FPGA Design and Implementation of Power Line Simulation System

Due to the ultra-large scale of the distribution network and the low cost, wide coverage and convenient deployment of power line communication. Power line communication provides an excellent device interconnection solution, so it has received widespread attention and has been widely used in smart grids, Internet access, smart homes and other fields.
However, since power lines are not designed for communication, the power line channel is relatively complex and harsh for high-frequency communication signals. Therefore, it is necessary to establish a standardized test platform for the research and development of power line communication equipment. For manufacturers, such a test platform can immediately and repeatably verify the algorithm performance at every step of product development. For users, such a platform can help them compare the performance of products from different manufacturers on the same platform, so as to make a more objective evaluation of the product. However, there is currently a lack of such tools for testing and verification of the physical layer. Most of the tests for power line communication equipment are mainly concentrated on the upper layer. Due to the use of multiple error correction technologies, the problems caused by the physical layer may be covered up.
Although the main frequency of the processor based on sequential execution is already very high, it is often unable to process complex data streams with large depth. The powerful parallel processing capability and flexible customizability of FPGA provide a good solution for the processing of such data.

1 System framework
1.1 Mathematical model of power line channel
The basic power line channel model is shown in Figure 1. The power line channel described by this model is divided into two parts, namely, channel transmission characteristics and noise. The power line channel can usually be described as a linear system, that is, represented by a unit impulse response or frequency response function. It can be equivalent to a signal passing through a linear filter. The noise in the power line channel is usually additive noise, which is equivalent to the sum of the signal voltage and the noise source voltage, as shown in formula (1). Where "" represents the convolution operation.

1.2 Hardware Structure
The hardware structure of the system is shown in Figure 2. In order to test power line devices with bidirectional communication function, each port of the simulation system should have bidirectional communication function. Directional couplers are used to isolate the received signal and the signal sent to the device under test. The FPGA controls the amplifier to amplify the input signal to achieve the maximum dynamic range, and then converts it into a digital signal through A/D sampling for further processing. The filter parameters used to simulate the channel are pre-stored in the FPGA. The filter is modified before each simulation and remains unchanged during the simulation. After passing through the virtual power line channel, the signal is converted into an analog signal again through D/A.

The noise sequence generator in the FPGA is used to generate various power line noises. The noise sequence is converted into an analog signal through another D/A converter, and the analog signal is output through an amplifier controlled by the SNR control unit to adjust the power of the noise component in the output signal. The SNR parameters are set and modified before simulation, just like the filter parameters.
2 Analysis of power line channel and noise characteristics
2.1 Analysis of power line transmission characteristics
The power line communication channel is different from other wired communication channels and is similar to a bus line. The signal usually does not pass directly from the transmitter to the receiver along a path, but passes through some additional paths or reflection paths. A simplest branch model can be used to analyze the power line channel, as shown in Figure 3. The signal is transmitted from point A to C, and the impedance mismatch at point B will cause a part of the signal to be reflected. The signal at point B will be transmitted to points C and D at the same time. Point D is not a receiving terminal, so there is also an impedance mismatch, which reflects part of the signal back to point B and circulates in sequence. The complex power line channel can be decomposed into a parallel or cascade of this model.

According to Manfred Zimmermann's research, the power line channel under multipath effect can be expressed as

Where A(f, di) is the attenuation of the ith path, which is related to the frequency and path length. τi is the delay of the signal on the ith path, and its value is given by formula (3)

Where c0 is the speed of light in a vacuum; εr is the dielectric constant of the conductor.
According to transmission line theory, power lines used to transmit high-frequency signals should be analyzed as low-loss transmission lines, and their characteristic impedance Z0 and transmission constant γ are defined by formula (4) and formula (5) respectively

Where α is called the attenuation constant, which represents the change in the amplitude of the wave per unit length on the transmission line; β is called the phase shift constant, which represents the phase change of the wave per unit length on the transmission line. The distributed resistance R1 within the unit length is caused by the skin effect, and it is in a certain proportion; the distributed conductance G1 within the unit line length is caused by dissipation, and it is in a certain proportion to f. Therefore, its transmission constant can be simplified as

Equation (9) represents the general model of power line transmission characteristics, and its parameter values ​​can be obtained from measurements or estimated by further analyzing the power line medium according to the transmission line principle. In simulation analysis, the accuracy of the model can be controlled by adjusting the number N of multipaths in the parameter model. 2.2 Classification of power line noise
Manfred Zimmermann divides power line noise into:
(1) Colored background noise. This type of noise has a relatively low power spectrum density, and the power varies with the frequency. This type of noise is composed of a large number of low-power noise sources superimposed, and its power spectrum density often varies with time, and the change period is generally a few minutes to a few hours.
(2) Narrowband noise. This type of noise is often generated by an amplitude-modulated sinusoidal signal. The most common source is the transmission signal of a radio broadcasting station coupled to the power line.
(3) Periodic pulse noise asynchronous with the grid frequency. The frequency of this type of noise is generally between 50 Hz and 200 kHz, so this type of noise has a discrete line spectrum, and the spectrum interval is the noise frequency. This noise is usually caused by switching power supplies or other electrical appliances, such as CRT monitors.
(4) Periodic pulse noise synchronized with the grid frequency. The frequency of this type of noise is generally 50 Hz or 100 Hz in China. This type of noise lasts for a very short time, usually at the μs level. It has a spectrum density that decreases with frequency. This type of noise is caused by the power supply through the rectifier diode, and is therefore synchronized with the industrial frequency AC power.
(5) Asynchronous pulse noise. This type of noise is caused by various electronic or mechanical switching transients. This type of noise usually appears randomly, with a duration ranging from μs to ms. Its power spectrum density is very large, with a maximum value of more than 50 dB higher than the background noise.
Among these five types of noise, the statistical characteristics of the first three types change slowly, generally with a change period of seconds, minutes or even hours, and the power spectrum is usually low, so these types of noise can be collectively referred to as background noise. The latter two types of noise are highly time-varying, usually at the μs and ms level. The most critical thing is that the power spectrum density values ​​of these two types of noise are usually very large, so they can cause bit errors or even burst continuous errors. Therefore, these two types of noise are the main difficulties that need to be considered and overcome in power line communication.
Michael Bauer measured and simulated the impulse noise of power lines and proposed that the time domain characteristics of impulse noise can be approximated by equation (10). The result is shown in Figure 4.

For the convenience of analysis, the above power line pulse noise can be simplified. It is considered that when the envelope of the above pulse reaches a certain value, it is the beginning of a pulse, and when it drops to a certain value, it is the end of the pulse. The characteristics of the simplified power line pulse noise can be described by three parameters: pulse amplitude A, pulse width tw and pulse arrival time tarr. According to the above model, the literature has conducted a statistical analysis of the time domain characteristics: the pulse noise width tw is generally tens of μs, the amplitude is hundreds of mV, and the power spectrum is about 50 dB higher than the background noise. In the household power line environment, the ratio of the pulse noise occurrence time is about 0.001 35%, and the average occurrence frequency is 0.122 times/s.

3 Design and implementation of simulation algorithm
3.1 Simulation of power line channel
Equation (9) can be used to perform measurement-based modeling for a specific channel. In order to make the simulation results not lose generality, according to the large number of random distribution branches in the actual power line channel, it can be assumed that the impulse signal will randomly generate signals of different amplitudes at different times through the channel and superimpose them at the receiving end. According to the central limit theorem, the distribution of the sum of a large number of independent and identically distributed random variables obeys the Gaussian distribution. Therefore, the envelope of the channel response obeys the Rayleigh distribution. When there is a direct component in the channel, that is, the case in the power line channel, the random variable obeys a Gaussian distribution with a non-zero mean. At this time, the envelope of the channel response obeys the Rice distribution. That is

Where A is the peak value of the main signal, that is, the direct signal; I0() is a modified 0th-order first-kind Bessel function. The Rice distribution is often described by the parameter K, which is defined as the ratio of the power of the determined signal to the variance of the multipath component.
In Matlab, a Rice channel filter can be generated by calling the Rice channel function, and the Rice channel can be simulated by processing the signal with this filter. The function prototype of the Rice channel is
CHAN=RICIANCHAN(TS, FD, K, TAU, PDB)
, where TS is the sampling frequency; FD is the Doppler frequency shift; K is the Rice distribution parameter; TAU is the delay vector of each path; and PDB is the gain vector of the corresponding path. According to Han Kim's research, the maximum value of the multipath delay is generally <50 ms. Zimmermann provides several values ​​of the multipath component gi of the channel described by equation (9). According to the above results, considering the complexity of the simulation, the number of multipaths is set to 50, and the multipath delay vector is generated by a normal random variable with a mean of 25ms and a variance of 2.5×10-6; the multipath component size is generated by a normal random variable with a mean of 0.05 and a variance of 0.05. After simulation, the Matlab simulation results of the Rice channel are shown in Figure 5.

3.2 Simulation of power line noise
According to the research results in this paper, power line noise can be mainly divided into five categories, among which colored background noise, narrowband noise and asynchronous periodic pulse noise are uniformly classified as background noise due to their small power spectrum density and relatively constant statistical characteristics. The sum of a large number of background noises can be simulated using Gaussian white noise.
The period of synchronous periodic pulse noise is 10 ms or 20 ms, which is equivalent to the duration of a data frame in the G3-PLC system. Therefore, only a few synchronous periodic pulses will appear in a frame of data. To simplify the processing, it can be incorporated into burst pulse noise. Manfred Zimmermann proposed to use Markov process to simulate the appearance of burst pulse noise. According to the research results, the model can simulate the appearance time of pulse noise more accurately, but the model brings difficulties in implementation due to the large amount of calculation. A simpler method without losing accuracy is to simulate according to the statistical characteristics of parameters such as the time of appearance and time width of burst pulses by equation (10).
The ratio of the pulse noise occurrence time in this paper is about 0.001 35%, and the average occurrence frequency is 0.122 times/s. Assuming that the system adopts a sampling frequency of fs, the probability of pulse noise appearing at each sampling point is Pimp=0.122/fs; the average width of the pulse noise is wimp=1.35×10-5×fs/0.122 sampling points. It is better to define the end time of the pulse noise when the amplitude of the pulse noise envelope drops to within 5% of the maximum value. Substituting the above parameters into formula (10), we can get

According to the derivation results of the above parameters, the power line noise can be simulated in Matlab by the following method:
Use the random number generation function Randsrc to generate a random vector with N-dimensional [0, 1] distribution as the pulse noise index vector, where P(x=1)=Pimp; then cyclically search the index vector, and when the value of the point is 1, call the pulse generation function from that point; then use the pulse generation function to first generate two independent random numbers A0 and b0 of normal distribution, and generate a random variable d of normal distribution, whose mean is obtained by formula (11). Finally, generate an output vector according to formula (10) and add it to the result vector.
The power line pulse noise generated by the above method is shown in Figure 6.

Since the probability of noise is low, the simulation time needs to be extended during simulation, which will result in too much data. Therefore, in this simulation, the sampling frequency is lowered, but this does not affect the simulation effect. It can be seen intuitively from the figure that the result is consistent with the actual noise environment of the power line.
3.3 Implementation of simulation algorithm
The characteristics of the channel should remain unchanged in a single simulation, and the channel can be designed with the help of a PC. According to the algorithm discussed in the article, the unit impulse response vector of the channel is obtained and sent to the simulation system through RS2 32 port or network port. The unit impulse response is implemented in the FPGA using an FIR filter. At the same time, in order to realize the simulation of the channel with a feedback loop, another parallel IIR filter can be implemented in the FPGA, and the outputs of the two filters can be switched through the parameters of the PC. The noise simulation method generates corresponding parameters on the PC and passes them in. FPGA, in order to ensure better real-time performance, a pseudo-random sequence generation circuit can also be used in the FPGA.

4 Conclusion
A standard real-time simulation platform for power line channels and noise is necessary for the development and testing of power line communication equipment. It can help developers quickly test the reliability at every step of equipment development and provide a unified test calibration platform for different power line communication products. Based on an in-depth analysis of power line channel characteristics and noise, this paper proposes a design method for a real-time simulation platform for power line channels. The algorithm is verified to be feasible using Matlab simulation. The platform can be implemented using FPGA-based hardware and has high practical value.