This paper proposes a real-time schedule model of a microgrid (MG) for maximizing battery energy storage (BES) utilization. To this end, a BES life model is linearized using piece-wise linearization and big-M method to assess the BES life loss (BLL) in a real-time manner. The cost-effective schedule model of the MG with multiple energy resources aims to maximize BES utilization while ensuring its sufficient lifespan. Corresponding to the optimization model, approximate dynamic programming (ADP) for maximizing BES utilization (ADP-MBU) in the real-time schedule is proposed to optimize the system under stochastic environments. In ADP-MBU, a new value function approximation method employing the BES cumulative life loss (BCLL) is developed to improve the optimality and applicability. The proposed ADP-MBU algorithm can achieve satisfactory approximate optimality while reflecting the variation of real-time BLL. Case studies validate the applicability of the proposed MG schedule model and the advantages of the proposed ADP-MBU algorithm.

This paper proposes a fully distributed approximate dynamic programming (FD-ADP) algorithm framework for real-time economic dispatch of a microgrid (MG). Firstly, a modified distributed consensus-based algorithm (DCBA) framework with power restriction factors is proposed to distributedly obtain the real-time ED decision of MG containing distributed energy resources with linear cost functions, which improves the convergence stability compared with the traditional DCBA framework. Then, combined with the approximate dynamic programming (ADP) theory, a FD-ADP algorithm is proposed to deal with data uncertainties. To this end, the piece-wise linear (PWL) function is applied to approximate the value function, and a distributed slope update approach is proposed to embed empirical knowledge into the value function while ensuring the distributed property in off-line training. With the well-trained PWL function assisting in decision, the distributed real-time ED strategy of MG with approximate global optimality is obtained by the proposed FD-ADP algorithm during the entire schedule horizon (e.g., 24 hours). Finally, case studies on the modified IEEE 6-bus MG system and IEEE 123-bus MG system demonstrate the superiority of solution convergence, validity of distributed training, and optimality of distributed schedule of the proposed FD-ADP algorithm.

This paper aims to promote the lifespan benefit of multiple battery energy storage (BES) in real-time scheduling. An effective real-time scheduling model is formulated with the proposed concept of multiple BES (MBES) comprehensive lifespan benefit, which makes a tradeoff between MBES short-term operation and long-term profits. Then, a novel piece-wise linear function (PLF) based continuous ADP (PLFC-ADP) algorithm is proposed to optimize the scheduling model under uncertainties. A new decomposed value function approximation method employing both BES state of charge and BES cumulative life loss is proposed to achieve high optimality and wide applicability. Combined with the difference-based decomposed slope update method to train the PLF slopes with empirical knowledge, the proposed PLFC-ADP algorithm can handle the increasing computation complexity of MBES scheduling and obtain the approximate optimality of stochastic real-time scheduling. Numerical analysis demonstrates the validity of the proposed scheduling model, and superior computation tractability and solution optimality of the proposed PLFC-ADP algorithm.

Due to the addition of the drag reducer in refined oil pipelines for increasing the pipeline throughput as well as reducing energy consumption, the classical method based on the Darcy-Weisbach Formula for precise pressure loss calculation presents a large error. Additionally, the way to accurately calculate the pressure loss of the refined oil pipeline with the drag reducer is in urgent need. The accurate pressure loss value can be used as the input parameter of pump scheduling or batch scheduling models of refined oil pipelines, which can ensure the safe operation of the pipeline system, achieving the goal of energy-saving and cost reduction. This paper proposes the data-driven modeling of pressure loss for multi-batch refined oil pipelines with the drag reducer in high accuracy. The multi-batch sequential transportation process and the differences in the physical properties between different kinds of refined oil in the pipelines are taken into account. By analyzing the changes of the drag reduction rate over time and the autocorrelation of the pressure loss sequence data, the sequential time effect of the drag reducer on calculating pressure loss is considered and therefore, the long short-term memory (LSTM) network is utilized. The neural network structure with two LSTM layers is designed. Moreover, the input features of the proposed model are naturally inherited from the Darcy-Weisbach Formula and on adaptation to the multi-batch sequential transportation process in refined oil pipelines, using the particle swarm optimization (PSO) algorithm for network hyperparameter tuning. Case studies show that the proposed data-driven model based on the LSTM network is valid and capable of considering the multi-batch sequential transportation process. Furthermore, the proposed model outperforms the models based on the Darcy-Weisbach Formula and multilayer perceptron (MLP) from previous studies in accuracy. The MAPEs of the proposed model of pipelines with the drag reducer are all less than 4.7% and the best performance on the testing data is 1.3627%, which can provide the calculation results of pressure loss in high accuracy. The results also indicate that the model’s capturing sequential effect of the drag reducer from the input data set contributed to improving the calculation accuracy and generalization ability.

This article develops a fully decentralized approximate dynamic programming (FD-ADP) algorithm for stochastic energy management (SEM) of a networked microgrid (NMG) system. First, considering the ac power flow constraints, an alternating direction method of multipliers (ADMM)-based decentralized SEM framework is proposed for NMG coordination. Then, a transactive energy scheme is introduced to further decouple each microgrid (MG) optimization for privacy enhancement and computation reduction. Next, a FD-ADP algorithm is proposed to cope with the real-time uncertainties. The piecewise linear function (PLF) is employed for value function approximation, and a fully decentralized PLF slope update method based on ADMM framework is designed for decentralized property preservation, which trains the value function just through each MG local information and neighboring communication, thus the well-trained decentralized PLF slopes can help achieve the global optimal SEM strategy for NMG coordination under stochastic environments. Finally, case studies demonstrate the effectiveness of the proposed ADMM-based FD-ADP algorithm in terms of decentralized optimization, decentralized training, and global optimality.