a b s t r a c tThe conventional approach for the control of distribution networks, in the presence of active generation and/or controllable loads and storage, involves a combination of both frequency and voltage regulation at different time scales. With the increased penetration of stochastic resources, distributed generation and demand response, this approach shows severe limitations in both the optimal and feasible operation of these networks, as well as in the aggregation of the network resources for upper-layer power systems. An alternative approach is to directly control the targeted grid by defining explicit and real-time setpoints for active/reactive power absorptions/injections defined by a solution of a specific optimization problem; but this quickly becomes intractable when systems get large or diverse. In this paper, we address this problem and propose a method for the explicit control of the grid status, based on a common abstract model characterized by the main property of being composable. That is to say, subsystems can be aggregated into virtual devices that hide their internal complexity. Thus the proposed method can easily cope with systems of any size or complexity. The framework is presented in this Part I, whilst in Part II we illustrate its application to a CIGRÉ low voltage benchmark microgrid. In particular, we provide implementation examples with respect to typical devices connected to distribution networks and evaluate of the performance and benefits of the proposed control framework.

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a b s t r a c tIn this second part, we evaluate the performances of our control framework by applying it to a case study that contains a minimum set of elements allowing to show its applicability and potentials. We show how the computation of the PQt profiles, belief functions, and virtual costs can be synthesized for generic resources (i.e., dispatchable and stochastic generation systems, storage units, loads). The metrics of interest are: quality-of-service of the network represented by voltages magnitudes and lines current magnitudes in comparison with their operational boundaries; state-of-charge of electric and thermal storage devices; proportion of curtailed renewables; and propensity of microgrid collapse in the case of renewables overproduction. We compare our method to two classic ones relying on droop control: the first one with only primary control on both frequency and voltage and the second one with an additional secondary frequency control operated by the slack device. We find that our method is able to indirectly control the reserve of the storage systems connected to the microgrid, thus maximizing the autonomy in the islanded operation and, at the same time, reducing renewables curtailment. Moreover, the proposed control framework keeps the system in feasible operation conditions, better explores the various degrees of freedom of the whole system and connected devices, and prevents its collapse in case of extreme operation of stochastic resources. All of these properties are obtained with a simple and generic control framework that supports aggregation and composability.

Abstract-We compute an optimal day-ahead dispatch plan for distribution networks with stochastic resources and batteries, while accounting for grid and battery losses. We formulate and solve a scenario-based AC Optimal Power Flow (OPF), which is by construction non-convex. We explain why the existing relaxation methods do not apply and we propose a novel iterative scheme, Corrected DistFlow (CoDistFlow), to solve the scenariobased AC OPF problem in radial networks. It uses a modified branch flow model for radial networks with angle relaxation that accounts for line shunt capacitances. At each step, it solves a convex problem based on a modified DistFlow OPF with correction terms for line losses and node voltages. Then, it updates the correction terms using the results of a full load flow. We prove that under a mild condition, a fixed point of CoDistFlow provides an exact solution to the full AC power flow equations. We propose treating battery losses similarly to grid losses by using a single-port electrical equivalent instead of battery efficiencies. We evaluate the performance of the proposed scheme in a simple and real electrical networks. We conclude that grid and battery losses affect the feasibility of the dayahead dispatch plan and show how CoDistFlow can handle them correctly.Index Terms-Dispatch plan; day-ahead; optimal power flow; grid losses; battery models; NOMENCLATURE PCCPoint of Common Coupling.Index of bus at the top and bottom of line l respectively.Parameters per line l r l Direct sequence longitudinal resistance.Direct sequence shunt susceptance.

Power distribution systems are experiencing a largescale integration of Converter-Interfaced Distributed Energy Resources (CIDERs). This complicates the analysis and mitigation of harmonics, whose creation and propagation are facilitated by the interactions of converters and their controllers through the grid. In this paper, a method for the calculation of the so-called Harmonic Power-Flow (HPF) in three-phase grids with CIDERs is proposed. The distinguishing feature of this HPF method is the generic and modular representation of the system components. Notably, as opposed to most of the existing approaches, the coupling between harmonics is explicitly considered. The HPF problem is formulated by combining the hybrid nodal equations of the grid with the closed-loop transfer functions of the CIDERs, and solved using the Newton-Raphson method. The grid components are characterized by compound electrical parameters, which allow to represent both transposed or non-transposed lines. The CIDERs are represented by modular linear time-periodic systems, which allows to treat both grid-forming and gridfollowing control laws. The method's accuracy and computational efficiency are confirmed via time-domain simulations of the CIGR É low-voltage benchmark microgrid. This paper is divided in two parts, which focus on the development (Part I) and the validation (Part II) of the proposed method.