Adaptive High Stability modeling for Analysis of Micro grid for DC Converters

This paper presents the analysis of dc network in a hybrid micro grid system. A hybrid micro grid consist if ac and dc sub grids inter connected through multi port power electronic interface (MPEIs). For modeling a multiple switching converter an averaging method is implemented. Pole zero analysis of a small signal model is performed for analyzing the stability of the network. Simulation results are verified. Index

Droop control methods are also used in MPEI to control the distribution network . A micro grid coordinator is used to assure the stability of dc bus and to control the micro grid. The controller monitors the condition of micro grid and the power flow in ac and dc buses. Using dynamic dispatch of reference power commands the stability of ac and dc buses can be maintained by the controller.

II. MODELLING OF DC MICROGRID
The model of micro grid consists of model of nodes and distribution network. The MPEI model is derived in. 20 kHz base frequency with averaging method is derived in this model . For single switching frequency the generalized averaging method is developed. This can be also able to study the behavior of the system at harmonics. Each dc unit have an identical switching frequency. Hence more general form of averaging technique is needed for stability analysis.It is assumed that the frequency of variations of duty cycle is less than the switching frequency for simplifying the Fourier transform calculation. The same assumption is made for generalized averaging method. In the power electronic converters while considering the non line arities, harmonics in the state variables is not limited to the switching frequency. Each product of these functions result in frequency modulation of all existing harmonics and so results in new harmonics. These offspring harmonics are in the form of linear combinations of the previous harmonics. Thus, based on the switching frequencies of the system, the state variables will have all of the linear combinations of these switching frequencies. The energy of these harmonics is negligible in power electronic converters. To clear this concept, back to back dc to dc converters are used as shown in the fig. 3. In an average dc-dc converter, it is designed to have a steady dc output voltage. Thus, dc is the principal harmonic. Fig. 4 shows an plot of harmonics contents in the back-to-back converter of Fig. 3. In practice, filtering equipments are used to reduce the harmonics though some harmonic remain dominant. Thus, a set of dominant harmonics can be defined for modeling the system with a satisfactory accuracy.

III.
STABILITY ANALYSIS USING EXTENDED AVERAGING METHOD In order to study the stability of the system, extended averaging method is introduced. Steady State Analysis of Multi Converter System The cascaded system is simulated to study the accurateness of the extended averaging method in assessment of performance of the system. 36V source is connected to the first converter dc-dc1. For 24V load dc -dc2 delivers a constant power of 120W. The dominant harmonics of this system are dc, ±3kHz and ±5 kHz and the extended averaging model is resultant of the given set of dominant frequencies. The accuracy of the existing extended averaging method is observed good from the simulation results. Yet, it is not capable to calculate the voltage ripple exactly and it also fails to generate the correct ripple on the dc bus. The proposed extended averaging method is capable to calculate the voltage ripple exactly. Thus for modeling a dc distribution network with multiple switching frequency, this method is implemented. . Stability Assessment Using the Extended Averaging Method From the previous section, closed loop pole zero assessment can be developed. Near the operating point which is the equilibrium point, where the non linear model is linearized. At the equilibrium point the system is stable. It is noted that a system consist of only one operating point. Thus if the operating point is stable the system is stable. From this method, stability assessment of the micro-grid formed between MPEI a and MPEI b can be calculated.  fig. 7. By increasing the droop coefficient, stability of the system is improved. However, in practical applications, the large droop coefficients are not feasible. This coefficient results in low voltage a regulation which reduces the power quality in a dc distribution network. Dynamic Behavior of Multi Converter System The dynamic behavior of the system with step load change is studied using the same model. The dc bus voltage is maintained in dc-dc1 converter. Where, dc-dc2 is set to zero. 120W is supplied to a fixed load by dc-dc2 at 0.1s. The dc bus voltage is shown in the fig. 8 where dc-dc1 operating at 5 kHz and dc-dc2 operating at 10 kHz. Here 200μF dc bus capacitor is used. In a data centre, in order to reduce the size of dc-dc converter, it is supplied with digital circuits operating with high frequencies. The switching frequencies of these converters are small i.e. < 20 kHz. Fig. 8 shows the simulation result with the switching frequency of the converter increased to 100 kHz. Fig.9 step response analysis with dc-dc operation at 5kHz and dc-dc operation at 100 kHz If the source converters cannot cope with the dynamic response of the load converters, oscillations and limit cycling can occur. This can be observed on the simulated system if the switching frequency of the load converter is increased to 100 kHz Fig.9 step response analysis with dc-dc operation at 5kHz and dc-dc operation at 100 kHz with 1000mf on the DC bus Hence, when capacitor size is increased, the effect on dc bus voltage is reduced. For this purpose the capacitor of 200μF is increased to 1000μF. Fig. 9 shows the step response analysis with dc-dc1 operating at 5 kHz and dc-dc2 operating at 100 kHz with 1000μF on the dc bus. From the simulation result it is identified that the system is stable and 4.7A of current is settled at the source converter.

IV.
CONCLUSION A hybrid microgrid with multi port power electronic interface (MPEI) was implemented in this paper. An extended generalized averaging method is introduced to study the stability of the system. The dc distribution network was also modeled using this method. In the developed model steady state performance model and dynamic pole zero analysis are performed. The accuracy of extended averaging method is illustrated in simulation results. Multi converter system can be modeled using extended averaging method and the results are verified. Using pole zero analysis, the stability assessment can be developed.

V.
ACKNOWLEDGMENT I would like to express my special thanks of Mr.Rakesh Oruganti (IJIEMR) as well as Dr. Dharamveer mangal who gave me the golden opportunity to do this wonderful project on the topic (Adaptive High Stability modeling for Analysis of Micro grid for DC Converters), which also helped me in doing a lot of Research and i came to know about so many new things I am really thankful to them. Secondly i would also like to thank my parents and friends who helped me a lot in finalizing this project within the limited time frame.