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- 1. Pulse Width Modulated Inverter Techniques Saurabh kumar, M.Tech (Electric Drives & Power Electronics, IIT ROORKEE) Abstract-This paper presents review of different modulation techniques for voltage source inverter. A variety of techniques, different in concept as naturally sampled PWM, regular sampled PWM, delta modulation techniques, delta sigma modulation techniques state vector modulation and Hysteresis PWM are described with corresponding waveform. I. Introduction One of the most widely utilized strategy for controlling the A.C. output of power electronics converters is the pulse width modulation (PWM), which varies the duty cycle (or mark space ratio) of converter switches at a high switching frequency to achieve target average low frequency output voltage or current. Modulation theory has been a major research area in power electronics for over three decades and continues to attract considerable attention and interest. This is not surprising since modulation is at the heart of nearly every modern power electronic converter. There have been clear trend in the development of PWM concept and strategies since 1970s, addressing the main objective of reduced harmonic distortion and increased output magnitude for a given switching frequency and development of modulation strategies to suit different converter topology. While there have been wealth of research investigating the modulation of DC/DC converters the actual PWM process for these converters is usually a simple comparison between reference waveform and a sawtooth or triangular carrier waveform. II. Scope of the Paper The work presented in this paper primarily relates to medium and high power level hard switched inverters (i.e. above 1 kW power level). This paper considers only modulation strategies which are appropriate for voltage source converter (VSI). Topics covered in this paper are 1. Naturally Sampled Pulse Width Modulation 2 Regular Sampled Pulse Width Modulation 3 Delta modulation techniques 4. Delta Sigma modulation techniques 5. Space vector modulation 6. Hysteresis Pulse Width Modulation 1. Naturally Sampled Pulse Width Modulation A. Sine-Sawtooth Modulation The earliest and most straightforward modulation strategies is termed as naturally sampled PWM, which compares a low frequency target reference waveform (normally sinusoid) against high frequency carrier waveform. In this process the phase leg switched to upper DC rail when the reference waveform is greater than the sawtooth carrier wave. To obtain a sinusoidal output using this modulation strategy, the reference waveform has the form Where M= modulation index with range 0<M<1 = target output frequency = arbitrary output phase With this type of sawtooth carrier, only the trailing edge of the pulse varies as M varies, and hence this type of modulation is termed trailing edge naturally sampled PWM For natural charge of capacitors in FCMIs, this method is specially used. A typical waveform for five level fling capacitor inverter is shown For using PSCPWM in a flying capacitor N -level inverter, N -1 carrier waveform is needed which phase shifted by 2 / (N -I). B. Sine triangle Modulation This is more common form of naturally sampled PWM uses a triangular carrier instead of sawtooth carrier to compare against refrence waveform. With this type of carrier, both side of the switched output pulse from the phase leg are modulated, which considerably improves the harmonic performance of the pulse train. This type of modulation is termed double-edge naturally sampled modulation. 2. Regular Sampled Pulse Width Modulation Regular sampled PWM control technique significantly reduces the number of calculations required to generate
- 2. PWM control in real-time. It also greatly simplifies the microprocessor software implementation, thereby considerably reducing the on-line computing requirements, and thus allows significantly higher switching frequency PWM to be generated using microprocessor techniques. In these strategies the low frequency reference waveforms are sampled and then held constant during each carrier interval. These sampled values are compared against the triangular carrier waveform to control the switching process of each phase leg. The sampled reference waveform must change values at either the positive or positive/negative peaks of carrier waveform, depending on the sampling strategies. A typical practical implementation of regular sampled PWM is illustrated in Fig. 2. As shown in the Figure, the sinusoidal modulating wave a is sampled at regular intervals tl, r2 etc., and stored by a sample-and hold circuit to produce an amplitude modulated wave b. Comparison of b with the triangular carrier wave c produces the points of intersection TI, T2 defining the switching edges of the PWM pulses d. The implementation of Fig. 2 is representative of a typical analogue or discrete digital hardware implementation, as shown in the diagram in Fig. 3. An important feature of Fig. 3 is that the modulating frequency , carrier frequency , and sampling frequency , are in general, as shown, independent, and therefore any desired relationship between them can be defined. The simplest relationship is to set , and therefore to sample the modulating wave at the carrier frequency, as shown in Fig. 3. This result in only one sample being taken every carrier cycle and therefore the sampled modulating wave is kept constant throughout the carrier period resulting in each edge of the PWM pulse being modulated equally; commonly referred to as symmetric modulation, as illustrated in Figs. 2 and 4. Alternatively, fs = 2fc can be used such that two samples of the modulating wave are taken each carrier cycle. The first sample taken at the start of the carrier cycle is used to modulate the leading edge of the pulse and the second sample, taken at the middle of the carrier cycle, used to modulate the trailing edge, resulting in asymmetric modulation, as shown in Fig. 4. Since more samples of the modulating wave are used to produce asymmetric PWM, the harmonic spectrum is superior to that of symmetric PWM.
- 3. 2. Delta Modulation (DM) Technique The delta modulation (DM) technique requires a very simple circuit implementation, provides a smooth transition between the PWM and single pulse modes of operation and offers constant volts per Hertz operation without the need of additional circuit complexity. Some of the key voltage waveforms associated with the delta modulation technique is illustrated in Fig. 5(a), (b). Fig. 5(c) shows their respective circuit implementation. In particular, Fig. 5(a) illustrates the method by which the DM switching function (Fig. 5(b)), applicable to the PWM inverter, is obtained. This method utilizes a sine reference waveform and a delta-shaped carrier waveform is allowed to "oscillate" within a defined "window" extending equally above and below the reference wave . The minimum "window" width and the maximum carrier slope determine the maximum switching frequency of the inverter switchers , Therefore, when setting values for these two parameters, care should be taken so that sufficient time is provided for the proper turn-on and turn-off of and . Fig. 5(b) shows the DM switching function which describes the operation of switching elements and . The subscript of the element that is gated at any instance is indicated by the sequence of ones and twos shown in Fig. 5(b). The temporal relation between the gating sequence of elements and the waveform of the DM switching function VI yields that the inverter phase voltage , and have the same waveforms. Fig. 5(c) depicts a circuit that is capable of producing the waveforms shown in Figs. 5(a) and 5(b). This circuit operates in the following manner. Sine reference wave is supplied to the input of the comparator while carrier wave VF is generated by the integrator as follows: whenever the output of exceed the upper or lower “window” boundaries (which are preset by the ratio), comparator A 1 reverses the polarity of at the input of . This action reverses the slope of VF at the output of , thus forcing to "oscillate" around the reference waveform at ripple frequency r. This forced oscillation ensures that the fundamental component of (i.e. ) and reference wave have the same amplitudes and that the dominant harmonics of and waveforms oscillate at frequencies close to the ripple frequency r. 3. Delta Sigma modulation techniques The delta-sigma modulator is effectively applied to a voltage source inverter system with PWM pattern generating scheme. The major feature of delta-sigma modulator is the inherent nature of spread spectrum characteristic in addition to simple configuration scheme. Besides, delta-sigma modulator can be considered as a sort of error amplifier. If the inverter circuit is taken into feedback loop as a quantizer, external DC voltage disturbances can be reduced in the output side of inverter. 4. Space vector modulation Multiphase motor drives are a very promising technology, especially for medium and high power ranges. As known, a multiphase motor drive cannot be analyzed using the space vector representation in a single d-q plane, but it is necessary to introduce multiple d-q planes. So far a general space vector modulation for multiphase inverters is not available due to the inherent
- 4. difficulty of synthesizing more than one independent space vector simultaneously in different d-q planes The basic scheme of a three-phase inverter is shown in Fig. 6. The signals are switch commands of the three inverter branches, and can assume only the values 0 or 1. The inverter output pole voltages are Where is the dc-link voltage. The main problem is to control the load phase voltages and according to the requirements imposed by the application, e.g. vector control of ac machines. An elegant solution to this problem is the space vector representation of the load voltages, which describes the inverter pole voltages introducing a space vector and a zero sequence component as follows: (2) (3) Where the coefficients k=1,2,3) are defined as follows: (4) The space vector and the zero sequence components can be expressed as functions of s1, s2 and s3 by substituting (1) in (2) and (3). (5) (6) It is well-known that the load voltages depend only on the space vector of the pole voltages, whereas the inverter zero sequence component affects only the potential of the load neutral point. In other words, to control the load, it is sufficient to control the vector . SVM for Three-Phase Inverters The modulation problem consists in controlling the switch states such that the mean values of the inverter output voltages are equal to the desired values in any switching period Tp. There are eight (namely ) possible configurations for a three-phase inverter, depending on the states of the three switch commands s1, s2 and s3. Six configurations correspond to voltage vectors with non-null magnitudes. These vectors, usually referred to as active vectors, are represented in Fig. 2, where the configurations of each vector are also expressed in the form ( . Two configurations, i.e. and lead to voltage vectors with null magnitudes, usually referred to as zero vectors. The space vector modulation selects two activevectors and applies each of them to the load for a certain fraction of the switching period. Finally, the switching period is completed by applying the zero vectors. The active vectors and their duty-cycles are determined so that the mean value of the output voltage vector in the switching period is equal to the desired voltage vector. The best choice is given by the two vectors delimiting the sector in which the reference voltage vector lies. Since two consecutive vectors differ only for the state of one switch, this choice allows ordering the active and the zero vectors so as to minimize the number of switch commutations in a switching period. For example, if the desired voltage vector lies in sector 1, as shown in Fig. 7, the two adjacent voltage vectors are and , whose configurations (0,0,1) and (0,1,1) differ for only one bit. After the active vectors have been chosen, the requested voltage can be expressed as a combination of them as follows: (7) where and are the duty-cycles of and in the switching period.
- 5. The explicit expressions of and can be easily calculated evaluating the following dot products: (8) (9) (10) (11) Once and have been calculated, the designer can still choose in which proportion the two zero vectors are used to fill the switching period. Fig. 8 shows the vector sequence corresponding to the example of Fig. 7. In the sequence of Fig. 3, the zero vectors are equally distributed in the switching period. 6. Hysteresis Pulse Width Modulation Hysteresis PWM refers to the technique where the output is allowed to oscillate within a predefined error band, called "hysteresis band". The switching instants in this case are generated from the vertices of the triangular wave shown in Fig. 9. Hysteresis PWM techniques does not require any information about the inverter load characteristics. As long as the reference signal is known and the inverter output voltage is not saturated, the inverter output will always follow the reference. However, the switching frequency of power devices is not fixed for this technique and will vary depending on the magnitude and frequency of the reference,. Therefore, switching losses for this techniques can be higher compared to other techniques. IV CONCLUSION In this term paper pulse width modulation inverter techniques has been presented. Through various modulation techniques a general hierarchical consensus appears to have emerged from this work which ranks space vector modulation techniques, regular sampled modulation and sine-triangle modulation strategies in decreasing order of merit based on harmonics performance V. REFRENCES [1] Lega, A.; Mengoni, M.; Serra, G.; Tani, A.; Zarri, L., "General theory of space vector modulation for five-phase inverters," Industrial Electronics, 2008. ISIE 2008. IEEE International Symposium on , vol., no., pp.237,244, June 30 2008-July 2 2008 [2] Holtz, J., "Pulsewidth modulation-a survey," Power Electronics Specialists Conference, 1992. PESC '92 Record., 23rd Annual IEEE , vol., no., pp.11,18 vol.1, 29 Jun-3 Jul 1992 [3] Bowes, S.R.; Lai, Y.S., "Investigation into optimising high switching frequency regular sampled PWM control for drives and static power converters," Electric Power Applications, IEE Proceedings - , vol.143, no.4, pp.281,293, Jul 1996 [4] Sanakhan, S.; Babaei, E.; Akbari, M.E., "Dynamic investigation of capacitors voltage of flying capacitor multilevel inverter based on sine-sawtooth PSCPWM," Power Electronics, Drive Systems and Technologies Conference (PEDSTC), 2013 4th , vol., no., pp.182,187, 13-14 Feb. 2013 [5] Zhenyu Yu; Mohammed, A.; Panahi, I., "A review of three PWM techniques," American Control Conference, 1997. Proceedings of the 1997 , vol.1, no., pp.257,261 vol.1, 4-6 Jun 1997 [6] Hirota, A.; Nagai, S.; Nakaoka, M., "A novel delta-sigma modulated DC-DC power converter operating under DC ripple voltage," Industrial Electronics Society, 1999. IECON '99 Proceedings. The 25th Annual Conference of the IEEE , vol.1, no., pp.180,184 vol.1, 1999 [7]Holmes,D.G. and Lipo , T.A. "Pulse Width Modulation for Power Converters:Principles and Practice "

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