谐波发生, 在非线性负载的传播和清除技术

Hadeed Ahmed Sher¹, Khaled E. Addoweesh ¹ and Yasin Khan²

^[1] 电机工程学系, King Saud University, Riyadh, 沙特阿拉伯

^[2] 电机工程学系, King Saud University, Riyadh, Saudi ArabiaSaudi Aramco Chair in Electrical Power, 电机工程学系, King Saud University, Riyadh,

1. 介绍

Industrial revolution has transformed the whole life with advanced technological improvements. The major contribution in the industrial revolution is due to the availability of electrical power that is distributed through electrical utilities around the world. The concept of power quality in this context is emerging as a “Basic Right” of user for safety as well as for uninterrupted working of their equipment. The electricity users whether domestic or industrial, need power, free from glitches, distortions, 闪烁, noise and outages. The utility desires that the users use good quality equipment so that they do not produce power quality threats for the system. 在这个工业世界中使用基于电力电子的设备在节省燃料和电力方面节省了巨额资金, 但另一方面由于谐波的产生而产生了问题. 商业和家庭用户都使用基于电力电子开关的设备，这些设备会吸收谐波电流. 该电流是产生谐波污染电压的主要因素. 用户的“基本权利”是拥有清洁的电源, 而公用事业的需求是拥有优质的仪器/设备. 这使得电能质量成为用户和公用事业公司共同关心的问题. 谐波是电能质量领域的热门话题，几十年来一直是一个讨论领域，各个国际组织和机构已经设计并发布了多项设计标准，以维持无谐波电源. 在更广阔的场景中, 无谐波环境意味着设备产生的谐波及其在系统中的存在被限制在允许的限度内，因此它们不会对包括变压器在内的电力系统组件造成任何损坏, 绝缘体, 开关装置等. 电力系统的放松管制迫使公用事业公司在发电结束时在谐波进入主流之前清除谐波，并成为系统不稳定的可能原因. The possible three stage scheme for harmonics control is

Identification of harmonics sources
Measurement of harmonics level
Possible purging techniques

To follow the above scheme the power utilities have R&D sections that are involved in continuous research to keep the harmonics levels within the allowed limits. Power frequency harmonics problems that have been a constant area of research are:

Power factor correction in harmonically polluted environment
Failure of insulation co-ordination system
波形失真
De-rating of transformer, 电缆, switch-gears and power factor correction capacitors

The above mentioned research challenges are coped with the help of regulatory bodies that are focused much on designing and implementing the standards for harmonics control. Engineering consortiums like IEEE, IET, and IEC have designed standards that describe the allowable limits for harmonics. The estimation, measurement, analysis and purging techniques of harmonics are an important stress area that needs a firm grip of power quality engineers. Nowadays, apart from the traditional methods like Y-∆ connection for 3^路 harmonic suppression, modern methods based on artificial intelligence techniques aids the utility engineers to suppress and purge the harmonics in a better fashion. The modern approaches include:

Fuzzy logic based active harmonics filters
Wavelet techniques for analysis of waveforms
Sophisticated PWM techniques for switching of power electronics switches

The focus of this chapter is to explain all the possible sources of harmonics generation, identification of harmonics, their measurement level as well as their purging/suppression techniques. This chapter will be helpful to all electrical engineers in general and the utility engineers in particular.

2. 什么是谐波?

In electrical power engineering the term harmonics refers to a sinusoidal waveform that is a multiple of the frequency of system. 因此, the frequency which is three times the fundamental is known as third harmonics; five times the fundamental is fifth harmonic; 等. The harmonics of a system can be defined generally using the eq. 1

fh= hfac

Where f_Ĥ is the h^日 harmonic and f_和 is the fundamental frequency of system.

Harmonics follow an inverse law in the sense that greater the harmonic level of a particular harmonic frequency, the lower is its amplitude as shown in Fig.1. 因此, usually in power line harmonics higher order harmonics are not given much importance. The vital and the most troublesome harmonics are thus 3^路, 5^日, 7^日, 9^日, 11^日和 13^日. The general expression of harmonics waveforms is given in eq. 2

Vn= Vrnsin (nωt)

哪里, 在_rn is the rms voltage of any particular frequency (harmonic or power line).

The harmonics that are odd multiples of fundamental frequency are known as Odd harmonics and those that are even multiples of fundamental frequency are termed as Even harmonics. The frequencies that are in between the odd and even harmonics are called inter-harmonics.

Although, the ideal demand for any power utility is to have sinusoidal currents and voltages in AC system, this is not for all time promising, the currents and voltages with complex waveforms do occur in practice. Thus any complex waveform generated by such devices is a mixture of fundamental and the harmonics. 因此, the voltage across a harmonically polluted system can be expressed numerically in eq. 3,

V = Vfpsin(ωt +ϕ1)+ V2psin(2ωt +ϕ2)+ V3psin(3ωt +ϕ3)+ Vnpsin(nωt +ϕn)

哪里,

在_fp = Peak value of the fundamental frequency

在_np= Peak value of the n^日 harmonic component

φ = Angle of the respected frequency

图 1.

Fundamental and harmonics frequency waveforms

同样, the expression for current through a given circuit in a harmonically polluted system is given by the expression given in eq. 4

I = Ifpsin(ωt +ϕ1)+ I2psin(2ωt +ϕ2)+ I3psin(3ωt +ϕ3)……+Inpsin(nωt +ϕn)

Harmonic components are also termed as positive, negative and zero sequence. In this case the harmonics that changes with the fundamental are called positive and those that have phasor direction opposite with the fundamental are called negative sequence components. The zero components do not take any affect from the fundamental and is considered neutral in its behavior. Phasor direction is pretty much important in case of motors. Positive sequence component tends to drive the motor in proper direction. Whereas the negative sequence component decreases the useful torque. “ 7^日, 13^日, 19^日等. are positive sequence components. The negative sequence components are 5^日, 11^日, 17^日等. The zero component harmonics are 3^路, 9^日, 15^日等. As the amplitude of harmonics decreases with the increase in harmonic order therefore, in power systems the utilities are more concerned about the harmonics up to 11^日 order only.

3. Harmonics generation

In most of the cases the harmonics in voltage is a direct product of current harmonics. 因此, the current harmonics is the actual cause of harmonics generation. Power line harmonics are generated when a load draws a non-linear current from a sinusoidal voltage. Nowadays all computers use Switch Mode Power Supplies (开关电源) that convert utility AC voltage to regulate low voltage DC for internal electronics. These power supplies have higher efficiency as compared to linear power supplies and have some other advantages too. But being based on switching principle, these non-linear power supplies draw current in high amplitude short pulses. These pulses are rich in harmonics and produce voltage drop across system impedance. 从而, it creates many small voltage sources in series with the main AC source as shown in Fig.2. Here in Fig.2 我₃ refers to the third harmonic component of the current drawn by the non-linear load, 我₅ is the fifth harmonic component of the load current and so on. R shows the distributed resistance of the line and the voltage sources are shown to elaborate the factor explained above. 因此, these short current pulses create significant distortion in the electrical current and voltage wave shape. This distortion in shape is referred as a harmonic distortion and its measurement is carried out in term of Total Harmonic Distortion (总谐波失真). This distortion travels back into the power source and can affect other equipment connected to the same source. Any SMPS equipment installed anywhere in the system have an inherent property to generate continuous distortion of the power source that puts an extra load on the utility system and the components installed in it. Harmonics are also produced by electric drives and DC-DC converters installed in industrial setups. Uninterrupted Power Supply (UPS) and Compact Fluorescent Lamp (CFL) are also a prominent source of harmonics in a system. Usually high odd harmonics results from a power electronics converter. 综上所述, the harmonics are produced in an electrical network by [2, 16, 26, 42]

Rectifiers
Use of iron core in power transformers
Welding equipment
Variable speed drives
Periodic switching of voltage and currents
AC generators by non-sinusoidal air gap, flux distribution or tooth ripple
Switching devices like SMPS, UPS and CFL

这里值得一提的是，交流发电机可能会直接出现电压谐波, 由于非正弦气隙, 通量分布, 或齿纹, 这是由插槽的影响引起的, 里面装有绕组. 在大型供应系统中, 尽最大努力确保发电机输出正弦波, 但即使在这种情况下，电路中的任何非线性都会在电流波形中产生谐波. 变压器中的铁芯也会产生谐波. 此类变压器铁芯具有非线性 B-H 曲线 [37].

图 2.

非线性电流引起的电压畸变

4. 与谐波相关的问题

谐波污染系统对其稳定性存在诸多威胁. 不仅影响电能质量 (PQ的) 但当电流富含谐波时, is drawn by some device, it overloads the system. For example third harmonic current has a property that unlike other harmonic component it adds up into the neutral wire of the system. This results in false tripping of circuit breaker. It also affects the insulation of the neutral cable. Overloading of the cables due to harmonically polluted current increases the losses associated with the wires. It should also be kept in mind that only the power from fundamental component is the useful power, rest all are losses. These additional losses make the power factor poor that results in more power losses. The overall summarized effects of harmonics in the power system include the following [9, 18, 39]

Harmonic frequencies can cause resonant condition when combined with power factor correction capacitors
Increased losses in system elements including transformers and generating plants
Ageing of insulation
Interruption in communication system
False tripping of circuit breakers
Large currents in neutral wires

The distribution transformers have a ∆-Y connection. In case of a highly third harmonic current the current that is trapped in the neutral conductor creates heat that increases the heat inside the transformer. This may lead to the reduced life and de-rating of transformer. The different types of harmonic have their own impact on power system. For instance let us consider the 3^路谐波. Contrary to the balanced three phase system where the sum of all the three phases is zero in a neutral system, the third harmonic of all the three phases is identical. So it adds up in the neutral wire. 这同样适用于三次n谐波 (的奇数倍 3 次基本像 9^日, 15^日等等). 这些谐波电流是造成接地故障保护继电器误跳闸和失效的主要原因. 它们还会在中性线上产生热量，因此如果系统中存在三次谐波污染，则系统需要更粗的中性线. 如果向电机提供含有三次谐波含量的电压波形, 只会造成额外损失, 因为有用功率仅来自基本成分.

5. 谐波监测标准

交流电网中谐波问题的识别, 迫使公用事业和监管机构制定谐波监测和评估标准. 因此，谐波控制标准同时针对消费者和公用事业. 因此, if the customer is not abiding by the regulations and is creating voltage distortion at the point of common coupling the utility can penalize him/her. Various renowned engineering institutes like IEEE, IEC and IET have devised laws to limit the injection of harmonic content in the grid. These standards are mostly helpful to achieve a user friendly healthy power quality system. IEEE standards are widely cited for their capability to address all the regions in the world. There are more than 1000 IEEE standards on electrical engineering fields. IEEE standards on power quality, 但, are our main inspiration here. IEEE standard on harmonic control in electrical power system was published in 1992 and it covers all aspects related to harmonics [7]. It defines the maximum harmonics distortion up to 5 % on voltage levels ≤ 69kV. 然而, as the voltage levels are increased the allowable limits for harmonics in this standard are decreased to 1.5 % on all voltages ≥ 161 千伏. It is also worth mentioning that individual voltage distortion starts from 3 % and ends at 1.0 % for voltage levels of ≤ 69kV and ≥ 161 kV respectively. Besides the standards that are designed keeping in view the global requirements, regional authorities devise their own standards according to their load profile and climatic conditions. Most of the standards are made according to the regional requirements of the country whereas few are based on the global needs and requirements. In Saudi Arabia there exists a regulatory body that defines the permissible limits and standard operational procedures for electricity transmission, distribution and generation. This body is known as electricity and co-generation regulatory authority [38]. Apart from devising standards they also follow some standards defined by UAE power distribution companies. One such standard defined by Saudi Electric Company (SEC) 在 2007 and is known as “Saudi Grid Code”. Harmonics limit set by the Saudi authorities is almost the same as IEEE standard but with a bit flexible limit of 3% THD for all networks operating within the range of 22kV-400kV [35, 38]. 表 1 compares the IEEE standard, the Abu Dhabi distribution company and the SEC standard for the harmonics limit in the electric network. It is interesting to mention that IEEE standard for controlling harmonics is silent for the conditions where a system is polluted with inter-harmonics (基频的非整数频率). 对于这种情况，电力公司使用 IEC 标准编号 61000-2-2。IEC 还在标准编号中定义了不同电子设备的类别 61000-3-2. 然后，这些设备会受到不同的 THD 允许限制. 例如, A类拥有所有三相平衡设备, 非便携式工具, 音响设备, 仅适用于白炽灯的调光器. A 类的限值根据谐波次数而变化. 因此对于 A 类设备，最大允许谐波电流为 1.08 一个为 2^ND, 2.3一个为 3^路, 0.43一个为 4^日, 1.14一个为 5^日谐波. 该 IEC 标准的优点在于它还满足功率因数的要求. 例如所有 C 类设备 (白炽灯调光器以外的照明设备) 有 3^路谐波电流限制与电路功率因数的函数关系.

	美国证券交易委员会标准	阿布扎比分销公司	IEEE 限制
谐波	THD limit is 5% 为 400 V system, 和 4% 和 3% 为 6.6- 20kV and 22kV-400kV respectively	THD limit is 5% 为 400 V system, 和 4% 和 3% 为 6.6- 20kV and 22kV-400kV respectively	5% for all voltage levels below 69kV and 3% for all voltages above 161 千伏

表 1.

Comparison of Harmonic Standards [7, 35, 38]

The modern systems based on artificial intelligent techniques like Fuzzy logic, ANFIS and CI based computations are reducing the difficulty of data mining that helps in redesigning the standards for power quality harmonics [24, 25]. In developed countries like Australia, 加拿大, USA the power distribution companies are already partially shifted to smart grid and they are using sophisticated sensors and measuring instruments.

In terms of smart grid environment these sensors will help in mitigating the problems by predicting them in advance. 智能电网, by taking intelligent measurements and by the aid of sophisticated algorithms will be able to predict the PQ problems like harmonics, fault current in advance. It is pertinent to mention that the power quality monitoring using the on-going 3G technologies has been implemented by Chinese researchers. They used module of GPRS that is capable of analyzing the real time data and its algorithm makes it intelligent enough to get the desired PQ information [22].

5. Harmonics measurement

The real challenge in a harmonically polluted environment is to understand and designate the best point for measuring the harmonics. Nowadays the revolution in electronics has messed up the AC system so much that almost every user in a utility is a contributor to the harmonics current. 此外, the load profile in any domestic area varies from hour to hour within a day. So in order to cope with the energy demand and to improve the power factor, utilities need to switch on and off the power factor correction capacitors. This periodic and non-uniform switching also creates harmonics in the system. The load information in an area although, provide some basic information about the order of harmonic present in a system. Such information is very useful as it gives a bird eye view of harmonic content. But for the exact identification of the harmonics it is necessary to synthesize the distorted waveform using the power quality analyzer or using some digital oscilloscope for Fast Fourier Transform (FFT). 例如 Fig.3 shows a general synthesis of the current drawn by a controlled rectifier. Once identified, the level and type of harmonics (3^路, 5^日等等) the steps to mitigation can be devised. It should be kept in mind that proper measurement is the key for the proper designing of harmonic filters. But the harmonics level may differ at different points of measurement in a system. 因此, utilities need to be very precise in identifying the correct point for harmonic measurement in a system. Among the standards, it is IEEE standard 519-1992 that outlines the operational procedures for carrying out the harmonic measurements. This standard however does not state any restriction regarding the integration duration of the measurement equipment with the system. It however, restricts the utility to maintain a log for monthly records of maximum demand [5]. Various devices are used in support with each other to carry out the harmonic measurements in a system. These include the following

Power Quality Analyser
Instrument transformers based transducers (CT and PT)

图 3.

Typical line current of a controlled converter [26]

Various renowned companies are designing and producing excellent PQ analyzers. These include FLUKE, AEMC, HIOKI, DRANETZ and ELSPEC. These companies design single phase and three phase PQ analyzers that are capable of measuring all the dominant harmonic frequencies. The equipment that is used for harmonic measurement is also bound to some limitations for proper harmonic measurement. This limitation is technical in nature as for accurate measurement of all harmonic currents below the 65^日谐波, the sampling frequency should be at least twice the desired input bandwidth or 8k samples per second in this case, to cover 50Hz and 60Hz systems [5]. Mostly, the PQ analyzers are supplied along with the CT based probes but depending on the voltage and current ratings a designer can choose the CT and PT with wide operating frequency range and low distortion. The distance of equipment with the transducer is also very important in measuring harmonics. If the distance is long then noise can affect the measurement therefore properly shielded cables like coaxial cable or fiber optic cables are highly recommended by the experts [5]. In short, the measurement of harmonics should be made on Point of Common Coupling (PCC) or at the point where non-linear load is attached. This includes industrial sites in special as they are the core contributors in injecting harmonic currents in the system.

6. Harmonics purging techniques

Techniques have been designed and tested to tackle this power quality issue since the problem is identified by the researchers. There are several techniques in the literature that addresses the mitigation of harmonics. All these techniques can be classified under the umbrella of following

Passive harmonic filter
Active harmonic filter
混合型谐波滤波器
Switching techniques

6.1. 被动式谐波滤波器

Passive filter techniques are among the oldest and perhaps the most widely used techniques for filtering the power line harmonics. Besides the harmonics reduction passive filters can be used for the optimization of apparent power in a power network. They are made of passive elements like resistors, capacitors and inductors. Use of such filters needs large capacitors and inductors thus making the overall filter heavier in weight and expensive in cost. These filters are fixed and once installed they become part of the network and they need to be redesigned to get different filtering frequencies. They are considered best for three phase four wire network [18]. They are mostly the low pass filter that is tuned to desired frequencies. Giacoletto and Park presented an analysis on reducing the line current harmonics due to personal computer power supplies [10]. Their work suggested that the use of such filters is good for harmonics reduction but this will increase the reactive component of line current. Various kind of passive filter techniques are given below [18, 19].

Series passive filters
Shunt passive filters
Low pass filters or line LC trap filters
Phase shifting transformers

6.1.1. Series passive filters

Series passive filters are kinds of passive filters that have a parallel LC filter in series with the supply and the load. Series passive filter shown in Fig.4 are considered good for single phase applications and specially to mitigate the third harmonics. 然而, they can be tuned to other frequencies also. They do not produce resonance and offer high impedance to the frequencies they are tuned to. These filters must be designed such that they can carry full load current. These filters are maintenance free and can be designed to significantly high power values up to MVARs [4]. Comparing to the solutions that employ rotating parts like synchronous condensers they need lesser maintenance.

图 4.

Passive Series Filter [18]

6.1.2. Shunt passive filters

These type of filters are also based on passive elements and offer good results for filtering out odd harmonics especially the 3^路, 5^日和 7^日. Some researchers have named them as single tuned filters, second order damped filters and C type damped filters [3]. As all these filters come in shunt with the line they fall under the cover of shunt passive filters, 如图 Fig.5. Increasing the order of harmonics makes the filter more efficient in working but it reduces the ease in designing. They provide low impedance to the frequencies they are tuned for. Since they are connected in shunt therefore they are designed to carry only harmonic current [18]. Their nature of being in shunt makes them a load itself to the supply side and can carry 30-50% load current if they are feeding a set of electric drives [13]. Economic aspects reveal that shunt filters are always economical than the series filters due to the fact that they need to be designed only on the harmonic currents. Therefore they need comparatively smaller size of L and C, thereby reducing the cost. 此外, they are not designed with respect to the rated voltage, thus makes the components lesser costly than the series filters [33]. 然而, these types of filters can create resonant conditions in the circuit.

图 5.

Different order type shunt filters [3]

6.1.3. Low pass filter

Low pass filters are widely used for mitigation of all type of harmonic frequencies above the threshold frequency. They can be used only on nonlinear loads. They do not pose any threats to the system by creating resonant conditions. They improve power factor but they must be designed such that they are capable of carrying full load current. Some researchers have referred them as line LC trap filters [19]. These filters block the unwanted harmonics and allow a certain range of frequencies to pass. 然而, very fine designing is required as far as the cut off frequency is concerned.

6.1.4. Phase shifting transformers

The nasty harmonics in power system are mostly odd harmonics. One way to block them is to use phase shifting transformers. It takes harmonics of same kind from several sources in a network and shifts them alternately to 180° degrees and then combine them thus resulting in cancelation. We have classified them under passive filters as transformer resembles an inductive network. The use of phase shifting transformers has produced considerable success in suppressing harmonics in multilevel hybrid converters [34]. 小号. Ĥ. Ĥ. Sadeghi et.al. designed an algorithm that based on the harmonic profile incorporates the phase shift of transformers in large industrial setups like steel industry [36].

6.2. 有源谐波滤波器

In an Active Power Filter (APF) we use power electronics to introduce current components to remove harmonic distortions produced by the non-linear load. 图 6 shows the basic concept of an active filter [27]. They detect the harmonic components in the line and then produce and inject an inverting signal of the detected wave in the system [27]. The two driving forces in research of APF are the control algorithm for current and load current analysis method [23]. Active harmonic filters are mostly used for low-voltage networks due to the limitation posed by the required rating on power converter [21].

图 6.

Conceptual demonstration of Active filter [27]

They are used even in aircraft power system for harmonic elimination [6]. Same like passive filters they are classified with respect to the connection method and are given below [40].

Series active filters
Shunt active filters

自, it uses power electronic based components therefore in literature a lot of work has been done on the control of active filters.

6.2.1. 系列有源滤波器

The series filter is connected in series with the ac distribution network as show in Fig.7 [33]. It serves to offset harmonic distortions caused by the load as well as that present in the AC system. These types of active filters are connected in series with load using a matching transformer. They inject voltage as a component and can be regarded as a controlled voltage source [33]. The drawback is that they only cater for voltage harmonics and in case of short circuit at load the matching transformer has to bear it [31].

6.2.2. Shunt active filter

The parallel filter is connected in parallel with the AC distribution network. Parallel filters are also known as shunt filters and offset the harmonic distortions caused by the non-linear load. They work on the same principal of active filters but they are connected in parallel as stated that is they act as a current source in parallel with load [21]. They use high computational capabilities to detect the harmonics in line.

图 7.

Series active filters [33]

Mostly microprocessor or micro-controller based sensors are used to estimate harmonic contents and to decide the control logic. Power semiconductor devices are used especially the IGBT. Some researchers claim that before the advent of IGBTs active filters were seldom use due to overshoot in budget [11]. 然而, despite of their usefulness shunt active filters have many drawbacks. Practically they need a large rated PWM inverter with quick response against system parameters changes. If the system has passive filters attached somewhere, as in case of hybrid filters then the injected currents may circulate in them [28].

6.3. Hybrid harmonic filters

These types of filters combine the passive and active filters. They contain the advantages of active filters and lack the disadvantages of passive and active filters. They use low cost high power passive filters to reduce the cost of power converters in active filters that is why they are now very much popular in industry. Hybrid filters are immune to the system impedance, thus harmonic compensation is done in an efficient manner and they do not produce the resonance with system impedance [29]. The control techniques used for these types of filters are based on instantaneous control, on p-q theory and i_ð-我_q. K.N.M.Hasan et.al. presented a comparative study among the p-q and i_ð-我_q techniques and concluded that in case of voltage distortions the i_ð-我_q method provides slightly better results [12]. They are usually combined in the following ways [21]

Passive series active series hybrid filters
Passive series active shunt hybrid filters
Passive shunt active series hybrid filters
Passive shunt active shunt hybrid filters

6.3.1. Passive series active series hybrid filters

These type of hybrid filters have both kind of filters connected in series with the load as shown in Fig.8 and are considered good for diode rectifiers feeding a capacitive load [32]

6.3.2. Passive series active shunt hybrid filters

This breed of hybrid filter has passive part in series with load and active filter in parallel. AdilM. Al-Zamil et al. proposed such type of filters in their paper and used the high power capability. of passive filter by placing them in series with the load. They used an active filter with space vector pulse with modulation (SVPWM) and implemented it on micro-controller. They used only line current sensors to compute all the parameters required for reference current generation. Their proposed system worked satisfactorily up to the 33^路 harmonic and the results shown are based on a system with line reactance of 0.13 可以. In their system the bandwidth required for active filter is relatively less due to the passive filter that takes care of the rising and falling edges of load current. They proposed that while designing hybrid system the line filter L and capacitance C of active filter needs a compromise in selection depending on the acceptable level of switching frequency ripple current and minimum acceptable ripple voltage [1].

6.3.3. Passive shunt active shunt hybrid filters

These types of filters have both the passive and active filters connected in shunt with the load as shown in Fig.9 [21]. In a comparative study J.Turunen et al. claimed that they require smallest transformation ratio of coupling transformer as a result they need a fairly high power rating for a small load and in case of high power loads the problem of dc link control results in poor current filtering [43].

6.3.4. Passive shunt active series hybrid filters

As its name implies it is a kind of hybrid filter that has an active filter in series and a passive filter in shunt as shown in Fig.10. Ĵ. Turunen et al. in a comparative study stated that this breed of hybrid filter utilizes very small transformation ratio therefore for same rating of load their power rating required is large compared to the load [43].

图 8.

Passive series active series hybrid filters [32]

图 9.

Passive shunt active shunt hybrid filters [21]

图 10.

Active series passive shunt hybrid filters [29]

6.4. Switching techniques

Besides using the method of installing filters, power electronics is so versatile that up to some extent harmonics can be eliminated using switching techniques. These techniques may vary from the increasing the pulse number to advance algorithm based Pulse Width Modulation (PWM). The most widely used sine triangle PWM was proposed in 1964. Later in 1982 Space Vector PWM (SVPWM) was proposed [20]. PWM is a magical technique of switching that gives unique results by varying the associated parameters like modulation index, switching frequency and the modulation ratio. The frequency modulation ratio ‘米’ if taken as odd automatically removes even harmonics [17, 26]. Here the increase in switching frequency reduces the current harmonics but this makes the switching losses too much. 此外, we cannot keep on increasing switching frequency because this imposes the EMC problems [15]. D.G.Holmes et al. 提出了基于载波的 PWM 分析，并声称可以使用一些分析解决方案来确定使用不同调制技术的谐波消除. 如果设计者使用自然或非对称规则采样 PWM，则可以消除边带谐波 [14]. 可以通过调整调制指数来提高输出. 一种特殊类型的 PWM 称为选择性谐波消除 (她) PWM 或程控谐波消除方案. 该技术基于相地电压的傅立叶分析. 它基本上是方波开关和 PWM 的组合. 这里适当的开关角度选择使目标谐波分量为零 [26, 30]. 在 SHE 技术中，至少 0.5 调制指数是可能的 [41]. 但即使是最好的 SHE 也会给系统留下一些未经过滤的谐波. Ĵ. 庞特等人. 提出了一种处理 SHE PWM 引起的未过滤谐波的技术. 他们表示，如果我们使用 SHE PWM 来消除 11^日和 13^日谐波为 12 脉冲配置，然后是阶次谐波 23^日, 25^日, 35^日和 37^日在定义电压畸变方面起着至关重要的作用. 他们建议使用三电平有源前端转换器. 他们建议调制指数为 0.8-0.98 减轻阶次谐波 23^路, 25^日和 35^日, 37^日 [30]. 经过一些修改，研究人员表明 SHE PWM 可以在非常低的开关频率下使用 350 赫兹. 哈维尔·那不勒斯等人. 提出了这项技术，并将其命名为“选择性谐波抑制” (健康管理) PWM. 他们使用了七种开关状态，结果使选择性谐波等于零 [8]. 这非常好，因为在 SHE PWM 中，选择性谐波不需要为零. 在传统的 PWM 中，将其控制在允许的限度以下就足够了. Siriroj Sirisukprasert 等人. 通过改变输出阶梯波形的性质和改变调制指数，提出了一种最佳谐波抑制技术. 他们在多电平逆变器上测试了他们提出的技术，该技术优于两电平传统逆变器. 他们从开关波形中排除了非常窄和非常宽的脉冲. 与上面讨论的 SHE PWM 不同，它们通过每个周期仅切换一次电源开关来确保最小的开启和关闭. 与传统 SHE PWM 相反, 在这种情况下，调制指数可以变化，直到 0.1. 输出是不同阶段的阶梯波形，它们将调制指数的产生分类为高, 低和中，真正感兴趣的是，对于所有这三类调制指数，每个开关每个周期一次切换 [41]. 有研究人员采用梯形PWM方法进行谐波控制. 这种 PWM 基于单极 PWM 开关. 这里将梯形波形与三角波形进行比较，并将所得 PWM 提供给电源开关. 与基于 PWM 的技术中的其他谐波消除技术一样，研究人员建议使用基于 AI 的技术，包括 FL 和 ANN.

7. 结论

本章总结了主要的电能质量问题之一，它是电网中许多电力系统扰动的原因. 讨论了可能的谐波源及其对配电系统组件（包括变压器）的影响, 开关装置和保护系统. 此处还介绍了谐波限制及其测量技术的监管标准. 还介绍了谐波的清除技术，并简要介绍了各种谐波滤波器. 加强知识基础, 本章还讨论了使用 PWM 技术控制谐波. 通过本章，我们尝试收集该领域的技术信息. 对谐波的透彻理解将为公用事业工程师提供解决谐波相关研究工作时经常需要的框架.