# Space Vector

**Topics:**Modulation, Carrier wave, Frequency modulation

**Pages:**8 (1779 words)

**Published:**March 24, 2013

Introduction

Inverters form an important class of power electronic circuits, which convert DC power to AC power. Vintage inverters, realized with Silicon Controlled Rectifiers (SCR), needed bulky components for the commutation of the SCRs. With the advent of power semiconductor technology, modern power devices such as BJTs, MOSFETs and IGBTs replaced SCRs at low and medium power level, as these devices do not require the complex commutation circuitry to turn them off. Of these devices, IGBTs have aroused a particular interest in recent times as these devices inherit the simplicity of control from MOSFETs and superior conduction characteristics from the BJTs.

Two-level Inverters and Modulation Schemes

Inverters built with aforementioned devices have become very popular and were accepted by the industry owing to their simplicity and ruggedness. With the advancements in the Pulse Width Modulated (PWM) control schemes, the harmonic spectrum of the output voltage can be maneuvered to contain a pronounced fundamental component and to transfer the harmonic energy to the components of higher frequency. This is desirable, as it is relatively easier to filter out the components of higher frequency compared to the components of the lower frequency. A typical two-level inverter is shown in Fig.9.1.

Figure 1 A conventional Induction motor drive using a two-level inverter

Sinusoidal Pulse Width Modulation (SPWM) is one of the most popular schemes devised for the control of a two-level inverter. In SPWM, a modulating sine wave corresponding to the fundamental frequency of the output voltage is compared with a

triangular carrier wave of high frequency, which corresponds to the switching frequency of the devices. Each leg of the two-level inverter is controlled by the corresponding modulating wave. The modulating waves for the individual legs are displaced by 1200 with respect to each other as shown in the top trace of Fig.9.2.

Vdc

0

time

Figure 2 Modulating and carrier signals in SPWM for a two-level inverter (Top) and pole voltage v AO (bottom) showing two levels

Thus, the inverter employed in the system shown in Fig.9.1 is a two-level inverter because any pole voltage e.g. v AO assumes one of the two possible values namely 0 (when S4 is turned on) or Vdc (when S1 is turned on) as shown in Fig.9.2.

The ratio of the peak value of the modulating signal and the peak value of the carrier signal is defined as the amplitude modulation ratio (also called modulation index) and is denoted as ma . The ratio of the frequencies of the carrier wave and the modulating wave is defined as the frequency modulation ratio and is denoted as m f . In the range of linear modulation,

0 < ma ma ≥ 0, then nsam = 192

If 0.4 > ma ≥ 0.2, then nsam = 96

If 0.866 > ma ≥ 0.4, then nsam = 48

where ma is the ratio between the length of the

reference voltage vector and the DC-link voltage Vdc

The relationship between the modulation index (ma) and the

number of samples per cycle (nsam)

26

It was stated earlier that the number of samples per cycle are different in different regions and it was shown that:

Ts,pu = √3 / (2 * ma * nsam)

As nsam assumes one of the three possible values namely 48, 96 and192 it follows that the above equation assumes one of the following forms depending on the range of modulation index:

Ts,pu = √3 / (96 * ma ) ; when nsam = 48 i.e. 0.866 > ma ≥ 0.4 Ts,pu = √3 / (192 * ma ) ; when nsam = 96 i.e. 0.4 > ma ≥ 0.2 Ts,pu = √3 / (384 * ma ) ; when nsam = 192 i.e.0.2 > ma ≥ 0 The 4.12f representation for the constants (√3 / 96), (√3 / 192) and (√3 / 384) respectively are 004Ah, 0025h and 0012h.

Hence the 4.12f expression of Ts is given by:

Ts (4.12f) = (004Ah * 212) / ma ; when nsam = 48 i.e. 0DDBh > ma ≥ 0666h Ts (4.12f) = (0025h * 212) / ma ; when nsam = 96 i.e. 0666h > ma ≥ 0333h Ts (4.12f) = (0012h * 212) / mi ; when nsamp = 192 i.e.0333h > mi ≥ 0000h It...

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