Modeling Method for Autonomous Current Inverters

d
and output U
L 
voltages. 
3. Stability of the output voltage when changing the
magnitude and power factor of the load. 
4. Absence of inversion disruptions in case of possible
overloads and frequent starts, etc., and in some cases even in 
case of short circuits in the receiving network. 
5. Ability to work in idle mode.
6. The ability to obtain a sufficiently close to a
sinusoidal shape of the output voltage curve. 
Of the general requirements given in private programs, 
only those points can be used that contribute to the 
disclosure of the set research objectives. 
The paper presents the results of developing a 
methodology to analyse the electromagnetic processes in 
parallel, parallel-to-parallel, series-parallel, serial, as well as 
in inverters with cut-off gates and with two-stage switching. 
The research methodology relies on the regular application 
of the Laplace transform to the corresponding equivalent 
substitution circuits. 
Qualitative analysis of electromagnetic processes in the 
above inverters made it possible to reduce them by the 
number of stages in the repeatability interval into three 
groups.
The first group includes inverters in which one stage 
with a corresponding substitution diagram takes place in the 
repeatability interval. This group includes parallel, parallel 
series and series parallel inverters. 
The second group can include inverters in which two 
stages with equivalent substitution circuits corresponding to 
each stage take place in the repeatability interval. Of the 
inverters considered, this group includes series inverters and 
parallel inverters with additional inductances to limit the 
di/dt of the thyristors. 
The third group includes all inverters with three or 
more stages. These are inverters with cut off gates, with 
two-stage switching and ACI with compensating device. 
The analysis of electromagnetic processes was 
performed for all inverters under generally accepted 
assumptions (gates are ideal, E
d
= cons and i
d
(t) is 
continuous) using the same methodology. 
On the basis of qualitative consideration of the inverter 
operation, the operator substitution diagrams for the stages 
are made. Then, the equations with respect to the images of 
inertial functions i
L
(p) and u
C
(p) are made according to the 
substitution diagram. To select an inverter circuit, the main 
condition is that the type of inverter matches the nature and 
modes of load control. According to this condition, it is 
necessary to determine whether the load is a controlled 
current or voltage controlled, whether the conditions of 
continuity of the supply sources and the load are ensured.
Using the images for currents and voltages i
L
(p) and 
u
C
(p), we find their originals i
L
(t) and u
C
(t). 
Taking into account the boundary conditions (initial and 
final) for each stage and the values of the originals i
L
(t) and 
u
C
(t) at the boundaries of the stages, we obtain a system of 
equations for determining the boundary conditions and 
durations of the stages. 
The system of equations for finding the boundary values 
of inertial parameters is solved. The obtained boundary 
values are used to describe the changes in the instantaneous 
values of currents and voltages on the repeatability interval 
according to the results of step 3. 
Here it should be mentioned, that steps 1-3 are obvious 
and the technique of their regular application can be 
considered to be established [22] also for complex electric 
circuits, what are schemes of substitution of different 
autonomous inverters. 
Further solution of the problem (steps 4, 5, 6) is specific 
to the regularly switched circuits, which are circuits of valve 
inverters and is carried out by different authors in different 
ways. Often just here [22] new simplifications, limitations, 
etc., are introduced, which demonstrate mastery and 
understanding of the problem essence, but destroying 
methodical unity in its solution. By the example of the ACI 
schemes considered below, it is shown that in all cases:
a) on the basis of qualitative study of processes
development on the repeatability interval; 
b) using the results of step 3, - a system of algebraic
equations of connection of all internal (at the boundaries of 
stages) and external (at the boundaries of recurrence 
interval) boundary values of inertial quantities and durations 
of stages can be made. The resulting system is solved 
according to step 5 to determine the numerical values of the 
boundary inertial quantities. They are needed to describe the 
changes of instantaneous values of currents and voltages 
according to step 3, as well as the durations of stages within 
the repeatability interval. 
The 
above 
mentioned 
peculiarities 
of 
electromagnetic processes in the repeatability interval have 
a decisive influence on the type of equation system resulting 
from step 4 of this technique. 
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Thus, when analysing inverters of the first group we 
obtain a system of equations like