Droop Controlled DC Microgrid Research Articles

Maximum span determination and optimal sizing of cable for improved performance of droop-controlled DC microgrid

DC microgrids are seen as smart solutions to interface DC loads and distributed energy resources (DERs). However, in DC microgrids, the placement of sources and loads as well as the size of cable impact the system’s span, regulation of voltage, and losses. This paper proposes novel algorithms to determine the maximum span and optimal size of cable for the improved performance of a droop-controlled DC microgrid. The proposed algorithms utilize an improved power flow analysis (IPFA) method based on Newton-Raphson technique to determine the maximum span and the optimal size of cable, enhancing the voltage regulation and reducing the cost. Additionally, the impacts of power rating, droop constants, and size of cable on the DC microgrid’s maximum span are investigated and reported. Owing to the intricate nature of the problem concerning the ideal size of cable for the droop-controlled DC microgrid, a heuristic optimization approach is employed. Further to enhance the rate of convergence and computational performance, an improved particle swarm optimization (IPSO) is also proposed. The constraint of keeping the bus voltage variations below the allowable voltage regulation limits is applied to the objective function of the optimization problem. In the case of a droop-controlled, DC microgrid having a specified configuration, the suggested algorithm can determine the ideal size of cable, guaranteeing both the least cost and enhanced voltage regulation. Comprehensive numerical and modelling results have been presented for a droop-controlled DC microgrid with different loads and DERs to verify the effectiveness of the proposed methods. Furthermore, the analysis reveals that configuration III of the DC microgrid with an optimal cable size of 19 mm2 lowers the absolute voltage regulation to as low as 1.06 V. The results of the detailed analysis validate the enhanced performance of the proposed algorithms and are highly useful to both system designers and consumers of the DC microgrids, eventually paving the way for the widespread use of DC microgrids in the future.

Impedance Shaping Method for System-Level Stabilization of Droop-Controlled DC Microgrids

Impedance Shaping Method for System-Level Stabilization of Droop-Controlled DC Microgrids

Control Strategy to Mitigate Voltage Ripples in Droop-Controlled DC Microgrids

Control Strategy to Mitigate Voltage Ripples in Droop-Controlled DC Microgrids

Large-signal stability analysis of islanded DC microgrids with multiple types of loads

Due to the lack of support for the power system, the small inertia of the system, and the access to negative impedance elements, the stable operation of the islanded DC microgrid can be challenging. To ensure the stability of the system in a large operating range, a system-level large-signal stability analysis is carried out for a droop-controlled dc microgrid in this article. Firstly, the system-level equivalent model of the DC microgrid is established, the steady-state of the DC microgrid is analyzed and the instabilities principle, as well as their physical interpretation, is revealed. Second, necessary and sufficient conditions of the DC microgrid are deduced by the Lyapunov direct method, and the load limit of the DC microgrid is obtained under the restriction of stability and voltage deviation. Third, the correctness of the theoretical analysis is verified by the simulation results of a droop-controlled DC microgrid system.

Disturbance Rejection Analysis of a Droop-Controlled DC Microgrid Through a Novel Mathematical Modeling

DC microgrids are gaining interest by the increase in dc loads and renewable resource penetrations. Photovoltaic (PV) arrays are the primary renewable resources utilized in dc microgrids with variations in their productions. Power variations are seen as disturbances from other sources’ point of view. The droop control method is frequently used to control dc microgrids and assures power sharing among parallel-connected converters. It is of great interest to assess droop controller functionality in rejecting disturbances, and maintain constant output voltage. Therefore, there is a need for a comprehensive converter and controller modeling to study the effect of disturbances on the system behavior. In this article, the converter’s small-signal model is utilized in deriving the system state space model. Via the derived model, the effect of different circuit parameters on time and frequency responses is studied. The line resistances’ effect on the parallel operation of converters is also studied. To verify the droop controller’s functionality, the converter’s output impedance is derived. Disturbances are applied to the load current, and the system response is analyzed. Finally, the dc microgrid plug and play feature is addressed by proposing an algorithm for deriving the multiple converters’ mathematical model. Simulations and hardware-in-the-loop (HIL) experiments are conducted to verify the mathematical model and controllers’ performance.

Comprehensive local control design for eliminating line resistance effect on power sharing degradation in DC microgrids

In droop-controlled DC microgrids, parasitic resistances of long conductive lines introduce additional terms for the power calculation and impact the power sharing accuracy. This paper proposed a comprehensive local control design for enhancing power sharing accuracy and restoring DC bus voltage while increasing stability performance in DC microgrids. A passive controller is used in the primary control to ensure the sufficient bandwidth of controller in case of frequent operation modes alteration and voltage deviation in the DC microgrid. A concept of Virtual Negative Line Resistance (VNLR) is used in the secondary control layer to compensate the real line resistance such that line resistance no longer degrades power sharing accuracy. The common DC bus voltage needs to be monitored in the proposed secondary controller. Simultaneously, the common DC bus voltage can be restored as the designed value. The monitored DC bus voltage signal is filtered by a designed low-pass filter such that mid-high frequency dynamics can be decoupled between secondary controls and primary controls. Then the entire local control scheme relaxes three Degrees of Freedom (DoF) which can be used for upper layer controls. Finally, the proposed control method has been experimentally validated in a 50 V DC microgrid laboratory testing system.

Virtual Resistance Tradeoff Design for DCMG Grid-Forming Converters Considering Static- and Large-Signal Dynamic Constraints

This article brings forward a design method of virtual resistance for droop-controlled dc microgrids (DCMGs). Although droop control is widely employed in coordinated DCMGs to coordinate different energy sources, few works address thoroughly the principles for a proper virtual resistance design. In this article, dynamic stability and static voltage deviation constraints are taken into consideration as the main criteria to be complied with by the virtual resistance design. In critical cases, constant power loads (CPLs) may substantially decrease system damping and adversely affects the stability of the system. In this sense, the large-signal stability model is developed including CPLs by using the Lyapunov function, and it is subsequently analyzed to infer the stability criterion. Theoretically, bus voltage is the most important index when addressing the DCMG control; hence, the impact of virtual resistance on the voltage deviation is explored as well. The research presented in this article finds out that virtual resistance influence on system stability is opposite to that on voltage deviation; thus, a tradeoff method based on the containment principle is developed. Throughout the proposed compromised design, we can adjust the weight coefficient to satisfy different performance requirements of DCMGs. The effectiveness of the proposed scheme is validated through experimental results.

System-Level Large-Signal Stability Analysis of Droop-Controlled DC Microgrids

In the literature, many studies on stability analysis of dc microgrids have been conducted. However, most of them mainly focus on small-signal stability. On the other hand, few works analyze large-signal stability, but the major part of these works is based on a single unit or a simple cascaded system as a case study. Different from those, this article aims to address the large-signal stability analysis of a dc microgrid from a system-level perspective. First, the equivalent model of a droop-controlled dc microgrid is developed. Subsequently, the Lyapunov-based large-signal stability analysis and the stability criterion are derived, and mixed potential theory is used to make comparisons to verify the effectiveness of the derived criterion. The equilibrium point stability for different operation stages was obtained by means of theoretical calculation. Furthermore, the instabilities principle as well as their physical interpretation is revealed. In this article, the bus voltage is used as the only index to assess the microgrid power balance. Hence, the power load limit can be obtained by taking into consideration the stability and voltage deviation constraints. Finally, simulation and experimental results from a four-converter dc microgrid system verify the feasibility of the proposed theoretical analysis.

An Improved Voltage-Shifting Strategy to Attain Concomitant Accurate Power Sharing and Voltage Restoration in Droop-Controlled DC Microgrids

This article proposes a distributed secondary level control strategy for dc microgrids, which achieves accurate and proportional power sharing and dc-bus voltage deviation restoration based on voltage shifting. In contrast to similar approaches, only one variable per converter is transmitted in the low-bandwidth communication link and with a simple integrator as the secondary level controller both objectives are achieved simultaneously. The information state shared between converters is a λ factor that incorporates the converter output voltage and power information. The secondary control computes the average λ locally and the controller generates an unique voltage-shifting term that modifies the converter output voltage reference. When all converters' λ converge to the average value, both proportional power sharing and dc-bus voltage restoration are attained. The proposed technique suppresses the need for a complex control structure and large amount of converter variables. The proposed control is evaluated through PLECS simulation and it is validated in a 6.4 kW dc microgrid setup.

Application of linearised load flow method for droop‐controlled DCMGs

In this study, the authors present a linear power flow method for droop-controlled DC microgrids (MGs). Traditional power flow techniques do not apply to droop-controlled DCMGs owing to the power and voltage flexibility capability of the droop-controlled dispatchable generation units. Therefore, new power flow techniques embodying the droop-control operation philosophy were developed by the researchers. The existing methods are time-consuming since they involve iterative solutions of a set of non-linear equations. The proposed linear power flow method is accurate, simple, and gives faster results in comparison to the existing methods. The power flow model applies to all load types (constant power, constant current, and constant resistance) and works for both radial and non-radial system configurations. The linear power flow can be applied for convex optimisation, optimal power flow, and network reconfiguration problems. The proposed method is validated on five test systems. A comparison with a modified Newton–Raphson power flow demonstrates that the proposed linear power flow technique provides accurate results. The maximum error in voltage calculation is not more than 0.0812%. The performance of the proposed method is also acceptable for heavy loads and high line resistances. The computational time reduces significantly with the proposed method.

Admittance matrix computation and stability analysis of droop controlled DC micro-grids with CPL

In this paper, an analytical method of computing the admittance matrix is introduced that facilitates the stability analysis of DC micro-grid systems, in presence of constant power loads (CPLs). Due to their nonlinear behaviour, CPLs can yield instability in DC micro-grids; an effect referred to as ‘negative impedance instability’. The proposed method is particularly useful when a typical controller (droop control, voltage regulation) is designed to control the DC bus voltage of the micro-grid, as it allows the factorisation of the admittance matrix separating singular matrices. In doing so, the closed-loop stability proof can be more easily approached by isolating the singularities and, then employing straightforward linear algebra tools to arrive at the stability conditions. In order to validate the proposed approach, compute the admittance matrix and test the stability conditions, a DC micro-grid with n DC/DC power converters connected to a CPL is considered. Simulation results are also displayed to demonstrate the desired operation of the DC micro-grid control and design framework.

Advanced Secondary Voltage Recovery Control for Multiple HESSs in a Droop-Controlled DC Microgrid

For distributed heterogeneous energy storage systems (HESSs) in a dc microgrid, a virtual impedance droop (VID) control, composed of virtual resistance droop control and virtual capacitor droop control, can realize low- and high-frequency power sharing between a battery and supercapacitor (SC) automatically. However, it still suffers from voltage deviation. In this paper, a secondary voltage recovery (SVR) control is proposed for a battery and SC on the basis of VID control. The SVR control for batteries is designed to regulate the average bus voltage to the reference value, depending on the communication between neighboring batteries. Nevertheless, the SVR control for SCs is decentralized to facilitate fast recovery of the state of charge, in spite of the existence of leakage current. Detailed impedance characteristics analysis and small-signal stability analysis are performed to find that the proposed SVR control does not affect the power sharing dominated by the primary VID control and the system stability. Simulations for both a single HESS and multiple HESSs are conducted to verify the effectiveness of the proposed control strategy.

Distributed Economic Power Dispatch and Bus Voltage Control for Droop-Controlled DC Microgrids

This paper proposes a distributed economic power dispatch (EPD) and bus voltage control solution for droop-controlled DC microgrids. For the proposed solution, a local power controller and a local voltage controller are added for each distributed generator (DG) to overcome the limitations of the conventional droop control. The power controller generates the first voltage correction term by comparing the local output power of DG with the reference instruction generated by the proposed distributed EPD algorithm, and thus, it can reduce the operation cost of the microgrid by optimally sharing the load demand among all the participating DGs. The voltage controller generates the second voltage correction term by comparing the nominal DC bus voltage value with the average bus voltage generated by the proposed distributed average bus voltage observation (ABVO) algorithm, and thus, it can realize the global bus voltage regulation of the DC microgrid. In contrast with conventional solutions, the control solution can distribute the computational and communication burdens among all the DGs working in parallel, which is more flexible, scalable, and robust against single-point failure. The effectiveness of the proposed control solution is demonstrated through simulation studies.

Stability Constrained Economic Operation of Islanded Droop-Controlled DC Microgrids

This paper proposes a method to determine optimal droop values of dispatchable distributed generation (DG) units in an islanded droop-controlled dc microgrid. Objectives are to minimize fuel cost and maximize small signal stability of the system. In this paper, a detailed state-space model of an islanded droop-controlled dc microgrid including the converter, network parameters, and network interconnection is developed. The developed model is then used to obtain the dominant eigen value of the system. Particle swarm optimization is used to determine the optimal droop values of the dispatchable DG units in order to simultaneously reduce the fuel cost, increase system damping, and push the most dominant eigen value away from the imaginary axis to the left of the s -plane. The bi-objective optimization is solved using a fuzzy max–min based approach. The proposed method is validated on a sample three-bus droop-controlled DCMG test system. Comparison of the result obtained by the fuzzy max–min approach with that of controlled elitist genetic algorithm is also presented in this paper.

A Novel Communication-Based Average Voltage Regulation Scheme for a Droop Controlled DC Microgrid

In a dc microgrid, enhanced voltage regulation (VR) and load sharing (LS) are necessary for the economic and reliable operation of the system. Traditionally, droop control is used for LS in microgrids. However, because of the nature of the droop control, good VR and accurate LS cannot be achieved simultaneously. To overcome this drawback, a low-bandwidth, communication-based average VR technique along with an algorithm for equal voltage correction factor is proposed in this paper. Here, precise LS is achieved via droop control using a high value of droop gain, while good VR is obtained through low-speed control area network (CAN) communication, which provides fault tolerance and expandability feature to the system. Only the local dc bus voltage information is exchanged over CAN by the grid connected converters, which ensure low communication traffic. Thus, sufficient bandwidth is available on the CAN bus that can be used for control and monitoring purpose—a highly desirable proposition for a smart grid application. Effect of communication delays on system stability has been modeled and analyzed. Simulation and experimental results are presented to validate the feasibility of the proposed scheme. Plug-n-play and fail-safe features of the proposed technique are highlighted.

Large signal stability analysis for DC microgrid under droop control based on mixed potential theory

Brayton–Moser's mixed potential theory has been used to analyse the large disturbance stability of DC microgrid with constant power load (CPL), such as current-mode controlled BUCK/BOOST converter with CPL or DC system with multi-stage LC filters. However, the stability analysis of other topology of DC–DC converter or multiple converters worked under droop control is rarely involved. Based on this issue, this paper first establishes the mixed potential model of a single bidirectional BUCK/BOOST converter with CPL. Then, the paper gives the method for establishing the mixed potential model of a droop-controlled DC microgrid with multiple bidirectional BUCK/BOOST converters and CPL. Afterwards, the stability criterion of the analytic form of the system under large disturbance is obtained, which shows that the parameters such as system parameters, control parameters, droop coefficients, and CPL power value have the effects on the system's large signal stability. This paper gives and discusses the relationship between system parameters and stability. Thus, instead of calculating and simulating repeatedly, the stability criterion can judge and ensure the stability of the system under large disturbance in the design process. Simulation results demonstrate the correctness of the simple and easily implemented stability criterion.

Observer-Based DC Voltage Droop and Current Feed-Forward Control of a DC Microgrid

An observer-based dc voltage droop and current feed-forward control for a dc microgrid has been proposed in this paper. With the proposed control scheme, dynamic response of dc voltage control can be improved effectively through using an observer. Moreover, the feedback current for dc voltage droop and the feed-forward current are both obtained from the observer without additional current measurement. Furthermore, system stability analysis shows that, the propose method has enhanced robustness and stability when compared to the traditional droop method under variations of system parameters, such as loads, cable impedances, and droop control gains. In a droop controlled dc microgrid, there exists a trade-off between the load demand sharing accuracy (which needs a high droop gain) and stability (which limits the droop gain). With the above mentioned advantages, the proposed method can effectively address this trade-off in such a system. The effectiveness of the proposed method is verified by experiments in a laboratory dc microgrid with two boost dc–dc converters based distributed generations and a buck type constant power dc load.

An Effective Method for Low-Frequency Oscillations Damping in MultiBus DC Microgrids

This paper proposes a new active method for low frequency (LF) current/power oscillations damping in droop-controlled dc microgrids. Since, LF oscillations are mainly affected by droop controllers of voltage controlled (VC) DGs, detailed small-signal analysis of VC-DGs is provided. Analysis shows that each droop-controlled VC-DG creates a pair of LF complex conjugate zeros. In the proposed method, these zeros are damped by a negative feedforward of the disturbance variables (output currents) of VC-DGs. Stability analysis of the overall dc microgrid reveals that the LF zeros of VC-DGs can affect the LF modes of the system. Therefore, in the proposed method, the effective tuning of feedforward gain of each VC-DG can increase the damping factor of microgrid LF modes and consequenctly improve the dynamic response of the whole system. Moreovere, to gurantee the plug-and-play performance of DGs, a coordinanted tuning criterion for adjusting the proper feedforward gains is presented. It is shown that the proposed method is also robust against structural changes in dc microgrids. A complete set of simulation studies using MATLAB/Simulink is provided which further supports the effectiveness of the proposed active damping method.

Energy Management Strategy for Supercapacitor in Droop-Controlled DC Microgrid Using Virtual Impedance

With a proper energy management strategy (EMS), supercapacitor can be integrated into droop-controlled dc microgrid as an independent supercapacitor energy storage system (SCESS). The resulted microgrid could supply repeatedly quick bursts of electrical power due to load or source transients and improve power quality and lifetime of other distributed generations (DGs) or distributed energy storages. In this paper, a novel control strategy for SCESS is proposed. The method uses the virtual impedance loop to add a virtual resistor and a virtual capacitor connected in series between the converter and dc bus, which decouples power flow between SCESS and other DGs while ensuring the plug `n' play feature. The results show that the proposed EMS has a competing dynamic performance with excellent flexibility as compared to existing methods.

Economic Dispatch for Operating Cost Minimization Under Real-Time Pricing in Droop-Controlled DC Microgrid

In this paper, an economic dispatch problem for total operation cost minimization in dc microgrids is formulated. An operating cost is associated with each generator in the microgrid, including the utility grid, combining the cost-efficiency of the system with demand response requirements of the utility. The power flow model is included in the optimization problem, thus the transmission losses can be considered for generation dispatch. By considering the primary (local) control of the grid-forming converters of a microgrid, optimal parameters can be directly applied to this control level, thus achieving higher control accuracy and faster response. The optimization problem is solved in a heuristic method. In order to test the proposed algorithm, a six-bus droop-controlled dc microgrid is used in the case studies. Simulation results show that under variable renewable energy generation, load consumption, and electricity prices, the proposed method can successfully reduce the operating cost by dispatching economically the resources in the microgrid.