arXiv subjects

Frederik Geth

Publications and source records attributed to Frederik Geth.

24 records · Page 2Linked to original sources

arXiv2022

Notes on BIM and BFM Optimal Power Flow With Parallel Lines and Total Current Limits

The second-order cone relaxation of the branch flow model (BFM) and bus injection model (BIM) variants of optimal power flow are well-known to be equivalent for radial networks. In this work we show that in meshed networks with parallel lines, BIM dominates BFM, and propose novel constraints to make them equivalent in general. Furthermore, we develop an improvement to the second-order cone relaxations of optimal power flow, adding novel and valid linear constraints on the lifted current expressions. We develop two simple test cases to highlight the advantages of the proposed constraints. These novel constraints tighten the second-order cone relaxation gap on test cases in the `PG Lib' optimal power flow benchmark library, albeit generally in limited fashion.

math.OC↗

arXiv2022

Load Balancing in Low-Voltage Distribution Networks via Optimizing Residential Phase Connections

Unbalance issues in low-voltage distribution networks (LVDN) can be worsened by increasing penetration of residential PV generation if unevenly distributed among three phases. To address this issue, the phase-switching device (PSD) provides a viable and efficient method by dynamically switching customers to other phases. This paper further investigates how to optimize residential phase connections by controlling PSDs efficiently. The optimization problem is formulated as a mixed-integer non-convex programming (MINCP) problem considering relevant operational requirements of an LVDN based on the exact formulation of unbalanced three-phase optimal power flow (UTOPF). Unlike most heuristic algorithms and the linearization techniques in our previous work, this paper proposes to solve the MINCP problem via an iteration-based algorithm after exact reformulations and reasonable approximations of some constraints. The proposed method is tested in a real LVDN and compared with the approach of Zhao et al. based on the well-known linear UTOPF formulation. Case studies based on the European low-voltage test feeder demonstrate the proposed method's efficiency in mitigating the network unbalance while ensuring network security and flexibility to deal with more controllable resources.

math.OC↗

arXiv2021

Improving Optimal Power Flow Relaxations Using 3-Cycle Second-Order Cone Constraints

This paper develops a novel second order cone relaxation of the semidefinite programming formulation of optimal power flow, that does not imply the `angle relaxation'. We build on a technique developed by Kim et al., extend it for complex matrices, and apply it to 3x3 positive semidefinite matrices to generate novel second-order cone constraints that augment upon the well-known 2x2 principal-minor based second-order cone constraints. Finally, we apply it to optimal power flow in meshed networks and provide numerical illustrations.

math.OC↗

arXiv2021

Realistic Differentially-Private Transmission Power Flow Data Release

For the modeling, design and planning of future energy transmission networks, it is vital for stakeholders to access faithful and useful power flow data, while provably maintaining the privacy of business confidentiality of service providers. This critical challenge has recently been somewhat addressed in [1]. This paper significantly extends this existing work. First, we reduce the potential leakage information by proposing a fundamentally different post-processing method, using public information of grid losses rather than power dispatch, which achieve a higher level of privacy protection. Second, we protect more sensitive parameters, i.e., branch shunt susceptance in addition to series impedance (complete pi-model). This protects power flow data for the transmission high-voltage networks, using differentially private transformations that maintain the optimal power flow consistent with, and faithful to, expected model behaviour. Third, we tested our approach at a larger scale than previous work, using the PGLib-OPF test cases [10]. This resulted in the successful obfuscation of up to a 4700-bus system, which can be successfully solved with faithfulness of parameters and good utility to data analysts. Our approach addresses a more feasible and realistic scenario, and provides higher than state-of-the-art privacy guarantees, while maintaining solvability, fidelity and feasibility of the system.

cs.CR↗

arXiv2020

A Flexible Storage Model for Power Network Optimization

This paper proposes a simple and flexible storage model for use in a variety of multi-period optimal power flow problems. The proposed model is designed for research use in a broad assortment of contexts enabled by the following key features: (i) the model can represent the dynamics of an energy buffer at a wide range of scales, from residential battery storage to grid-scale pumped hydro; (ii) it is compatible with both balanced and unbalanced formulations of the power flow equations; (iii) convex relaxations and linear approximations to allow seamless integration of the proposed model into applications where convexity or linearity is required are developed; (iv) a minimalist and standardized data model is presented, to facilitate easy of use by the research community. The proposed model is validated using a proof-of-concept twenty-four hour storage scheduling task that demonstrates the value of the model's key features. An open-source implementation of the model is provided as part of the PowerModels and PowerModelsDistribution optimization toolboxes.

eess.SY↗

arXiv2020

PowerModelsDistribution.jl: An Open-Source Framework for Exploring Distribution Power Flow Formulations

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.

cs.CE↗