Optimal State Of Charge Research Articles

Optimal scheduling for profit maximization of energy storage merchants considering market impact based on dynamic programming

This paper analyzes how electricity merchants' market impact affects merchants' profit. Energy storage has long been studied for its role in maximizing profit, and merchant decisions are assumed to have no impact on market prices. However, the trading decisions of large-scale energy storage merchants (e.g., pumped storage hydro) will affect the market prices. This paper employs dynamic programming theory to investigate merchants' optimal economic dispatch considering the market impact and physical characteristics of storage systems. Our findings show that the State-of-Charge (SOC) based analytical solution significantly facilitates energy storage merchants' decision-making. The SOC range is segmented into three regions by two optimal SOC reference points, which depend on the available energy in storage, given prices, and market impact. By comparing the current storage SOC with the reference points, the merchant can get the corresponding optimal actions. We analytically show that if the merchant neglects the market impact on the power market, she will exaggerate her expected profit when the price-taker and price-maker merchants have the same generating and pumping upper limits offered to Independent System Operators (ISOs). The profit-maximizing merchant must, therefore, assay to balance the trade-off correctly between the intensity of market impact and the dispatched power. Our findings are verified by numerical simulation, and results demonstrate the ramifications for electricity merchants in energy arbitrage decisions.

Flexible Operation of Hybrid Distributed Energy System Based on Reliability Redundancy

This paper establishes a reliable-economic power sharing scheme of distributed energy system (DES) consists of Li-ion storage battery and photovoltaic (PV) source connected to the utility grid through a distribution feeder. The system is intended to supply a vehicle charging station that requires dense energy production for efficient and short time charging process. Therefore, the issue of battery state-of-charge (SOC) optimal scheduling and power routing among the sources are considered as a technical-economic problem from system dynamic reliability point of view. In the developed optimization framework, the required energy reserve, the optimal SOC scheduling, and the impact of the station on the utility grid are considered and investigated. A new PSO based optimization is proposed to optimize the power sharing of the sources using reliability based optimal power flow scheduling. The proposed methodology quantifies the reliability redundancy of the system to reliably dispatch the power between the sources. The reliability redundancy concept is proposed as a tool to dynamically schedule the battery SOC and updates the power dispatching among the sources in order to: (1) establish a flexible reserve margin, (2) increase the overall number of battery charging/ discharging cycles, (3) economically dispatch the power, and (4) provide an indirect grid service by decreasing the impact of the charging station on the utility grid. The results show that the system reliability is maintained and the number of accumulated cycles is increased by 134 cycles. Furthermore, the maximum imported grid power is decrease from 40.0 kW to 28.3 kW.

An adaptive PMP-based model predictive energy management strategy for fuel cell hybrid railway vehicles

In order to achieve ecological driving without pollutant emissions on non-electrified rail tracks, the focus is on the development of railway vehicles powered by fuel cell and battery systems. A key issue is to reduce hydrogen consumption while maintaining the battery’s state of charge (SoC). In that context, this paper proposes a new casual energy management strategy based on Pontryagin’s Minimum Principle (PMP) within the framework of Model Predictive Control (MPC). The entire energy management problem is formulated by solving a cost function in the prediction horizon, different from the typical one found in other work using model predictive control to realize energy management. The main advantage of this strategy is that by introducing the PMP’s co-state, which is adaptively evaluated using average power estimation and actual SoC, into the cost function, a predicted optimal SoC trajectory is no longer required within the framework of MPC. Therefore, the strategy does not require complete information on the rail track and behaves casually. In addition, the dynamic of the fuel cell power is considered by introducing a tuning factor into the cost function, which benefits the service life of fuel cells. The proposed strategy is tested and validated in a realistic driving cycle by a hardware-in-the-loop (HiL) test bench at the Center for Mobile Propulsion (CMP) of RWTH Aachen University. The simulation results show an optimum close to the offline PMP results and up to 12.1% hydrogen savings compared to a typical MPC strategy using constant SoC reference. The HiL results demonstrate the real-time capability of the proposed strategy and show the excellent fuel economy with merely 2.7% more hydrogen consumption than the global optimum result.

Attractive Ellipsoid Sliding Mode Observer Design for State of Charge Estimation of Lithium-Ion Cells

This work investigates the real-time estimation of the state-of-charge (SoC) of Lithium-ion (Li-ion) cells for reliable, safe and efficient utilization. A novel attractive ellipsoid based sliding-mode observer (AESMO) algorithm is designed to estimate the SoC in real-time. The algorithm utilizes standard equivalent circuit model (ECM) of a Li-ion cell and provides reliable and efficient SoC estimate in the presence of bounded uncertainties in the battery parameters as well as exogenous disturbances. The theoretical framework of the observer design is not limited to the SoC estimation problem of Li-ion cell but applicable to a wider class of nonlinear systems with both matched and mismatched uncertainties. The main advantage of the proposed observer is to provide a fast and optimal SoC estimate based on minimization over the uncertainty bound. The proposed method is experimentally tested and evaluated for a range of temperatures using the hybrid pulse power characterization test (HPPC), EPA's Federal Test Procedure (FTP75) and Supplemental Test Procedure (US06) data, which demonstrate its effectiveness and feasibility.

Optimal SoC Estimation Considering Hysteresis Effect for Effective Battery Management in Shipboard Batteries

The energy storage is critical in shipboard systems since there is no alternate energy in case of primary energy source failure. Hence, a battery management system (BMS) is necessary to monitor the state of the battery. Since a BMS operates the battery based on its state, an accurate estimation of the state of charge (SoC) is essential. Hysteresis is predominantly present in lead–acid batteries, whose effect is generally not accounted for in existing SoC estimation methods. In this work, the effect of hysteresis on SoC estimation is considered and the differential evolution-based SoC estimation technique is applied to accurately estimate the SoC while minimizing the hysteresis effect. A dynamic charge and discharge dynamic model of a 100-Ah lead–acid battery with ship thruster load is used to study the battery hysteresis. The battery model with the proposed SoC estimation and the BMS algorithm is simulated in MATLAB/SIMULINK 2018A and is tested under different charging and discharging conditions. The proposed model is validated in a real-time testbed comprising of a 62-Ah lead–acid battery connected to a 25 HP thruster of a boat. From the test results, it has been demonstrated that the proposed estimation algorithm reduces the estimation error thereby achieving an accurate SoC.

Precise fabrication of single-atom alloy co-catalyst with optimal charge state for enhanced photocatalysis.

While the surface charge state of co-catalysts plays a critical role for boosting photocatalysis, studies on surface charge regulation via their precise structure control remain extremely rare. Herein, metal-organic framework (MOF) stabilized bimetallic Pd@Pt nanoparticles, which feature adjustable Pt coordination environment and a controlled structure from core-shell to single-atom alloy (SAA), have been fabricated. Significantly, apart from the formation of a Mott-Schottky junction in a conventional way, we elucidate that Pt surface charge regulation can be alternatively achieved by changing its coordination environment and the structure of the Pd@Pt co-catalyst, where the charge between Pd and Pt is redistributed. As a result, the optimized Pd10@Pt1/MOF composite, which involves an unprecedented SAA co-catalyst, exhibits exceptionally high photocatalytic hydrogen production activity, far surpassing its corresponding counterparts.

Optimum State-of-Charge Operating Range for Frequency Regulation of Energy Storage Systems Using a Master–Slave Parallel Genetic Algorithm

Lithium batteries are used for frequency regulation in power systems because of their fast response and high efficiency. Lithium batteries have different life characteristics depending on their type, and it is necessary to set the optimal state-of-charge (SOC) operating range considering these characteristics to obtain the maximum gain. In general, narrowing the operating range increases the service life but may lower the performance of charging and discharging operations in response to frequency fluctuations, and vice versa. We present performance assessment indicators that consider charging and discharging due to frequency variations and lifespan of the batteries. However, to evaluate the performance, while reflecting the non-linear life characteristics of lithium batteries, simulating the entire operation is necessary, which requires a long calculation time. Therefore, we propose a master–slave parallel genetic algorithm to derive the optimal SOC operating range with reduced calculation time. A simulation program was implemented to evaluate the computational performance that determines the optimal SOC range. The proposed method reduces the calculation time while considering the non-linear life characteristics of lithium batteries. It was confirmed that a more accurate SOC operating range could be calculated by simulating the entire life span.

An energy management system for optimal operation of BSS in DC distributed generation environments based on a parallel PSO algorithm

Abstract This paper proposes an energy management system (EMS) for the day-ahead dispatch of battery storage systems (BSS) under a distributed generation environment for direct current (DC) networks, with the main objective of reducing the cost of the energy purchased to the utility grid. This approach considers the state-of-charge (SOC) of the BSS and the production variation of the renewable generators, in particular of wind and photovoltaic technologies, and the variations in the power consumption and energy costs. The proposed EMS uses a master-slave strategy formed by a parallel implementation of the particle swarm optimizer (PPSO) and a multi-period power flow method based on successive approximations (SA), with the aim of achieving the optimal daily operation of the BSS. The objective function selected for the optimization was the reduction of the energy purchasing costs, also including the power balance, devices capabilities and voltage regulation. The effectiveness of the EMS is evaluated in a test system of 21 buses, comparing the solution quality and speed with three optimization techniques published in literature: a black hole optimizer, a continuous genetic algorithm with matrix structure, and a traditional Chu & Beasley genetic algorithm. In addition, two simulation scenarios were used to identify the optimal final SOC conditions for the BSS. Finally, the results show that the proposed EMS provides the best trade-off between quality solution and speed. The simulations are conducted in MATLAB software using sequential quadratic programming.

Self‐learning energy management for plug‐in hybrid electric bus considering expert experience and generalization performance

A self-learning energy management is proposed for plug-in hybrid electric bus, by combining Q-Learning (QL) and Pontryagin's minimum principle algorithms. Different from the existing strategies, the expert experience and generalization performance are focused in the proposed strategy. The expert experience is designed as the approximately optimal reference state-of-charge (SOC) trajectories, and the generalization performance is enhanced by a multiply driving cycle training method. In specific, an efficient zone of SOC is firstly designed based on the approximately optimal reference SOC trajectories. Then, the agent of the QL is trained off-line by taking the expert experience as reference SOC trajectories. Finally, an adaptive strategy is proposed based on the well-trained agent. Specially, two different reward functions are defined. That is, the reward function in the off-line training mainly considers the tracking performance between the expert experience and the SOC, while mainly considering the punishment in the adaptive strategy. Simulation results show that the proposed strategy has good generalization performance and can improve the fuel economy by 22.49%, compared to a charge depleting-charge sustaining (CDCS) strategy.

Optimal State-of-Charge Value for Charge-Sustaining Mode of Plug-In Hybrid Electric Vehicles

For plug-in hybrid electric vehicles or extended range electric vehicles, battery stored energy often cannot fully meet the travel needs, and the battery needs to stay in a charge-sustaining mode to allow for backup sources such as gasoline or diesel to power the vehicle. It is crucial to identify the optimal state-of-charge (SOC) value for the battery to maintain this charge-sustaining mode since this SOC has significant impact to battery degradation. In existing studies, Just-in-Time control proposes that this SOC should be maintained at 55% but without theoretical justification. With the help of a battery degradation model based on solid electrolyte interphase growth, this article develops a method to decide the optimal SOC value for charge-sustaining mode. Following the principle of superposition, degradation during the battery discharging process is divided as a fixed degradation caused by the drop of SOC from maximum to minimum values during charge-depleting mode, and a dynamic degradation caused by the oscillation at the charge-sustaining SOC value. Then this oscillation-caused degradation is further modeled and minimized through the investigation of the side reaction current density. The optimal SOC value obtained will be the SOC at which the side reaction current density has the slowest changing rate. This SOC value indeed relies on battery parameters, charging/discharging current and ambient temperature, and a case study shows that the best range of SOC value is 36%~38% for a 1.8Ah SONY 18650 cell. An average SOC of 37% is therefore recommended for charge-sustaining mode considering the possible errors in SOC estimation.

Synthesis of Optimal Battery State-of-Charge Trajectory for Blended Regime of Plug-in Hybrid Electric Vehicles in the Presence of Low-Emission Zones and Varying Road Grades

The powertrain efficiency for plug-in hybrid electric vehicles (PHEV) can be maximized by gradually discharging the battery in a blended regime, where the engine is regularly used all over the driving cycle. A key step in designing an optimal PHEV control strategy for the blended regime corresponds to synthesis of battery state-of-charge (SoC) reference trajectory. The paper first demonstrates that the optimal SoC trajectory can significantly differ from a typical linear-like shape in the case of varying road grade and presence of low-emission zones (LEZ). Next, dynamic programming (DP)-based optimizations of PHEV control variables are conducted for the purpose of extracting and analyzing optimal SoC trajectory patterns. It is shown that the optimality is closely related to the minimization of SoC trajectory length with respect to travelled distance. This finding is used for SoC reference trajectory synthesis in the presence of LEZ and varying road grades. Finally, the overall PHEV control strategy is applied to a PHEV-type city bus and verified by means of computer simulations in comparison with the DP optimization benchmark.

Analysis of Optimal Battery State-of-Charge Trajectory for Blended Regime of Plug-in Hybrid Electric Vehicle

Plug-in hybrid electric vehicles (PHEV) typically combine several power sources, which call for the use of optimal control strategy design techniques. The PHEV powertrain efficiency can be improved if the battery is gradually discharged by blending fully electric and hybrid driving modes during the whole trip. Here, the battery state-of-charge (SoC) trajectory profile is of particular importance to achieving near-optimal powertrain operation. In order to reveal optimal patterns of SoC trajectory profiles, numerical optimizations of PHEV control variables based on the dynamic programing (DP) algorithm are conducted in the paper. The obtained optimal SoC trajectories are found to form linear-like profiles of minimum length when expressed with respect to travelled distance. Detailed analyses of the DP results point out that the SoC trajectory length is minimized in order to minimize electric losses, which is then reflected in reduced total fuel consumption. This finding is further justified by analyzing the problem of optimal discharging for the simplified battery-only system and for the powertrain as a whole. The impact of engine specific fuel consumption characteristic on the optimal SoC trajectory profile under simplified driving conditions is analyzed, as well.

An adaptive equivalent consumption minimization strategy for plug-in hybrid electric vehicles based on traffic information

Energy management strategies play an important role in performance optimization of plug-in hybrid electric vehicles (PHEVs), and can be further improved by incorporating external traffic information. Motivated by this, an adaptive equivalent consumption minimization strategy considering traffic information is proposed in this study to facilitate the effective energy management of PHEVs. First, the initial equivalent factors in terms of different initial state of charge (SOC) and driving distance are searched by genetic algorithm. Then, the simplified dynamic programming is leveraged to determine the optimal SOC trajectory according to the traffic information with fast calculation speed. The fuzzy controller is employed to regulate the equivalent factor dynamically, thus enabling effective tracking of the reference SOC trajectory. A hardware-in-the-loop simulation platform based on the virtual scene is developed to validate the performance of controller. Simulation and experimental results highlight that the proposed strategy can lead to less fuel consumption, compared to traditional equivalent consumption minimization strategy, thereby proving its feasibility.

Mitigating the Effect of Noise Uncertainty on the Online State-of-Charge Estimation of Li-Ion Battery Cells

Real-time battery state-of-charge (SOC) estimation is critical in many applications. The extended Kalman filter (EKF) has been successfully deployed in SOC estimation allowing real-time SOC monitoring. However, modeling inaccuracies, measurement faults, and wrong initialization can cause the estimation algorithm to diverge. The precise knowledge of statistical information about process and measurements noise is crucial for accurate system modeling and estimation. This paper presents a novel SOC estimation approach based on maximum-likelihood estimation (MLE). The process and measurements models are transformed to an error state propagation system where the innovation covariance is utilized to maximize the likelihood of the multivariate innovation distribution with respect to process and measurement covariances. The MLE formulation allows the estimation of the process and measurement noise covariance magnitudes, which are used to obtain an optimal SOC estimate. The proposed method is validated experimentally using a number of Li-ion battery cells under various testing conditions. The estimation performance is compared with that of the conventional EKF technique as well as previously published results based on autocovariance least-squares measurements noise estimation. The results indicate an enhanced performance for the new algorithm over the traditional EKF across all conducted tests.

Wireless battery charging control for electric vehicles: a user‐involved approach

This study presents a user-involved wireless battery charging approach for electric vehicles, which enables the battery to reach the user-specified state by regulating the charging current provided by a wireless charger with double-sided inductor–capacitor–capacitor compensation topology. Specifically, an optimal state of charge (SOC) trajectory is first generated through formulating and solving an optimisation issue with the consideration of user demand and operating constraints. Next, a cascade control strategy is proposed to regulate the wireless charger to make the battery track the scheduled charging trajectory. The out loop control designs suitable charging current for SOC trajectory tracking, which can effectively suppress the violation of the charging constraints by on-line compensating the battery model bias. In the inner loop, a fuzzy proportion–integration (PI) algorithm is proposed to control the wireless charger to provide the charging current designed by the out loop, in which fuzzy logic algorithm is utilised to on-line tune the PI gains to improve the control performance. Extensive real-time results demonstrate the effectiveness and promise of the proposed user-involved wireless battery charging control strategy.

Optimal Scheduling of Storage Batteries and Power Generators Based on Interval Prediction of Photovoltaics—Monotonicity Analysis for State of Charge

This letter focuses on a day-ahead scheduling problem on thermal power plants and storage batteries based on the information of the interval prediction of photovoltaic (PV) power and demand. To realize an optimal operation, there are three kinds of decision variables to plan, which correspond to a generating power schedule, a charge/discharge (C/D) power schedule, and a state of charge (SOC) schedule. Our purpose is to obtain the exact range of each optimal schedule for any possible PV/demand profiles of the interval prediction. In the previous work, we proposed a method to find the exact ranges of the optimal generation power schedule and the optimal C/D power schedule by showing the sign patterns of the Jacobians with respect to an uncertain renewable parameter. However, the range of the optimal SOC schedule is not derived so far. If the exact range is found, we can offer a guideline for a necessary and sufficient capacity of storage batteries at each time step. To get the range, we show that the sign pattern of the Jacobian for SOC is invariant, more specifically, its sign pattern has negative elements in the lower triangle and positive elements in others. The key to analyzing the sign pattern is to utilize particular properties of an ${M}$ -matrix and a diagonally dominant matrix. As a result, we clarify the sign pattern mathematically, which enables to effectively calculate the exact range of the optimal SOC schedule. This letter completes the monotonicity analysis of all the decision variables in the optimal scheduling problem.

Receding horizon control-based energy management for plug-in hybrid electric buses using a predictive model of terminal SOC constraint in consideration of stochastic vehicle mass

The factor of stochastic vehicle mass can greatly affect the optimality of energy management for plug-in hybrid electric buses. However, current studies usually take the vehicle mass as constant, which is inevitably far away from reality. This paper responds to this problem by investigating a receding horizon control (RHC)-based energy management together with a predictive model of terminal state of charge (SOC) constraint. The predictive model can reinforce the local feature of the terminal SOC constraint, by a piecewise nonlinear regression model considering the stochastic vehicle mass. Especially, the stochastic vehicle mass is designed as stochastic variable at each road segment (the route between neighbored bus stops), and Optimal Latin Hypercube Design algorithm is deployed to sample and probe the design space constituted by the stochastic variables. Besides, the predictive model is constructed by partial least squares method, based on the sampled design space and corresponding optimal SOCs from dynamic programming. Simulation results show that the proposed predictive model is reasonable and can optimally predict the terminal SOC constraint at every receding horizon. Furthermore, although the fuel economy of the RHC strategy is worse than the DP strategy, it can be improved by 5.29% at least, compared to the rule-based strategy.

Noninvasive Vehicle‐to‐Load Energy Management Strategy to Prevent Li‐Ion Batteries Premature Degradation

Today, electric vehicles available in the market aspire to offer different connections to the end user, for instance, Vehicle to Grid (V2G), Vehicle to Building (V2B), Vehicle to Home (V2H), Vehicle to Vehicle (V2V), and Vehicle to Load (V2L), among others. Notwithstanding these versatility options toward the development of a sustainable society, the additional degradation of the energy storage systems once those operate in extra discharge modes is inevitable. Therefore, in this paper, an energy management strategy (EMS) which operates autonomously and noninvasively as an additional layer to the battery management system (BMS) is proposed. The EMS limits the current flow avoiding high and low temperatures, low state of charge (SoC), high deep of discharge (DoD), noncentered DoD around an optimal SoC point, and high charge and discharge rates. The proposed EMS is evaluated by long‐term simulations with a Li‐Ion battery degradation model and realistic weather conditions, during standard driving cycles including the V2L operation. The effectiveness and simplicity of tuning of the proposed EMS allow estimating and increasing the life expectancy of the Li‐Ion battery bank, by limiting the energy used for V2L operation.

Adaptive Fuzzy Logic Energy Management Strategy Based on Reasonable SOC Reference Curve for Online Control of Plug-in Hybrid Electric City Bus

The key challenge in energy management of plug-in hybrid electric vehicles is how to macroscopically plan the battery energy considering trip information while microscopically distributing the torque between power sources to improve the energy efficiency of the hybrid propulsion system. Nowadays, future partial trip information can be obtained from an intelligent transportation system and a navigation system when traveling starts. But how to use these trip information sufficiently remains to be further studied. Moreover, the online energy management strategy should not take up too many resources of micro-controller. Based on these conditions, we proposed a novel energy management strategy for plug-in hybrid electric city buses. First, Pontryagin’s minimum principle was used to obtain the optimal results of different driving cycles. Then, a neural network module was designed and trained to learn the mechanisms of optimal state-of-charge (SOC) curves. When trip starts, the neural network module can be used to generate a reasonable battery SOC reference curve according to the partial trip information available. Finally, an adaptive fuzzy logic controller was applied to follow the trend of the SOC reference curve. The main contribution of this paper is that the effectiveness of battery energy planning by comprehensively considering the future partial trip information and historical optimal SOC curves is verified, which provides a new perspective for real vehicle energy management. Simulation results show 4.61%–13.49% fuel savings on the trained and untrained driving cycles as compared with the charge-depleting and charge-sustaining strategy.

Profit-Maximizing Planning and Control of Battery Energy Storage Systems for Primary Frequency Control

We consider a two-level profit-maximizing strategy, including planning and control, for battery energy storage system (BESS) owners that participate in the primary frequency control market. Specifically, the optimal BESS control minimizes the operating cost by keeping the state of charge (SoC) in an optimal range. Through rigorous analysis, we prove that the optimal BESS control is a “state-invariant” strategy in the sense that the optimal SoC range does not vary with the state of the system. As such, the optimal control strategy can be computed offline once and for all with very low complexity. Regarding the BESS planning, we prove that the minimum operating cost is a decreasing convex function of the BESS energy capacity. This leads to the optimal BESS sizing that strikes a balance between the capital investment and operating cost. This paper here provides a useful theoretical framework for understanding the planning and control strategies that maximize the economic benefits of BESSs in ancillary service markets.