附 錄 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. 開環 PWM 控制技術 正弦脈寬調制 (SPWM) 在功率開關應用 中， SPWM 技術是其中最流行的一種調制技術 之一 。在 SPWM 中，一個 正弦參考電壓波形 與 一個三角形的載波信號波形 相比較， 產生門 信號使 開關逆變器工作。應用 大功率時， 功率消耗是其中一個最重要的問題。 SPWM 控制基頻算法 可以 最大限度地減少開關損耗。基于 SPWM 控制的方法也已開始實施 來 提高 多級 逆變器的性能 ,按水平或者垂直排列 ，對 載波信號 進行分類 。垂直 載體 分布技術被定義相 位耗散 (PD)， 相位相對耗散(POD),選擇性相位相對耗散 (APOD),而耗散水平排列被稱為相移 (PS)控制技術。事實上PS-PWM 僅僅是有用的串級 H-bridges 和 浮動 電容器是比較有用的 ,而 PD-PWM 多用在NPC。 以上提到的各種基于 SPWM 的 控制技術 的分析如 圖 1。由于許多優點 ，如 容易實施 ,低諧波輸出 借助 其他的 技術 ,以及低的開關損耗 ， 正弦脈寬調制型是目前應用最廣泛的 PWM控制方法。在 SPWM 控制 中 ,高頻三角載波信號 與 一種低頻正弦調制信號 在一個 模擬或邏輯比較器裝置 進行比較 。正弦信號的調制頻率定義所需的 線 電壓 ， 在逆變器輸出 。 圖 1： SPWM 控制技術分析： (a) PD, (b) POD, (c) APOD, (d) PS (圖見英文 ) 三相全橋逆變器和 SPWM 調制器 已經設計用來產生開關信號， 三相全橋逆變器 如 圖 2。在 設計 的 三電平逆變器 中，調制 SPWM 信號 控制 逆變 器的 MOSFET 開關、諧波畸變率分析輸出電壓和電流 已完成，如 表 1。 圖 2： SPWM 控制的逆變器：（ a）完整的體系 （ b）逆變器的調制器 表 1：全橋逆變器的電壓、電流諧波畸變率分析 設計參數如下 ； 直流電壓 (VDC)= 300V 調制指數 (mi)= 0.6 mi 1.4 開關頻率 (fsw)= 1KHz fsw 10KHz 負載端電阻 (RL)= 5 負載阻抗 (L)= 5 mH 額定功率 = 10KVA 在 對 SPWM 控制的逆變器 進行 諧波分析 中 設計采用 Simulink 仿真 ；當前最低 的諧波畸變率為 0.88%， 而 調制指數是 0.6， 開關頻率 是 10KHz。同 樣的 操作條件 下，線電壓的諧波畸變率為 5.36%。 非線性調制范圍， 線電壓 變化規律見式 1， 在線性調制范圍 變化如式 2。 （ 1） （ 2） 在 SPWM 控制技術 ,輸出電壓 是在 線性調制范圍 內得到的。 另一個使用 SPWM 技術 的 應用程序已經實施 ，它可以控制一個 五級別 的 CHB-MLI，如圖 3。 逆變器的設計是基于拓撲圖 4,包括雙 H-bridge,如圖 5 每階段生成一種五級輸出電壓。最初所做的 主要拓撲計算能力 表明 提高逆變器的性能 需要 調制器和逆變器 ，和一個合適的 調制算法 。 圖 3： SPWM 控制的五個級別的 CHB-MLI 逆變器 : (a)的完整體系 ,(b)CHB