DC to AC converters or inverters find wide applications in industry for AC motor drives. They are also widely used in FACTS devices, HVDC transmission, Uninterruptible Power Supplies, ship propulsion systems, etc. The most basic and still prominently used inverter configuration is the two-level Voltage Source Inverter (VSI), shown in Fig. 1. A number of modulation techniques have been developed over the years for the two-level VSI. However, the most commonly used modulation techniques employed are the Sinusoidal Pulse-Width Modulation (SPWM) and the Space Vector Modulation (SVM) technique. In this article, we attempt to compare the two techniques and illustrate the advantages that the SVM technique has over the SPWM technique.
Sinusoidal Pulse-Width Modulation (SPWM)
The wide popularity of the SPWM technique for the modulation of the two-level VSI can be attributed to its simplicity. It is a carrier-based technique in which each phase leg of the inverter is independently controlled. SPWM can be unipolar as well as bipolar. Since Space Vector Modulation is a bipolar modulation technique, so to maintain consistency in the comparison, bipolar SPWM is considered here. It employs a common carrier wave for all the three phases whose frequency fcr is much higher than the inverter output frequency. It also employs three modulating waves, one for each phase. The modulating wave for each successive phase leg of the inverter is phase displaced by 120°, as shown in Fig. 2. The frequency f of the modulating waves is same as the desired inverter output frequency. The amplitudes of the carrier and modulating waves are Am and Acr respectively. The ratio fcr/f is called the frequency modulation index mf of the inverter; while the ratio Am/Acr is called the amplitude modulation index ma. The value of ma ranges from zero to one for the linear modulation range and decides the amplitude of the fundamental component of the output voltage of the inverter. On the other hand, mf decides the harmonic spectrum of the inverter output voltage. It also decides the device switching frequency as well as the inverter switching frequency (which is same for bipolar SPWM).
The implementation of the SPWM technique is pretty simple. For each inverter phase leg, the modulating wave is compared with the carrier wave. Whenever the modulating wave is greater than the carrier wave, the upper switch of that inverter leg is turned on; otherwise the lower switch is turned on. The inverter output line-line voltage and its frequency spectrum for mf = 23 and ma = 1 with a DC link voltage Vdc = 200 V are shown in Fig. 3. Note that these results are obtained without any output filter. In practice, the inverter will employ an output filter to limit the harmonics and the Total Harmonic Distortion (THD) within permissible limits.
Space Vector Modulation (SVM)
Space Vector Modulation is another popular scheme for the modulation of voltage source inverters. The modulation scheme is notable for its ease of digital implementation, especially in the case of multilevel inverters since the number of carriers does not increase with the number of inverter levels.
The operating status of the switches in each inverter leg of Fig. 1 can be represented by switching states. Switching state P indicates that the upper switch of that particular inverter leg is on and the voltage of that phase leg with respect to terminal n of the DC rail is Vdc. Conversely, the state O indicates that the lower switch is on and the corresponding voltage is zero. Since no two switches of the same inverter leg can be on at the same time, we can have eight possible combinations of switching states for a two-level VSI. These are [POO], [PPO], [OPO], [OPP], [OOP], [POP, [PPP] and [OOO]. Among the eight switching states, [PPP] and [OOO] are zero states, while the others are active states.
Conceptually, a set of three-phase waveforms can be represented by a single rotating vector, often called a Park’s vector. This concept can be applied to the three-phase output voltages of the two-level inverter. The active and zero switching states can then be represented by active and zero space vectors, respectively. These space vectors, when drawn graphically, result in a regular hexagon with the active space vectors (V1 to V6) as its vertices, and the zero vectors (Vo) as its centre. This regular hexagon is called the Space Vector Diagram (SVD) of a two-level inverter, and is shown in Fig. 4. The SVD also shows a reference vector Vref, which represents the reference sinusoidal wave desired to be generated by the inverter. The basis of SVM is to generate Vref as closely as possible using the Nearest Three Vectors (NTVs) to the reference vector. Note that the active and zero vectors are stationery vectors whereas Vref is rotating continuously in space at a frequency w rad/s and subtends an angle q with respect to the reference axis. Here w is the desired output frequency of the inverter in rad/s.
The amplitude of Vref decides the amplitude of the fundamental component of the output voltage. It can be expressed as a function of the amplitude modulation index ma, where ma corresponds to the radius of the largest inscribed circle of the space vector hexagon and ranges from zero to one for the linear modulation range. The reference vector is sampled at regular intervals of time. During a sampling interval Ts, Vref and θ are held constant and Vref is synthesized using the NTVs to Vref. The reciprocal of Ts is called the sampling frequency fs (≡ fcr). The ratio fs/f, where f is the inverter output frequency, is called the frequency modulation index mf and decides the inverter output voltage harmonic spectrum as well as the device switching frequency.
The inverter output line-line voltage and its frequency spectrum for mf = 23 and ma = 1 with a DC link voltage Vdc = 200 V with Space Vector Modulation are shown in Fig. 5. Note again that these results are obtained without any output filter. Since the lower order harmonics are eliminated in both the modulation schemes, the output filter size is considerably reduced. The THD of the output current waveform would be even lower on account of the load inductance.
Key Points of Comparison
Utilization of DC link voltage: In case of sinusoidal PWM, the amplitude of the fundamental component of the output line voltage is found to be 172.9 V (peak value) or 122.2 V (rms). Thus, the amplitude of the fundamental component for SPWM is 122.2/200 = 0.612 or 61.2% of Vdc. In case of Space Vector Modulation, the amplitude of the fundamental component of the output line voltage is 199.4 (peak value) or 141 V (rms). Thus, for the case of SVM, the amplitude of the fundamental component is 141/200 = 0.707 or 70.7% of Vdc. Thus, the SVM scheme is able to extract more fundamental component of the output line voltage as compared to SPWM. Specifically, for the same DC link voltage, the output line voltage magnitude for SVM is 0.707 Vdc /0.612 Vdc = 1.155 or 15.5% greater than that obtained with SPWM.
Output line voltage THD: The output line voltage THD values obtained for the two-level inverter without any output filter are 67.73% and 52.99% for SPWM and SVM respectively. Thus, the THD is significantly lower in case of Space Vector Modulation, which is to be expected since the amplitude of the fundamental component of the output line voltage has increased.
Output current THD: Considering a 0.8 lagging power factor load, the output line current THD values are obtained as 3.53% and 2.85% for SPWM and SVM respectively. For the same load, these values correspond to the output line voltage values and are significantly within limits in both the cases. Note that these values are obtained for a frequency modulation index of 23.
Device switching frequency: The number of switchings of each power electronic device in one cycle of the inverter output voltage is equal to the frequency modulation index for both the techniques. Thus, there is no difference between the two techniques as far as device switching frequency is concerned.
Frequency spectrum: Comparison of Figs. 3(b) and 5(b) shows that the SPWM gives a much cleaner frequency spectrum as compared to SVM, even though the THD is greater. This is because the output line voltage in case of SVM is inherently half-wave asymmetric, as a result of which even-order harmonics are also present in the output voltage. However, the harmonics can be eliminated by making some changes in the switching sequence design.
Ease of implementation: SPWM is much easier to implement as compared to SVM as the concept behind it is pretty simple. However, it must be noted that the sinusoidal modulating waves and the carrier wave cannot be generated using digital processors; instead look-up tables have to be used. The accuracy of the generated waves depends on the number of data points in the look-up tables. Also, if carrier-based PWM schemes are used for multilevel inverters, the number of such look-up tables goes on increasing. No such look-up tables are required for SVM implementation. In fact, it is possible to have algorithm based all-digital SVM implementation even for multilevel inverters using techniques such as the g-h coordinate transformation technique.
Design flexibility: There is no flexibility in design afforded by the SPWM technique. However, this flexibility is available in case of SVM wherein it is possible to design the switching sequence as per the requirements of the implementing personnel. There is the option to use which switching states to use, how many segments to have in one sampling period Ts etc. The design options increase significantly in case of multilevel inverters. As such, SVM has been, and continues to be, a favourite for researchers.
Sinusoidal Pulse-Width Modulation is conceptually simpler to understand as well as implement as compared to Space Vector Modulation for DC to AC converters. However, the advantages offered by SVM are significant as compared to SPWM. Even though SVM requires some effort to master it, its advantages in the long run over SPWM make it worthwhile to do so. To an engineer, the design flexibility offered by SVM is also very encouraging and interesting.
Dr. Irfan Ahmed,
Asstt. Professor, Electrical Engineering Department
National Institute of Technology Durgapur,
Durgapur, West Bengal, India
Dr. Altaf Badar,
Asstt. Professor, Electrical Engineering Department
National Institute of Technology Warangal,
Warangal, Telangana, India