Mumbai University > Electronics Engineering > Sem7 > Power Electronics 2

Marks: 10M

a) The SV-based modulating technique is a digital technique in which the objective is to generate PWM load line voltages that are on average equal to given load line voltages.

b) This is done in each sampling period by properly selecting the switch states from the valid ones of the VSI (Table14.3) and by proper calculation of the period of times they are used. The selection and calculation times are based upon the space-vector transformation.

c) State space vector transformation : Any three-phase set of variables that add up to zero in the stationary abc frame can be represented in a complex plane by a complex vector that contains a real (α) and an imaginary (ß) component.

d) For instance, the vector of three-phase line modulating signals

$ [v_c]_{abc}=[v_{ca} \ v_{cb} \ v_{cc}]^T \\ \; \\ v_c=[v_c]_{a\beta}=[v_{ca}v_{c\beta}] $

can be represented by the complex vector

by means of the following transformation

$v_{ca}=\frac{2}{3}[v_{ca}-0.5(v_{cb}+v{cc})] \\ \; \\ v_{c\beta}=\frac{\sqrt3}{3}(v_{cb}-v{cc}) $

e) are three balanced sinusoidal waveforms that feature an amplitude $\hat{v}$ and an angular frequency ὡ , the resulting modulating signals in the αß stationary frame
$V_c=[v_c]_{\alpha\beta}$ become a vector of fixed module $\hat{v_c}$ which rotates at frequency ὡ (Fig. 14.18).

f) Similarly, the SV transformation is applied to the line voltages of the eight states of the VSI normalized with respect to vi (Table14.3), which generates the eight space vectors (Vi ,i = 1;2;...;8) in Fig. 14.18. As expected, V1 to V6 are non-null line voltage vectors andV7 and V8are null line voltage vectors.

g) Objective : The objective of the SV technique is to approximate the line-modulating signal space Vc with the eight space vectors($V_i$, i = 1;2;...;8) available in VSIs.

h) However, if the modulating signal Vi is laying between the arbitrary vectors $V_i$ and $V_{i+1}$ , only the nearest two nonzero vectors (Vi and Vi+1) and one zero SV (Vz =V7 or V8) should be used. Thus, the maximum load line voltage is maximized and the switching frequency is minimized.

i) To ensure that the generated voltage in one sampling period Ts (made up of the voltages provided by the vectors $V_i , V_{i+1}$ and $V_z$ used during times $T_i , T_{i+1}$ , and $T_z$ ) is on average equal to the vector $V_c$, the following expression should hold

$$V_c.T_s=V_i.T_i+V_{i+1}.T_{i+1}+V_z.T_z$$