Prof. dr. ir. G. Deconinck
Prof. Dr. ir. J. Berlamont (chair)
Prof. Dr. ir. J. Driesen
Dr. Dipl.-Ing. H. Ergun
Prof. Dr. T. Holvoet
Dr. ir. F. Geth (CSIRO, Australia)
Prof. Dr. M. Gibescu (Utrecht University, Netherlands)
Electricity distribution networks have been around for a long time; in Europe, about 30% of deployed lines are more than 40 years old. In recent years, more and more new devices are
being connected to these networks: photovoltaic generation, electric vehicles, heat pumps and battery storage systems to name a few. Efforts to reduce greenhouse gas emissions are likely to lead to increased electrification, requiring significant adaptation of distribution networks. Historically, these networks were designed with a passive ‘fit-and-forget’ approach. By making the network strong enough to handle the worst-case peak demand, no further action was required. An active distribution network takes an alternative approach. By actively managing the connected devices and the power flows they cause, network management engines can use the available capacity more efficiently.
Mathematical optimization offers a convenient framework to solve various problems in active distribution networks, including optimal control, state estimation and system identification. Even when it is deemed impractical because of limited communication and/or computational infrastructure, it can still serve as a benchmark for alternative approaches. Applying the formalism of mathematical optimization consists of two key steps: modeling and solving. The modeling step translates the problem to a set of variables and constraints, and an objective function. There are multiple ways to do so, leading to alternative ‘formulations’ of the same physical model. Once in this form, optimization solvers can obtain the solution. An extensive literature review covers the different aspects of this process.
This dissertation focuses on the modeling step, i.e. how to translate the steady-state physics governing the distribution network to a set of variables and constraints. For transmission networks, single-phase equivalent models are typically used, which implicitly assume the system is balanced across the three phases. The network optimization literature often uses this type of network model. In distribution networks however, significant unbalance can occur. State-of-the-art simulation tools for distribution networks therefore rely on detailed models which represent all the conductors explicitly, capturing the effects of phase unbalance. This dissertation develops optimization models which have the same level of detail as state-of-the-art simulation tools. The models are validated against OpenDSS on a wide range of popular benchmarks, leading to voltage profiles which deviate by less than 1E-6 pu, within the margins of numerical tolerance. These models and their various formulations are made available as part of an open-source Julia software package.
When deploying these models, practitioners are faced with two main challenges: computational constraints and missing or inaccurate model data. With respect to the computational constraints, this dissertation has two main contributions. Firstly, it is shown that it is possible to solve a four-wire, non-linear network optimization model, with a solve time that scales roughly with the number of nodes in the network. This is achieved by an appropriate initialization of the multi-conductor model and selection of the variable space. Secondly, recent advances in the use of convex relaxations for multi-phase radial networks are combined and extended to include exponential load models, though only for Kron-reduced networks. These relaxations lead to relatively small, though non-zero optimality gaps.
In practice, it often turns out that offline distribution network data is either missing or inaccurate. However, the rollout of smart meters offers an opportunity to identify or correct the model parameters. This dissertation presents a methodology to estimate the length of distribution lines based on smart meter data. Applied to the LVTestCase feeder, it shows that a lack of GPS synchronization does not have to be an obstacle for system identification, a common concern when working with smart meter data. This is a promising starting point for future work.