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


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.


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.


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



 Fig.1.distributed network with multiple dc -ESs



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.


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.


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.


[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.

A Simple Active and Reactive Power Control for Applications of Single-Phase Electric Springs


Aiming at effective power management in micro grids with high penetration of renewable energy sources (R E S s), the paper proposes a simple active and reactive power control for the so-called second-generation, single-phase electric springs (ES-2), that overcomes the shortcomings of the existing Electric  Springs control methods. By the proposed control, the unpredictable power generated from R E S s is divided into two parts, i.e. the one absorbed by the ES-2 that still varies and the other injected into the grid that turns to be controllable, by a simple and accurate signal manipulation that works both at steady-state and during RES transients.


is believed that such a control is suitable for the distributed power generation, especially at domestic homes.  In the paper, the proposed control is supported by a theoretical background. Its effectiveness is at first validated by simulations and then by experiments. To this purpose, a typical RES application is considered, and an experimental setup is arranged, built up around an Electric Springs -2 implementing the proposed control. Testing of the setup is carried out in three steps and proves not only the smooth operation of the Electric Springs-2 itself, but also its capability in running the application properly.



  1. Electric springs
  2. Smart load
  3. Microgrids
  4. active and reactive Power control
  5. Grid connected
  6. Distributed generation.





Fig. 1: Topology of Electric Springs -2 and associated circuitry


Fig. 2: Simulation wave forms under different variations of the input active power. (a) From 1.6 kW to 1.1 kW and then back to 1.6 kW @ VG=230 V. (b) From 8 kW to 2 kW and then back to 8 kW @ VG=200 V. (c) From 8 kW to 4 kW and then to 2 kW @ VG=200 V.

Fig. 3: Transient ES-2 responses to a change of the line voltage with Pinref=1.5kW. (a) From 240V to 210V. (b) From 210V to 240V.

Fig. 4: Simulation waveforms before and after grid distortion. (a) Results of PLL. (b) Results of active and reactive power of ES system.


The input active and reactive power control is proposed for the purpose of practical application of ES-2 in this paper. An overall review and analysis have been done on the existing control strategies such as δ control and RCD control, revealing that the essences of the controls on ES-2 are to control the input active power and reactive power. If being equipped together with the distributed generation from RESs, the ES-2 can manage the fluctuated power and make sure the controllable power to grid, which means that the ES-2 is able to deal with the active power captured by MPPT algorithm.


have been done on the steady and transient analysis and also under the grid anomalies, validating the effectiveness of the proposed control. Three steps have been set in the experiments to verify the three typical situations and namely the active power generated by the GCC from RESs are, 1) more than; 2) less than; 3) the same as the load demand. Tested results have validated the proposed active and reactive power control.



  • Cheng and Y. Zhu, “The state of the art of wind energy conversion systems and technologies: A review,” Energy Conversion and Management, vol. 88, pp. 332–347, Dec. 2014.
  • Sotoodeh and R. D. Miller, “Design and implementation of an 11-level inverter with FACTS capability for distributed energy systems,” IEEE J. Emerging Sel. Topics Power Electron., vol.2, no. 1, pp. 87–96, Mar. 2014.
  • Wang, and D. N. Truong, “Stability enhancement of a power system with a PMSG-based and a DFIG-based offshore wind farm using a SVC With an adaptive-network-based fuzzy inference system,” IEEE Trans. Ind. Electron., vol. 60, no. 7, pp. 2799–2807, Jul. 2013.
  • active and reactive power control projects

Mitigating Distribution Power Loss of DC Microgrids with DC Electric Springs


DC microgrids fed with substantial intermittent renewable energy sources (RES) face the immediate problem of power imbalance and the subsequent DC bus voltage fluctuation problem (that can easily breach power system standards). It has recently been demonstrated that DC electric springs (DCES), when connected with series non-critical loads, are capable of stabilizing the voltage of local nodes and improving the power quality of DC microgrids without large energy storage.


In this paper, two centralized model predictive control (CMPC) schemes with (i) non-adaptive weighting factors and (ii) adaptive weighting factors are proposed to extend the existing functions of the DCES in the microgrid. The control schemes coordinate the DCES to mitigate the distribution power loss in the DC microgrids, while simultaneously providing their original function of DC bus voltage regulation. Using the DCES model that was previously validated with experiments, simulations based on MATLAB/SIMULINK platform are conducted to validate the control schemes. The results show that with the proposed CMPC schemes, the DCES are capable of eliminating the bus voltage offsets as well as reducing the distribution power loss of the DC microgrid.


  1. DC microgrids
  2. DC electric springs (DCES)
  3. Centralized model predictive control (CMPC)
  4. Non-adaptive weighting factors
  5. Adaptive weighting factors
  6. Distribution power loss




Fig. 1. An m-bus DC microgrid with n RES units.



 Fig. 2. Waveforms of the power supply by RES and the bus voltages of the DC microgrid without DCES.

Fig. 3. Waveforms of the bus voltages of the DC microgrid when the DCES is installed at the five buses.

Fig. 4. Waveforms of the bus voltages of the DC microgrid with three DCES installed at bus 1, bus 4 and bus 5.

Fig. 5. The comparisons of the power loss on the distribution lines between α=1 and α=0.9 when three DCES are installed.

Fig. 6. Waveforms of the bus voltages of the DC microgrid with four DCES installed at bus 1, bus 2, bus 4 and bus 5.

Fig. 7. Comparisons of the power loss on the distribution lines for different values of α when four DCES are installed.


 DC electric springs (DCES) is an emerging technology that can be used to stabilize and improve the power quality of DC microgrids. In this paper, a centralized model predictive control (CMPC) with both non-adaptive weighting factors and adaptive weighting factors is proposed for multiple DCES to further mitigate the power loss on the distribution lines of a DC microgrid.


Using a DCES model previously verified with experiments, simulation studies have been conducted for a DC microgrid setup. Simulation results on a 48 V five-bus DC microgrid show that the energy is saved about 49.4% in the 5 seconds when three DCES are controlled by the CMPC with non-adaptive weighting factors and is saved about 58.5% in the 5 seconds when four DCES are controlled by the CMPC with non-adaptive weighting factors. It is also demonstrated that the power loss on the distribution lines of the DC microgrid can be further reduced by the CMPC with adaptive weighting factors, as compared to the CMPC with non-adaptive weighting factors.


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[5] T. Gragicevic, X. Lu, J. C. Vasquez, and J. M. Guerrero, “DC microgrids−part I: a review of control strategies and stabilization techniques,” IEEE Trans. Pow. Elect., vol. 31, no. 7, Jul. 2016.

An Improved Beatless Control Method of AC Drives for Railway Traction Converters


The traction converter consists of a single phase AC DC rectifier and a three phase DC AC invert er. Due to special structural characteristics of single phase rectifier, a fluctuating voltage component with the frequency twice of the grid’s, exists in DC link voltage. Fed by fluctuating DC link voltage, a beat phenomenon occurs in traction motor, and harmonic components appear in both stat or current and electromagnetic torque, especially when motor operates near the ripple frequency. In this paper, the mechanism and influence of fluctuating voltage are analyzed in detail. Based on modeling analysis of motor and switching function of invert er, a frequency compensation factor is derived in vector control of induction motor. Then an improved frequency compensation control method is proposed to suppress beat phenomenon without LC resonant circuit. Finally the simulation verifies the modified scheme.


  1. Fluctuating DC voltage
  2. Beat phenomenon
  3. Vector control
  4. Beat less control



 Fig. 1. F O C with frequency compensation for Induction Motor


 Fig. 2. Waves of stat or current and electromagnetic torque of traction Motor

Fig. 3. FF T of stat or current and electromagnetic torque before adding frequency compensation method

Fig. 4. FF T of stat or current and electromagnetic torque after adding traditional frequency compensation method

Fig. 5. FF T of stat or current and electromagnetic torque after adding improved frequency compensation method


 In high power traction converters, without LC filter circuit paralleled in DC link, a fluctuating voltage twice of the grid frequency contains in DC link voltage. This paper aims at adopting software control method to suppress beat phenomenon in traction motor caused by DC ripple voltage. According to theoretical analysis, output power of motor, DC link capacitor and power factor influenced the DC ripple voltage. Then, the aspect of switching function and motor model analyzed the influences of fluctuating voltage in detail. Based on above analysis, combining with rotor field oriented control of traction motor, the frequency of switching function is modified to suppress beat phenomenon. An improved frequency compensation control method is proposed. Simulation model is built to verify the proposed scheme. Finally, the drag experiment on a dynamo meter test platform verified the proposed control method.


[1] J. K l i ma, M. Ch  o mat, L. Sch re i e r, “Analytical Closed-form Investigation of P WM Invert er Induction Motor Drive Performance under DC Bus Voltage Pulsation,” I ET Electric Power Application, Vol. 2, No. 6, pp. 341–352, Nov, 2008.

[2] H. W. van d e r Bro e ck and H. C. S k u d e l n y, “Analytical analysis of the harmonic effects of a P WM AC drive,” in IEEE Transactions on Power Electronics, vol. 3, no. 2, pp. 216-223, Apr 1988.

[3] K Na k at a, T N a k a m a chi , K Na k am u r a, “A beat less control of invert er-induction motor system driven by a rippled DC power source,” Electrical Engineering in Japan, Vol.109, No.5, pp.122-131,1989.

[4] Z Sal am, C.J. Goodman, “Compensation of fluctuating DC link voltage for traction invert er driver,” Power Electronics and Variable Speed Drives, 1996. Sixth International Conference on (Conf. Pub l. No. 429), pp. 390-395, 1996.

[5] S. K o u r o, P. Le z an a, M. An g u lo and J. Rodriguez, “Multi carrier P WM With DC-Link Ripple Feed forward Compensation for Multilevel Invert er s,” IEEE Transactions on Power Electronics, vol. 23, no. 1, pp. 52- 59, Jan. 2008.

Integrated Photovoltaic and Dynamic Voltage Restorer System Configuration


This paper presents a new system structure for integrating a grid-connected photo voltaic (P V) system together with a self-supported dynamic voltage restorer (DVR). The proposed system termed as a “six-port converter,” consists of nine semiconductor switches in total. The proposed configuration retains all the essential features of normal P V and DVR systems while reducing the overall switch count from twelve to nine. In addition, the dual functionality feature significantly enhances the system robustness against severe symmetrical/asymmetrical grid faults and voltage dips. A detailed study on all the possible operational modes of six-port converter is presented. An appropriate control algorithm is developed and the validity of the proposed configuration is verified through extensive simulation as well as experimental studies under different operating conditions.


  1. Bidirectional power flow
  2. Distributed power generation
  3. Photovoltaic (PV) systems
  4. Power quality
  5. Voltage control




 Fig. 1. Proposed integrated PV and DVR system configuration.


Fig. 2. Simulation results: operation of proposed system during health grid mode (PV-VSI: active and DVR-VSI: inactive). (a) Vpcc; (b) PQload; (c) PQgrid; (d) PQpv-VSI; and (e) PQdvr-VSI.

Fig. 3. Simulation results: operation of proposed system during fault mode (PV-VSI: inactive and DVR-VSI: active). (a) Vpcc; (b) Vdvr; (c) Vload; (d) PQload; (e) PQgrid; (f) PQpv-VSI; and (g) PQdvr-VSI.

Fig. 4. Simulation results: operation of proposed system during balance three phase sag mode (PV-VSI: active and DVR-VSI: active). (a) Vpcc; (b) Vdvr-VSI; (c) Vload; (d) PQgrid; (e) PQpv-VSI; and (f) PQdvr-VSI.

Fig. 5. Simulation results: operation of proposed system during unbalanced sag mode (PV-VSI: active and DVR-VSI: active). (a) Vpcc; (b) Vdvr-vsi; (c) Vload; (d) PQgrid; (e) PQpv-VSI; and (f) PQdvr-VSI.

Fig. 6. Simulation results: operation of proposed system during inactive PV plantmode (PV-VSI: active and DVR-VSI: active). (a) Vpcc; (b) Vload; (c) Vdc; (d) PQload; (e) PQdvr-VSI; and (f) PQpv-VSI.


 In this paper, a new system configuration for integrating a conventional grid-connected P V system and self supported DVR is proposed. The proposed configuration not only exhibits all the functionalities of existing P V and DVR system, but also enhances the DVR operating range. It allows DVR to utilize active power of P V plant and thus improves the system robustness against sever grid faults. The proposed configuration can operate in different modes based on the grid condition and P V power generation. The discussed modes are healthy grid mode, fault mode, sag mode, and P V inactive mode. The comprehensive simulation study and experimental validation demonstrate the effectiveness of the proposed configuration and its practical feasibility to perform under different operating conditions. The proposed configuration could be very useful for modern load centers where on-site P V generation and strict voltage regulation are required.


[1] R. A. Walling, R. Saint, R. C. Dugan, J. Burke, and L. A. Kojovic, “Summary of distributed resources impact on power delivery systems,” IEEE Trans. Power Del., vol. 23, no. 3, pp. 1636–1644, Jul. 2008.

[2] C. Meza, J. J. Negroni, D. Biel, and F. Guinjoan, “Energy-balance modeling and discrete control for single-phase grid-connected PV central inverters,” IEEE Trans. Ind. Electron., vol. 55, no. 7, pp. 2734–2743, Jul.2008.

[3] T. Shimizu, O. Hashimoto, and G. Kimura, “A novel high-performance utility-interactive photovoltaic inverter system,” IEEE Trans. Power Electron., vol. 18, no. 2, pp. 704–711, Mar. 2003.

[4] S. B. Kjaer, J. K. Pedersen, and F. Blaabjerg, “A review of single-phase grid-connected inverters for photovoltaic modules,” IEEE Trans. Ind.Appl., vol. 41, no. 5, pp. 1292–1306, Sep./Oct. 2005.

[5] T. Esram, J. W. Kimball, P. T. Krein, P. L. Chapman, and P. Midya, m“Dynamic maximum power point tracking of photovoltaic arrays using ripple correlation control,” IEEE Trans. Power Electron., vol. 21, no. 5, pp. 1282–1291, Sep. 2006.