RADIO ELECTRONICS AND ANALYSIS OF METHODS FOR AUTOMATED RESEARCH OF DC VOLTAGE CONVERTERS OF MODULAR STRUCTURE

Context. DC voltage converters (DCV) are part of modern power supply systems (PSS) and power supply ensuring the operation of electronic and radio devices, telecommunication systems and communication and to a large extent determine their power consumption, reliability, time of readiness for operation, weight, size and cost indicators. Even though there are a large number of different software packages used in engineering practice for the study and design of radio engineering devices, such computer-aided design (CAD) systems and virtual computer simulation of electronic circuits have some limitations that do not allow to quickly carry out the entire complex of studies of DCV required for the analysis of electrical processes in various operating modes. Objective. In this section, the goal is to select the most suitable methods and algorithms that allow the development of software necessary for solving the problems of research and analysis of electrical processes for select energy parameters of the DCV of a modular structure in a separate power channel (PWC). Method. The paper proposes a method that consists in using mathematical models describing electrical processes in DC voltage converters and creating, on the basis of the developed calculation algorithms, specialized software for the automated study of electrical processes in the DCV of a modular structure using a computer. Results. The paper discusses the main methods of automated research of radio engineering devices, which can be used to analyze the electrical processes of pulsed DC voltage converters of a modular structure. Algorithms of calculation are given and, as an exam-ple, some results of automated research obtained using this method. Conclusions. The analysis of the known methods of automated research of DC voltage converters of modular structure is carried out. Their advantages and disadvantages are given. It is shown that the most suitable method is based on the use of mathematical models describing electrical processes in DC voltage converters of this type. On the basis of the mathematical models presented in the second section of the work, algorithms and specialized software have been developed that allow them to be widely used in the automated research and design of modular-structured DC voltage converters.

N max is a maximum number of power channels DCV; С in is a capacitance of the input filter capacitor; С out is a capacitance of the output filter capacitor; Ū in is a relative supply voltage; R r is an operating mode -stabilization (tracking); R p is a conversion mode -SPC (MPC); P out mode is a type of calculation: P out = const, (P outk = const); R outk is a load resistance k-th PWC; P outk is a load power k-th PWC; f ak is an accumulation factor k-th PWC; f rk is a return factor k-th PWC; U ink is an input voltage (power supply) k-th PWC; f bk is a boundary value of the converting frequency; Т k is a converting period; I m1k is a choke current ripple PWC on the accumulation interval; I m2k is a choke current ripple PWC on the return interval;

INTRODUCTION
Modern DCV of power supply and power supply systems, as a rule, use the high-frequency (pulse) principle of power conversion. This allows you to create devices and systems with higher power density and characteristics that are unattainable using other methods.
The modular structure of the construction of pulse DC voltage converters from N of the same type of interchangeable PWC simultaneously operating on a common load provides increased reliability, reduced manufacturing labor intensity, and increased level of unification and standardization of DCV. The use of the modular principle of construction of the DCV contributes to solving issues of redundancy, increasing the reliability of converters, increased manufacturability, adapting to changes in their operating modes, and saving energy.
In the study and computer-aided design of radiotechnical devices, simulation of their operation on a computer is widely used today, when instead of expensive long-term experimental testing of electrical energy converters on breadboards, research using mathematical models describing the processes of the devices under study is used. Therefore, in the work are selected: The object of study is the electrical processes in pulse DCV of modular structure.
The subject of study is automated methods for studying the electrical processes of modular DCV. The purpose of the work is to develop the methods and algorithms that allow the development of software necessary for solving the problems of research and analysis of electrical processes for select of energy parameters of the DCV modular structure.
To achieve this, it is necessary to solve the following tasks -to analyze modern methods of automated research of radio engineering devices, using the selected mathematical model to develop algorithms and software for solving the problems of research and analysis of electrical processes DCV and to analyze the obtained results.
To carry out a set of necessary studies, the software must ensure the study of converters with SPC and MPC principles of converting electrical energy, the results of which are necessary in the design in order to improve the technical and economic indicators of the DCV.

PROBLEM STATEMENT
Mathematical models described in [1,2,3] describing electrical processes in a separate power channel and the converter as a whole, allow investigating the dependences: currents and voltages in the PWC elements, in its supply circuits and the load of the converter at a given operating mode. This makes it possible at any time to determine the magnitude of instantaneous currents, their maximum and minimum values, as well as the magnitude of the absolute and relative ripple of voltages and currents at the input and output of the DCV, respectively, with the SPC and MPC, as well as other electrical and energy parameters of the modular structure converters required to select the optimal parameters of the elements, operating modes of the power unit and control algorithms.
The indicated mathematical models also allow us to construct the dependences of the quality indicators of the electrical processes of DCV and energy parameters on the value of the values of the accumulation factors f a and the transformation coefficient n 21 , the numbers N of PWC and other parameters for different modes of operation [1].
These dependencies make it possible to identify the features of electrical processes (for example, under different operating modes) with other parameters unchanged (N, L k , С k ) and to assess the degree of influence of one parameter or another on the nature of the dependence in the entire control range, both in any individual PWC, as well as and in the converter as a whole (Fig. 1). Thus, the software package for the study of DCV should solve the following main tasks, which are presented in the form of an information model ( Fig. 2): 1. Calculation of basic parameters; 2. Calculation of parameters in the time domain (timing diagrams of voltages and currents in the power section, as well as in the input and output circuits of the PWC and DCV); 3. Investigation of the parameters of electrical processes (values of voltages and currents on the elements of the power section of the DCV); 4. Study of quality indicators of electrical processes (absolute and relative values of voltage and current ripple in the input and output circuits of the DCV); 5. Investigation of energy parameters (values of operating currents, power losses on the elements of the power unit, efficiency factor of the DCV).

REVIEW OF THE LITERATURE
In the process of automated research and design of electronic devices, as a rule, it is necessary to use a whole set of different software packages. Many sources provide descriptions and examples of modeling electrical processes of radio engineering devices using well-known CAD systems [7,8,9]. For example, at the stage of developing a structural diagram, programs such as SysCalc, System View, Simulink, LabView can be used. And when creating schematic diagrams -PSpice (as part of the Des-ignLab package), Micro-Cap, Electronics Workbench, and when designing UHF devices such specialized programs as Super Compact, Touchstone, Aplac and others [1,2,4,8,9].
These software products allow engineering studies to create, edit schematic diagrams and make a calculation of a number of parameters, calculate frequency characteristics and transients, perform a variety of device analyzes, and implement other service functions [3,5,6].
However, having some limitations, such software products do not allow to fully serve as a tool for researching voltage converters. All these programs are quite expensive and universal, and, as a rule, do not allow complex studies of several parameters at the same time. Also, the construction of dependencies in a relative form, for example, such as the ripple coefficients of voltages and currents, efficiency and other parameters, becomes much more complicated [3,6,7,9]. Therefore, to study and analyze the specified parameters of various converter circuits under different operating modes, it is required to create specialized software -a software package (SP), which allows, using a mathematical model [2,3,8] describing electrical processes in the DCV, to carry out all the necessary calculations to solve the problems of automated research and design of converters of modular structure.

MATERIALS AND METHODS
When developing such a software package, the allocation of individual software modules -subroutines (SR) is used to calculate the parameters corresponding to the tasks being solved [2,3,5,9]. This is due to the fact that the main computational procedures and operations that make up the individual stages of research should be interconnected and not be duplicated when solving various research problems, which contributes to the reduction of computational operations. Thus, a unified software algorithm can be represented as a set of software modules that will create the most clear and rational software structure.
As a result, the following basic requirements for a software package for studying converters of a modular structure can be distinguished: 1. The rational structure of the software information model, reflecting information links between individual SR when solving research problems, which helps to reduce time costs and resources for software development.
2. The software must ensure the study of the DCV at various parameters of the PWC elements and the selected operating mode for the SPC and MPC.
3. Availability of a separate software module (control program) to control the operation of the software complex (selection of research tasks, change of initial data, providing information links between individual SR at a given stage of research), using the same initial data and calculated relationships of the used mathematical model.
In accordance with the tasks solved by the software package for the study of DCV (Fig. 1) [2,3,5], the following parameters are related to the simulation results: 1. To study time dependences -instantaneous values of currents and voltages in the input i ink (t), u ink (t) and output i outk (t), u outk (t) circuits of a single k-th PWC, their total values for the DCV i s.in (t), u s.in (t), i s.out (t), u s.out (t) at SPC and i мsk (t), u мs (t), i м.out (t), u м.out (t) MPC.
2. To study the dependencies of the quality indicators of the electrical processes of the DCV on the values of the accumulation and transformation coefficients, the value of the output power, the relative supply voltage and load, the number of power channels, and other parameters: -absolute ripple of currents ΔI ink , ΔI outk , ΔI s.in , ΔI s.out , ΔI м.in , ΔI м.out and voltages ΔU ink , ΔU outk , ΔU s.in , ΔU s.out , ΔU м.in , ΔU м.out , respectively, at the input and output to the PWC and DCV during SPC and MPC; -the ripple coefficients of currents C rs.in , C rs.out , C rm.in , C rm.out and voltages C rs.inu , C rs.outu , C rm.inu , C rm.outu at the input and output of the DCV at the SPC and MPC, respectively; -smoothing factor of the converter for current S i and voltage S u ; -smoothing coefficients of the structure at the input S in , S inu and the output S out , S outu in terms of current and voltage; -adjusting characteristics (U in /U out =f(f a ) or U out /U in =f(f a )).
In this case, the smoothing coefficient is determined by the ratio S i =C r.in /C r.out , S u = C r.inu /C r.out is used to characterize the efficiency of suppression of alternating currents or voltages in a device that has a filtering effect (for example, a rectifier, converter, filter), where C r.in , C r.out , C r.inu , C r.outu -ripple coefficients, respectively, of the input and output current or voltage at the input and output of the DCV.
Smoothing coefficients of the structure of a modular converter in the power supply circuits S in , S inu and loads S out , S outu in terms of current and voltage characterize the efficiency of suppression of alternating components in the MPC, relative to the similar case of the SPC in the corresponding circuits of the converter. For SPC S in =S out =1, S inu =S outu =1 [7,8]. For MPC S inм , S outм can be used as indicators characterizing the efficiency of smoothing the relative decrease in variable components in the MPC in comparison with the SPC made of the same number N PWC [6,7].
3. To study the energy parameters of converters, which include: -effective values of currents on PWC elements I Cinke , I S1ke , I L1ke , I VD1ke , I L2ke , I L12ke , I Coutke , their total values for DCV I S1e , I L1e , I VD1e , I L2e , I L12e , while the effective values of currents of capacitors of input and output smoothing filters during SPC and MPC will be different (in MPC, the maximum value of the corresponding currents is less) and I Cinмe < I Cinse and I Coutмe < I Coutse .
-power losses on PWC elements P Cink , P S1k , P L1k , P VD1k , P L2k , P L12k , P Coutk , their total values for DCV P S1 , I VD1 , P L1 , P L2 , P L12 , while power losses on capacitors of input and output smoothing filters during SPC and MPC will be different and (P Cм = P Cinм + P Coutм ) < (P Cs = P Cins + +P Couts ).
-the coefficients of efficiency of the power channel η pwck and the converter of modular structure at SPC η spc and MPC η mps .
Based on the foregoing, the tasks solved by the developed software will be a set of interconnected functional blocks, which are presented in the form of an information model, Fig. 2. With an automated study of converters of modular structure in accordance with the information model ( Fig. 2), the software package allows you to: 1) study of the parameters of electrical processes in the time domain for various parameters of the elements, operating modes of both a single PWC, and the DCV as a whole; 2) a study of the influence of the magnitude of the values of the initial data and basic parameters on the quality indicators of electrical processes (on the absolute and relative pulsations of voltages and currents in the input and output circuits, and the smoothing coefficients) of the converter; 3) study of the influence of changing the number N of the PWC of the converter on the quality indicators of the electrical processes of the converter. 4) study of the influence of changes in these parameters on the energy performance of the DCV in different modes of operation.
In accordance with the tasks of the study of the DCV, the following functions of the investigated parameters have been identified, which are necessary to assess the quality of electrical processes, energy parameters in the PWC elements, as well as in the input and output circuits of the converter ( To solve each of the tasks of the automated research, the "Control program" [4] is used, which controls the computational process, as well as the input of the initial data, the output of the calculation results, including the construction of graphs of the selected dependencies. The control program carries out the required research using separate functional (depending on the tasks to be solved) program modules, implemented in the form of dynamically linked libraries [4]. During research, the con-trol program uses a set of software modules in the form of dynamic libraries containing a set of tools necessary for solving a particular problem.

EXPERIMENTS
To perform these studies using a computer, it is advisable, on the basis of an analysis of all the calculated ratios and the formulated research tasks, to divide the entire process of calculating the processes and parameters of the converter into a number of independent tasks. Next, distribute them (Fig. 3) by type of research and for each problem to be solved, compose a calculation algorithm, on the basis of which the software should be implemented in the form of appropriate subroutines. After that, it is necessary to combine all the subprograms into a single software complex for the study of DCV, consisting of software modules with various tasks to be solved.
Let us consider in more detail, taking into account the adopted approach -separation into a separate software module -a module for calculating basic parameters that are common for any type of research.
Let's select separate subroutines (SR), which are part of the algorithm for studying the DCV (Fig. 3), implemented in the form of a dynamically connected library: 1) SR "Calculation of basic parameters" serves for preliminary calculation of parameters and their prepara-tion as initial data for calculating the investigated quantities (block (bl.) 3, Fig. 3); 2) SR "Time dependencies" for calculating timing diagrams (bl. 11, Fig. 3) both in the circuits of a separate power channel, and at the input and output of the converter as a whole (Fig. 1); 3) SR "Quality indicators" (bl. 10, Fig. 3) for calculating the dependences on the accumulation coefficient (with the possibility of changing the number N of PWC, bl. 5, Fig. 3 and the transformation ratio n 21 -bl. 6, Fig. 3) quality indicators (Fig. 3) of the electrical processes of the DCV (absolute pulsations, pulsation coefficients, smoothing coefficients); 4) SR "Energy parameters" (bl. 9, Fig. 3) for calculating the effective values of currents in the elements of the PWC, the converter, as well as the efficiency at different values of the accumulation coefficients f a and transformation n 21 , values, output power P out and various the number N of power channels of the DCV.
The algorithm of the software complex for the study of DCV contains the following blocks and subroutines: After the start of the program (bl. 1) of the algorithm (Fig. 3), in bl. 2, the initial data are entered: the parameters of the elements, the required type of research, the required type of dependence that needs to be obtained. Depending on the selected type of study, the type of dependence in the subroutine (bl. 3), the basic parameters  are calculated, which are used in the corresponding calculations (time dependences, quality indicators or energy parameters) in the PWC or DCV. In bl. 4, depending on the given type of the investigated dependence, the computational process branches out: bl. 5, if the selected dependence on the accumulation coefficient -f(f a ), or bl. 6, dependence on the transformation ratio -n 21 or bl. 7, if the study of time dependences f (t) is selected. The specified bl. 5, bl. 6, bl. 7 are the beginning of the corresponding cycles for the selected type of dependence. For example, for dependence on the accumulation coefficientf(f a ), in bl. 5, its minimum f amin and maximum f amax values are determined, as well as the step Δf a , with which the accumulation coefficient will change. The accuracy of the calculation depends on the size of the step interval Δf a . With an increase in Δf a , the error increases. A decrease in Δf a in order to increase the calculation accuracy leads to an increase in the calculation time.
In addition to calculating the parameters of elements and plotting dependencies, it is important to study the characteristics of the device under various operating modes and when changing the parameters of the elements.
To create the software, the calculation method was used [4], while the study of electrical processes is implemented in the form of an array of input data elements and the corresponding array of elements of the calculation results, that is, in the form of a function Y m =f(X n ) where Y is an array of calculation results, X is an array initial data, m -element number in the array of calculation results, nelement number in the initial data array. This makes it possible at the program level to separate the study that operates with the values of m and n from the mathematical model using the corresponding arrays of initial data -X and calculation results -Y. In this case, the control program is universal, and the change in the applied purpose of the study can be carried out by replacing the mathematical model and arrays X and Y, which are implemented using a separate dynamically linking libraries (DLL) program module. Therefore, to carry out any research using a universal control program, it is sufficient to create additional DLL [4].
The principle of operation of a specialized program for research is to calculate the array of results in the main function using the appropriate subroutines (the required set of DLL) based on the array of initial data and basic parameters (Fig. 4) [4].
To carry out automated studies of the DCV, a program was used that allows you to work with DLL [4]. At the same time, the program itself is not tied to a specific mathematical model and can be used to study a wide range of technical devices. Changing the application purpose of the program is done by replacing the dynamic library file (mathematical model).
The algorithm of the program for the research is described in detail in [4]. This control program, being a universal one, allows to carry out a wide range of automated studies of DCV in accordance with the mathematical model implemented in the DLL. When studying converters in the time domain, as well as the influence of the value of the accumulation coefficient -f a , the transformation ratio -n 21 and other parameters on the quality indicators and energy parameters of the DCV of the modular structure of construction, several directions can be distinguished: 1) Investigation of the influence of these parameters on the quality indicators of the DCV at a constant load power, when the load power P out =const, and the consumption and load current of the k-th power channel is N times less than the total current of the DCV P out =I out U out , P outk =P out /N = (U out I outk /N)U out , I outk =I out /N. Such a construction of converters allows you to build converters from low-power (low-current) and, accordingly, cheaper element base with better dynamic characteristics. Here, the output voltage and load current of the converter are taken as the initial data, and the load resistance will be determined as R out = U out /I out , and in the k-th power channel it will be R outk = U out /I outk or R outk = R out ꞏN.
2) Investigation of the influence of the above parameters on the quality indicators of the DCV with a constant power P outk =const of the k-th power channel. Then the load power will increase with an increase in the number of power channels P out = NP outk = (I outk U out ) N. Such a construction of converters allows unifying the converter modules and increasing its power by connecting additional modules. Here, as the initial data, the voltage U out and the current I outk of the load of the k-th power channel are taken, and the load resistance of the k-th power channel will be determined, as shown in Table 1, and in the DCV it will be R out = R outk ꞏN. For both single-phase and multiphase converters at the boundary mode of operation [5,6], the regulation (stabilization) of the output parameters occurs by changing the frequency and duration of the control pulses, which compensate for the change in the parameters of the input voltage and load resistance. But at the same time, the frequency in individual power channels remains the same.
When researching converters of a modular structure (when the number N of power channels is increased, connecting them in parallel to each other, their equivalent inductance changes, and therefore the conversion frequency f b , therefore the results obtained in this way are incorrect. conversion f b it is necessary to ensure a constant value of the equivalent inductance of the choke. When the power channels are connected in parallel to the total load, the resistance R out (current I out ) of the load will be evenly distributed between the k-th power channels at a constant load power, when the load power P out =const, (R outk = R out N) and, accordingly (I outk = I out /N).
The frequency of converting the DCV is determined by the parameters of the inductances of the chokes L1 k and the load resistances R outk in separate power channels. However, from [5] it follows that with a change (power P out ), resistance R outk , at the same value of the inductance of the choke L1 k , the conversion frequency f a will change accordingly.
So, the increase in the number N of power channels connected in parallel with each other at a constant value of the load power (P out = const) of the converter will not cause a change in the conversion frequency (f b ), since the frequency is proportional to the value R outk /(2ꞏL1 kN ), where L1 kN -the equivalent inductance of the choke L1 kN = L1 kNmax /N, which is obtained when forming the equivalent circuit of the DCV from, for example, N max = 8 the number of power converter modules of the same type containing N equivalent power channels with the same parameters of the elements of the power channels (Fig. 5).
In order to conduct research on converters of modular structure at a constant value of the conversion frequency f b , it is necessary to change the inductance L1 k of the chokes in proportion to the change in the resistance R outk (power P outk ) of the load [5].
At the same time, to study converters of modular structure with single-phase and multiphase principles of transformation in the boundary mode of operation, an algorithm (Fig. 9) and a technique for calculating the basic parameters are used [5].
Let us take the following assumptions: with a singlephase conversion principle, the PWC of the converter operate synchronously and in phase, and all chokes, as connected in parallel, can be replaced with an equivalent choke L1=L1 k /N. Thus, a single-phase pulse converter of N modules connected in parallel with each other -PWC (Fig. 5a, 6a, 7a) can be considered as one power module (Fig. 5b, 6b, 7b), with an equivalent inductance L1 with the corresponding total currents in its circuits.
It should be taken into account that the distribution of the load resistance and inductance of the choke will be carried out in the SPC and MPC differently.
Depending on the direction of research, the inductance of the choke, the load resistance and, accordingly, the currents in the circuits (equivalent - Fig. 5b), 6b), 7b) of the converter will be redistributed in different ways. In this case, it should also be taken into account that if the research is carried out at a constant value of the load power P out = const, regardless of other conditions, then with an increase in the number N of parallel-connected power channels, the value of the total currents in the consumption circuit I in and load I out , as well as their average values will not change. And the currents in the circuits of a separate k-th power channel will be N times less than the value of the indicated total currents of the DCV.
In this case, the inductance of the choke will be distributed to N power channels L1=L1 k /N. For example, in a single-phase converter of a modular structure of 8 parallel-connected PWC with inductance of chokes in separate power channels L1 k = 100 μH, the equivalent choke L1 will have inductance L1 = 100/8 = 12.5 μH.
When forming, for example, N max = 8, the number of power converter modules of the same type containing N equivalent power channels with the same parameters of elements, their equivalent circuits can be considered as a converter with N equivalent chokes L1 kN = L1 kNmax /N and resistances R outkN = R outkNmax ꞏ/N k-х equivalent PWC.
If we replace the chokes L1.1, L1.2, …L1 k , …L1 N of the converter of N power channels with equivalent L 1kN , for example, for N max = 8, it can be seen that it is possible by combining them to form a converter with the number of N equivalent power channels (1 ≤ N ≤8) -8-channel, 4channel, 2-channel and SPC of 8 PWC. This approach is illustrated in Figure 8, where it is shown how, on the basis of the DCV of 8 PWC N max = 8, an equivalent DCV is formed with parallel connection of the chokes, while ensuring the constancy of the conversion frequency f b . Table 1 shows how the equivalent resistances R нkN and inductances L1 kN will be determined when forming N channel converters of eight (N max = 8) identical k-th PWC. Table 1 -Equivalent resistances and inductances of the SPC at N max = 8 Carrying out research for SPC and MPC in different modes of operation with a different number of N PWC, provided that (P out =const, I out =const, R out =const) and in order to ensure the constancy of the conversion frequency, the calculations must be carried out as follows: The initial data in this case will be the parameters of the DCV -the output voltage U out , the load current I out , the number N PWC and the inductance of the choke L1.
Calculation results: -DCV output power -P out = I out ꞏU out ; -Load resistance DCV -R out = U out /I out ; -Output power of the k-th PWC -P outk = P out / N; -Load resistance of the k-th PWC -R outk =(P out ꞏN)/N max ; -Load current of the k-th PWC -I outk = U out /R outk ; The inductance of the choke of the k-th PWC L1 k =(L1ꞏN)/N max , where N max is the (basic) maximum number of PWC from which the DCV is formed. For example, as shown in Figure 8, N max = 8. Table 2, the main (basic) parameters of inductance, resistance, power and current of the k-th power channel corresponding to the indicated type of research are given, with P out =const.

Further in
When conducting a study of the dependences of quality indicators on the parameters of the elements of the power channels in various modes of operation with a different number N of PWC, provided that (P outk =const, I outk =const, R outk =const) with the same constant frequency as in the previous case conversion f b , calculations must be carried out in accordance with Table 3.
The initial data in this case will be the output voltage U out , the load current I outk of the k-th PWC, the number N of power channels and the inductance of the choke L1.
Calculation results: -Output power of the k-th PWC -P outk = U out ꞏI outk ; -DCV output power -P out = P outk ꞏN; -Load current DCV -I out =I outk ꞏN; -Load resistance of the k-th PWC -R outk = U out /I outk ; -Load resistance DCV -R out = U out /I out ; -The inductance of the k-th PWC choke L1 k =L1.
Taking into account the foregoing, the following algorithm for analyzing the electrical processes of the DCV with increasing N number of power channels with a constant power of the k-th PWC P outk = const (proportional increase in the output power of the DCV and at a constant load power P out = const (implementation of the DCV from a larger number N of power channels of lower power). Thus, the equivalent inductance L1 kN and the resistance R outkN of the k-th power channels will be determined differently (Tables 2, 3).
To obtain correct results, it is necessary to take into account the indicated features of calculating the parameters of the DCV when studying the electrical processes of the converter, both in the time domain and the dependences on the accumulation coefficients (f a ), transformation (n 21 ), the value of the relative supply voltage (Ū in ), the number N of power channels and value of output power (P out ) of the DCV.
For all the specified studies of the DCV, the basic parameters U in , Т, f b , L2 k , R outk , R out , I in , P in , P out , I m1 , I m2 necessary for carrying out the necessary studies will be calculated in the SR, the conditional name of which is "Basic parameters" The initial data in the SP for calculations will use the parameters presented in Table 4. The main basic parameters of the k-th power channel PWC (coefficients of accumulation f ak and return f rk , power supply voltage U ink , load resistance R outk , conversion frequency f bk =1/T bk , accumulation time t ak and return time t rk of energy by a power choke, current ripple ranges I m1k , I m2k of the choke, average values of current consumption I ink and load I outk , out power P outk ) are presented in Table 5.
In the case under consideration, with the symmetry of the electrical processes and the identity of the parameters of the elements in the k-th PWC DCV U ink =U in , In this case, the indicated intermediate (basic parameters) will be preliminarily calculated, which are the initial data for subsequent calculations and studies using the ratios that are presented in Table 5. Using a mathematical model [2,3] and algorithms (Fig. 3, 9), software has been developed for the automated study of DC voltage converters [6,7].

RESULTS
Using the specified software, the dependences of the energy parameters were obtained (Fig. 10 -Fig. 12). The dependences of the relative effective values of the currents of the switch S1 k and the diode VD1 k are shown in Fig. 10. The first study (Fig. 10 a) was carried out at a fixed load voltage and a variable input voltage (the input voltage was set in such a way that at a given accumulation factor f a the output voltage remained constant. The second study was carried out at a fixed ratio of input and output voltages Ū in of the converter (Fig. 10 b).
The analysis of the conducted studies shows that the influence of the transformation ratio of the choke on the relative effective values of the currents of the keys S1 k (I eS1k /I outk ) and VD1 k (I eVD1k /I outk ) (where I outk is the load current of the power channel) is quantitatively and qualitatively the same as for a fixed power of the power P outk =const (when the power of the converter is proportional to the number of power channels P out = NP outk ), and for a fixed power of the converter P out =const (when the power of PWC is inversely proportional to the number of power channels P outk = P out /N).
From the graphs (Fig. 10) it can be seen that by choosing the transformation ratio of the choke, it is possible to increase or decrease the relative currents of the power switching elements. In this case, the degree of influence of the transformation ratio of the choke depends both on the value of the accumulation coefficient and on the value of the relative supply voltage.
With the accumulation coefficient f a = 0.5 and the transformation ratio of the choke n 21 = 1, the relative effective current of the key S1 k is equal to the relative effective current of the diode VD1 k (Fig. 10 a). This is due to the equality of both the relative durations of the open state of these power switching elements (f a = f r ) and the range of their pulsations (I m1 = I m2 ) (Fig. 11 a). This feature of the operation of the power section of the converters is useful in practice, since it allows the use of power elements S1 k and VD1 k with the same installed power or, in the case when a transistor is used instead of the diode VD1 k , the same elements. The operation of the converter at a different value of kn leads to a redistribution of the effective values of the currents of the power switching elements. With an increase in f a , the relative effective current of the transistor S1 k increases, the diode VD1 k decreases (Fig. 10 a). A decrease in kn leads to the opposite phenomenon: a decrease in the relative effective current of the transistor S1k and an increase in the relative effective current of the diode VD1 k .
Choosing the transformation ratio of the choke allows you to align the relative effective values of the currents of the power switching elements. So, for example, with the accumulation coefficient f a = 0.2, the equality of the relative effective values of the currents Ī eS1k = Ī eVD1k occurs when using a choke with a transformation ratio n 21 = 2, and for f a = 0.8 -at n 21 = 0.5 (Fig. 6, but). The diagrams of the choke currents for this case are illustrated in the figure in 11, b, c.
The dependence of the relative operating currents of the switches S1 k and VD1 k on the value of the transformation ratio n 21 at various values of the relative supply voltage Ū in is shown in Fig. 12.
It can be seen from the graphs that an increase in the transformation ratio n 21 leads to an increase in the relative effective current of the switch S1 k , and a decrease in the relative current of the diode VD1 k at any values of the relative supply voltage Ū in .
However, the degree of influence of the transformation ratio of the choke on the values of the relative effective currents of the power elements is different. Thus, in the range 1 < n 21 <5, the relative effective value of the diode current decreases by 0.75 times, while the relative effective value of the current increases by 1.5 times (Fig. 12).  Figure 12 -Dependence of the effective value of the currents of the keys S1 k (a) and VD1 k (b), on n 21 at different values of the relative supply voltage Ū in 6 DISCUSSION Thus, to equalize the effective values of the currents in the power switching elements in the tracking mode with the accumulation ratio f a < 0.5, it is necessary to use a choke with a transformation ratio n 21 < 1, with an accumulation ratio f a > 0.5, it is necessary to use an inductor with a transformation ratio n 21 > 1. In the stabilization mode, to equalize the effective value of the current between the power switching elements with a supply voltage to load ratio Ū in > 2, it is necessary to use a choke with a transformation ratio n 21 > 1, with Ū in <2, the transformation ratio of the choke should be less than one n 21 < 1. It should also be noted, that when the effective values of the currents in the power switching elements are equal, the relative effective value of the current in them is 50% of the load current (Ī eS1k = Ī eVD1k =0.5).

CONCLUSIONS
Based on the results of this article, the following conclusions can be drawn: The paper discusses the main methods of automated research and design of radio engineering devices that can be used to analyze the electrical processes of pulsed DC voltage converters of a modular structure.
The main tasks to be solved by the developed software are formulated; the basic requirements for the software for the study of pulsed DCV are given; with the help of the information model of the software complex, the connection of the research tasks to be solved with individual software modules is shown.
Algorithms of calculations are given, the analysis of research results obtained using the proposed method is given.
The scientific novelty of obtained results is that the algorithms and software modules have been firstly developed that constitute the computational basis for the analysis and study of electrical processes and energy parameters of converters of modular structure.
The practical significance of obtained results is that the developed calculation algorithms and software can be used to solve the problems of analysis and research of DCV, which have increased functional capabilities in comparison with the existing CAD systems of radio engineering devices.
Prospects for further research -the proposed approach is the basis for solving the problems of research and design of DCV of modular structure, plays an important role in identifying the features of functioning, choosing the optimal modes of its functioning and the option of circuit design.