Droop-controlled Inverters Research Articles

Design of Fuzzy Logic based Adaptive Active Power Controller to Enhance Power sharing among DGs in an Autonomous Microgrid

This paper presents the design of an adaptive active power controller to enhance the power-sharing capabilities of distributed generators (DGs) in an autonomous microgrid. Each DG in an autonomous microgrid consists of a droop-controlled inverter to control active and reactive power by regulating frequency and voltage correspondingly. The high droop gain can be used in the power controller to encourage faster power sharing among the DGs. However, high droop gain can cause undamped growing oscillations during load fluctuations or generation losses. During such events, attaining faster power-sharing between DGs using high droop gains is difficult. So, the problem with an autonomous microgrid is the conflict between faster power sharing and stability. Stability needs to be compromised to attain quicker power sharing and vice versa. Hence, to achieve power-sharing swiftly with high droop gain and to diminish the growing oscillations caused, this paper proposes a fuzzy logic-based adaptive active power controller (FLAPC). The proposed FLAPC is adaptive and easy to implement. It offers faster power sharing for different values of droop gains and step change in load. The FLAPC is developed in MATLAB 2018a/Simulink environment, and time domain simulations are performed to see the efficacy of the proposed controller. The results of time domain simulations are compared with a droop controller without any additional controller, conventional lead-lag power system stabilizer, and proposed controller for step change in load at different droop gains. The results show that the proposed controller enhances the power-sharing performance and also ameliorates the system’s stability by reducing the settling time and overshoot in active power responses of DGs.

Reduced-Order Modeling of Droop-Controlled Inverters Using Slow Coherency and Aggregation Algorithm

By considering time-scale separation characteristics and nonlinear node voltage equation, an improved slow coherency algorithm has been proposed, and for the first time, applied to the slow coherency model widely used for modeling three-phase droop-controlled grid-connected inverters. The method works by combining two coherency clustering results, which in turn, are computed from mode matrix, representing slow mode and damping coefficient of the slow coherency model. Subsequently, fuzzy C-means spatial clustering algorithm and aggregation method are used for identifying coherent generators and building the reduced-order model, respectively. Compared to the traditional slow coherency algorithms, the presented method can accurately identify oscillating mode between power supplies under the condition of selecting any number of areas. Its range of application can moreover be expanded to cover distributed networks with multiple droop-controlled inverters. These expectations, and accuracy and effectiveness of the proposed method have eventually been verified by simulations performed with both detailed and reduced-order models under different faults.

Improving the power sharing transients in droop-controlled inverters with the introduction of an angle difference limiter

This paper derives a mathematical model suitable for analysis of connection behavior of the inverter-based grids and, using that model, it presents guidelines to control grid-forming inverters’ rate of change in frequency as function of output power (virtual inertia), or in other words “measured power filters”. Furthermore, in order to improve the transient response, an angle difference limiter control is proposed. An angle difference limiter is a control algorithm which is constantly checking the angle difference between the inverter and the grid in the connection point limiting power peaks during the transients. The performance of the angle difference limiter is analyzed in detail and validated with an experimental microgrid consisting of two three-phase inverters and a variable load. The paper analyzes the connection of inverters in weak and strong grids validating the performance of the proposed angle difference limiter.

Minimax Flow Over Acyclic Networks: Distributed Algorithms and Microgrid Application

Given a flow network with variable suppliers and fixed consumers, the minimax flow problem consists in minimizing the maximum flow between nodes, subject to flow conservation and capacity constraints. We solve this problem over acyclic graphs in a distributed manner by showing that it can be recast as a consensus problem between the maximum downstream flows, which we define here for the first time. Additionally, we present a distributed algorithm to estimate these quantities. Finally, exploiting our theoretical results, we design an online distributed controller to prevent overcurrent in microgrids consisting of loads and droop-controlled inverters. Our results are validated numerically on the CIGRE benchmark microgrid.

Frequency Restoration of Grid-Forming Inverters in Pulse Load and Plug-in Events

This article presents a restoration technique using grid-forming inverters in an islanded microgrid during pulse load and plug-in events. In a microgrid powered by droop-controlled inverters, frequency is the variable that is accessible to all inverters for adjusting their power contributions. The problem is that the microgrid frequency deviates from its nominal value after a load change. The presented method enables the inverters to restore the frequency to the nominal value and regulate their bus voltage amplitudes. The frequency and voltage restorations are performed without communication while achieving the desired power-sharing between grid-forming inverters. The restoration is activated after detecting any active or reactive power changes. In this article, the dynamic model of an inverter equipped with enabled restoration paths is developed to verify the stability of the inverter controller under various conditions. The frequency and voltage restorations are examined during pulse load and plug-in events. This study is performed using a laboratory-scale islanded microgrid powered by two 208 V, 60 Hz, 5 kVA inverters.

Parameters design and optimization for droop-controlled inverters considering impedance characteristics and power stability

The droop-controlled inverters (DCIs), which can simulate synchronous generators’ frequency and voltage behavior and provide active and reactive power support for the utility grid, are universally regarded as grid-friendly interfaces. This paper aims to give a general parameter design outline for the DCIs to simplify the complicated parameter tuning task while assuring good performances. For this purpose, the DCIs’ equivalent output impendence and admittance models are first developed, based on which the effects of parameters on impedance characteristics and power stability are analyzed in detail. Afterward, the general parameter design outline with a comprehending parameter tuning scheme is proposed based on the impedance analysis results. In the end, a 15-kVA prototype is established and tested in the laboratory. The experimental results verified the effectiveness of the proposed parameter design and optimization method.

Stability Bounds of Droop-Controlled Inverters in Power Grid Networks

Stability Bounds of Droop-Controlled Inverters in Power Grid Networks

Spontaneous Phase Balancing in Delta-Connected Single-Phase Droop-Controlled Inverters

Power grids are evolving toward a highly distributed architecture with power-electronics circuits interfacing a majority of generation, storage, and loads. To ensure stability as synchronous machines are retired, grid-forming (GFM) inverters will be needed across the board. In this article, we investigate whether systems built with interconnected single-phase droop-controlled GFM inverters are capable of self organizing into balanced three-phase systems. We model, analyze, and build a system comprised of three delta-connected droop-controlled single-phase inverters connected across loads. After deriving a model of the angle dynamics for this system, we show that its stable equilibria coincide with balanced conditions, where each phase is offset by <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$1/3$</tex-math></inline-formula> of an ac cycle. Furthermore, we observe that the desirable equilibrium with balanced phase offsets is robust against voltage and load imbalances. This demonstrates the feasibility of assembling three-phase systems using fleets of decentralized single-phase GFM inverters. The analytical developments are substantiated experimentally on a system of three delta-connected single-phase inverters. Spontaneous emergence of phase balancing from startup with nonidentical initial conditions are validated in the experimental setup. Empirical observations further illustrate robust operation during unbalanced conditions.

A Fast Power Calculation Algorithm for Three-Phase Droop-Controlled-Inverters Using Combined SOGI Filters and Considering Nonlinear Loads

The power calculation is an indispensable element in droop-controlled inverters because the bandwidth of the measured power has a direct impact on the controller performance. This paper proposes a fast and accurate power calculation algorithm based on the combined Second Order Generalized Integrator (SOGI) filters in stationary coordinates for a three-phase system, which takes into consideration the use of nonlinear loads. The power calculation scheme is formed by the two-stage SOGI filters that are employed for obtaining the active and reactive powers required to perform a droop-based inverter operation, respectively. From the two-stage structure, the first SOGI is used as a band-pass filter (BPF) for filtering harmonics and obtaining the fundamental current of the nonlinear load; The second SOGI is used as a low-pass filter (LPF) for extracting the DC-component, which corresponds with the average power. A small-signal model of a two droop-controlled inverters system is built to obtain the dynamical response and stability margin of the system. And compared it with the dynamical behaviour of a standard droop-control method. Next, the proposed power calculation system is designed in order to achieve the same ripple amplitude voltage as that obtained with the standard droop-control method by adjusting the bandwidth gains. Through simulation and hardware in the loop (HIL) validation, the proposed approach presents a faster and more accurate performance when sharing nonlinear loads, and also drives the inverters’ output voltage with lower distortion.

Reduced Model of Droop-controlled Converters for Transient Simulation Analysis

In recent years, the transient stability problems encountered by power grids have increasingly attracted interest due to the connection of renewable energy resources. One of the effective methods for studying the transient characteristics of a system is transient simulation analysis. To reduce the simulation time, especially in a system with numerous renewable energy resources, model reduction has been widely employed. However, when a general reduced model is adopted to analyze different transient characteristics, a tradeoff between accuracy and simulation speed emerges. In this study, reduced model selection is implemented to resolve this problem. Considering the droop-controlled converter as an example, this approach allows the transient simulation analysis of voltage, frequency, and power angle characteristics. First, a full-order model of the droop-controlled inverter is formulated. Thereafter, the singular perturbation method is applied to derive different reduced-order models. Then, considering accuracy and simulation speed simultaneously, the most suitable reduced models for transient angle, voltage, and frequency simulation analyses are determined through time-domain simulation comparison. Finally, the simulation results based on Matlab/Simulink are used to verify the correctness of the reduced model selection.

Transient Stability of Hybrid Power Systems Dominated by Different Types of Grid-Forming Devices

This paper investigates the transient stability of power systems co-dominated by different types of grid-forming (GFM) devices. Synchronous generators (SGs and VSGs) and droop-controlled inverters are typical GFM devices in modern power systems. SGs/VSGs are able to provide inertia while droop-controlled inverters are generally inertialess. The transient stability of power systems dominated by homogeneous GFM devices has been extensively studied. Regarding the hybrid system jointly dominated by heterogeneous GFM devices, the transient stability is rarely reported. This paper aims to fill this gap. It is found that the synchronization behavior of the hybrid system can be described by a second-order motion equation, resembling the swing equation of SGs. Moreover, two significant differences from conventional power systems are discovered. The first is that the droop control dramatically enhances the damping effect, greatly affecting the transient stability region. The second is that the frequency state variable exhibits a jump at the moment of fault disturbances, thus impacting the post-fault initial-state location and stability assessment. The underlying mechanism behind the two new characteristics is clarified and the impact on the transient stability performance is analyzed and verified. The findings provide new insights into transient stability of power systems hosting heterogeneous devices.

Three-Stage Hierarchically-Coordinated Voltage/Var Control Based on PV Inverters Considering Distribution Network Voltage Stability

Intermittent photovoltaic (PV) power generation brings voltage fluctuation and stability issues to distribution networks. Meanwhile, PV inverters can support voltage/Var control (VVC) to address these issues. Utilizing PV inverters, this paper proposes a three-stage hierarchically-coordinated (TSHC-) VVC method considering network voltage stability. The first stage schedules on-load tap changers one day ahead, the second stage hourly dispatches reactive power outputs of inverters, and the third stage implements real-time local voltage droop control of inverters. To efficiently address mutual impacts between these stages, the first two central-hierarchy stages are coordinated through interval optimization. Meanwhile, the last two stages are hierarchically coordinated by simultaneously optimizing inverter base reactive power outputs and droop control functions under real-time uncertainty. In the previous work, local droop control functions are not fully optimized, and network voltage stability is not fully considered. To overcome such limitations, this paper develops new constraints of individual control gain for each inverter, taking voltage stability into account. The proposed TSHC-VVC method with the optimized control gains is tested and compared with existing methods. Simulation results verify its better performance in reducing network power losses and bus voltage deviations, as well as maintaining network voltage stability.

Droop-Controlled Inverters as Educational Control Design Project

Electric grids are seeing increasing adoption of renewables interfaced with power electronics. As the share of renewable generation increases, the inverters are expected to operate in grid-forming mode to replace large conventional synchronous generation. Further, in geographical islands and isolated/rural areas, inverters interfacing renewable generators and storage are used to form the grids and share the loads. Given the expected presence of grid-forming inverters in future power systems, there is an urgent need to revise education curricula about the stability issues arising from these interconnected inverters. Existing training is overly reliant on numerical simulation or on expensive tools such as real-time simulators. In this paper, we present a laboratory hands-on project dealing with small-signal stability in droop-controlled inverters. It entails simulation and hands-on experimentation for which an inexpensive microgrid set up was developed in-house at the National University of Singapore. The design project can be integrated into power engineering courses offered to senior and postgraduate students.

Synchronization of Inverters in Grid Forming Mode

This article compares two strategies for seamless (re)connection of grid-forming inverters to a microgrid powered by droop-controlled inverters. While an incoming inverter must be synced to the microgrid, seamless syncing and power-sharing are technical challenges for grid-forming inverters. In the first strategy, called the output-sync method, an incoming inverter is synced to the microgrid, and then the circuit breaker is closed for power-sharing. In the second strategy, called the controller-sync method, the inverter initially contributes at zero power following the microgrid frequency, and then the controller is transferred to the mode of power-sharing. Remarkably, the circuit breaker can be kept closed during the syncing process using the controller-sync method as the inverter starts from zero power contribution. In this novel strategy, two controller sets run in parallel, i.e., two parallel control paths are in place for obtaining the magnitude and the phase angle of the PWM reference signal. These parallel paths are synced for seamless transitions when only one of them is engaged to generate the PWM reference signal. The efficacy of these control strategies has been tested in a hardware setup of a microgrid fed by two 5kVA 208V droop-controlled inverters, and the results are presented in this article. This article is also accompanied by a video clip demonstrating the performance of the output-sync and controller-sync methods in the laboratory.

Distributed Hierarchical Control for Fast Frequency Restoration in VSG-Controlled Islanded Microgrids

As microgrids develop rapidly, more inverters are adopted to achieve DC&#x002F;AC or AC&#x002F;DC&#x002F;AC conversion of distributed generators (DGs). The virtual synchronous generator (VSG) control has started to replace the traditional droop control for inverters. In order to restore the frequency to its nominal value, most existing secondary frequency control (SFC) methods are based on frequency measurements. However, while reducing the rate of change of frequency (ROCOF), virtual inertia also slows down the convergence of frequency-based SFC. Therefore, this paper proposes a new distributed hierarchical control for fast frequency restoration. Based on the real-time VSG control at the bottom level, a novel frequency restoration control is designed. The power reference values generated by the proposed control can accelerate the frequency restoration with accurate power sharing. Meanwhile, by designing event-triggering conditions, parallel inverter controllers only need to communicate with neighbors at the event-triggered moments. Simulations have been performed in MATLAB&#x002F;Simulink environment. Furthermore, the proposed control has also been tested on the experiment platform, which contains practical physical circuits and real-time controllers. Both simulation and experiment results verify the effectiveness of the proposed control strategy.

Parameters Design and Optimization for Droop-Controlled Inverters Considering Impedance Characteristics and Power Stability

Parameters Design and Optimization for Droop-Controlled Inverters Considering Impedance Characteristics and Power Stability

A New Current Limiting and Overload Protection Scheme for Distributed Inverters in Microgrids Under Grid Faults

Unlike a synchronous generator that could withstand a large overcurrent, an inverter-based distributed generation (DG) has low thermal inertia, and the inverter is likely damaged by overcurrents during grid faults. In this article, a new strategy, namely positive- and negative-sequence limiting with stability enhanced <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">P</i> - <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">f</i> droop control (PNSL-SEPFC), is proposed to limit the output currents and active power of droop-controlled inverters in islanded microgrids. This strategy is easy to implement in the inverter controller and does not require any fault detection. Inverter stability is analyzed mathematically, which gives guidelines to design the parameters of the PNSL-SEPFC strategy. PSCAD/EMTDC simulation based on a four-DG microgrid shows that the proposed PNSL-SEPFC can limit inverter output currents and powers with better performance under both symmetrical and asymmetrical faults. Furthermore, hardware experiments demonstrate that the proposed PNSL-SEPFC can ensure the inverters riding through grid faults safely and stably. (A video of experimental waveforms is attached.)

Filter Deballasting Control of Droop-Controlled Inverters

In microgrids with droop-controlled inverters, the supervisory controller must the tune the droop gains in real time to maintain stability as the system topology or the number of inverters change. Stability could be compromised due to delays in the dispatch of supervisory control inputs or due to communication link failures. This article proposes a filter deballasting control (FDC) method for maintaining stability in the interim period until the supervisory inputs become available. FDC employs a quasi-open-loop control structure to leverage the inductance of the LC filter as a stability ballast, which under normal operation does not contribute to the dynamic behavior of the system. To further improve the stability, a lead-lag compensator is implemented to compensate the lagging dynamics of the deballasted system. The proposed method does not affect the steady-state active and reactive power share of the inverters, enabling a smooth transition between the conventional and FDC operating modes. The effectiveness of the proposed control strategy is verified through theoretical and experimental means.

Frequency Trajectory Planning Based Strategy for Improving Frequency Stability of Droop-Controlled Inverter Based Standalone Power Systems

Inverter-based standalone power systems (ISPSs), with limited inertia/damping, are prone to significant changes in frequency indicators encompassing frequency deviation and rate of change of frequency (RoCoF), which can easily exceed the pertinent relay thresholds and cause power outages. Limited by estimating the disturbance and system inertia/damping deficiency, existing controls cannot ensure system frequency stability. To overcome this issue, a frequency trajectory planning (FTP) based strategy is developed in this article to improve frequency stability of droop-controlled ISPS. This frequency-indicator-oriented control relates system frequency with several pre-defined planning parameters, decoupling from system’s disturbances and inertia/damping deficiency that are difficult to evaluate. During normal operation or when the disturbance level is insignificant, the inverter operates in standard droop mode since the system intrinsic inertia/damping features suffice to regulate the frequency. In the event of a large disturbance, an FTP block is triggered by detected frequency indicators, and a marginally safe frequency trajectory is planned according to the requirement of the grid code. In this case, by tracking the planned frequency trajectory, the inverter provides suitable inertia/damping support needed by the system, thereby guaranteeing frequency stability of the ISPS. Finally, simulation and experimental results proved the effectiveness and advancement of the FTP based strategy.

Transient Stability of Droop-Controlled Inverter Networks With Operating Constraints

Due to the rise of distributed energy resources, the control of networks of grid-forming inverters is now a pressing issue for the power system operation. Droop control is a popular control strategy in the literature for frequency control of these inverters. In this article, we analyze transient stability in droop-controlled inverter networks that are subject to multiple operating constraints. Using a physically meaningful Lyapunov-like function, we provide two sets of criteria (one mathematical and one computational) to certify that a postfault trajectory achieves frequency synchronization while respecting operating constraints. We show how to obtain less-conservative transient stability conditions by incorporating information from loop flows, i.e., net flows of active power around cycles in the network. Finally, we use these conditions to quantify the scale of parameter disturbances to which the network is robust. We illustrate our results with numerical case studies of the IEEE 24-bus system.