Improving the Stability of Cascaded DC Power Supply System by Adaptive Active Capacitor Converter

- When all links are changes in the cascade is the corner of the shape in the dc division energy orbit (DEO). When resistances are intermission betwixt one by one stylish changes in that would possibly end up so the cascaded orbits are unsteady. They are antecedent we can place in a nearer to the useful in the cascaded orbit can be got in compelled to vary the supply they have load changes in the internal structure of the same regions in the electrical device they can be opposed in a quality of the characteristic of dc DEO. Throughout the Associate in nursing adaptation active device in the (AACC) we can know another determined in the cascaded orbit. Therefore the AACC was connected by side by side in the cascaded orbit’s they can mediate in between the carries and completely a requirement of a notice then they carries the voltage with none modification in this subsystems. when the cascaded orbits have their quantity of it slowly it will extend in time. They have activity fundamental truth to stop their magnificence thought in the AACC are mentioned throughout of this project, it can have four thousand eight hundred and zero watts cascaded orbit was contain a strive of process to move in a full-bridge changes they can be styli shed and evaluated. So when the simulation solutions have to clear the performance of the arrangement of AACC.

defense electronic power systems for the last 20 years [1]- [5], due to its flexile system configuration, high-efficiency energy conversion, and high-density power delivery capability .One of the dc DEO'S attractive characteristics is modularity design [6], in which each Subsystem is first designed individually as a module, and then all subsystems are integrated to form a dc DEO. The modularization characteristic of dc DEO cuts down the system's development cycles and costs effectively. In a dc DPS, there are various ways to connect the subsystems, among which, a typical connection style is cascaded converts. The cascaded system may have stability problem due to the interaction between the subsystems, even though each subsystem is individually well designed to be stable on its own [7]- [10]. was shown that for the typical cascaded system shown in Fig. 1, the ratio of the source converter's output impedance Zo and the load converter's input impedance Zin, Zo /Zin , can be equivalently represented as the loop gain of the cascaded system. It was also pointed out that if both the ource converter and the load converter are stable individually, and Zo is less than Zin in the entire frequency ranges, the stability of the cascaded system will be guaranteed. This is the so-called Middle brook criterion. Subsequently, various impedance criteria aiming at a more accurate and practical prediction of the subsystem interaction had been developed in the last two This paper first analyzes the impedance characteristics and instability problem of the cascaded system in Section II, and presents the concept, operating principle, ad control strategy of AACC in Section III. The design procedure and a design ample of AACC are given in Section IV. Section V shows he experimental results that verify the effectiveness of the proposed method.

A. Review of Subsystem's Impedance Characteristic And Cause of Instability
For cascaded systems, the impedance characteristics of subsystems and the cause of instability have been studied extensively during the last two decades. Some general conclusions are summarized as follows: 1) Impedance characteristic of Zo : Zo is the source converter's output impedance independent of its load resistor. As shown in the dotted line of Fig. 2, Zo is similar to the output impedance of an LC filter. Iff < fc S, Zo presents the characteristic of an inductor; and if f > fc S, Zo presents the characteristic of source converter's output filter capacitor. Here, fc S is the cutoff frequency of the source converter's voltage loop. Note that Zo 's peak value ,Zo peak, appears at fc S and is inversely proportional to source converter's output filter capacitor. 2) Impedance characteristic of Zin : In Fig. 2, the solid line Represents Zin that is the input impedance of load converter Operating in continuous current mode (CCM). Iff < fc L, Zin behaves as a negative resistor, whose value equals to −V 2 bus/Po , where Vbus is the intermediate bus voltage and Po is the load converter's output power

B. Solving the Instability Problem by Adding Intermediate Bus Capacitor
There is nothing more desirable than a total separation between Zo and Zin to ensure that the cascaded system is stable. Since |Zo peak| is inversely proportional to source converter's output filter capacitor [30], one intuitive way is to reduce the source converter' output impedance by adding an intermediate bus capacitor Cbus to the cascaded system, as shown in Fig. 3.Here, Cbus can be treated as an additional output filter capacitor of the source converter, and the equivalent LC output impedance model of source converter with Cbus is given in Fig. 4. In Fig. 4, Le S is the equivalent filter's inductor, Ce S is the equivalent filter's capacitor, Rle S is the parasitic resistor of where fesr S is the zero caused by the ESR of Ce S . According to (1)-(3), the peak value of Zo in Fig. 4 is derived as (4) Thus, in order to ensure that Zo < Zin in the entire frequency ranges, |Zo peak| must satisfy (4) and (5), the required value of Cbus can be obtained as According to (6), the required Cbus increases with the increase of Po , so, if a capacitor is employed, its value must be selected by (6) at full load. However, a larger Cbus results in a smaller bandwidth of the source converter that is already modularly designed, In this way, the cascaded system does not only ensure stable, but also achieves a better dynamic response.

A. Topology of AACC
The adaptively varying Cbus mentioned in Section II can be Emulated by a converter, as shown in the dashed block in Fig. 5.The converter is referred to as AACC. The AACC is composed of switches Qa1 and Qa2 , inductor La , and capacitor Ca. It is connected to the intermediate bus of the cascaded system. By controlling La 's current appropriately, the terminal characteristic at the bus side of AACC will present an adaptively varying Cbus that ensures the stability of the cascaded system and improves the dynamic response. The AACC is also suitable for the cascaded system with multiple load converters. In this case, the AACC has the same operation principle with the system of Fig. 5, which just makes the source converter's output impedance lower than the total input impedance of the multiple load converters.This paper analyzes the case shown in Fig. 5, but the conclusion applies to the system with multiple load converters.

B. Control of AACC
Since the function of AACC is to emulate the adaptive Cbus, the current of La, ia , should be controlled as According to (6) and (7), it can be known that ia varies with Po . Considering Po can be reflected by the oscillation ripple of vbus, Δvbus [13], ia could be controlled by Δvbus, whose control cicuit is realized by a simple analog circuit, as shown in Fig. 6. The control circuit for ia would only need to detect vbus without changing any part of the existing subsystems. Thus, the AACC can be designed as a standard module for dc DPS.As shown in Fig. 6, vbus first goes through a differential circuit (sub circuit A) to get the form of ia ref (dvbus/dt), defined as v1 . Meanwhile, Δvbus is extracted from vbus by the filter comprising C2 and R5 , and then it is sent to the rectifier circuit. The shutdown signal of UC3525 is generated by sub circuit F that determines the working mode of AACC automatically. If the Fig. 6. Control circuit of the AACC Cascaded system is unstable, the magnitude of Δvbus, v2 , will be larger than the permitted value, denoted as ΔVbus mode, and the shutdown signal of UC3525 will become low. In this case, the AACC works normally. Otherwise, the shutdowns signal will go high, shutting down the AACC. Here, ΔVbus mode is set at a value below ΔVbus allow to ensure that AACC works well.

A. Output Filter Capacitor Ca
With AACC, ignoring the switching harmonics of the cascaded system's intermediate bus voltage, vbus can expressed as vbus = Vbus +ΔVbus allow sin ωt.
According to (7) and (10), the waveforms of the instantaneous input power Pa ,inductor current ia , and output filter capacitor voltage va of AACC are depicted in Fig. 7. It can be seen that Ca is discharged from Tos /4 to 3Tos /4, and va decreases; and Ca is charged from 3Tos /4 to 5Tos /4, and va increases. Consequently, the maximum and minimum values of va occur, respectively, atTos /4 and 3 Tos /4. The energy charging Ca from 3Tos /4 to 5Tos /4 Here, ΔEa (t) can also be expressed as [ΔEa (t)=1/2CaV]_a^2(t) -1/2CaV]_(a min) ^2 where Va min is the minimum voltage of the capacitor Ca . Putting (12) in (11) Substitution of t = 5Tos /4 into (14), the maximum voltage of the capacitor Ca can be derived as Where C * a is the normalized Ca with base of Cbus. According to (18) and (19), V * a max and V * adc as functions of C * a are plotted in Fig. 8. Here, Va max increases as Ca reduces.
In order to adopt film capacitors or ceramic capacitors instead of electrolytic capacitors, the value of Ca should be small enough However, this will result in high Va max. A high Va max induces high voltage stress on Qa1 and Qa2 . Thus, Ca needs to be selected eclectically. Note that Ca must be selected at full load because it is the worst case for the cascaded system and the required Ca has the maximum value.

B. Selection of Qa1 and Qa2
According to Fig. 5, the voltage stress of Qa1 and Qa2 is the Maximum voltage of va , i.e., VQa 1 = VQa 2 = Va max.
(20) The current stress of Qa1 and Qa2 is the maximum current of La , and can be derived from (7) and (8)

C. Inductor of AACC
Two factors must be taken into consideration when choosing the value of La . One is to ensure that the inductor current is Capable of tracking the current reference and the other is that the inductor current ripple should be kept small. Here, the AACC's inductor current, ia , needs to track the Oscillation ripple, whose oscillation frequency is the cutoff frequency of the source converter's voltage loop gain. Hence, the switching frequency of AACC, fsa , should be chosen much higher than the oscillation frequency fc S . In this case, the tracking speed of ia is ensured and it would be sufficient to choose the value of La with sole consideration given to the inductor current ripple. As the two power switches of AACC operate in a complementary manner, the AACC is operating in continuous current conduction mode. Thus, the duty cycle of Qa1 is dQa 1 (t) = 1 -Vbus va (t) .

D. Design Example
In this part, an AACC is designed for a cascaded system, as seen in Fig. 9, the system is composed by two phase-shifted full-bridge converters. Table I gives its parameters. In Fig.  9, both the source converter and load converter's voltage regulator are employing a PI controller. In this paper, fc Sand phase margin of source converter are set at 550 Hz and 45•, respectively, and fc L and phase margin of load converter are set at 5 kHz and 45•, respectively. According to the circuit and control parameters of the cascaded system, the Bode plots of the source converter's output impedance Zo and the load converter's input impedance Zin at different loads are plotted in Fig. 10. It can be seen that when the load is lower than 35% full load, Zo peak is less than Zin , and the cascaded system is stable. Otherwise, there is interaction between Zo and Zin , the system  Fig. 10. Impedances of the source and load converters at different loads Will become unstable, and the AACC is needed. In practice, the impedance characteristics of Zo and Zin can be measured by a network analyzer without knowing the intrinsic parameters of the subsystems. From Fig. 10, it can be seen that, Zo peak = 13.5 Ω, the input impedance of load converter at full load Zin f d is equal to4.8 Ω, Rce S = 0.017 Ω, fc S = 550 Hz, and fesr S = 22.5 kHz. Using (1)-(3) and (7), we can calculate the oscillation angular frequency and Cbus max, i.e., ω = 2πfc S = 3455 rad/s and Cbus max = 1950 μF. Setting Δvbus allow at 1%Vbus, the main circuit parameters of AACC can be designed as follows  (14) and (24), the curve of minimum value of La, La min, in an oscillation period can be plotted in Fig. 11, where the  Maximum value of La min is 395 μH. Here, we choose La = 395 μH. Considering the cost is a matter of concern in practical, Table II lists the selected components of AACC, passive capacitor solution, and the original cascaded system. Currently, the cost of AACC is slight higher than the passive capacitor solution, and accounts for about 9% of the original cascaded system.
In order to verify the validity of the proposed AACC, a prototype has been built and tested. The parameters of the prototype have been given in Section IV-D. Fig. 12 shows the steady-state experimental waveforms of the source converter and load converter operating individually. Fig. 13(a) and (b) shows the individual dynamic waveforms of the source and load converters when their load steps between full load and 10% full load, respectively. As seen from the figures, both source and load converters are stable and working well. Considering that the cascaded system can be stable with a 1950 μF passive capacitor (Cbus max) or AACC in the full load range. Fig. 18 compares their dynamic performance when the load steps between full load and 10% full load. It shows that the system with AACC has a faster dynamic response than that of the system using the passive capacitor solution.
According to the reason can be explained as follows. The equivalent capacitor of AACC is adaptively varied by the load. Its value is always smaller than 1950 μF and approaches zero when the system is stable. And a smaller Cbus, of course, means a faster dynamic performance for the cascaded system. In addition, compared with Figs. 13 and 18(b), it seems that the cascaded system with AACC has a similar dynamic performance with its individual subsystems. Fig. 13. Waveforms of cascaded system when the load steps between full load and 10% full load: (a) with the AACC (b) without the AACC When the AACC is a good suggests that to resolve the instability downside of the dc distributed power supply. In the presents days they will offers the AACC as identical adjective bus capacitance will be changeable per then the cascaded system have their output power, so we can avert the electrical resistance can communicate to the cascaded system with the quantity of the output electrical resistance in the supply convertor. Betting in the edge of the undisturbed conditions in the cascaded system, therefore the AACC is adjectively functionaries. Once the move in the cascaded system was broad in the AACC supply to the additional power of the produce to the bigger importance capacitance. Once they can moves in the cascaded system have a very small value, when the AACC can supply less power in the produce have smaller importance capacitance. They will tally in the present technique, the projected convertor solely has they discover the cascaded system to the bus voltage while not dynamic something in the present subsystems, thus they will be a stylish to the customary can be measuring in the dc DPS. Then AACC will been ascertain carefully see the power values that is four thousand eight hundred zero watts and we can see different voltage ratings in the cascaded system. After we can see the exacta output results of the experimental in the validity of the analysis.