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.

Model Predictive Control of PV Sources in A Smart DC Distribution System Maximum Power Point Tracking and Droop Control



In a dc distribution system, where multiple power sources supply a common bus, current sharing is an important issue. When renewable energy resources are considered, such as photovoltaic (PV), dc/dc converters are needed to decouple the source voltage, which can vary due to operating conditions and maximum power point tracking (MPPT), from the dc bus voltage. Since different sources may have different power delivery capacities that may vary with time, coordination of the interface to the bus is of paramount importance to ensure reliable system operation. Further, since these sources are most likely distributed throughout\ the system, distributed controls are needed to ensure a robust and fault tolerant control system. This paper presents a model predictive control-based MPPT and model predictive control-based droop current regulator to interface PV in smart dc distribution systems. Back-to-back dc/dc converters control both the input current from the PV module and the droop characteristic of the output current injected into the distribution bus. The predictive controller speeds up both of the control loops, since it predicts and corrects error before the switching signal is applied to the respective converter.


  1. DC microgrid
  2. Droop control
  3. Maximum power point tracking (MPPT)
  4. Model predictive control (MPC)
  5. Photovoltaic (PV)
  6. Photovoltaic systems




Fig. 1. Multiple-sourced dc distribution system with central storage.



Fig. 2. Ideal bus voltage and load power as system impedance increases and loads are interrupted to prevent voltage collapse. (a) Bus voltage decreases in response to increased system impedance at t1 to reach the operating point on the new P–V curve at t2 . The new bus voltage is below the UVP limit, so control action cause load to be shed, moving to a new operating point on the same P–V curve at t3 with a higher bus voltage. (b) Load power in the system changes as point-of-load converters are turned OFF to reduce total system load when the bus voltage drops below the UVP.


Fig. 3. Response of dc bus voltage to step changes in the power drained by load.


Fig. 4. Response of dc bus voltage and output power to imbalanced input PV sources


Fig. 5. Response validation of dc bus voltage to step changes in the power drained by load.


Fig. 6. Response validation of dc bus voltage and output power to imbalanced input PV sources.


Fig. 7. Response of dc bus voltage and output power to the input PV sources of Fig. 7.


 High efficiency and easy interconnection of renewable energy sources increase interests in dc distribution systems. This paper examined autonomous local controllers in a single-bus dc microgrid system for MPP tracked PV sources. An improved MPPT technique for dc distribution system is introduced by predicting the error at next sampling time using MPC. The proposed predictive MPPT technique is compared to commonly used P&O method to show the benefits and improvements in the speed and efficiency of the MPPT. The results show that the MPP is tracked much faster by using the MPC technique than P&O method.

In a smart dc distribution system for microgrid community, parallel dc/dc converters are used to interconnect the sources, load, and storage systems. Equal current sharing between the parallel dc/dc converters and low voltage regulation is required. The proposed droop MPC can achieve these two objectives. The proposed droop control improved the efficiency of the dc distribution system because of the nature of MPC, which predicts the error one step in horizon before applying the switching signal. The effectiveness of the proposed MPPT-MPC and droop MPC is verified through detailed simulation of case studies. Implementation of the MPPT-MPC and droop MPC using dSPACE DS1103 validates the simulation results.


[1] Z. Peng, W. Yang, X. Weidong, and L. Wenyuan, “Reliability evaluation of grid-connected photovoltaic power systems,” IEEE Trans. Sustain. Energy, vol. 3, no. 3, pp. 379–389, Jun. 2012.

[2] W. Baochao, M. Sechilariu, and F. Locment, “Intelligent DC microgrid with smart grid communications: Control strategy consideration and design,” IEEE Trans. Smart Grid, vol. 3, no. 4, pp. 2148–2156, Dec. 2012.

[3] R. Majumder, “A hybrid microgrid with DC connection at back to back converters,” IEEE Trans. Smart Grid, vol. 5, no. 1, pp. 251–259, Jun. 2013.

[4] R. Lasseter, A. Akhil, C. Marnay, J. Stephens, J. Dagle, R. Guttromson, A. S. Meliopoulous , R. Yinger, and J. Eto, “Integration of distributed energy resources. The CERTS microgrid concept,” U.S. Dept. Energy, Tech. Rep. LBNL-50829, 2002.

[5] T. Esram and P. L.Chapman, “Comparison of photovoltaic array maximum power point tracking techniques,” IEEE Trans. Energy Convers., vol. 22, no. 2, pp. 439–449, Jun. 2007.