Predictive control-based flow battery energy storage system for microgrid peak shaving

Abstract

The incorporation of energy storage systems, particularly vanadium redox flow batteries (VRFBs), is critically significant for the operation of microgrids, facilitating effective peak shaving and load balancing. VRFBs exhibit essential attributes such as high flexibility, fast response times, and prolonged operational lifespans, rendering them particularly advantageous for small-scale microgrid applications. Building upon this foundation, the present study proposes a novel microgrid system that is fundamentally based on VRFB technology. This system integrates biomass gasification and solid oxide fuel cells (SOFCs) as primary power generation sources, thereby ensuring a reliable and consistent electricity supply that is specifically tailored to the energy requirements of rural areas. To enhance the charge-discharge efficiency of VRFBs, a new predictive control methodology is introduced, aimed at maximizing the utilization of energy stored within the batteries. This predictive control approach dynamically modifies battery operations in response to real-time battery conditions and projected load demands. The study also assesses peak-shaving strategies in terms of their effectiveness in mitigating demand peaks and enhancing grid stability. In comparison to traditional fixed control methods, the proposed predictive control strategy demonstrates superior intelligence and adaptability, allowing for seamless adjustments to the fluctuating power needs of microgrid systems. By significantly improving the efficiency of VRFBs and lowering operational costs, this innovative approach has the potential to advance the sustainability and resilience of microgrid infrastructures.

Keywords

microgrid energy storage vanadium redox flow battery (VRFB)biomass gasification predictive control

Introduction

Traditional centralized electricity grids have faced longstanding criticism due to their inefficiencies, which are marked by significant energy losses over extensive transmission distances and the necessity for considerable investments in infrastructure, particularly in remote mountainous areas of developing countries.¹ Although rural electrification is crucial for improving living standards and promoting economic development, it is frequently hindered by financial limitations.² In this context, distributed power systems that utilize renewable energy sources have emerged as a viable alternative.³ Nevertheless, these systems face challenges in effectively balancing power consumption and production, primarily due to the inherent uncertainties related to load fluctuations and the intermittent nature of renewable energy sources.⁴ Achieving a stable equilibrium between these elements is a vital goal for enhancing the feasibility and sustainability of decentralized energy systems.

This research investigates the creation of a self-sustaining microgrid system that integrates flow batteries, with a particular focus on utilizing biomass-based energy solutions specifically designed for rural areas.⁵ The primary objective is to develop an electricity system that is both stable and reliable, tailored to meet the distinct energy requirements of rural communities.⁶ By emphasizing the use of biomass energy sources, which are both stable and appealing in these contexts, the study aims to tackle the persistent challenges associated with rural electrification.⁷ The integration of flow batteries within the microgrid framework is intended to significantly improve the overall efficiency and resilience of the energy system. This initiative is anticipated to contribute to the sustainable development and advancement of rural communities, thereby ensuring a dependable and sustainable energy supply for their inhabitants.

Biomass is recognized as a promising renewable energy source, particularly when utilized through advanced technologies such as biomass gasification, which facilitates efficient power generation.⁸ Solid oxide fuel cells (SOFCs) powered by biomass represent a significant innovation in the context of microgrid applications, providing a notable combination of high efficiency and operational flexibility.⁹ Energy storage systems (ESSs) are essential to the functioning of microgrids, effectively supporting the power generation component. Within these decentralized energy frameworks, vanadium redox flow batteries (VRFBs) have emerged as a critical technology, enabling effective power balancing.¹⁰ The integration of these technologies allows microgrids to optimize energy utilization and enhance overall grid resilience, thereby making a substantial contribution to the sustainable development of energy systems.

Microgrid systems encounter a range of challenges, including uncertainties related to both energy supply and demand, as well as the varied specifications associated with different microgrid configurations.¹¹ A significant obstacle is the effective management of peak loads, which necessitates the implementation of efficient strategies to address fluctuations in energy demand.¹² To effectively confront these challenges, the integration of flexible power plants and energy storage systems (ESS) is essential.¹³ Flexible power plants exhibit a high degree of adaptability, allowing them to respond efficiently to changing demand patterns. ESS plays a crucial role by storing excess energy during periods of low demand and releasing it during peak demand, thereby ensuring a stable power supply. The combination of these solutions enables microgrid operators to optimize energy utilization, improve grid stability, and accommodate the diverse energy requirements of various microgrid environments, ultimately contributing to a more resilient and sustainable energy infrastructure.

The current literature on microgrid systems primarily focuses on the use of photovoltaics, wind energy, and fossil fuels, while biomass resources have received relatively limited attention.¹⁴ This highlights the innovative potential of utilizing biomass for distributed generation within microgrid frameworks.¹⁵ Furthermore, there is a significant emphasis on the integration of solid oxide fuel cell (SOFC) waste heat recovery systems, which can substantially improve overall energy efficiency and resource utilization.¹⁶ The adoption of vanadium redox flow batteries (VRFB) for energy storage also represents a promising strategy for mitigating the intermittency and variability associated with renewable energy sources.¹⁷ This study underscores the pioneering integration of biomass utilization, SOFC waste heat recovery, and VRFB energy storage, marking a notable advancement in microgrid technology. This integration not only advances the development of more sustainable and resilient energy systems but also paves the way for a more efficient and environmentally sustainable future.

The research presents a comprehensive and effective power generation system specifically designed for microgrid applications, which integrates biomass-based solid oxide fuel cells (SOFCs) with vanadium redox flow batteries (VRFBs). A novel predictive control strategy has been developed to enhance charge-discharge efficiency, thereby optimizing the utilization of energy stored within the batteries. Additionally, the study investigates peak-shaving strategies through the analysis of daily load profiles, with the objective of mitigating demand peaks and enhancing grid stability. Crucially, profitability evaluations of energy storage systems (ESSs) are performed, incorporating time-of-use tariffs, which are vital for assessing the economic feasibility and potential returns on investment associated with such microgrid configurations. Through rigorous analysis and innovative methodologies, this research offers significant insights into the complex design, efficient operation, and cost-effectiveness of biomass-integrated microgrid systems. These findings pave the way for the advancement of more sustainable and economically viable energy solutions in rural and remote regions.

Problem description

At the heart of this system is the energy storage unit, which primarily consists of the vanadium redox flow battery (VRFB) and an energy management system (EMS). This energy storage unit is crucial for the effective storage and management of surplus energy produced during periods of low demand, facilitating its release during peak consumption times. The VRFB serves as the central element of the energy storage system, characterized by its high energy density and extended cycle life, rendering it an optimal choice for the storage of substantial energy quantities. Conversely, the EMS is responsible for the intelligent regulation of energy flow within the system, optimizing the charging and discharging processes of the VRFB to enhance overall efficiency.¹⁸

In addition to the energy storage unit, the microgrid system incorporates renewable energy sources, such as solar panels and wind turbines, alongside conventional power generation units. These components function synergistically to address the varied energy requirements of the residents within the microgrid’s service area, thereby ensuring a reliable and sustainable power supply.

The complex operations of the microgrid system are meticulously designed to maximize energy efficiency. Central to this process is the biomass steam gasification technique, which is essential for converting biomass into hydrogen-rich biosyngas.¹⁹ This biosyngas, a critical element for power generation, undergoes a comprehensive purification process that includes several careful steps to remove impurities, thereby ensuring its purity and efficacy in powering the system. These detailed operations not only enhance the performance of the system but also contribute to its sustainability and environmental friendliness.

An in-depth examination of the microgrid’s functionality reveals the critical role of its energy storage component, which significantly influences the overall power generation capabilities of the system. Within this context, the vanadium redox flow battery (VRFB) is identified as a key element, particularly in situations where power generation exceeds consumption. Under the precise management of the EMS, the VRFB effectively captures and stores excess energy, thereby facilitating its optimal use.²⁰ Conversely, in instances where power generation falls short, the VRFB adeptly shifts to supply additional energy, thereby reconciling the disparity between supply and demand. A fundamental aspect of the VRFB’s operational efficiency is the dynamic regulation of electrolyte flow rates, which is meticulously adjusted according to current operational demands and the battery’s status. This careful modulation, achieved through pumps located on either side of the system, enhances efficiency and reinforces the VRFB’s reliability as a foundational element of the microgrid’s energy storage framework.

The importance of investigating this issue is critical in addressing the significant challenges faced by traditional centralized electricity grids, particularly in remote and rural areas of developing nations. These regions frequently experience considerable energy losses during transmission, which necessitates substantial investments in infrastructure. Furthermore, financial limitations often impede efforts toward rural electrification, resulting in restricted access to dependable power sources. This study aims to explore innovative solutions, such as the integration of biomass-based microgrid systems with VRFB energy storage. By pursuing this line of inquiry, we aspire to establish stable, efficient, and sustainable electricity provision in rural locales, thereby overcoming the shortcomings of conventional grids. This research has the potential to transform rural electrification, yielding long-term advantages in energy security, economic development, and environmental sustainability.

Mathematical formulation

In VRFB systems, the interaction of various interconnected variables, such as heat transfer and electrochemical reactions, introduces significant complexities, particularly under non-ideal conditions. To effectively address these challenges, it is essential to implement reasonable assumptions that can simplify the system model. By reducing the complexity of variables, idealized conditions allow for a more concentrated analysis of the overall system performance. This methodological approach not only enhances the understanding of VRFB behavior but also supports the development of effective optimization strategies. Therefore, the adoption of idealized conditions is crucial for advancing VRFB technology and overcoming the substantial challenges associated with system intricacies.

The integration of reasonable assumptions within an idealized framework typically results in minimal impact on simulation outcomes, as any discrepancies that arise are generally considered acceptable. This perspective is corroborated by prior research, which underscores the efficacy of utilizing such assumptions to analyze complex models and streamline computational processes. This pragmatic methodology is frequently employed in the performance analysis of intricate systems, allowing researchers to adeptly navigate complexities while ensuring computational clarity. By leveraging idealization assumptions, researchers can derive valuable insights into system dynamics and behavior, ultimately fostering advancements in optimization strategies and practical applications.

In the effort to simplify the modeling approach for VRFB, fundamental assumptions are meticulously formulated to minimize disruption to simulation outcomes. These assumptions encompass critical factors, including the uniform physical properties of electrolytes, electrodes, and membranes, as well as the diffusion of ions through the membrane. It is also assumed that thorough mixing of electrolytes occurs in both the positive and negative tanks, while ambient temperatures for cell stacks and electrolytes remain constant. Additionally, negligible concentration gradients in pipes and uniform electric resistance in cell stacks are taken into account. The introduction of porous electrodes is also considered to enhance the active area and reduce activation overpotential. By incorporating these assumptions, the VRFB modeling process is streamlined, facilitating efficient analysis while preserving the integrity and accuracy of simulation results.

Electrochemical model

The electrochemical mechanisms of the vanadium redox flow battery are defined by the division of the cell stack into two separate half-cells, which are separated by a membrane. This configuration ensures that the charging and discharging processes within the positive and negative electrolytes occur independently. During the charging phase, VO2+ ions in the positive half-cell are oxidized, resulting in the generation of electrons. These electrons then migrate to the negative half-cell, where they facilitate the reduction of V3+ ions. This conversion of chemical energy into electrical energy is crucial for the battery’s operation, enabling effective energy storage and release. Conversely, during the discharging phase, this process is reversed, allowing for the release of stored electrical energy as chemical bonds are formed. The reversibility of these reactions constitutes the fundamental principle underlying vanadium redox flow batteries, which facilitates efficient energy storage and retrieval, thereby supporting a variety of applications with consistent reliability and sustainability.

V^{3 +} + e^{-} \to V^{2 +}

(1)

{VO}_{2}^{+} + H_{2} O \to {VO}_{2}^{+} + 2 H^{+} + e^{-}

(2)

The open circuit voltage is a critical parameter for characterizing the behavior of a cell, representing the voltage difference between its positive and negative electrodes when no current is flowing. This voltage is essential for understanding the electrochemical properties of the cell and is derived from the Nernst equation, a fundamental equation in electrochemistry. The Nernst equation establishes a quantitative relationship between the electrochemical potential of the cell, the concentration of reactants, and other relevant factors. By utilizing this equation, researchers can accurately calculate the open circuit voltage, providing valuable insights into the cell’s performance under diverse operating conditions. This voltage serves as a reference point for evaluating the cell’s state and behavior, which is vital for optimizing its design and operation in practical applications.

E_{OCV} = E_{0} + \frac{R T}{n F} \ln (\frac{C_{cs}^{2} \cdot C_{cs}^{5}}{C_{cs}^{3} \cdot C_{cs}^{4}})

(3)

The formation potential, $E_{0}$ , is crucial in VRFB systems and is determined experimentally. At 50% SOC, it is 1.4 V. R designates the gas constant, T represents ambient temperature, and F signifies Faraday’s constant. The symbol C denotes ion concentration, whereas cs refers to the cell stack configuration. SOC, or state of charge, serves as a pivotal metric for batteries, reflecting the proportion of stored energy relative to its maximum capacity. Derived from measurements of ion concentrations within the electrolyte tank, SOC provides crucial insights into the operational status and overall efficiency of the battery system. Vanadium ions are capable of migrating across the membrane, a phenomenon that can lead to self-discharge and electrolyte imbalances, ultimately affecting the overall performance and lifespan of the battery system. To accurately capture the variations in SOC that result from the different diffusion rates of these ions, it is crucial to mathematically model the SOC of both half-cells.

The proposed modeling not only deepens our comprehension of the complex mechanisms occurring within battery systems but also facilitates the formulation of more effective operational strategies and optimized management techniques for charging and discharging. This methodology offers a quantitative framework for assessing the state of charge (SOC) of the negative half-cell, while considering the intricate interactions and dynamic processes inherent in the battery system. The mathematical representation of the SOC for the negative half-cell is a critical instrument in this analytical process. By employing this equation, researchers and engineers can achieve greater precision in predicting and regulating the SOC of the battery, which ultimately contributes to enhanced battery performance, increased reliability, and improved safety. This scholarly approach is vital for the advancement of battery science and engineering.

S O C^{-} = \frac{C_{t k}}{C_{t k 2} + C_{t k 3}}

(4)

S O C^{+} = \frac{5 C_{t k 4} + C_{t k}}{C_{t k 5}}

(5)

The “tk” variable signifies the tank, a vital component in VRFB systems, housing electrolytes critical for energy storage. This meticulous approach ensures effective monitoring and control of ion concentrations, boosting energy storage capacity and minimizing wastage. These calculations enable the determination of the distribution of vanadium ions within the VRFB system, allowing for a comprehensive understanding of the electrolyte dynamics and facilitating accurate modeling of the system’s behavior.

The mathematical formula provided can be written as follows:

V_{c s} \cdot d C_{c s} / d t = Q_{c s} \cdot (C_{t k_{i}} - C_{c s_{i}} + Φ_{i} + S_{i})

(6)

The equation characterizes a rate of change, maintaining a constant $V_{c s}$ . Terms $Φ_{i}$ and $S_{i}$ factor into the changing concentrations over time. Additionally, V, Q, t, Φ, and S correspond to volume, mass flow rate, time, molar flux, and source term, respectively. The variable i takes on values of 2, 3, 4, or 5, reflecting distinct vanadium ion species. Lastly, the equivalent overpotential, $η_{o a}$ , is derived from the product of current density and resistivity, encompassing both Ohmic and activation overpotentials.

η_{o a} = η_{o h m} + η_{a c t} = i r

(7)

Concentration overpotential, a fundamental aspect in electrochemical systems like VRFBs, results from concentration disparities between the bulk electrolyte and electrode surface. This mismatch, quantified in equation (8), significantly influences system efficiency and operation. It essentially represents the resistance ions encounter during migration, shaping the kinetics of electrochemical reactions. Managing this overpotential is crucial for enhancing VRFBs’ performance and lifespan, vital for optimal energy storage.

η_{c o n} = \frac{R T}{n F} \cdot \ln (1 - \frac{1.6 \times 10^{- 4} n F Q_{c s}}{A_{f l} C_{r e a}})

(8)

Cell voltage, a determinant of electrochemical system performance in charging and discharging, plays a crucial role in its efficiency. This parameter offers crucial insights into the system’s energy storage and release capabilities, reflecting its overall functionality and practical application. Managing the factors that affect cell voltage is essential for optimizing system operation and maximizing its benefits in energy storage systems, including VRFBs.

E_{c h c e l l} = E_{O C V} + η_{o a} + η_{c o n}

(9)

E_{d i s c e l l} = E_{O C V} - η_{o a} - η_{c o n}

(10)

E_{s t a c k} = N_{c e l l} \cdot E_{c e l l}

(11)

The variable $N_{c e l l}$ denotes the number of cell stacks housed within a module, a pivotal factor influencing the overall capacity and functionality of the VRFB system. The quantity of cell stacks directly impacts the system’s energy storage capacity, power output, and scalability, as well as affecting considerations such as system complexity, cost, and maintenance requirements. Thus, selecting an appropriate number of cell stacks per module is crucial for tailoring the system to meet specific application demands while ensuring optimal performance and efficiency. Moreover, comprehending the correlation between the number of cell stacks and system parameters is essential for designing and deploying VRFB systems that effectively address a wide range of energy storage requirements and operational conditions.

Pump power and energy efficiency

This process involves various components such as pipelines, porous electrodes, and flow channels, ensuring efficient electrolyte flow throughout the system. By consuming power, pumps enable the continuous movement of electrolytes, which is essential for maintaining battery performance and overall system functionality in VRFB applications. Thus, understanding and optimizing the operation of pumps is paramount to enhancing the efficiency and reliability of VRFB systems.

Δ p = Δ p_{p i p e} + Δ p_{c e l l}

(12)

Δ p_{p i p e} = \frac{32 μ L}{ρ \cdot D_{p i p e}^{2}}

(13)

Δ p_{c e l l} = \frac{4 μ l}{ρ \cdot D_{f}^{2}} (\frac{1 - ϵ}{ϵ^{3}}) f \cdot \frac{K}{d}

(14)

The power consumption of the pump in a VRFB system is a critical aspect affecting its overall energy efficiency. This power consumption is primarily associated with overcoming flow resistance within the system, including pressure losses in the piping and within the cell stack itself. The electrolyte’s dynamic viscosity (μ) and density (ρ), along with electrode porosity (ε), Darcy friction factor (f), and Kozeny–Carman constant (K), jointly determine pressure losses in VRFB systems. These parameters significantly impact electrolyte flow dynamics and overall system performance. Efficient electrolyte circulation, crucial for mass transport, heat dissipation, and reaction kinetics, requires precise consideration of these factors. Accurate integration of these variables is therefore essential for effective VRFB design and operation, ensuring reliability and cost-efficiency. Additionally, the dimensions of the piping and electrode flow channels, represented by parameters such as length (L, l), area ( $A_{p i p e}$ , $A_{f l}$ ), and diameter ( $D_{p i p e}$ , $D_{f}$ ), further influence the overall pressure losses.

Evaluating pump power consumption is key to assessing VRFB system’s energy efficiency, considering total pressure losses and pump efficiency as per equation (15). This analysis offers insights into operational costs and energy needs for electrolyte circulation. Understanding pump power consumption facilitates optimization strategies that improve system efficiency and reduce energy losses, promoting VRFB technology’s overall performance and sustainability. Efficient pump operation is vital for maintaining optimal flow rates and minimizing energy losses in the VRFB system.

P_{p u m p} = \frac{Δ p \cdot Q}{η_{p u m p}}

(15)

The efficiency of a VRFB system is crucial for its practical application and economic viability. Efficiency measures, such as the charging efficiency ( $η_{c h}$ ), discharging efficiency ( $η_{d i s}$ ), and overall efficiency (η), provide insights into the energy conversion processes within the system. Charging efficiency ( $η_{c h}$ ) compares the stored energy to the total energy consumed during charging, while discharging efficiency ( $η_{d i s}$ ) compares the energy delivered to the total energy released during discharging. The overall efficiency (η) encapsulates the full charging-discharging cycle’s effectiveness. These metrics are crucial for evaluating VRFB performance and guiding improvements in energy storage and retrieval. These efficiency metrics are essential for assessing the performance and economic feasibility of VRFB systems, guiding system design and optimization efforts to enhance energy utilization and cost-effectiveness.

η_{c h} = \frac{E_{s t o r a g e}}{E_{i n p u t}}

(16)

η_{d i s} = \frac{E_{o u t p u t}}{E_{r e l e a s e}}

(17)

η = \frac{E_{r e l e a s e}}{E_{i n p u t}}

(18)

Using mathematical modeling, the battery’s performance is evaluated across defined ranges of current and electrolyte flow rates. Simulations determine the optimal flow rate for maximum efficiency at specific current and SOC levels. This approach offers insights into efficiency dynamics, guiding future research and optimization.

Solution method

Predictive control, leveraging algorithms for modeling, optimization, and feedback, is crucial for maintaining peak efficiency. This study explores its application in electrolyte flow rate regulation and VRFB system efficiency optimization. Using SVM algorithms for precise predictions with limited data reduces workload while ensuring accuracy. Moreover, Particle Swarm Optimization (PSO) is applied to solve the optimization problem presented in Section 3. Specifically, PSO is used to find the optimal parameters for the predictive control method, which enhances the control strategy. Figure 1 schematically illustrates the intricate interactions driving VRFB efficiency optimization.

J = \min ({(η_{r_{i + 1}} - η_{i + 1} + λ {(Q_{i + 1} - Q_{i})}^{2})}^{2})

(19)

Figure 1.

Diagram of predictive control model.

The PSO’s objective function J and the weighting coefficient $λ$ are key in determining the peak-shaving control strategy for microgrid sizing. The power plant size, represented by rated power ( $P_{power}$ ), is iteratively calculated using equations (20)–(22) which are satisfied with a small ω value for accuracy. Accurate load data is essential to ensure the microgrid’s load ( $P_{load}$ ) remains representative throughout the year and meets demand under various conditions.

if P_{power} > P_{load} : P_{ch} = P_{power} - P_{load}

(20)

if P_{power} < P_{load} : P_{dis} = P_{load} - P_{power}

(21)

η_{ch} η_{dis} \int_{t 1} P_{ch} d t - \int_{t 2} P_{ch} d t < ω

(22)

The ESS, composed of a specific number of stack modules, operates within a designated rated power mode, maintaining a constant battery power output for stability and reliability. The current within the system varies dynamically based on the stack voltage, as defined by equation (23), reflecting the intricate interaction between electrical characteristics and operational parameters. To optimize charging and discharging processes, the determination of operational modules follows equation (24) for charging and equation (25) for discharging, taking into account maximum power requirements, battery state of charge, and energy conversion efficiency. This mathematical framework not only enhances our understanding of ESS operation but also enables the development of more efficient and reliable energy storage solutions, contributing to the progress of sustainable energy systems.

N_{ch} \cdot P_{ch} < P_{ch} η_{ch} < (N_{ch} + 1) P_{ch}

(23)

N_{dis} \cdot \frac{P_{dis}}{stack} < P_{dis} η_{dis} < \frac{N_{dis}}{stack + 1} \cdot P_{dis}

(24)

I = \frac{P_{stack}}{E_{stack}}

(25)

In the academic realm of microgrid peak shaving, the SOC of the VRFB system holds significant importance. Beyond the application of equation (26), the SOC offers a comprehensive understanding of the VRFB’s energy storage status, reflecting the total energy accumulated or released during its operation. This metric is crucial for academic research, enabling precise analysis and optimization of the VRFB’s performance in peak-shaving scenarios within microgrids. By meticulously studying the SOC, scholars can gain deeper insights into charging and discharging strategies, battery management systems, and overall microgrid design, thereby contributing to the advancement of sustainable energy systems. This energy is computed using equation (27), facilitating SOC determination through equation (28).

E N = \int_{t}^{t} N_{stack} P_{stack} d t

(26)

\frac{E N_{initial} + E N_{ch}}{E N_{tot}} {SOC}_{ch} = \frac{E N_{initial} - E N_{dis}}{E N_{tot}}

(27)

\frac{E N_{initial} - E N_{dis}}{E N_{tot}} {SOC}_{dis} = \frac{E N_{tot}}{E N_{tot}}

(28)

Case study

This section validates the proposed design concepts outlined earlier, emphasizing energy losses, performance enhancement, economic indicators, and peak shaving in VRFB systems. Moreover, our analysis underscored the effectiveness of strategies such as surface fitting for enhancing efficiency. Economic indicators were explored, revealing the potential profitability of VRFB systems in microgrid setups. Lastly, VRFBs were shown to effectively balance loads and shave peaks, contributing significantly to microgrid resilience and efficiency.

Energy losses

Figure 2(a) and 2(b), respectively, show the direct correlation between pump power and flow rate, and the increasing trend of concentration overpotential with current but decreasing trend with flow rate during late charging (SOC = 90%). It becomes clear that optimizing flow rate alone cannot simultaneously minimize both pump power and concentration overpotential. Therefore, the focus should be on mitigating the combined impact of these factors to enhance VRFB performance.

Figure 2.

Variations in power loss with electrolyte flow rates and current: Pump power and concentration overpotential analysis. (a) Pump power changes with different electrolyte flow rates. (b) Concentration overpotential changes with different electrolyte flow rates and current.

Efficiency optimization

Harnessing optimal electrolyte flow rate data across varying charging and discharging currents offers a promising approach to enhancing VRFB efficiency via software control. However, obtaining this optimal flow rate often necessitates extensive experimentation. To overcome this challenge, we propose a solution in this section that surpasses previous methods by employing a surface-fitting approach. Given the difficulty in acquiring performance data across all operating conditions, we use this method to interpolate charge/discharge efficiency and electrolyte flow rate. By prioritizing maximum efficiency as the control objective and employing a fifth-order polynomial fitting equation as shown in equation (29), we aim to minimize potential errors and optimize VRFB operating efficiency effectively.

η^{fit} = \sum p_{m n} S O C^{m} I^{n} (0 \leq m \leq 5; 0 \leq n \leq 5; m + n \leq 5)

(29)

Figure 3 depicts the efficiency comparison between the traditional and proposed methods, revealing an average efficiency of 90.78% and 91.12%, respectively, throughout the charging process. Notably, the disparity in efficiency becomes more pronounced during the later stages of charging. Similarly, differences in electrolyte flow rates between the two methods are more pronounced towards the end of charging. This observation suggests heightened concentration polarization towards the end of charging, underscoring the criticality of precise electrolyte flow rate control during this phase.

Figure 3.

Changes in efficiency and electrolyte flow rates with different SOC.

Economic indicators

This study delves into the economic aspects of a microgrid system, focusing on total investment cost and payback period evaluation. Employing the concept of power arbitrage alongside a time-of-use electricity pricing system featuring peak, flat, and valley periods, the profitability and payback period of VRFB are assessed. Specifically, the VRFB energy storage system capitalizes on low-demand hours to charge using surplus-generated power and discharges during peak hours to fulfill system demand. Based on the provided pricing structure in Table 1, the daily profit of VRFB is computed at $1,340. With an investment cost of $8.14×10⁶, mainly attributed to electrolyte procurement, the estimated payback period for VRFB is determined to be 16.64 years.

Table 1.

Electricity prices and consumptions at valley, transition, and peak periods.

	Valley period	Transition period	Peak period
Electricity price ($/kWh)	0.0417	0.1118	0.1896
Electricity consumption (kWh)	−11869.3	833.98	9184.93

However, the investment cost of VRFB is influenced by various factors, which in turn affect its profitability and payback period. The results, presented in Figure 4, indicate that profitability exerts the most substantial influence on VRFB’s payback period, followed by electrolyte cost. Notably, reducing electrolyte cost by 45% shortens the payback period to 10.70 years, while a corresponding 45% increase in profitability reduces it to 12.08 years. Hence, implementing suitable time-of-use electricity pricing schemes or decreasing electrolyte prices can significantly enhance the economic viability of VRFB.

Figure 4.

Sensitive analysis of the payback period to the daily profit and key component costs.

Peak shaving

Utilizing VRFB within microgrids facilitates load balancing and power supply regulation, making peak shaving and load leveling integral functions. Figure 5 illustrates the outcomes of a peak-shaving control strategy, where the original microgrid load profile is represented by the black line. Using this approach, the initial rated power of the generation system is set at 6.12 MW, marked by the red line. Beneath this line, green bars represent the charging zone, indicating power intake from the grid, while above the line, blue bars depict the discharging zone, reflecting power supply to the grid. Despite energy losses, the total energy intake during charging (green bars) exceeds that discharged (blue bars). Calculations reveal a maximum charging power of 2.14 MW and discharging power of 1.66 MW, necessitating approximately 500 VRFB modules to meet peak charging/discharging demands, each module requiring a 0.4 L electrolyte tank volume to fulfill energy capacity requirements.

Figure 5.

Diagram of the load and charging/discharging power.

Conclusion

In this study, we have explored various aspects of vanadium redox flow battery (VRFB) systems, focusing on energy losses, efficiency optimization, economic indicators, and peak-shaving capabilities. Through detailed analysis and modeling, several key findings have emerged:

1. Energy Losses: The study delved into the intricate relationship between electrolyte flow rates, current, pump power, and concentration overpotential. It observed that pump power is primarily influenced by the electrolyte flow rate, while concentration overpotential is jointly affected by both current and flow rate. This revealed a trade-off scenario, where reducing one factor might exacerbate the other. Consequently, a balanced approach is imperative to minimize the combined total pump power and concentration overpotential, thereby enhancing the overall performance of the system.

2. Efficiency Optimization: We proposed a novel approach to optimize VRFB efficiency by employing a surface-fitting method to interpolate performance data. By selecting maximum efficiency as the control objective and utilizing fifth-order polynomial fitting equations, we achieved a higher average efficiency than that of traditional methods. Notably, precise control of electrolyte flow rate during later charging stages proved crucial for efficiency enhancement.

3. Economic Indicators: Economic viability analysis showcased the potential profitability of VRFB systems within microgrid setups. Through power arbitrage and time-of-use electricity pricing schemes, we calculated a daily profit of $1,340 with an estimated payback period of 16.64 years. Sensitivity analysis further highlighted the significant impact of profitability and electrolyte cost on the payback period, indicating avenues for improvement through pricing optimization or cost reduction strategies.

4. Peak Shaving: VRFB systems demonstrated their utility in load balancing and peak shaving within microgrid environments. Through a control strategy, VRFBs efficiently managed load fluctuations by charging during low-demand periods and discharging during peak hours. The analysis revealed the required number of VRFB modules and electrolyte tank volumes to meet peak charging/discharging power demands.

The study proposes an innovative approach to optimize VRFB system efficiency and economics. However, there is a need for further technical refinement to enhance system reliability and stability, particularly in electrolyte circulation and stability. Additionally, the economic analysis indicates the potential profitability of VRFB systems in microgrids, but the current payback period of 16.64 years may deter some investors. Future research could focus on reducing system costs and shortening the payback period through more efficient electrolyte preparation methods or the use of cheaper materials.

Statements and declarations

Footnotes

Conflicting interest

The authors declared no potential conflicts of interest with respect to the research, authorship, and/or publication of this article.

Funding

The authors received no financial support for the research, authorship, and/or publication of this article.

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