Mixed Potential Function Research Articles

Large-signal stability analysis of an islanded DC microgrid with constant power loads based on mixed potential function

Abstract In DC microgrids, power electronic converters are widely used to connect loads and renewable energy sources to generate different voltages. These loads operate as constant power loads (CPL) within a closed control loop. When voltage fluctuates, these loads display negative impedance characteristics, potentially leading to system instability. Therefore, the analysis of the impact of CPL on DC microgrids during large disturbances is crucial. This paper employs mixed potential theory to study the large disturbance stability of DC microgrids under CPL. Deriving the stability criterion for the system under significant perturbations reveals the impact of load types and control parameters on system stability and provides a detailed analysis of how specific system parameters affect stability. Consequently, the stability criterion can ensure the system’s stability under large disturbances without the need for repeated calculations and simulations. Simulation results verify the correctness of this stability criterion.

Multi-scale analysis of corrosion-induced fracture failure mechanisms of high-strength steel wire

Currently, research on the mechanical properties of corroded steel wire is primarily conducted through corrosion testing, with a lack of in-depth theoretical investigations into the underlying mechanisms. Addressing this research gap, this study employs molecular dynamics (MD) and finite element theory to explore the corrosion process, micro- and macro-mechanical properties of corroded steel wire, and the fracture mechanisms after corrosion. The study achieves a coupling of micro- and macro-scale analyses. Firstly, a molecular dynamics model is established based on the chemical composition of high-strength steel wire, and a novel mixed potential function derived from quantum mechanics is employed to analyze the fracture mechanisms of corroded steel wire. Secondly, a simplified model of randomly corroded pits in steel wire is developed using Python in Abaqus, based on experimental measurements. Finally, the macroscopic fracture process and fracture strength of corroded steel wire are analyzed based on the results from molecular dynamics simulations. These results are then compared to experimental data to validate the accuracy of the theoretical analysis.

Large-Signal Stability Analysis for Islanded DC Microgrids with n+1 Parallel Energy-Storage Converters

In islanded DC microgrids, the negative impedance characteristics of constant power loads (CPLs) usually introduce instability influences; on the contrary, hybrid energy-storage systems (HESSs) constituted of batteries and supercapacitors (SCs) have stabilization advantages. To guarantee the large-signal stability of islanded DC microgrids with n+1 parallel energy-storage converters, an equivalent model is first constructed based on the control strategies of the converters. Then, according to the mixed potential function theory, a large-signal stability criterion, considering powers, inductors, capacitors, the DC bus voltage, the equivalent internal resistances of batteries, the proportional parameters of the inner current loop of n battery DC–DC converters, the proportional parameter of the outer power control loop of the SC DC–DC converter, and the proportional parameter of the inner current loop of the CPLs, is derived. Furthermore, the proposed large-signal stability criterion is optimized via the use of droop control for n battery converters, and coefficients related to the droop coefficients are also taken into account. These involved control parameters reveal the process of regulating the HESS and CPLs instead of ideal modeling and significantly reduce the conservatism of the criterion to some extent. In addition, on the basis of the large-signal stability criterion presented herein, the maximum CPL power that the islanded DC microgrids can stably support is obtained. Finally, simulation and experimental results verify the validity of the provided large-signal-stability criterion. The given procedure of analyzing large-signal stability is more consistent with planning and operating actual DC microgrids.

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

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

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

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

Saturated Attitude Control of Multi-Spacecraft Systems on SO(3) Subject to Mixed Attitude Constraints With Arbitrary Initial Attitude

In this paper, for multi-spacecraft systems (MSSs) with a directed complete communication topology and a time-varying virtual leader, an adaptive saturated attitude controller is proposed to achieve attitude consensus and attitude tracking under arbitrary initial attitude, mixed attitude constraints, input saturation and external disturbances. Firstly, considering the time-varying desired attitude provided by the virtual leader in a directed complete topology, an MSS attitude error function and an MSS attitude error dynamics based on SO(3) are developed. Next, an effective mixed potential function for the MSS on SO(3) is proposed for the static attitude-forbidden zones, the relative dynamic attitude-forbidden zones and the attitude-mandatory zones. In particular, different from the existing potential functions, the proposed mixed potential function is suitable for arbitrary initial attitude of the spacecraft in MSS, relaxing the restriction on the initial attitude associated with each static and dynamic attitude constraint zones. Then, an adaptive saturated attitude controller is designed to realize attitude consensus and tracking for the MSSs on SO(3) under arbitrary initial attitude, mixed attitude constraints, saturation constraints and external disturbances. Finally, simulation results of an MSS with a time-varying virtual leader are demonstrated to illustrate the efficiency of the proposed attitude controller.

Voltage Control of DC Microgrids: Robustness for Unknown ZIP-Loads

In this letter we propose a new passivity-based control technique for Buck converter based DC microgrids comprising ZIP-loads, i.e., loads with the parallel combination of constant impedance (Z), current (I) and power (P). More precisely, we propose a novel passifying input and a storage function based on the mixed potential function introduced by Brayton and Moser, relaxing restrictive (sufficient) conditions on Z, P and the voltage reference, which are usually assumed to be satisfied in the literature. Consequently, we develop a new passivity-based controller that is robust with respect to uncertain ZIP-loads.

Study on the evolution mechanism of subsurface defects in nickel-based single crystal alloy during atomic and close-to-atomic scale cutting

Nickel-based single crystal alloys are widely used in aerospace industry. From the point of view of defect evolution and energy change, the evolution mechanism of subsurface defects in the atomic and close-to-atomic scale (ACS) cutting single crystal nickel-based alloy with silicon nitride tool was studied, combining with the molecular dynamics method. The mixed potential function was used to describe the force interaction between atoms in the ACS cutting system. The process of nucleation, propagation and transformation of subsurface defects were analyzed. Based on the dislocation emission model, the relationship between dislocation slip length and change of energy was described. The variety, quantity and area of subsurface defect changes caused by the change of cutting speed, crystal orientation and cutting depth were discussed. The result shows that increasing cutting speed can effectively reduce the number and area of subsurface defects and improve the quality of machined parts. The larger the cutting speed, the larger the chip volume. With the increase of cutting depth, the number of stacking fault tetrahedrons in the subsurface area of workpiece increases. When crystal orientation 010 00 1 ¯ is used for cutting, more defects will be produced in the subsurface region. When crystal orientation are 111 10 1 ¯ and 011 01 1 ¯ , the dislocation emission angle is π /2, it is the most favorable for the emission of partial dislocations and easy to remove materials. The research content provides important references for the optimization of machining parameters and improvement of processing quality for the ultraprecision cutting of nickel-based alloy.

Investigation of the adhesive contact between a diamond indenter and single-Crystal copper substrate at low temperatures

ABSTRACT Considering the elastoplastic deformation of a single-crystal copper substrate, based on the atomic scale, a mixed potential function (EAM and Morse) and the Verlet algorithm were used to simulate the adhesion contact and separation process between a hemispherical diamond indenter and a single-crystal copper substrate at low temperatures. The influences of the temperature on the micro/nanomechanical properties of the material surface and on the mechanism of the subsurface deformation process were analysed. The results show that as the simulated temperature decreases, the time for adhesion to occur is delayed, and the adhesion forces increase slightly. While the indenter is being pressed, the temperature affects the generation and interaction of the dislocations in the substrate. As the temperature decreases, a large number of dislocations in the substrate are generated and then relatively reduced, and the load on the indenter fluctuates. A calculation of the mechanical properties of the material found that the contact stiffness was related to the elastic recovery energy. A smaller elastic recovery energy leads to a greater contact stiffness; thus, the indentation hardness is related to the plastic deformation energy. An increased plastic deformation energy results in a decreased indentation hardness.

Power-based modelling and control: experimental results on a cart-pole double inverted pendulum

This paper is concerned with the modeling framework based on power and control for a mechanical system that has nonlinear, unstable, and under-actuated characteristic features, based on an analogy, which is developed by using the Brayton and Moser's (BM) equations between mechanical and electrical systems. The analogy is based on a mixed-potential function generalized for BM. The mixed-potential function for a cart - pole double inverted pendulum (CPDIP) system is used as a new building block for modeling, analysis, and controller design. The analogy allows for the exact transfer of results from electrical circuit synthesis and analysis to the mechanical domain. This paper focuses mainly on the development of the electrical equivalent circuit of CPDIP inspired by the power-based modeling framework. In this brief, a real time CPDIP experimental setup was modeled by using this framework and a linear quadratic regulator (LQR) controller was designed for the stabilization of the system. Experimental results validated that this framework can be used as a new and advantageous modeling method and is a convenient and practical alternative to the Lagrangian framework.

Influence of anisotropy of nickel-based single crystal superalloy in atomic and close-to-atomic scale cutting

Nickel-based single crystal superalloy is widely used in the field of aerospace and nuclear reaction equipment due to its good properties. Ultra-precision machining technology is an important means to ensure the surface quality of parts. However, the anisotropy of materials has great influence on the evolution of surface and subsurface defects and the removal of materials in the process of machining. In this paper, The MD (molecular dynamics) modeling and simulation verification of cutting anisotropic nickel-based single crystal superalloy workpiece with silicon nitride tool is carried out by using the mixed potential function simulation. Through cutting simulation and visualization, the types, number, deformation area and dislocation evolution of the machined surface defects and inside of the workpiece defect of nickel-based single crystal superalloy with different crystal orientations are analyzed. The evolutionary mechanism of the machined surface defects and the law of material removal are discussed. The research content provides a theoretical basis for parameter optimization and improvement of machining quality in the atomic and close-to-atomic scale (ACS) cutting process, and technical support for efficient and precise machining process of the nickel-based superalloy.

Large‐disturbance stability analysis method based on mixed potential function for AC/DC hybrid distribution network with PET

The dynamics of the power electronic transformers (PETs) have brought great challenges to stability analysis of the AC/DC hybrid distribution network with PETs. In this study, a large disturbance stability analysis method is proposed for the AC/DC hybrid distribution network with PETs, based on the mixed potential function (MPF) theory. Firstly, the simple average models of the converters based on the controlled sources with the control links are presented to describe the dynamic characteristics of the AC/DC system, which are suitable for the MPF theory. Subsequently, the method of constructing the MPF for the non-linear links in PET is proposed to derive a stability criterion for the AC/DC hybrid distribution network. The effects of the AC and DC dynamic characteristics and the non-linear control links are both included in the criterion. Multiple scenarios of the faults or the large disturbances are used to investigate the effect of the stability criterion, and the results show that the stability state of the multi-PET distribution network could be reflected by the stability criterion under various large disturbances. Finally, the parameter-influence analysis method is proposed to improve the stability of the system.

Direct Method-Based Transient Stability Analysis for Power Electronics-Dominated Power Systems

With the extensive application of power electronics interfaced nonsynchronous energy sources (NESs) in modern power systems, the system stability especially the transient stability is prominently deteriorated, and it is crucial to find a comprehensive and reasonably simple solution. This paper proposes a direct method-based transient stability analysis (DMTSA) method which concludes the key steps as follows: (1) the system modeling of Lyapunov functions using mixed potential function theory and (2) the stability evaluation of critical energy estimation. A voltage source converter- (VSC-) based HVDC transmission system is simulated in a weak power grid to validate the proposed DMTSA method under various disturbances. The simulation results verify that the proposed method can effectively estimate the transient stability with significant simplicity and generality, which is practically useful to secure the operation and control for power electronics-dominated power systems.

The Control Parameter Determination Method for Bidirectional DC-DC Power Converters Interfaced Storage Systems Based on Large Signal Stability Analysis

In DC microgrid (DC-MG), the loads connected with converters under strict control areconsidered as CPLs (constant power loads). When the voltage of CPLs decreases, the currentincreases and the negative impedance characteristic of CPLs cause instability easily. Fortunately,appropriate control for energy storage units could improve the system stability. However, mosttraditional control methods for bidirectional DC-DC power converters (BDC) connected withbattery storage units do not quantitatively consider the stability influences of control parameters.This paper quantitatively analyzes the stability influence of the BDC current-mode controlparameters and the negative impact of CPLs and derives the control parameter determinationmethod for BDC interfaced storage systems. Large signal stability constraints are obtained in termsof mixed potential function. According to the constraints, the large signal stability is improved whenthe BDC control parameter kp increases, while the stability is degraded when the power of CPLsincreases. The control parameter determination method is very effective and convenient to apply,and the appropriate parameter kp for BDC is determined. The regions of asymptotic stability (RAS)identify that the proposed control parameter determination method could improve the systemstability effectively. The determination method is fully verified by the simulation and experimental results.

Research on Large-Signal Stability of DC Microgrid Based on Droop Control

Ensuring the large signal stability of the DC microgrid is the premise of the safe operation of the DC microgrid, but the research on the large-signal stability of microgrids with multiple droop control micro-sources is still scarce. In this paper, a DC microgrid system model with multiple droop control micro-sources was established by appropriate simplification. Addressing the problem that most stability research methods cannot be quantitatively analyzed, the mixed potential function method was used to analyze the large signal stability of the system. However, the criterion obtained by the conventional mixed potential function method is complicated and contains multiple time-varying parameters, which is not convenient for analysis. Therefore, the simple form of the criterion was obtained through simplification and the analysis proved the rationality of the simplification. On this basis, a nonlinear droop control method was proposed to improve the anti-interference ability of the system. Finally, the accuracy of the large signal stability criterion and the effectiveness of nonlinear droop control on the system’s large signal stability were verified by simulation.

Large-Signal Stability Analysis of the Undersea Direct Current Power System for Scientific Cabled Seafloor Observatories

A large number of power electronic converters and long-distance submarine cables are an important part of the undersea direct current (DC) power system of the scientific cabled seafloor observatories (CSOs). However, the constant power load (CPL) characteristics of the converters and the distributed parameter characteristics of long-distance submarine cables greatly affect the stability of the CSO DC power system. This paper analyzes the large-signal stability of the CSO DC power system, and the equivalent circuits of long-distance submarine cables are established by theoretical analysis and computer simulation. A simplified computer simulation model and an equivalent experimental prototype model of a single-node CSO DC power system was built in the laboratory to study this issue. The mixed potential function method is used to analyze the large-signal stability of the CSO DC power system, and the large-signal stability criterion is obtained theoretically. The validity of the large-signal stability criterion is proved by simulations and experiments. The conclusion is that reducing the inductance of the submarine cable, increasing the capacitance of the submarine cable, increasing the output voltage of the shore station power feeding equipment (PFE) or reducing the power consumption of the undersea station, are beneficial to improve the large-signal stability of the CSO DC power system.

A low-voltage ride-through strategy using mixed potential function for three-phase grid-connected PV systems

This paper presents a new control strategy for low-voltage ride-through for 3-phase grid-connected photovoltaic systems. The proposed fault ride through control algorithm, which is designed based on mixed potential function, can protect the inverter from overcurrent failure under both symmetric and asymmetric faults, reduce the double frequency oscillation and provides reactive power support by applying a voltage compensation unit. With the proposed method, the inverter can also inject sinusoidal current during asymmetric faults. The method does not require a hard switch to switch from the Maximum Power Point Tracking (MPPT) to a non-MPPT algorithm, which ensures a smooth transition.

Stability Analysis and Trigger Control of LLC Resonant Converter for a Wide Operational Range

The gain of a LLC resonant converter can vary with the loads that can be used to improve the efficiency and power density for some special applications, where the maximum gain does not apply at the heaviest loads. However, nonlinear gain characteristics can make the converters unstable during a major disturbance. In this paper, the stability of an LLC resonant converter during a major disturbance is studied and a trigger control scheme is proposed to improve the converter’s stability by extending the converter’s operational range. Through in-depth analysis of the gain curve of the LLC resonant converter, we find that the switching frequency range is one of the key factors determining the system’s stability performance. The same result is also obtained from a mathematical point of view by utilizing the mixed potential function method. Then a trigger control method is proposed to make the LLC resonant converter stable even during a major disturbance, which can be used to extend the converter’s operational range. Finally, experimental results are given to verify the analysis and proposed control scheme.

A Passivity-Based Power-Shaping Control of Building HVAC Systems

Regulating indoor air environment is one of the core functions of building energy management system. Heating, ventilation, and air-conditioning (HVAC) control systems play an important role in adjusting the room temperature to provide occupants a desired level of comfort. Occupant comfort has a direct effect on the energy consumption and providing an optimal balance between comfort and energy consumption is a challenging problem. This paper presents a framework for control of building HVAC systems using a methodology based on power-shaping paradigm that exploits the passivity property of a system. The system dynamics are expressed in the Brayton–Moser (BM) form which exhibits a gradient structure with the mixed-potential function, which has the units of power. The power-shaping technique is used to synthesize the controller by assigning a desired power function to the closed-loop dynamics so as to make the equilibrium point asymptotically stable. The proposed methodology is demonstrated on HVAC subsystems: RC network building zone model and a heat exchanger system.

Generalization of the jump postulate and Brayton‐Moser's mixed potential for the analysis of RTD circuits

SummaryIn this paper, the series connection of resonant tunneling diodes (RTDs) will be analyzed with respect to their stability properties. An alternative approach to the commonly used loadline construction for the analysis of circuits utilizing the series connection of RTDs is presented. Furthermore, the basins of attraction of multiple operating points will be determined analytically by Brayton‐Moser's mixed potential function. Therewith, the jump postulate by Andronov et al. will be generalized for series connected N‐type nonlinearities. In addition, the numerical results will be verified by measurements. At the end, the discussed method is applied to the monostable‐bistable transition logic element, which today is one of the most promising logic circuits in nanoelectronics. Copyright © 2015 John Wiley & Sons, Ltd.