Page 132 - Modern Control of DC-Based Power Systems

96 Modern Control of DC-Based Power Systems

reliability or ease of maintenance and repair, etc. [2,3]. One basic objec-
tive of parallel-connected converters is to share the load current between
the converters. To achieve this goal some form of control has to be used
to equalize the currents among the converters [4].
An ideal voltage source can always maintain its output voltage at nom-
inal voltage, regardless of the current supplied. If several ideal sources are
connected in parallel, it is unclear which voltage source contributes how
much to the total generation, since theoretically each source can take
over the complete generation (up to the maximum power) regardless of
the voltage level. Theoretically, the source with the highest initial voltage
would take over the complete load. From this theoretical thought it fol-
lows that ideal voltage sources connected in parallel cannot provide load
sharing. Furthermore, the Kirchhoff voltage and current laws have to be
obeyed when connecting sources together. The Kirchhoff voltage law
states that the sum of voltages of all branches forming a loop must be
equal to zero. This again means that two ideal voltages sources cannot be
connected in parallel, even if the voltage sources would be theoretically of
the same magnitude, the current values would be undefined [5].
Kirchhoff current law dictates that the sum of currents in a node must
equal zero. While in practice ideal voltage and current sources do not
exist, power electronics controller power sources are a very close approxi-
mation of this behavior.
A real voltage source, on the other hand, has an internal resistance
that drops the voltage as the current increases. Normally this is undesired
as a voltage level independent of the current is requested: on the other
hand, the resistive effect creates automatically a power sharing effect. In
effect, it can be shown that the power sharing is dependent on the value
of the internal resistance. Acting on the slope of the characteristic allows
the power sharing to be refined.
While adding a resistance in series to the source is not a practical
approach because of the induced losses, simulating the resistive behavior
with the control brings the sharing capability and no physical losses. This
type of regulation is called the Voltage Droop control. In summary, this
means that the output voltages of the voltage sources connected in parallel
have a linear correlation with the power or current generated.

3.6.1 Voltage Droop
In general, a voltage/current dependence can be created by adding in
series a virtual output impedance, which corresponds to an increase in