Methods for Controlling Autonomous DC Systemson the Basis of Switching by Capacitors

The article demonstrates methods for constructing pulse-amplitude (PAM) and pulse-width (PWM) controlled DC systems on the basis of switched-capacitor structures. Represented is the optimal structure of the system of DC electrical power interchanges (SEI), which excludes the use of additional elements. Proposed are the algorithms for controlling SEI transistor keys and their regulating characteristics. Studied are the features of their work and obtained are the equations for calculating the power circuit parameters


I. Introduction
As it is known, a frequency converter (FC) is an electronic device that converts AC electric power of one frequency to AC electric power of another frequency.
Currently, in the autonomous systems there are used two types of frequency converters (FC) with an intermediate DC link and direct frequency converters (DFCs), designed on the basis of power semiconductor devices.Such converters, if compared to the electromechanical ones, have superior performance specifications (1).
FC can be used for both step-up and to decreasing frequency of the current generated by independent power supply sources.Regardless of the conditions provided, they can perform two functions: stabilize current frequency and voltage.Furthermore, these two functions are performed by the FC control system independently (1).
Converters with an intermediate DC link, due to the double-conversion of electric power (they convert AC to DC and then DC to AC of the required frequency) possess low efficiency values, extra weight and dimensions in comparison with DFCs.
Modern power supply of autonomous systems is often made from several DC sources with differently time-varying voltages.As a result, there arises a problem of controlling the fluxes of electrical power when they are combined into a single system of DC electrical power interchanges (SEI).One of the simplest solutions is the use of bi-directional DC-DC converters with a variable conversion coefficient.The basic requirements of this installation include high efficiency, wide range of adjustment, low harmonic factor of the input and output currents, and linearity of regulating characteristics.Power circuit schematic (PC) is a simplest bilevel SEI based on the bidirectional converter module (BCM) (Figure 1) (Zotov, 2011).
Oscillatory forming circuits, which consist of capacitance C 1 and inductance L 1 , provide for switching all transistor keys at a time point when the currents passing through them are equal to zero (soft switching mode).Thus, losses in transistor keys at switching are minimized.
Reactors L 1 and capacitors C 1 form series-oscillatory circuits that provide for switching all transistor keys at the time points when the currents passing through them are equal to zero (soft switching mode).As a result, the switching losses in the transistor keys are minimized, which has a positive effect on efficiency.However, a disadvantage of such a system is the lack of electric power adjustment, which P 1 and P 2 are interchanged by low-voltage E 1 and high-voltage E 2 power supplies during SEI operation in both directions (Resonant DC-DC converters on the basis of switched-capacitor structures for autonomous power supply systems."Radio industry ", 2012, Vol. 1: 103-113;Zotov and Zinoviev, 2014;Evseev and Yurov, 2011;Golubkina, I.V. et al. 2011;Gorskii and Sysenko, 2009;7. Boroday et al., 2008).
Figure 1.Power circuit schematic of a bilevel SEI on the basis of BCM Regulation of the system given is impossible without additional diodes across the inductance L 1 .The absence of regulation is necessary, as the situation may arise when the value of voltage separation │(N + 1)•E 1 -E 2 │may reach quite a high level.This will lead to a significant reduction in plant efficiency and, in addition, may cause a substantial increase in currents through the elements of power circuit being above the calculated ones, which will result in their failure.
The simplest solution to this problem is to use a PWM regulator at the BCM input and output.The main advantage is a high efficiency level.The disadvantage is a high harmonics factor value of DC source being a donor.

Regulated SEI Structure
The basic requirements for a regulated SEI is a high level of efficiency and low values of harmonic factors of the input and output currents.Therefore follows the solution of the problem, which is to impose functions of regulating elements on thetransistor keys already existing in SEI (Figure 3).This offers new opportunities for regulation performance by a variety of methods.

Regulated SEI (PAM)
The most obvious regulation method is based on the SEI pulse amplitude modulation (PAM).
It is carried out by changing the active resistance R T of transistor keys VT (i, j) included into the BCM power circuit.In this case it is necessary to consider the behaviour of the SEI (PAM) efficiency -η(R T ) and the power level in both directions P 1 (R T ), P 2 (R T ) from the regulating parameter R T .
At SEI operation in the mode of continuous electric power transmission, and this is possible if the system is controlled by charging and discharging BCM keys.The system operates as an ideal current transformer.Current conversion coefficients depend only on the number of capacitances involved in the conversion of N and are determined by Consequently, the efficiency of SEI (PAM) At specified values E 1 and E 2, the adjustment of output power P 1 (R T ), P 2 (R T ) is carried out at a constant efficiency level, and the boundary conditions of permitted deviation E 1max and E 2max , at which the adjustment is allowed, are determined through the target values of the minimum efficiency η пр min and η обр min during the SEI operation.It follows from the expressions (2) and (3) that When using this method, the inductances L 1 may be excluded from power circuit, but it should be noted that the harmonic factors of the input and output currents are meanwhile strongly distorted.In addition, there comes a substantial reduction of the regulated power level and a significant increase in the amplitude of current pulses through the transistor keys of SEI power circuit.
In this case, control matrices of the corresponding transistor keys VT (i, j) being as a part of BCM will take the following form Where X -is a periodic sequence of SEI power circuit control pulses; X -is an inverted control signal X; 0-is a blocking signal of a corresponding transistor key.
Adjustment characteristics of SEI (PAM) in the forward and reverse directions of work (Figure 4 and Figure 5).The values of capacitances and inductance of SEI power circuit are determined by the following expressions Where ΔU C1 -is a permissible value of the voltage ripple on capacitors C 1 , R 1 2 -is an overall resistance of the transistor keys in low-voltage and high-voltage SEI circuits.
At the coordination of output power P 2 (R T ), there is a change in ripple value ΔU C .Standard dependences ΔU C (R T ) are shown in Figure 6.
. Dependences of the voltage ripple across the BCM capacitors on the resistance of transistor keys

Regulated SEI (PWM)
Control over the electric power fluxes in SEI is also possible within the pulse-width modulation (PWM) method (Figure 3).PWM application allows for step-up SEI efficiency level.PC (Fig. 3) allows various adjustment methods on the basis of PWM.Adjustment in both directions can be performed using PWM of transistor keys of both low voltage [VT (1.I) , VT (3,I) ], and high-voltage VT (2.I) BCM circuits.
If the adjustment is carried out through the transistor keys of a high voltage circuit in the forward direction, then it is realized through the change in duty factor γ (2,3) of the control pulses U (2,3) of a transistor key VT (2,3) .At SEI operating in a reverse direction, the adjustment is carried out by changing duty factor γ (2,1) of the control pulses U (2,1) of the extreme transistor key VT (2,1) .The change γ (2,1) takes place within the range of 0 to 0.5.The work of the SEI power circuit transistor keys in forward and reverse directions is respectively described by the following control matrices There is also possible a combined method of regulation, when adjustment in the forward direction is carried out through the change in duty factor of the control pulses U (3,2) and U (3,3) of the transistor keys VT (3,2I) , VT (3,3) of a low-voltage circuit, and in the reverse direction it is carried out through the change in duty factor γ (2,1) of the control pulses U (2,1) of the transistor key VT (2,1) of a high-voltage circuit.Change in the γ (3,i) and γ (2,1) coefficients also happens within the range of 0 to 0.5.
Control matrices of the combined SEI (PWM) during its operation, respectively, in the forward and reverse directions have the following form ] during the operation of SEI (PWM) with a combined control, respectively, in forward and reverse directions are shown in Figure 7 and Figure 8.

Multilevel DCRs with a Sectionalized Input Source
Multizone pulse-width DC regulators (DCR) with a sectionalized input source, which distinguishing features are: increased efficiency level and linearity of a regulating characteristic.Block-diagram of a bilevel bidirectional DCR with a sectionalized input source (Smirnov, 2008;Afonina et al. 2004;Smirnov, 2005;Goryachev et al. 1996) is shown in Figure 9.
Figure 9. Block-diagram of a bilevel bidirectional DCR with a sectionalized input source in forward and reverse directions DCR consists of a multi-level power unit (MPU), control unit (CU) and (R H , L H ) load.MPU is intended to form the discrete levels of input voltage spaced apart at regular intervals by the E value.E value is equal to the input source voltage E 1 for a step-up DCR, and 1 E K -for a step-down DCR, and K -is a number of regulation levels.
CU is represented by two PWM regulating elements on the bases of bidirectional transistor keys VT 1 and VT 2 .
The main drawback of such DCRs is a big number of regulating transistor keys equal to the number of regulation levels K.
The use of step-up MDCR on the basis of the switched-capacitor structures allows reducing the number of regulating transistor keys down to two at any number of regulation levels.Efficiency is achieved by managing discrete levels of U A and U B voltages (Figure 10) by changing the MPU structure (Belenkov, 2002;Vikentyev, 2001;Zubritsky, 2002;Mazur, 2001;Bernardzhevskaya, 2005;Strutynsky et al., 2000;Tailor, 2004).

Bilevel Bidirectional DCR with a Sectionalized Input Source on the Basis of Condenser DC-DC Converters of Resonant Type
The simplest solution is a bilevel DCR.Block-diagrams of bidirectional bilevel step-up and step-down DCR are identical.The principle of DCR operation in the forward and reverse directions is shown in Figure 9.
The difference lies in the structure of their MPU.Circuit MPU schematics of the step-up and step-down bidirectional bilevel DCRs are shown in Figure 10.The work of a bilevel step-down DCR is as follows.In the initial state, the transistor key VT 1 in CU is locked.
Voltage 1 1 2 U E I = ⋅ from the output of the step-down BCM, which is a part of MPU, is applied to the B input of the transistor key VT 2 .At the same time, voltage of the input source E 1 =U A is applied to the A input of the transistor key VT 1 .U L adjustment within the range of 1 0, is carried out at N=1 through the change in duty factor γ 1 of control pulses U 2 of the transistor key VT 2 within the range of [0,1].Then, to the control input of transistor key VT 1 applied are the control pulses 1 2 U U = and the U H adjustment occurs within the range of . It is carried out at N= 0.1 through a simultaneous change in duty factors γ 2 and γ 2 =1-γ 2 , respectively, within the ranges of [1,0] and [0,1].
Operating principle of the step-up and step-down bilevel DCRs in the reverse direction (regenerative behaviour) is based on the impact of the E 2 source, which is the EMF of load, for example of an electric motor.The matrices of controlling transistor keys in MPU of step-up (а) and step-down (b) bilevel DCRs, at operating in the reverse direction possess the following form: Regulating characteristics at operation of bilevel step-up (а) and step-down (b) DCRs in the reverse direction are demonstrated in Figure 12.
-is a maximum allowed relative ripple of voltage on the capacitor C 1 , I H (max) -is a maximum current in the load of a bilevel DCR, f k -is a switching frequency of the power transistors in MPU.
An important property of the considered bilevel regulators is that the levels of voltages applied to all the elements of their power circuit are identical and equal to E 1 -for step-up and 0.5•E 1 -for step-down DCRs.
Besides, the currents passing through all the power circuit elements of their MPU are also similar in form and their average values are equal to -for a step-up and I H -for a step-down DCR.

Step-Up Three-Level Bidirectional Dcrs with a Sectionalized Input Source on the Basis of Condenser DC-DC Converters of Resonant Type
An important advantage of step-up DCRs is that the CU consists of two transistor keys (Figure 9) at any number of regulation levels.A power circuit schematic of MPU of a step-up three-level bidirectional DCR is shown in Figure 13.It consists of BCM 1 and BCM 2 possessing the conversion coefficients, respectively K t1 =(N 1 +1)=3 and K t2 =(N 2 +1)=2.A low pass filter (L F , C F ) is intended for ripple smoothing of the current consumed by DCR from the input source E 1 .It may be excluded from the MPU power circuit, if the requirements to the ripple value of the input current are absent.The work of a three-level DCR in the forward direction is as follows.In the initial Matrices of controlling the MPU power circuit keys at regulator's operating in the reverse direction, for variation ranges Regulating characteristics of a step-up three-level DCR at its operation in reverse direction are shown in Figure 15.
The main advantage of the DCR under study is the simplicity of its CU.CU consists of only two adjusting transistor keys VT 1 and VT 2 .The effect is achieved by changing the structures of BCM1 and BCM2 in its MPU.The disadvantage is that the change in the number of capacitors in BCM 1 and BCM 2 is accompanied by transient phenomena of voltages at their output capacitors C F1 and С F2 .This leads to a delay in setting U A and U B voltages to the time  ≅ 5 • .The drawback specified is eliminated, if the structures of BCM1 and BCM2 are not changed during the process of adjustment.However, in this case, it is necessary to introduce the third regulating transistor key VT 3 into CU (Figure 16).A regulating characteristic in the forward direction is shown in Figure 14b.
The form of regulation characteristics in the reverse direction is not changed.The difference is that in the left graph (Figure 15) along the axis of abscissas one should delay γ 3 =1-γ 2 .
The weight/volume indicators of DCR are significantly improved through the replacement of BCM 1 and BCM 2 with the bidirectional multicycle resonant converters -BMRC 1 and BMRC 2. BMRC is a k of parallel connected, identical BCM, working on the total load with a time shift relative to each other by the value t ( ) T t k k Δ = and containing N capacitors each.The total capacity of the BMRC power circuit is reduced in the inverse proportion to the number of conversion cycles k , compared to the equivalent in power single-cycle BCM is due to a proportional increase in the frequency of conversion ( ) = • ( = 1) of its constituent individual BCM. ( = 1)-is a conversion frequency of the equivalent by power, single-cycle BCM.Increase of k also leads to a significant reduction in capacity C F1 .It is reduced by 2•K 2 times -for odd and by K 2 times -for even K values.In order to minimize the harmonic distortion factor of the input current ( ) 1 I t Σ , consumed by the regulator from the primary source E 1 in the forward direction, and delivered to the source E 1 at regeneration, the signals for controlling respective transistor keys in BMRC1 and BMRC2 -X1 and X2 are shifted with respect to each other.The time shift k τ is chosen from the condition for square minimum of the effective value of total input current ( ) 1 I t Σ -in the forward direction, and of total output current ( ) 2 I t Σ -in the reverse direction Since the permanent components of the currents I 1MRC1 (t), I 1MRC2 (t) in both directions, do not depend on the time shift k τ then is clear that the defined criteria shall also mean the minimization of square of the effective value  In this case, BCM 2 is excluded from the MPU power circuit.As a result, the power circuit of a step-up three-level MPU is simplified by three IGBT transistor keys and one capacitor.The main drawback of such DCR is related to the asymmetry of its power circuit operation.It is conditioned by the difference in discharge currents of capacitors C 1 of different chains.This makes it difficult to provide a soft-switching mode of transistor keys included into the MPU.By increasing capacitance of the capacitors C 1 and C ф1 , C ф2 this drawback disappears.However, such method of its eliminating degrades the weight/volume indicators of MDCR as a whole.The weight/volume indicators of DCR with a midpoint are significantly improved through replacement of its BCM by a bidirectional multicycle resonant converter (BMRC) with a midpoint.Figure 18.
Figure 18.BMRC with a midpoint circuit schematic Type of adjusting characteristics of the DCR with a midpoint in forward and reverse directions totally coincides with the characteristics given in Figure 14 and Figure 15 for a three-level DCR, Figure 13 (Rydell-Tormanen et al., 2012).

Summary and Conclusions
Analysis of the characteristics of the SEI (PAM) and SEI (PWM) specified allows the following conclusions.
1.When the initial value of the process of filling coefficients γ (3,2) = γ (3,3) = γ (2,1) = 0,5 of SEI (PAM) and SEI (PWM) operate in a continuous transmission of electric energy,that is, the system controls the charging and PD bit keys.In this case, the system works as an ideal transformer currents and efficiencies of PAM and PWM ESR identical and are defined by expressions (2) and (3).
2. From the analysis of the adjustment characteristics (Figure 7.8) shows that with the increase in the value of the inductance L1 regulated power ESR (PWM) decreases, its Efficiency according to equations ( 1) and (2) increases.
3. Subject to the boundary conditions, tolerances E1max, E2max and setpoint power sources E1 and E2, made adjustments to the settings, and the Efficiency remains unchanged as shown by the expressions (4) and (5).6. Introduced is the concept of control matrix, giving an idea of the algorithm for controlling transistor keys of the DCR power circuit and allowing to simplify the development of a circuit and its management.
7. Obtained are the adjusting characteristics of DCR at its operation in the forward and reverse directions.
8. Obtained are the formulas for calculating parameters of the DCR power circuit elements.9.It is demonstrated that the application of multicycle DCRs allows not only reducing the current's harmonics factor of the consumed primary source, but also significantly reducing the amount of the total capacitance of its power circuit.

Figure 2 .
Figure 2. Block-diagram of SEI with PWM regulators

Figure 3 .
Figure 3. Power circuit schematic of a regulated SEI

Figure 4 .
Figure 4. Adjustment characteristics of SEI (PAM) in the forward direction

Figure 7 .
Figure 7. Regulating characteristics of a combined SEI (PWM) in forward direction

Figure 10 .
Figure 10. Circuit MPU schematic of the step-up and step-down bidirectional bilevel DCR

Figure 11 .
Figure 11.Regulating characteristics of step-up (а) and reducing (b) bilevel DCRs in the forward direction

Figure 12 .
Figure 12.Regulating characteristics at operation of bilevel step-up (а) and step-down (b) DCRs in the reverse direction

Figure 14 .
Figure 14.Regulating characteristics of step-up three-level DCRs at their operation in forward direction

Figure 15 .
Figure 15.A regulating characteristic of a step-up three-level DCR at its operation in reverse direction for even and odd values of К. Parameters of the elements of the step-up and step-down, bilevel DCRs are determined by the following expressions: Three-Level Bidirectional DCRs with a Midpoint and a Sectionalized Input Source on the Basis of Condenser DC-DC Converters of Resonant TypeMultilevel DCRs with the midpoint possess the easiest MPU (Figure17).Simplification is achieved by using intermediate points in the MPU circuit for obtaining voltages of discrete levels E 1 , 2•E 1 , 3•E 1 , required for the operation of a step-up MDCR.

Figure 17 .
Figure 17.MPU circuit schematic of a step-up three-level DCR with a midpoint

4.
The regulation characteristics analyzing(Figure 7.8)  shows that the middle of the linear portion (operating point) dependences P2 [γ (3, i)], P1 [γ (2,1)] for all considered variables L1 corresponds to the value of the loop parameter γ (3, i) = γ (2,1) = 0,275.5. Considered are the principles of construction and operation of bidirectional multi-level DCRs with a sectionalized input source on the basis of condenser DC-DC converters of the resonant type.