Small-signal State-space Model Research Articles

Analysis and Suppression of Oscillations in Doubly Fed Variable Speed Pumped Storage Hydropower Plants Considering the Water Conveyance System

The doubly fed variable speed pumped storage (DFVSPS) system is a hydraulically, mechanically, and electrically coupled system, and the characteristics of the components from the water conveyance system to the transmission line need to be fully considered in the oscillation analysis. Hence, the model of the water conveyance system is included to investigate the oscillation characteristics of the DFVSPS connecting to the grid via a series-compensated line. A small-signal state-space model of the DFVSPS system in the generation mode is first established. The oscillation characteristics of the DFVSPS are studied, and the dominant state variables for each oscillation mode are identified. The impact of system parameters on oscillations is further studied, and simulations are carried out to validate the accuracy of the model. The results indicate the oscillation mode of the DFVSPS comprises the electrical sub-synchronous oscillation (SSO) mode and the hydraulically, mechanically coupled low-frequency mechanical oscillation modes. When the series compensation level is high, the SSO becomes divergent, and the system is more likely to be unstable. Optimizing the rotor-side control parameters and the governor control parameters, sub-synchronous and low-frequency oscillations could be effectively suppressed, respectively. This study provides reference suggestions for the development and use of the future DFVSPS system.

Optimal linear quadratic regulator-based reduced order model for hybrid AC/DC microgrid

The stability of hybrid microgrids represents an elementary requirement to ensure their security and reliability. This paper aims to propose a supplementary controller that can enhance the hybrid microgrid dynamic performance while preserving its stability. At first, the paper derives the small signal state-space model of a hybrid microgrid that includes inverter-based and conventional generation. This model is then reduced using the balanced truncation method. The reduced order model is utilized to design a supplementary linear quadratic output regulator known for its efficiency and high performance. A Kalman observer is employed to measure the states of the reduced order model to complete the control process. Finally, time domain simulations are used to validate the reduced order model and verify the performance of the proposed controller. The results revealed the accuracy of the model and the effectiveness of the controller.

Small Signal Modelling and Stability Analysis of a Grid Connected Inverted Based Microgrid

Objectives: This work focuses on the stability analysis of grid connected microgrids. It considers the impact of load disturbance and grid voltage change on voltage and current levels, as well as reactive and active power responses, is analysed. Methods: A comprehensive small-signal state-space model is developed for an inverter-based microgrid, incorporating submodules of inverters, phase-locked loops (PLLs), and LCL filters. The model is linearized around a stable operating point, and eigenvalue analysis is performed and validated through MATLAB/Simulink simulations. A current controller operating in the d-q frame is proposed to enhance stable power conversion and maintain microgrid stability. Findings: The proposed model and control strategy demonstrate the microgrid's ability to maintain transient voltage stability under severe dynamic conditions. During a 10% grid voltage fluctuation, the microgrid exhibits stable active and reactive power responses, with currents and voltages at the point of common coupling stabilizing within 0.2 seconds. Furthermore, when a 25 kVA active load is disconnected, the microgrid effectively manages the power transition, maintaining stable operation with minimal deviations in key parameters. The current controller simplifies AC current control, integrating active power management from solar input, DC-link voltage stability, and reactive power control. Novelty: The novelty lies in the comprehensive analysis of transient voltage stability in grid-connected microgrids under grid voltage fluctuations and load disturbances, areas that have received limited attention in previous research. By developing a detailed small-signal state-space model incorporating PLL and LCL filter dynamics and proposing a robust control strategy with the current controller, this study offers new insights into enhancing the resilience and reliability of grid-connected microgrids during transient events. Keywords: Microgrid, Small Signal Stability, Voltage Source Inverter, State Space model, Eigen Values

Small-Signal Stability of Hybrid Inverters with Grid-Following and Grid-Forming Controls

In the modern power grid, characterized by the increased penetration of power electronics and extensive utilization of renewable energy, inverter-based power plants play a pivotal role as the principal interface of renewable energy sources (RESs) and the grid. Considering the stability characteristics of grid-following (GFL) inverters when the grid is relatively weak, the application of grid-forming (GFM) controls becomes imperative in enhancing the stability of the entire power plant. Thus, there is an urgent need for suitable and effective models to study the interaction and stability of the paralleled inverters employing GFL and GFM controls. Thus, the small-signal modeling with full-order state-space model and eigenvalues analysis are presented in this paper. First, the small-signal state-space model of the individual GFL and GFM inverters is obtained, considering the control loop, interaction, reference frame, transmissions, and time delays. Then, the models of the individual inverter are extended to the hybrid inverters to study the effects of the GFM inverters on the small-signal stability of the entire system. And the impacts of the inertia and damping are analyzed by the eigenvalues of the state-transition matrix. A case comprising three parallel GFL inverters and two GFL inverters with one GFM inverter, respectively, are studied to examine the effectiveness and accuracy of the model. Finally, the stability margin obtained from the eigenvalue analysis of the entire system is verified by time-domain simulations.

Model of quasi-Z-source inverter-based PV power systems for stability studies of multi-terminal AC grid-connected PV power systems

Photovoltaic (PV) power systems are becoming one of the most popular green power systems. Power converters are used in these systems. Among them, quasi-Z-source inverters (qZSIs) are currently on the rise. However, instabilities can appear in multi-terminal AC grid-connected power electronics, such as PV power systems, due to the interaction between power electronic controls and the grid. Modeling of qZSI-based PV power systems is lacking in the literature and stability assessment of grid-connected qZSI-based PV power systems is not yet well understood. Accordingly, the present paper contributes with an s-domain dq-real admittance transfer matrix model of qZSI-based PV power systems derived from their small-signal state-space averaged model. The paper also describes a systematic procedure to study multi-terminal AC grid-connected qZSI-based PV power systems by the nodal admittance method, where the proposed qZSI-based PV power system model is incorporated into the nodal admittance matrix to study stability concerns. Thus, AC grid dynamics in the presence of qZSI-based PV power systems can be investigated using impedance-based stability criteria. The proposed model and the procedure are applied in a stability study of two applications where solutions for improving stability issues are presented. In these applications, the two main causes of instabilities in AC-grid connected PV-qZ systems are analyzed in detail. The study is validated by PSCAD/EMTDC simulation. .

A New Communication-Free Grid Frequency and AC Voltage Control of Hybrid LCC-VSC-HVDC Systems for Offshore Wind Farm Integration

We propose frequency and voltage control method for a hybrid high-voltage direct current (HVDC) system for integrating an offshore wind farm into transmission networks. Conventionally, DC voltage level is maintained as constant regardless of the wind velocity and the grid frequency, so AC voltage fluctuates with active power variation in a hybrid HVDC system due to the innate reactive power absorption of inverter side line-commutated converter (LCC). However, in the proposed method, the DC voltage changes according to the wind velocity. Furthermore, DC voltage is simultaneously regulated to participate in frequency control in a communication-free manner. These two characteristics can be achieved by using five droop control methods proposed here. Additionally, by determining droop constants using the proposed determination methods, AC voltage can be maintained as constant during active power fluctuations. Therefore, using the proposed method, an offshore wind farm can be stably connected to mainland transmission networks and successfully used as frequency supporting resources, because voltage characteristics of the AC network are not destabilized. A small-signal state-space (SS) model of the target system was also developed to investigate stability of the proposed control. The utility of the proposed method is demonstrated by case studies using PSCAD and SS models.

Distributed Adaptive-MPC Type Optimal PMS for PV-Battery Based Isolated Microgrid

In the absence of an external grid, supplying quality power to critical loads in renewables, i.e., solar photovoltaics (PV)-battery-based self-sustained isolated microgrid (MG) system is quite troublesome. Because of involved generation arbitrage and variable load conditions, a robust power management scheme is essential. In this article, a distributed strategy with an adaptive model predictive control (MPC) principle is proposed. It considers all possible uncertainties, viz., intermittent generation as time-varying solar irradiance, variable load profile, alongside maintaining smooth charging/discharging cycle of storage units and shedding of noncritical loads. For this purpose, a novel comprehensive small-signal state-space model of MG with PV-battery systems having dedicated parallel <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">RLC</i> loads and a low-voltage network is considered, which accounts for inverter dc-bus link dynamics. The controller tracks the maximum power point of PV and keeps the MG power balance intact for both active and reactive powers by considering interconnected bus dynamics. The viability of the proposed scheme is verified by performing extensive testing, viz., variable solar irradiance profile, continuous small and large variations of loads, shedding of the noncritical loads, multiple topology subsystems, comparative study with state-of-art MPC, and smooth transition of battery charging/discharging cycles using MATLAB platform over 24 and 48 h duration.

Dynamic Analysis and Active Stabilization of a Utility-Scale Grid-Connected Current-Source Inverter-Based PV System Considering Source Dynamics

This paper investigates the effects of the dynamic properties of a photovoltaic generator (PVG) on the stability of a grid-connected current-source inverter (CSI)-based photovoltaic system and presents a simple yet effective active compensator to ensure system stability. A detailed equivalent model of the PVG that considers the dynamic resistance, diffusion capacitance, series inductance, and dc cable resistance and inductance is used, and the effects of these parameters are assessed. It has been found that when the PVG operates in the constant-current region (CCR), the phase margin becomes negative in the control-to-input dynamics, which alters the stability of the dc-link current control. The change in the system dynamics when the operating point of the PVG shifts from the constant-voltage region (CVR) to CCR is verified through a detailed small-signal state-space model of the complete system. Furthermore, an active compensator is proposed to ensure stable dc-link current control operation at all operating points of the PVG. The influence of different control parameters on the integrated system dynamics is examined to determine the range of the control parameters required for stable operation. The performance of the proposed system under utility-grid fault, grid voltage parameter variation, weak grid, and changes in insolation level is also evaluated. Detailed nonlinear time-domain simulation results, using a typical utility-scale CSI-based PV system, validate the analytical results and the effectiveness of the proposed active stabilization under different operating conditions.

Control Design and Parameter Tuning for Islanded Microgrids by Combining Different Optimization Algorithms

Load and supply parameters may be uncertain in microgrids (MGs) due for instance to the intermittent nature of renewable energy sources among others. Guaranteeing reliable and stable MGs despite parameter uncertainties is crucial for their correct operation. Their stability and dynamical features are directly related to the controllers’ parameters and power-sharing coefficients. Hence, to maintain power good quality within the desirable range of system parameters and to have a satisfactory response to sudden load changes, careful selection of the controllers and power-sharing coefficients are necessary. In this paper, a simple design approach for the optimal design of controllers’ parameters is presented in an islanded MG. To that aim, an optimization problem is formulated based on a small-signal state-space model and solved by three different optimization techniques including particle swarm optimization (PSO), genetic algorithm (GA), and a proposed approach based on the combination of both PSO and GA. The optimized coefficients are selected to guarantee desirable static and dynamic responses in a wide range of operations regardless of the number of inverters, system configuration, output impedance differences, and load types. Through the proposed design and tuning method, the performance of the MG is improved as compared to those obtained using state-of-art techniques. This fact is demonstrated by using numerical simulations performed on a detailed model implemented in PSIM© software.

Distributed-Diode-Rectifiers-Based Offshore Wind Power MVDC Direct-Transmission System

An offshore wind power medium-voltage direct-current (MVDC) transmission system based on distributed diode rectifiers (DRs) is proposed to realize the DC transmission of offshore wind power and eliminate offshore platforms. A coordinated control strategy between wind turbines (WTs) is proposed to greatly reduce the transmission voltage ripple and current ripple for this system. A small-signal state-space model for the WT line-side converter control system is established. The less damped terms in the control system are found through system eigenvalues, and the stabilization control method is further proposed. A joint control strategy between the onshore converter station and offshore WTs is proposed to achieve system fault ride-through. This strategy can quickly transmit the onshore AC grid's fault information to each WT and consume unbalanced power by the dc choppers inside WTs. The simulation results in PSCAD verify the effectiveness of the proposed control strategy.

Study on a Frequency Fluctuation Attenuation Method for the Parallel Multi-VSG System

Virtual synchronous generator (VSG) is one of the inverter control methods which can provide extra virtual moment of inertia and achieve frequency support by mimicking the output characteristics of a rotating synchronous generator (RSG), which makes VSG particularly suitable for multi-access point applications, or called the multi-VSG system. However, frequency fluctuations may often occur in the case of power variation. In terms of this issue, this study presents the small-signal state-space model of VSG and analyzes the cause of frequency fluctuation, first. And then, a novel VSG control method is proposed for frequency fluctuation attenuation. The proposed method is especially fit for the parallel multi-VSG system because it does not take grid angular frequency into computation so that it can get rid of the ill effect introduced through PLL. The damping power item is reconstrued with a new means to judge whether the system is in a steady state or not. At the same time, the parametric design method of the proposed method is also figured out. Finally, the simulation experiments are performed, and the results verify that the proposed method performs better than the conventional one in terms of dynamic response and power-sharing among the multi-VSG system.

Consensus‐based distributed control scheme for PCC voltage harmonic mitigation and enhanced power sharing in islanded microgrids

In the islanded microgrid, it is necessary to distribute the harmonic powers correctly among generators and mitigate the voltage harmonics at the point of common coupling (PCC) for effective microgrid operation. These control objectives are hard to satisfy at the same time with only one virtual impedance component. To simultaneously improve the microgrid voltage quality and share the distortion powers, a consensus-based distributed power-sharing scheme is proposed along with PCC harmonics mitigation. In the proposed control scheme, the controllable parts of output impedance at the fundamental and harmonic frequencies are separately tuned by simple integral controllers without depending on feeder impedance parameters. Compared to conventional control schemes, the proposed method is less complicated while ensuring a high voltage quality despite sudden changes in load power. A small-signal state-space model of the microgrid is analysed to validate the stability of the proposed control scheme, and its effectiveness is verified by experiments with a scaled-down microgrid system.

Solution to Fault of Multi-Terminal DC Transmission Systems Based on High Temperature Superconducting DC Cables

In this paper, we developed the small-signal state-space (SS) model of hybrid multi-terminal high-voltage direct-current (HVDC) systems and fault localization method in a failure situation. The multi-terminal HVDC (MTDC) system is composed of two wind farm side voltage-source converters (VSCs) and two grid side line-commutated converters (LCCs). To utilize relative advantages of the conventional line-commutated converter (LCC) and the voltage source converter (VSC) technologies, hybrid multi-terminal high-voltage direct-current (MTDC) technologies have been highlighted in recent years. For the models, grid side LCCs adopt distinct two control methods: master–slave control mode and voltage droop control mode. By utilizing root-locus analysis of the SS models for the hybrid MTDC system, we compare stability and responses of the target system according to control method. Furthermore, the proposed SS models are utilized in time-domain simulation to illustrate difference between master–slave control method and voltage droop control method. However, basic modeling method for hybrid MTDC system considering superconducting DC cables has not been proposed. In addition, when a failure occurs in MTDC system, conventional fault localization method cannot detect the fault location because the MTDC system is a complex form including a branch point. For coping with a failure situation, we propose a fault localization method for MTDC system including branch points. We model the MTDC system based on the actual experimental results and simulate a variety of failure scenarios. We propose the fault localization topology on a branch cable system using reflectometry method. Through the simulation results, we verify the performance of fault localization. In conclusion, guidelines to select control method in implementing hybrid MTDC systems for integrating offshore wind farms and to cope with failure method are provided in this paper.

Small-Signal Stability Analysis and Current Control Reference Optimization Algorithm of DFIG-Based WT During Asymmetric Grid Faults

The stability issues of weak grid-connected doubly fed induction generator (DFIG) based wind turbines during asymmetric grid faults become very acute. In this article, a small-signal state-space model was established to deal with the stability problems of the DFIG system during asymmetric grid faults. Based on the model, the interaction mechanism between the power grid and the DFIG system during asymmetric faults is described and the modal analysis is performed. The analysis results show that the dominant unstable poles of the system are mainly affected by the phase-locked loop (PLL). Then, according to the vector relationships of voltages and currents, the effect of positive-sequence (PS) and negative-sequence (NS) d -axis currents on the PLL output angle is analyzed. It is pointed out that the system stability can be effectively improved by injecting reasonable d -axis components of PS and NS currents into the power grid during faults. Furthermore, considering the current capacity limitation of DFIG, a novel PS and NS current control reference optimization algorithm is proposed, which can suppress the oscillation of the system. Finally, the correctness of the theoretical analysis and the effectiveness of the proposed control strategy are validated by the simulation and experiments.

Modeling and parameter analysis for consensus based secondary control of parallel Virtual Synchronous Generators

In recent years, the consensus control has become a research hotspot in microgrid cooperative control. However, when the VSG control is applied, the system has higher order, more parameters and more complex dynamic response. And there are few studies on the dynamic characteristics of parallel VSGs with the consensus control. Aiming at this problem, the small signal state space model of parallel VSG with consensus based secondary control is established in this paper firstly. Then the influences of damping, inertia, secondary control parameters on dynamic response are analyzed, and the design criterion of secondary control parameters is proposed. Finally, the simulation results verify the accuracy of model and correctness of conclusions.

Equivalent Multiple $dq$-Frame Model of the MMC Using Dynamic Phasor Theory in the $\alpha \beta z$-Frame

This article introduces an equivalent multiple dq-frame model of the modular multilevel converter (MMC) that is derived from a dynamic phasor based small-signal state-space MMC model in the stationary αβz frame. When compared to a model in the stationary ABC frame, the order of the model in the αβz frame can be reduced for balanced operation, during which some voltage, and current harmonics are inherently separated in an αβz representation. The proposed method enables further model order reduction through a generalized transformation towards multiple dq-frames. The development of the model, and the generalized transformation are explained in detail, and the obtained equivalent multiple dq-frame models are verified against a nonlinear averaged model in MATLAB/Simulink. An eigenvalue-based small-signal stability analysis highlights the effect of higher-order harmonics in system-level small-signal stability studies, and two case studies of active harmonic suppression illustrate how the presented model allows an in-depth investigation of the impact of extended control functionalities on the small-signal stability.

Virtual Synchronous Machine/Dual-Droop Controller for Parallel Interlinking Converters in Hybrid AC–DC Microgrids

This paper addresses the operation of parallel interlinking converters (ICs) in hybrid AC–DC microgrids from different perspectives, then proposes a unified mitigation technique. Firstly, the influence of the system nonlinearity on circulating currents between parallel ICs is investigated. Secondly, it is shown that ICs might induce voltage harmonics due to the antiparallel diodes of the power electronic switches which are seen by the AC subgrid as nonlinear diode rectifiers. Lastly, the synchronization of ICs following abnormal operating conditions is discussed and new findings are presented. In order to enhance the operation of ICs and overcome the preceding challenges, a modified virtual synchronous machine (VSM) strategy with a dual-droop (DD) controller is proposed. The positive influence of the proposed VSM-DD controller on the overall system dynamics is clearly justified. Small-signal state-space modeling for the entire system is conducted to verify the results analytically. A nonlinear time-domain simulation model is developed using PSCAD/EMTDC to validate the impact of the VSM-DD controller experimentally.

DC Current and Voltage Droop Control Method of Hybrid HVDC Systems for an Offshore Wind Farm Connection to Enhance AC Voltage Stability

A new DC current-voltage droop control method for a hybrid high-voltage direct-current (HVDC) system featuring a voltage-sourced converter (VSC) rectifier and a line-commutated converter (LCC) inverter is presented. The proposed method utilizes DC voltage droop control to reduce the AC voltage fluctuation at the inverter side, to exploit the hybrid HVDC system for connecting offshore wind farms to weak grids without necessitating continuous reactive power compensation facilities. Additionally, an optimal droop coefficient calculation method is proposed to keep the AC voltage constant for wind power fluctuations. To evaluate the stability of the proposed method, a small-signal state-space (SS) model of the target system is derived and the root locus analysis is given. Simulation case studies are performed using an electromagnetic transient model in PSCAD and an SS model in MATLAB. The results demonstrate that a hybrid HVDC system with the proposed method successfully integrates offshore wind energy and weak grids without additional facilities because the AC voltage can be maintained at a near constant during wind fluctuations.

Virtual Impedance Control Scheme to Compensate for Voltage Harmonics With Accurate Harmonic Power Sharing in Islanded Microgrids

In case of voltage harmonic compensation at the point of common coupling (PCC) in islanded microgrids, it is important to share the harmonic load power correctly among the distributed generators (DGs) to use the DGs' capacity effectively. In previous DG control schemes, it is impossible to satisfy the requirements of PCC voltage quality and accurate harmonic power sharing simultaneously with only a virtual impedance controller (VIC). In this article, we propose an enhanced DG VIC to provide accurate harmonic power sharing along with voltage harmonic compensation in islanded microgrids. The proposed VIC is developed based on simple integral controllers with two controllable parts and no information about the feeder impedances or load currents. The control performance is theoretically analyzed using a small-signal state-space model to evaluate the system dynamics and stability. The feasibility and effectiveness of the method are validated by simulated and experimental results.

Distributed control scheme for accurate reactive power sharing with enhanced voltage quality for islanded microgrids

This study presents a distributed control scheme for islanded microgrids to eliminate power sharing errors as well as frequency and voltage deviations based on distributed cooperative control. A consensus algorithm is developed through adaptive regulation of the virtual impedances for accurate power sharing regardless of load variations. The proposed power sharing controller is quite easy to implement with only one simple integral gain. It is achieved without using information about the feeder impedances, load powers or detailed microgrid structure. To remove the deviations in the frequency and voltage magnitude, conventional droop equations are enhanced by adding compensating signals, which are simply determined from the neighbors’ droop information without a PI controller. Therefore, the control complexity is significantly reduced. The control performance is theoretically analyzed using a small-signal state-space model to evaluate the system dynamics and stability. A digital simulation is done using PSIM, and experiments are carried out with a scaled-down microgrid prototype to verify the proposed scheme.