• Energy Research

This paper proposes a probabilistic optimal power flow (POPF) for unbalanced three-phase electrical distribution systems considering robust constraints. Wind velocity, solar irradiation, and demands are considered as exogenous random variables with dissimilar probability distribution functions. The proposed two-stage POPF model determines the optimal generation dispatch that minimizes the average production cost while satisfying probabilistically robust constraints. The robustness of the solution is adjusted through a parameter involving the first two moments of the random state variables. The $2m+1$ point estimate method (PEM) provides the scenarios for the proposed POPF model, which can be solved using commercial solvers. The model's accuracy is evaluated by comparing the results obtained with the PEM and with a classical scenario generator technique. The model is validated through two IEEE distribution feeders with 13 and 123 nodes, comprising dispatchable and renewable generation. Results show that the model can accurately estimate the mean and standard deviation of the state random variables when compared with results obtained through Monte Carlo simulations. Various levels of conservatism are assessed, demonstrating the model's flexibility and applicability.

This paper proposes a two-stage stochastic market clearing (SMC) model based on a semidefinite programming (SDP) relaxation. The SMC model aims at determining the day-ahead schedule (DA) and the real-time (RT) balance settlement that minimize the total expected production cost. The network capacity constraints are considered in the proposed model through an AC power flow formulation, while the uncertainty in the renewable-based generation is taking into account using a set of stochastic scenarios. In order to solve the proposed non-linear programming model, a SDP relaxation is used. An illustrative example (3-bus test system) and the IEEE Reliability 24-bus test system are used to show the effectiveness and accuracy of the proposed model. Results shown that the proposed SDP relaxation introduce a negligible error, when compared with the solution after solving the original non-linear model.

With the recent advancements in power electronics for wind turbines (WTs) and increasing penetration of wind energy, wind power plants (WPP) have become necessary contributors of reactive power support for the bulk power system. Balancing reactive power support with individual WT operating requirements in a cost-effective manner is a challenge for WPP designers. In this paper, we present a methodology to optimize the WPP reactive power capability as seen from the point of common coupling (PCC), accounting for steady-state operating capabilities of the WPP equipment. Thus, the proposed methodology determines the configuration of the tap-changing transformers within the WPP that maximizes the amount of reactive power the WPP can either consume or inject to the network, considering uncertain levels of wind power generation and voltage magnitudes at the PCC. The optimized reactive power capability (ORPC) problem is initially formulated as a mixed-integer nonlinear programming (MINLP) model. Then, a set of efficient linearization techniques are used to obtain a mixed-integer linear programming (MILP) model that can be solved via off-the-shelf mathematical programming solvers. Results demonstrate that the proposed MILP model is a scalable, flexible and accurate method to maximize the reactive power capability of WPP.

Abstract This paper presents a mixed-integer second-order conic programming (MISOCP) model to solve the reconfiguration problem of electrical distribution systems, considering the simultaneous minimization of total active power losses and improvement of customer-oriented reliability indices. The reliability indices considered in this paper are the system average interruption frequency index (SAIFI), the system average interruption duration index (SAIDI), and the energy not supplied (ENS). Under radiality, the proposed model satisfies the operational constraints of the reconfiguration problem, i.e., the voltage magnitude limits of the nodes and the current capacities of the conductors are not violated. The use of an MISOCP model guarantees convergence to optimality via convex optimization software tools. A multi-objective optimization approach is used to generate a full Pareto front surface that shows the conflict between the active power loss minimization and the improvement of the reliability indices in the reconfiguration problem. Finally, in order to test and verify the proposed methodology, a 43-node test system and a real 136-node system were employed.

This paper presents a stochastic mixed-integer nonlinear programming (MINLP) model for the optimal operation of islanded microgrids in the presence of stochastic demands and renewable resources. In the proposed formulation, the microgrid is modeled as an unbalanced three-phase electrical distribution system comprising distributed generation (DG) units with droop control, battery systems (BSs) and wind turbines (WTs). The stochastic nature of the consumption and the renewable generation is considered through a scenario-based approach, which determines the optimal values of the decision variables that minimize the average operational cost of the microgrid. A set of efficient linearizations are used to transform the proposed MINLP model into an approximated convex model that can be solved via commercial solvers. In order to assess the effectiveness of the obtained solution, Monte Carlo simulations (MCS) are carried out. Results show that the proposed model considers the uncertainty while reducing the average operational costs and load curtailments, when compared with a deterministic model.

This paper presents a novel approach for distributed management of energy communities. The proposed method utilizes a stochastic profile steering algorithm as a greedy heuristic. The optimization process considers random parameters such as local forecasted demand, photovoltaic (PV) production, and the initial energy of electric vehicles (EVs) as embedded scenarios. Profile steering coordinates the flexible electricity assets within an energy community by determining the contribution of each prosumer’s profile to the average value of the objective function. It iteratively selects the prosumer that contributes the most until no further improvements can be made. This process scales linearly with the number of controllable prosumers and can achieve various community-level objectives, such as maximizing self-sufficiency or minimizing aggregated cost-of-energy, even when dealing with non-convex optimization problems for modeling each prosumer’s local energy management system. The outcome of the proposed method optimizes the average value of the community’s objective while ensuring that grid limitations are met within a specified probability. The proposed method is evaluated through simulations involving small-scale communities (5 households) and large-scale communities (100 households). The results demonstrate the efficiency, flexibility, and scalability of the proposed method, as well as its ability to reschedule the aggregated demand to ensure that grid limits are not violated with at least a 95% probability.

Unlike centralized versions, a distributed self-healing system (SHS) for electrical distributed systems is less vulnerable to single-point failures (or attacks), requires less information from the agents, and is more scalable. However, optimality is challenging to achieve because binary variables are used in the modelling of the distributed service restoration problem. To deal with this challenge, this paper proposes an enhanced alternating direction method of multipliers (ADMM)based algorithm used to developed a fully distributed SHS in electrical distribution networks. Hereby, three ADMM-based heuristics are executed in parallel to improve the chances of obtaining a feasible solution. However, if none of the heuristics converge within given reasonable time, the proposed distributed SHS uses a basic restoration plan that is feasible in terms of topology and operational constraints. Results using the IEEE 123node system show that the proposed distributed SHS is reliable and it always provides a feasible solution.

Abstract This paper presents a stochastic mixed-integer nonlinear programming model for the optimal energy management system of unbalanced three-phase of alternating current microgrids. The proposed model considers the following random variables: nodal demands, nodal renewable generation and voltage reference at the point of common coupling. Furthermore, the proposed model is aimed at providing resilient energy management system solutions via contingency constraints. The proposed mixed-integer nonlinear programming model is transformed into a mixed-integer linear programming model through a set of linearizations that can be solved via off-the-shelf convex programming solvers. The analyzed microgrid comprises photovoltaic generation, energy storage systems, electric vehicle chargers, direct load control, and non-renewable generation, which operates when the microgrid is in islanded mode. The stochastic nature of the problem is considered through a scenario-based approach. The solution to the model determines the day-ahead operation of the microgrid resources that minimizes the average operational cost. An unexpected islanded operation at any given time is considered via contingency constraints. Tests are performed using data of the real microgrid at the Laboratory of Intelligent Electrical Networks (LabREI), at University of Campinas. Results show that the proposed model produces resilient day-ahead energy management system solutions while minimizing the average operational costs and maximizing the use of local renewable energy sources.

The optimal operation planning (OOP) of electrical distribution systems (EDS) is very sensible to the quality of the short-term load forecasts. Assuming aggregated demands in EDS as univariate non-stationary seasonal time series, and based on historical measurements gathered by smart meters, this paper presents a parsimonious short-term load forecasting method to estimate the expected outcomes of future demands, and the standard deviations of forecast errors. The chosen short-term load forecasting method is an adaptation of the multiplicative autoregressive integrated moving average (ARIMA) models. Seasonal ARIMA models are parsimonious forecasting techniques because they require very few parameters and low computational resources to provide an adequate representation of stochastic time series. Two approaches are used in this paper to estimate the parameters that constitute the proposed multiplicative ARIMA model: a frequentist and a Bayesian approach. Advantages and disadvantages of both methods are compared by simulating a centralized self-healing scheme of a real EDS that uses the forecasts to deploy a robust restoration plan. Results show that the proposed seasonal ARIMA model is a fast, precise, straightforward, and adaptable load forecasting method, suitable for OOP of highly supervised EDS.