电力有源滤波器的MATLAB仿真

基于MATLAB的有源滤波器的设计与仿真对并联型有源电力滤波器的控制方法进行研究，应用MATLAB软件建立了仿真模型，利用SimPower工具箱谐波电流检测方法进行建模和仿真。

在simulink 环境下，对提出的定时比较控制方法和并联型APF抑制谐波效果进行了仿真实验。

标签：MATLAB；有源电力滤波器；仿真近年来，电力电子技术发展的越来越快，其发展的重大障碍是电力电子装置的谐波污染问题。

目前在主要采用被动型谐波抑制方案来抑制谐波，本文对并联型有源电力滤波器进行研究，应用MATLAB软件建立了仿真模型。

1 有源电力滤波器(APF)有源电力滤波器一般可分为：并联型APF、串联型APF和串并联混合型APF,其一般由检测回路，控制回路和主电路构成，理论上讲，有源滤波器可以对任意谐波电流进行补偿，并联有源滤波器其与系统相并联，可等效为一受控电流源，通过适当控制APF可产生与负载谐波大小相等、方向相反的谐波电流，从而将电源侧电流补偿为正弦波[1]。

2 并联有源滤波器2.1 谐波电流检测原理及仿真模型设立谐波电流检测利用ip、iq运算方式，该方法用一锁相环和一正、余弦发生电路得到与电源电压同相位的正弦信号sin wt和对应的余弦信号-cos wt，这两个信号与ia、ib、ic一起计算出有功分量电流ip和iq无功分量电流，经低通滤波器LPF滤波得出ip、iq的直流分量ip、iq对应于三相电流中的基波正序分量，再经过2/3 变换，得到三相电流基波正序分量[2]。

负载电流发生模块source，三项/两项变换模块C32，运算模块C，两项/三项变换模块C23以及低通滤波器构成了其主要的仿真模型[3]，其中各模块所需元件可在simulink模块库中找到，比如交流电源，电压、电流测量模块，RLC 串联电路，电感元件，三相桥式整流器。

图1 ip、iq运算方式检测谐波电流的整体仿真模型2.2 三项并联型有源电力滤波器仿真图2 三项并联型有源电力滤波器仿真2.3 仿真结果谐波检测电路采用基于瞬时无功功率理论的ip、iq检测法的工作原理，使用MATLAB中SIMULIINK仿真模块。

并联型有源电力滤波器的Matlab仿真摘要：并联混合型有源电力滤波器能够很好地实现谐波抑制和无功补偿。

给出了有源电力滤波器系统结构，建立了数学模型，还给出了主电路直流侧电容电压值和交流侧电感值的选取方法，利用Matlab＼simulink＼PsB构建了仿真模型，得到了仿真结果。

关键词：有源电力滤波器；直流侧电容电压；交流测电感：Matlab／simulinkAbstract ：Shunt hybrid active power filter can commendably achieve hannonic suppression and reactive power compensation．In this paper,it shows the APF’s architecture and sets up amathematical model．And the way ofchoosing the value ofthe main circuit’s voltage ripple of DC side capacitor and the AC side inductance is proposed．MA TLAB＼Simulink＼PSB is used to build simulation model and then get the simulation results．Key words：APF；V oltage of DC side capacitor；AC side inductance；Matlab／Simulink引言：在谐波含量较高的配电网中，对无功功率补偿有着严格的要求。

目前电力系统中无功补偿大都是采用机械开关控制的电容器投切，谐波补偿大多采用无源滤波装置，负序治理的工作尚未大范围开展。

另外，无功补偿、负序电流补偿、谐波抑制是分别单独地进行的。

由于不是按统一的数学模型综合地进行治理，常出现顾此失彼的情况，且响应速度慢、经济性差、安装维护工作量大，妨碍了电网污染治理工作的顺利进行。

并联型有源电力滤波器的Matlab仿真摘要：并联混合型有源电力滤波器能够很好地实现谐波抑制和无功补偿。

给出了有源电力滤波器系统结构，建立了数学模型，还给出了主电路直流侧电容电压值和交流侧电感值的选取方法，利用Matlab＼simulink＼PsB构建了仿真模型，得到了仿真结果。

关键词：有源电力滤波器；直流侧电容电压；交流测电感：Matlab／simulinkAbstract ：Shunt hybrid active power filter can commendably achieve hannonic suppression and reactive power compensation．In this paper,it shows the APF’s architecture and sets up amathematical model．And the way ofchoosing the value ofthe main circuit’s voltage ripple of DC side capacitor and the AC side inductance is proposed．MA TLAB＼Simulink＼PSB is used to build simulation model and then get the simulation results．Key words：APF；V oltage of DC side capacitor；AC side inductance；Matlab／Simulink引言：在谐波含量较高的配电网中，对无功功率补偿有着严格的要求。

目前电力系统中无功补偿大都是采用机械开关控制的电容器投切，谐波补偿大多采用无源滤波装置，负序治理的工作尚未大范围开展。

另外，无功补偿、负序电流补偿、谐波抑制是分别单独地进行的。

由于不是按统一的数学模型综合地进行治理，常出现顾此失彼的情况，且响应速度慢、经济性差、安装维护工作量大，妨碍了电网污染治理工作的顺利进行。

能力拓展训练任务书学生姓名：专业班级：电气指导教师：胡红明工作单位：自动化学院题目: 三相有源电力滤波器的仿真电路初始条件：VS1-VS3为标准三相正旋电压源，相电压有效值为220V。

要求完成的主要任务:（1）设计出主电路拓扑结构和控制系统原理图；（2）采用MATLAB搭建系统仿真电路，对仿真结果进行分析：a补偿后输入电压与输入电流波形 b非线性负载输入电压与输入电流波形c三相APF输入电压与输入电流波形时间安排：2012年7月9日至2012年7月13日，历时一周，具体进度安排见下表参考文献：[1]洪乃刚.《电力电子和电力拖动控制系统的MATLAB仿真》.北京：机械工业出版社，2006指导教师签名：年月日目录摘要 (1)1 有源滤波器介绍 (2)1.1有源滤波器基本原理 (2)1.2有源滤波器的优点 (2)1.3有源电力滤波器的分类 (3)1.4有源滤波器的关键技术 (4)2有源电力滤波器的控制策略 (4)2.1滞环比较控制 (4)2.2三角波比较方式 (5)3有源电力滤波器的主电路设计 (6)3.1直流侧电容量的选择 (6)3.2直流侧电压的选择 (8)4 MATLAB仿真 (11)4.1仿真模型图 (11)4.2仿真结果图 (12)参考资料 (15)摘要有源电力滤波器是当前对电网中谐波污染补偿或抵消的有效手段, 文中对有源电力滤波系统的工作原理进行了理论研究和分析。

MATLAB/SIMULINK提供的SimPower工具箱基本涵盖了电力系统建模和仿真的各个方面。

该文利用SimPower工具箱对有源电力滤波器装置进行了建模和仿真，使用该方法能够将有源电力滤波器的工作过程及有关波形准确直观地显示出来,验证了理论分析的正确性。

关键词：有源电力滤波器谐波仿真三相有源电力滤波器的仿真电路1 有源滤波器介绍1.1 有源滤波器基本原理有源电力滤波器是一种用于动态抑制谐波、补偿无功的新型电力电子装置,它能对大小和频率都变化的谐波以及变化的无功进行补偿，其应用可克服IC滤波器等传统的谐波抑制和无功补偿方法的缺点。

目前，对有源电力滤波器的研究越来越广泛。

一方面，研究者众多，不仅有高等院校、研究所，而且也有许多电力局、大型企业等；另一方面，研究涉及谐波检测方法、控制策略、PWM 波的形成等有源滤波技术的各个方面，对谐波检测控制方法和谐波检测电路的实现方法研究尤其活跃，出现了许多新的方法，这些方法都是旨在提高谐波检测的实时性和检测精度，因为谐波检测方法及谐波检测电路的实时性和检测精度对有源电力滤波器的滤波性能起着决定性的作用。

本文将使用Simulink 来建立并联型有源电力滤波器的仿真模型，然后对仿真结果进行分析。

1有源电力滤波器的原理及分类1．1有源电力滤波器的基本原理有源电力滤波器分为串联型和并联型两种。

串联型有源滤波器是向串联变压器副边注入基波补偿电流。

使串联变压器对电网基波电流呈低阻抗。

对谐波电流呈高阻抗。

从而抑制谐波；并联型有源滤波器是向电网注入与负载的无功和谐波电流大小相等、方向相反的电流来补偿无功和抑制谐波。

并联型有源电力滤波器的系统框图如图1所示（电感、电容等电路元件均包含在主电路中），其工作原理为：指令电流运算电路在检测到负载电流后，通过运算把负载电流信号中的谐波电流、无功电流及负序电流和零序电流检测出来,然后把这些电流信号转换成相应的变流器触发信号，再通过电流跟踪控制电路形成触发脉冲去驱动变流器，使变流器产生的电流为上述电流之和，极性相反，再回注入电网，则电网中的谐波电流、无功电流、负序电流和零序电流被抵消为零，只剩下基波有功正序电流。

1．2有源电力滤波器的分类有源电力滤波器分类的方法很多，可以按照接入电网的方式、变流电路的结构、补偿系统的相数、补偿对象交直流性来分类。

按接入电网的方式分为并联型、串联型和混合型；按变流电路的结构分为电流型和电压型；按补偿的相数可以分为单相、三相三线、三相四线；按补偿对象交直流性分为直流APF 和交流APF 。

根据APF 与电力系统的连接方式可将其分为并联型、串联型及串－并联混合型。

周昊 王毅（北京交通大学电气工程学院，北京市 １０００４４）Zhou Hao Wang Yi(School of Electrical Engineering of Beijing Jiaotong University, Beijing 100044)电力有源滤波器（ＡＰＦ）控制方法研究及Ｍａｔｌａｂ仿真Simulation and Study of the Voltage Control Method for Active Power FilterAbstract: The paper introduced the active power filter based on the i p , i q arithmatic of the instantaneous reactive power theory and proposed the PI control method on the DC side. Based on the theory analyse, it used the Simpowersystems module in the Matlab to build the model and simulate the APF system. ItÕs proved that the DC side voltage through that method is stable, and the compensation result is good.Key words: APF Matlab DC Voltage Control Instantaneous Reactive Power Theory【摘 要】通过瞬时无功功率理论的ｉｐ、ｉｑ算法设计了电力有源滤波器，提出直流侧电压的ＰＩ控制。

在理论分析的基础上，利用Ｍａｔｌａｂ中的电力系统仿真工具箱对并联型电力有源滤波器进行了建模和仿真研究。

基于matlab的电力系统有源滤波器设计有源滤波器常用于电力系统中的谐波补偿。

下面是一个简单的基于matlab的有源滤波器设计示例：1. 系统模型首先，我们需要建立电力系统的模型。

假设我们要设计一个谐波滤波器来补偿电网中的第5次谐波。

系统模型如下图所示：其中，U1是电网电压，U2是负载电压，L和C分别是电路中的电感和电容。

Vin是有源滤波器的输入电压，Vout是输出电压，R是有源滤波器中的电阻，G 是电容的导纳，s是Laplace算子。

2. 控制器设计有源滤波器的控制器通常使用PI控制器和H∞控制器。

这里我们选择使用PI控制器。

PI控制器的传递函数为：Kp + Ki/s其中，Kp是比例增益，Ki是积分增益。

3. 滤波器设计有源滤波器的设计通常是在仿真中进行的。

我们使用simulink工具箱来进行仿真。

以下是有源滤波器的设计步骤：- 设置系统参数为了方便起见，我们首先设置了一些系统参数。

以下是参数列表：- 电网电压：400V- 电阻：0.01Ω- 电容：200μF- 电感：10mH- 负载电阻：10Ω- 有源滤波器输入电压：20V- 积分时间常数：0.001s- 比例增益：0.5在simulink中，我们使用Signal Builder模块来产生模拟信号，如下图所示：- 建立系统模型我们使用simulink模块建立电力系统模型，如下图所示：通过调整控制器的比例增益和积分增益，我们可以使滤波器输出的电压与需补偿的谐波相位相同，如下图所示：最终输出的谐波滤波器电压与需补偿的谐波电压相消，进一步将系统中的谐波降到可接受的水平，如下图所示：通过这个例子，我们可以看到使用simulink进行有源滤波器设计的基本步骤。

在实际应用中，我们需要根据具体情况进行参数调整和系统优化。

APPLICATION OF A SHUNT ACTIVE POWER FILTER TO COMPENSATE MULTIPLE NON-LINEAR LOADSTABLE OF CONTENTS:1.ABSTRACT2.INTRODUCTION3.SHUNT ACTIVE POWER FILTER OPERATION3.1 Series Inductance3.2 Direct Control of the Grid Current3.3 Ramp time Current Control4. A SHUNT ACTIVE POWER FILTER WITH HARMONIC VOLTAGESOURCING LOADS4.1 Compensation for Harmonic Voltage Sources4.2 Series Inductance XL5. A THREE-PHASE SHUNT ACTIVE POWER FILTER WITH MULTIPLENON-LINEAR LOADS5.1 Mixed-Type Harmonic Sources And Unbalanced loads5.2 DC Bus6. CONCLUSION7. REFERENCESABSTRACTIn this paper, the implementation of a shunt active power filter with a small series reactor for a three-phase system is presented. The system consists of multiple non-linear loads, which are a combination of harmonic current sources and harmonic voltage sources, with significant unbalanced components. The filter consists of a three-phase current-controlled voltage source inverter (CC-VSI) with a filter inductance at the ac output and a dc-bus capacitor. The CC-VSI is operated to directly control the ac grid current to be sinusoidal and in phase with the grid voltage. The switching is controlled using ramptime current control, which is based on the concept of zero average current error. The simulation results indicate that the filter along with the series reactor is able to handle predominantly the harmonic voltage sources, as well as the unbalance, so that the grid currents are sinusoidal, in phase with the grid voltages and symmetrical.2. INTRODUCTIONNon-linear loads, especially power electronic loads, create harmonic currents and voltages in the power systems. For many years, various active power filters (APF) have been developed to suppress the harmonics, as well as compensate for reactive power, so that the utility grid will supply sinusoidal voltage and current with unity power factor.Conventionally, the shunt type APF acts to eliminate the reactive power and harmonic currents produced by non-linear loads from the grid current by injecting compensating currents intended to result in sinusoidal grid current with unity power factor. This filter has been proven to be effective in compensating harmonic current sources, but it cannot properly compensate for harmonic voltage sources. Many electronic appliances, such as switched mode power supplies and electronic ballasts, are harmonic voltage sources. A voltage sourcing series active power filter is suitable for controlling harmonic voltage sources, but it cannot properly compensate for harmonic current sources.In many cases, non-linear loads consist of combinations of harmonic voltage sources and harmonic current sources, and may contain significant load unbalance (ex. single phase loads on a three phase system). To compensate for these mixed non-linear loads, a combined system of a shunt APF and a series APF can be effective .In this paper, a combination of a grid current forcing shunt APF with a series reactor installed at the Point of Common Coupling (PCC) is investigated to handle the harmonic and unbalance problems from mixed loads ( Figure 1).Figure 1. Active Power Filter configuration3. SHUNT ACTIVE POWER FILTER OPERATIONThe three-phase shunt active power filter is a three-phase current controlled “voltage source inverter” (CC-VSI) with a mid-point earthed, split capacitor in the dc bus and inductors in the ac output .Conventionally, a shunt APF is controlled in such a way as to inject harmonic and reactive compensation currents based on calculated reference currents. The injected currents are meant to “cancel” the harmonic and reactive currents drawn by the non-linear loads. However, the reference or desired current to be injected must be determined by extensive calculations with inherent delays, errors and slow transient response.3.1 Series InductanceA key component of this system is the added series inductance XL(see Figure 2), which is comparable in size to the effective grid impedance, ZS. Without this inductance (or a series active filter), load harmonic voltage sources would produce harmonic currents through the grid impedance, which could not be compensated by a shunt APF. Currents from the APF do not significantly change the harmonic voltage at the loads. Therefore, there are still harmonic voltages across the grid impedance, which continue to produce harmonic currents..3.2 Direct Control of the Grid CurrentIn this scheme (see Figure 1), the CC-VSI is operated to directly control the ac grid current rather than it’s own current. The grid current is sensed and directly controlled to follow symmetrical sinusoidal reference signals in phase with the grid voltage. Hence, by putting the current sensors on the grid side, the grid current is forced to behave as a sinusoidal current source and the grid appears as a high-impedance circuit for harmonics. By forcing the grid current to be sinusoidal, the APF automatically provides the harmonic, reactive, negative and zero sequence currents for the load, following the basic current summation rule:igrid = iAPF + i loadThe sinusoidal grid current reference signal is given by:iref = k vgrid-1where vgrid-1 is the fundamental component of the grid voltage, and k is obtained from an outer control loop regulating the CC-VSI dc-bus voltage.Figure 2. Circuit equivalent for harmonics3.3 Ramp time Current ControlThe performance and the effectiveness of the filter are enhanced by the use of the ramp time current control technique to control the CC-VSI. The principle operation of ramp time current control is based on the concept of zero average current error (ZACE). In this application, the current error signal is the difference between the actual grid current and the desired/reference grid current waveform.4. A SHUNT ACTIVE POWER FILTER WITH HARMONIC VOLTAGE SOURCING LOADS4.1 Compensation for Harmonic Voltage SourcesTo show a compensation for harmonic voltage sources, a simulation was conducted using circuit constants from the literature based on a three-phase ac system with a grid voltage of 400V-50Hz, a 60kW diode rectifier load with dc filter capacitor, a filter inductance (Linv) of 0.45mH (5.3%), ZS of 1.8%, and XL of 1.8%, without a high frequency filter. The circuit equivalent from the harmonic point of view is shown in Figure 2.The three-phase shunt APF successfully forces sinusoidal current from the grid, as shown in Figure 3(a) and 3(b). In doing this, the APF compensates the harmonic voltages because the load harmonic voltage in Figure 3(c) appears across XL in Figure 3(d). These same harmonic voltages appear in the inverter voltage in Figure 3(e) and across the inverter inductance in Figure 3(f). Thus, the load harmonic voltages do not appear across ZS and load harmonic currents are not created through this grid impedance. Also, assuming the grid voltage harmonics are negligible, the ac grid voltage at the PCC will be sinusoidal.Figure 4 shows that when XL is reduced to 0.5%, the filter cannot suppress the harmonics properly, so that the grid currents are still distorted and contain significant amount of harmonics. The load harmonic voltage cannot be removed completely by the harmonic voltage on XL, because the inverter cannot produce sufficient harmonic voltage to compensate load harmonic voltage. Then, harmonic voltages still occur across grid impedance. As a result, the inverter loses its controllability; and the compensation by the active filter cannot be accomplished.4.2 Series Inductance XLThere are several ways to determine the size of XL. It is suggested that the minimum value of XL is 6%. The XL is used for a different purpose and not related to harmonic voltage type loads.The practical choice of XL is that it should be as small as possible to minimize cost. Furthermore, if the APF can directly force the grid current to be sinusoidal, the voltage at the PCC will have similar characteristics to the grid (except very small fundamental voltage drop and very small phase shift). In order to make the loads operate in the similar operating point to which they were connected directly to the grid, then the size of XL should be chosen close to ZS XS in per-unit value (usually the resistance of the grid impedance is very small compared to its inductance).From the above simulation, it is proven that with the XL = 1.8%, the compensation is successful. The value of XL could be lower than 1.8% provided that minimum di/dt of Linv exceeds the maximum di/dt permitted by the inductance XL. Otherwise, the value of Linv has to be reduced. However, decreasing the Linv will increase the high switching frequency ripple in the ac grid currents.Fig.3 Simulation results for XL=1.8% a)I grid b)I grid spectrumFigure 3. Simulation results for XL = 1.8%; (c) spectrum of V load harmonics, (d) V on XL, (e) V output CC-VSI, (f) V on filter inductance, (g) V at PCC5. A THREE-PHASE SHUNT ACTIVE POWER FILTER WITH MULTIPLE NON-LINEAR LOADSBy directly controlling the grid current, a three-phase shunt APF can be provided for all non-linear loads at the PCC instead of compensating each load individually. The system is simpler and more efficient because only one current sensor for each phase is located in the grid side.Figure 4. Simulation results for XL = 0.5% ; (a) Igrid, (b) Igrid spectrumFigure 4. Simulation results for XL = 0.5%; (c) spectrum of V load harmonics,(d) V on XL, (e) V output CC-VSI, (f) V on filter inductance, (g) V at PCCFrom the preceding explanation, the shunt APF with a series reactor can compensate the harmonic voltage sources in the loads. This filter combination can also succeed for harmonic current sources. In this case, the reactor will function to limit the slope of the falling and rising edges of the load current . For mixed loads, it is practical to provide a series reactor for total loads. The reactor is installed at the PCC and integrated with the APF. The size can be chosen for the possible maximum power of harmonic voltage sources.A three-phase shunt APF has been proven for balanced loads. However, the system may contain significant amounts of load unbalance as in commercial buildings with non-linear single- phase computer type loads. Such loads produce large negative sequence and harmonic currents. Hence, the filter has to inject the inverse of the negative sequence current to balance the unbalanced loads. The shunt APF discussed previously has the ability to balance the asymmetrical current. This is because the CC-VSI is operated to directly control the ac grid current to follow a three-phase balanced sinusoidal reference signal without measuring and determining the negative sequence component. Once the grid currents are able to follow the reference signal, the inverter creates the inverse of the negative sequence currents automatically. At the PCC, all three currents are potentially accessible to be directly controlled by the CC-VSI.5.1 Mixed-Type Harmonic Sources And Unbalanced loadsFigures 6 and 7 show results with several non-linear loads to demonstrate the validity of the filter. In Figure 6, the shunt active power filter combined with the series reactor is able to successfully compensate the total mixed loads that produce harmonic and unbalanced currents. The grid currents become sinusoidal and in phase with the grid voltage. The magnitude is determined by the active power required by the system.Furthermore, the grid currents are symmetrical in magnitude and phase. These currents are balanced because the CC-VSI is able to generate three different currents for each phase. For each phase, the current controller is able to force the average current error, which is the difference between the reference signal and the actual current to be zero. Then, the individual phase current can follow its reference signal closely. From Figure 7, it is obvious that phase B of the inverter current is not the same as other two phases, since the single-phase load is connected between phase A and C. Hence, the inverter not only generates harmonics to eliminate the load harmonics but also provide balancing to create the symmetrical grid currents.Fig.5 3-Ph. Load currents Fig.6 3-Ph. Currents after compensationFigure 7. Three-phase output currents of the CC-VSI5.2 DC BusFigure 8 shows the simulation results of the dynamic condition of the dc-bus voltage. It can be seen that the dc-capacitor voltage is decreased when the load is increased. This is because the active power demanded by the load is higher than that supplied from the grid. The dc-bus has to provide the active power to fulfill the power balance.Figure 8. Dynamic state of dc-bus when the load is changing; upper graph: load and grid currents - phase A; lower graph: dc-bus voltageOnce the transient interval is finished, the dc-bus voltage is recovered and remains at the reference voltage – 800V (by using a PI controller), and the magnitude of the grid active currents is fixed at a designated value. At this time, the total active power demanded by the load is supplied from the grid, because the active power filter only supplies the reactive power.This same process will occur when the load is decreased. In this case, the dc-capacitor voltage will increase in a transient state. Hence, the dc bus capacitor must be sized not only to minimize the ripple but also to provide maximum expected power unbalance until the PI loop again achieves steady state. The above result shows that the amplitude of the grid currents is regulated directly by controlling the dc bus voltage, and the calculation process of the grid current amplitude can be eliminated. Figure 8 also shows that the dc-bus contains a ripple voltage at the second harmonic frequency since the system has a single-phase diode rectifier load.6. CONCLUSIONThis paper proposes the implementation of a three-phase active power filter together with a decoupling reactor in series with the load operated to directly control the ac grid current to be sinusoidal and in phase with the grid voltage. From the simulation results, this system provides unity power factor operation of non-linear loads with harmonic current sources, harmonic voltage sources, reactive, and unbalanced components.7.REFERENCES1.Power Electronics , P.C.Sen , 2000n.dwork theory and filter design, Vasudev K Atre, 1998 n.d, Wiley Eastern3.M.El-Habrouk, M.K Darwish and P.Mehta , “ Active Power Filter : A Review” ,IEEE Proc. Electric Power Appl. , Sept 20004. B.Singh, K.Al-Haddad and A.Chandra, “ A Review of Active Filter for PowerQuality Improvements” , IEEE T rans. On Industrial Electronics, Feb. 1999。