Probabilistic OPF Model for Unbalanced Three-Phase Electrical Distribution Systems Considering Robust Constraints

Probabilistic Power Flow Analysis Based on Point-Estimate Method for High Penetration of Photovoltaic Generation in Electrical Distribution Systems

“…This approximate technique performs as many deterministic analysis as two times uncertain variables are considered plus one deterministic analysis for the expected value of all uncertain variables (Giraldo et al, 2019). Let represents a set of points for the uncertain variable , where ∈ { , , … , } .…”

“…Another alternative for the PPF is the 2m+1 point estimate method (PEM). That approach was used to solve the optimal PPF with the objective to minimize cost grid operation for unbalanced three phase MV networks (Giraldo et al, 2019).…”

A Linear AC-OPF Formulation for Unbalanced Distribution Networks

“…The proposed formulation minimizes the total energy production cost over a period of time, discretized in a finite number of time-steps t ∈ Ω T , each with a duration of ∆t hours as shown in (2), where the first term relates the cost of importing energy from the main grid and the second one the operation cost of the DG units. Notice that a quadratic cost function could be linearized by using piece-wise linear approximations as in [21] or [25].…”

“…However, the growing penetration of distributed energy resources (DERs) into electrical distribution systems has created the need for accurate and efficient AC-OPF models aimed at medium/lowvoltage networks [1]. One of the main characteristics of such systems is that unbalances between phases are more pronounced than in high-voltage ones, mainly due to single and two-phase loads, single phase laterals, and untransposed lines [2]. Classical AC-OPF formulations are nonlinear, nonconvex, optimization problems containing both continuous and discrete variables.…”

Applications of optimization models for electricity distribution networks

“…A common approach is to model an inverter as a controllable injection of power in each phase. The per‐phase power is constrained through an upper bound on the apparent power magnitude (Jha et al, 2019; Y. Liu et al, 2019a; Nguyen et al, 2019), lower and upper bounds on active and/or reactive power (Dall'Anese et al, 2012; Y. Liu et al, 2019a), limits on the PF (Giraldo et al, 2019; Y. Liu et al, 2019a), or by restricting the active and reactive power to an affine (Meng et al, 2018) or convex set (Gan & Low, 2014). These constraints and parameters can be identical or vary across the phases of a multiphase inverter.…”