Inverter-based Microgrids Research Articles

Direct-Quadrature Sequence Models for Energy-Function Based Transient Stability Analysis of Unbalanced Inverter-Based Microgrids

The reliability of supply in distribution networks can be improved by islanding (parts of) the network as autonomous microgrids in case of a contingency. Microgrids are commonly fed by inverter-based distributed energy resources, which causes transient stability challenges due to the lack of inertia and strongly coupled dynamics. The transient stability of inverter-based microgrids is conventionally analyzed by time-domain analysis. However, energy-function based transient stability analysis has advantages over time-domain analysis, as it provides a stability result for all initial conditions and allows uncertainty to be taken into account with the domain of attraction. Microgrids are generally unbalanced, however models for unbalanced energy-function based transient stability analysis are lacking in the literature. In this paper, coupled sequence components models of distributed energy resources and load devices in the dq reference frame are proposed, and experimentally validated with unbalanced voltage transients. The validated models are used for energy-function based transient stability analysis of an unbalanced inverter-based case study microgrid. Finally, the impact of unbalanced connection of devices on transient stability is analyzed. The results indicate that the proposed models accurately represent the behavior of physical devices and that the unbalanced connection of devices significantly impacts the transient stability of inverter-based microgrids.

Distributed robust secondary voltage control for islanded microgrid with nonuniform time delays

This paper proposes a nonuniform delay-dependent robust secondary voltage control strategy with a finite-time voltage reference observer for an islanded microgrid. A discrete-time consensus algorithm is introduced to track the output voltage. By model transformation, a closed-loop microgrid control system is obtained. And then, the corresponding global stability and robust performance analysis theorems are derived. After implementing a series of trial studies, the impacts of secondary voltage control gains, sampling time on energy-to-peak robust performance are obtained. And the feasible optimal voltage control gains can be derived. Besides, a distributed cooperative secondary frequency control is introduced. Simulations of a four inverter-based microgrid test system are presented to verify the control performance. The simulation results indicate that our proposed method can maintain accurate voltage/frequency restoration and active power sharing. In addition, the voltage control gain parameters, arbitrary nonuniform time delays, and especially sampling time effects on the secondary voltage control performance are also verified.

Resilience for Communication Faults in Reactive Power Sharing of Microgrids

In this paper, we consider the distributed reactive power sharing control problem for an autonomous inverter-based microgrid with resilience for communication faults, which may be caused by partial communication link failures or some channel manipulation attacks. Under the standard decoupling approximation for bus angle differences, the reactive power flow of each inverter can be controlled by manipulating the voltage amplitudes of itself and its neighbor inverters. By designing an adaptive resilient cooperative control scheme, accurate reactive power sharing can be guaranteed even in the presence of communication faults. Some simulation results are presented to verify the superiority of the proposed control approach compared with the existing methods.

Fault Ride-Through Analysis of Current- and Voltage-Source Models of Grid Supporting Inverter-Based Microgrid

Withstanding fault is a crucial technical challenge for inverter-based systems. Evolving grid codes require microgrids to possess fault ride-through (FRT) capabilities and support the grid voltage recovery. The traditional grid forming and grid feeding models lack such abilities. Consequently, this article enhanced these traditional models with droop control-virtual impedance and secondary power reference generation to form two models of a grid-supporting system. The first is a current source for grid feeding control, and the second is regulated as a voltage source for grid forming control. The result presents grid fault impact and FRT compliance in the proposed and traditional systems. Furthermore, the fault current curtailment and FRT improvement of the virtual impedances in the grid forming control were investigated within the MATLAB/Simulink environment. These proposed systems achieved FRT under a dynamic period and reverted to appropriate power delivery control under a static period.

Distributed Robust Finite-Time Secondary Control for Stand-Alone Microgrids With Time-Varying Communication Delays

In this paper we consider the problem of restoring the voltage for stand-alone inverter-based Microgrids despite the effects of the time-delays arising with the information exchange among the electrical busses. To guarantee that all Distributed Generators (DGs) reach in a finite-time and maintain the voltage set-point, as imposed by a virtual DG acting as a leader, we suggest a novel robust networked-based control protocol that is also able to counteract both the time-varying communication delays and natural fluctuations caused by the primary controllers. The finite-time stability of the whole Microgrid is analytically proven by exploiting Lyapunov-Krasovskii theory and finite-time stability mathematical tools. In so doing, delay-dependent stability conditions are derived as a set of Linear Matrix Inequalities (LMIs), whose solution allows the proper tuning of the control gains such that the control objective is achieved with required transient and steady-state performances. A thorough numerical analysis is carried out on the IEEE 14-bus test system. Simulation results corroborate the analytical derivation and reveal both the effectiveness and the robustness of the suggested controller in ensuring the voltage restoration in finite-time in spite of the effects of time-varying communication delays.

A General Linear Framework for Analysis of Islanded Inverter-Based Microgrids

Simulation and stability analysis of power systems are challenging topics due to nonlinear models. Fortunately, most power components are weakly nonlinear and by taking the advantages of this characteristic and also using the first-order term of the Taylor expansion, a general linear time-variant model for such systems is derived. Specifically, this article analyzes islanded inverter-based microgrids (IBMGs) using the proposed linear model driven directly from a general nonlinear model of IBMGs, and it is just as comprehensive as the reference one. Two methods to linearize the weakly and severely nonlinear state-space models are presented. A new time-step simulation is developed to modify the model dynamically and to calculate time-domain response as well as eigenvalues directly, which are much faster and more efficient than numerical methods and small-signal stability analyses. The capabilities of the proposed models make it possible to easily develop a time-saving eigenvalue calculator as well as a fast- and low computational direct power flow analysis. Different time-domain simulations in MATLAB/Simulink and other tests are investigated to verify the performance of the proposed simulations and their applications.

Optimal tuning of the control parameters of an inverter‐based microgrid using the methodology of design of experiments

The design of the control system in an inverter-based microgrid (μGs) is a challenging problem due to the large number of parameters involved. Different optimisation methods based on obtaining an approximated mathematical model of the μG can be found in the literature. In these approaches, the non-linearities and uncertainties of the real system are typically not considered, which may result in a non-optimal tuning of the control parameters. In addition, in most applications, the problem has been simplified, assuming that all controllers have the same value for their control parameters. However, in this case, the behaviour of the system is sub-optimal since the particularities of each node of the μG are not taken into account. In this study, an experimental approach for tuning the control parameters of an inverter-based μG is introduced. The approach is based on the methodology of design of experiments and it considers different values for the control parameters of all controllers. In this study, this methodology is applied to the design of a droop-free control scheme; however, it can be easily extended to other control schemes. The validity of the proposal is verified through selected experimental results.

Control design and small-Signal stability analysis of inverter-Based microgrids with inherent current limitation under extreme load conditions

A novel droop controller that ensures a desired inverter current limitation and guarantees the stable operation of inverter-based microgrids under extreme load conditions, is proposed in this paper. Opposed to existing dq framework-based droop controllers that align the output voltage on d axis, here the inverter current is aligned on d axis in order to achieve two main goals: i) limitation of the RMS value of each inverter current during transients, without a need for saturation units that guarantee only steady-state limitation and require adaptation techniques for adjusting their limits and ii) a rigorous proof of closed-loop system stability for the entire microgrid. In particular, the proposed approach significantly simplifies the stability analysis of the microgrid, since it can be investigated through a Jacobian matrix of reduced size. Simulation results are given to highlight the superiority of the proposed controller when compared to a conventional droop controller under extreme load conditions, while experimental validation in a lab-scale microgrid is also provided.

Improved Distributed Prescribed Finite-Time Secondary Control of Inverter-Based Microgrids: Design and Real-Time Implementation

The aim of this study is to develop a novel distributed robust prescribed finite-time secondary control for both frequency and voltage restoration along with accurate active power sharing in islanded microgrids (MGs). The prescribed finite-time convergence property irrespective of the values of initial conditions helps to design an offline settling time that leads to power loss reduction. Moreover, thanks to the use of a piecewise-function based approach the upper bound of convergence time is reduced. The fixed-time stability of the proposed scheme is rigorously confirmed by applying the Lyapunov theory, which results in a set of tuning rules. The main challenge is to establish the stability conditions through asymmetrical connections under a directed graph. Finally, the architecture of the experimental setup is constructed for an inverter-based microgrid consisting of six distributed generators (DGs). The OPAL-RT real-time simulator is exploited to verify the applicability of the proposed distributed fixed-time controller.

Identification of critical clusters in inverter-based microgrids

In this paper, we investigate the stability properties of inverter-based microgrids by establishing the possible presence of the so-called critical clusters - groups of inverters with their control settings being close to the stability boundary. For this, we consider the spectrum of the weighted admittance matrix of the network and show that its distinct eigenvalues correspond to inverter clusters, whose structure can be revealed by the corresponding eigenvector. We show that the maximum eigenvalue of the weighted admittance matrix corresponds to the cluster, closest to stability boundary. We also establish that there exists a boundary on the value of this eigenvalue, that corresponds to the stability of the overall system. Thus, we make it possible to certify the stability of the system and find the groups of inverters in which control settings are closest to the stability boundary.

Review on Multi-Objective Control Strategies for Distributed Generation on Inverter-Based Microgrids

Microgrids have emerged as a solution to address new challenges in power systems with the integration of distributed energy resources (DER). Inverter-based microgrids (IBMG) need to implement proper control systems to avoid stability and reliability issues. Thus, several researchers have introduced multi-objective control strategies for distributed generation on IBMG. This paper presents a review of the different approaches that have been proposed by several authors of multi-objective control. This work describes the main features of the inverter as a key component of microgrids. Details related to accomplishing efficient generation from a control systems’ view have been observed. This study addresses the potential of multi-objective control to overcome conflicting objectives with balanced results. Finally, this paper shows future trends in control objectives and discussion of the different multi-objective approaches.

Optimal Damping Recovery Scheme for Droop-Controlled Inverter-Based Microgrids

Inverter-based microgrids may experience small-signal stability issues as the generation, loading or network topology change in real-time. This paper presents an event-triggered damping recovery scheme to improve the stability of a system with droop-controlled inverters and synchronous machines in the event of poorly damped power flows. The droop coefficients of the controllable inverters are manipulated in real-time based on their node sensitivities so as to obtain the maximum damping effort per unit additional power injected. This prevents the overloading of any one inverter or group of inverters in the system and reduces the power sharing disparity that arises from the damping recovery process. For determining the node sensitivities, a novel damping sensitivity formula is presented as an alternative to conventional sensitivity analysis. This enables the reduction of computation complexity from $O(n^{3})$ to $O(n)$ , making the proposed algorithm scalable to large systems. Experimental and simulation case studies are presented to demonstrate the effectiveness of the proposed control scheme in restoring damping, as well as its robustness to communication failure.

A State-Space Model of an Inverter-Based Microgrid for Multivariable Feedback Control Analysis and Design

In this work, a synchronous model for grid-connected and islanded microgrids is presented. The grid-connected model is based on the premise that the reference frame is synchronized with the AC bus. The quadrature component of the AC bus voltage can be cancelled, which allows to express output power as a linear equation for nominal values in the AC bus amplitude voltage. The model for the islanded microgrid is developed by integrating all the inverter dynamics using a state-space model for the load currents. This model is presented in a comprehensive way such that it could be scalable to any number of inverter-based generators using inductor–capacitor–inductor (LCL) output filters. The use of these models allows designers to assess microgrid stability and robustness using modern control methods such as eigenvalue analysis and singular value diagrams. Both models were tested and validated in an experimental setup to demonstrate their accuracy in describing microgrid dynamics. In addition, three scenarios are presented: non-controlled model, Linear-Quadratic Integrator (LQI) power control, and Power-Voltage (PQ/Vdq) droop–boost controller. Experimental results demonstrate the effectiveness of the control strategies and the accuracy of the models to describe microgrid dynamics.

Under Frequency Load Shedding in Inverter Based Microgrids by Using Droop Characteristic

In this article, a new Under Frequency Load Shedding (UFLS) method for Inverter-Based Microgrids (IBMs) is presented. The proposed strategy uses frequency variations to estimate the power deficit in IBMs without using wide communication platform and calculating system inertia time constant. Variations of power generation are considered during the load shedding process. The shortage of power is also compensated by the load shedding during several stages. Estimated droop coefficient is updated in each load shedding stage, enabling the proposed method to have a reliable performance in the case of the microgrid's parameters changes which could happen during the load shedding process. The proposed method is simulated and implemented in an IBM by using MATLAB\Simulink software package; the obtained results show the effectiveness and the correctness of the proposed scheme to recognize power deficit and to compensate power shortage.

A Zeno-Free Event-Triggered Secondary Control for AC Microgrids

This paper proposes a secondary voltage, frequency, and active power sharing control for autonomous inverter-based microgrids with event-triggered communications. A proportional-integral consensus-based control scheme is introduced which benefits from need-based (event-triggered) data exchange among distributed generators. The employed event-triggering condition i ) ensures the system stability, ii ) ensures that the system is Zeno-free and there exists a controllable minimal inter-event time, iii ) removes the redundant communications during both transient and steady-state stages, iv ) accounts for directed communication network architectures, and v ) is fully distributed from both design and implementation standpoints. Effectiveness of the proposed controller for various case studies is verified via MATLAB/Simulink-based simulations. Comparison between different cases and conventional strategies are also included.

Resilient cooperative control of AC microgrids considering relative state‐dependent noises and communication time‐delays

In this study, a resilient distributed control algorithm is proposed for the secondary voltage and frequency restoration of an autonomous inverter-based microgrid considering simultaneous relative state-dependent noises and communication time-delays (CTDs). The proposed algorithm is robust against potential time-varying stochastic noises and CTDs, which corrupt the data exchanges in the secondary control layer. Additionally, this study considers the contribution of both distributed generation and distributed energy storage (DES) units in islanded AC microgrids. The presence of DES creates the need for an extra control algorithm to provide state-of-charge (SoC) balancing for these units and having precise active power-sharing. The theoretical concepts of the proposed control algorithm, including the mathematical modelling of microgrid, basic lemma, and controller design procedure, are outlined. The performance assessment of the presented control algorithm is evaluated through simulations on a test microgrid in MATLAB/Simulink software. Then, some previously-reported algorithms are selected to compare the proposed control algorithm with them. The obtained results show the effectiveness and robustness of the presented algorithm in regulating the voltage and frequency, matching SoCs, and as a result, having precise active power-sharing.

Energy Storage Requirements for Inverter-Based Microgrids Under Droop Control in d-q Coordinates

This article proposes a novel distributed control approach for Hamiltonian Surface Shaping and Power Flow Control (HSSPFC) method to determine Energy Storage Systems (ESSs) requirements for three-phase, inverter-based Microgrids (MGs). Here, local system references are obtained through a primary d-q droop control which is supported by a level-zero Hamiltonian controller. ESS devices are the actuators of the system to enforce reference points. The control approach as well as power flow and energy transfer model of the MG enables the ESS capacity and bandwidth to be obtained. As a result, a zero-output ESS element analysis is defined which can further be used to study storage requirements versus additional constraints. Communication network update-rate can affect ESSs and filtering requirements. The developed analysis is demonstrated in parallel and looped nine-bus WSCC reduced-order MG system examples to obtain ESS requirements versus communication network update-rate (bandwidth).

Distributed Small-Signal Stability Conditions for Inverter-Based Unbalanced Microgrids

The proliferation of inverter-based generation and advanced sensing, controls, and communication infrastructure have facilitated the accelerated deployment of microgrids. A coordinated network of microgrids can maintain reliable power delivery to critical facilities during extreme events. Low-inertia offered by the power-electronics interfaced energy resources, however, can present significant challenges to ensuring stable operation of the microgrids. In this work, distributed small-signal stability conditions for inverter-based microgrids are developed that involve the droop-controller parameters and the network parameters (e.g. line impedances, loads). The distributed closed-form parametric stability conditions derived in this paper can be verified in a computationally efficient manner, facilitating the reliable design and operations of networks of microgrids. Dynamic phasor models have been used to capture the effects of electromagnetic transients. Numerical results are presented, along with PSCAD simulations, to validate the analytical stability conditions. Effects of design choices, such as the conductor types, and inverter sizes, on the small-signal stability of inverter-based microgrids are investigated to identify interpretable stable/unstable region estimates.

Multiloop low bandwidth communication-based power sharing control for microgrids

<span>In parallel-connected inverter-based microgrids, the reactive power sharing accuracy can not have satisfactory results effortlessly. Mismatch in feeder impedances of the parallel-connected inverter-based microgrids is a significant cause of inaccurate reactive power-sharing. In voltage source inverters (VSI) based microgrids, especially for the islanded mode of operation, the conventional centralized or decentralized control techniques are not much helpful to control the voltage deviations due to impedance mismatch. Mismatch of the feeder impedance is compensated by the addition of fixed virtual impedance. Whereas, the change in the virtual impedance is compensated by adaptive virtual impedance-based control techniques which are helpful to mitigate power-sharing errors, but in most of the control schemes virtual impedance-based control mechanism needs pre-knowledge of feeder impedance which increases the computational burden. This paper presents a decentralized virtual impedance-based power sharing control. In the proposed control solution to mitigate reactive power sharing errors in distributed generation (DG) units, mismatch of the parallel-connected feeder impedance is equalized by regulating the addition of equivalent impedance to each DG inverter. Proposed control technique offers an independent implementation without any pre-knowledge of the feeder impedance. Hence, the implementation of the control scheme is a straightforward and computational burden is also reduced. Simulation results show the effectiveness of the control scheme. </span>

Fault Detection and Protection Strategy for Islanded Inverter-Based Microgrids

This article proposes a fault detection and protection strategy for islanded inverter-based microgrids (IBMGs). Reliable and accurate protection is one of the main challenges in the proliferation of modern microgrids (MGs). Considering the limited fault current of the voltage–frequency-controlled inverter-based distributed energy resources (VF-IBDERs), the protection is more challenging in islanded IBMGs. In this regard, the control scheme of VF-IBDER with a current limiting strategy plays an important role. Due to the limited fault currents close to the converter nominal current, the conventional fault detection methods do not work properly. In addition, bidirectional fault currents worsen protection coordination. In this article, first, an analytical sequence network modeling for VF-IBDERs is derived to specify their behavior under fault conditions. Then, a voltage-restrained negative-sequence resistance-based fault detection approach is proposed, which is based on the derived sequence networks. This quantity inherently detects the fault and its direction and is independent of the fault current magnitude. The proposed feature can be employed in both the conventional and communication-assisted coordination strategies. In addition, a protection coordination strategy based on a definite-time grading approach is employed. Finally, the performance of the proposed scheme is demonstrated by applying different faults in a test MG in PSCAD/EMTDC environment.