Lecture Note 10 DC-AC PWM Inverters Prepared by Dr. Oday A Ahmed Website: https://odayahmeduot.wordpress.com Email: 30205@uotechnology.edu.iq Scan QR
DC-AC PWM Inverters Inverters are AC converters used to convert the DC input into a sinusoidal AC output with variable frequency and amplitude. Applications of Inverter: adjustable-speed ac drives Induction heating, stand by air-craft power supplies, UPS (uninterruptible power supplies) for computers, HVDC transmission lines Inverters can be broadly classified into two types; voltage source inverters and current source inverters. A voltage-source inverter (VSI), is one in which the DC source has small or negligible impedance. In other words, a voltage source inverter has stiff DC voltage source at its input terminals. 1
A current-source inverter (CSI) is fed with adjustable current from a DC source of high impedance, i.e. from a stiff DC current source. In a CSI fed with stiff current source, output current waves are not affected by the load. voltage-source inverter (VSI), Inverter Switch Control Current-source inverter (CSI), The inverter output voltage can be shaped based on the switch ON/OFF control that use with the inverter. Thus, two types of switch control can be used which are Square Wave Scheme PWM variable width Scheme Square Wave Scheme 2
Single-Phase Inverter PWM variable width Scheme Single-phase inverters classified generally into two types, Half-Bridge and H-Bridge inverters as shown in the figures below: Half-bridge inverter Half-Bridge inverter Also known as the inverter leg. H-Bridge inverter Basic building block for full bridge, three phase and higher order inverters. G is the centre point. Both capacitors have the same value. Thus the DC link is equally spilt into two. The top and bottom switch has to be complementary, i.e. If the top switch is closed (on), the bottom must be off, and vice-versa. Suitable for low power inverter. Big capacitor size and not economic, for high power rating. 3
Single-phase, Full-bridge Full bridge (single phase) is built from two half-bridge leg. The switching in the second leg is delayed by 180 degrees from the first leg. Same time closing would cause a short circuit from Vdc to ground (shootthrough) To avoid shoot-through when using real switches (i.e. there are turn-on and turn-off delays) a dead-time or blanking time is implemented Either S1,2 or S3,4 at the same time Shoot through fault and Dead-time In practical, a dead time as shown below is required to avoid shootthrough faults, i.e. short circuit across the DC rail. Dead time creates low frequency envelope. Low frequency harmonics emerged. This is the main source of distortion for high-quality sine wave inverter. 4
To illustrate the concept of AC waveform generation, see the following figure: where the inverter states shown below: 5
Square-wave Inverter with RL load With an inductive load i is delayed behind the voltage v l although the voltage wave is still a square. At steady circuit conditions, the current wave-shape becomes repetitive. The current will grow up exponentially during the positive half cycle from (-I n ) up to (I p ) through: grows exponentially instantaneous output current can be found 6
The output voltage for square wave inverter with R or RL load is as shown below: Load instantaneous voltage can be expressed as 7
Variable Voltage Variable Frequency Capability Output voltage frequency can be varied by period of the square-wave pulse. Output voltage amplitude can be varied by varying the magnitude of the DC input voltage. Very useful: e.g. variable speed induction motor drive Voltage source inverter (VSI) with variable DC link DC link voltage is varied by a DC-to DC converter or controlled rectifier. Generate square wave output voltage. Output voltage amplitude is varied as DC link is varied. Frequency of output voltage is varied by changing the frequency of the square wave pulses. 8
VSI with fixed DC link DC voltage is held constant. Output voltage amplitude and frequency are varied simultaneously using PWM technique. Good harmonic control, but at the expense of complex waveform generation Harmonics in square Wave Inverters The output voltage of an inverter is rectilinear in nature, and therefore contains harmonics. Harmonics reduce the efficiency and may have adverse effects on the load. Harmonic reduction can be achieved by filtering and/or using harmonic elimination techniques For example, the Harmonic Effect on Induction machines can generate three different sequences which are effect of stable operation of motor: 1, 7,13 are produce +ve sequence (a b c) 5,11,17 produce ve sequence (acb) Triple harmonics: 3, 9, 15 produce zero sequence Harmonics cause distortion on the output voltage. Lower order harmonics (3 rd, 5 th etc.) are very difficult to filter, due to the filter size and high filter order. They can cause serious voltage distortion. Why need to consider harmonics? Power Quality issue. Harmonics may cause degradation of equipment. to be de-rated. Equipment need 9
5 t Total Harmonic Distortion (THD) is a measure to determine the quality of a given waveform. V, 10
Harmonics Filtering Output of the inverter is chopped AC voltage with zero DC component. It contains harmonics. An LC section low-pass filter is normally fitted at the inverter output to reduce the high frequency harmonics. In some applications such as UPS, high purity sine wave output is required. Good filtering is a must. In some applications such as AC motor drive, filtering is not required. 11
Fourier Series Study of harmonics requires understanding of wave shapes. Fourier Series is a tool to analyze wave shapes. Harmonics of Square-wave 12
Spectra of Square Wave Spectra (harmonics) characteristics: Harmonic decreases with a factor of (1/n). Even harmonics are absent Nearest harmonics is the 3rd. If fundamental is 50 Hz, then nearest harmonic is 150 Hz. Due to the small separation between the fundamental an harmonics, output low-pass filter design can be very difficult. Quasi-Square Wave (QSW) Inverters To reduce the harmonics order of the square wave inverter or to get a variable rms voltage of the inverter output, QSW can be used. The QSW states are shown below: S1 S2 S3 S4 1 0 1 0 1 1 0 0 0 1 0 1 0 0 1 1 13
Thus the following output voltage can be obtained: 14
Example : 15
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Three-Phase Inverters Each leg (Red, Yellow, Blue) is delayed by 120 degrees. A three-phase inverter with star connected load is shown on the right 180 0 Conduction Mode In this mode, each switch conduct for 180 degree, in each 60 0 state three switches conductus together either two positive switches and one negative or two negative switches and one positive. For example, if T1, T5, and T6 conduct then the equivalent circuit of the inverter can be derived as shown below: T1 T5 R Y B V s T1 R T5 Y V s /3 T6 V s R N R R R R R T6 B 2V s / 3 N 17
In this mode the inverter switches states are: 18
S1 1 1 1 0 0 0 S2 0 1 1 1 0 0 S3 0 0 1 1 1 0 S4 0 0 0 1 1 1 S5 1 0 0 0 1 1 S6 1 1 0 0 0 1 With R load. The diode across the transistors have no functions. If the load is inductive, the current in each arm of the inverter would be delayed to the voltage as shown in the figure below: When T4 is off, the only path for the negative current i R is via D 1. Hence the load terminal R is connected to the DC source via D1 until the load current reverses its polarity at t=t 1. During period 0 t t 1, T1 will not conduct. Similarly, T4 will only start to conduct at t=t2. The transistors must be continually gated, since the conduction time of transistors and diodes depends on the load power factor. 120 0 Conduction Mode In this mode, each switch conduct for 120 degree, in each 60 0 state two switches conductus together one connected to the positive terminal and other one connected to the negative. The equivalent circuit of inverter for each state can be obtained as shown below: 19
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Example: Compare between 180 0 and 120 0 conduction modes for three-phase DC-AC converter 21
Example: 22
Multi Level Inverter To reduce the effect of inverter harmonics and to increase the RMS Ac output votlage multi-level inverter can be used. These multilevel-output voltages are more sinelike in quality and thus reduce harmonic content. The multilevel inverter is suitable for applications including adjustable-speed motor drives and interfacing renewable energy sources such as photovoltaics to the electric power grid. Multilevel Converters with Independent DC Sources One multilevel inverter method uses independent dc sources, each with an H bridge. 23
EXAMPLE For the two-source multilevel inverter with Vdc 100 V: (a) Determine the Fourier coefficients through n =9, for α 1 =20 0 and α 2 = 40 0, (b) Determine α 1 and α 2 such that the third harmonic (n 3) is eliminated. Solution a) to evaluate the Fourier coefficients, resulting in V1 = 217, V3 = 0, V5 = -28.4, V7 = -10.8, and V9 = 0. Note that the third and ninth harmonics are eliminated. The even harmonics are not present. b) To achieve elimination of the third harmonic requires the solution to the equations 24
The preceding concept can be extended to a multilevel converter having several dc sources. For k separate sources connected in cascade, there are 2k1 possible voltage levels. As more dc sources and H bridges are added, the total output voltage has more steps, producing a staircase waveform that more closely approaches a sinusoid. For a five-source system as shown in figure below, there are11 possible output voltage levels. Equalizing Average Source Power with Pattern Swapping In the two-source inverter the source and H bridge producing the voltage v1 supplies more average power (and energy) than the source and H bridge producing v2 due to longer pulse widths in both the positive and negative half cycles. If the dc sources are batteries, one battery will discharge faster than the other. A technique known as pattern swapping or duty swapping equalizes the average power supplied by each dc source. 25