Design of hybrid power filter based on fast control model

At present, power filters are mostly implemented with digital controllers, which requires engineers to have high software programming skills. In this way, most of the time in the filter design cycle will be spent on program writing and optimization. Considering the establishment of mathematical models, algorithm design, and offline debugging, the entire development time will be very long and the cost will increase accordingly.

The design of rapid control prototyping (RCP) reduces the design cycle. Using Simulink's graphical programming method, there is no need for complex program writing: for hardware engineers, changing model parameters can achieve on-site debugging; for theoretical researchers, only the speed and practicality of the algorithm need to be considered.

Wavelet transform is a fast and effective method for analyzing non-steady-state voltage and current waveforms. Like FFT, wavelet transform decomposes signals into frequency components. However, discrete wavelet transform (DWT) has variable frequency resolution, which can effectively solve the voltage flicker caused by load mutations, and can track harmonics in real time. This is a useful feature for analyzing transient signals. In addition, wavelet analysis does not need to be performed simultaneously in the entire frequency domain, and the calculation amount is concentrated in a certain frequency range, which reduces the calculation amount and speeds up the analysis.

This paper models the hybrid active power filter (HAPF) based on Simulink software, uses the Wavelet toolbox to perform harmonic analysis and simulation, generates DSP code from MATLAB/Simulink/Embedded Target for TI C2000, and finally implements the hardware in TMS320F2812.

1 Rapid Control Model (RCP)

RCP consists of two parts: computer-aided design software Simulink and proprietary hardware TMS320F2812 with real-time operating system, as shown in Figure 1. This graphical programming method replaces the writing of traditional programs and only requires engineers to focus on the optimization of functions and performance. The complete system proposed in this paper is carried out in a simulation environment.

Embedded Target for TI C2000 connects software and hardware. The Simulink toolbox provides various models required in this article, providing an integrated platform for designing, simulating and implementing embedded control systems on general-purpose DSPs. Figure 2 shows the design process.

By using Embedded Target, efficient DSP code can be generated through CCS (Cede Composer Studio). By connecting the host and DSP through the interface, the DSP can be controlled and optimized online. For complex algorithms that require cyclic calculations, the fast execution function of RCP will show great advantages. In view of the prospect of wavelet transform analysis of power system harmonics and the convenience of modeling, the active part control algorithm of this filter uses wavelet transform to analyze power grid harmonics.

2 Wavelet Analysis
2.1 Multiresolution Decomposition Method
The implementation of wavelet analysis usually adopts the multiresolution decomposition method (Multiresolution Signl Decomposition, MSD) of the signal. The high-pass filter h and the low-pass filter g are respectively constructed by wavelet functions, as shown in Figure 3.

Scale 1 in Figure 3 contains information from the Nyquist frequency to 1/4 of the sampling frequency, scale 2 contains information from 1/4 to 1/8 of the sampling frequency, and so on for other scales. Wavelet decomposition can be terminated at any scale, and the final smoothed output contains information on all remaining scales. However, the number of decomposition layers of the signal is not arbitrary. A signal of length N can only be decomposed into log2N layers at most.
2.2 Wavelet transform
The wavelet transform of a continuous signal f(t) is defined as:

where is the mother wavelet, a is the scaling factor, and b is the translation factor. Whether it is stretched or contracted in the time domain depends on a.
In the discrete wavelet transform, some wavelet coefficients m and n are given, which depend on the order of the scaling factor and the translation factor. Then the discrete wavelet coefficients can be expressed as:

Although this transform is continuous in time, the wavelet form is discrete. The inverse discrete wavelet transform is as follows:

Formula (3): K=(A+B)/2, A and B are the maximum values ​​(frame values) of a and b respectively.
The choice of mother wavelet is different for different problems, and the selection of mother wavelet has a great influence on the obtained structure. Orthogonal wavelets ensure that the signal can be reconstructed from its transform coefficients. Wavelets with symmetrical filter coefficients can produce linear phase shifts. The wavelet group derived by Daubechies covers the field of orthogonal wavelets.
2.3 Model implementation of control algorithm
Simulink toolbox provides a wealth of mathematical models, from which C28xADC, C28x PWM, F2812 eZdsp (DSP code cannot be generated without this module), DWT and IDWT modules are selected to form the model shown in Figure 4.

Among them, the Environment Control, Buffer, DWT and IDWT modules are integrated in the Wavelet subsystem to perform harmonic analysis on the sampled and quantized signals, and generate compensation voltage command signals, and then control the shutdown of the IGBT through the PWM output signal to achieve the purpose of reducing harmonics and reactive power compensation. During the simulation process, the duty cycle of the C28x PWM is adjusted in real time as needed to generate a suitable output waveform.

3 Hybrid active power filter modeling
3.1 Hybrid active power filter
Currently, LC resonant passive filters (PPF) are mainly used for high-voltage and large-capacity harmonics. These filters also have reactive power compensation functions. Although PPF has the advantages of small initial investment and high operating efficiency, the filtering effect of PPF is greatly affected by the impedance of the power system, and can only eliminate harmonics of a specific order. The filtering effect is not good for loads with frequently changing harmonic orders.
It may also resonate with the system, causing the LC filter to overload or even burn out. Active power filter (APF) is equivalent to a variable resistor, with a fundamental impedance of 0 and a high impedance state for harmonics. Although APF can overcome the defects of PPF, its installation capacity is limited by the capacity of the switching device.
The passive filter and the active filter are combined to form a hybrid active power filter (HAPF), and the active power filter is only used to improve the filtering effect of the passive filter and suppress possible resonance. In this way, the active power filter does not bear the fundamental voltage of the AC power supply, so the device capacity is greatly reduced, usually only about 1/10 of the total capacity of the nonlinear load is required, so that the active power filter can be used in high-power occasions.
Large power supply and distribution stations usually hope to perform reactive power compensation while filtering harmonics, which will inevitably increase the technical difficulty and cost of inverter implementation, thereby limiting the application of active power filters in large substations. By coupling the inverter output voltage to the inductor and capacitor of the filter branch of the passive filter through a transformer, the active power filter neither bears the fundamental voltage nor the fundamental current, thereby greatly reducing the capacity of the active power filter.
3.2 Control system structure
In the past, the control part of the active power filter was composed of an industrial computer and a single-chip microcomputer. The industrial computer realizes harmonic detection, analysis, and control signal calculation, while the single-chip microcomputer generates control signals. Due to the processing speed of the single-chip microcomputer, this paper integrates signal sampling, harmonic analysis, and PWM pulse width signal generation in TMS320F2812 to give full play to the computing efficiency of the 32-bit DSP. The control circuit structure is shown in Figure 5.

The zero-crossing point of phase A voltage is selected as the initial value. The three-phase current is is measured by the Hall sensor after the initial moment, and the measured value is sent to the DSP. After high-speed A/D conversion, the sampling value is obtained. Then the sampling value is subjected to discrete wavelet transformation to obtain the fundamental value is1 of the three-phase current. The fundamental value is subtracted from the sampling value of the three-phase current to obtain the three-phase harmonic current value ish that the active power filter needs to compensate. The command signal U=KIsh of the output compensation voltage of the active power filter can be obtained. Then, the inverter is controlled by the PWM module of the DSP to obtain the desired voltage waveform.
3.3 Simulation model of hybrid active power filter
The powerful Simulink toolbox contains all the algorithms and peripherals of the C2000 DSP series involved in this article, which will undoubtedly provide convenient conditions for the simulation design of the controller. The model of the hybrid active power filter is shown in Figure 6.

The three-phase AC voltage source 35 kV, 50 Hz, 500 kVA simulates the power grid and is stepped down to 400 V, 50 Hz through a transformer. The inverter output voltage of the active filter is coupled to the inductance and capacitance of the filter branch of the passive filter through a transformer to reduce the capacity of the active power filter, as shown in Figure 7. B1 and B2 are measuring instruments, respectively, and the nonlinear load consists of an asymmetric rectifier.

4 Experimental results
DC bus capacitor:

Wherein, the rated voltage of the capacitor is Vn=Vc/1.83, and the apparent power of the distribution line is Sn=, which is the power of the capacitor at f=50 Hz.
Minimum filter capacitance:

Wherein, is the current per-unit value of the nth harmonic, and is the voltage fundamental per-unit value.
Then, the filter inductance is obtained according to formula (6):

ωs is a certain sub-angular frequency. From the above formula, the parameter values ​​of this simulation system are shown in Table 1.

The waveforms before and after current compensation are shown in Figure 8. It can be concluded from the waveform that after passive filtering and compensation current, a more accurate three-phase sinusoidal current waveform is obtained.

After the calculation and analysis of harmonics by the wavelet analysis toolbox and the hybrid active power filter, the distortion coefficient is reduced from 22.50% to 1.88%, which is in line with the IEEE-519-1992 standard, as shown in Figure 9.

5 Conclusions
Compared with traditional power filters, the fast control model has a short design cycle, low investment cost and obvious filtering effect. The operation results show that the fast model established using DSP as the controller can accurately track the grid voltage flicker caused by load mutation, thereby performing harmonic compensation. The equipment has high reliability, strong anti-interference ability, good economic benefits, and is suitable for engineering application and promotion.