Keywords

1 Introduction

For the past decades, electronics-based equipment has proliferated the consumer market. The most prominent of them is adjustable speed drives (ASDs) providing efficient output to the industry. However, it produces a significant change in the sinusoidal nature of voltage and current. Hence, attempts have been made to meet the challenge of using drives by a reduction in distortion [1, 2]. When an ASD is connected to the system, it is responsible for producing harmonic distortion. These ASDs draw non-sinusoidal current from the supply filled with harmonics which in turn flows into the system and distorts voltage and current waveform. This was noted not only for ASDs but also for converter circuits, UPS and other AC-DC and DC-AC conversion systems. Thus, deviation of a waveform to non-sinusoidal is attributed to harmonics and distortion [3, 4]. Conditioning of load and conditioning of line are the two ways to address harmonic related issues. The latter comprises passive and active filter methodology. Resonance and distinct filter for each frequency limit the implementation of the passive filter. Therefore, active filters paved the way for cutting-edge solutions for voltage and current-related disturbances [5,6,7]. Control techniques employed in the system make it most suitable and in-demand industrial solution. Hence, active filter accomplishes harmonic limitation and reactive power compensation [8,9,10,11,12].

2 Active Power Filters

Conventionally, passive filters were used with the combination of inductor and capacitor [5]. Although they were low in cost and less complex in design, they were more prone to impact resonance and hence active filters were designed. Active filters generally employ IGBT or MOSFET to provide switching circuits [6]. Figures 1, 2 and 3 depict the general active filter mechanism in use. The controller is shown with only one gate signal. In all the cases, an internal goto signal is used in MATLAB to provide current information which is used to generate a compensating current in the system.

Fig. 1
A circuit diagram of S A P F. A C source, rectifier, shunt filter, and Controller are depicted in the diagram.

SAPF circuit diagram

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Fig. 2
A circuit diagram of a filter used as a voltage source connected with a capacitor contains Line impedance, impedance, rectifier, filter inductance, shunt filter, and controller.

SAPF being used as voltage source

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Fig. 3
A circuit diagram of a filter used as a current source connected with an inductor contains line impedance, impedance, rectifier, filter inductance, shunt filter, and controller.

SAPF being used as current source

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In this, a rectifier is connected across linear or nonlinear load which converts AC-DC and hence harmonic generation from the load side. A parallel active filter is connected which gives compensating current based on controller and therefore prevents harmonic current to reach AC source. In this way, the harmonic current is prevented to distort the source voltage. Active filters are dynamic in nature. They can be used as a current source and voltage source. Figure 2 shows when a filter is used as a voltage source connected with a capacitor and Fig. 3 depicts when a filter is used as a current source connected with an inductor. Passive filter topologies are shunt LC and shunt low pass filter. Active filter topologies are series, shunt and a combination of series-shunt called hybrid [7]. Active filter offers the convenience of configuration for over current in system and can result in less harmonics with an increase in frequency component. Figure 4 shows the control scheme based on instantaneous P-Q theory.

Fig. 4
A schematic diagram based on P-Q theory. I n a, i n b, i n c, voltage source, num over den in s, and not, are depicted in the diagram.

Control scheme based on P-Q theory

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3 Instantaneous P-Q Power Theory

The P-Q theory also referred to as instantaneous power theory is based on Clarke and Parke transformations. In Clarke transformation, voltages and current for a three-phase system are reconstructed in terms of α and β [8].

$$i_{{\alpha \beta {\text{o}}}} = \surd {2}/{3}\left[ {\begin{array}{*{20}c} 1 & { - 1/2} & { - 1/2} \\ 0 & {\sqrt 3 /2 } & { - \sqrt 3 /2} \\ {1/\surd 2} & {1/\surd 2} & {1/\surd 2} \\ \end{array} } \right]i_{{{\text{abc}}}}$$
(1)
$$v_{{\alpha \beta {\text{o}}}} = \surd {2}/{3}\left[ {\begin{array}{*{20}c} 1 & { - 1/2} & { - 1/2} \\ 0 & {\sqrt 3 /2} & { - \sqrt 3 /2} \\ {1/\surd 2} & {1/\surd 2} & {1/\surd 2} \\ \end{array} } \right]v_{{{\text{abc}}}}$$
(2)

Here, iabc is the three-phase source current and vabc is the three-phase source voltage of the system. Similarly, active and reactive power components are represented. Equation 3 represents instantaneous real power and Eq. 4 represents instantaneous imaginary power where voltage and current are represented in terms of a-b-c coordinates and α-β coordinates.

$$p = v_{\alpha } i_{\alpha } + v_{\beta } i_{\beta }$$
(3)
$$q = v_{\alpha } i_{\beta } - v_{\beta } i_{\alpha }$$
(4)

In matrix form, the above equation is represented as

$$\left[ {\begin{array}{*{20}c} p \\ q \\ \end{array} } \right] = \left[ {\begin{array}{*{20}c} {v_{\alpha } } & {v_{\beta } } \\ { - v_{\beta } } & {v_{\alpha } } \\ \end{array} } \right]\left[ {\begin{array}{*{20}c} {i_{\alpha } } \\ {i_{\beta } } \\ \end{array} } \right]$$
(5)

Then, active and reactive power is divided into AC and DC components. A low pass filter is connected across the circuit to obtain the DC component of both active and reactive power.

$$p = \overline{p} + \tilde{q}$$
(6)
$$q = \overline{q} + \tilde{p}$$
(7)

The P-Q theory states that the DC component of active power is represented in terms of α and β reference current as

$$i_{\alpha \beta }^{*} \, = \frac{1}{{v_{\alpha }^{2} + v_{\beta }^{2} }}\left[ {\begin{array}{*{20}c} {v_{\alpha } } & {v_{\beta } } \\ { - v_{\beta } } & {v_{\alpha } } \\ \end{array} } \right]\left[ {\begin{array}{*{20}c} p \\ q \\ \end{array} } \right]$$
(8)

And thus, the reference current is given as

$$i_{\alpha \beta }^{*} = \surd {2}/{3}\left[ {\begin{array}{*{20}c} 1 & 0 \\ { - 1/2} & {\sqrt 3 /2 } \\ { - 1/\surd 2} & { - \sqrt 3 /2} \\ \end{array} } \right]i_{\alpha \beta }^{*}$$
(9)

4 Simulation Results and Discussion

Shunt active power filter circuit for simulation is shown in Fig. 5. Figure 6 shows the P-Q controller for shunt APF simulation. The authors have calculated THD under three different load conditions. In the first case, RL load is considered connected to the DC side of the rectifier. Figures 7, 8, 9, 10, 11 and 12 depict waveforms for rectifier with RL load. In Fig. 7, source voltage of all three phases is depicted. In Fig. 8, source current is depicted in phase-a. In Fig. 9 load current is depicted. In Fig. 10 compensating current is depicted. In Fig. 11 THD for load current is depicted which is 24.49%. In Fig. 12, THD for source current is depicted which comes out to be 5.44%. In the second case, RC load is connected to the DC side of the rectifier. THD in source current for this came out to be 6.44%. Figures 13, 14, 15 and 16 show waveforms for rectifiers with RC load. Figure 13 shows the source current and in Fig. 14 load current is shown. In Fig. 15, THD for load current is depicted which is 22.49%. In Fig. 16, THD for source current is depicted which is 6.44%. And, in the third case R load is connected to the DC side of the rectifier. THD of source current comes out to be 10.27%. Waveforms from Figs. 17, 18, 19 and 20 are shown for rectifier with R load. In Fig. 17 source current is depicted. In Fig. 18 load current is shown. In Fig. 19, THD for load current is depicted which is 21.64%, and in Fig. 20 THD for source current is depicted which is 10.27%. Table 1 shows the parameters and their values. Table 2 shows order-wise source current harmonics with rectifier R-L load using SAPF. Table 3 shows the THD values of load current and source currents for different types of rectifier loads (Fig. 21).

Fig. 5
A circuit diagram of shunt active power filter circuit for simulation. The rectifier and Active filter are depicted in the diagram.

Shunt APF showing Rectifier with R load

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Fig. 6
A circuit diagram contains V s a, V s b, V s c, I c a, I c b, I c c, f, u, 2 voltage sources, and 1 i n a, 2 i n b, and 3 i n c.

P-Q controller for Shunt APF

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Fig. 7
A graph of x-axis values from 0 to 0.2 versus source voltage, with values negative 200 to 200. The 3 plotted lines oscillate.

Three-phase source voltage for RL load

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Fig. 8
A graph of current in A, with values negative 100 to 100 versus time in s, with values 0 to 0.2. The line plotted fluctuates.

Source current for RL load

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Fig. 9
A graph of current in amperes with values negative 100 to 100 versus time in seconds, with values 0 to 0.2. The line plotted oscillates.

Load current for RL load

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Fig. 10
A graph of current in amperes, with values negative 40 to 60 versus time in seconds, with values 0 to 0.2. The line plotted is fluctuating in trend.

Compensating current for RL load

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Fig. 11
A graph of signal magnitude versus time in seconds with oscillating line plotted. A bar graph with fundamental, 50 hertz, 95.06, and T H D is 24.49 percent.

THD for load current with RL load

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Fig. 12
A graph of signal magnitude versus time in seconds, with fluctuating line plotted. A bar graph with fundamental, 50 hertz, 102.2, and T H D is 5.44 percent.

THD for source current with RL load

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Fig. 13
A graph of current in amperes, with values negative 0.05 to 0.05 versus time in seconds, with values 0 to 0.2. The line plotted oscillates.

Source current for RC load

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Fig. 14
A graph of current in amperes, with values negative 10 to 5 versus time in seconds, with values 0 to 0.2. The line plotted fluctuates steadily.

Load current for RC load

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Fig. 15
A graph of signal magnitude versus time in seconds with an oscillating line. A bar graph with fundamental, 50 hertz, 5.41, and T H D is 22.79 percent.

THD for load current with RC load

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Fig. 16
A graph of signal magnitude versus time in seconds with a fluctuating line. A bar graph with fundamental, 50 hertz, 0.04874, and T H D is 6.44 percent.

THD for source current with RC load

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Fig. 17
A graph of current in amperes, with values negative 100 to 100 versus time in seconds, with values 0 to 0.2. A fluctuating line is plotted.

Source current for R load

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Fig. 18
A graph of current in amperes, with values negative 100 to 100 versus time in seconds, with values 0 to 0.2. The line plotted is oscillating in trend.

Load current for R load

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Fig. 19
A graph of signal magnitude versus time in seconds with an oscillating line plotted. A bar graph with fundamental, 50 hertz, 130.6, and T H D is 21.64 percent.

THD for load current with R load

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Fig. 20
A graph of signal magnitude versus time in seconds with fluctuating line plotted. A bar graph with fundamental, 50 hertz, 133.6, and T H D is 10.27 percent.

THD for source current with R load

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Table 1 Parameter values
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Table 2 Harmonic components in source current for Rectifier RL load
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Table 3 Computation of THD
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Fig. 21
A graph of signal magnitude versus time in seconds with an oscillating line. A bar graph with fundamental, 50 hertz, 133.6, and T H D is 10.27 percent.

THD for source current with R load harmonic order

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5 Conclusion

Shunt active filter is implemented using a P-Q theory-based controller in this paper. SAPF has been able to mitigate harmonic components present in the source current due to the rectifier which is a nonlinear load. A control mechanism is used to provide compensating current in the system so as to maintain the source current sinusoidal. THDs obtained through FFT analysis for different loads conclude that THD in source current is considerably reduced for all three loads. MATLAB simulation has been carried out in order to inspect the waveforms and their THD components associated with them. Tabular representation is also provided for different loads to analyze its effect.