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INVERTERS 893<br />

U<br />

DC voltage level<br />

U<br />

DC voltage level<br />

AC voltage<br />

AC voltage<br />

(a)<br />

t<br />

(b)<br />

t<br />

Figure 19.37 (a) Step-down conversion in the forward power-flow mode. (b) Step-up conversion<br />

in the reverse power-flow mode<br />

19.2.4.3.7 Bi-directional step-up/step-down conversion<br />

The concept described above allows reversed power flow only in cases in which the DC<br />

voltage level is always higher than the peak voltage of the AC side, which means that<br />

U DC ≥ 358 V for 230 V AC. However, there are two possibilities to lower the DC voltage<br />

level, that is, to install a transformer at the AC side or to install a bi-directional DC-DC<br />

converter at the DC side. Since a conventional step-down converter, as was described<br />

earlier, is not able to act as a step-up converter in the reversed power-flow mode, either<br />

two converters in anti-parallel mode or a different conversion concept would be necessary.<br />

One topology developed by Cuk [8] in 1977, which is able to fulfil these requirements,<br />

is given in Figure 19.38.<br />

This conversion principle is in fact able to perform step-up as well as step-down<br />

conversion in both directions. The relation between the input voltage U 1 and the output<br />

voltage U 2 becomes:<br />

U 2 = U 1 ·<br />

(t off + t on ) ·<br />

t on<br />

(<br />

1 −<br />

)<br />

t on<br />

(t off − t on )<br />

Switches S1 and S2 operate complementarily, for example, if S1 is on, S2 is off and<br />

vice versa.<br />

L1 R1 C1 L2 R2<br />

U 1<br />

DC input DC output<br />

S1 S2 C2 U 2<br />

Figure 19.38<br />

Bi-directional Cuk converter

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