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A B S T R A C T The probabilistic and intermittent output power of Wind Turbines (WT) is one major inconsistency of these Renewable Energy Sources (RES). Battery Energy Storage Systems (BESS) are a suitable solution to mitigate this intermittency by smoothening WT’s output power. Although the main benefit of BESSs mentions as peak shaving and load-shifting, but in this research, it will verify that optimal placement and sizing them jointly with WTs can lead to more benefits like compensating the required system’s reactive power support from WTs. The reactive power size of WTs and BESSs will be derived from the result of the joint sizing and placement in this study, as well as their active power output to meet the load demand. This can facilitate WTs and BESSs contribution to cover the system’s required reactive power and their participation in the reactive power market and ancillary services. This paper also proposes new cost functions for both WTs and BESSs and minimizes their cost while ensuring minimal total loss (active and reactive) in the power distribution system. This can benefit both WTs’ and BESSs’ owners as well as system operators. Suitable placement and sizing of the WTs and BESSs can also improve the load bus voltage profiles, which can benefit the end-users, and will verify using the proposed optimization by different case studies on the 33 bus distribution system. The results of case studies ascertain the consistency of the proposed formulation for placement and sizing BESSs and WTs jointly, as well as other benefits to the power system, the power plant owners, and system operators. 

A B S T R A C T This paper proposes a model for parameter estimation of Vanadium Redox Flow Battery based on both the electrochemical model and the Equivalent Circuit Model. The equivalent circuit elements are found by a newly proposed optimization to minimized the error between the Thevenin and KVL-based impedance of the equivalent circuit. In contrast to most previously proposed circuit models, which are only introduced for constant current charging, the proposed method is applicable for all charging procedures, i.e., constant current, constant voltage, and constant current-constant voltage charging procedures. The proposed model is verified on a nine-cell VRFB stack by a sample constant current-constant voltage charging. As observed, in constant current charging mode, the terminal voltage model matches the measured data closely with low deviation; however, the terminal voltage model shows discrepancies with the measured data of VRFB in constant voltage charging. To improve the proposed circuit model’s discrepancies in constant voltage mode, two Kalman filters, i.e., hybrid extended Kalman filter and particle filter estimation algorithms, are used in this study. The results show the accuracy of the proposed equivalent with an average deviation of 0.88% for terminal voltage model estimation by the extended KF-based method and the average deviation of 0.79% for the particle filter-based estimation method, while the initial equivalent circuit has an error of 7.21%. Further, the proposed procedure extended to estimate the state of charge of the battery. The results show an average deviation of 4.2% in estimating the battery state of charge using the PF method and 4.4% using the hybrid extended KF method, while the electrochemical SoC estimation method is taken as the reference. These two Kalman Filter based methods are more accurate compared to the average deviation of state of charge using the Coulomb counting method, which is 7.4%. 

ABSTRACT State of Charge (SoC) and discharge capacity of the batteries are parameters that cannot be determined directly from the battery monitoring and control system and requires estimation. Current and voltage sensors have inherent error and delay leading to inaccurate measurements leading to inaccurate SoC and discharge capacity estimations. These sensors also have an additional cost to the battery system. This paper proposes a sensorless approach to estimate parameters of Vanadium Redox Flow Batteries (VRFBs) for both CC and CV charging methods by estimating battery current in CV mode and terminal voltage in CC mode. The results of estimations by the sensorless approach show a maximum relative error of 0.0035 in estimating terminal voltage in CC charging and a maximum relative error of 0.045 in estimating charging current in CV mode. Furthermore, long- term operation of vanadium redox flow batteries causes ion diffusions across the membrane and the depletion of active materials, which leads to capacity fading in VRFBs and inaccurate SoC estimation. To address the inaccuracy of SoC estimation in the long-term use of the battery, the capacity fading model is also considered for VRFBs in this paper. Experimental results show a 19% electrolyte volume change in the positive and negative tanks after 200 cycles of charge/discharge due to the bulk electrolyte transfer between the positive and negative sides of the battery system. This change of electrolyte volume results in 13.73% capacity fading after 200 cycles of charging/discharging. The SoC also changes by 7.1% after 200 cycles, due to the capacity and electrolyte volume loss, which shows the necessity of considering capacity fading in long-term use of the battery.