Exploring the Optimizations for Main Harmonic Filtering for Power Systems

. As the global demand for sustainable and environmentally friendly energy supply continues to increase, photovoltaic technology, as an important form of new energy, has received extensive attention. Photovoltaic grid-connected system is currently the most widely used form of photovoltaic power generation system. It converts direct current into alternating current and injects it into the grid to meet the power demand of users. However, the power grid imposes a series of requirements on grid-connected photovoltaic systems, one of which is the handling of harmonic problems. This article will focus on harmonic generation and how to perform THD (Total Harmonic Distortion) mitigation. As the key equipment of photovoltaic grid-connected system, inverter plays an important role in harmonic filtering. With a brief introduction to inverter-related THD. In this paper, by exploring how to optimize harmonic filtering to improve the performance and reliability of grid-connected photovoltaic systems, it is found that the method of suppressing THD by changing the PMW modulation is simple in calculation, easy to implement, and has high output waveform quality. And the method of suppressing THD by changing the equipment can reduce the harmonic quality.


Introduction
Against the backdrop of growing global energy demand, people have begun to seek more sustainable and environmentally friendly ways to supply energy.Traditional fossil fuel resources are becoming increasingly scarce, and their use produces large amounts of harmful gases such as carbon dioxide, which cause serious pollution to the environment.Therefore, the global search for renewable energy alternatives has become inevitable.Photovoltaic (PV) technology, as an important form of renewable energy, has gained widespread attention and application.Photovoltaic power generation systems can use solar energy to convert light energy into electrical energy to achieve a clean, renewable power provision [1].The gridconnected PV system, as a major form of connecting the Photovoltaic power system connected to the grid, is environmentally friendly and renewable, and can provide a new solution for energy supply on a global scale.Fig. 1.System diagram of a PV system [1].
The block diagram, as shown in Fig. 1, can be achieved in a grid-connected PV system simply described as a PV array converting DC power to AC power through an inverter, and then connecting the AC power to the grid to meet the electricity demand of customers.In this process, the grid-connected PV system must meet a number of grid requirements for PV system interconnection.The requirements of the grid-connected PV system include stability, reliability and requirements for power quality [2].The power system has strict requirements for stability and reliability, and the PV system connected to the grid must have stable power output and reliable operation performance to ensure the normal operation of the grid.In addition, power quality is also an important consideration.The grid requires that the electrical current and voltage produced by a gridconnected solar PV system should have low harmonic distortion (total harmonic distortion, THD) [3].Harmonics are generated by nonlinear loads and are introduced into the power system.The presence of harmonic signals can negatively impact the stability and operational efficiency of the power system.Hence, it's crucial to mitigate the harmonics.THD is an important measure of the degree of harmonics in a power system, and it indicates the percentage of harmonic current or voltage in the total current or voltage.The presence of harmonics leads to an increase in THD, and excessive THD can affect the stability and dependability of the power system.Therefore, it is very important to maintain the THD level in the power system.
Harmonics may be caused by various factors, such as nonlinear loads, imperfections in power equipment, and grounding problems in the power system.Among them, nonlinear loads are the main sources of harmonic generation, such as electronic devices, dimmers, inverters, etc. [4].These devices introduce harmonic signals during their operation and interfere with the power system.The inverter, as a key device in the gridconnected PV system, plays the role of converting DC power to AC power.It not only needs to have this basic function, but also needs to meet the requirements of the grid for harmonics.The inverter can filter the harmonic signal by built-in harmonic filter or external filter to reduce the harmonic interference to the power system.There are two types of harmonic filters for inverters: active filters and passive filters, each with its own advantages and disadvantages.Active filters are filters that actively compensate for harmonics, detecting them and generating a corresponding compensation signal to eliminate them.These filters can effectively reduce harmonic currents and voltages, improving the reliability and stability of power systems.However, active filters are more expensive and have higher control and management requirements.A passive filter is a filter that filters harmonics through passive components such as inductors and capacitors.It has no active control function, but can effectively reduce harmonic levels.Passive filters have the advantage of lower cost and simple structure, but may not be effective for complex harmonic waveforms [5].
In addition to filters, inverters can also reduce harmonic interference by regulating the power signal through pulse width modulation (PWM) technology, which regulates the waveform of the output voltage and current by adjusting the pulse width and frequency, thereby reducing harmonic generation.In summary, photovoltaic technology has been widely used and promoted as a form of renewable energy.However, the problem of harmonic filtering still exists in gridconnected PV systems.Harmonic generation may be caused by several factors, among which nonlinear loads are the main harmonic sources.To meet the requirements of the grid for harmonics, inverters play an important role in grid-connected PV systems.Through proper filter design and the application of PWM technology, the harmonic level can be effectively reduced to improve the stability of the PV system connected to the grid and the power system's reliability.With the continuous progress and innovation of technology, we believe we can find more effective harmonic filtering solutions to promote the development of grid-connected PV systems and the promotion of sustainable energy.This article will explore how to optimize harmonic filtering to improve the performance and reliability of grid-connected PV systems.

Origin of Harmonics
A harmonic is a repetitive waveform with a frequency that is a whole number multiple of the fundamental frequency.In power engineering, harmonic refers to a voltage or current waveform that has a frequency which is a whole number multiple of the frequency of the fundamental waveform.These harmonics are caused by nonlinear loads.such as arc furnaces, DC governors, etc., cause the current waveform to lose its sinusoidal shape and produce harmonic.in addition, magnetic and capacitive loads can also cause harmonic generation [6].The harmonic components can be expanded using a Fourier series to decompose the waveform into a fundamental waveform and various harmonic components.Assume a periodic waveform f(t) with period T, which can be expressed as： where ω=2π/T is the fundamental frequency and n=1,2,3,... represents the number of harmonic.an and bn are fourier level coefficients, which represent the amplitude of each harmonic component.As for the single-phase inverter, there are three main sources of its main harmonics, which are the grid, the load, and the inverter itself [7][8][9][10].

Nonlinear loads
Many loads in the grid are nonlinear, such as lighting fixtures, electronic devices, power electronics, etc.The correlation between current and voltage of these loads is nonlinear.When the load current is sinusoidal, the load voltage is not sinusoidal, which will introduce a large number of harmonics.
Various switching operations in power systems cause instantaneous changes in voltage and current, and these changes can generate various harmonics, such as rectangular waves and sawtooth waves.Especially the switching operation of power electronic devices is more likely to cause the generation of high-frequency harmonics.These harmonics will affect the stability of power equipment and systems, the work and life of electronic equipment, and the interference of communication and control systems.In short, the voltage and current of the grid contain main harmonics, and these main harmonics are transmitted to the load side through the single-phase inverter.Grid main harmonics are generated due to non-linear loads and switching operations in the power system, among other factors, which increase the degree of harmonic content in the grid voltage and current

Switching operations
.

Nonlinear characteristics
The loads themselves have nonlinear characteristics, such as inductors, capacitors and resistors, and these nonlinear components generate main harmonics.When these loads are connected to the circuit, it will make the voltage and current output of the circuit also contain main harmonics.

Operation mode
The operation mode of the load will also have an impact on the generation of main harmonics.For example, the switching operation of electronic devices can also cause the generation of main harmonics.In addition, the generation of load main harmonics can cause many problems to the power equipment and system, such as reducing the efficiency of the power equipment, affecting the stability of the power system, and interfering with the communication and control system.Therefore, to ensure the proper functioning of power equipment and systems, it is necessary to regulate and filter the primary harmonics of the load.

Nonlinear characteristics
As a nonlinear element, the switching tube in the inverter will operate at high frequencies for switching, resulting in sharp changes in current and voltage and generating high harmonics.In the inverter, the on and off processes of the switching tubes cause nonlinear changes in current and voltage, resulting in various harmonics.

Influence of other components:
Components such as capacitors and inductors in the inverter will also have an effect on the main harmonics.
Components such as capacitors and inductors filter the current and voltage, but due to their own characteristics, they also generate main harmonics.In addition, other components in the inverter, such as resistors and transformers, will also have some effect on the main harmonics.Hence, the primary cause of harmonics in the inverter itself is primarily attributed to the non-linear characteristics of the switching tubes and the impact of other components.It is crucial to regulate and filter these harmonics to guarantee the proper functioning of the power equipment and system.The inverter main harmonic formula is obtained by Fourier level expansion of the inverter output voltage or current to obtain the amplitude of each harmonic component.For the inverter output voltage the main harmonic equation can be expressed as where V(t) is the waveform function of the inverter output voltage, V1, V3, Vn, etc. denote the amplitudes of fundamental, 3 rd harmonic, n th harmonic, etc, respectively, and ω is the fundamental frequency [2].
For the inverter output current the main harmonic equation can also be expressed as where I(t) is the waveform function of the inverter output current, I1, I3, In, etc. denote the amplitudes of fundamental, 3 rd harmonic, n th harmonic, etc., respectively, and ω is the fundamental frequency.The amplitudes of the above main harmonic components can be obtained by experimental measurement or simulation calculation, and the amplitude distribution of main harmonics will be different for different inverter designs and control strategies.The equation for the primary harmonics of the inverter can be utilized to gain a deeper understanding of the harmonic elements present in the output waveform of the inverter, so that the design and optimization of harmonic filters can be carried out to reduce the impact of harmonics on the grid and load.

THD mitigation methods
As shown in Fig. 2, the mitigation for THD can be briefly classified into PWM modulation based and equipment-based solution.

Sinusoidal PWM modulation
Sine PWM modulation is a method used for inverter control, which controls the output voltage and current of the inverter by modulating a sinusoidal wave signal.The basic idea of sinusoidal PWM modulation is to compare between a triangular wave signal of a fixed frequency and a sinusoidal signal and to generate a PWM signal with varying pulse width according to the comparison result to control the voltage and current produced by the inverter's output [2].As shown in Fig. 3, in sinusoidal PWM modulation, the frequency of the triangular wave signal is usually fixed, while the frequency and amplitude of the sinusoidal signal are adjusted as needed.By modulating the sinusoidal signal, the voltage and current that the inverter generates at its output.canbe made to have characteristics similar to those of a sinusoidal waveform, thus reducing the generation of harmonics and improving the efficiency and performance of the inverter.
Sinusoidal PWM modulation is a relatively common inverter control method for many different types of inverters, such as single-phase bridge inverters, threephase bridge inverters, etc [9].
Sine PWM modulation is a method that generates PWM signals by comparing the modulated signal with a triangular wave signal, and controls The voltage and current that the inverter generates at its output.

Delta PWM modulation
Triangular PWM modulation is a modulation method widely used in inverter control.It is based on the principle of comparing a triangular waveform with a reference signal to generate a PWM signal.
Specifically, a triangle waveform generator generates a periodic waveform similar to a triangle, the period and frequency of which can be adjusted as needed.This triangular waveform is then compared to a reference signal, which is typically a sine or square waveform generated by the control system.The comparison process can be implemented using components such as comparator circuits or operational amplifiers [5] During the comparison process, the inverter's output voltage and current can be controlled by adjusting the amplitude and frequency of the reference signal, which determines the duty cycle and frequency of the PWM signal.If the amplitude of the reference signal exceeds that of the triangular waveform, the output signal will be high; conversely, if the amplitude is lower, the output signal will be low.This allows for control over the waveform of the inverter's output voltage and current.
The advantages of triangular PWM modulation are its simple implementation, easy calculation, high control accuracy, low harmonic content, etc.Therefore, its widely used in the fields of inverter control and AC motor drive.

Symmetric PWM modulation
Symmetric PWM modulation is a simple PWM modulation method, the basic principle of which is to use the same PWM waveform in the positive and negative half-cycle to control the output voltage of the inverter.Symmetric PWM modulation is suitable for low power and low frequency inverter control and has the advantages of simple control algorithm and low hardware design cost, but its output waveform quality is poor and there is a large main harmonic component [2].A triangular waveform with fixed frequency and amplitude is generated using a triangular waveform generator.A reference signal is generated as needed to serve as a comparison reference.Usually, the reference signal is generated using a control algorithm, such as a voltage regulation algorithm based on PI control or a current control algorithm based on space vector modulation.A comparator is utilized to compare the triangle wave with the reference signal to generate a PWM signal.When the output of the comparator is high, the inverter output voltage is in the positive range; when the outcome is low, the voltage generated by the inverter is negative.Based on the PWM signal output from the comparator, the duty cycle of the inverter's output is determined.In symmetric PWM modulation, the duty cycle is calculated by the following formula Duty cycle = duty cycle = (effective time / time of one cycle) x 100%.Where, the effective time is the time when the signal is at high or low level.And the cycle is the time it takes for the signal to go from one pole to another.Generate inverter output: Convert the PWM signal into inverter output voltage and current using the inverter bridge arm [6].Adjust the amplitude and frequency of the reference signal and other control parameters as needed to optimize the waveform of the inverter output voltage and current [7].Finally, the advantages of symmetric PWM modulation are that it is simple to implement, easy to calculate, high control accuracy, and low harmonic content, so it is widely used in the fields of inverter control and AC motor drive.

Modulation ratio optimization with harmonic offset
Modulation ratio optimization with harmonic offset technology is a technique for regulating the primary harmonics of an inverter by manipulating the PWM pulse width ratio.The basic principle is to generate a reverse harmonic component by a reverse harmonic generator, which cancels the main harmonic component in the inverter output current, thus realizing the control of the main harmonic.The modulation ratio optimization of the harmonic cancellation technique is suitable for inverter control of medium power and frequency, and has the advantages of good main harmonic control and high output waveform quality, but it requires additional hardware and is costly.
Specifically, when there isa predominant harmonic element in the output current of the inverter, the primary harmonic element can be eliminated by adding a reverse , 02005 (2023) harmonic component.This reverse harmonic component can be achieved by increasing the modulation ratio of the inverter, even if the positive and negative half-cycle times of the inverter output current are not equal.By adjusting the modulation ratio, the reverse harmonic the constituent of the inverter output current can be made to cancel the main harmonic component, thus reducing the main harmonic component.
The modulation ratio optimization method based on the harmonic offset technique can improve the inverter output waveform quality by adjusting the control parameters of the inverter to eliminate the main harmonic components without adding additional hardware.However, this method requires more accurate control of the modulation ratio of the inverter and more accurate measurement and analysis of the main harmonic components in the inverter output current, so it has high requirements on the control algorithm and hardware design.

Filter-based modulation ratio optimization
Modulation ratio optimization of filters is a method to control the main harmonics of an inverter by adding harmonic filters.The basic principle is to filter out the harmonic components from the inverter output current by selecting appropriate component parameters such as inductors and capacitors to achieve the control of main harmonics [8].The modulation ratio optimization of the filter is suitable for high power and high frequency inverter control and has the advantages of good main harmonic control and high output waveform quality, but it requires additional hardware and is costly.
Specifically, when main harmonic components are present in the inverter output current, these can be filtered out by adding a harmonic filter.This harmonic filter can be implemented by selecting appropriate component parameters such as inductors and capacitors.When the inverter output current passes through the harmonic filter, the harmonic components are filtered out of it, thus reducing the main harmonic components.
The filter-based modulation ratio optimization method can improve the output waveform quality by adding a harmonic filter to control and suppress the main harmonic components without changing the basic structure and control algorithm of the inverter.However, this method requires the addition of a harmonic filter, which raises the intricacy and expense of the system, and requires the selection of appropriate component parameters such as inductors and capacitors, thus requiring high requirements in terms of hardware design and optimization parameters.

Comparison between different strategies
Symmetric PWM-based modulation is a basic PWM modulation technique marked by a substantial fundamental component and a significant harmonic content, which requires additional filters for harmonic filtering.The advantage is that it is computationally simple and easy to implement for some low requirement applications [9].
Delta-based PWM modulation is a PWM modulation technique that controls the magnitude and adjusting the slope of the delta wave to modify the frequency of the inverter output voltage, which is characterized by a high fundamental content and a low harmonic content.Additional filters are required for harmonic filtering.The shape of the output waveform based on delta PWM is close to a sine wave, which reduces the harmonic distortion and enhances the output waveform quality, making it suitable for applications that require high quality output waveform.The calculation of delta PWM based modulation is relatively simple, only need to calculate the frequency and amplitude of the delta waveform, as well as the modulation ratio, suitable for some applications with low requirements.
Triangle-based PWM modulation requires no additional control link, just a simple filter at the output, making it a relatively simple hardware implementation compared to other PWM modulation methods.Deltabased PWM modulation has a high quality output waveform and can be used for high-power applications such as inverter air conditioners, motor drives, etc [3].
Sine based PWM modulation is a PWM modulation technique that obtains the PWM waveform of the inverter output by comparing the fundamental sinusoidal signal with a high frequency triangle waveform, which is characterized by the output waveform being closer to the sinusoidal waveform with lower harmonic content and is suitable for applications requiring high output waveform quality [10].The advantages of sinusoidal PWM-based modulation are mainly as follows: the output waveform shape based on sinusoidal PWM modulation is close to sine wave, which can reduce the harmonic content and improve the output waveform quality, making it suitable for applications with high requirements for output waveform quality.Sine based PWM modulation is suitable for applications with different frequencies and powers, because by modifying the frequency and amplitude of the sine waveform, one can adjust the frequency and amplitude of the inverter output voltage, thus adapting to different applications.Sinusoidal PWM based modulation enables high precision control because the frequency and amplitude of the inverter output voltage can be precisely controlled by changing the frequency and amplitude of the sinusoidal waveform, thus meeting different control requirements.Sine PWM based modulation can be applied to high frequency applications because the sine wave frequency can be adjusted to a higher frequency to cater to the requirements of high-frequency applications.The output waveform quality based on sinusoidal PWM modulation is high, which not only reduces harmonic components, but also reduces noise, making it suitable for applications with high noise requirements, such as audio amplifiers [10].
The harmonic offset based modulation ratio optimization is an optimization method for symmetric PWM modulation, which reduces the level of harmonic distortion.by adjusting the modulation ratio so that the harmonic components at the output of the inverter current can cancel each other.It requires an additional harmonic cancelling control link in the control system and is computationally complex.Filter-based modulation ratio optimization is an inverter output filter optimization method that decreases the harmonic level of inverter output by adjusting the filter parameters and modulation ratio to maximize the attenuation of the filter over a certain frequency range.The parameters need to be adjusted for different applications and the calculation is more complicated [8].
The key features of the THD mitigation strategies are summarized in Table 1.

Future Aspects
The future outlook for filtering harmonics in photovoltaics is very positive.First, filtering harmonics can improve the efficiency and reliability of PV power systems and reduce energy losses.Second, filtering harmonics can reduce interference and pollution to the grid and improve the stability and reliability of the grid.In the future, with the continuous progress and development of technology, we can foresee the emergence of new filter design and manufacturing technologies that will be more efficient and reliable and better able to filter harmonics in PV.In addition, the application of artificial intelligence technology will also provide more possibilities and solutions for harmonic filtering.In conclusion, we have reasons to believe that the problem of filtering harmonics in PV will be better solved, which will create better conditions for the development of PV power generation systems.

Conclusion
This paper focuses on the harmonic problems in gridconnected photovoltaic systems and how to deal with them.First, the background section points out the increased global demand for sustainable, environmentally friendly energy supplies and the importance of photovoltaic technology as a new form of energy.Grid-connected PV systems are currently the most widely used form of PV power generation systems, but the grid imposes a number of requirements on them, one of which is the treatment of harmonic problems.Next, the main content section details the definition, causes and decomposition of harmonics.Harmonics are periodic waveforms whose frequency is a multiple of the fundamental frequency and are caused by nonlinear loads, such as arc furnaces and DC governors.In addition, magnetic and capacitive loads can also cause the generation of harmonics.For single-phase inverters, the sources of main harmonics are mainly the grid, the load and the inverter itself.Then, for the harmonic problem, the paper presents different THD (total harmonic distortion) suppression methods, including sinusoidal PWM-based modulation, delta PWM-based modulation, symmetric PWM modulation, modulation ratio optimization based on harmonic cancellation techniques, and filter-based modulation ratio optimization.Finally, a brief comparison of these five different PWM modulation methods for three-phase inverters is presented, and future directions are envisioned.Overall, this paper provides some guidance and optimization directions for the performance and reliability of grid-connected PV systems by introducing the causes of harmonic generation and different treatment methods.

Table 1 .
Comparison between different THD mitigation strategies