin{array}{c}{i}_{\alpha }\\ i_{\beta }\end{array}\right]=\left[\begin{array}{cc}{e}_{\alpha }& e_{\beta }\\ -e_{\beta }& e_{\alpha }\end{array}\right]\left[\begin{array}{c}p\\ q\end{array}\right]$

(26.6)

Note that the determinant with respect to e_α and e_β in Equation 26.5 is not zero. The instantaneous currents on the α-β coordinates, i_α and i_β, are divided into two kinds of instantaneous current components, respectively:

$\begin{array}{ll}\left[\begin{array}{c}{i}_{\alpha }\\ i_{\beta }\end{array}\right]\hfill & ={\left[\begin{array}{cc}{e}_{\alpha }& e_{\beta }\\ -e_{\beta }& e_{\alpha }\end{array}\right]}^{-1}\left[\begin{array}{c}p\\ 0\end{array}\right]+{\left[\begin{array}{cc}{e}_{\alpha }& e_{\beta }\\ -e_{\beta }& e_{\alpha }\end{array}\right]}^{-1}\left[\begin{array}{c}0\\ q\end{array}\right]\hfill \\ \hfill & \equiv \left[\begin{array}{c}{i}_{\alpha p}\\ i_{\beta p}\end{array}\right]+\left[\begin{array}{c}{i}_{\alpha q}\\ i_{\beta q}\end{array}\right]\hfill \end{array}$

(26.7)

Let the instantaneous powers in the α-phase and the β-phase be p_α and p_β, respectively. They are given by the conventional definition as follows:

$\left[\begin{array}{c}{p}_{\alpha }\\ p_{\beta }\end{array}\right]=\left[\begin{array}{c}{e}_{\alpha }{i}_{\alpha }\\ e_{\beta }{i}_{\beta }\end{array}\right]=\left[\begin{array}{c}{e}_{\alpha }{i}_{\alpha p}\\ e_{\beta }{i}_{\beta p}\end{array}\right]+\left[\begin{array}{c}{e}_{\alpha }{i}_{\alpha q}\\ e_{\beta }{i}_{\beta q}\end{array}\right]$

(26.8)

The three-phase instantaneous real power, p, is given as follows, by using Equations 26.7 and 26.8:

$\begin{array}{ll}p\hfill & =p_{\alpha }+p_{\beta }=e_{\alpha }{i}_{\alpha p}+e_{\beta }{i}_{\beta p}+e_{\alpha }{i}_{\alpha q}+e_{\beta }{i}_{\beta q}\hfill \\ \hfill & =\frac{e_{\alpha }^2}{e_{\alpha }^2+e_{\beta }^2}p+\frac{e_{\beta }^2}{e_{\alpha }^2+e_{\beta }^2}p+\frac{-e_{\alpha }{e}_{\beta }}{e_{\alpha }^2+e_{\beta }^2}q+\frac{e_{\alpha }{e}_{\beta }}{e_{\alpha }^2+e_{\beta }^2}q\hfill \end{array}$

(26.9)

The sum of the third and fourth terms on the right-hand side in Equation 26.9 is always zero. From Equations 26.8 and 26.9, the following equations are obtained:

$p=e_{\alpha }{i}_{\alpha p}+e_{\beta }{i}_{\beta p}\equiv p_{\alpha p}+p_{\beta p}$

(26.10)

$0=e_{\alpha }{i}_{\alpha q}+e_{\beta }{i}_{\beta q}\equiv p_{\alpha q}+p_{\beta q}.$

(26.11)

Inspection of Equations 26.10 and 26.11 leads to the following essential conclusions:

•  The sum of the power components, p_αp and p_βp, coincides with the three-phase instantaneous real power, p, which is given by Equation 26.3. Therefore, p_αp and p_βp are referred to as the α-phase and β-phase instantaneous active powers.

•  The other power components, p_αq and p_βq, cancel each other and make no contribution to the instantaneous power flow from the source to the load. Therefore, p_αq and p_βq are referred to as the α-phase and β-phase instantaneous reactive powers.

•  Thus, a shunt active filter without energy storage can achieve instantaneous compensation of the current components, i_αq and i_βq or the power components, p_αq and p_βq. In other words, the Akagi-Nabae theory based on Equation 26.5 exactly reveals what components the active filter without energy storage can eliminate from the α-phase and β-phase instantaneous currents, i_α and i_β or the α-phase and β-phase instantaneous real powers, p_α and p_β.

26.2.2  Energy Storage Capacity

Figure 26.4 shows a system configuration of a shunt active filter for harmonic compensation of a diode rectifier, where the main circuit of the active filter consists of a three-phase voltage-fed PWM inverter and a DC capacitor, C_d. The active filter is controlled to draw the compensating current, i_AF, from the utility, so that the compensating current cancels the harmonic current flowing on the AC side of the diode rectifier with a DC link inductor.

Referring to Equation 26.6 yields the α-phase and β-phase compensating currents,

$\left[\begin{array}{c}{i}_{AF\alpha }\\ i_{AF\beta }\end{array}\right]={\left[\begin{array}{cc}{e}_{\alpha }& e_{\beta }\\ -e_{\beta }& e_{\alpha }\end{array}\right]}^{-1}\left[\begin{array}{c}{p}_{AF}\\ q_{AF}\end{array}\right].$

(26.12)

FIGURE 26.4  Shunt active filter.

Here, p_AF and q_AF are the three-phase instantaneous real and imaginary power on the AC side of the active filter, and they are usually extracted from p_L and q_L. Note that p_L and q_L are the three-phase instantaneous real and imaginary power on the AC side of a harmonic-producing load. For instance, when the active filter compensates for the harmonic current produced by the load, the following relationships exist:

$p_{AF}={\tilde{p}}_L,q_{AF}=-{\tilde{q}}_L.$

(26.13)

Here, ${\tilde{p}}_L$ and ${\tilde{q}}_L$ are AC components of p_L and q_L, respectively. Note that the DC components of p_L and q_L correspond to the fundamental current present in i_L and the AC components to the harmonic current. In general, two high-pass filters in the control circuit extract ${\tilde{p}}_L$ from p_L and ${\tilde{q}}_L$ from q_L.

The active filter draws p_AF from the utility, and delivers it to the DC capacitor if no loss is dissipated in the active filter. Thus, p_AF induces voltage fluctuation of the DC capacitor. When the amplitude of p_AF is assumed to be constant, the lower the frequency of the AC component, the larger the voltage fluctuation (Akagi et al., 1984, 1986). If the period of the AC component is 1 h, the DC capacitor has to absorb or release electric energy given by integration of p_AF with respect to time. Thus, the following relationship exists between the instantaneous voltage across the DC capacitor, v_d and p_AF:

$\frac{1}{2}{C}_d{v}_d^2\left(t\right)=\frac{1}{2}{C}_d{v}_d^2\left(0\right)+{\displaystyle \underset{0}{\overset{t}{\int }}{p}_{AF}dt.}$

(26.14)

This implies that the active filter needs an extremely large-capacity DC capacitor to suppress the voltage fluctuation coming from achieving “harmonic” compensation of ${\tilde{p}}_L$. Hence, the active filter is no longer a harmonic compensator, and thereby it should be referred to as a “DC capacitor-based energy storage system,” although it is impractical at present. In this case, the main purpose of the voltage-fed PWM inverter is to perform an interface between the utility and the bulky DC capacitor.

The active filter seems to “draw” q_AF from the utility, as shown in Figure 26.4. However, q_AF makes no contribution to energy transfer in the three-phase circuit. No energy storage, therefore, is required to the active filter, independent of q_AF, whenever p_AF = 0.

26.2.3  Classification of Active Filters

Various types of active filters have been proposed in technical literature (Moran, 1989; Grady et al., 1990; Akagi, 1994; Akagi and Fujita, 1995; Fujita and Akagi, 1997; Aredes et al., 1998). Classification of active filters is made from different points of view (Akagi, 1996). Active filters are divided into AC and DC filters. Active DC filters have been designed to compensate for current and/or voltage harmonics on the DC side of thyristor converters for high-voltage DC transmission systems (Watanabe, 1990; Zhang et al., 1993) and on the DC link of a PWM rectifier/inverter for traction systems. Emphasis, however, is put on active AC filter in the following because the term “active filters” refers to active AC filters in most cases.

26.2.4  Classification by Objectives: Who Is Responsible for Installing active Filters?

The objective of “who is responsible for installing active filters” classifies them into the following two groups:

•  Active filters installed by individual consumers on their own premises in the vicinity of one or more identified harmonic-producing loads.

•  Active filters being installed by electric power utilities in substations and/or on distribution feeders.

Individual consumers should pay attention to current harmonics produced by their own harmonic-producing loads, and thereby the active filters installed by the individual consumers are aimed at compensating for current harmonics.

Utilities should concern themselves with voltage harmonics, and therefore active filters will be installed by utilities in the near future for the purpose of compensating for voltage harmonics and/or of achieving “harmonic damping” throughout power distribution systems or “harmonic termination” of a radial power distribution feeder. Section 26.4 describes a shunt active filter intended for installation by electric power utilities on the end bus of a power distribution line.

26.2.5  Classification by System Configuration

26.2.5.1  Shunt Active Filters and Series Active Filters

A standalone shunt active filter shown in Figure 26.4 is one of the most fundamental system configurations. The active filter is controlled to draw a compensating current, i_AF, from the utility, so that it cancels current harmonics on the AC side of a general-purpose diode/thyristor rectifier (Akagi et al., 1990; Peng et al., 1990; Bhattacharya et al., 1998) or a PWM rectifier for traction systems (Krah and Holtz, 1994). Generally, the shunt active filter is suitable for harmonic compensation of a current harmonic source such as diode/thyristor rectifier with a DC link inductor. The shunt active filter has the capability of damping harmonic resonance between an existing passive filter and the supply impedance.

Figure 26.5 shows a system configuration of a series active filter used alone. The series active filter is connected in series with the utility through a matching transformer, so that it is suitable for harmonic compensation of a voltage harmonic source such as a large-capacity diode rectifier with a DC link capacitor. The series active filter integrated into a diode rectifier with a DC common capacitor is discussed in section V. Table 26.1 shows comparisons between the shunt and series active filters. This concludes that the series active filter has a “dual” relationship in each item with the shunt active filter (Akagi, 1996; Peng, 1998).

FIGURE 26.5  Series active filter.

TABLE 26.1 Comparison of Shunt Active Filters and Series Active Filters

	Shunt Active Filter	Series Active Filter
System configuration	Figure 26.4	Figure 26.5
Power circuit of active filter	Voltage-fed PWM inverter with current minor loop	Voltage-fed PWM inverter without current minor loop
Active filter acts as	Current source: iAF	Voltage source: vAF
Harmonic-producing load suitable	Diode/thyristor rectifiers with inductive loads, and cycloconverters	Large-capacity diode rectifiers with capacitive loads
Additional function	Reactive power compensation	AC voltage regulation
Present situation	Commercial stage	Laboratory stage

26.2.5.2    Hybrid Active/Passive Filters

Figures 26.6 through 26.8 show three types of hybrid active/passive filters, the main purpose of which is to reduce initial costs and to improve efficiency. The shunt passive filter consists of one or more tuned LC filters and/or a high-pass filter. Table 26.2 shows comparisons among the three hybrid filters in which the active filters are different in function from the passive filters. Note that the hybrid filters are applicable to any current harmonic source, although a harmonic-producing load is represented by a thyristor rectifier with a DC link inductor in Figures 26.6 through 26.8.

Such a combination of a shunt active filter and a shunt passive filter as shown in Figure 26.6 has already been applied to harmonic compensation of naturally-commutated 12-pulse cycloconverters for steel mill drives (Takeda et al., 1987). The passive filters absorbs 11th and 13th harmonic currents while the active filter compensates for 5th and 7th harmonic currents and achieves damping of harmonic resonance between the supply and the passive filter. One of the most important considerations in system design is to avoid competition for compensation between the passive filter and the active filter.

FIGURE 26.6  Combination of shunt active filter and shunt passive filter.

FIGURE 26.7  Combination of series active filter and shunt passive filter.

FIGURE 26.8  Series active filter connected in series with shunt passive filter.

TABLE 26.2 Comparison of Hybrid Active/Passive Filters

	Shunt Active Filter Plus Shunt Passive Filter	Series Active Filter Plus Shunt Passive Filter	Series Active Filter Connected in Series with Shunt Passive Filter
System configuration	Figure 26.6	Figure 26.7	Figure 26.8
Power circuit of active filter	•  Voltage-fed PWM inverter with current minor loop	•  Voltage-fed PWM inverter without current minor loop	•  Voltage-fed PWM inverter with or without current minor loop
Function of active filter	•  Harmonic compensation	•  Harmonic isolation	•  Harmonic isolation or harmonic compensation
Advantages	•  General shunt active filters applicable •  Reactive power 8 controllable	•  Already existing shunt passive filters applicable •  No harmonic current flowing through active filter	•  Already existing shunt passive filters applicable •  Easy protection of active filter
Problems or issues	•  Share compensation in frequency domain between active filter and passive filter	•  Difficult to protect active filter against overcurrent	•  No reactive power control
		•  No reactive power control
Present situation	•  Commercial stage	•  A few practical applications	•  Commercial stage

The hybrid active filters, shown in Figure 26.7 (Peng et al., 1990, 1993; Kawaguchi et al., 1997) and in Figure 26.8 (Fujita and Akagi, 1991; Balbo et al., 1994; van Zyl et al., 1995), are right now on the commercial stage, not only for harmonic compensation but also for harmonic isolation between supply and load, and for voltage regulation and imbalance compensation. They are considered prospective alternatives to pure active filters used alone. Other combined systems of active filters and passive filters or LC circuits have been proposed in Bhattacharya et al. (1997).

26.2.6  Classification by Power Circuit

There are two types of power circuits used for active filters; a voltage-fed PWM inverter (Akagi et al., 1986; Takeda et al., 1987) and a current-fed PWM inverter (Kawahira et al., 1983; van Schoor and van Wyk, 1987). These are similar to the power circuits used for AC motor drives. They are, however, different in their behavior because active filters act as nonsinusoidal current or voltage sources. The author prefers the voltage-fed to the current-fed PWM inverter because the voltage-fed PWM inverter is higher in efficiency and lower in initial costs than the current-fed PWM inverter (Akagi, 1994). In fact, almost all active filters that have been put into practical application in Japan have adopted the voltage-fed PWM inverter as the power circuit.

26.2.7  Classification by Control Strategy

The control strategy of active filters has a great impact not only on the compensation objective and required kVA rating of active filters, but also on the filtering characteristics in transient state as well as in steady state (Akagi et al., 1986).

26.2.7.1    Frequency-Domain and Time-Domain

There are mainly two kinds of control strategies for extracting current harmonics or voltage harmonics from the corresponding distorted current or voltage; one is based on the Fourier analysis in the frequency-domain (Grady et al., 1990), and the other is based on the Akagi-Nabae theory in the time-domain. The concept of the Akagi-Nabae theory in the time-domain has been applied to the control strategy of almost all the active filters installed by individual high-power consumers over the last 10 years in Japan.

26.2.7.2    Harmonic Detection Methods

Three kinds of harmonic detection methods in the time-domain have been proposed for shunt active filters acting as a current source i_AF. Taking into account the polarity of the currents i_S, i_L and i_AF in Figure 26.4 gives

$\begin{array}{ll}\text{load-current}\text{detection:}{i}_{AF}\hfill & =-i_{Lh}\hfill \\ \text{supply-current}\text{detection}:i_{AF}\hfill & =K_S\cdot i_{Sh}\hfill \\ \text{voltage}\text{detection}:i_{AF}\hfill & =K_V\cdot v_h.\hfill \end{array}$

Note that load-current detection is based on feedforward control, while supply-current detection and voltage detection are based on feedback control with gains of K_S and K_V, respectively. Load-current detection and supply-current detection are suitable for shunt active filters installed in the vicinity of one or more harmonic-producing loads by individual consumers. Voltage detection is suitable for shunt active filters that will be dispersed on power distribution systems by utilities, because the shunt active filter based on voltage detection is controlled in such a way to present infinite impedance to the external circuit for the fundamental frequency, and to present a resistor with low resistance of 1/K_V [Ω] for harmonic frequencies (Akagi et al., 1999).

Supply-current detection is the most basic harmonic detection method for series active filters acting as a voltage source v_AF. Referring to Figure 26.5 yields

$\text{supply}\text{current}\text{detection}:v_{AF}=G\cdot i_{Sh}.$

The series active filter based on supply-current detection is controlled in such a way to present zero impedance to the external circuit for the fundamental frequency and to present a resistor with high resistance of G [Ω] for the harmonic frequencies. The series active filters shown in Figure 26.5 (Fujita and Akagi, 1997) and Figure 26.7 (Peng et al., 1990) are based on supply current detection.

26.3  Integrated Series Active Filters

A small-rated series active filter integrated with a large-rated double-series diode rectifier has the following functions (Fujita and Akagi, 1997):

•  Harmonic compensation of the diode rectifier

•  Voltage regulation of the common DC bus

•  Damping of harmonic resonance between the communication capacitors connected across individual diodes and the leakage inductors including the AC line inductors

•  Reduction of current ripples flowing into the electrolytic capacitor on the common DC bus

26.3.1  System Configuration

Figure 26.9 shows a harmonic current-free AC/DC power conversion system described below. It consists of a combination of a double-series diode rectifier of 5 kW and a series active filter with a peak voltage and current rating of 0.38 kVA. The AC terminals of a single-phase H-bridge voltage-fed PWM inverter are connected in “series” with a power line through a single-phase matching transformer, so that the combination of the matching transformers and the PWM inverters forms the “series” active filter. For small to medium-power systems, it is economically practical to replace the three single-phase inverters with a single three-phase inverter using six IGBTs. A small-rated high-pass filter for suppression of switching ripples is connected to the AC terminals of each inverter in the experimental system, although it is eliminated from Figure 26.9 for the sake of simplicity.

FIGURE 26.9  The harmonic current-free AC/DC power conversion system.

The primary windings of the Y-Δ and Δ-Δ connected transformers are connected in “series” with each other, so that the combination of the 3-phase transformers and two 3-phase diode rectifiers forms the “double-series” diode rectifier, which is characterized as a 3-phase 12-pulse rectifier. The DC terminals of the diode rectifier and the active filter form a common DC bus equipped with an electrolytic capacitor. This results not only in eliminating any electrolytic capacitor from the active filter, but also in reducing current ripples flowing into the electrolytic capacitor across the common DC bus.

Connecting only a commutation capacitor C in parallel with each diode plays an essential role in reducing the required peak voltage rating of the series active filter.

26.3.2  Operating Principle

Figure 26.10 shows an equivalent circuit for the power conversion system on a per-phase basis. The series active filter is represented as an AC voltage source v_AF, and the double-series diode rectifier as the series connection of a leakage inductor L_L of the transformers with an AC voltage source v_L. The reason for providing the AC voltage source to the equivalent model of the diode rectifier is that the electrolytic capacitor C_d is directly connected to the DC terminal of the diode rectifier, as shown in Figure 26.9.

FIGURE 26.10  Single-phase equivalent circuit.

FIGURE 26.11  Single-phase equivalent circuit with respect to harmonics.

The active filter is controlled in such a way as to present zero impedance for the fundamental frequency and to act as a resistor with high resistance of K[Ω] for harmonic frequencies. The AC voltage of the active filter, which is applied to a power line through the matching transformer, is given by

$v_{AF}^{\star }=K\cdot i_{Sh}$

(26.15)

where i_Sh is a supply harmonic current drawn from the utility. Note that v_AF and i_Sh are instantaneous values. Figure 26.11 shows an equivalent circuit with respect to current and voltage harmonics in Figure 26.10. Referring to Figure 26.11 enables derivation of the following basic equations:

$I_{Sh}=\frac{V_{Sh}-V_{Lh}}{Z_S+Z_L+K}$

(26.16)

$V_{AF}=\frac{K}{Z_S+Z_L+K}\left(V_{Sh}-V_{Lh}\right)$

(26.17)

where V_AF is equal to the harmonic voltage appearing across the resistor K in Figure 26.10.

If K ≫ Z_S + Z_L, Equations 26.16 and 26.17 are changed into the following simple equations.

$I_{Sh}\approx 0$

(26.18)

$V_{AF}\approx V_{Sh}-V_{Lh}.$

(26.19)

Equation 26.18 implies that an almost purely sinusoidal current is drawn from the utility. As a result, each diode in the diode rectifier continues conducting during a half cycle. Equation 26.19 suggests that the harmonic voltage V_Lh, which is produced by the diode rectifier, appears at the primary terminals of the transformers in Figure 26.9, although it does not appear upstream of the active filter or at the utility-consumer point of common coupling (PCC).

26.3.3  Control Circuit

Figure 26.12 shows a block diagram of a control circuit based on hybrid analog/digital hardware. The concept of the Akagi-Nabae theory (Akagi et al., 1983, 1984) is applied to the control circuit implementation. The p-q transformation circuit executes the following calculation to convert the three-phase supply current i_Sv, i_Sv, and i_Sw into the instantaneous active current i_p and the instantaneous reactive current i_q.

$\left[\begin{array}{c}{i}_p\\ i_q\end{array}\right]=\sqrt{\frac{2}{3}}\left[\begin{array}{cc}\cos \omega t& \sin \omega t\\ -\sin \omega t& \cos \omega t\end{array}\right]\cdot \left[\begin{array}{lll}1\hfill & -1/2\hfill & -1/2\hfill \\ 0\hfill & \sqrt{3}/2\hfill & -\sqrt{3}/2\hfill \end{array}\right]\left[\begin{array}{c}{i}_{Su}\\ i_{Sv}\\ i_{Sw}\end{array}\right].$

(26.20)

FIGURE 26.12  Control circuit for the series active filter.

The fundamental components in i_Su, i_Sv, and i_Sw correspond to DC components in i_p and i_q, and harmonic components to AC components. Two first-order high-pass-filters (HPFs) with the same cut-off frequency of 10 Hz as each other extract the AC components ${\tilde{i}}_p$ and ${\tilde{i}}_q$ from i_p and i_q, respectively. Then, the p-q transformation/inverse transformation of the extracted AC components produces the following supply harmonic currents:

$\left[\begin{array}{c}{i}_{Shu}\\ i_{Shv}\\ i_{Shw}\end{array}\right]=\sqrt{\frac{2}{3}}\left[\begin{array}{cc}1& 0\\ -1/2& \sqrt{3}/2\\ -1/2& -\sqrt{3}/2\end{array}\right]\cdot \left[\begin{array}{cc}\cos \omega t& -\sin \omega t\\ \sin \omega t& \cos \omega t\end{array}\right]\left[\begin{array}{c}{\tilde{i}}_p\\ {\tilde{i}}_q\end{array}\right].$

(26.21)

Each harmonic current is amplified by a gain of K, and then it is applied to the gate control circuit of the active filter as a voltage reference $v_{AF}^{\star }$ in order to regulate the common DC bus voltage, $v_{AFf}^{\star }$ is divided by the gain of K, and then it is added to ${\tilde{i}}_p$.

The PLL (phase locked loop) circuit produces phase information ωt which is a 12-bit digital signal of 60 × 2¹² samples per second. Digital signals, sin ωt and cos ωt, are generated from the phase information, and then they are applied to the p-q (inverse) transformation circuits. Multifunction in the transformation circuits is achieved by means of eight multiplying D/A converters. Each voltage reference, $v_{AF}^{\star }$ is compared with two repetitive triangular waveforms of 10 kHz in order to generate the gate signals for the IGBTs. The two triangular waveforms have the same frequency, but one has polarity opposite to the other, so that the equivalent switching frequency of each inverter is 20 kHz, which is twice as high as that of the triangular waveforms.

26.3.4  Experimental Results

In the following experiment, the control gain of the active filter, K, is set to 27 Ω, which is equal to 3.3 p.u. on a 3ϕ 200-V, 15-A, 60-Hz basis. Equation 26.16 suggests that the higher the control gain, the better the performance of the active filter. An extremely high gain, however, may make the control system unstable, and thereby a trade-off between performance and stability exists in determining an optimal control gain. A constant load resistor is connected to the common DC bus, as shown in Figure 26.9.

Figures 26.13 and 26.14 show experimental waveforms, where a 5-μF commutation capacitor is connected in parallel with each diode used for the double-series diode rectifier. Table 26.3 shows the THD of i_S and the ratio of each harmonic current with respect to the fundamental current contained in i_S. Before starting the active filter, the supply 11th and 13th harmonic currents in Figure 26.13 are slightly magnified due to resonance between the commutation capacitors C and the AC line and leakage inductors, L_S and L_L. Nonnegligible amounts of third, fifth, and seventh harmonic currents, which are so-called non-characteristic current harmonics for the 3-phase 12-pulse diode rectifier, are drawn from the utility.

FIGURE 26.13  Experimental waveforms before starting the series active filter.

FIGURE 26.14  Experimental waveforms after starting the series active filter.

TABLE 26.3 Supply Current THD and Harmonics Expressed as the Harmonic-to-Fundamental Current Ratio %, Where Commutation Capacitors of 5 μF Are Connected

Figure 26.14 shows experimental waveforms where the peak voltage of the series active filter is imposed on a limitation of ±12 V inside the control circuit based on hybrid analog/digital hardware. Note that the limitation of ±12 V to the peak voltage is equivalent to the use of three single-phase matching transformers with turn ratios of 1:20 under the common DC link voltage of 240 V. After starting the active filter, a sinusoidal current with a leading power factor of 0.96 is drawn because the active filter acts as a high resistor of 27 Ω, having the capability of compensating for both voltage harmonics V_Sh and V_Lh, as well as of damping the resonance. As shown in Figure 26.14, the waveforms of i_S and v_T are not affected by the voltage limitation, although the peak voltage v_AF frequently reaches the saturation or limitation voltage of ±12 V.

The required peak voltage and current rating of the series active filter in Figure 26.14 is given by

$3\times {12}^{\text{v}}/\sqrt{2}\times {15}^{\text{A}}=0.38\text{kVA,}$

(26.22)

which is only 7.6% of the kVA-rating of the diode rectifier.

The harmonic current-free AC-to-DC power conversion system has both practical and economical advantages. Hence, it is expected to be used as a utility interface with large industrial inverter-based loads such as multiple adjustable speed drives and uninterruptible power supplies in the range of 1–10 MW.

26.4  Practical Applications of Active Filters for Power Conditioning

26.4.1  Present Status and Future Trends

Shunt active filters have been put into practical applications mainly for harmonic compensation, with or without reactive-power compensation. Table 26.4 shows ratings and application examples of shunt active filters classified by compensation objectives.

Applications of shunt active filters are expanding, not only into industry and electric power utilities but also into office buildings, hospitals, water supply utilities, and rolling stock. At present, voltage-fed PWM inverters using IGBT modules are usually employed as the power circuits of active filters in a range of 10 kVA to 2 MVA, and DC capacitors are used as the energy storage components.

Since a combined system of a series active filter and a shunt passive filter was proposed in 1988 (Peng et al., 1990), much research has been done on hybrid active filters and their practical applications (Bhattacharya et al., 1997; Aredes et al., 1998). The reason is that hybrid active filters are attractive from both practical and economical points of view, in particular, for high-power applications. A hybrid active filter for harmonic damping has been installed at the Yamanashi test line for high-speed magnetically-levitated trains (Kawaguchi et al., 1997). The hybrid filter consists of a combination of a 5-MVA series active filter and a 25-MVA shunt passive filter. The series active filter makes a great contribution to damping of harmonic resonance between the supply inductor and the shunt passive filter.

TABLE 26.4 Shunt Active Filters on Commercial Base in Japan

Objective	Rating	Switching Devices	Applications
Harmonic compensation with or without reactive/negative-sequence current compensation	10 kVA ~ 2 MVA	IGBTs	Diode/thyristor rectifiers and cycloconverters for industrial loads
Voltage flicker compensation	5 MVA ~ 50 MVA	GTO thyristors	Arc furnaces
Voltage regulation	40 MVA ~ 60 MVA	GTO thyristors	Shinkansen (Japanese “bullet” trains)

26.4.2  Shunt Active Filters for Three-Phase Four-Wire Systems

Figure 26.15 depicts the system configuration of a shunt active filter for a three-phase four-wire system. The 300-kVA active filter developed by Meidensha has been installed in a broadcasting station (Yoshida et al., 1998). Electronic equipment for broadcasting requires single-phase 100-V AC power supply in Japan, and therefore the phase-neutral rms voltage is 100 V in Figure 26.15. A single-phase diode rectifier is used as an AC-to-DC power converter in an electronic device for broadcasting. The single-phase diode rectifier generates an amount of third-harmonic current that flows back to the supply through the neutral line. Unfortunately, the third-harmonic currents injected from all of the diode rectifiers are in phase, thus contributing to a large amount of third-harmonic current flowing in the neutral line. The current harmonics, which mainly contain the third, fifth, and seventh harmonic frequency components, may cause voltage harmonics at the secondary of a distribution transformer. The induced harmonic voltage may produce a serious effect on other harmonic-sensitive devices connected at the secondary of the transformer.

Figure 26.16 shows actually measured current waveform in Figure 26.15. The load currents, i_La, i_Lb, and i_Lc, and the neutral current flowing on the load side, i_Ln, are distorted waveforms including a large amount of harmonic current, while the supply currents, i_Sa, i_Sb, and i_Sc, and the neutral current flowing on the supply side, i_Sn, are almost sinusoidal waveforms with the help of the active filter.

26.4.3  The 48-MVA Shunt Active Filter for Compensation of Voltage Impact Drop, Variation, and Imbalance

Figure 26.17 shows a power system delivering electric power to the Japanese “bullet trains” on the Tokaido Shinkansen. Three shunt active filters for compensation of fluctuating reactive current/negative-sequence current have been installed in the Shintakatsuki substation by the Central Japan Railway Company (Iizuka et al., 1995). The shunt active filters, manufactured by Toshiba, consist of voltage-fed PWM inverters using GTO thyristors, each of which is rated at 16 MVA. A high-speed train with maximum output power of 12 MW draws unbalanced varying active and reactive power from the Scott transformer, the primary of which is connected to the 154-kV utility grid. More than 20 high-speed trains pass per hour during the daytime. This causes voltage impact drop, variation, and imbalance at the terminals of the 154-kV utility system, accompanied by a serious deterioration in the power quality of other consumers connected to the same power system. The purpose of the shunt active filters with a total rating of 48 MVA is to compensate for voltage impact drop, voltage variation, and imbalance at the terminals of the 154-kV power system, and to improve the power quality. The concept of the instantaneous power theory in the time-domain has been applied to the control strategy for the shunt active filter.

FIGURE 26.15  Shunt active filter for three-phase four-wire system.

FIGURE 26.16  Actual current waveforms. (a) Supply currents. (b) Load currents.

FIGURE 26.17  The 48-MVA shunt active filter installed in the Shintakatsuki substation.

FIGURE 26.18  Installation effect (a) Before compensation. (b) After compensation.

Figure 26.18 shows voltage waveforms on the 154-kV bus and the voltage imbalance factor before and after compensation, measured at 14:20–14:30 on July 27, 1994. The shunt active filters are effective not only in compensating for the voltage impact drop and variation, but also in reducing the voltage imbalance factor from 3.6% to 1%. Here, the voltage imbalance factor is the ratio of the negative to positive-sequence component in the three-phase voltages on the 154-kV bus. At present, several active filters in a range of 40-60 MVA have been installed in substations along the Tokaido Shinkansen (Takeda et al., 1995).

Acknowledgment

The author would like to thank Meidensha Corporation and Toshiba Corporation for providing helpful and valuable information of the 300-kVA active filter and the 48-MVA active filter.

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