Sander Claeys

Unbalanced optimal power flow refers to mathematical optimization problems subject to the physics of grids with phase unbalance. They can serve as a core technology, or benchmark, for centralized or distributed optimal control solutions. In recent years, convex relaxations of this problem have attracted significant interest in the community. For many common test feeders, it turned out they return exact solutions. However, more research is needed to study how well this holds up in more complicated modelling contexts. This paper therefore studies gang-operated on-load tap changers in detail. Analogous to balanced optimal power flow, it is possible to reformulate the problem exactly without an explicit tap variable. This is a non-trivial result that is discussed in detail. Furthermore, this paper describes in detail how a solution in the lifted variable space can be projected back to the original variable space. Best case, it then becomes possible to solve the problem as a convex optimization problem instead. Worst case, it provides a lower bound on the objective value. Two numerical case studies, a simple test case and IEEE13, are included. The case studies are made publicly available.

Increased penetration of low‐carbon technologies, such as residential photovoltaic systems, electric vehicles, and batteries, can potentially cause voltage quality issues in distribution networks. Active distribution networks adopt control schemes where these assets are actively managed to prevent potential issues, increasing the network utilization. Mathematical optimization is a key technology in enabling such applications, either directly as the underlying solution, or for benchmarking effectiveness. As networks are operated closer to their engineering limits, models representing distribution network physics become increasingly important. This article reviews how distribution networks are modeled with varying degrees of detail in the context of optimization problems. It goes on to catalog the applications that use such models, and ends with an overview of toolchains to implement them, to enable the transition from the passive to active management of the distribution system.This article is categorized under: Energy Systems Analysis > Systems and Infrastructure

Mathematical models representing the behavior of electrical loads are an important part of any optimal power flow problem. The current state-of-the-art in unbalanced optimal power flow mostly considers wye-connected, constant power loads. However, for applications such as conservation voltage reduction, it is crucial to model how the consumption of the loads depends on the voltage of the network. This article develops a unified framework to handle a wide variety of load types: delta- or wye-connected, constant power, constant current and exponential load models. Furthermore, it proposes a novel convex relaxation for the exponential model, using power cones, that is intersected next with a well-known semi-definite relaxation of unbalanced OPF. Finally, numerical results on the LVTestCase feeder are included for both the exact, non-linear equations and the convex relaxation, which show how considering the voltage sensitivity and connection type can lead to different objective values and voltage profiles. Additional results for 128 low-voltage networks, examine the quality of the solutions obtained with the proposed relaxation.

This study proposes a model for multi‐phase, multi‐winding, lossy transformers. A methodology is developed to decompose such transformers into a sub‐network of multi‐conductor ‐sections, shunts and idealised (lossless) two‐winding transformers. The approach, therefore, can be used to include three‐phase transformer models in any unbalanced power flow or optimal power flow tool that is able to represent these three basic components. The study derives the mathematical formulation and an implementation is provided in Julia/JuMP/PowerModelsDistribution.jl. The obtained voltage profile for several distribution test cases deviates from OpenDSS by at most . A case study applies this model to optimise the tap settings in the context of conservative voltage reduction. This illustrates that the optimised tap settings can vary by as much as 30% depending on the vector group of the transformer.

In this work we introduce PowerModelsDistribution, a free, open-source toolkit for distribution power network optimization, whose primary focus is establishing a baseline implementation of steady-state multi-conductor unbalanced distribution network optimization problems, which includes implementations of Power Flow and Optimal Power Flow problem types. Currently implemented power flow formulations for these problem types include AC (polar and rectangular), a second-order conic relaxation of the Branch Flow Model (BFM) and Bus Injection Model (BIM), a semi-definite relaxation of BFM, and several linear approximations, such as the simplified unbalanced BFM. The results of AC power flow have been validated against OpenDSS, an open-source "electric power distribution system simulator", using IEEE distribution test feeders (13, 34, 123 bus and LVTestCase), all parsed using a built-in OpenDSS parser. This includes support for standard distribution system components as well as novel resource models such as generic energy storage (multi-period) and photovoltaic systems, with the intention to add support for additional components in the future.

This paper presents experimental validation of a distributed optimization-based voltage control system. The dual-decomposition method is used in this paper to solve the voltage optimization problem in a fully distributed way. Device-to-device communication is implemented to enable peer-to-peer data exchange between agents of the proposed voltage control system. The paper presents the design, development and hardware setup of a laboratory-based testbed used to validate the performance of the proposed dual-decomposition-based peer-to-peer voltage control. The architecture of the setup consists of four layers: microgrid, control, communication, and monitoring. The key question motivating this research was whether distributed voltage control systems are a technically effective alternative to centralized ones. The results discussed in this paper show that distributed voltage control systems can indeed provide satisfactory regulation of the voltage profiles.