[b]1 Introduction[/b] In the past decade or so, active power filters (APFs) have rapidly developed as a new type of power electronic device for controlling power grid harmonics. APFs have better adaptability than passive power filters (PPFs), and by changing their control strategies, they can meet the control requirements of different harmonic sources. Research on APFs has focused on parallel structures, while research on hybrid filtering systems with series active power filters (SAPFs) is relatively limited, especially experimental research. In this hybrid filtering system, the SAPF can improve the filtering characteristics of the PPF and can also act as a harmonic isolation between the system and the PPF, suppressing potential resonance between them. Based on the analysis of the principle of this hybrid filtering system, this paper studies the decomposition technology of harmonic current in single-phase systems for harmonic control of single-phase nonlinear loads (such as electric traction locomotives). Through research on the space vector method of three-phase inverters, a new waveform control method for single-phase system APFs is proposed. This method effectively improves the switching efficiency of the inverter and has higher control accuracy. Under existing experimental conditions, a detailed comparative study was conducted on the filtering effects before and after the application of SAPF. The results show that in the hybrid filtering system, SAPF can significantly improve the filtering characteristics of PPF. 2. Principle of Single-Phase Hybrid Filtering System with SAPF The schematic diagram of the single-phase hybrid filtering system with SAPF is shown in Figure 1. [img=264,170]http://zszl.cepee.com/cepee_kjlw_pic/files/wx/dwjs/2001-1/43-1.jpg[/img] The operating principle of this system is as follows: The control circuit of SAPF separates the harmonic component ish in the system power supply current through transformation calculation. By controlling the output of APF, the output control voltage Vc = K·ish of the primary side of the series transformer is made. Since Vc = K·ish, SAPF behaves as a pure resistance K for the harmonic current flowing through the system; SAPF behaves as zero impedance for the fundamental current flowing through the system. Figures 2 and 3 are the equivalent circuits of the hybrid filtering system for the fundamental and harmonic currents, respectively. Figure 2 shows that the SAPF has no voltage drop or loss on the fundamental frequency. As can be seen from the equivalent circuit in Figure 3, the resistor K provided by the SAPF isolates the power supply from the harmonic source and the PPF to a certain extent, making the filtering effect of the PPF almost unaffected by the system impedance. Of course, it also prevents the phenomenon of parallel resonance leading to harmonic amplification. Simultaneously, other harmonic currents in the system will not be injected into the PPF, causing it to overload, thus effectively improving the filtering characteristics of the PPF. [img=271,289]http://zszl.cepee.com/cepee_kjlw_pic/files/wx/dwjs/2001-1/44-1.jpg[/img] 3 Principle of Harmonic Current Detection in Single-Phase Circuits Examining the three-phase circuit harmonic current detection method based on instantaneous reactive power theory [1, 4], it was found that the detected three-phase signals are always first converted into two-phase signals in a mutually perpendicular α-β coordinate system before further calculation. For single-phase circuits, the above method can be simplified by constructing a phase current that lags the actual current by T/4 (T being the power frequency period), directly forming a hypothetical two-phase coordinate system signal. Let the instantaneous current value of the single-phase circuit be [img=305,247]http://zszl.cepee.com/cepee_kjlw_pic/files/wx/dwjs/2001-1/44-2.jpg[/img]. From the instantaneous reactive power theory, we can obtain [img=301,264]http://zszl.cepee.com/cepee_kjlw_pic/files/wx/dwjs/2001-1/44-3.jpg[/img]. In the above equations, sinωt and cosωt are standard sinusoidal signals obtained by synchronizing and using a phase-locked loop (PLL) with the voltage signal. The "-" above the variable represents the DC component, and "~" represents the AC component. ip and iq represent the active and reactive DC components of the current, respectively. The fundamental currents iαf and iβf can be obtained by performing the inverse transformation of ip and iq corresponding to equation (3). [img=284,133]http://zszl.cepee.com/cepee_kjlw_pic/files/wx/dwjs/2001-1/44-4.jpg[/img] The principle of single-phase circuit harmonic current detection based on the above method is shown in Figure 4. Here, e-st is the element that lags the signal by T/4, and the meanings of C22 and C-122 are given in equation (8). [img=303,227]http://zszl.cepee.com/cepee_kjlw_pic/files/wx/dwjs/2001-1/44-5.jpg[/img] 4 Waveform Control Methods for Single-Phase APF Currently, commonly used pulse width modulation (PWM) techniques include: ① PWM technology based on sine wave modulation of triangular wave; ② HEPWM technology based on eliminating specified harmonics; ③ PWM technology based on current hysteresis tracking control (also known as adaptive PWM technology). The first method is suitable for analog systems and is rarely used in microcomputer control systems; the second method requires pre-calculation of several specified harmonics to be eliminated, and the tracking characteristic is difficult to guarantee when the load changes frequently; the third method is more suitable for microcomputer control. Its principle is to detect the inverter output in real time and compare it with the tracking target. When the deviation exceeds the allowable sideband, the controller acts to reduce the deviation. Therefore, this method always results in a time delay between the inverter output and the ideal waveform, and reducing the sideband of the deviation requires increasing the inverter's operating frequency. This paper applies the Space Vector Pulse Width Modulation (SVPWM) method to the waveform control of an APF for the first time. In each control cycle, the inverter outputs two "precise" vectors, effectively improving the inverter's switching efficiency and significantly enhancing control accuracy. The equivalent circuit of a single-phase inverter is shown in Figure 5. [img=253,150]http://zszl.cepee.com/cepee_kjlw_pic/files/wx/dwjs/2001-1/45-1.jpg[/img] In Figure 5, switches A and B have four possible state combinations, which can be represented as vectors V0 to V3, where V1 = Vdc and V2 = -Vdc. V0 and V3 are zero vectors. When the zero vector is active, the inverter's DC voltage does not output any energy, but it forms a loop with the output current and adjusts the duration of vectors V1 and V2, making it indispensable in control. When the inverter needs to output voltage Va, it can be expressed as follows: TSVa = T1Vy + T0Vx (9) where Vy represents vector V1 or V2; Vx represents zero vector V0 or V3; T1 is the duration of vector Vy; T0 is the duration of Vx; Ts is the control cycle, and it must be: T0 = Ts - T1 (10) When T0 ≥ 0, equation (9) is completely valid. The inverter switches A and B operate once within one control cycle Ts, and can output "precise" vector Va. When T0 < 0, equation (9) is not valid. The inverter output cannot track the change of Va. Therefore, T0 ≥ 0 in equation (10) indicates the condition for whether the single-phase inverter is completely controllable. In adaptive control PWM technology, the inverter output vector that replaces equation (9) is either TS Vy or Ts Vx. The duration of the zero vector is either 0 or Ts. Therefore, the inverter output can only reduce the deviation and cannot achieve precise control. 5. Experimental Results of Single-Phase Filtering System with SAPF To analyze the influence of SAPF on the filtering characteristics of PPF, a hybrid compensation system experimental device containing SAPF was designed and fabricated. The principle structure of the SAPF system is shown in Figure 1. The primary circuit of the system mainly consists of three parts: a single-phase rectifier load, PPF, and inverter. The switching devices of the inverter are IGBT modules from SEMIKON, Germany. The control system of the system consists of a high-performance digital signal processor TMS320C50 and high-speed peripheral chips, which completes the decomposition of harmonic currents, the calculation of control vectors and corresponding vector action times. The PWM drive is completed by the SEMIKON matching drive circuit, which also has the protection function for bridge arm short circuits and other faults. 5.1 Passive Filter Bank In the hybrid compensation system, PPF provides the path for harmonic currents. The PPF parameters used in the experiment are shown in Table 1. Due to experimental limitations, a high-pass filter was not fabricated; only 3rd and 5th order single-tuned filters were fabricated, and their parameters are shown in Table 1. [img=300,98]http://zszl.cepee.com/cepee_kjlw_pic/files/wx/dwjs/2001-1/45-2.jpg[/img] 5.2 Experimental Results Table 2 compares the harmonic content of the system current before and after the PPF and SAPF are switched on. The waveforms of the system voltage and system current before and after the PPF and SAPF are switched on are shown in Figures 6 and 7. The instrument used for measurement and recording in the experiment is the F43 power quality analyzer from FLUKE Corporation, USA. [img=291,132]http://zszl.cepee.com/cepee_kjlw_pic/files/wx/dwjs/2001-1/45-3.jpg[/img] As shown in Table 2, because the 3rd and 5th single-tuned filters provide channels for the 3rd and 5th harmonics respectively, when the SAPF is active, more of the 3rd and 5th harmonic currents flow through the PPF, significantly reducing the harmonic content of the system current. For the 7th and 9th harmonic currents, since there are no corresponding harmonic channels, the harmonic content did not change significantly before and after the SAPF was activated. The total distortion rate of the system harmonic current changed significantly; the total distortion current decreased from 14.6% to 8.0% after the SAPF was activated. These conclusions verify the results of the theoretical analysis. The above results were obtained when the harmonic content of the power supply voltage reached 5.8%. Experimental studies were also conducted on different harmonic contents of the system power supply voltage and under the condition of passive filter detuning. These studies also verified the improvement effect of SAPF on PPF characteristics and greatly reduced the total distortion rate of system harmonic current. [img=236,271]http://zszl.cepee.com/cepee_kjlw_pic/files/wx/dwjs/2001-1/46-1.jpg[/img][img=271,282]http://zszl.cepee.com/cepee_kjlw_pic/files/wx/dwjs/2001-1/46-2.jpg[/img] [b]6 Conclusion[/b] Theoretical analysis and experimental results show that the SVPWM technology based on the space vector method enables the waveform control of a single-phase system to have higher control accuracy than the adaptive PWM technology. Small-scale experimental results show that the effect of SAPF is related to that of PPF connected in parallel. In the presence of corresponding harmonic channels, SAPF can significantly improve the filtering effect of PPF. For large-capacity single-phase loads such as electric locomotives, SAPF is an effective harmonic mitigation device.