Charge-discharge Mode Research Articles

Design and Control Strategy of an Integrated Floating Photovoltaic Energy Storage System

Floating photovoltaic (FPV) power generation technology has gained widespread attention due to its advantages, which include the lack of the need to occupy land resources, low risk of power limitations, high power generation efficiency, reduced water evaporation, and the conservation of water resources. However, FPV systems also face challenges, such as a significant impact from aquatic environments on the system’s stability and safety and high operational and maintenance costs, leading to large fluctuations in the grid-connected power output. Therefore, it is necessary to integrate energy storage devices with FPV systems to form an integrated floating photovoltaic energy storage system that facilitates the secure supply of power. This study investigates the theoretical and practical issues of integrated floating photovoltaic energy storage systems. A novel integrated floating photovoltaic energy storage system was designed with a photovoltaic power generation capacity of 14 kW and an energy storage capacity of 18.8 kW/100 kWh. The control methods for photovoltaic cells and energy storage batteries were analyzed. The coordinated control of photovoltaic cells was achieved through MPPT control and improved droop control, while the coordinated control of energy storage batteries involved a droop charge–discharge mode, a constant-voltage charging mode, and a standby mode. The simulations were realized in MATLAB/Simulink and the results validated the effectiveness of the coordinated control strategy proposed in this study. The strategy achieved operational stability and efficiency of the integrated photovoltaic energy storage system.

Multi-level coordinated control of islanded DC microgrid integrated with electric vehicle charging stations with fault ride-through capability

This paper presents an integrated control framework for islanded DC microgrid (MG) with electric vehicle (EV) charging stations, energy storage unit, and AC/DC loads. The proposed DC MG consists of two DC buses with different voltages, photovoltaic (PV) arrays as intermittent power generation sources, energy storage, three EV charging stations, and a three-phase inverter to power time-varying three-phase loads. Control strategies are proposed to select the charge-discharge mode of EVs that does not negatively affect the MG, as well as coordinate the production and demand management. A central control system enables the operation of MG under different working conditions by managing generation, consumption, and energy storage and also monitors the performance of the charging/discharging unit and the issues relevant to commands of different charging/discharging programs. A specific control strategy has also been implemented to provide fault ride-through (FRT). As a result, the MG feeds its loads in any operating condition. Nonlinear simulations are carried out in MATLAB/SIMULINK software to show that the proposed control methods easily and effectively achieve all objectives, including supplying DC/AC loads, managing battery/resources/charging stations, and detecting/dealing with AC faults.

Data-driven state-of-health estimation for lithium-ion battery based on aging features

Reliable state-of-health (SOH) estimation is crucial to the safe operation of lithium-ion battery. Data-driven SOH estimation becomes a hot research topic with the booming of high-performance machine learning algorithms. The effectiveness of a data-driven approach will be enhanced significantly if the input features are extracted properly. In order to improve the SOH estimation accuracy, the features highly associated with battery degradation should be utilized in the data-driven model. In this paper, an aging feature extraction method based on electrochemical model (EM) is proposed to account for the battery degradation mechanisms. The aging features of EM such as charge transfer resistance, solid phase diffusion coefficient and electrode volume fraction are defined as internal health features (IHFs) for SOH estimation. Moreover, external health features (EHFs) are directly extracted from the voltage and temperature curves that split into multiple stages. Then, IHFs and multi-stage EHFs are selected appropriately for SOH estimation in offline and online application scenarios. Finally, two well-known machine learning algorithms are employed to construct data-driven SOH estimation model using IHFs and EHFs. Experimental data are used to prove that the proposed method can effectively improve the accuracy of SOH estimation under different application scenarios and battery charge–discharge modes.

RESEARCH OF A COMBINED HEAT SUPPLY SYSTEM WITH ALTERNATIVE ENERGY SOURCES

The configuration of an energy-efficient combined heat supply system of the educational building of the Odessа Polytechnic National University with alternative energy sources is proposed. An experimental database of wind speed, which is tied to the dislocation of the combined heat supply system, was obtained. The averaged data on the wind speed of the Odesa weather site during the heating period have been adjusted. The conditions for using the energy potential of the wind to create a combined system are considered. A calculation model was obtained for the integral repeatability of the wind speed according to the Weibull probability distribution for the heating period. On the basis of the developed mathematical model of the dynamics of thermal processes of the elements of the combined system and the model of the energy potential of the wind, the modes of operation of the heat supply system when the temperature of the outside air changes are investigated. With the application of a mathematical model of the heating system, the optimal daily schedule of the intermittent operation of the heating system in terms of energy efficiency is given. The optimal schedules of the electrical and thermal load of the elements of the combined heat supply system in the intermittent heating mode have been worked out. Daily schedules of charge-discharge modes of the water heat accumulator and the electric accumulator battery have been developed, which ensure optimal loading of the system elements. The evaluation of the effectiveness of the substitution coefficient at a change in the outside air temperature from 5 to –15 °С was carried out. The energy balances of the combined system were studied in order to substantiate the rational parameters of its elements and the system as a whole. The possibility of creating a highly efficient autonomous heating system based on modern energy technologies using alternative energy sources and taking into account their local potential has been confirmed.

A solid-state lithium-oxygen battery operating at ambient temperature and full charge-discharge

Solid-state Li-O2 batteries (SSLOBs) have been denoted as the holy grail in next-generation Li metal batteries for their high theoretical energy density, manipulation of ambient air to energy storage as well as high safety. However, the solid rigid interfaces both at the cathode and anode side introduce ultra-high resistances in the battery system and impede its operation under ambient temperature. Moreover, the high-reductive Li anode and semi-open cathode would cause severe side reactions during cycling which further degrade battery performance. To manage the above-mentioned issues, a rationally designed SSLOBs based on plastic crystal electrolyte is proposed in this study to enable SSLOBs operation at ambient temperature and in full charge-discharge mode. The brand-new Li-O2 battery has been improved mainly from two aspects. First, we propose a polyacrylonitrile (PAN) modified succinonitrile (SN) electrolyte (PAN-SN) to retard the polymerization of SN and meanwhile suppress the degradation of Li ionic conductivity. Second, we propose an alternative mixed electron/ion complex conductor (MEIC) cathode to coordinate with plastic crystal electrolyte with an expanded Li-O2 reactive zone and improved interfacial charge transfer during the charge-discharge process. The fabricated flexible SSLOBs based on PAN-SN electrolyte and MEIC cathode could be successfully fully charged-discharged (cutoff 2.0–4.5 V) for tens of cycles at ambient temperature under simulated air condition (20 vol% oxygen), with high-capacity retention of around 85 %.

An integration and selection scheme for capacity estimation of Li-ion battery based on different state-of-charge intervals

Much research has been done to predict batteries' cyclic aging state-of-health (SOH) over the entire state-of-charge (SOC) range in constant-voltage and constant-current charge-discharge mode. Considering that the battery cycle is usually carried out in part of the SOC range in the actual use process, this paper further studies the cycle degradation characteristics of Lithium-ion (Li-ion) batteries in the partial SOC ranges. First, to clarify the factors that affect battery cycle aging, the changes in battery degradation characteristics caused by various stresses are analyzed. Then, a scheme to construct the state of charge - voltage (SOC-V) curve based on the first-order equivalent circuit and lumped thermal model is introduced for accurately extracting health indexes (HIs) on incremental capacity (IC) and differential voltage (DV) curves. Meanwhile, the least-squares method is used to identify the offline parameters of the proposed model. Perform a sensitivity analysis on the equation complexity and fitting effect, which can determine the exact model order. Multiple regression models are employed, which map the relationship between HIs fluctuations and capacity degradation for real-time estimation of SOH in different SOC intervals. Finally, different SOC intervals screen out the most accurate prediction models to realize the SOH prediction in all SOC cycle ranges. In this framework, the results show that SOH prediction based on SOC interval is desirable. Analysis results reveal the above measures' trustworthiness, with the average predicted error being within 1 % under the cross-validation test. What's more, a set of different types of batteries are used to verify the robustness of this method.

Mathematical Model of a Local Grid with Small Modular Reactor NPPs

The technical and economic processes of the Local Grid, regional electricity system comprising small modular reactor nuclear power plants, renewable electricity generators, and electricity storage systems are investigated. Smart grid technologies are used in the management of such a system. In relation to the electricity system, the Local Grid acts as a consumer or producer of electricity depending on the price situation in the wholesale market and its own ability to balance the volume of electricity generation-consumption.
 The Local Grid market is considered to be perfect, otherwise the wholesale electricity market is characterized by imperfect competition. The mathematical model of the Local Grid is offered. The presented model adequately reproduces the characteristics of the interaction between the local market and the wholesale market. The mathematical model is generated in the form of the commitment problem for small modular reactors and electricity storage systems. The model reflects the technological limitations for the loading modes of small modular reactors and units of the energy storage system, which operate in the modes of direct and reverse energy conversion. In particular, the model reflects the shunting modes and start-shutdown modes of small modular reactors and charge-discharge modes of energy storage system units, which together determine flexibility of the operation modes for the entire power system. The commitment problem of small modular reactors of a nuclear power plant, units of the electricity storage system, and transmission lines connecting the Local Grid with the power system is a mixed integer programming problem with an objective function of minimized system costs.
 Cluster integer functions are used to reduce the dimensionality of the problems of mathematical modeling the loading modes of the Local Grid in the descriptions for the sets of the same type small modular reactors, as well as the same type energy storage units. The Local Grid model reproduces the modes of its disconnection from the system operator's network to increase nuclear safety in the event of a natural disaster or hostilities. The results of computational experiments on modeling the commitment modes of the local electrical grid are presented.
 The experiments used standard data on the volume of electricity consumption and its production from renewable energy sources. The results of the computational experiment confirm the adequacy of the suggested mathematical model for the Local Grid. The presented model is suitable for the use both independently – to analyze Local Grid functioning - and in combination with the models of electric power industry - to determine the impact of the Local Grids on the electricity system.
 The article is developed based on the results of the research carried out under target program “Support of State-Priority Research and Scientific and Technical (Experimental) Solutions of the Department of Physical and Technical Problems of Energy of the NAS of Ukraine for 2022 – 2023” with program expenditure classification code 6541230 (applied research).

Experimental analysis of influence of different charge-discharge modes on lithium storage performance of reduced graphene oxide electrodes

In this paper we conduct comprehensive experimental research and analyze the effect of charge-discharge modes on the performance of lithium storage. Four charge-discharge modes are designed, and the lithium storage performance experiments of the reduced graphene oxide electrode under different charge-discharge modes are carried out to analyze the effect mechanism of charge-discharge mode on lithium storage time and capacity from two aspects of electrode dynamic reaction performance and strain. The experimental results show that the shorter the lithium storage time of the electrode, the more the capacity loss under different charge-discharge modes. Comprehensive data analysis indicates that the charge transfer resistance, diffusion coefficient, overpotential and strain in the electrochemical process show non-linear and staged characteristics, resulting in the different lithium storage performances’ mechanism of different stages under different charge-discharge modes. Finally, “High current-low current” mode is proposed as a feasible optimization plan for charging and discharging. In the initial stage-I, the dual role of large electric field drive and concentration gradient drive enhances the migration and diffusion rate and shortens the lithium storage time; in the stage-II, the small current relieves local concentration accumulation and increases the amount of lithium inserted, thereby giving full play to the greatest advantage of current in each stage and balance the discrepancy between time and capacity. And this discussion provides certain guidance for designing and optimizing the fast charging technology.

Influence of Wind Speed Forecasting Error on the Choice of the Number of Balancing System Batteries

In the energy balancing system of distributed generation systems with RES (renewable energy sources), in particular with wind turbines, the effective use of the battery of the balancing system depends on the charge-discharge modes that are implemented. To be effectively used in an energy balancing system, the RES control system should coordinate the processes of energy generation and accumulation in the system through the implementation of operational management with forecasting. Depending on the characteristics of the battery and the accuracy of the measurement or prediction of the energy the battery capacity (or the number of batteries) that will provide the specified control range (controlled operation area) needs to be chosen. Empirical relations (equations) devoted to the dependence of the battery capacity on the discharge current and to the change of voltage at the terminals of the battery during direct current discharge were listed. Among the equations Peukert’s law was chosen. A general view of the dependence of the battery capacity on the discharge current was shown. The formula for Peukert's constant (coefficient) was given. 5 Packert's law limitations were listed including the fact that the effect of temperature on the battery is not taken into account. The influence of depth charge-discharge and the number of discharge cycles on the capacitance was shown. In the process of using the battery and increasing the number of charge-discharge cycles, the capacity decreases. Peukert’s formula was extended to be influenced by temperature: both the Peukert’s capacity and the Peukert’s coefficient depend on the temperature because the Peukert’s coefficient depends on the capacity. For further calculations, a rechargeable battery HZB12-180FA from manufacturer HAZE Battery Campany Ltd was chosen. The temperature was taken into account by empirical dependences from the manufacturer and then they were approximated by 3rd order polynomials. Graphical results of the approximation were shown. The formula of dependency between the power of the wind turbine and the wind speed was shown. The connection between wind speed prediction error, amount of power that could not be obtained because of that and the number of batteries that would provide the specified control range (controlled operation area) was shown. Thus, for calculation of the number of batteries the depth of discharge, temperature and prediction (measurement) error were taken into account. Example dependences of the number of batteries on the wind speed error at temperatures of -20 °C, 0 °C and 20 °C were shown. Curves of dependence of the number of batteries of the balancing system on the ambient temperature and the error of wind speed forecasting was constructed. As an example, when the prediction error increases from 10% to 15%, the number of batteries needs to be increased by 1.17 times, and when the temperature decreases from 20 °C to 0 °C, the number of batteries needs to be increased by 1.48 times. The results of the work can be used at the stage of planning the wind turbine when choosing the number and capacity of the batteries to be installed. Possible areas of further research are using Peukert's formulas, generalized for other or different types of batteries, using other formulas, except for Peukert’s one, for taking into account the dependence of battery capacity on discharge current, using a non-empirical approach to include dependency on temperature.

Experimental Study of the Influence of the Porosity of Thin-Film Silicon-Based Anodes on Their Charge-Discharge Characteristics

The effect of porosity on the charge-discharge characteristics of thin films based on an Si–O–Al nanocomposite with two types of structure, homogeneous and columnar, is studied. An additional increase in the porosity of thin Si–O–Al films is achieved by removing the $${\text{Si}}{{{\text{O}}}_{x}}$$ phase, where $$1 < x \leqslant 2,$$ when etching in a solution of hydrofluoric acid. The charge-discharge characteristics of the films were investigated in half-cells in the galvanostatic mode. It is shown that processing films with a columnar structure leads to an increase in their specific capacity and stability under extreme charge-discharge modes.

Electrical Performance Improvement of Lead-Acid Battery under the Impact of Micro Carbon Additives

The features and changes in the microstructure of the electrode material of the negative electrode of the lead–acid starter accumulator battery appearing on the addition of two different specimens of carbon carbon black and hybrid carbon, are investigated. The X-ray phase analysis and the scanning electron microscopy analysis are conducted. It is established that using carbon black or hybrid carbon as an additive to the material of the negative electrode influences its structure causing changes in the processes of its impregnation and formation. Based on the structural analysis, a qualitative description, according to which hybrid carbon increases the dispersity of the negative active mass and impedes the diffusion of sulfate-ions, is proposed. The standard tests were conducted by intensive cycling in the partial state of charge lead–acid starter batteries in the charge–discharge mode. The batteries were manufactured using negative plates with additives of technical or hybrid carbon. The influence of each type of carbon additive on the electrical characteristics of the starter batteries is determined. It is shown that the additive of hybrid carbon increases the service life of starter batteries under operation in the partial state of the charge. This additive increases the charge acceptance on average by 9% and the deep discharge stability of the battery. The capacity loss after deep discharge is less than 4.4% if hybrid carbon is used as an additive and 7.2% in the case of carbon black.

Experimental Study on Storage and Maintenance Method of Ni-MH Battery Modules for Hybrid Electric Vehicles

This paper investigates the performance changes of nickel–metal hydride (Ni-MH) battery modules for hybrid electric vehicles (HEVs) using different storage and maintenance methods. The effects of charge–discharge mode, maintenance period, rest time, charge rate, and storage state of charge (SOC) on the storage performance of Ni-MH battery modules are studied. Based on the experimental results and engineering application requirements, this paper proposes some important recommendations and methods for storage and maintenance of Ni-MH battery modules for HEVs. The experimental results show that, compared with the six benchmark methods, the proposed storage and maintenance method provides superior storage and maintenance outcomes and significantly saves maintenance time.

Facile synthesis and characterization of three-dimensional graphene/polyaniline composites with enhanced electrochemical properties

In situ polymerization of aniline was carried out within graphene hydrogels with the ultrasonic treatment, and thus the polyaniline (PANI) was loaded and the three-dimensional (3D) graphene/PANI aerogel composite (GPA) was facilely obtained after freeze drying. The investigation shows that the polyaniline as twisted nano-rods was formed and scattered in the interconnected porous 3D graphene. When a supercapacitor electrode was fabricated with the composite GPA, the specific capacitance at a current density of 1 A g−1 can reach as high as 618 F g−1. The capacity retains 89% of the initial value in constant current charge–discharge mode (at the current density of 10 A g−1) after 2000 cycles. The improved electrochemical properties were confirmed to be resulted from the unique network morphology, enhanced conductivity and the synergy effect between graphene and polyaniline. The composite GPA is self-supporting and can be directly used as the electrode material without adding binders. This contribution provides a simple method to prepare the electrode material with enhanced electrochemical properties based on graphene. The GPA composite shows great potential for application in supercapacitors.

High water recovery and improved thermodynamic efficiency for capacitive deionization using variable flowrate operation

Water recovery is a measure of the amount of treated water produced relative to the total amount of water processed through the system, and is an important performance metric for any desalination method. Conventional operating methods for desalination using capacitive deionization (CDI) have so far limited water recovery to be about 50%. To improve water recovery for CDI, we here introduce a new operating scheme based on a variable (in time) flow rate wherein a low flow rate during discharge is used to produce a brine volume which is significantly less than the volume of diluent produced. We demonstrate experimentally and study systematically this novel variable flowrate operating scheme in the framework of both constant current and constant voltage charge-discharge modes. We show that the variable flowrate operation can increase water recovery for CDI to very high values of ∼90% and can improve thermodynamic efficiency by about 2- to 3-fold compared to conventional constant flowrate operation. Importantly, this is achieved with minimal performance reductions in salt removal, energy consumption, and volume throughput. Our work highlights that water recovery can be readily improved for CDI at very minimal additional cost using simple flow control schemes.

Carbon additive structure influence on electrochemical double-layer capacitor electrode behavior

Electrochemical double-layer capacitors (EDLC) are widely used as power sources for peak load or peak generation leveling in transport and stationary applications sometimes in combination with accumulator battery. For such applications EDLC need low sensitivity (from lifetime and capacity point of view) to high current mode operation, which is usually crucial for traditional accumulators’ types. Capacity loss in high current mode operation due to both transport and resistive limitations is observed both for accumulators and supercapacitors but much less for latter due to initial low internal resistance and electrochemical reactions absence. Carbon nanotubes (CNT) and nanofibers (CNF) as alternative to carbon blacks as conductive additive for electrodes are good possibility to improve high current operation both for accumulators and EDLC. This paper is devoted to investigation of carbon nanotubes and nanofibers comparison with traditional carbon black additive. CNF structure usually contains more defects and has lower aspect ratio than single-walled nanotubes but this kind of materials is less expensive than CNT, that is also important for final customer. Electrode samples with Vulcan XC72R carbon black were prepared for reference measurements. All electrode samples were tested in galvanostatic charge-discharge mode at different current levels in laboratory-scale EDLC cell, characterized by impedance spectroscopy. Obtained results showed improved high-current operation for CNT-containing electrodes. Economic estimation for different kinds of additives has also been carried out.

Deconstructing three-dimensional (3D) structure of absorptive glass mat (AGM) separator to tailor pore dimensions and amplify electrolyte uptake

Absorptive glass mat (AGM) separator is a vital technical component in valve regulated lead acid (VRLA) batteries that can be tailored for a desired application. To selectively design and tailor the AGM separator, the intricate three-dimensional (3D) structure needs to be unraveled. Herein, a toolkit of 3D analytical models of pore size distribution and electrolyte uptake expressed via wicking characteristics of AGM separators under unconfined and confined states is presented. 3D data of fiber orientation distributions obtained previously through X-ray micro-computed tomography (microCT) analysis are used as key set of input parameters. The predictive ability of pore size distribution model is assessed through the commonly used experimental set-up that usually apply high level of compressive stresses. Further, the existing analytical model of wicking characteristics of AGM separators has been extended to account for 3D characteristics, and subsequently, compared with the experimental results. A good agreement between the theory and experiments pave the way to simulate the realistic charge-discharge modes of the battery by applying cyclic loading condition. A threshold criterion describing the invariant behavior of pore size and wicking characteristics in terms of maximum permissible limit of key structural parameters during charge-discharge mode of the battery has also been proposed.

A new storage management on stochastic charge-discharge mode

The energy management problem of the battery is always a technical challenge, especially when incomplete charging-discharging alternation happens continuously under the complex state, as the application participating in a real-time schedule of wind farm power. This paper focuses on the energy management of the battery which participates in wind power optimal forecast. First, innovative energy management strategy is designed to avoid non-linear model construction of the battery. In terms of the energy-exchange equivalent prediction method, the energy management scheme can make full use of peripheral parameters tested from charge-discharge interface circuit. Then, the charge-discharge power is obtained from the active demand of wind power forecast error correction, the converter efficiency, and the self-discharge factor. In addition, a diagnosis method of health status based on judgment of coefficient mutation and a life cycle algorithm based on integral statistics of the whole process are studied, respectively. Second, to facilitate the subsequent prediction, the capacity change of the actual storage system is revised in a manner where the static and dynamic parameters consist of actual current-time integration during the charge or discharge process and equivalent parameter correction of the relation between power energy throughput and charge capacity change. The transmission efficiency correction of converter and self-discharge efficiency, the dynamic determination of the battery health state, and life cycle statistics are also considered. Finally, a practical application case is introduced to validate the above strategies. The results verify that both the dynamic forecast of the state of charge and the feasible management of energy storage are achieved.

Optimal Control Based on Maximum Power Point Tracking (MPPT) of an Autonomous Hybrid Photovoltaic/Storage System in Micro Grid Applications

This paper investigates how to increase the efficiency of a photovoltaic/energy storage generation unit supplying dynamic loads by regulating and managing both the photovoltaic generator and the storage battery charge-discharge modes. The proposed photovoltaic/energy storage unit is proposed to supply an induction motor driven industrial pump with controlled speed and/or a DC motor driven water pump. An optimal proportional-integral-derivative control based on an Artificial Bee Colony Optimization algorithm is used to regulate the photovoltaic generator in case of normal operation or in case of maximum power point tracking (MPPT) and to also control the battery storage charge discharge modes. A vector control based on the proposed optimal control is used to regulate the induction motor rotor speed at its low reference values needed by the industrial pump. First, a total model of the entire system is obtained. The controller performance with the proposed system is studied with both a DC motor and/or induction motor loads. Simulation results show that the proposed photovoltaic/storage generator is able to supply the suggested dynamic loads under different conditions and with good performance. Also, it is noticed that operating the photovoltaic base on maximum power point tracking condition will give about 43% extra generation power than the normal operation case.

Experimental Study of Field-Effect Transistors in Charge-Discharge Mode of a Substrate Capacitor

We conduct an experimental study of field-effect transistors KP304A in charge-discharge mode of a substrate capacitor in a switching circuit with an additional resistor between the drain–source and the substrate. We propose a method of measuring the power in the resistors and switches using a switching circuit and the digital oscilloscope B-421.

Fabrication and performance evaluation of rare earth lanthanum sulfide film for supercapacitor application: Effect of air annealing

Abstract In this work, the electrochemical properties of rare earth lanthanum sulfide (La 2 S 3 ) films obtained by chemical bath deposition method are investigated as an electrode material for supercapacitor application. The effect of air annealing on structural, surface morphological and wettability properties of La 2 S 3 films is studied. The X-ray diffraction and FT-Raman analysis confirm the formation La 2 S 3 film. A porous spongy network of La 2 S 3 film reveals the hydrophilic nature. The supercapacitive properties of La 2 S 3 electrode are evaluated using cyclic voltammetry and galvanostatic charge–discharge mode. The maximum specific capacitance of 294 F g − 1 is achieved for air-annealed La 2 S 3 electrode at a scan rate of 5 mV s − 1 with 89 % electrochemical cyclic stability over 1000 cycles. The spongy network of air-annealed La 2 S 3 film enhances the supercapacitive performance. The auspicious properties of La 2 S 3 electrode are effective for the fabrication of flexible La 2 S 3 /LiClO 4 -PVA/La 2 S 3 solid-state supercapacitor device. The specific capacitance of supercapacitor device with diverse bending angles and cyclic stability is examined.