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附 录 Open loop PWM control techniques Sinusoidal PWM (SPWM) SPWM technique is one of the most popular modulation techniques among the others applied in power switching inverters. In SPWM, a sinusoidal reference voltage waveform is compared with a triangular carrier waveform to generate gate signals for the switches of inverter. Power dissipation is one of the most important issues in high power applications. The fundamental frequency SPWM control method was proposed to minimize the switching losses. The multi-carrier SPWM control methods also have been implemented to increase the performance of multilevel inverters and have been classified according to vertical or horizontal arrangements of carrier signal. The vertical carrier distribution techniques are defined as Phase Dissipation (PD), Phase Opposition Dissipation (POD), and Alternative Phase Opposition Dissipation (APOD), while horizontal arrangement is known as phase shifted (PS) control technique. In fact PS-PWM is only useful for cascaded H-bridges and flying capacitors, while PD-PWM is more useful for NPC。 Each of the mentioned multi-carrier SPWM control techniques have been illustrated in Fig. :1, respectively. The sinusoidal SPWM is the most widely used PWM control method due to many advantages including easy implementation, lower harmonic outputs according to other techniques, and low switching losses. In SPWM control, a high frequency triangular carrier signal is compared with a low frequency sinusoidal modulating signal in an analog or logic comparator devices. The frequency of modulating sinusoidal signal defines the desired line voltage frequency at the inverter output . Fig. 1. Multi-carrier SPWM control strategies:(a) PD, (b) POD, (c) APOD, (d) PS. Fig. 2. An SPWM controlled inverter : (a) complete system, (b) modulator block of inverter ma Switching freq. (Hz) Line voltages (V) Line currents (A) Switching angle THD ratios (% THD) Line current Line voltage 1 0.6 1000 202.8 16.19 30 9.34 107.25 2 0.6 2000 212 16.19 30 4.46 92.72 3 0.6 5000 202.8 16.27 30.4 1.71 25.21 4 0.6 10,000 206.3 16.28 29.89 0.88 5.36 5 0.8 1000 277.1 21.58 30 8.30 81.72 6 0.8 2000 295.7 22.94 29.86 5.41 64.91 7 0.8 5000 293.8 23.01 29.96 2.97 33.63 8 0.8 10,000 303.9 24.04 29.55 5.01 17.28 9 1 1000 351.6 27.31 30.14 8.28 61.21 10 1 2000 355.7 27.68 29.78 4.16 51.78 11 1 5000 377 29.23 29.67 3.78 32.66 12 1 10,000 409.1 32.1 26.62 4.82 14.23 13 1.2 1000 385.1 29.98 30.05 7.95 52.68 14 1.2 2000 387.7 30.22 29.92 4.60 48.42 ma Switching freq. (Hz) Line voltages (V) Line currents (A) Switching angle THD ratios (% THD) Line current Line voltage 15 1.2 5000 389.8 32.47 22.34 10.59 32.10 16 1.2 10,000 425.9 33.15 26.4 7.57 22.01 17 1.4 1000 399.8 31.12 30.3 7.43 49.37 18 1.4 2000 403.9 31.58 29.93 4.14 46.43 19 1.4 5000 424.4 32.47 28.23 4.83 27.75 20 1.4 10,000 441.3 33.36 23.53 7.13 15.31 Table 1. Current and voltage THD analysis of full bridge inverter. A three-phase full bridge inverter and the SPWM modulator that has been designed to generate switching signals for three-phase full bridge inverter is depicted in Fig. 2a and Fig. 2b . In the designed three-level inverter, modulated SPWM signals have been used to control MOSFET switches of the inverter, and THD( Total Harmonic Distortion) analysis of output voltage and current have been performed as seen in Table 1. The design parameters were as follows; DC voltage (VDC) = 300 V Modulation index (mi) = 0.6 mi 1.4 Switching frequency (fsw) = 1 kHz fsw 10 kHz Load resistance (RL) = 5 Load impedance (L) = 5 mH Rated power = 10 kV A In the harmonic analyses of SPWM controlled inverter designed using Simulink; the lowest THD for current has been measured as 0.88% while modulation index is 0.6 and switching frequency at 10 kHz. The THD for line voltage has been measured as 5.36% for the same operating conditions The line voltage has increased almost proportional to Eq. ( 1) in over-modulation range, while proportional to Eq. (2) in linear modulation range. In SPWM control technique, the output voltage is obtained in linear modulation range, ( 1) ( 2) Another application has been implemented using SPWM technique to control a five-level CHB-MLI as seen in Fig 3. The designed VSI is based on the topology of Fig. 4 which includes dual H-bridge cells as shown in Fig. 5 per phase to generate a five-level output voltage. The main topological calculations which are performed initially indicate the requirements of modulator and inverter blocks, and allow obtaining a well prepared modulation algorithm to increase the performance of inverter. Fig.3. An SPWM controlled five-level CHB-MLI controlled inverter: (a) complete system, (b) CHB-MLI block. Fig. 4. Three-phase five-level topology of cascaded H-bridge multilevel inverter Fig. 5: three-level CHB-MLI. The proposed inverter includes six H-bridges and four SPWM switching signals to control each bridge respectively. The modulation algorithm has been performed in SPWM modulator block to generate 24 separate SPWM pulses for H-bridges. The SPWM modulator has a switching bandwidth between 0 and 40 kHz to control H-bridges. Fig. 6 shows the values which are obtained at 5 kHz switching conditions, while mi = 1. Fig. 6a and b represent the FFT analysis of the current THD (THDi) and voltage THD (THDv) ratios in Simulink. Fig. 6. THD analysis of inverter while fsw = 5 kHz and mi = 1: (a) THD for current is 1.34%, (b) THD for phase voltage is 23.59%. The switching frequency of SPWM modulator has been limited to 110 kHz, and modulation indexes are selected in 0.6 mi 1.4 ranges to analyze the effect of fsw and mi on THD of inverter. It has been observed by the performed tests that reducing the THD of current and voltage is depended on increasing the switching frequency in linear modulation range as shown in Fig.7a and b respectively. Fig. 7. THD analysis of inverter at various switching frequencies and modulation indexes: (a) THD for current in %, (b) THD for phase voltages in % The output current and voltage values have been increased in over-modulation range since mi is over 1, but the THD rates have been changed nonlinearly. The lowest THD for current of the designed MLI has been measured as 0.1% during 10 kHz switching frequency and mi = 0.8 conditions. The THD analyses of two different inverter topologies controlled with SPWM have been depicted in Fig. 8 applying 5 kHz switching frequency while modulation index was 1. Fig. 8. Current THD comparison of topologies, while mi = 1 fsw = 5 kHz: (a) five-level CHB-MLI inverter output, (b) three-level full bridge inverter output. The current THD of five-level CHB-MLI has been found 1.34%, while current THD of three-level full bridge multilevel inverter was 3.78%. The least THD of CHB-MLI has been determined as 0.1% for 10 kHz switching frequency and mi = 1 conditions. The lower switching frequency in linear modulation range has caused to higher THD for current and voltage at the output of inverter. 开环 PWM 控制技术 正弦脉宽调制 (SPWM) 在功率开关应用 中, SPWM 技术是其中最流行的一种调制技术 之一 。在 SPWM 中,一个 正弦参考电压波形 与 一个三角形的载波信号波形 相比较, 产生门 信号使 开关逆变器工作。应用 大功率时, 功率消耗是其中一个最重要的问题。 SPWM 控制基频算法 可以 最大限度地减少开关损耗。基于 SPWM 控制的方法也已开始实施 来 提高 多级 逆变器的性能 ,按水平或者垂直排列 ,对 载波信号 进行分类 。垂直 载体 分布技术被定义相 位耗散 (PD), 相位相对耗散(POD),选择性相位相对耗散 (APOD),而耗散水平排列被称为相移 (PS)控制技术。事实上PS-PWM 仅仅是有用的串级 H-bridges 和 浮动 电容器是比较有用的 ,而 PD-PWM 多用在NPC。 以上提到的各种基于 SPWM 的 控制技术 的分析如 图 1。由于许多优点 ,如 容易实施 ,低谐波输出 借助 其他的 技术 ,以及低的开关损耗 , 正弦脉宽调制型是目前应用最广泛的 PWM控制方法。在 SPWM 控制 中 ,高频三角载波信号 与 一种低频正弦调制信号 在一个 模拟或逻辑比较器装置 进行比较 。正弦信号的调制频率定义所需的 线 电压 , 在逆变器输出 。 图 1: SPWM 控制技术分析: (a) PD, (b) POD, (c) APOD, (d) PS (图见英文 ) 三相全桥逆变器和 SPWM 调制器 已经设计用来产生开关信号, 三相全桥逆变器 如 图 2。在 设计 的 三电平逆变器 中,调制 SPWM 信号 控制 逆变 器的 MOSFET 开关、谐波畸变率分析输出电压和电流 已完成,如 表 1。 图 2: SPWM 控制的逆变器:( a)完整的体系 ( b)逆变器的调制器 表 1:全桥逆变器的电压、电流谐波畸变率分析 设计参数如下 ; 直流电压 (VDC)= 300V 调制指数 (mi)= 0.6 mi 1.4 开关频率 (fsw)= 1KHz fsw 10KHz 负载端电阻 (RL)= 5 负载阻抗 (L)= 5 mH 额定功率 = 10KVA 在 对 SPWM 控制的逆变器 进行 谐波分析 中 设计采用 Simulink 仿真 ;当前最低 的谐波畸变率为 0.88%, 而 调制指数是 0.6, 开关频率 是 10KHz。同 样的 操作条件 下,线电压的谐波畸变率为 5.36%。 非线性调制范围, 线电压 变化规律见式 1, 在线性调制范围 变化如式 2。 ( 1) ( 2) 在 SPWM 控制技术 ,输出电压 是在 线性调制范围 内得到的。 另一个使用 SPWM 技术 的 应用程序已经实施 ,它可以控制一个 五级别 的 CHB-MLI,如图 3。 逆变器的设计是基于拓扑图 4,包括双 H-bridge,如图 5 每阶段生成一种五级输出电压。最初所做的 主要拓扑计算能力 表明 提高逆变器的性能 需要 调制器和逆变器 ,和一个合适的 调制算法 。 图 3: SPWM 控制的五个级别的 CHB-MLI 逆变器 : (a)的完整体系 ,(b)CHB
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