Variable Irradiance Conditions Research Articles

Development of Grid-Forming and Grid-Following Inverter Control in Microgrid Network Ensuring Grid Stability and Frequency Response

This paper proposes a control strategy for grid-following inverter control and grid-forming inverter control developed for a Solar Photovoltaic (PV)–battery-integrated microgrid network. A grid-following (GFL) inverter with real and reactive power control in a solar PV-fed system is developed; it uses a Phase Lock Loop (PLL) to track the phase angle of the voltages at the PCC and adopts a vector control strategy to adjust the active and reactive currents that are injected into the power grid. The drawback of a GFL inverter is that it lacks the capability to operate independently when the utility grid is down due to outages or disturbances. The proposed grid-forming (GFM) inverter control with a virtual synchronous machine provides inertia to the grid, generates a stable grid-like voltage and frequency and enables the integration of the grid. The proposed system incorporates a battery energy storage system (BESS) which has inherent energy storage capability and is independent of geographical areas. The GFM control includes voltage and frequency control, enhanced islanding and black start capability and the maintenance of the stability of the grid-integrated system. The proposed model is validated under varying irradiance conditions, load switching, grid outages and temporary faults with fault ride-through (FRT) capability, and fast frequency response and stability are achieved. The proposed model is validated under varying irradiance conditions, load switching, grid outages and line faults incorporating fault ride-through capability in GFM-based control. The proposed controller was simulated in a 100 MW solar PV system and 60 MW BESS using the MATLAB/Simulink 2023 tool, and the experimental setup was validated in a 1 kW grid-connected system. The percentage improvement of the system frequency and voltage with FRT-capable GFM control is 69.3% and 70%, respectively, and the percentage improvement is only 3% for system frequency and 52% for grid voltage in the case of an FRT-capable GFL controller. The simulation and experimental results prove that GFM-based inverter control achieves fast frequency response, and grid stability is also ensured.

Use of Natural Zeolite Clinoptilolite in the Preparation of Photocatalysts and Its Role in Photocatalytic Activity

The use of natural zeolite clinoptilolite in preparing photocatalysts and its function in photocatalysis are discussed in this review. The importance of advanced oxidation processes (AOPs) and the potential of heterogeneous photocatalysis in removing environmental pollutants are emphasized. The review focuses on the synergistic effects of clinoptilolite with semiconductors (TiO2, ZnO, CuO, SnO2, and NiO) to prepare stable and active photocatalysts, highlighting recent advancements in this field. It explores clinoptilolite’s structural characteristics, highlighting its microporous nature, adaptable framework, and improved textural properties due to acid and alkali treatments. Particle size, crystal phase, and calcination temperature are three key synthesis parameters that affect photocatalytic activity and are highlighted in the discussion of these parameters and their methods. A discussion is held regarding the processes and mechanisms of photocatalytic degradation of different organic compounds under varying irradiation conditions, including UV, visible, and ambient sunlight. Clinoptilolite is vital in improving supported semiconductor oxides’ photocatalytic efficiencies, which aid in pollutant degradation and environmental remediation.

A centralized EMPC scheme for PV-powered alkaline electrolyzer

Photovoltaic (PV)-powered alkaline electrolyzer system (PVPAES) is an advanced technique to convert the off-grid and intermittent PV-based solar energy into the storable and transportable electrolyzer-based hydrogen energy with zero carbon emissions. However, it is difficult to realize the coordinated control of the off-grid PV module and the alkaline electrolyzer, due to the multiple timescale dynamics. To address this challenge, the PVPAES is decomposed into slow part and fast part based on the dynamic time scale. Exploiting the decomposed subsystems, the slow one is assumed to be managed well by the auxiliary controller. For the fast one, a centralized economic model predictive control (CEMPC) scheme is constituted. This CEMPC integrates the energy management system and local feedback control into a single optimal control framework. A mathematical model of the PVPAES is established, on the basis of which the CEMPC directly adopts the economic indices as the cost function to realize the flexible power point tracking, power supply–demand balance, and dynamic economic optimization. Moreover, the inherent strong nonlinearity of PVPAES results in the nonconvex mixed-integer nonlinear programming optimization problem in the CEMPC. The exhaustive search algorithm utilizing finite converter switching states is adopted to achieve the global economic optimum. The effectiveness of the proposed CEMPC controller is illustrated through simulations under varying irradiance conditions.

PSO Training Neural Network MPPT with CUK Converter Topology for Stand-Alone PV Systems Under Varying Load and Climatic Conditions

Temperature and irradiance levels are two examples of environmental variables that affect the power value produced by photovoltaic panels. Therefore, in order to transfer the maximum power value from the PV panel to the load under varying climatic conditions, maximum power point tracking (MPPT) algorithms and DC-DC converter topologies are used. In this study, the performances of boost converter and CUK converter circuit topologies are investigated under variable irradiance and variable load conditions by using a neural network-based MPPT algorithm learning particle swarm optimization (PSO). As the first scenario, it is analyzed assuming that the temperature and irradiance values coming to the panel are constant. As the second scenario, the performance evaluation of the converter topologies according to the current, voltage and power parameters is made for the variable load situation. As the last scenario, the difference in the irradiance value coming to the panel depending on the sun's condition during the day has been examined. Canadian Solar CS6P-250P PV panel is used in the study. 50 kHz is selected as the switching frequency. According to the results obtained, it has been observed that the CUK converter circuit topology reaches the maximum power point faster than the boost converter circuit topology both in dynamic environmental conditions and load change, and the oscillation at this point is less. It is aimed to increase the performance of this method, which uses boost converter topology and MPPT in the literature, by applying CUK converter topology.

Modeling and Simulation of Grid-Tied Three-Phase PV System in Lahore, Pakistan

This research examines the implementation of grid-tied solar inverters in Lahore’s energy infrastructure, considering the city’s growing energy demands. Utilizing MATLAB/Simulink for modeling solar photovoltaic systems in Lahore’s arid climate, our study focuses on a house in Askari X housing society, Lahore, Pakistan, with a 5.1 kW load. The results demonstrate the expected system variation of a Grid-Tied PV System during grid disruptions, and the model’s consistent performance across varying irradiance conditions suggests potential economic advantages through net metering. These findings offer practical insights into the economic feasibility and dependability of grid-tied solar inverters in Lahore, highlighting their potential to contribute to the city’s energy needs.

Passivity-based Rieman Liouville fractional order sliding mode control of three phase inverter in a grid-connected photovoltaic system.

Photovoltaic (PV) system parameters are always non-linear due to variable environmental conditions. The Maximum power point tracking (MPPT) is difficult under multiple uncertainties, disruptions and the occurrence of time-varying stochastic conditions. Therefore, Passivity based Fractional order Sliding-Mode controller (PBSMC) is proposed to examine and develop a storage function in error tracking for PV power and direct voltage in this research work. A unique sliding surface for Fractional Order Sliding Mode Control (FOSMC) framework is proposed and its stability and finite time convergence is proved by implementing Lyapunov stability method. An additional input of sliding mode control (SMC) is also added to a passive system to boost the controller performance by removing the rapid uncertainties and disturbances. Therefore, PBSMC, along with globally consistent control efficiency under varying operating conditions is implemented with enhanced system damping and substantial robustness. The novelty of the proposed technique lies in a unique sliding surface for FOSMC framework based on Riemann Liouville (R-L) fractional calculus. Results have shown that the proposed control technique reduces the tracking error in PV output power, under variable irradiance conditions, by 81%, compared to fractional order proportional integral derivative (FOPID) controller. It is reduced by 39%, when compared to passivity based control (PBC) and 28%, when compared to passivity based FOPID (EPBFOPID). The proposed technique led to the least total harmonic distortion in the grid side voltage and current. The tracking time of PV output power is 0.025 seconds in PBSMC under varying solar irradiance, however FOPID, PBC, EPBFOPID, have failed to converge fully. Similarly the dc link voltage has tracked the reference voltage in 0.05 seconds however the rest of the methods either could not converge, or converged after significant amount of time. During solar irradiance and temperature change, the photovoltaic output power has converged in 0.018 seconds using PBSMC, however remaining methods failed to converge or track fully and the dc link voltage has minimum tracking error due to PBSMC as compared to the other methods. Furthermore, the photovoltaic output power converges to the reference power in 0.1 seconds in power grid voltage drop, whereas other methods failed to converge fully. In addition power is also injected from the PV inverter into the grid at unity power factor.

Enhancing PV Systems with Intelligent MPPT and Improved control strategy of Z-Source Inverter

Abstract The Improved Z-Source Inverter (IZSI) has gained attention in the photovoltaic industry for its ability to boost PV voltage with a single-stage topology, simplifying system design and reducing costs. However, research on integrating IZSI into PV systems, particularly regarding the Maximum Power Point Tracker (MPPT) and IZSI control strategy, is limited. This study proposes an Intelligent Improved Particle Swarm Optimization (IPSO) algorithm as an MPPT method for PV systems under constant and varying irradiance conditions. The IPSO algorithm is compared to the FPA, CSA, and traditional MPPT algorithm (PSO), and the results demonstrate that IPSO outperforms all algorithms in terms of speed, efficiency, and convergence in finding the Maximum Power Point (MPP). Two methods, Simple Boost Control (SBC) and Maximum Constant Boost Control with Third Harmonic Injection (THIMCBC), are employed to control IZSI. Simulation results using MATLAB-Simulink show that both strategies successfully find and track the MPP, but THIMCBC exhibits superior voltage-boosting performance compared to SBC. Overall, the proposed IZSI topology with the IPSO MPPT method and THIMCBC IZSI control strategy offers several advantages, including improved voltage boost ability, reduced z-source capacitor voltage stress, inherent inrush current limitation, and cost-effectiveness. These advantages make the proposed system a promising solution for photovoltaic systems.

Modeling of intelligent controllers for solar photovoltaic system under varying irradiation conditions

The increasing demand for solar renewable energy resources, driven by the global energy crisis and the depletion of conventional energy sources, has underscored the importance of harnessing solar energy. Solar photovoltaic (PV) systems, however, exhibit nonlinear output power due to their weather-dependent nature, impacting overall system efficiency. This study focuses on the development and comparative analysis of three intelligent Maximum Power Point Tracking (MPPT) controllers using the MATLAB Simulink. The controllers employ distinct methodologies, namely, Artificial Neural Networks (ANN), Adaptive Neural and Fuzzy Inference System (ANFIS), and Fuzzy Logic Controller (FLC). The results demonstrate that ANFIS achieved the highest accuracy at 99.50%, surpassing ANN and FLC with accuracies of 97.04% and 98.50%, respectively, thus establishing ANFIS as the superior MPPT controller. Additionally, the positives and negatives of all three MPPT-based algorithms are also compared in this work.

Modeling and Management of Hybrid System Photovoltaic-FC-Ultracapacitors Power Systems

This study shows an improved DC microgrid power management technique. The value of utilizing renewable energy has long been debatable, and this article suggests a typical DC microgrid because of the advantages it has over AC technology. A solar cell (PV), fuel cell (FC) and storage component - an ultracapacitor (UC)-make up the standard microgrid. The most important goal of the paper is to optimize the management strategy for the bus voltage with arranged power-sharing between these types of renewable energy that are used here. For variable solar irradiance and various loading conditions, the proposed management seeks to deliver high-quality energy to the load while taking into consideration the FC state. The ultracapacitor was prepared to furnish the transient period due to the FC's slow dynamics. To maintain the DC bus voltage steady in the face of load variations, a management algorithm is put into practice. To generate the references, the management controller relies on a differential flatness method. The electricity from the ultracapacitor controls the DC bus. Earlier studies showed that the circuit of the fuel cell was integrated with a standalone photovoltaic system and discovered that the fuel cell doesn't have the same properties. In the current research, observations were made on power quality elements like voltage, current, and power for energy storage systems. With several self-definition elements of the photovoltaic, fuel cell, and ultracapacitor, along with their parameters, simulation is used as the study method medium. The outcome demonstrates that since the ultracapacitor serves as the primary storage, the fuel cell integration has little impact on it, and only small changes in voltage and current were observed. Due to the fuel cell integration characteristic of providing the system a major perturbation, most perturbation from the system had been absorbed while in an ultracapacitor

Design and Control of a Photovoltaic Distribution System Based on Modular Buck-Boost Converters

The main contribution of this research is the design of a series hybrid topology for a photovoltaic distribution system using Buck-Boost converter modules. This design incorporates a maximum power point tracking (MPPT) algorithm based on the perturb and observe method, linear PI controllers, and an energy management algorithm. The controllers' design is validated through simulation using PSIM and SISOTOOL/MATLAB. This work aims to achieve active power-sharing in the AC grid through a control loop implemented with a three-phase inverter. The validation of the topology and controller design demonstrates tracking and robustness in four test scenarios for the state variables in microgrids: constant and variable irradiance conditions, auxiliary storage device (ASD) protection and control loops, and power-sharing with the AC grid, while considering the DC system dynamics.

Conventional and Switched Capacitor Boost Converters for Solar PV Integration: Dynamic MPPT Enhancement and Performance Evaluation

This paper designs two DC-DC converter configurations integrated with solar PV renewable energy resource. Its focuses on comparing two converter topologies: the conventional boost converter and the switched capacitor boost converter. The Perturb and Observe (P&O), Incremental Conductance (INC), Genetic Algorithm (GA), and Particle Swarm Optimization (PSO) algorithms are employed to dynamically enhance the Maximum Power Point Tracking (MPPT) performance for both converters. The simulation results demonstrate that both converter topologies, when integrated with appropriate MPPT algorithms, can effectively harvest maximum power from the solar PV. However, the switched capacitor topology converter exhibits advantages in terms of current capabilities and voltage performance. In addition, combing the switched capacitor boost converter with the GA-MPPT algorithm improved the output voltage profile. The switched capacitor topology demonstrates distinct advantages by exhibiting enhanced current control, enabling improved handling of dynamic load changes and varying irradiance conditions. It shows voltage regulation, resulting in reduced output voltage fluctuations and enhanced stability, thereby optimizing energy extraction. The GA-MPPT simulation demonstrates a substantial increase in maximized output current for the switched capacitor boost configuration (70 A) when compared to the conventional type (10 A). The validation and implementation of the system models are carried out using MATLAB/Simulink.

Parameter extraction of photovoltaic cells and modules by hybrid white shark optimizer and artificial rabbits optimization

This study presents the parameter extraction of photovoltaic (PV) cells and modules using a new hybrid metaheuristic algorithm developed based on the white shark optimizer (WSO) and the artificial rabbits optimization (ARO) algorithm. The accurate forecasting of economic benefits and the performance of PV based applications are heavily dependent upon the model accuracy of PV devices. Therefore, the main objective of this study is to obtain the most accurate model for the PV cells and modules that are commercially available in the market. For this purpose, the proposed hybrid algorithm (hWSO-ARO) is used for the modeling of two PV cells and six PV modules made by different manufacturers. A total of sixteen models for eight PV devices consisting of single diode (SDM) and double diode model (DDM) for each device have been developed. To verify the success, the results are compared against the results of seven different state-of-the-art algorithms. According to the results of 30 runs, the proposed algorithm has yielded the smallest objective function/root mean square error (RMSE) values in average, maximum, and minimum evaluation metrics. The hybrid algorithm achieves the best minimum average RMSE of 1.8354513E−04. It is then followed by the WSO algorithm with 1.8557680E−04 and with a difference of 1.11% and the ARO algorithm with 2.1286641E−04 and with a difference of 15.97%. Similarly, when the maximum RMSE metric is evaluated, the hybrid algorithm comes the first again with the lowest maximum RMSE of 2.0001806E−04. It is then followed by the WSO with 2.0897277E−04 and with a difference of 4.48% and again the ARO with 2.2591014E−04 and with a difference of 12.94%. When the last metric, the standard deviation, is analyzed, hWSO-ARO, out of 16 models, achieves the most minimum standard deviation of 3.6904635E−19. In addition, the Friedman rank test issues the highest rank to the hybrid algorithm. Moreover, the Wilcoxon rank test is producing results in favor of the proposed algorithm in 110 of 112 pairwise comparisons of algorithms and showing a 98.21% success rate. Later, a sensitivity analysis is performed using the datasheets values of the selected cells and modules. At every comparison, a perfect match is achieved between the calculated and the experimentally measured data. It is even maintained under variable irradiance and temperature conditions. In conclusion, it is demonstrated that the hybrid algorithm stands out in solving the PV parameter extraction problem with great success under all conditions and enables the development of the most accurate PV models with high computational accuracy.

Model predictive current control for maximum power point tracking of voltage source inverter based grid connected photovoltaic system

<p>Due to the high demand of grid connected photovoltaic systems, there is a need to track the maximum power point of the PV system. As the output of PV system is dc, there should be a converter, acting as medium between PV system and dc bus capacitor to track maximum power at all the loads. Usually boost converter is acting as medium between PV system and dc link capacitor as the duty cycle of the insulated-gate bipolar transistor in boost converter is in between 0 to 1 for maximum loads during maximum power point tracking (MPPT). To make PV system stable, the balance point is dc bus. If the dc bus voltage is constant, the system will be stable. Then the transfer power will just depend on current. For this purpose, the active current reference signal is to be generated by setting up the reference voltage across dc bus. Here to generate active reference current, PI controller is used and the reference voltage is taken according to the peak voltage of the inverter output voltage. The proposed control strategy was evaluated on a three-phase inverter linked to the grid and supplied by the PV system, which is working under varying irradiation conditions.</p>

Importance of spectrally invariant broadband attenuation of light in indoor photovoltaic characterization

Indoor photovoltaic (IPV) devices are poised to make a significant contribution to the proliferation of the “Internet of Things” (IoT). For the accurate intercomparison of IPVs (and, hence, to advance the rational development of the technology), lighting conditions representative of those in typical indoor settings must be created reproducibly. As indoor lighting is invariably broadband, this will typically require the use of optical attenuation to achieve varying irradiance conditions at the device under test location. However, most forms of optical attenuation will suffer from some degree of spectral dispersion, creating sources of uncertainty for key figures of merit, such as power conversion efficiency. In this work, we examine the contribution of the mode of optical attenuation to the accurate characterization of IPV systems. We discuss requirements for broadband light source attenuation for the accurate characterization of photovoltaic devices under indoor illumination and consider the importance of using suitable reference devices for light intensity calibration. Furthermore, we experimentally verify attenuation methods typically used, including power control of the light source itself, use of neutral density filters, and advanced attenuation based on tandem prism attenuators. Finally, spectral shape alteration-induced uncertainties in performance parameter determination of photovoltaic cells under indoor illumination are quantified for three common broadband light attenuation methods, where we found ∼2%, ∼6%, and up to ∼15% ambiguity in photovoltaic device efficiency when using LED power control, prism attenuators, and neutral density filter-based broadband light attenuation, respectively.

A Comprehensive Evaluation of Up-to-Date Optimization Algorithms on MPPT Application for Photovoltaic Systems

ABSTRACT Maximum Power Point Tracking (MPPT) plays a significant role in obtaining maximum power at PV system outputs. Recent research has focused on minimizing the adverse effects of partial shading and dynamic environmental conditions on MPPT. Metaheuristic optimization algorithms have attracted attention with their success in these issues. The growing body of literature lacks a study that comprehensively evaluates current metaheuristic algorithms. In this study, the performances of 20 metaheuristic algorithms under five different shading conditions, nonuniform temperature distribution, and variable irradiance conditions have been investigated. The successes of the algorithms in the convergence of the global maximum value and their convergence rates have been calculated through various statistical metrics with different aspects. This study provides a novel approach to objectively evaluating the performances of the algorithms by using the three-dimensional Pareto Front method. As the result of this multicriteria evaluation, RKO, MPA and CGO algorithms are able to provide non-dominated results. These three algorithms are further tested using case analysis designed for dynamic operating conditions, and the RKO algorithm exhibited the most favorable results. Additionally, the RKO algorithm exhibits remarkable performance by reaching the LMPP/GMPP point within an average time of 3.2 milliseconds in all cases. Moreover, it demonstrates an average efficiency value exceeding 0.999.

Modeling and Performance Analysis of a Grid-Connected Photovoltaic System with Advanced Controller considering Varying Environmental Conditions

This paper presents a mathematical model of 255 kW grid-connected solar photovoltaic (SPV) system. To study the performance characteristics of the grid-connected SPV system, a new hybrid adaptive grasshopper optimization algorithm with the recurrent neural network (AGO-RNN) control technique was implemented. Furthermore, the power quality at the point of common coupling (PCC) has been studied using the conventional (PSO) and proposed AGO-RNN controllers. The characteristics of the PV system were analyzed under varying environmental (variable irradiance and temperature) conditions considering 3 different cases such as (i) standard test conditions (STC), (ii) variable radiation with constant temperature, and (iii) variable radiation with variable temperature. For each case, the total harmonic distortion (THD) has been calculated using the proposed AGO-RNN control technique, and the results were compared with particle swarm optimization (PSO) technique. The 255 kW PV model is initially developed and connected to a three-level NPC inverter, an MPPT-based perturbation and observation algorithm. Later, the PV model is controlled by an AGO-RNN pulse width modulation (PWM) controller and is then integrated to the main grid at PCC. The main advantage of this technique is exploiting the separate DC-DC converter between the SPV module and the inverter. Finally, the proposed grid-connected SPV system was simulated on MATLAB for analyzing the performance of the system based on its I-V and P-V characteristics, inverter voltage, grid power, gird voltage, grid current, power factor, and THD under different environmental conditions. The simulation results demonstrate that the current magnitude and THD of the SPVGC system are improved with the cutting-edge AGO-RNN controller compared to PSO in all three different scenarios, and this value is less than 1.6%, which is within the permitted limits of IEC 61727 standards.

MPPT for Microgrid Connected PV System using ANN, InCond and P&O Techniques

The paper examines MPPT algorithms based on P&O, InCond, and ANN with a boost converter that supplies constant output to the load in a PV stand-alone system operating under varying irradiance conditions. To generate the duty cycle of a converter, the Perturb and Observe (P&O), Incremental Conductance (InCond), and Artificial Neural Network (ANN) algorithms are utilised. MATLAB and Simulink are used to conduct simulation research on the PV system. As the world approaches an alarming energy crisis, the demand for renewable energy sources increases daily. India is aiming to develop 20 GW of solar power by the year 2022. In a tropical nation like ours, solar energy is an essential source of energy. The principal issue with solar PV systems is their low efficiency and high initial investment. In this research paper, we discuss the various varieties of MPPT techniques in order to devise a method for obtaining the utmost possible output from a PV module and supplying it to the grid in order to increase the overall efficacy.

An improved weather adaptable P&O MPPT technique under varying irradiation condition

Perturb and Observe algorithm is most familiar due to its wide range of utilization in tracking maximum power point. Besides, being simple and economical, perturb and observe algorithm has the major disadvantage of atmosphere insensitivity, resulting in fluctuation of output characteristics under varying irradiation conditions. An Improved Weather Adaptable perturb and observe maximum power point tracking is projected in this paper to overcome the disadvantages due to weather insensitivity in perturb and observe algorithm. Additionally, in the proposed algorithm, irradiation and temperature sensors are employed in estimating nearest location to maximum power point, resulting in faster response. The system is designed to update the PI controller gain values according to weather variations, resulting in satisfactory operating characteristics at all possible irradiation cases. The proposed Weather Adaptable perturb and observe tracking scheme is developed in MATLAB and hardware cases, the conclusions shows that the system follows good dynamic properties, low oscillations under steady state and better tracking efficiency compared to existing MPPT schemes. Following these advantages, the proposed system is simple with low mathematical burden, leads to easy real time implementation.

Solar PV Transient Mitigation using Superimposed Sliding Mode-Perturb and Observe MPPT under Varying Irradiation Conditions

Solar PV Transient Mitigation using Superimposed Sliding Mode-Perturb and Observe MPPT under Varying Irradiation Conditions

Thermal and Radiation Stability in Nanocrystalline Cu

Nanocrystalline metals have presented intriguing possibilities for use in radiation environments due to their high grain boundary volume, serving as enhanced irradiation-induced defect sinks. Their promise has been lessened due to the propensity for nanocrystalline metals to suffer deleterious grain growth from combinations of irradiation and/or elevated homologous temperature. While approaches for stabilizing such materials against grain growth are the subject of current research, there is still a lack of central knowledge on the irradiation-grain boundary interactions in pure metals despite many studies on the same. Due to the breadth of available reports, we have critically reviewed studies on irradiation and thermal stability in pure, nanocrystalline copper (Cu) as a model FCC material, and on a few dilute Cu-based alloys. Our study has shown that, viewed collectively, there are large differences in interpretation of irradiation-grain boundary interactions, primarily due to a wide range of irradiation environments and variability in materials processing. We discuss the sources of these differences and analyses herein. Then, with the goal of gaining a more overarching mechanistic understanding of grain size stability in pure materials under irradiation, we provide several key recommendations for making meaningful evaluations across materials with different processing and under variable irradiation conditions.