Abstract: With the widespread application of various power devices, a large amount of harmonics and reactive current flows into the power grid, causing grid pollution and resulting in increasingly serious power quality problems. Active power filters (APFs), as a primary means of suppressing harmonics, have become a research hotspot in academia and engineering over the past few decades. This paper provides a detailed analysis and comparison of APF topologies, current sensing methods, and control methods, elucidates the development trend of active filters, and proposes the idea of combining memristors with active power filters, providing new insights for future research.
Keywords: Active power filter; Current detection method; Control method; Memristor
Active Power Filter Technology and Its Development
introduction
With the emergence of various nonlinear and unbalanced loads, a large number of harmonics and reactive power are generated in the power grid, which increases the power grid energy loss, reduces power quality, and shortens the life of power supply and consumption equipment. Therefore, it is increasingly urgent to solve the problem of power system harmonic suppression and reactive power compensation. The traditional method is to use passive power filters [1] , which have the advantages of simple structure and high reliability. However, due to the disadvantage that they can only eliminate specific harmonics and are easily affected by system parameters and cause resonance, APF gradually replaced passive filters as the main means of suppressing harmonics and compensating reactive power after the 1980s. APF [2] injects a compensation current into the power grid that is equal in magnitude and opposite in direction to the load harmonics and reactive current, so that the harmonics and reactive power of the power grid are zero. It can dynamically compensate for any harmonics and reactive power, and is not easily affected by system parameters during operation, with high safety and reliability.
Currently, research on active power filters (APFs) mainly focuses on topology [3-7] , current detection methods [8-13] , and voltage-current tracking control methods [14-25] . This paper describes the current research status of these areas, and based on this, elaborates on the development trend of APFs. It also proposes the idea of applying memristors to active power filters, which has theoretical guiding significance for the research of active power filters.
1. APF Topology
With the development of APF technology, various topologies have emerged: standalone (series and parallel); hybrid (APF combined with passive filter); and series-parallel APF.
(1) Parallel APF: An APF is connected in parallel with the load to the system. By generating a compensation current equal in magnitude but opposite in direction to the harmonic current, it makes the load current sinusoidal. It can suppress harmonics and compensate reactive power for current-source nonlinear loads and balanced three-phase systems. However, since the APF needs to withstand the fundamental voltage, its application in high-power applications is limited. In addition, traditional parallel APFs use a single large inductor filter, and a large inductor inevitably leads to a large output impedance, affecting the compensation performance. Replacing the inductor in the circuit with an LCL filter composed of inductors and capacitors can enable the circuit to obtain a higher high-frequency attenuation rate and improve system performance, which is currently a research hotspot.
(2) Series-connected APF: The series-connected APF is connected in series with the load through a transformer, which can eliminate the voltage harmonics of three-phase imbalance and voltage-sensitive loads. However, since a high load current flows through the APF, the rated parameters of the transformer will increase and the loss will increase, which limits its application. Reference [5] proposes to connect the APF in series to the DC side, and by controlling two active switches, change the polarity of the energy storage capacitor to achieve continuous control of the inductor current, thereby achieving the function of suppressing harmonics. In addition, the two active switches operate at the same frequency, which can simplify the control circuit and drive circuit and reduce the cost.
(3) Hybrid APF and Passive Filter (PF): The hybrid type of series APF and parallel PF and the hybrid type of parallel APF and parallel PF are two basic structures. In the latter, the PF shares most of the harmonics, while the APF only plays the role of compensating for the required harmonics and improving system performance, thereby increasing the system capacity level and reducing system cost. The APF and PF are connected in parallel after being connected in series. The system is equivalent to a current-controlled voltage source. The APF only needs to generate a compensation voltage proportional to the harmonic voltage, which is suitable for high-voltage systems. Moreover, the injection transformer is connected to the neutral point of the PF, making insulation and maintenance more convenient. Both series resonant injection APF and parallel resonant injection APF utilize the characteristic of the capacitor and inductor resonating at the fundamental frequency to reduce the fundamental voltage of the grid that the APF bears. However, in order to have a better harmonic injection capability, a larger injection capacitor is selected, which can easily lead to excessive reactive power and affect the operation of the grid. Reference [6] proposes a hybrid structure in which the active part is connected in parallel with the series resonant branch composed of L2 and C2 through a coupling transformer, and then connected in series with the parallel resonant injection branch composed of L1 and C1 to the power grid. In the harmonic domain, the active part only bears a very small harmonic voltage distributed on L2 and C2 , thereby effectively reducing the capacity of the active part module and reducing the system cost.
(4) Series-Parallel APF: The system consists of series APF and parallel APF, combining the characteristics of both. The parallel APF is mainly used for harmonic suppression and reactive power compensation, while the series APF is mainly used for isolation and voltage regulation. It is also known as a unified power quality regulator and is currently a hot topic in APF research. However, the system structure is complex and the control is difficult, requiring further research.
(5) Switched Capacitor Filter: This is a new circuit structure that combines switching devices with small-capacity capacitors and inductors. By controlling the switching on and off, it can filter out harmonics and provide reactive power to the system, thereby replacing the large energy storage components and converters in the traditional APF main circuit. This effectively simplifies the circuit structure, reduces the size, and lowers the cost and circuit capacity.
2 Harmonic Detection Algorithm in APF
The earliest detection methods were implemented using analog circuits. However, analog circuits have limitations: they can only filter out harmonics of fixed frequencies, have large detection errors for harmonics in time-varying signals, and are highly sensitive to changes in component parameters. These limitations restricted their application. With the rapid advancement of computer and electronic technologies, digital detection algorithms have been widely developed. Based on their development process, these algorithms can be divided into three categories: frequency domain, time domain, and modern intelligent control. These algorithms will be introduced in detail below.
(1) Fourier Transform and its Improved Algorithms: The traditional Fourier detection method performs a Fourier transform on the detected current to obtain the fundamental and integer harmonic currents. However, this method has a large computational load and poor real-time performance, so improved algorithms have been developed, including Fast Fourier Transform, Discrete Fourier Transform, and Recursive Discrete Fourier Transform. These three improved methods have improved the detection accuracy and reduced the computational load to some extent, but they all require strict synchronous sampling, which limits their application.
(2) Kalman Filter: This algorithm is the optimal linear estimate based on the minimum mean square error criterion. It estimates the current process state in real time using state equations and recursive methods, based on the previous and most recent observation data. Dynamic noise and saturation are two important factors affecting filter performance; determining these two quantities is a challenge in applying the Kalman filter.
(3) Detection method based on wavelet theory: Wavelet transform is performed on the detection current, and the signal is decomposed into various frequencies by utilizing the bandpass characteristics, while retaining the time information of each component of the signal. The wavelet detection method has good characteristics for the extraction of signal features, but there is no unified theoretical basis for selecting the wavelet mother function, which needs further research. Reference [12] proposes a time-varying harmonic detection method based on wavelet transform, which uses wavelet transform to transform the estimation problem of time-varying harmonic amplitude into constant coefficient estimation, which can accurately detect time-varying harmonics and has a fast tracking speed.
The above three methods are frequency domain-based harmonic detection methods, which are very effective for harmonic detection of stable signals. However, their harmonic detection capability will be reduced for time-varying and non-periodic signals. Therefore, time domain-based harmonic detection methods are needed to supplement them.
(4) Synchronous Detection Algorithm: This algorithm is based on average power and can be divided into equal power method, equal current method, and equal resistance method according to different compensation components. That is, the power, current, and resistance of each phase are equal after compensation, and the voltage and current are in phase. This method can effectively eliminate reactive power and harmonics, reduce line losses, and balance line current. However, when the three-phase voltage is unbalanced, it will cause the compensated current to be unbalanced and the time delay to increase, which limits its application.
(5) Detection algorithms based on instantaneous reactive power: These mainly include detection algorithms based on instantaneous active and reactive power (PQ method), detection algorithms based on instantaneous active and reactive current (IP-IQ method), and algorithms based on synchronous rotating coordinates (DQ method). These three algorithms primarily obtain the fundamental and harmonic components in the corresponding coordinate system through coordinate transformation, and then obtain the quantities required for calculation through inverse transformation. The quantities involved in the calculation of the PQ method are the three-phase instantaneous phase voltage and instantaneous line current, while the quantities involved in the calculation of the IP-IQ method are the three-phase symmetrical unit sine and cosine quantities. In terms of hardware implementation, the latter has a simpler circuit and is easier to implement. The DQ method can achieve compensation for a specified harmonic, but when implemented using analog circuits, it requires too many low-pass filters, which increases the complexity of the system.
(6) Fryze-based harmonic detection algorithm: This method treats the load in the actual circuit as an ideal conductive element, assuming that all power in the circuit is consumed in this equivalent conductance. The current is decomposed based on the equivalent conductance, and the properties of each current component are discussed. It can be divided into direct and indirect methods. The direct method uses the waveform of the power supply voltage to analyze the current, obtaining the fundamental active and reactive components, thereby detecting the harmonic current components. The indirect method uses a phase-locked loop to generate a reference voltage in phase with the power supply voltage, which replaces the actual voltage during the calculation process, thus accurately detecting each current component. This method has a wide range of applications and can detect the fundamental current and any harmonic current.
In addition to the methods mentioned above, other time-domain harmonic detection methods include DC-side voltage control algorithms, generalized integral algorithms, and unity power factor algorithms. These algorithms have good detection capabilities for time-varying load currents, but they suffer from drawbacks such as computational complexity and low accuracy. With the development of modern intelligent control, these problems are expected to be solved.
(7) Adaptive Detection Method: This method is based on the principle of adaptive interference cancellation. It uses voltage as a reference input and load current as the original input. It removes the active component that is the same as the voltage waveform from the load current to obtain the harmonic and reactive components that need to be compensated. It also has good adaptive capability under voltage waveform distortion. The disadvantage is that the dynamic response speed is relatively slow.
(8) Neural Network Detection Method: The neural network harmonic current detection method detects harmonic current through adaptability or training weights. It not only avoids the complex calculation for a given compensation current, but also has wide adaptability and can detect harmonic current, reactive current, fundamental negative sequence current and zero sequence current at the same time.
(9) Predictive control algorithm: Utilizing the state information at the current sampling moment, the trajectory of the compensation current in the next sampling cycle is predicted, thereby determining the inverter's switching function and enabling the compensation current to follow the changes in the current reference value, thus realizing predictive control of harmonic current. Combining it with neural networks or adaptive algorithms can form a composite algorithm, achieving rapid and accurate detection of harmonic current.
Intelligent control algorithms have significant advantages in detection accuracy and calculation speed, but current technology does not yet allow these algorithms to be applied in practice, and further research is needed.
3. APF Control Algorithm
Once the main circuit structure and current detection algorithm of the APF are determined, the control system becomes the key factor affecting the performance and efficiency of the APF. Control methods can be broadly categorized into two types: First, traditional control methods, such as hysteresis current control, space vector control, single-cycle control, deadbeat control, triangular wave comparison, linear control based on coordinate transformation, and direct control algorithms. Second, novel intelligent control methods, including adaptive control, fuzzy control, neural network control, iterative self-learning control, repetitive control, predictive control, sliding mode variable structure control, instantaneous current control algorithms, and control algorithms based on Lyapunov functions.
(1) Single-cycle control algorithm: Its basic idea is to control the duty cycle of the switch so that the average value of the inverter switching variable is equal to or proportional to the control reference value in each cycle, thereby eliminating steady-state and transient errors. It has the advantages of high accuracy, simple circuit, and insensitivity to changes in system parameters. However, this method is difficult to accurately obtain the equivalent impedance of the APF and harmonic load in parallel, and is only suitable for the case of simultaneous harmonic and reactive power compensation.
(2) Deadbeat Control Algorithm: This is a predictive control algorithm that can be implemented entirely digitally. Based on the load current and compensation current at time K, it calculates the command current value at time K+1 and the predicted values of the compensation current under various possible switching states. Then, it selects the switching state that minimizes the current error as the basis for selecting the switching state at time K+1. Using grey system theory, the prediction can be extended to step K+2, predicting and comparing the harmonic reference current and possible output current at step K+2, and then determining the switching state at step K+1 after comprehensive analysis. This method can quickly respond to sudden changes in current and is particularly suitable for fast transient control. However, it suffers from high computational complexity and high parameter dependence.
(3) Voltage space vector control algorithm: From the perspective of the motor, the inverter and the motor are regarded as a whole. By controlling the action time of the three switching vectors closest to the reference vector, the average effect of the switching vector output within one control cycle is made close to the reference circular flux. It has high voltage utilization and can effectively suppress current over-adjustment. However, the control algorithm is complex and requires a long calculation time. Reference [15] proposed a hysteresis current control method based on voltage space vector. It uses the spatial distribution of the current error vector and the reference voltage vector to give the optimal voltage vector switching time, so that the current error is controlled within the hysteresis width. It can effectively eliminate the phase-to-phase influence and its implementation is simple and does not require complex vector transformation.
(4) Direct control algorithm: This algorithm is based on DC side capacitor voltage control and compensation current feedback control. Starting from the perspective of the transmission of instantaneous active and reactive power in the system, it aims to regulate the active power of the grid input APF and directly control the input current. This eliminates the cumbersome process of detecting active and reactive current components, thus simplifying the system.
Traditional control methods are widely used in practice, offering fast response times, simple control circuits, and good control accuracy. However, some inherent drawbacks of traditional control methods limit their further application, necessitating the development of new intelligent control methods.
(5) Sliding mode variable structure control method: Its principle is to rely on high-frequency conversion to force the closed-loop system to reach and maintain on the designed sliding surface, and directly select the switching mode by determining which side of the surface the tracking error is on. However, in existing sliding mode variable structure control, the switching surface is constructed with zero tracking error, which will cause adjustment error. In addition, the inverter switching frequency is not fixed, the frequency range of switching harmonics is wide and not easy to filter out, which requires further research.
(6) Instantaneous Current Control Algorithm: This algorithm analyzes the direct control effect of different switching states of the grid-connected inverter on the instantaneous current, deriving a set of instantaneous current displacement factor formulas. When regulating the output current, pulse width modulation is used to select different displacement factors and control their duration, completing the transfer of the current to the command current at the next moment, thereby achieving the control objective of the output current tracking the command current. This method can realize high-performance and fast detection and control of active power filters using only a single digital signal processor (DSP), is simple and practical, and can effectively reduce the output inductance.
(7) Control algorithm based on Lyapunov function: The active power filter system is modeled using coordinate transformation, and a control algorithm based on the model is established using Lyapunov function theory to regulate the system. This method has a simple harmonic detection link and low computational load; the control strategy does not rely on circuit parameters; the coupling relationship can be eliminated during the calculation process, eliminating the decoupling link of the PI controller and simplifying the circuit structure.
(8) Repetitive control algorithm: The dynamic model of the external signal acting on the system is implanted into the controller to form a high-precision feedback control system. Under the premise that the system period remains unchanged, the control error of the previous period is applied to the generation of the current control quantity, so that it has a good ability to suppress periodic disturbances. Reference [24] proposes a control method that connects PI control and repetitive control in parallel. The repetitive control is used to improve the steady-state accuracy of the APF, and the dynamic performance of the APF is guaranteed by PI control, so that the system can obtain good stability.
(9) Neural network algorithm: This algorithm is an imitation of the brain's information processing and retrieval functions. It can solve large-scale real-time calculation problems in control systems and has adaptive and learning capabilities for complex uncertain problems. When applied to APF, this method can directly obtain the inverter's switching mode based on the load current information, thereby improving the system's stability and speed. Reference [25] proposes a recursive PI control algorithm based on neural networks. Based on the forward channel error backpropagation adjustment of the weights with variable learning rate, the algorithm introduces the particle swarm algorithm to correct the weights, thereby optimizing the proportional and integral parameters of the PI controller.
Although intelligent control methods have been extensively used in the research of active power filters, these technologies cannot yet be practically applied. Introducing intelligent control into traditional control methods, leveraging the advantages of intelligent control to improve the shortcomings of traditional control methods, and thus enhancing control performance, is currently a hot research topic.
4. Development Trends
The current research status and application level show that most APF research is still in the simulation and experimental stage. To further improve existing research results and apply them in practice, future research needs to further refine the harmonic detection theory, improve the system's compensation characteristics and current detection methods; apply modular and multi-level technologies to improve system reliability and reduce switching losses; improve the control methods and structures of converters to provide effective ways to improve APF performance; apply DSP to APF systems to achieve fully digital detection and control of harmonic currents; and expand the functions of APF to achieve reactive power compensation, voltage imbalance elimination, and flicker elimination, in addition to harmonic elimination, so that power system harmonic management can develop in a dynamic, intelligent, and economically efficient direction.
In addition, the emergence of some new technologies will also provide new directions for the development of APF. In 2008, HP Labs developed a nanoscale device with memristor effect, making memristors a current research hotspot. Combining memristors [26] with inductors and capacitors to form a device with filtering properties, adding it to APF, and forming a hybrid APF can effectively improve the voltage level of the system. Furthermore, since memristors are nanoscale devices, their application will make the modularization and multiplication of APF easier. In addition, the application of memristors is expected to build a neural network model, turn neural network control into reality, and improve the stability of APF. Compressed sensing [27] is a new sampling theory. Once proposed, it has attracted widespread attention from the academic and industrial communities and was rated as one of the top ten scientific and technological advances of 2007 by the American Science and Technology Review. It obtains discrete samples of the signal by random sampling under conditions much smaller than the Nyquist sampling rate by developing the sparsity characteristics of the signal, and then perfectly reconstructs the signal through a nonlinear reconstruction algorithm. It can discard most of the intermediate processes that involve useless data, thus effectively alleviating the pressure of high-speed sampling and reducing the costs of processing, storage, and transmission. Using compressed sensing theory to detect load harmonics and reactive power provides real-time and accurate analysis capabilities for both abrupt and non-stationary signals, effectively improving the speed and accuracy of harmonic detection and further enhancing the performance of active filters.
5. Conclusion
This paper introduces the current research status of active power filters (APFs), analyzes the basic principles of some structures and algorithms, compares their advantages and disadvantages, and looks forward to the future development direction of this field. With the further improvement of APF technology and its application in practice, it will undoubtedly contribute to improving my country's power quality, providing a clean electrical environment for the power grid, and creating a "green power grid."
