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.

Autonomous Power Management for Interlinked AC-DC Microgrids


The existing power management schemes for interlinked AC-DC microgrids have several operational drawbacks. Some of the existing control schemes are designed with the main objective of sharing power among the interlinked microgrids based on their loading conditions, while other schemes regulate the voltage of the interlinked microgrids without considering the specific loading conditions. However, the existing schemes cannot achieve both objectives efficiently. To address these issues, an autonomous power management scheme is proposed, which explicitly considers the specific loading condition of the DC microgrid before importing power from the interlinked AC microgrid. This strategy enables voltage regulation in the DC microgrid, and also reduces the number of converters in operation. The proposed scheme is fully autonomous while it retains the plug-nplay features for generators and tie-converters. The performance of the proposed control scheme has been validated under different operating scenarios. The results demonstrate the effectiveness of the proposed scheme in managing the power deficit in the DC microgrid efficiently and autonomously while maintaining the better voltage regulation in the DC microgrid.


  1. Autonomous control
  2. Distributed control
  3. Droop control
  4. Hybrid microgrids
  5. Interlinked microgrids
  6. Power management



Fig. 1. Interlinked AC-DC microgrids and their control strategy.


Fig. 2 Scenario 1: Results showing (a) generators and tie-converter power, (b) DC microgrid voltage and (c) tie-converter control signals for four different load operating conditions.

Fig. 3. Scenario 2: Results showing (a) DC microgrid load demand, (b) generators and tie-converter power, (c) DC microgrid voltage and (d) tie-converter control signals at varying solar PV and load operating conditions.


An autonomous power management scheme has been presented for interlinked AC-DC microgrids having different configurations. The proposed scheme manages the power deficit in the DC microgrid efficiently and autonomously. The number of tie-converters in operation has been reduced with the proposed prioritization to avoid unnecessary operational losses. The scheme has demonstrated better voltage regulation in the DC microgrid. The performance and robustness of the proposed scheme have been validated for two different scenarios of the DC microgrid at variable load conditions.


[1] J. Rocabert, A. Luna, F. Blaabjerg, and P. Rodr´ıguez, “Control of power converters in AC microgrids,” IEEE Transactions on Power Electronics, vol. 27, no. 11, pp. 4734–4749, Nov. 2012.

[2] M. Liserre, T. Sauter, and J. Y. Hung, “Future energy systems: integrating renewable energy sources into the smart power grid through industrial electronics,” IEEE Industrial Electronics Magazine, vol.4. no. 1, pp. 18–37, Mar. 2010.

[3] M. Tsili and S. Papathanassiou, “A review of grid code technical requirements for wind farms,” IET Renewable Power Generation, vol. 3, no. 3, pp. 308–332, Sep. 2009.

[4] T. Strasser, F. Andr´en, J. Kathan, C. Cecati, C. Buccella, P. Siano, P. Leit˜ao, G. Zhabelova, V. Vyatkin, P. Vrba, and V. Maˇr´ık, “A review of architectures and concepts for intelligence in future electric energy systems,” IEEE Transactions on Industrial Electronics, vol. 62, no. 4,pp. 2424–2438, Apr. 2015.

[5] A. Kwasinski, “Quantitative evaluation of dc microgrids availability: Effects of system architecture and converter topology design choices,” IEEE Transactions on Power Electronics, vol. 26, no. 3, pp. 835–851, Mar. 2011.