Page 259 - Rashid, Power Electronics Handbook

248 J. Espinoza

i ˆ
c

FIGURE 14.31 The space-vector representation in CSIs.

is on average equal to the vector I , the following expressions
c
should hold:
FIGURE 14.32 Possible state transitions in Sector
2 involving a
^
T ¼ T i sinðp=3 ÿ yÞ ð14:56Þ zero SV. (a) Transition: I 1 , I z , I 2 or I 2 , I z , I 1 ; (b) transition:
i
s
c
^
T iþ1 ¼ T i sinðyÞ ð14:57Þ I 1 , I z , I 1 ; (c) transition: I 2 , I z , I 2 .
c
s
T ¼ T ÿ T ÿ T iþ1 ð14:58Þ
z
s
i
to minimize uncharacteristic harmonics. As an example, Fig.
^
where 0 i 1. Although, the SVM technique selects the
c 14.33 shows the relevant waveforms of a CSI SVM for f ¼ 18
sn
vectors to be used and their respective on-times, the sequence ^
and i ¼ 0:8. Figure 14.33 also shows that the ®rst set of
c
in which they are used, the selection of the zero space vector,
relevant harmonics in the load line current are at f .
sn
and the normalized sampled frequency remain undetermined.
14.4.4.2 Space-Vector Sequences and Zero 14.4.5 DC Link Voltage in Three-Phase CSIs
Space-Vector Selection
An instantaneous power balance indicates that
Although there is no systematic approach to generate a SV
sequence, a graphical representation shows that the sequence v ðtÞ i ðtÞ¼ v ðtÞ i ðtÞþ v ðtÞ i ðtÞþ v ðtÞ i ðtÞ
I , I iþ1 , I (where the chosen I depends upon the sector) i i an oa bn ob cn oc
z
i
z
provides high performance in terms of minimizing unwanted ð14:59Þ
harmonics and reducing the switching frequency. To obtain
the zero SV that minimizes the switching frequency, it is where v ðtÞ, v ðtÞ, and v ðtÞ are the phase ®lter voltages as
cn
an
bn
assumed that I lays in Sector
2 . Then Fig. 14.32 shows all shown in Fig. 14.34. If the ®lter is large enough and a relatively
c
the possible transitions that could be found in Sector 2. It can
be seen that the zero vector I should be chosen to minimize
9
the switching frequency. Table 14.6 gives a summary of the TABLE 14.6 Zero SV for minimum
switching frequency in CSI and
zero space vector to be used in each sector in order to
minimize the switching frequency. However, it should be sequence I i , I iþ1 , I z
noted that Table 14.6 is valid only for the sequence I , I iþ1 , Sector I i I iþ1 I z
i
I . Another sequence will require reformulating the zero space- 1
z
vector selection algorithm. I 6 I 1 I 7
2 I 1 I 2 I 9
3 I 2 I 3 I 8
14.4.4.3 The Normalized Sampling Frequency 4 I 3 I 4 I 7
5 I 4 I 5 I 9
As in VSIs modulated by a space-vector approach, the normal- 6
ized sampling frequency f should be an integer multiple of 6 I 5 I 6 I 8
sn