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The dynamic dispatch (DD) of battery energy storage systems (BESSs) in microgrids integrated with volatile energy resources is essentially a multiperiod stochastic optimization problem (MSOP). Because the life span of a BESS is significantly affected by its charging and discharging behaviors, its lifecycle degradation costs should be incorporated into the DD model of BESSs, which makes it non-convex. In general, this MSOP is intractable. To solve this problem, we propose a reinforcement learning (RL) solution augmented with Monte-Carlo tree search (MCTS) and domain knowledge expressed as dispatching rules. In this solution, the Q-learning with function approximation is employed as the basic learning architecture that allows multistep bootstrapping and continuous policy learning. To improve the computation efficiency of randomized multistep simulations, we employed the MCTS to estimate the expected maximum action values. Moreover, we embedded a few dispatching rules in RL as probabilistic logics to reduce infeasible action explorations, which can improve the quality of the data-driven solution. Numerical test results show the proposed algorithm outperforms other baseline RL algorithms in all cases tested.

The dynamic dispatch (DD) of battery energy storage systems (BESSs) in microgrids integrated with volatile energy resources is essentially a multiperiod stochastic optimization problem (MSOP). Because the life span of a BESS is significantly affected by its charging and discharging behaviors, its lifecycle degradation costs should be incorporated into the DD model of BESSs, which makes it non-convex. In general, this MSOP is intractable. To solve this problem, we propose a reinforcement learning (RL) solution augmented with Monte-Carlo tree search (MCTS) and domain knowledge expressed as dispatching rules. In this solution, the Q-learning with function approximation is employed as the basic learning architecture that allows multistep bootstrapping and continuous policy learning. To improve the computation efficiency of randomized multistep simulations, we employed the MCTS to estimate the expected maximum action values. Moreover, we embedded a few dispatching rules in RL as probabilistic logics to reduce infeasible action explorations, which can improve the quality of the data-driven solution. Numerical test results show the proposed algorithm outperforms other baseline RL algorithms in all cases tested.

Fast decoupled state estimation (FDSE) is proposed for distribution networks, with fast convergence and high efficiency. Conventionally, branch current magnitude measurements cannot be incorporated into FDSE models; however, in this paper, branch ampere measurements are reformulated as active and reactive branch loss measurements and directly formulated in the proposed FDSE model. Using the complex per unit normalization technique and special chosen state variables, the performance of this FDSE can be guaranteed when it is applied to distribution networks. Numerical tests on seven different distribution networks show that this method outperforms Newton type solutions and is a promising method for practical application.

Fast decoupled state estimation (FDSE) is proposed for distribution networks, with fast convergence and high efficiency. Conventionally, branch current magnitude measurements cannot be incorporated into FDSE models; however, in this paper, branch ampere measurements are reformulated as active and reactive branch loss measurements and directly formulated in the proposed FDSE model. Using the complex per unit normalization technique and special chosen state variables, the performance of this FDSE can be guaranteed when it is applied to distribution networks. Numerical tests on seven different distribution networks show that this method outperforms Newton type solutions and is a promising method for practical application.

State estimation (SE) of distribution networks heavily relies on pseudo measurements that introduce significant errors, since real-time measurements are insufficient. Interval SE models are regularly used, where true values of system states are supposed to be within the estimated ranges. However, conventional interval SE algorithms cannot consider the correlations of same interval variables in different terms of constraints, which results in overly conservative estimation results. In this paper, we propose a Linear Programming (LP) Contractor algorithm that uses a relative distance measure (RDM) interval operation to solve this problem. In the proposed model, measurement errors are assumed to be bounded into given sets, thus converting the state variables to RDM variables. In this case, the SE model is a non-convex model, and the solution credibility cannot be guaranteed. Therefore, each nonlinear measurement equation in the model is transformed into dual inequality linear equations using the mean value theorem. The SE model is finally reformulated as a linear programming contractor that iteratively narrows the upper and lower bounds of the system state variables. Numerical tests on IEEE three-phase distribution networks show that the proposed method outperforms the conventional interval-constrained propagation, modified Krawczyk-operator and optimization based interval SE methods.

State estimation (SE) of distribution networks heavily relies on pseudo measurements that introduce significant errors, since real-time measurements are insufficient. Interval SE models are regularly used, where true values of system states are supposed to be within the estimated ranges. However, conventional interval SE algorithms cannot consider the correlations of same interval variables in different terms of constraints, which results in overly conservative estimation results. In this paper, we propose a Linear Programming (LP) Contractor algorithm that uses a relative distance measure (RDM) interval operation to solve this problem. In the proposed model, measurement errors are assumed to be bounded into given sets, thus converting the state variables to RDM variables. In this case, the SE model is a non-convex model, and the solution credibility cannot be guaranteed. Therefore, each nonlinear measurement equation in the model is transformed into dual inequality linear equations using the mean value theorem. The SE model is finally reformulated as a linear programming contractor that iteratively narrows the upper and lower bounds of the system state variables. Numerical tests on IEEE three-phase distribution networks show that the proposed method outperforms the conventional interval-constrained propagation, modified Krawczyk-operator and optimization based interval SE methods.

This paper introduces a robust sparse recovery model for compressing bad data and state estimation (SE), based on a revised multi-stage convex relaxation (R-Cap-ped-L1) model. To improve the calculation efficiency, a fast decoupled solution is adopted. The proposed method can be used for three-phase unbalanced distribution networks with both phasor measurement unit and remote terminal unit measurements. The robustness and the computational efficiency of the R-Capped-L1 model with fast decoupled solution are compared with some popular SE methods by numerical tests on several three-phase distribution networks.

This paper introduces a robust sparse recovery model for compressing bad data and state estimation (SE), based on a revised multi-stage convex relaxation (R-Cap-ped-L1) model. To improve the calculation efficiency, a fast decoupled solution is adopted. The proposed method can be used for three-phase unbalanced distribution networks with both phasor measurement unit and remote terminal unit measurements. The robustness and the computational efficiency of the R-Capped-L1 model with fast decoupled solution are compared with some popular SE methods by numerical tests on several three-phase distribution networks.