**ABSTRACT:**** **

Recently, dc electric springs (dc-ESs) have been proposed to understand voltage regulation and power quality improvement in dc microgrids. This paper establishes a distributed unified control framework for multiple dc- ESs in a dc microgrid and presents the small-signal stability separation of the system. The primary level implements a droop control to coordinate the operations of multiple dc-ESs. 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-ESs.

**ELECTRIC SPRINGS**

With the design, the cooperative control can achieve average dc-bus voltage consensus and maintain SOC balance among different dc-ESs using only neighbor-to-neighbor information. Furthermore, a small-signal model of a four dc-ESs 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 islanded dc microgrid under different scenarios through simulation and experimental studies.

**KEYWORDS:**

- Consensus
- Dc microgrid
- Distributed control
- Electric springs (ES)
- Small-signal stability

**SOFTWARE:** MATLAB/SIMULINK

**SCHEMATIC DIAGRAM:**

** **Fig.1.distributed network with multiple dc -ESs

** ****EXPECTED SIMULATION RESULTS:**

** **

Fig. 2.SEZ. Controller comparison. (a) Node bus voltage, (b) dc-ESs output

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

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

Fig. 4. dc-ES4 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-ESs. (a) Node bus voltage, (b) output power, and (c) SOC*.*

* ***CONCLUSION:**

A hierarchical two-level voltage control scheme was proposed for dc-ESs in a microgrid using the consensus algorithm to estimate the average dc-bus voltage and promote SOC balance among different dc-ESs. The small-signal model of four dc-ESs 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.

###### MICROGRID

Results show that the control can improve the voltage control accuracy of dc-ESs 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.

**REFERENCES:**

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

[2] Q. Shafiee, T. Dragicevic, J. C. Vasquez, and J. M. Guerrero, “Hierarchical control for multiple DC-microgrids clusters,” *IEEE Trans. Energy Convers.*, vol. 29, no. 4, pp. 922–933, Dec. 2014.

[3] W. Yao, M. Chen, J. Matas, J. M. Guerrero, and Z. M. Qian, “Design and analysis of the droop control method for parallel inverters 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. Nasirian, S. Moayedi, A. Davoudi and F. Lewis, “Distributed cooperative control of DC microgrids,” *IEEE Trans. Power Electron.*, vol. 30, no. 4, pp. 6725–6741, Dec. 2014.

[5] J. M. Guerrero, J. C. Vasquez, J. Matas, L. G. de Vicu˜na, and M. Castilla, “Hierarchical control of droop-controlledAC andDCmicrogrids—A general approach toward standardization,” *IEEE Trans. Ind. Electron.*, vol. 58, no. 1, pp. 158–172, Jan. 2011.