Environmental Engineering Reference
In-Depth Information
speed the induced voltage
u
i
(
i
m
) is analogue to the flux curve in Fig. 3.7; depen-
dence on the speed is shown in the curve
u
i
,
08
(
i
m
) for 80% rated speed, as an ex-
ample. The linear capacitor voltage function
u
c
(
i
c
), for rated speed and a selected
capacitance value, has an intersection with the machine voltage curve at a stable
working point which is unity in the figure. The machine becomes a self-excited
induction generator (SEIG). Note that the course of attaining this voltage requires
an initial remanent flux which is normally present in the machine. When, with un-
changed capacitance, the speed is reduced to 80% rated value,
u
c
,
08
(
i
c
) applies and
there is no working point and no self-excitation any longer. The same is observed
when at rated speed the capacitance value is reduced to 80%. Consequently for each
speed there is a minimum capacitance required for self-excitation.
Figure 3.12a shows a setup where 1 is a driving motor, 2 is the cage induction ma-
chine, 3 is the capacitor bank, 4 is a switch and 5 an adjustable ohmic-inductive load.
Part b of the same figure is a simplified per-phase equivalent circuit where the induc-
tion machine is represented by the so-called gamma-equivalent model and the stator
winding resistance neglected. Given the magnetization characteristic and the speed
Ω
, see (3.1), voltage and currents can be calculated by a suitable iterative method.
Calculated and measured characteristics of a an example setup with a 7,5 kW, 4
pole, 60 Hz induction machine under resistive load are shown in Fig. 3.13. Note that
without control measures the terminal voltage strongly decreases with increasing
load, and becomes unstable at a specific load dependent on speed and capacitance.
The breakdown reflects the point of maximum available capacitive current as dif-
ference between capacitor and machine reactive currents at a given voltage (see
Fig. 3.11).
The strong dependance of voltage on capacitance would suggest to use variable
compensation. However a stepwise switching of capacitor banks to regulate the volt-
age would not give acceptable results, neither static nor dynamic. Several proposals
have been made to realize adjustable voltage control for SEIG. A simple solution
is to add in Fig. 3.12a a compensation device as shown in Fig. 3.10a1, using a
phase-controlled inductive load parallel to a capacitor. While this is a possible way
to achieve a satisfactory voltage controlled stand-alone supply, modern solutions
using self-controled inverters are far more preferable, see [Chat06].
b)
a)
Fig. 3.12
Self-excited induction generator with passive load (
a
) Circuit diagram; (
b
) Equivalent
circuit with ohmic load only
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