SEARCH · Search NASA
Results for “small signal modeling”
Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.
Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.
Farm-level Interactions Study of a Novel Tri-port Soft-switching Medium-Voltage String Inverter (MVSI) based Large-scale PV-Plus-Storage Farms
A medium-voltage photovoltaic power conversion unit supported by battery based on a novel topology of soft switching solid state transformer is presented in this paper. It can reduce the Levelized Cost of Energy (LCOE) of PVS farm in an extended degree. However, its capability to provide grid-support services, such as frequency response, reactive power support, etc, have not been demonstrated. A series/parallel combination of these modules form a large 20 MVA solar farm. To validate them with reduced computation burden, a small-signal model of MVSI is firstly derived and validated in this paper. The model has been validated to match the full-switch model in both steady-state and dynamic conditions. Next, a farm-level simulation based on the proved small-signal model was implemented to demonstrate grid-support services. Real irradiation date from NREL is used to show the operational capabilities of the system. As a result, the overall farm is simulated based on MATLAB/Simulink domain to check the performance for various cases namely: power transfer from dc-ac side, reactive power support during grid voltage sag and utilization of battery during grid voltage disturbance or partial shading over PV panels.
Small-Signal Stability of Grid-Forming Inverters Using Current-Limiting and Frequency Stabilization
This paper presents a small-signal stability analysis of grid-forming (GFM) inverters under current-limiting conditions. It examines how adjustments in virtual impedance angles, implemented through advanced current-limiting and frequency stabilization techniques, influence small-signal stability. This paper studies a GFM inverter control integrating a fictitious power technique stabilizing primary control by adding a virtual power term and a hybrid current limiter integrating virtual impedance in the anti-wind-up feedback with current reference saturation limiting. A small-signal model is developed to assess the impact of virtual impedance angles on GFM inverter dynamics during grid disturbances, such as voltage drops. The findings indicate that although increasing the virtual impedance angle (to make it more inductive) enhances large-signal stability and voltage support during faults, it can induce oscillations and lead to instability if the angle exceeds certain thresholds. Based on the small-signal models, this paper provides design considerations for the current-limiter impedances to ensure reliable GFM inverter behavior under grid disturbances while maintaining small-signal stability.
Holistic Small-Signal Stability Analysis for Large-Scale Inverter-Intensive Power Systems with Coupled and Full-Order Dynamics from Control Systems and Power Networks
The increasing penetration of inverter-based resources (IBRs) into the existing power systems introduces tremendous benefits for enhanced sustainability but also poses inevitable challenges in terms of insufficient inertia, potential instability, and complex network dynamics, among others. However, the additional coupling introduced by the interactions among gridfollowing (GFL) and grid-forming (GFM) IBRs and the other components (i.e., synchronous generators [SGs], loads, and network, etc.) has not been clearly explored. A holistic, scalable, and quantitative stability analysis framework with the control systems and power networks is still missing. Here, in this paper, to fill in the technical gaps, a holistic small-signal model of the entire system with both rotating generation units and IBRs is established. An extended power flow model with operation dynamics from both generator control schemes and power networks is proposed to provide the varying steady-state operating points for small-signal modeling. The proposed method is compared with MATLAB solvers, and the results show that the proposed approach has a minimum calculation time, which can be less than 12 seconds for a large-scale power system with up to 2,000 buses. Furthermore, a quantitative method is developed to identify the impacts of IBRs on system performance with emphases on the potential stability issues with GFL IBRs, additional benefits of employing GFM IBRs, the feasibility of replacing SGs with GFM IBRs, and the impact of penetration level of different kinds of generation units. Finally, a field island power system is used to verify the proposed approach, and hardware-in-the-loop (HIL) tests are provided to further demonstrate the effectiveness of the proposed analysis.
Virtual Oscillator Grid-Forming Inverters: State of the Art, Modeling, and Stability
Not provided.
Stacked Low-Inertia Converter or Solid-State Transformer: Modeling and Model Predictive Priority-Shifting Control for Voltage Balance
This paper presents control challenges of stacked low-inertia converter (SLIC) or cascaded reduced dc-link solid-state transformer (SST) and proposes a novel model predictive priority-shifting (MPPS) control with implicit modulator and a discrete-time large-signal model for voltage balancing and dc-link regulation. Low-inertia converters, featuring small electrolytic capacitor-less dc links, dramatically reduce cost, size, and weight compared to conventional solutions. However, without a large dc-link buffer, the input and output are tightly coupled, leading to significant control challenges. The control becomes even more challenging with these converters stacked input-series output-parallel (ISOP) for medium-voltage (MV) grid, which causes coupling between the modules besides the coupling within each module. This paper analyzes the multi-objective, multi-degree of freedom control problem, using the modular soft-switching solid-state transformer (M-S4T) as an example of the SLIC. First, distribution of control efforts under controller saturation is critical because multiple control objectives can be conflicting, especially when the module voltages are unbalanced and are being restored. The MPPS can shift the priorities to address this issue. Second, due to the low inertia and high dc-link ripple, classic space vector pulse-width modulation (SVPWM), average model with small-ripple assumption, and control design based on small-signal model cannot accurately modulate, model, and control the nonlinear reduced dc link. Therefore, a discrete-time large-signal model of the M-S4T is established to derive the predictive control in the MPPS. The MPPS and the PI control are compared in MV simulations to show the issue of applying the PI to the SLIC and the effectiveness of the MPPS for voltage balancing and dc-link regulation in a deadbeat manner. Finally, the proposed control is tested on a 5 kV ISOP SiC SST prototype to verify priority shifting to address controller saturation issue and fast and robust voltage balancing.
Time Delay of Wide Area Damping Control in Urban Power Grid: Model-Based Analysis and Data-Driven Compensation
Due to the rapid development of economies, large urban cities consume an increasing amount of energy and have a higher requirement for power quality. Voltage source converter based high voltage direct current (VSC-HVDC) is a promising device to transmit clean power from remote regions to urban power systems, while also providing wide area damping control (WADC) for frequency stabilization. However, the time-delay naturally existing in the VSC-HVDC system may degrade the performance of WADC and even result in instability. To address this issue, this paper develops a time-delay correction control strategy for VSC-HVDC damping control in urban power grids. First, a small signal model of WADC is built to analyze the negative impacts of time delay. Then, a data-driven approach is proposed to compensate for the inherent time delay in VSC-HVDC damping control. The extensive training data will be generated under various disturbances. After offline training, the long short-term memory network (LSTM) can be implemented online to predict the actual frequency deviation based on real-time measurements. Finally, the proposed method is validated through MATLAB-Simulink in a two-area four-machine system. The results indicate that the data-driven compensation has a strong generalization ability for random delay time constants and can improve the performance of WADC significantly.
Small-Signal Stability Support from Dynamically Configurable Grid-Forming/Following Inverters for Distribution Systems: Preprint
As the penetration of inverter-based resources (IBRs) continues to increase in modern power systems, system stability is challenged by the insufficient inertia induced by IBRs; hence, there is a need to develop various methods to address the potential instabilities. In this paper, grid-forming (GFM) and grid-following (GFL) controls are implemented for inverters with flexible-mode transitions between them. The operation mode transition between GFM and GFL controls is adopted as an additional degree of control flexibility to adjust the small signal stability margin. Further, a holistic and detailed small signal model of the entire system with the dynamics from both synchronous generators (SGs) and IBRs is derived. The effectiveness of the proposed work in adjusting the system small signal stability margin is validated by conducting case studies with varying penetration levels of IBRs. A test system with one SG and five inverters was implemented in MATLAB/Simulink to demonstrate the effectiveness of the proposed approach. Index Terms - grid-following control, grid-forming control, operation mode transition, small-signal stability analysis
A Lyapunov-Based Generalized Dc-Side Controller Design for PV-Connected Systems
The objective of this paper is to realize a universal dc-side controller for photovoltaic (PV) systems where the control is agnostic to the downstream converter configuration. To achieve this, the downstream power converter and its controls are manipulated into an effective power control loop that is then cast into a generalized multi-loop design framework. On the dc side, a nonlinear small-signal model of the PV input is realized exclusively in terms of PV datasheet parameters (i.e., open-circuit voltage, short-circuit current, and maximum power point). Finally, a linear controller is used to modulate the dc-side PV system with the generic downstream power controller. A Lyapunov candidate is proposed to analyze the stability of the interconnected system and provide a streamlined approach for the controller design. The proposed design is validated on a 1k VA experimental setup that interfaces a PV module to the grid.
Small-Signal Stability Support from Dynamically Configurable Grid-Forming/Following Inverters for Distribution Systems
The growth of inverter-based resources (IBRs) in modern power systems can challenge system stability since they do not natively provide inertia, prompting a need to develop new methods to address the potential instabilities. In this paper, a dynamically configurable grid-forming (GFM) and grid-following (GFL) control is proposed, which enables inverters to flexibly transition to support system needs. The operation mode transition between GFM and GFL controls is adopted as an additional degree of control flexibility to adjust the small-signal stability margin. In addition, a holistic and detailed small-signal model for a distribution feeder that captures the dynamics from both synchronous generators (SGs) and IBRs is also derived and used to evaluate the effectiveness of the proposed GFM/GFL controls to augment the system small-signal stability margin. Case studies with varying levels of IBRs were implemented in MATLAB/Simulink to demonstrate the effectiveness of the proposed approach.
Region-Based Stability Analysis of Resilient Distribution Systems with Hybrid Grid-Forming and Grid-Following Inverters
In this paper, distribution system stability considering mixed grid-forming (GFM) and grid-following (GFL) inverters is discussed. A holistic small-signal model of the distribution feeder accommodating both GFM and GFL inverters is derived. In contrast to conventional point-by-point stability analysis, a region-based stability assessment approach is proposed and implemented to evaluate small-signal system stability with both GFM and GFL controls. Furthermore, to enhance the computational efficiency, an Artificial Intelligence (AI) assisted Kernel Ridge Regression (KRR) approach is developed to obtain the stability region boundary. Therefore, with the derived stability region, the impact of critical parameters on system stability is intuitively shown, and more importantly, the relationship between the maximum penetration level and the corresponding feasible range of the selected control parameters can be quantified. The proposed approach has been validated using MATLAB/Simulink.
Introduction of a Variable Inductance Transformer for the Design of Resonant Power Converters
Magnetic integration is a hot topic in power electronics that concerns the use of a transformer’s leakage and magnetizing inductances purposefully in isolated power electronic converters, thereby giving the opportunity to save the cost and footprint of any additional inductor. This is of prime interest, especially in CLLLC resonant converters which require up to three inductors. For a complete integration of these inductances, the concept of a variable inductance transformer (VIT) is introduced in this thesis. A VIT is an adaptive magnetic structure that facilitates an easy adjustment of both magnetizing and leakage inductances to meet their desired values. However, for a more promising design, an accurate estimation of these inductances is necessary. While the evaluation of magnetizing inductance is quite straightforward, the calculation of leakage inductance is rather convoluted, because the leakage inductance is influenced by both the winding layout and the operating frequency. In this thesis, three new semi-analytical methods for calculating the frequency-independent leakage inductance, and a novel semi-analytical method for evaluating the frequency-dependent leakage inductance are proposed. These methods can calculate the respective leakage inductances of a VIT within an outstanding ±5% uncertainty. Finally, a bidirectional CLLLC resonant dc-dc converter is investigated for the constant current constant voltage (CCCV) charging of the next-generation 900 V traction battery of an electric vehicle. A new voltage gain equation is derived for designing the CLLLC resonant tank, and a small-signal model is presented for designing the variable-frequency feedback controller. Furthermore, a new methodology to design a VIT is developed to overcome the challenges associated with small coupling coefficients and guarantee a complete magnetic integration of the tank inductances. All theoretical results presented herein are verified through simulations and experiments performed on hardware prototypes designed in the lab.
Small-Signal Analysis of Current-Limiting Grid-Forming Inverters
Grid-forming (GFM) inverters are equipped with a current limiter to protect the device during grid disturbances. Because the intervention of the current limiter can compromise the transient stability of the GFM inverter, various types of current limiter designs and additional frequency-stabilization control methods have been proposed in recent literature to aid in transient GFM inverter stability; however, the small-signal stability implications of adding these additional control blocks during, in particular, off-nominal conditions are not fully understood. To address this challenge, this paper presents a generic small-signal model of a GFM inverter that incorporates various types of current limiters and frequency stability-enhancing controls. With the proposed model, we analyze the root causes of inverter instability, which reveals two critical design trade-offs. First, due to current-limiter engagement caused by a disturbance, the GFM inverter dynamics are altered, which can lead to voltage oscillations. Second, additional frequency-stabilization controls can improve the small-signal stability of the GFM inverter, but at the cost of reduced power and voltage support to the grid. Comprehensive hardware experiments validate the theoretical concept and analysis. The findings in this work underscore the importance of incorporating both transient-response and small-signal dynamics requirements into the design procedure of GFM current limiters and frequency-stabilization controls.
On Stability of PQ-Controlled Grid-Following and Droop-Control Grid-Forming Inverters
In this paper, the nonlinearity impacts of PQ-control schemes and LCL filter parameter variations on the stability of grid-interactive inverters are studied under weak grid conditions. This work demonstrates that the control nonlinearity and parameter variations can cause unexpected instability at low power levels. This instability issue in the nominal operating range may occur under specific control parameters due to the shift of the low-frequency eigenvalues of PQ-controlled inverters. A full-order small-signal model for PQ-controlled inverters is applied to analyze this instability issue. Furthermore, the impacts of the droop coefficients on the stability of the droop-controlled grid-forming inverter are also investigated using the closed-loop inverter model. The findings are experimentally verified using a small-scale two-level 208 V, 5 kVA inverter feeding a 12 kW NHR 9410 power grid emulator and a hardware setup of a microgrid fed by two 5 kVA 208V inverters.
Quantitative Small-Signal Stability Analysis of Grid-Forming Inverters in Large-Scale Power Systems
In this paper, the challenges induced by the integration of inverter-based resources (IBRs) into existing power systems are discussed. Although the grid-forming (GFM) control has been used to enhance system performance in multiple sections of electric power systems (e.g., transmission and distribution systems, microgrids, among others), the coupling mechanism between GFM inverter and various types of other components in modern power systems should be clearly explored. Existing analyses mainly focus on qualitative investigations that verify the effectiveness of deploying GFM inverters for stability enhancement. A holistic system-level quantitative analysis is still missing to verify the detailed benefits of GFM inverters and their interactions with other generation units (e.g., synchronous generators [SGs], conventional grid-following [GFL] inverters, synchronous condensers, among others). To fill in the technical gaps, a holistic small-signal model of the entire system with both rotating generation units and IBRs is established along with the customized power flow analysis for varying steady-state operating points. Further, a quantitative method is proposed to identify the impacts of GFM inverters on system performance with an emphasis on a quantifiable stability margin and a complete modal analysis at the system level. Finally, a realistic test system is used to verify the proposed approach.
An Inrush Current Limiting Strategy for Virtual-Oscillator-Controlled Grid-Forming Inverters
Not provided.
The Heuristic Dynamic Programming Approach in Boost Converters
In this study, a heuristic dynamic programming controller is proposed to control a boost converter. Conventional controllers such as proportional-integral-derivative (PID) or proportional-integral (PI) are designed based on the linearized small-signal model near the operating point. Therefore, the performance of the controller during the start-up, the load change, or the input voltage variation is not optimal since the system model changes by varying the operating point. The heuristic dynamic programming controller optimally controls the boost converter by following the approximate dynamic programming. The advantage of the HDP is that the neural network-based characteristic of the proposed controller enables boost converters to easily cope with large disturbances. An HDP with a well-trained critic and action networks can perform as an optimal controller for the boost converter. To compare the effectiveness of the traditional PI-based and the HDP boost converter, the simulation results are provided.
A Lyapunov-Based Generalized Dc-Side Controller Design for PV-Connected Systems: Preprint
The objective of this paper is to realize a universal dc-side controller for photovoltaic (PV) systems where the control is agnostic to the downstream converter configuration. To achieve this, the downstream power converter and its controls are manipulated into an effective power control loop that is then cast into a generalized multi-loop design framework. On the dc side, a nonlinear small-signal model of the PV input is realized exclusively in terms of PV datasheet parameters (i.e., open-circuit voltage, short-circuit current, and maximum power point). Finally, a linear controller is used to modulate the dc-side PV system with the generic downstream power controller. A Lyapunov candidate is proposed to analyze the stability of the interconnected system and provide a streamlined approach for the controller design. The proposed design is validated on a 1-kVA experimental setup that interfaces a PV module to the grid.