# Computational Optimal Control of Battery Energy Storage Systems

• Julio Cesar Gonzalez-Saenz

Student thesis: Doctoral Thesis

### Abstract

The interest in various renewable energy topics has dramatically increased since the world is moving towards a zero-carbon economy, and as humanity tackles climate change. Of particular interest are the various aspects of using rechargeable batteries, specifically fast charging procedures. This work studied three different engineering optimal control problems: temperature consideration in the energy dispatch in a wind turbine-grid-battery configuration, optimal charging time using different battery models, and the optimal battery cycle considering degradation in the day-ahead electricity market. The problems were formulated as optimal control problems.
Energy dispatch using a model predictive control methodology in a wind turbine- grid-battery configuration was studied. A mathematical model of a lead-acid battery and an unscented Kalman filter were employed for the problem formulation. The investigation aimed to study how and to what extent the temperature affected the battery operation. The controller, based on the model predictive control framework, utilises an online optimisation algorithm to determine the optimal current charging profile of the lead-acid battery, which brings the energy supplied to the grid closer to the forecasted wind energy. The study found that by considering the internal temperature of the electrolyte in the problem formulation, the performance of the optimal controller improved significantly.
Optimal control methods were used to determine the most efficient charging patterns for lithium-ion batteries. The study involved numerical simulations that modelled various charging current profiles using the equivalent circuit battery model specifically de- signed for lithium-ion batteries. The effectiveness of the Constant Current - Constant Voltage (CC-CV) protocol was evaluated, and crucial enhancements were proposed to mitigate temperature-induced damage. To formulate the optimal control strategy, both the minimum time approach and the maximisation of input current approach were utilised. To the author’s knowledge, this is the first time this charging approach has been framed as an optimal control problem and solved using direct collocation methods.
An efficient way of charging a lithium-ion battery was proposed using a simplified electrochemical model and direct collocation methods for optimal control. To effectively address the problem, an optimal control problem formulation and a direct solution approach were adopted. The problem was transformed into a linear state form. The results reveal that, in some cases, the optimal current profile is similar to the current profile used in the Constant Current–Constant Voltage charging protocol. The suggested approach deals with the minimum time optimal control scenario and considers the balance between the overall charging duration, the enhancement of lithium bulk concentration, and energy effectiveness, which can have practical applications.
A case study was conducted on Belgium’s day-ahead electricity market to deter- mine the best charging and discharging schedules with varying objectives, specifically maximising profits while considering capacity degradation. Two models were used to simulate battery cell behaviour and degradation mechanisms: the equivalent circuit model combined with empirical degradation parameters and the bucket model. The results showed that integrating degradation costs into the market strategy for battery operators is significant, as it affects the battery’s dynamic behaviour. The approach taken in this study offers a more comprehensive model, capturing the intricacies of battery degradation, providing a fine and adaptive time domain representation, focusing on the day-ahead market, and utilising accurate direct methods for optimal control.
Date of Award 25 Jun 2024 English University of Portsmouth Victor Becerra (Supervisor) & Branislav Vuksanovic (Supervisor)

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