Stability Analysis Of DC Microgrid Research Articles

Passivity-Based Stability Analysis of DC Microgrids Using Physically Decoupled Model

Passivity-Based Stability Analysis of DC Microgrids Using Physically Decoupled Model

Dynamic stability analysis of DC microgrid and construction of stability region of control parameters based on Pioncáre map

In the DC microgrid, the difficulty to maintain the stable operation of DC-DC power electronic devices will increase due to the random fluctuations or step changes of power. However, nonlinear dynamics' instability behaviour is very challenging to obtain through an average linearized stability analysis. Therefore, based on the Pioncáre map, this paper derived a global discrete iterative model and its explicit Jacobian matrix in the polynomial form using second-order Taylor series expansion, to detect nonlinear instability behaviour for DC microgrids. A global polynomial Pioncáre map for the microgrid is established, which contains the voltage-current controlled bidirectional DC-DC converter. Then, the derived discrete-time stability analysis method is compared with the average linearized stability analysis method based on the state space average model. Further discussion about the interactive effect on the parameters is conducted through the Jacobian matrix’ eigenvalues, bifurcation diagrams, Pioncáre sections and phase trajectories, leading to the 2-D and 3-D stable regions of operating parameters. Finally, dynamic simulation is carried out on MATLAB/Simulink. Results show that the method proposed can accurately capture the Neimark–Sacker bifurcation critical point in the DC microgrid, construct the stability region of the control parameters, and could help select the controller parameters of DC microgrids.

Complete Large-Signal Stability Analysis of DC Distribution Network via Brayton-Moser’s Mixed Potential Theory

For a nonlinear RLC network, Brayton and Moser have proposed the so-called general mixed potential function (GMPF) whose time-derivative is negative semi-definite. Then, the equilibrium of the RLC network is stable if it is a local minimum of the GMPF. Therefore, Brayton-Moser’s mixed potential theory is a powerful methodology, which has been widely used in the stability analysis of DC microgrid. However, most of the results in existing references are flawed and incomplete. This paper carries out the complete stability analysis of the DC distribution network with constant power loads via Brayton-Moser’s mixed potential theory. Firstly, several critical points in this theory that are often mistaken are emphasized. Secondly, based on Brayton-Moser’s mixed potential theory, the condition that the equilibrium is a local minimum is proposed. All the low-voltage equilibria are proved to be unstable, and only the high-voltage equilibrium can be stabilizable and the complete stability conditions are provided. Thirdly, some unsolved problems about the stability issue of DC microgrid via Brayton-Moser’s mixed potential theory are presented. Finally, hardware-in-the-loop (HIL) experimental results verify the proposed stability conditions.

Mixed-potential-function-based large-signal stability analysis of DC microgrid with constant power loads

With the development of power grid technology, a large number of constant power loads (CPL) are introduced into the power grid system. The negative damping characteristic of CPL poses a great challenge to the stability of power grid under the condition of large signal disturbance. This paper focuses on the large signal stability and dynamic response characteristics of DC microgrid with CPL. The mixed potential function (MPF) method is adopted to model the large signal characterstic of load converter controlled by the traditional PI control strategy and the new virtual DC motor (VDM) control strategy. The large signal stability criteria and the asymptotic stability region of the DC microgrid system under the two control strategies are derived. The dynamic response characteristics of the DC microgrid are compared under three large signal operation conditions of the load step, load linear change and the load fault. The results show that VDM control strategy can effectively improve dynamic response characteristics of the DC microgrid system compared with those of PI control, and enhance the stability and anti-interference ability of the DC microgrid system.

T-S Fuzzy Model Based Large-Signal Stability Analysis of DC Microgrid With Various Loads

T-S Fuzzy Model Based Large-Signal Stability Analysis of DC Microgrid With Various Loads

Stability analysis of DC micro-grids with CPLs under novel decentralized primary and distributed secondary control

This paper investigates the stability of meshed DC micro-grids with constant power loads (CPLs), under decentralized primary and distributed secondary control schemes to achieve accurate power sharing and voltage restoration, with the latter being more significant to the case of parallel converters in a micro-grid architecture. The DC micro-grid consists of multiple DC/DC boost converters, which have nonlinear dynamics, feeding local CPLs, which also exhibit a nonlinear behaviour and introduce negative impedance characteristics that are well-known to yield instability. At the primary control layer, the droop control concept is suitably formulated and implemented using the recently proposed state-limiting PI controller to accomplish an inherent current limitation for each converter and simultaneously facilitate the stability analysis. Using limited information of the injected power from neighbouring converters and, depending on the micro-grid configuration, the load voltage, a distributed secondary controller is formulated to enhance the power sharing and accurately regulate the voltage to the rated value. By analysing for the first time both the dynamics of the converters with the CPLs and the two-layer control, singular perturbation theory is applied to analytically prove the stability of the entire DC micro-grid. The scalability of the system is also ensured through relevant passivity analysis. Simulation and experimental testings are performed to confirm the effectiveness and validity of the proposed method.

Stability Analysis of DC Microgrids With Switched Events

This paper analyzes the stability of a direct current microgrid with a decentralized switched control using differential-algebraic equations and Lyapunov functions. The decentralized controllers regulate the voltage, achieve the power-sharing condition, and guaranty the non-Zeno condition. They also fulfill the droop-control condition for optimal power dispatch. The event of either connecting or disconnecting a converter is analyzed as a switched event. It is shown that the system is asymptotically stable under this class of switching events after either connecting or disconnecting a distributed generator.

Power management and control of a grid-independent DC microgrid with hybrid energy storage system

In this paper, a novel power management strategy (PMS) for power-sharing among battery and supercapacitor (SC) energy storage systems has been proposed and applied to resolve the demand-generation difference and DC bus voltage regulation. The proposed compensation for PI controller managed hybrid energy storage systems (HESSs) provides for improved DC bus regulation with minimal battery stress levels. Further, redirections of unwaged battery currents to SCs for fast compensations in the proposed PMS enhances battery life span. Moreover, the stability analysis of DC microgrid is also evaluated. The proposed PMS effectiveness was investigated by simulations, including a comparison of peak deviations in dc bus voltage with a traditional control strategy. The results have been experimentally verified by hardware-in-loop (HIL) on an FPGA-based real-time simulator.

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.

Design and Stability Analysis of DC Microgrid Connected with Renewable Energy Sources

Design and Stability Analysis of DC Microgrid Connected with Renewable Energy Sources

Stability analysis of DC microgrid considering the action characteristics of relay protection

The stability of microgrid is the key issue of microgrid operation control. This paper focuses on the transient stability after the correct operation of relay protection. In this paper, 400V DC microgrid with photovoltaic and energy storage system is taken as the research object. Research on the fault characteristics of voltage and current after the system is subjected to short-circuit, it is proposed to introduce current differential protection. With bus voltage as the only indicator, whether the transient stability is improved after the protection system operates correctly. The DC microgrid is modeled and simulated based on MATLAB/Simulink to confirm the validity of the proposed statement. The simulation results show that the fault can be correctly located, accurately isolated and timely removed by the protection system after the short-circuit fault occurs, bus voltage is restored to maintain stable operation of the system.

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.

Design and Stability Analysis of DC Microgrid With Hybrid Energy Storage System

This paper deals with the design and stability analysis of a dc microgrid with battery-supercapacitor energy storage system under variable supercapacitor operating voltage. The conventional design method reported in the literature considers the rated supercapacitor voltage in the modeling and design of controllers. However, the supercapacitor unit can discharge as low as 10% of its rated voltage due to self discharge. It is observed that the conventional method of controller design can potentially make the system unstable or introduce ringing in the dc link voltage at low supercapacitor voltage. In this paper, the sensitivity of dc microgrid stability with respect to supercapacitor voltage variation is analyzed, an optimal supercapacitor voltage to be considered in the design is calculated and a design method is proposed to ensure the stability of dc microgrid in all operating modes. The stability of the dc microgrid with controllers designed using the proposed method is evaluated with digital simulation and experimental studies.

Distributed virtual inertia control and stability analysis of dc microgrid

A dc microgrid is a low inertia system dominated by power converters. As a result, the change rate of the dc voltage is very fast under power variation. In this study, a distributed virtual inertia control is proposed to enhance the inertia of the dc microgrid and decrease the change rate of the dc voltage. The inertia of the dc microgrid can be enhanced by the kinetic energy in the rotor of the permanent magnet synchronous generators (PMSG)-based wind turbine, the energy stored in batteries and the energy from the utility grid. By introducing a virtual inertia control coefficient, a general expression of the inertial power provided by each controllable power sources is defined. The proposed inertia control is simply a first-order inertia loop and is implemented in the grid-connected converter, the battery interfaced converter and the PMSG interfaced converter, respectively. The small-signal model of the dc microgrid with the proposed inertia control is established. The range of virtual inertia control coefficient is determined through stability analysis. Finally, a typical dc microgrid is built and simulated in Matlab/Simulink, and the effectiveness of the proposed control strategy and correctness of the stability analysis are verified.

Stability analysis of islanded DC microgrid for the proposed distributed control strategy with constant power loads

Droop control by means of virtual resistance in control loop is applied for parallel operation of sources in order to minimize circulating currents. The droop control approach is widely used in DC microgrids. The conventional droop control schemes are unable to mitigate trade-off between effective equal load-sharing (in per unit) and bus voltage regulation for unequal cable line parameters. The stability analysis becomes important when constant power loads (CPLs) are applied to DC bus due to the impact of the negative impedance of CPLs. In this paper, the distributed control scheme is proposed with a digital communication link for an averaging current signal to compensate the cable line voltage drop and load sharing error. The proposed control scheme based on the hysteresis current controller is found robust in terms of simplex tuning procedure than conventional cascaded proportional integral controllers. The stability analysis of the DC microgrid is done with the effect of the proposed distributed controller and CPLs. This analysis covers a specific range of droop gain, communication time delay, and CPLs. The performance analysis of the system is done based on three source units and common CPL.

Stability analysis of DC microgrids with constant power load under distributed control methods

Constant power loads (CPLs) often cause instability due to its negative impedance characteristics. In this study, the stability of a DC microgrid with CPLs under a distributed control that aims at current sharing and voltage recovery is analyzed. The effect of the negative impedance on the behavior of distributed controller is investigated. The small-signal model is established to predict the system qualitative behavior around equilibrium. The stability conditions of the system with time delay are derived based on the equivalent linearized model. Additionally, eigenvalue analysis based on inertia theorem provides analytical sufficient conditions as a function of the system parameters, and thus it leads to a design guideline to build reliable microgrids. Simulations are performed to confirm the effectiveness and validity of the proposed method.

Robust Stability Analysis of DC Microgrids With Constant Power Loads

This paper studies stability analysis of DC microgrids with uncertain constant power loads (CPLs). It is well known that CPLs have negative impedance effects, which may cause instability in a DC microgrid. Existing works often study the stability around a given equilibrium based on some nominal values of CPLs. However, in real applications, the equilibrium of a DC microgrid depends on the loading condition that often changes over time. Different from many previous results, this paper develops a framework that can analyze the DC microgrid stability for a given range of CPLs. The problem is formulated as a robust stability problem of a polytopic uncertain linear system. By exploiting the structure of the problem, we derive a set of sufficient conditions that can guarantee robust stability. The conditions can be efficiently checked by solving a convex optimization problem whose complexity does not grow with the number of buses in the microgrid. The effectiveness and non-conservativeness of the proposed framework are demonstrated using simulation examples.

Small-signal stability analysis of DC microgrids considering electric vehicles

This paper presents a generalized model for small signal stability in dc microgrids considering electric vehicles. The proposed model considers four type of terminals, namely: constant power, constant voltage, constant current and constant impedance. A Newton-Raphson methodology is used to calculate the operation point of the microgrid and a sensitivity analysis is also presented. Some general features of the dc microgrid based on the intrinsic characteristics of the model are presented. Simulation results on different type of microgrids show the proposed small signal model is accurate compared to dynamical simulations.

Mathematical modeling and stability analysis of DC microgrid using SM hysteresis controller

The use of dc microgrids in the residential and commercial complexes are increasing due to the high reliability, high efficacy, and easy integration with renewable energy sources. This paper presents the voltage stability of dc microgrid based on decentralized control architecture. Droop controllers cascaded with proportional integral (PI) controllers are being used for stability of dc microgrid. Droop control is not effective due to the error in steady state voltages and load power variations. Additionally, PI controllers cannot ensure global stability. It exhibits slower transient response and control parameters cannot be optimized with load power variations. To address the aforementioned limitation, sliding mode hysteresis control is proposed in this paper. Main advantages are high robustness, fast dynamic response and good stability for large load variations. To analyze the stability and dynamic performance of the proposed scheme, a system model is derived and its controllability, observability and stability are verified. Modeled dynamics are graphically plotted and presented. Detailed simulations are carried out to show the effectiveness of SM controller and results are compared with droop controller. The transient behavior on step load is also investigated and presented which shows the good performance of the proposed controller. A scaled down experimental setup of a source is also presented in the Appendix A.

Stability Analysis and Controller Design of DC Microgrids With Constant Power Loads

DC microgrids consist of multiple power electronic converter units interconnected in a network with sources and loads. They are commonly found in the power systems of electric ships, aircrafts, etc. The main focus of this paper is to study the stability of power converters-based dc microgrids. These high switching frequency electronics are controlled in a way as to maintain constant voltage, current, or power to the load. Due to their high bandwidth, they can be simplified as a constant power load. For this reason, a nonlinear system arises where it is no longer satisfactory to assume local stability. Methods presented in the literature will be reviewed and a method based on semidefinite programming (SDP) will be developed to simplify the stability analysis of these dc microgrids. Furthermore, a robust controller approach based on a similar SDP technique is proposed in order to guarantee and expand the stability region using energy storage.