STUDY OF THE TRANSIENT PROCESS LENGTH IN A STEP VOLTAGE REGULATOR
BARUDOV Emil, BARUDOV Stefan and PANOV Emil
Technical University – Varna, 9010, No.1 Studentska str.
Email: ugl@abv.bg
Abstract: The voltage of the individual consumers in limited power networks can be maintained within the allowed boundaries by automated step changeover of an autotransformer. Examinations of the length of the transient process as a function of the switching phase and the character of the load – R, RL or RC, were carried out.
Keywords: step changeover, autotransformer, regulator, model, load, switching phase
Introduction: There are electrical networks where the phase voltage varies far above the allowable limits depending on the operational modes of some of the ultimate consumers. This forces application of individual regulation of the phase voltage directly at the very consumers. The regulation can be effected by stepwise automated changeover of the autotransformer terminals. The general principles related to the solution of similar problems are discussed in [1...4].
The paper presents the results of examination of the length of the transient process as a function of the switching phase of the thyristors of a respective booster element (buck converter), accounting the load character (active, activeinductive or activecapacitive). The applied mathematical model, the limitations and assumptions are indicated in the references [5]. Fig 1 presents the blockdiagram of a monophase step voltage regulator, where ÁÊ is a switching block consisting of four switches K. ÀÒð is a booster transformer with terminals for changeover and Z_{T} is a load. Figures 2, 3, 4, 5 present the equivalent circuits of the examined regulator for the three time intervals. The determination of the parameters of the equivalent circuit elements is according to [5].
The transient process should be considered within three intervals:
First interval – the voltage drops from 170V to 165V, Ê_{3 }open, Ê_{2} closed, Ê_{1} and Ê_{0} open (the last but one level of the regulator is activated).
Second interval – Ê_{3 }closes with phase delay from zero e(t), but Ê_{2} is not opened – there is interwinding short circuit.
Third interval – Ê_{3 }is closed and Ê_{2} opens when the current i_{4}(t) becomes zero
Fig 2 shows the voltage regulator with the existing magnetic links among the separate autotransformer sections. The description of the electrical equilibrium of the voltage regulator is made according to the meshcurrent method as it leads to a minimal order differential equation systems. The examination was made for R, RL or RC loads with the assumption that Ê_{0} – Ê_{3} are ideal switches, which gives sufficiently accurate image of the processes.

Fig.1 Block diagram of a monophase step voltage regulator. 
The systems of differential equations (1), (2) and (3) describe the electrical and magnetic processes in the studied time intervals. They are resolved by solving the first system (1) according to GaussJordan method in the complex – frequency domain. The second and third systems (2) and (3) are solved by Euler method of numerical solution of system of differential equations.
1. Steady state mode at (first interval).
(1) 

2. First transient process after switching of K_{3} (second interval).
(2) 

3. Third interval – after the switching of K_{2}.
(3) 

A program AVTO1 under MATLAB was developed for determination of the response of a voltage regulator during transition from 170V to 165V, for active, activeinductive and activecapacitive loads, respectively. The program allows to define the length of the transient process for various switching phases (second interval) from 0^{î} to 360^{ î} , with a step of 22,5^{ î} . The load values for the respective mode of operation are presented in Table 1.
Table 1
Load 
Graphic
symbols of the results for the respective load 
R_{T},
Ω 
L_{T},
H 
C_{T},
F 
R 
* 
R_{T}=3,3846Ω 
 
 
RL 
* 
R_{T}=3,0675Ω 
L_{T}=4,5531.10^{3}H 
 
o 
R_{T}=2,3933Ω 
L_{T}=7,6181.10^{3}H 
 

x 
R_{T}=0,8760Ω 
L_{T}=10,4064.10^{3}H 
 

RC 
* 
R_{T}=3,0675Ω 
 
C_{T}=2,2253.10^{3}F 
o 
R_{T}=2,3933Ω 
 
C_{T}=1,33.10^{3}F 

x 
R_{T}=0,8760Ω 
 
C_{T}=9,7364.10^{4}F 
The following regularities were observed during the computer simulations for the studied switching of the voltage regulator:
There is a symmetry of the results in the intervals 0^{î }... 180^{î} and 180^{î} ... 360^{î}
In case of active load, the length of the transient process is largest at φ=22,5^{î} and 202,5^{î}
and is shortest at φ=0^{î}, 180^{î} and 360^{î}.
At activeinductive load, the length of the transient process is largest for the case:
“õ” – Z_{T}=3,3846.e^{+j75o}Ω, for almost all phases φ and is smallest for:
“*” – Z_{T}=3,3846.e^{+j25o}Ω , for almost all phases.
At activecapacitive load, the length of the transient process is largest for the case:
“*” – Z_{T}=3,3846.e^{j25°}Ω for most of the phases and is negligibly small for
“õ” – Z_{T}=3,3846.e^{}^{j75}^{°}Ω.
Figures 6, 7 and 8 show the graphs of the dependence of the transient process from the changes of the switching phase of the thyristors for active, activeinductive and activecapacitive loads respectively.


Fig.2 Equivalent diagram of the step voltage regulator 
Fig. 3 Equivalent diagram for the first interval of the transient process. 


Fig. 4 Equivalent diagram for the second interval.. interval of the transient process. 
Fig. 5 Equivalent diagram for the third of the transient process 


Fig 6 Dependence of the switching time from the change of the switching phase for active load. 



Fig. 7 Dependence of the switching time from the change of the switching phase for activeinductive load. 



Fig. 8 Dependence of the switching time from the change of the switching phase for active capacitive load. 
CONCLUSIONS
The suggested model and the analytical examinations allow to define the length of the transient process depending on the switching phase and the type of the load. The experimental investigations of specific values of the phase and the load show sufficiently good correlation with the results of the computer simulation of the transient processes.
The study of the transient processes and their length is of great importance for determination of an operational mode with shortest transient processes. This is related to the regimes with most reduced loads to the switching elements and the regulator.
The suggested method can be used for calculation of booster step regulators (buck converters) for various power and operational modes. This gives rise to the idea for development of a specialized logic controller, which by tracking of the character of the load could allow switching only in the most favorable time periods, determined by the minimal risk of overloading or breakdown of the elements.
REFERENCES
[1] Minchev Ì., Penchev P. Contactless Apparatuses, Technika 1976 (in Bulgarian)
[2] Porudominskiy V. Switching Devices for Transformers under Load, Energia 1974 (in Russian)
[3] Lipkowskiy Ê. TransformerSwitching Actuator Structures of the Alternating Current Converters, Naukova Dumka 1983 (in Russian)
[4] Barudov St., Dimitrov D, Barudov Em. Functional Performance of Transformers in a Contactless Voltage Stabilizer SIELA 2001 (in Bulgarian)
[5] Barudov Em., Barudov St., Panov Em. Study of the Length of the Transient Process in a Step Voltage Regulator. Annual Scientific Session 2003 of the Technical University Varna