The operation of a community energy storage system (CESS) is challenging due to the volatility of photovoltaic distributed generation, electricity consumption, and energy prices. Selecting the optimal CESS setpoints during the day is a sequential decision problem under uncertainty, which can be solved using dynamic learning methods. This paper proposes a reinforcement learning (RL) technique based on temporal difference learning with eligibility traces (ET). It aims to minimize the day-ahead energy costs while maintaining the technical limits at the grid coupling point. The performance of the RL is compared against an oracle based on a deterministic mixed-integer second-order constraint program (MISOCP). The use of ET boosts the RL agent learning rate for the CESS operation problem. The ET effectively assigns credit to the action sequences that bring the CESS to a high state of charge before the peak prices, reducing the training time. The case study shows that the proposed method learns to operate the CESS effectively and ten times faster than common RL algorithms applied to energy systems such as Tabular Q-learning and Fitted-Q. Also, the RL agent operates the CESS 94% near the optimal, reducing the energy costs for the end-user up to 12%.@en

This paper proposes a new power flow (PF) formulation for electrical distribution systems using the current injection method and applying the Laurent series expansion. Two solution algorithms are proposed: a Newton-like iterative procedure and a fixed-point iteration based on the successive approximation method (SAM). The convergence analysis of the SAM is proven via the Banach fixed-point theorem, ensuring numerical stability, the uniqueness of the solution, and independence on the initializing point. Numerical results are obtained for both proposed algorithms and compared to well-known PF formulations considering their rate of convergence, computational time, and numerical stability. Tests are performed for different branch R/X ratios, loading conditions, and initialization points in balanced and unbalanced networks with radial and weakly-meshed topologies. Results show that the SAM is computationally more efficient than the compared PFs, being more than ten times faster than the backward–forward sweep algorithm.@en

Linear optimal power flow (OPF) formulations are powerful tools applied to a large number of problems in power systems, e.g., economic dispatch, expansion planning, state estimation, congestion management, electricity markets, among others. This article proposes a novel mixed-integer linear programming formulation for the ac-OPF of three-phase unbalanced distribution networks. The model aims to minimize the total energy production cost while guaranteeing the network's voltage and current magnitude operational limits. New approximations of the Euclidean norm, which is present in the calculation of nodal voltage and branch current magnitudes, are introduced by applying a linear transformation of weighted norms and a set of intersecting planes. The accuracy, optimality, feasibility, and scalability of the proposed linearizations are compared with common linear approximations in the literature using two unbalanced distribution test systems. The obtained results show that the proposed formulation is computationally more efficient (almost twice) while being as accurate and more conservative than the benchmarked approaches with maximum errors lower than 0.1%. Thus, its potential application in a variety of distribution systems operation and planning optimization problems is endorsed.@en

In this paper, a Reinforcement Learning (RL)-based approach to optimally dispatch PV inverters in unbalanced distribution systems is presented. The proposed approach exploits a decentralized architecture in which PV inverters are operated by agents that perform all computational processes locally; while communicating with a central agent to guarantee voltage magnitude regulation within the distribution system. The dispatch problem of PV inverters is modeled as a Markov Decision Process (MDP), enabling the use of RL algorithms. A rolling horizon strategy is used to avoid the computational burden usually associated with continuous state and action spaces, coupled with a computationally efficient learning algorithm to model the action-value function for each PV inverter. The effectiveness of the proposed decentralized RL approach is compared with the optimal solution provided by a centralized nonlinear programming (NLP) formulation. Results showed that within several executions, the proposed approach converges either to the optimal solution or to solutions with a PV curtailment excess of less than 2.5% while still enforcing voltage magnitude regulation.@en

This paper introduces an energy management system (EMS) aiming to minimize electricity operating costs using reinforcement learning (RL) with a linear function approximation. The proposed EMS uses a Q-learning with tile coding (QLTC) algorithm and is compared to a deterministic mixed-integer linear programming (MILP) with perfect forecast information. The comparison is performed using a case study on an industrial manufacturing company in the Netherlands, considering measured electricity consumption, PV generation, and wholesale electricity prices during one week of operation. The results show that the proposed EMS can adjust the prosumer's power consumption considering favorable prices. The electricity costs obtained using the QLTC algorithm are 99% close to those obtained with the MILP model. Furthermore, the results demonstrate that the QLTC model can generalize on previously learned control policies even in the case of missing data and can deploy actions 80% near to the MILP's optimal solution.@en

This article proposes a framework to identify, visualize, and quantify risk of potential over/under voltage due to annual energy consumption and PV generation growth. The stochastic modeling considers the following: (i) Active and reactive power profiles for distribution transformers, dependent on annual energy consumption and activity in the serviced areas. (ii) Variable solar irradiance profiles that allow a broader range of PV generation scenarios for sunny, overcast, and cloudy days. The proposed framework uses multivariate-t copulas to model temporal correlations between random variables to generate synthetic scenarios. A probabilistic power flow is computed using the generated scenarios to define critical static operating regions. Results show that classical approaches may underestimate the maximum PV capacity of distribution networks when local irradiance conditions are not considered. Moreover, it is found that including annual energy consumption growth is critical to establishing realistic PV installation capacity limits. Finally, a sensitivity analysis shows that taking a 5% of overvoltage risk could increase up to 15% of the PV installed capacity limits.@en

A photovoltaic (PV)-rich low-voltage (LV) distribution network poses a limit on the export power of PVs due to the voltage magnitude constraints. By defining a customer export limit, switching off the PV inverters can be avoided, and thus reducing power curtailment. Based on this, this paper proposes a mixed-integer nonlinear programming (MINLP) model to define such optimal customer export. The MINLP model aims to minimize the total PV power curtailment while considering the technical operation of the distribution network. First, a nonlinear mathematical formulation is presented. Then, a new set of linearizations approximating the Euclidean norm is introduced to turn the MINLP model into an MILP formulation that can be solved with reasonable computational effort. An extension to consider multiple stochastic scenarios is also presented. The proposed model has been tested in a real LV distribution network using smart meter measurements and irradiance profiles from a case study in the Netherlands. To assess the quality of the solution provided by the proposed MILP model, Monte Carlo simulations are executed in OpenDSS, while an error assessment between the original MINLP and the approximated MILP model has been conducted.@en

This paper presents a new linear optimal power flow model for three-phase unbalanced electrical distribution systems considering binary variables. The proposed formulation is a mixed-integer linear programming problem, aiming at minimizing the operational costs of the network while guaranteeing operational constraints. Two new linearizations for branch current and nodal voltage magnitudes are introduced. The proposed branch current magnitude linearization provides a discretization of the Euclidean norm through a set of intersecting planes, while the bus voltage magnitude approximation uses a linear combination of the L1 and the L norm. The proposed approach is compared to a nonlinear power flow for an unbalanced distribution system with fixed power injections. The obtained results showed errors of less than 4% for currents and 0.005% for voltages, demonstrating that satisfactory accuracy may be obtained using the proposed linearizations. @en