The energy efficiency is one of the key metrics of a vanadium redox flow battery (VRFB), reflecting its ability to perform specific tasks for grid support. Due to ambient temperature fluctuations, this parameter can dramatically change, narrowing the applicability of VRFB. This study presents a comprehensive analysis of VRFB efficiency during prolonged operation under different ambient temperatures and realistic operating conditions. For this, the non-isothermal zero-dimensional model is used, which is validated against experimental data from a kW-scale setup, demonstrating high accuracy with voltage and temperature calculation errors below 2 % and 3 %, respectively. Battery efficiency and energy are systematically investigated across a wide range of load current densities (40-120 mA/cm2), pump power levels (20-80 W) and ambient temperatures (5-25 degrees C). The results reveal that the energy efficiency generally decreases with increased pump power due to the high influence of energy losses, while the absolute discharge energy can increase as a result of enhanced electrolyte flow rate. In addition, the multi-objective optimization analysis of the VRFB system is performed, highlighting the trade-offs between capacity, power, and energy efficiency. Specifically, high system power can be achieved at low temperatures due to better ambient cooling; however, it requires more power from the pumps due to the higher viscosity of the electrolyte. Conversely, high capacity and efficiency are achieved at room temperature, but the power can be limited to avoid overheating and ohmic losses. Using the Pareto front analysis, the balanced optimal point is found at 1.49 kWh capacity, 2.93 kW power, and 69.9 % energy efficiency, showing the compromise between all three parameters. The presented method serves as a tool for informed decision-making, based on the specific context and objectives. The findings offer practical insights for optimal operating conditions of industrial-scale VRFB systems, ensuring their efficient and reliable operation across a wide range of ambient temperatures.

The Shapley value, a concept from cooperative game theory, plays a crucial role in fair distribution of payoffs among participants based on their individual contributions. However, the exact computation of the Shapley values is often impractical due to the exponential complexity. The currently available approximation methods offer some benefits but come with significant drawbacks, such as high computational overhead, variability in accuracy, and reliance on heuristics that may compromise fairness. Given these limitations, there is a pressing need for approaches that ensure consistent and reliable results. A deterministic method could not only improve computational efficiency but also ensure reproducibility and fairness. Leveraging principles from the so-called compressed sensing, techniques which exploit data sparsity, and elementary results from the matrix theory, this paper introduces a novel algorithm for approximating Shapley values, emphasizing deterministic computations that ensure reproducible data valuation and lessen computational demands. We illustrate the efficiency of this algorithm within the framework of data valuation in the two-settlement electricity market. The simulations convincingly indicate essential advantages of the proposed method over the existing ones. In particular, our method achieved an average increase of 33.8% in approximation accuracy, as measured by relative error, while maintaining consistent performance across multiple trials.

The subject of this paper is the family of linear difference equations widely used in the modeling of population dynamics. We analyze the nonasymptotic behavior of stable solutions of this equation for various initial conditions in the unit box, paying special attention to possible large deviations of solutions from the initial values at finite time instants, a phenomenon referred to as peak effect. We first identify the worst-case initial conditions yielding maximum deviation. Next, we consider a parameterized subfamily and prove two results on the properties of the roots of its characteristic polynomial and on computation of threshold peak-promoting values of the parameter of the family. Several special cases are analyzed and illustrative examples are provided.

The performance of large-scale stationary energy storage systems such as vanadium flow batteries (VRFB) can be severely reduced by ambient temperature fluctuations due to changing thermodynamic properties. In this work, a new non-isothermal VRFB model is developed and its thermal behavior at room (25 degrees C) and low (5 degrees C) ambient temperatures is investigated. The model allows to predict the dynamic behavior of temperature, voltage, capacity and power of the VRFB taking into account the variation of the electrolyte viscosity. Validation of this model is carried out based on available numerical and experimental data. The model is used to simulate the operation of a 5 kW VRFB in constant electrolyte flow rate and constant pump power modes. The results show that at low temperatures in constant electrolyte flow mode, there is a power drop due to intensive pump operation. In constant pump power mode, a battery capacity drop of up to 12 % is observed due to increased electrolyte viscosity. The obtained results emphasize the significant change in battery dynamic performance at low ambient temperatures, indicating the importance of developing optimal operating strategies for specific climatic conditions. The developed modeling principles can be extended to advanced real-time VRFB simulations.

The performance of vanadium flow batteries (VRFB) can be severely reduced when operating at low temperatures due to changing electrolyte properties. In this work, we develop a non-isothermal model of VRFB dynamics that takes into account changes in electrolyte viscosity depending on temperature. The model is using available experimental and numerical data from recent literature. Using this model, the operation of 5-kW VRFB at low (5°C) and room (25°C) ambient temperatures is analyzed in two modes: constant electrolyte flow rate and constant pump power. As a result, the power loss is observed at constant flow rate due to intensive pump operation, and the capacity loss is reached 12% in the initial cycles of VRFB operation at constant pump power of 50 W. The results of this study highlight the significant change in battery dynamic characteristics at low ambient temperatures, indicating the importance of developing optimal cycling strategies for specific climatic conditions.

As renewable energy sources interconnected to the electric grid increase, deploying distributed energy storage systems along the grid is a viable solution to sustain grid stability. One of the critical aspects of any energy storage system is its efficiency in transferring power to the grid. Another important aspect is managing high power levels in a short time and being easily expandable in terms of energy capacity and power handling. For this reason, supercapacitors are suitable energy storage devices to fulfill these requisites. This article focuses on analyzing the losses and improving the efficiency of a supercapacitor energy storage system based on a modular multilevel converter, which accomplishes all the abovementioned functions and capabilities. The analyzed energy storage system is based on submodules, including the power electronic interface and the supercapacitors. Hence, the system can be easily expanded because the submodule provides the functions of balancing the energy storage devices, the DC/AC, and the DC/DC conversions by using the modular multilevel converter topology approach. Therefore, any number of submodules can be connected, and the operator can make an array of the desired power, energy, and voltage ratings. This study details a probabilistic loss analysis for the proposed supercapacitor energy storage system and presents a case study using 3000F supercapacitor cells for a 6.6 kW single-phase system. The improved submodule version is validated through simulations and experimentally with a lab-scale prototype. The results show how the proposed methodology increases the system's overall efficiency with a 95 % confidence level.

The optimization of vanadium redox flow batteries (VRFBs) is closely related to the flow rate control: a proper regulation of the electrolyte flow rate reduces losses and prolongs battery lifetime. To this end, a flow factor control strategy in VRFBs was proposed in the literature provided with numerical/experimental validations. Yet, a theoretical justification of this approach was lacking. The respective control law is a generalization of Faraday’s law of electrolysis since it employs a special scaling parameter referred to as the flow factor. In this paper, we show that this coefficient is directly related to the conversion rate of electrolyte in the cell. Furthermore, we pose an optimal control problem with maximization of total battery power integrated over time to determine an optimal flow factor. To this end, we use a simple stochastic policy gradient algorithm. The case studies illustrate the application of the computed optimal controller under various load currents and demonstrate that there is no single flow factor for all modes, the optimal performance of the battery can only be guaranteed by different values of this parameter. As a result, the proposed control strategy can be used for advanced control and monitoring tools for industrial VRFB systems.

When developing dynamical models of vanadium redox flow batteries (VRFBs), it is important to find a trade-off between simplicity, convenience, and model accuracy. Crossover can contribute significantly to the dynamics of such batteries, especially when the number of charge-discharge cycles is large. In this work, we propose a crossover flux modeling approach that takes into account the membrane properties associated with its preparation and operation, when detailed information about its physical characteristics is not available. The proposed approach showed good agreement with the experimental data over 25 cycles with an average error of less than 2 %. A detailed analysis of the contribution of different crossover components revealed that the main influence on the observed capacity drop is related to the diffusion component, which dominates over migration and convection across all cycles, presenting more than 60 % of the losses. In addition, the results showed that migration and convection "mitigate" the influence of diffusion during long-term cycling, thereby reducing the capacity drop. As a result, the proposed approach can be used to analyze the effects of different types of crossover on the capacity decay, which provides researchers and engineers with important information for improving the design and operating conditions of VRFBs to ensure their reliable and fail-safe operation under long-term cycling.

In this paper, we propose a new passivity-based controller design technique for discrete-time fully actuated systems. The controller establishes finite-time and fixed-time convergence of dynamical system trajectories to an equilibrium state. A new form of a dissipation function, selected a priori, is introduced to design a feedback control rule to achieve such convergence properties. An energy shaping and damping injection methodology is extended to achieve non-asymptotic stabilization. A numerical example to validate the proposed methods is provided.

This paper investigates the critical issue of ensuring stable operation in grid-connected inverters and inverter-based distribution grids, focusing on the influence of variable $R / X$ ratios and parallel connections of inverters on system stability in weak grids. Utilizing the power-hardware-in-the-loop methodology, an experimental setup is designed for authentic assessments of grid-connected inverters under diverse conditions. This setup includes an RTDS real-time simulator, a Ponovo 4-quadrant amplifier, a real 4 kW inverter, and a modeled grid with simulated inverters, connected in parallel with the real inverter. The results include experimentally obtained stability regions considering grid R and L parameters. Notably, findings indicate an expanded stability region with parallel inverters, enabling operation with lower $R / X$ ratios. This research contributes to understanding inverter stability at a distribution level of 0.4 kV. The insights gained are crucial for improving grid-connected inverter performance and streamlining the integration of renewable energy sources, thereby advancing the reliability and sustainability of power systems.

The study of spectra of Laplacian matrices is important in decentralized optimization and multi-agent control problems. Namely, the largest and the smallest nonzero eigenvalues significantly affect both the stability of decentralized algorithms and their convergence rate. In this paper, we study the Laplacian spectra of some basic graphs and hierarchical graphs obtained from them. Explicit expressions for the eigenvalues of interest are given and analyzed.

Vanadium redox flow batteries (VRFBs) have been in the focus of attention of the energy storage community over the past years. Adequate, reliable and user-friendly mathematical models are required for the development and optimal application of this type of battery. A large amount of literature has been devoted to dynamic models of VRFBs, but insufficient attention has been paid to the comparison and critical analysis of their applicability. The article provides a comprehensive overview of available dynamic models, comparing their applicability for real-time simulation of industrial-scale vanadium redox flow batteries. In addition, a methodology for the models comparison is proposed, which takes into account different modes of operation and allows to determine the applicability range of a particular model. The results of the study show that lumped-parameter models with crossover performs well for simulating battery dynamics in the wide range of operating conditions: state of charge (SOC) - (0.1-0.8), load current - (20-290 mA/cm2 ), flow velocity - (0.4-2.7 cm/s). Also, such models can be tuned even if some physical parameters of the battery components (e.g. electrodes and membrane) are unknown. The results obtained can be used to provide more accurate simulation of vanadium redox flow batteries in real-time monitoring and control tasks, when accuracy and performance are important

In this paper, we consider an application of the 5-kW vanadium redox flow battery to perform the peak shaving task in a residential grid. The battery behavior is simulated with application of zero-dimensional model considering real load conditions. The optimal battery operation strategy (battery usage protocol) is determined to minimize capacity fading during long-cycling battery operation. In this regard, different strategies of electrolyte rebalancing are considered, which allow periodic restoration of battery capacity. The result shows that with an increase of the total volume of electrolyte, fewer rebalancing services are required. It is found that for the considered case (1 year of battery operation with 1 charge and 1 discharge per day) the optimal volume of the electrolyte is 140 L. The obtained results show a good potential of the VRFB systems as stationary storage for residential applications.

This article addresses the problem of multiagent communication in networks with a regular directed ring structure. These can be viewed as hierarchical extensions of the classical cyclic pursuit topology. We show that the spectra of the corresponding Laplacian matrices allow exact localization on the complex plane. Furthermore, we derive a general form of the characteristic polynomial of such matrices, analyze the algebraic curves its roots belong to, and propose a way to obtain their closed-form equations. In combination with frequency-domain consensus criteria for high-order single-input single-output linear agents, these curves enable one to analyze the feasibility of consensus in networks with a varying number of agents.

In this work, we propose a two-stage parameter identification algorithm for the zero-dimensional model of vanadium redox flow battery (VRFB) based on the fitting of the available experimental data. Specifically, in the first stage, the parameters of overpotentials are obtained from the discharge polarization curve at the state of charge of 50%. In the second stage, the parameters of capacity loss and crossover are identified by the minimization of square error between the predicted and experimental charge-discharge curves at a certain value of load current. The algorithm allows to assess the degree of degradation of the battery components, and capture the effects associated with crossover and mass transfer limitations at high load currents and low flow rates. We verify this algorithm with a reference simulation considering the most interesting practical cases of battery use and validate it with three experimental VRFB systems with power and capacity ratings in the range of 5–10 kW and 5–100 kWh, correspondingly. The results show a good agreement with experimental data having an average error value of less than 1%. The results of the study are an important step in further developments of advanced control algorithms for large-scale energy storage systems.

This article discusses the sliding mode control problem, where the reaching phase is achieved non-monotonically, and the sliding phase can be achieved either monotonically or non-monotonically. Once the reaching phase is completed, the state variables slide on the sliding manifold and then reach the equilibrium point. A practical second-order example of the ball motion model is considered to show the non-monotonic reaching phase. Simulation results verify the non-monotonic behavior of the reaching phase.

Data reconciliation is an essential tool in data processing in various industries. It helps to improve accuracy of decision-making algorithms by reducing the influence of random errors in measurements. In this paper, we consider large-scale data reconciliation problems in which multiple areas communicate over a network to obtain an optimal solution of the centralized problem. Our proposed approach accounts for the boundaries between different areas avoiding a mismatch and sub-optimality as well as reduces computational and communication complexities. The proposed distributed data reconciliation method is compared to a centralized reference in different scenarios.

Energy storage systems are expected to play a key role in the transition towards low-carbon power systems. The increased pace of renewable energy deployment requires the integration of batteries ensuring stability and safety of the grid and smoothing the intermittent behavior of renewables. Efficient operation of batteries itself is also important. It prolongs the batteries lifetime reducing operational costs. One of the key technologies helping with battery management is the state of charge (SoC) monitoring. The paper provides a critical analysis of the explicit methods for calculating SoC of Vanadium Redox Flow Batteries (VRFBs): the OCV-based method and the Coulomb counting method. We study the interrelation between them and how they can be used together to achieve more robust and accurate SoC monitoring. In contrast to existing works, we obtain an analytical expression for the overall SoC accounting for both main components of the battery, namely its stack and tanks. Our analysis of their contributions makes it possible to reveal some drawbacks of the existing approaches widely used for VRFB state of charge calculation and monitoring.

Optimization of the performance of vanadium redox flow batteries (VRFBs) is closely related to flow rate control: a proper flow rate adjustment reduces the losses and extends the battery lifetime. In this regard, the so-called flow factor control strategy of VRFBs has been recently proposed in the literature and some numerical/experimental validations have been performed. The strategy is a generalization of Faraday's frst law of electrolysis as it uses a special scaling parameter referred to as the flow factor. In our paper, we show how this factor is related to the conversion rate (fraction conversion per pass) and geometrical properties of the battery. Finally, we investigate the flow factor as a function of the fraction conversion per pass and stack/tank volumes, and perform numerical simulations to confrm the theoretical results.

Cyclic pursuit is one of the oldest multi-agent strategies with many interesting features. The vast majority of the papers dedicated to this strategy cover various extensions related to the models of interacting agents, delays, uncertainties, asynchronous communication, etc. A certain line of research studies hierarchical topologies that extend the conventional single-layer scheme. Our paper contributes to this line. Motivated by the fact that such structures are scalable, we study the spectral properties of their Laplacian matrices. First, we consider a two-layer cyclic pursuit strategy and analyze its Laplacian spectrum as the number of agents tends to infinity. Next, we propose a more sparse two-layer topology, study its spectrum, and describe the curves that contain a limit location of the eigenvalues of the corresponding Laplacian matrix.