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2021, 10, 115
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between the generator and the load. Large disturbance stability analysis over the long
term necessitates the investigation of dynamic interactions of power line characteristics,
tap changing transformer operation, and load dynamics. On the other hand, small distur-
bance voltage stability analysis is investigated for the load dynamics and system control
methodology for governing V-Q sensitivity. A network with X
R is usually stable where
dQ
dV
is positive.
2.4. The Effect of Load Dynamics
Besides disturbances in the network, load dynamics affect the voltage instability. Load
dynamics depend upon several parameters such as the power factor or variation of active
and reactive power flows with voltage and frequency. Usually, a microgrid with a constant-
impedance static load has stable dynamics. Conversely, a microgrid with a constant-power
load (CPL) may become unstable due to incremental negative impedance, which may
result in the collapse of the load bus voltage. Many loads like motor drives or electronic
loads with closed-loop power electronic converters behave as CPLs. On the other hand,
the open-loop converter behaves like a resistive load [
53
]. During a small disturbance,
the load current increases to keep the constant power output and at the same time, the
load voltage will decrease. In case of an improper converter control, the load voltage may
drop to very small values close to zero and may lead to complete voltage collapse [
54
].
Fault-induced delayed voltage recovery (FIDVR) is also a factor in the voltage stability of
microgrids having high penetration of inductive loads. Induction motors under stalling
condition may absorb up to three times their nominal reactive power to re-magnetize. The
insufficient reactive power supply in such cases leads to system voltage instability. An
effective strategy to improve voltage stability in a microgrid with multi-induction motor
(MIM) loads was proposed by applying methods of superimposed starting strategy and
fast motor cutting strategy [
55
].
Even though load shedding is proposed in many cases to improve the dynamic
voltage stability, it is not a desirable solution in many cases. If the loads are supplied by
transformers with automatic under load tap-changing (ULTC), when the voltage decreases,
the tap-changer action will try to raise the load voltage. This effectively reduces the
impedance as seen from the system. This in turn can lower the voltage regulation and may
lead to a progressive reduction of the voltage, which in some conditions may eventually
move towards a voltage collapse.
For a constant sending-end voltage, a sudden reduction in the receiving-end load
lagging power factor (i.e., an increase in receiving-end load reactive power) can cause
the system to change from a stable operating condition to an unsatisfactory and possibly
unstable operating condition [
56
], as shown in the P-V curve in Figure
3
, with comparison
of the curve related to cos ϕ
=
1.0 with the curve related to cos ϕ
=
0.95 lag.
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