Distributed Cooperative Control and Stability Analysis of Multiple DC Electric Springs in a DC Microgrid


Recently, dc electric springs (dc-ES s) have been proposed to understand voltage regulation and power quality improvement in dc micro grids. This paper establishes a distributed unified control framework for multiple dc- ES s in a dc micro grid and presents the small-signal stability  separation of the system. The primary level implements a droop control to coordinate the operations of multiple dc-ES s. The secondary control is based on a unity algorithm to regulate the dc-bus voltage reference, incorporating  the state-of-charge (SOC) balance among dc-ES s.


With the design, the cooperative control can achieve average dc-bus voltage consensus and maintain SOC balance among different dc-ES s using only neighbor-to-neighbor  information. Furthermore, a small-signal model of a four dc-ES s system with the primary and secondary controllers is developed. The eigenvalue analysis is presented to show   the effect of the communication weight on system stability. Finally, the effectiveness of the proposed control scheme and the small-signal model is verified in an is landed dc micro grid under different scenarios through simulation and  experimental studies.


  1. Consensus
  2. Dc micro grid
  3. Distributed control
  4. Electric springs (ES)
  5. Small-signal stability



 Fig.1.Distributed network with multiple dc -ES s



Fig. 2.SE Z. Controller comparison. (a) Node bus voltage, (b) dc-ES s output

power, (c) SOC, and (d) state variables xi .

Fig. 3. Proposed controller with different a i j . (a) and (d) Average  bus voltages with a i j = 0.5 and a i j = 10. (b) and (e) State variables with a i j = 0.5 and a i j = 10. (c) and (f) Bus voltages with a i j = 0.5  and a i j = 10.

Fig. 4. dc-ES 4 failure at 5 s. (a) Node bus voltage, (b) output power,  and (c) SOC.

Fig. 5. Proposed controller with communication delay τ . (a) Node bus  average voltage, (b) SOC, and (c) state variables xi .


Fig. 6. Proposed controller with five dc-ES s. (a) Node bus voltage, (b) output power, and (c) SOC.


A hierarchical two-level voltage control scheme was proposed for dc-ES s in a micro grid using the consensus algorithm to estimate the average dc-bus voltage and promote SOC balance among different dc-ES s. The small-signal model of four dc-E S s system incorporating the controllers was developed for eigenvalues analysis to investigate the stability of the system. The consensus of the observed average voltages and the defined state variables has been proven.


Results show that the control can improve the voltage control accuracy of dc-E S s and realize power sharing in proportion to the SOC. The resilience of the system against the link failure has been improved and the system can still maintain operations as long as the remaining communication graph has a spanning tree. Simulation and experimental results also verify that the correctness and effectiveness of the proposed model and controller strategy.


[1] X. Lu, K. Sun, J. M. Guerrero, J. C. Vasquez, and L. Huang, “State-of charge balance using adaptive droop control for distributed energy storage systems in DC micro grid applications,” IEEE Trans. Ind. Electron., vol. 61, no. 6, pp. 2804–2815, Jun. 2014.

[2] Q. Sh a f i e e, T. Drag ice v i c, J. C. Vasquez, and J. M. Guerrero, “Hierarchical control for multiple DC-micro grids clusters,” IEEE Trans. Energy Con v e r s., vol. 29, no. 4, pp. 922–933, Dec. 2014.

[3] W. Ya o, M. Chen, J. Mat as, J. M. Guerrero, and Z. M. Q i an, “Design and analysis of the droop control method for parallel invert er s  considering the impact of the complex impedance on the power sharing,” IEEE Trans. Ind. Electron., vol. 58, no. 2, pp. 576–588, Feb. 2011.

[4] V. Na s i r i an, S. M o a y e d i, A. D a v o u d i and F. Lewis, “Distributed cooperative control of DC micro grids,” IEEE Trans. Power Electron., vol. 30, no. 4, pp. 6725–6741, Dec. 2014.

[5] J. M. Guerrero, J. C. Vasquez, J. Mat as, L. G. d e Vi cu˜n a, and M. Cast i l la, “Hierarchical control of droop-controlled AC and DC micro grids—A general  approach toward standardization,” IEEE Trans. Ind. Electron., vol. 58, no. 1, pp. 158–172, Jan. 2011.

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