Innovative Methods for Modeling, Management and Control of Smart Distribution Grids

The rapid growth of distributed energy resources (DERs) and smart technologies require new modeling, and advanced management and control methods to achieve the efficient, reliable, and secure operation of distribution grids. In this scenario, this doctoral thesis proposes significant contributions by developing: (i.) a highly versatile linear power flow (PF) methodology for analyzing the steady-state operation of distribution systems incorporating DERs and voltage control devices (VCDs); (ii.) optimized probabilistic forecasting techniques for managing load uncertainties that ensure high accuracy in predictive modeling; and (iii.) a highly accurate and computationally efficient multi-objective optimization (MOO) method for the short-term dispatch of DERs, accounting for the inherent uncertainties in decision-making processes. Linear PF methods are used to model the steady-state operation of distribution grids through linear approximations, which reduce computational effort compared to traditional nonlinear PF methods. However, linearizations often compromise the accuracy of the solutions and offer limited versatility in accommodating models of emerging components, such as DERs and VCDs. Recently, a constrained Jacobian-based linear method for steady-state analysis of radial distribution systems with DERs has been proposed. It achieves high accuracy while maintaining high efficiency providing the closed-form expression of sensitivity coefficients of grid power flows and voltages to the DER injections. This doctoral thesis extends this linear PF method to account for voltage variations forced by VCDs or caused by the slack bus. The models of both VCDs that directly impose a voltage source and VCDs that indirectly adjust voltage by injecting reactive current are formulated, encompassing devices with or without voltage regulators and with continuous or discrete control actions. Furthermore, an algorithm capable of handling the control law of discrete VCDs is proposed, that maintains high computational efficiency avoiding the use of any iterative procedures. The extended linear PF method has been validated on both small and large real distribution feeders under various operating conditions, considering the presence of combined effects of DERs and VCDs. Numerical results demonstrate the high accuracy of the linear PF methods in response to the variations of both power injected by DERs and voltage control action of VCDs, significantly improving the applicability of the method in modern distribution systems. Moreover, the proposed linear PF method maintains low computational effort thanks to the non-iterative procedure even in presence of VCDs with discrete control action, making it suitable for real-time applications. Among probabilistic forecasting methods, non-parametric models are typically preferred because they enable the modeling of uncertainties in load forecasting without assuming a canonical probability density function (PDF) for the involved variables (i.e., the target variable and the regressors). Quantile regression (QR) is a widely-used non-parametric forecasting method, that directly calculates the quantiles of the target variable by assuming a linear relationship between the variables. Recently, an empirical copula (EC)-based method has been applied to power systems; leveraging the copula theory, it calculates quantiles without assuming a linear dependence among the variables nor canonical PDFs. In this doctoral thesis the accuracy of both QR and EC-based methods is improved by introducing two optimization strategies. Concerning the QR, a mixed-integer optimization problem is formulated to automatically identify the most informative regressors. This optimal model selection is performed off-line and once for all, and theoretically avoids the need for preliminary analysis; however, its application increases the computational burden during the training process. The EC-based method is improved by optimizing the bandwidths used by the Beta-Kernel density estimation of the unknown PDF because the choice of bandwidths requires a compromise between the amplitude of the bias and the variance of the forecasting output. The optimization problem minimizes the integrated squared error between the true and estimated densities, resulting in an accurate estimation of the unknown PDF. As a drawback, the optimization of the computational burden increases exponentially with the number of bandwidths to optimize. Both QR and EC-based methods are applied to real-world load consumption data, considering both residential and public buildings at different levels of aggregation (i.e., single building or group of buildings). Numerical results demonstrate the effectiveness of both methods, with the EC-based method emerging as a competitive alternative to QR. MOO methods are used to assist distribution system operators in effectively managing and controlling the grid by simultaneously minimizing multiple conflicting objectives. MOO problems are typically solved using Pareto optimality; however, evaluating the Pareto front is computationally intensive and then defining a criteria to select an optimal solution on the Pareto front is difficult for the decision makers (DMs). Recently, a MOO method addressing the optimal dispatch of DERs has been proposed, which minimizes the bus voltage deviations, the network losses, and the current security index. To reduce computational burden and the uncertainty faced by DMs, the MOO problem is transformed into a single-objective optimization problem by the weighted sum (WS) method, with weights assigned using a surrogate weights method (SWM). This approach avoids the evaluation of the Pareto front and directly provides a Pareto optimal solution depending only on the order of preferences of the DM. In this doctoral thesis this MOO method is improved in two ways. First, the nonlinear PF equations in the MOO problem are linearized according to the constrained Jacobian-based method previously studied, obtaining a reduction of the computational burden. Second, a novel validation procedure is proposed to identify the most suitable SWM among six different SWMs which can be applied to specific management and control problem. The proposed MOO method is validated on a real distribution system over a 24-hour operational horizon by comparing its results with those obtained by solving the MOO using nonlinear PF equations. Numerical results demonstrate high accuracy and significant reduction of computational effort of the proposed MOO method.