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Mathematical Analysis
When the current flow in the dc link is continuous, the average output voltage
can be calculated as outlined in the previous page. It is difficult to estimate
what the average output would be if there is a source present in the dc link
and the conduction is discontinuous. If there be no source in the dc link,
the average output voltage for discontinuous conduction is expressed by equation
(1). The analysis of the circuit is along the lines described for the single-phase
controlled rectifier circuit. In order to get an expression for the line/phase
current, it is necessary to get an expression for the load current. The expression
for load current is obtained from the expression for output voltage. The output
voltage is described by equation (2).
The differential equation that describes the load current is expressed by
equation (3). The solution is of the form expressed by equation (4). The impedance
of load is Z and the load angle is f. They are
defined as shown in equation (5).
In the equation above, w is the angular frequency in radians/second corresponding
to the source frequency. When the load current is continuous, equation (6)
is valid. Using equation (6), equation (7) is obtained. Solving for A, we
get equation (8). When the conduction is discontinuous, iL(0) =
0 and then A is evaluated as shown in equation (9).
Once the value of A is known, the load current can be found out. From the
load current, an expression for the line current can be obtained. When SCR
S1 is ON, the line current equals the load current. The line current
is the negative of load current when SCR S4 is ON, and it is zero
when neither S1 nor S4 is ON. From the expression of
the load current, the rms value of line current, the rms value of the fundamental
component of line current, the THD in line current, the harmonic spectrum
of line current, the DPF and the apparent power factor can be determined as
outlined in the earlier pages.
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