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Energy and Power Engineering, 2013, 5, 803-806 doi:10.4236/epe.2013.54B154 Published Online July 2013 (http://www.scirp.org/journal/epe) The Research on Stability of DC/DC in Parallel System Ye Xu, Pengfei Hou, Jinquan Wang, Lei Xu, Chaohong Shi PLA University of Science & Technology, Nanjing, China Email: 19890224hpf@163.com Received February, 2013 ABSTRACT In this paper, a main structure of DC distributed power system is introduced; the stab ility of the output vo ltage in paral- lel system is put forward. This paper analyses the output impedance of master-slave current sharing mode and average current sharing, analyses the stability o f parallel system through simulation , there is Right-h alf plane (RHP) polar in the Bode plot of input impedanc e. At last this p aper distingu ishes whether this system is stability and ve rifies the validity of the simulation. Keywords: DC; Parallel System; Output Impedance; Bode; RHP Polar 1. Introduction With the development of distributed power system, the role of power electronic devices is more and more im- portant. In the actual power system，power supply mod- ule is inevitably involved in cascade, parallel, series, combination of collaborative work form. The interaction between each subsystem effects on the overall perform- ance of the power system including stability analysis, dynamic performance, steady state harmonic power in- fluence the quality and electromagnetic interference and other related fields. Meanwhile, each module may come from different suppliers; the power supply module is gradually standardized to meet industry needs at the same time. The compatibility match also needs to stan- dardize the definition in order to ensure the universality and interchangeability. The integrated system perform- ance degradation even be shocked. For DC Distributed Power System, usually diesel units after rectifier connected to the DC grid, the battery after a bidirectional DC/DC connected to the grid. Supply pow- er to the DC load side by DC/DC transformer, Supply power to the AC load side by DC/AC transformer. As shown in Figure 1 for DC Distributed System. The method of stability analysis of the previous sys- tem needs to know module structure and parameter while the criterion is complex, the method based on single module impedance measurement only needs Cur- rent-sharing method of parallel system and working con- dition. Measuring the output impedance of single module independently is through the relationship between total output impedance and output impedance of parallel sys- tem with a single module to get the total output imped- ance, according to whether the output impedance of par- allel system has the right half plane pole to judge the stability of the parallel system. 2. Total Output Impedance of Parallel System Based on Master-slave Current Sharing Mode As shown in Figure 2 is equivalent circuit model based on master-slave current sharing mode. When the current communication line interface is hanged, voltage loop plays a role and current-sharing loop is inv alid. When the flow line of communication interface is connected with constant voltage source, current disturbance is 0, Output impedance contains all information flow regulator [1]. * * 1 csi csi csi oi oM Z Z Z Z Z (1) Among them oM Z is the output impedance of the main module, oi Z is output impedance of i when mod- ule communication line is hanged, * csi Z is output im- pedance of i when module communication line is con- nected with constant voltage source. The total output impedance of the system is: Figure 1. DC distributed power system. Copyright © 2013 SciRes. EPE Y. XU ET AL. 804 M F v K () v A s ˆ d Gd ˆ d OLi Z ˆ ol i ˆ o v ˆ oM i () c A s Figure 2. Circuit model of parallel system based on mas- ter-slave current sharing mode. 1 1/ scsj Z Z (2) 3. Total Output Impedance of Parallel System Based on Average Current Sharing Mode The same, as shown in Figure 3 is equivalent circuit model based on average current sharing mode [4]. Output impedance of module i is: * *** 1 1() / csi csi oi csi oicsi csi Z Z Z ZZ Z Z (3) oi Z is output impedance of i when module communica- tion line is hanged, csi Z is output impedance of i when module communication line is connected with constant voltage source [2]. Hence, The total output impedance of the system is: * 11 1 / 1/ oj scsj csj csj Z ZZn * Z Z (4) Among them csj Z is the output impedance of j when modules are worked in parallel, csj Z is output imped- ance of j when module communication line is hanged. csj Z is output impedance of j when module communica- tion line is connected with constant voltage source [3]. 4. Simulation of Parallel System As shown in Figure 4 is Bode graph of total output im- pedance of the parallel system based on master-slave current sharing mode. The graph shows that the output impedance of the amplitude and phase changes with fre- quency, the upper one is the direct measurement result and the lower one is computin g result. As can be seen by comparing, the measurement results and the computing results are in agreement. Therefore the acquisition me- thod of output impedance of parallel system based on master-slave current sharing mode is validated. As shown in Figure 5 is Bode graph of total output impedance of the parallel system based on average cur- rent sharing mode. The lower one is the direct measure- ment result and the upper one is computing result. As can be seen by comparing, the measurement results and the M F v K () v A s ˆ d Gd ˆ d OLi Z ˆ ol i ˆ o v 1ˆoi i n () c A s Figure 3. Circuit model of parallel system based on average current sharing mode. Figure 4. Total output impedance of the parallel system based on master-slave current sharing mode: Direct meas- urement result (up), computing re sult (down). Figure 5. Total output impedance of the parallel system based on average current sharing mode: Direct measure- ment result (down), computing r e sult (up). Copyright © 2013 SciRes. EPE Y. XU ET AL. 805 computing results are in agreement. Therefore the acqui- sition method of output impedance of parallel system based on average current sharing mode is validated. 5. Simulation Analysis of Parallel System Stability For the total output impedance of parallel systems, the parallel system is stable if there are not RHP poles in the total output impedance; the parallel system is not stable while there are RHP poles. As shown in Figure 6 is Bode graph of total output impedance obtained from simulation in stable parallel system, there are no RHP poles in the graph. As shown in Figure 7 is simulation results in time domain of parallel system, it shows two parallel con- verter output current signal and the output voltage signal, from the graph we can see the output voltage is stable. As shown in Figure 8 is Bode graph of total output impedance obtained from simulation in unstable parallel system, there are RHP poles in the graph. From the graph we can see there are RHP poles around 7.2 kHz. As shown in Figure 9 is simulation results in time domain of parallel system, from the graph we can see there is turbulence in the output voltage of parallel sys- tem and there is ripple in output curren t, it prov es that the system is unstable. Figure 6. Bode graph of total output impedance in stable parallel system. Figure 7. Simulation results of parallel system in time do- main. 6. Experiment on Validating Stability of Parallel System Through the above analysis, DC power is put as the power supply for the parallel system, two DC/DC power electronic loads work in parallel, measuring the output impedance of parallel system by network analyzer. Both a stable system (Experiment 1) and an unstable system (Experiment 2) are measured. As shown in Figure 10 is Bode graph of total output Figure 8. Bode graph of total output impedanc e in unstable parallel system. Figure 9. Simulation results of parallel system. Figure 10. The experimental result of experiment 1. Copyright © 2013 SciRes. EPE Y. XU ET AL. Copyright © 2013 SciRes. EPE 806 impedance obtained from experiment 1.There are no RHP poles, so the system is stable. For the output voltage of parallel system correspond- ing with the experiment 1, simulation results in the time domain are shown in Figure 11: Experiment verifies the simulation results, for the si- mulation of stable system, the experimental system is stable at the same time, and there are no RHP poles in output impedance. As shown in figure 12 is Bode graph of total output impedance obtained from experiment 1.There are RHP poles around 5 kHz, so the system is unstable. Figure 13. Simulation results of experiment 2. Simulation results of experiment 2 in the time domain are shown in Figure 1 3. 7. Conclusions This paper analyzes the DC distributed system structure firstly. In parallel with a plurality of power electronic module in DC distributed system will cause instability, then it analyses the output impedance of master-slave current sharing mode and average current sharing, and verify the method of obtaining output impedance in par- allel system, after that it simulates the stability of the parallel system. At last experiment verifies the correct- ness of the simulation. For unstable system in experiment 2, there are a large number of ripples in output voltage, the system is unsta- ble. There are RHP poles in Bode graph of output im- pedance, the experiment is verified through simulation. REFERENCES [1] W. P. Zhang, “Modeling and Control of Switching Con- verters,” China Electric Power Press, Beijing, 2006, pp. 25-27. [2] D. H. Ding, “Power Electronic Technology,” Aviation Industry Press, Beijing, 2006, pp. 43-45. Figure 11. Simulation results in the time domain of experi- ment 1. [3] P. R. Gray, P. J. Hurst, S. H. Lewis, et al., “Analysis an d Design of Analog Integrated Circuit,” 4th Edition, John Wiley & Sons Ltd., Chichester, 2001. [4] A. Emadi, A. Khaligh, C. H. Rivetta and G. A. William- son, “Constant Power Loads and Negative Impedance In- stability in Automotive Systems: Definition, Modeling, Stability, and Control of Power Electronic Converters and Motor Drives,” Vehicular Technology, IEEE Transac- tions on, Vol. 55, pp. 1112-1125, 2006. [5] Z. Yao, P. G. Therond and B. Davat, “Stability Analysis of Power Systems by the Generalized Nyquist Criterion,” in Control, 1994.Control '94. International Conference on, 1994, pp. 739-744, Vol. 1. [6] X. Sun, Y.-S. Lee and D. H. Xu, “Modeling, Analysis, and Implementation of Parallel Multi-Inverter Systems with Instantaneous Average-Current-Sharing Scheme,” Power Electronics, IEEE Transactions on, Vol. 18, No. 3, 2003, pp. 844-856. doi:10.1109/TPEL.2003.810867 Figure 12. The experimental result of experiment 2. |