0 Introduction Power electronic devices such as AC speed regulators and various industrial power supplies have become important sources of harmonics in power systems. Harmonics are very detrimental to power systems. On the one hand, they consume a large amount of reactive power reserves; on the other hand, they lead to increased losses in power components and malfunctions of protection devices, seriously affecting the safe and economical operation of the system and power devices [1, 2]. Using external filtering devices to reduce the harmonic power injected into or absorbed by various power electronic devices connected to the power grid is currently the main means of eliminating harmonic currents from high-power power electronic devices. Passive filters (PFs) remain the main method currently used due to their low cost and mature technology. However, they have many shortcomings, such as: the resonant frequency and filtering characteristics are strongly dependent on the components and grid parameters; therefore, they can only filter major harmonics, and the drift of LC parameters will lead to changes in filtering characteristics. In addition, there may be series and parallel resonances between the power grid and the filter. However, using parallel active power filters (APFs) to eliminate harmonics also has certain limitations: when the load harmonic current content is high, the capacity of such APF devices must also be very large; they are only suitable for compensating inductive loads; and the output of three-phase inverters directly bears the grid voltage. Combining passive and active filters can reduce the cost of compensation systems. Work in this area includes: designing novel harmonic injection circuits using passive networks [3-5] so that the APF does not directly bear the grid voltage or load fundamental current; methods to let the PF share most of the harmonics [6-9]; and using APFs to improve the filtering characteristics of PFs, etc. In 1988, Peng et al. proposed a hybrid active filter structure of series APF plus parallel PF [8]. In this structure, the APF presents high impedance to harmonics and low impedance to power frequency. Therefore, the APF is equivalent to a harmonic isolation device between the power supply and the load. The harmonic voltage of the grid will not be applied to the load and PF, and the harmonic current of the load will not flow into the grid. This method can make full use of the PF already connected to the device and is very suitable for harmonic suppression of general power electronic devices. Based on the above structure, this paper proposes a novel composite controlled source scheme, in which the controlled source is simultaneously controlled by the grid-side harmonic voltage and the load-side harmonic current. This allows the active filter to suppress the influence of grid-side harmonic voltage through harmonic cancellation and the active filter to suppress the influence of load-side harmonic current through variable resistance. Simultaneously, a simple series-parallel resonant passive filter network is proposed, limiting the bypass fundamental current of the passive filter while providing a relatively low-impedance branch for harmonic currents within the main harmonic frequency range, thus simplifying the structure of the hybrid active filter. [b]1 Design of a Novel Series Hybrid Active Filter[/b] The overall block diagram of the compensation system is shown in Figure 1. [img=426,183]http://zszl.cepee.com/cepee_kjlw_pic/files/wx/dlxtzdh/dlxtzdh99/dlxtzdh9907/image/20.gif[/img] Fig.1 The control block diagram of the hybrid active power filter (HAPF) The dashed box in the figure represents the control circuit, which consists of a three-phase symmetrical sine wave generation circuit, a DC-side capacitor voltage feedback control circuit for the three-phase inverter circuit, a harmonic calculation circuit, and a controller. The control circuit generates a gate drive signal to control the three-phase inverter circuit, generating harmonic voltages, which are connected in series between the grid and the load through a coupling transformer. The phase-locked loop (PLL) and EPROM provide standard sine and cosine signals for the harmonic calculation circuit and generate a triangular carrier signal for the pulse width modulation (PWM) circuit. The harmonic current is calculated using dq transformation, as shown in the block diagram in Figure 2. The dq transform converts the fundamental positive-sequence component into a DC component in dq coordinates, which can be separated using a low-pass filter. By inverse dq transform, the fundamental positive-sequence active and reactive current components can be obtained, and thus the harmonic current components can be obtained [10]. Since this method does not need to start from the concept of instantaneous power, it eliminates the need for voltage detection when calculating harmonics, thereby eliminating the interference of harmonic voltage or the negative-sequence and zero-sequence components of voltage on the calculation of harmonic current [11]. [img=394,105]http://zszl.cepee.com/cepee_kjlw_pic/files/wx/dlxtzdh/dlxtzdh99/dlxtzdh9907/image/21-1.gif[/img] Fig.2 Harmonic current calculation diagram by dq transfirmation In Fig.2, the 3/2 transformation matrix C and the dq transformation matrix D are respectively: [img=232,137]http://zszl.cepee.com/cepee_kjlw_pic/files/wx/dlxtzdh/dlxtzdh99/dlxtzdh9907/image/21-01.gif[/img] The purpose of capacitor voltage feedback control is to maintain the DC side capacitor voltage of the inverter circuit of the active filter at a basically constant value when the active filter is working. Since the APF is only used for harmonic suppression in the circuit and does not provide average active power, the DC side power supply of the APF can be replaced by a DC capacitor. However, due to heat loss during circuit operation, the capacitor voltage will drop. In addition, sudden changes in load harmonics will cause capacitor voltage fluctuations, so capacitor voltage control is necessary. In Figure 1, the controller of the hybrid active filter uses a proportional regulator K(s) = K, and in this paper, K = 2 is chosen. When designing the passive filter, setting K = 0, we can obtain the expressions for the fundamental current is on the grid side and the harmonic current iLh on the load side. Obviously, in order to make is as equal as possible to the fundamental component of the load current, |ZF(ω0)| must be large enough, while in order to make the harmonic voltage on the load side as small as possible, |ZF(ω)| must be as small as possible. Furthermore, to achieve the expected harmonic suppression effect, K must satisfy |ZF + Zs|. Analysis shows that if K is too large, it will cause system instability, so K cannot be very large, which means that |ZF(ω)| must be relatively small. If a passive filter with 5th, 7th, and higher-order filters connected in parallel is used, it can be ensured that the passive filter branch provides sufficiently small impedance to the main harmonic components [7]. Of course, a C-type high-pass filter can also be used [12]. The hybrid active filter proposed in this paper adopts a simple series-parallel resonant passive filter structure, as shown in Figure 3. Among them, Lr1 and C resonate at the fundamental frequency, while Lr1, Lr2, and C resonate at the 6th harmonic frequency. For the fundamental frequency, ZF(ω0) has a sufficiently large impedance due to parallel resonance, and the filter branch is equivalent to an open circuit. For the harmonic frequencies, due to the effect of the active filter, the narrow low-impedance band of ZF(ω) is widened. Its YF(s) is: [img=357,40]http://zszl.cepee.com/cepee_kjlw_pic/files/wx/dlxtzdh/dlxtzdh99/dlxtzdh9907/image/21-02.gif[/img][img=144,80]http://zszl.cepee.com/cepee_kjlw_pic/files/wx/dlxtzdh/dlxtzdh99/dlxtzdh9907/image/21-2.gif[/img] Fig.3 Cinfiguration of the proposed passive filter (PF) The quality factor of the filter can be changed by changing R. However, the additional series resistance will increase the filter loss. Therefore, in practical applications, R is the internal impedance of the reactor. A smaller R means a narrower bandwidth. Because an active filter is connected in series, and the active filter acts as a resistor for harmonics, the equivalent damping resistance in the filter branch is very large, approximately equal to K, thus ensuring the harmonic bandwidth of the hybrid filter. The design formula for the passive filter parameters is obtained from the series-parallel resonant frequencies. Table 1 lists three different sets of filter parameters, and their corresponding amplitude-frequency characteristics are shown in Figure 4. [img=176,53]http://zszl.cepee.com/cepee_kjlw_pic/files/wx/dlxtzdh/dlxtzdh99/dlxtzdh9907/image/21-03.gif[/img] Table 1 Filter Parameters [table][tr][td]Filter[/td][td]Lr1/mH [/td][td]Lr2/mH [/td][td]C/μF [/td][td]r[sub] 1 [/sub] [/td][/tr][tr][td]1 [/td][td]20.0 [/td][td]0.57 [/td][td]507 [/td][td]0.01 [/td][/tr][tr][td]2 [/td][td]19.0 [td]0.80 [td]368 [td]0.04 [td]3 [td]9.5 [td]0.40 [td]740 [td]0.03[/td][/tr][/table][img=315,191]http://zszl.cepee.com/cepee_kjlw_pic/files/wx/dlxtzdh/dlxtzdh99/dlxtzdh9907/image/21-3.gif[/img] Fig. 4 The amplitude-frequency characteristics of the passive filter. Considering the role of the transformer, the current transfer function is given by [img=333,48]http://zszl.cepee.com/cepee_kjlw_pic/files/wx/dlxtzdh/dlxtzdh99/dlxtzdh9907/image/22-01.gif[/img], where HI′(s) can be derived from the circuit shown in Figure 5. [img=209,151]http://zszl.cepee.com/cepee_kjlw_pic/files/wx/dlxtzdh/dlxtzdh99/dlxtzdh9907/image/22-1.gif[/img] Fig.5 Harmonic equivalent circuit with considered coupling transformer Let the primary and secondary inductances and mutual inductances of the coupling transformer be L1, L2 and M respectively, then Vch=sL2 Ish-sMIh′. Ignoring the switching harmonics and circuit delay of the three-phase inverter circuit, the three-phase inverter circuit can be equivalent to a controlled voltage source. The losses of the switching circuit and transformer are replaced by the losses on the resistor R, then we can obtain: [img=154,42]http://zszl.cepee.com/cepee_kjlw_pic/files/wx/dlxtzdh/dlxtzdh99/dlxtzdh9907/image/22-03.gif[/img] Then [img=154,42]http://zszl.cepee.com/cepee_kjlw_pic/files/wx/dlxtzdh/dlxtzdh99/dlxtzdh9907/image/22-03.gif[/img ][img=337,87]http://zszl.cepee.com/cepee_kjlw_pic/files/wx/dlxtzdh/dlxtzdh99/dlxtzdh9907/image/22-04.gif[/img] Although the fundamental current mainly flows through the secondary side of the transformer during normal operation, and the harmonic current is very small, the transformer parameters do indeed affect the system characteristics. Especially in the active filter circuit presented in this paper, the poor filtering characteristics of the system in the high-frequency range are improved due to the influence of the transformer's distributed parameters. [b]2 Simulation Analysis of a Novel Series Hybrid Active Filter[/b] Based on the above analysis and design, the hybrid active filter system was simulated. The parameters used in the simulation are as follows: a. System parameters: Grid phase voltage: fundamental is 220 V, 5th harmonic component of phase voltage is 5%; Grid frequency: 50 Hz; System impedance: Ls=100 μH, Rs=2 mΩ. b. Control unit parameters: current control amplification factor K=2. c. Harmonic calculation unit Butterworth filter cutoff frequency is 20 Hz. d. Passive filter parameters: L1=19 mH, C=533 μF, L2=0.544 mH. Figure 6(a) shows that the load current contains 5th (70% I1), 7th (80% I1), 11th (10% I1), 13th (10% I1), and 17th (10% I1) harmonics; Figure 6(b) shows that the grid voltage has slight distortion and contains 5th and 7th harmonics. As can be seen from Figure 6, the load current on the grid side basically reaches a sinusoidal waveform after compensation. Before compensation, the grid side load current distortion rate ATHD = 108%, and after compensation, ATHD = 4.6%, in which the 5th, 7th, 11th, and 13th harmonics are effectively suppressed. [img=315,378]http://zszl.cepee.com/cepee_kjlw_pic/files/wx/dlxtzdh/dlxtzdh99/dlxtzdh9907/image/22-2.gif[/img] Fig.6 Waveforms and frequency spectrum of the proposed hybrid active power filter Fig.7 shows the effect of the equivalent series resistance r of the passive filter on the amplitude-frequency characteristics of the system HI(s). As can be seen from the figure, the filtering characteristics of the system are not significantly related to the quality factor of the passive filter. [img=315,194]http://zszl.cepee.com/cepee_kjlw_pic/files/wx/dlxtzdh/dlxtzdh99/dlxtzdh9907/image/22-3.gif[/img] Fig.7 The HI(f) characteristics effected by the equivalent series resistance r of the PF Fig.8 shows the effect of the current control amplification factor K of the active filter (APF) controller on the HI(s) amplitude-frequency characteristics of the system. In the figure, curve 1 corresponds to the amplitude-frequency characteristics of the system without APF compensation when K=0. After adding current compensation, when K=2 and K=6, they correspond to curves 2 and 3 in the figure. As can be seen from the figure, the harmonic current is effectively suppressed over a wide range, and the larger K is, the better the filtering effect. At the fundamental frequency, since the passive filter is in a parallel resonance state, the fundamental current basically does not flow. [img=315,183]http://zszl.cepee.com/cepee_kjlw_pic/files/wx/dlxtzdh/dlxtzdh99/dlxtzdh9907/image/23.gif[/img] Fig.8 The influence of K on HI(f) of HAPF The capacity of the APF can be estimated by |IL1||KIsh|, which is generally about 2% to 3% of the capacity of the compensation object. [b]3 Conclusion[/b] The theoretical analysis and simulation results of the proposed novel hybrid active filter show that its harmonic suppression characteristics are not significantly related to the quality factor of the passive filter. Although the larger the current control amplification factor K is, the better the filtering effect, the value of K should not be too large, otherwise it may cause system instability. For a nonlinear load with an ATHD of 108% for the load current distortion rate, the novel hybrid active filter was used for compensation. Simulation results show that when K=2, the ATHD of the grid-side current can be reduced to 4.6% after compensation, and the 5th, 7th, 11th and 13th harmonics can be significantly suppressed. [b]References[/b] ［1］Wu Jingchang, Sun Shuqin, Song Wennan. Power System Harmonics. Beijing: Hydropower Press, 1988 ［2］Tang Tongyi. Power System Harmonics. Xuzhou: China University of Mining and Technology Press, 1991 ［3］Wang Zhaoan. Power Semiconductor Converter Circuit. Beijing: Machinery Industry Press, 1993 ［4］Qian Zhaoming, Ye Zhongming, Dong Bofan. Harmonic Suppression Technology. Automation of Electric Power Systems, 1997, 21(10): 48-54 ［5］Jin Haiming. AC Frequency Converter Output Harmonic Suppression Technology: Doctoral Dissertation. Hangzhou: Zhejiang University, 1996 ［6］Akagi H, Fujita H. A New Power Line Conditioner for Harmonic Compensation in Power Systems. IEEE Trans on Power Delivery, 1995, 10(3): 1570-1575 ［7］Peng FZ, Akagi H, Nabae A. 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