Abstract : This paper takes a parallel voltage-source active power filter (APF) as the research object, and systematically analyzes its working principle, compensation characteristics, harmonic current detection method, compensation current control strategy, and DC-side voltage control. In the design of the control circuit, digital PWM control technology is adopted, and a DC-side voltage feedback control loop is introduced to ensure that the APF has good compensation and following characteristics. Harmonic current detection is implemented in hardware, which is simple, easy to implement, and has good real-time performance. Simulations of load current compensation control are performed, and the results show that good compensation function can be achieved by selecting appropriate parameters.
Keywords : harmonic suppression, parallel voltage-type active power filter, instantaneous reactive power PI control
1 Introduction
With the increasing severity of power grid harmonic pollution and the growing demands for power supply reliability and quality, traditional passive filters can no longer fully meet the power quality requirements of electricity users. Active power filters (APFs) can overcome the shortcomings of traditional harmonic suppression methods such as passive filters and have attracted widespread attention due to their superior filtering performance. With the rapid development of digital signal processing technology, active power filters implemented with digital control technology have become a new research hotspot in power electronics technology.
Active power filtering technology, as a new and advanced harmonic control technology, is an effective tool for eliminating harmonic pollution and improving power quality. Therefore, this article will focus on the implementation of parallel active power filtering technology in low-voltage distribution networks, based on passive harmonic control measures for power grids.
2. Basic Principles of Active Power Filters
Figure 1 shows the schematic diagram of a basic active power filter system. In the figure, es represents the AC power supply potential, is represents the AC power supply current, the load is a harmonic source that reduces the system power factor and generates harmonics, iL represents the load current, ic represents the compensation current, ic* represents the command signal for the compensation current, and HPF represents a high-pass filter.
An active power filter system consists of two main parts: a harmonic current detection circuit and a compensation current generation circuit (comprising a compensation current control circuit, an isolation and drive circuit, and a main circuit). The core of the harmonic current detection circuit is to detect the harmonic current components in the current being compensated. The compensation current generation circuit generates the actual compensation current based on the compensation current signal obtained from the harmonic current detection circuit. The compensation current control circuit calculates the command signal for the compensation current based on the detected voltages and currents using a control algorithm. The main circuit generates the compensation current, and currently, a PWM converter is typically used.
Figure 1. Schematic diagram of the active power filter system.
The basic working principle of the active power filter shown in Figure 1 is to detect the voltage and current of the object to be compensated, calculate the command signal of the compensation current through the command current calculation, amplify the signal through the compensation current generation circuit to obtain the compensation current, and cancel out the harmonic current to be compensated in the load current to finally obtain the desired power supply current.
3. Mathematical Model of Voltage-Type Active Filter
There are two types of main circuits for active power filters: current-source PWM inverter circuits and voltage-source PWM inverter circuits. Their function is to generate non-sinusoidal current to compensate for harmonic currents generated by nonlinear loads. While current-source active power filters have high reliability, they also have high losses and require a large inductor in parallel on the AC side, thus they are less commonly used in general applications. Voltage-source PWM converters have a large capacitor on their DC side; due to their portability and good characteristics, they are more widely used. The voltage-source structure used in this paper is shown in Figure 2.
Figure 2. Schematic diagram of voltage-type active power filter structure.
A large capacitor is connected to the DC side. Under normal operation, its voltage remains essentially constant and can be considered a voltage source. To maintain a constant DC voltage, the DC voltage needs to be controlled. Compared to current-source PWM converters, voltage-source PWM converters have the advantage of not generating significant losses. However, a short-circuit fault can occur when the main circuit switching devices shoot through. Therefore, certain protective measures are needed to prevent the switching devices from shooting through.
For a three-phase AC inductor, the following formula can be derived according to Kirchhoff's voltage law:
(1) Among them,
Meanwhile, the DC bus voltage relationship is:
Since the DC bus voltage of the APF is the series connection of two capacitors, the formula should be:
(2)
Therefore, equation (1) can be written as
(3)
Transform the matrix by 3/2:
Therefore, equations (2) and (3) can be simplified to the following, where equation (3) is negligible due to its small value. Thus, the mathematical model of the APF is expressed by equations (4) and (5):
(4)
(5)
4. Harmonic Detection Algorithm Based on Instantaneous Reactive Power Theory
The detection method based on Akaggi's three-phase instantaneous reactive power theory has played a significant role in the development of active power filters (APFs) and is currently the most widely used detection method in APFs. This method transforms the three-phase electrical vectors to α and β coordinates, redefines instantaneous active and reactive power, and then inverts these powers into three-phase compensation currents. It mainly uses the ip/iq and p/q operation methods. The p/q method involves the three-phase instantaneous phase voltages and instantaneous line currents, while the ip/iq method does not involve the three-phase instantaneous phase voltages themselves, but rather the synchronous three-phase symmetrical unit sine and cosine quantities. In terms of hardware implementation, the p/q method requires 10 multipliers and 2 dividers, while the ip/iq method only requires 8 multipliers and a corresponding synchronous three-phase sine and cosine generation circuit. When the power supply voltage is symmetrical and undistorted, and the load current is symmetrical, both methods can accurately detect the active, reactive, and harmonic current components of the fundamental current. When both the power supply voltage and load current are distorted, the ip/iq calculation method can still accurately detect harmonic currents, while the p/q calculation method has errors. When the three-phase voltage or three-phase current is unbalanced, both the ip/iq and p/q calculation methods will have detection errors when applied directly.
The instantaneous value of the three-phase harmonic current can be obtained by subtracting the instantaneous value of the three-phase fundamental current from the total three-phase current. The detection process is shown in Figure 3.
Figure 3 shows the detection process of the IP-IQ method for detecting harmonic currents in the power grid.
5. Harmonic Compensation Closed-Loop Control Strategy
Figure 4. APF Closed-Loop Control Block Diagram
Figure 4 shows the SAPF closed-loop control block diagram. The area within the dashed box represents the outer loop control of the DC-side voltage. Ucf is the real-time detected DC-side voltage, and Ucr is the reference voltage value. The difference between them, after passing through a PI regulator, yields the error adjustment signal Δip. This Δip is then superimposed on the instantaneous active DC component ip detected by the ip-iq method to obtain the fundamental active information in the compensation current, which also represents the information on the energy exchange between the DC-side capacitor and the AC grid, ultimately maintaining the DC-side voltage at the given value. The harmonic command current is detected by the ip-iq method and superimposed on the fundamental active current command to become the total command signal. Through the inner current loop control, the voltage-source inverter ensures that iouta, ioutb, and ioutc can track the command current signals iaf, ibf, and icf in real time by changing the amplitude and phase of the output voltage, thereby achieving the purpose of harmonic mitigation control.
5.1 PI control current inner loop
The electrical model of the inner current loop is shown in Figure 5.
Figure 5 Current inner loop control model
In the diagram, Gc(s) is the transfer function of the controller, which is determined by the control method employed. The inverter amplifies the power of the modulated wave and also introduces a delay. Ginv(s) is the inverter transfer function, and GL(s) is the transfer function of the system's filtering stage. For the current loop, we use the linear feedback method, and its mathematical model is derived as follows.
thereby
Therefore, we only need to correct the resistance of the inductor.
Therefore we can adopt
This corresponds to the control of the current loop.
thereby
After applying the linearized feedback described above, we can obtain the simplified transfer function of the current loop as follows:
Considering the system sampling delay and the small inertia of the system PWM control, we can set it to...
Among them, ... Thus, our corrected Bode plot is shown in Figure 6:
Figure 6. Bode plot of current loop correction
We set the correction stage to , at which point our cutoff frequency is , and the phase margin is approximately 42 degrees.
5.2 Control Voltage Loop Design
In steady state, it can be assumed that, therefore, the above equation in (5) can be written as, at the same time, when the cutoff frequency of the voltage loop is low, and the load is constant, we can determine it as a certain value from equation (4).
At the same time, from equation (5), we can obtain (here, due to the switching function in, it is relatively small, that is, so we have)
and thus
After we obtain the fundamental frequency of the load current (or the power filter), we can get...
Therefore, the current given for the APF is as follows:
in
In reality, it compensates for the active power of the APF, which is an essential power source for maintaining the balance and stability of the bus voltage.
Therefore, we can consider the voltage loop to be...
We also consider the inertial element of the current loop to be equivalent to, where, Therefore, we can obtain the result shown in Figure 7:
Figure 7. Bode plot of voltage loop correction
We selected a cutoff frequency of approximately 200 rad/s and a phase margin of approximately 43 degrees.
6. Experiments and Analysis
Generally speaking, time-domain detection methods have a fast response speed and can also implement selective harmonic detection methods (this type of detection method consumes a lot of computation time to perform dq0 transformation, i.e., 5th, 7th, etc., so it is not applicable). Currently, most harmonic detection is performed using instantaneous reactive power theory.
Frequency domain detection is applicable to both single-phase and three-phase systems. Although it has a significant time delay, it offers a major advantage in detecting harmonics in periodic loads and can effectively detect specific harmonics, providing considerable flexibility. We employ Discrete Fourier Transform (DFT) for harmonic detection. The simulation waveform is shown in Figure 8.
Figure 8 Simulation waveform of three-phase nonlinear balanced load
Figure 9 shows the operating waveforms of the low-voltage hybrid active power filter connected to the 0.4kV side of the power grid. The active part of the system uses a deadbeat control method. Figure (a) shows the current and voltage waveforms on the grid side after only the passive filter is connected. It can be seen that the current waveform is severely distorted, and the voltage waveform is also distorted. At this time, the power factor on the grid side is 0.94. Figure (b) shows that after the active filter is connected, the current and voltage waveforms of the power grid are greatly improved and are basically sinusoidal. The harmonic current of the power grid is effectively suppressed, and the power factor on the grid side is increased to 0.98.
(a) Current waveform on the grid side before APF is connected (b) Voltage waveform on the grid side before APF is connected
(c) Current waveform on the grid side after APF is connected (d) Voltage waveform on the grid side after APF is connected
7. Conclusion
With the advancement of modern science and technology, especially power electronics, the application of power electronic devices has become increasingly widespread. Loads on power distribution networks, such as rectifiers, electric arc furnaces, electrified railways, and variable frequency drives, are constantly increasing. Due to the nonlinear, unbalanced, and impulsive characteristics of these loads, voltage and current waveforms in the power network are distorted, potentially leading to problems such as low power factor, voltage fluctuations, voltage flicker, and three-phase imbalance. Therefore, improving power quality has become a pressing task. Passive and active power filters, due to their excellent harmonic suppression effects, flexible control, low maintenance costs, and adaptability to various operating conditions, have gradually become an important and popular research topic in the field of harmonic suppression.
This paper details the working principle of active power filters, proposes corresponding harmonic mitigation schemes, and focuses primarily on low-voltage parallel active power filters. It presents Fourier series and ip and iq harmonic current detection algorithm models, which can detect all high-frequency components other than the fundamental frequency in real time, with fast response speed and meet system performance requirements.
About the Author
Zhou Jiaqi (1983-) is a male with a master's degree. He currently works at Harbin Jiuzhou Electric Co., Ltd. as an intermediate engineer. He is mainly engaged in the research and development of new energy power generation technology and reactive power compensation technology.
Wang Lei (1984-) is a female master's degree holder who currently works at Harbin Jiuzhou Electric Co., Ltd. as an intermediate engineer. She is mainly engaged in the design and development of DC systems and integrated power supplies for power plants.
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