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Publication# Voltage Control in Active Distribution Networks Under Uncertainty in the System Model: A Robust Optimization Approach

Résumé

Within the context of ancillary services for Active Distribution Networks (ADNs), application of intelligent control techniques is required in order to achieve specific operation objectives. Despite their differences, most control mechanisms proposed in the literature rely on the assumption that the Distribution Network Operator (DNO) has an accurate and upto- date model of the network topology and a complete knowledge of the line parameters, i.e., a correct network admittance matrix Y. However, this assumption does not always hold in reality due to both an incomplete knowledge of the grid asset and /or a physical change of the line parameters. In this work, we consider the problem of optimal voltage control in ADNs under uncertain, but bounded, line parameters with no assumptions on the parameters’ uncertainty distribution. In particular, availability of a monitoring infrastructure is assumed and the goal is to control the active and reactive power injections of a number of distributed generators connected to the network buses in coordination with the transformers on-load tap changers (OLTC). The optimal control problem is formulated as a mixedinteger linear problem by means of sensitivity coefficients and a robust optimization framework is used in order to account for the uncertainties in the network admittance matrix. In order to estimate the benefits of the proposed method, the evaluation of the algorithm is carried out by using both the IEEE 13-and the IEEE 34-nodes test feeder.

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Réseau de distribution électrique

Un réseau de distribution électrique est la partie d'un réseau électrique desservant les consommateurs. Un réseau de distribution achemine l'énergie électrique d'un réseau de transport (Haute tensio

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Ancillary services (electric power)

Ancillary services are the services necessary to support the transmission of electric power from generators to consumers given the obligations of control areas and transmission utilities within those

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Decentralized generation, distributed energy storage systems and active participation of end-users in the lower level of the electrical infrastructure, intelligently managed to provide grid support, define the notion of Active Distribution Networks (ADNs). The presence of distributed generation in ADNs incurs severe impacts on planning and operational procedures and calls for intelligent control techniques. This thesis focuses on the compelling problem of optimal operation and control of ADNs, with particular reference to the design of real-time voltage control and lines congestion management algorithms. In the first part of the thesis, we adopt a centralized architecture for voltage control and lines congestion management in ADNs. The goal of the proposed controller is to schedule the active and reactive power injections of a set of controllable resources, in coordination with traditional resources, in order to achieve an optimal grid operation. The controller relies on a linearized approach that links control variables and controlled quantities using sensitivity coefficients. Once the proposed algorithm is validated, as a further step, we relax the assumption that the DNO has an accurate knowledge of the system model, i.e., a correct admittance matrix and we adapt the proposed control architecture to such a scenario. When the controllable resources are heterogeneous and numerous, control schemes that rely on two-way communication between the controllable entity and the DNO cannot scale in the number of network buses and controllable resources. In this direction, in the second part of this thesis, we propose the use of broadcast-based control schemes that rely on state estimation for the feedback channel. We propose a low-overhead broadcast-based control mechanism, called Grid Explicit Congestion Notification (GECN), intended for provision of grid ancillary services by a seamless control of large populations of distributed, heterogeneous energy resources. Two promising candidates in terms of controllable resources are energy storage systems and elastic loads. Therefore, we choose to validate GECN in the case of aggregations of thermostatically controlled loads, as well as of distributed electrochemical-based storage systems. In the last part of the thesis, we formulate the control problem of interest as a non-approximated AC optimal power flow problem (OPF). The AC-OPF problem is non-convex, thus difficult to solve efficiently. A recent approach that focuses on the branch-flow convexification of the problem is claimed to be exact for radial networks under specific assumptions. We show that this claim, does not hold, as it leads to an incorrect system model. Therefore, there is a need to develop algorithms for the solution of the non-approximated, inherently non-convex OPF problem. We propose an algorithm for the AC-OPF problem in radial networks that uses an augmented Lagrangian approach, relies on the method of multipliers and does not require convexity. We design a centralized algorithm that converges to a local minimum of the original problem. When controlling multiple dispersed energy resources, it is of interest to define also a distributed method. We investigate the alternating direction method of multipliers (ADMM) for the distributed solution of the OPF problem and we show cases for which it fails to converge. As a solution we present a distributed version of the proposed OPF algorithm that is based on a primal decomposition.

Konstantina Christakou, Jean-Yves Le Boudec, Mario Paolone, Dan-Cristian Tomozei

Typical optimal controls of power systems, such as scheduling of generators, voltage control, losses reduction, have been so far commonly investigated in the domain of high-voltage transmission networks. However, during the past years, the increased connection of distributed energy resources (DERs) in power distribution systems results in frequent violations of operational constraints in these networks and has raised the importance of developing optimal control strategies specifically applied to these systems. In particular, two of the most important control functionalities that have not yet been deployed in active distribution networks (ADNs) are voltage control and lines congestion management. Usually, this category of problems has been treated in the literature by means of linear approaches applied to the dependency between voltages and power flows as a function of the power injections. On the one hand, recent progress in information and communication technologies, the introduction of new advanced metering devices such as phasor measurement units and the development of real-time state estimation algorithms present new opportunities and will, eventually, enable the deployment of processes for optimal voltage control and lines congestion management in distribution networks. On the other hand, ADNs exhibit specific peculiarities that render the design of such controls compelling. In particular, it is worth noting that the solution of optimal problems becomes of interest only if it meets the stringent time constraints required by real-time controls and imposed by the stochasticity of DERs, in particular photovoltaic units (PVs), largely present in these networks. Moreover, control schemes are meaningful for implementation in real-time controllers only when convergence to an optimal solution is guaranteed. Finally, control processes for ADNs need to take into account the inherent multi-phase and unbalanced nature of these networks, as well as the non-negligible R/X ratio of longitudinal parameters of the medium and low-voltage lines, together with the influence of transverse capacitances. Taking into consideration the aforementioned requirements, the distribution management systems (DMSs) need to be updated accordingly in order to incorporate optimization processes for the scheduling of the DERs. This chapter starts with a general description of a centralized DMS architecture that includes voltage control and lines congestion management functionalities. Then, the formulation of the corresponding optimal control problems is described, based on a linearized approach linking control variables, e.g., power injections, transformers tap positions, and controlled quantities, e.g., voltages, current flows, by means of sensitivity coefficients. Computation processes for these sensitivity coefficients are presented in Sections 8.2 and 8.3. Finally, in Section 8.4, we provide case studies of optimal voltage control and lines congestion management targeting IEEE distribution reference networks suitably modified to integrate distributed generation.

Konstantina Christakou, Jean-Yves Le Boudec, Mario Paolone, Dan-Cristian Tomozei

The problem of optimal control of power distribution systems is becoming increasingly compelling due to the progressive penetration of distributed energy resources in this specific layer of the electrical infrastructure. Distribution systems are, indeed, experiencing significant changes in terms of operation philosophies that are often based on optimal control strategies relying on the computation of linearized dependencies between controlled (e.g. voltages) and control variables (e.g. power injections). As the implementation of these strategies in real-time controllers imposes stringent time constraints, the derivation of analytical dependency between controlled and control variables becomes a non-trivial task to be solved. With reference to optimal voltage and power flow controls, this paper aims at providing an analytical derivation of node voltage and line current flows as a function of the nodal power injections. Compared to other approaches presented in the literature, the one proposed here is based on the use of [Y] compound matrix of a generic multi-phase unbalanced network. In order to estimate the computational benefits of the proposed approach, the relevant improvements are also quantified versus traditional methods. The validation of the proposed method is carried out by using both IEEE 13 and 34 node test feeders. The paper finally shows the use of the proposed method for the problem of optimal voltage control applied to the IEEE 34 node test feeder.

2012