arXiv subjects

Veit Hagenmeyer

Publications and source records attributed to Veit Hagenmeyer.

107 records · Page 6Linked to original sources

arXiv2020

Open data base analysis of scaling and spatio-temporal properties of power grid frequencies

The electrical energy system has attracted much attention from an increasingly diverse research community. Many theoretical predictions have been made, from scaling laws of fluctuations to propagation velocities of disturbances. However, to validate any theory, empirical data from large-scale power systems are necessary but are rarely shared openly. Here, we analyse an open data base of measurements of electric power grid frequencies across 17 locations in 12 synchronous areas on three continents. The power grid frequency is of particular interest, as it indicates the balance of supply and demand and carries information on deterministic, stochastic, and control influences. We perform a broad analysis of the recorded data, compare different synchronous areas and validate a previously conjectured scaling law. Furthermore, we show how fluctuations change from local independent oscillations to a homogeneous bulk behaviour. Overall, the presented open data base and analyses constitute a step towards more shared, collaborative

physics.soc-ph↗

arXiv2020

Approximating Power Flow and Transmission Losses in Coordinated Capacity Expansion Problems

With rising shares of renewables and the need to properly assess trade-offs between transmission, storage and sectoral integration as balancing options, building a bridge between energy system models and detailed power flow studies becomes increasingly important, but is computationally challenging. W compare approximations for two nonlinear phenomena, power flow and transmission losses, in linear capacity expansion problems that co-optimise investments in generation, storage and transmission infrastructure. We evaluate different flow representations discussing differences in investment decisions, nodal prices, the deviation of optimised flows and losses from simulated AC power flows, and the computational performance. By using the open European power system model PyPSA-Eur we obtain detailed and reproducible results aiming at facilitating the selection of a suitable power flow model. Given the differences in complexity, the optimal choice depends on the application, the user's available computational resources, and the level of spatial detail considered. Although the commonly used transport model can already identify key features of a cost-efficient system while being computationally performant, deficiencies under high loading conditions arise due to the lack of a physical grid representation. Moreover, disregarding transmission losses overestimates optimal grid expansion by 20%. Adding a convex relaxation of quadratic losses with two or three tangents to the linearised power flow equations and accounting for changing line impedances as the network is reinforced suffices to represent power flows and losses adequately in design studies. We show that the obtained investment and dispatch decisions are then sufficiently physical to be used in more detailed nonlinear simulations of AC power flow in order to better assess their technical feasibility.

physics.soc-ph↗

arXiv2020

A Scalable Method for Scheduling Distributed Energy Resources using Parallelized Population-based Metaheuristics

Recent years have seen an increasing integration of distributed renewable energy resources into existing electric power grids. Due to the uncertain nature of renewable energy resources, network operators are faced with new challenges in balancing load and generation. In order to meet the new requirements, intelligent distributed energy resource plants can be used which provide as virtual power plants e.g. demand side management or flexible generation. However, the calculation of an adequate schedule for the unit commitment of such distributed energy resources is a complex optimization problem which is typically too complex for standard optimization algorithms if large numbers of distributed energy resources are considered. For solving such complex optimization tasks, population-based metaheuristics -- as e.g. evolutionary algorithms -- represent powerful alternatives. Admittedly, evolutionary algorithms do require lots of computational power for solving such problems in a timely manner. One promising solution for this performance problem is the parallelization of the usually time-consuming evaluation of alternative solutions. In the present paper, a new generic and highly scalable parallel method for unit commitment of distributed energy resources using metaheuristic algorithms is presented. It is based on microservices, container virtualization and the publish/subscribe messaging paradigm for scheduling distributed energy resources. Scalability and applicability of the proposed solution are evaluated by performing parallelized optimizations in a big data environment for three distinct distributed energy resource scheduling scenarios. The new method provides cluster or cloud parallelizability and is able to deal with a comparably large number of distributed energy resources. The application of the new proposed method results in very good performance for scaling up optimization speed.

cs.DC↗

arXiv2020

On Norm-Based Estimations for Domains of Attraction in Nonlinear Time-Delay Systems

For nonlinear time-delay systems, domains of attraction are rarely studied despite their importance for technological applications. The present paper provides methodological hints for the determination of an upper bound on the radius of attraction by numerical means. Thereby, the respective Banach space for initial functions has to be selected and primary initial functions have to be chosen. The latter are used in time-forward simulations to determine a first upper bound on the radius of attraction. Thereafter, this upper bound is refined by secondary initial functions, which result a posteriori from the preceding simulations. Additionally, a bifurcation analysis should be undertaken. This analysis results in a possible improvement of the previous estimation. An example of a time-delayed swing equation demonstrates the various aspects.

eess.SY↗

arXiv2020

PolyChaos.jl -- A Julia Package for Polynomial Chaos in Systems and Control

Polynomial chaos expansion (PCE) is an increasingly popular technique for uncertainty propagation and quantification in systems and control. Based on the theory of Hilbert spaces and orthogonal polynomials, PCE allows for a unifying mathematical framework to study systems under arbitrary uncertainties of finite variance; we introduce this problem as a so-called mapping under uncertainty. For practical PCE-based applications we require orthogonal polynomials relative to given probability densities, and their quadrature rules. With PolyChaos we provide a Julia software package that delivers the desired functionality: given a probability density function, PolyChaos offers several numerical routines to construct the respective orthogonal polynomials, and the quadrature rules together with tensorized scalar products. PolyChaos is the first PCE-related software written in Julia, a scientific programming language that combines the readability of scripted languages with the speed of compiled languages. We provide illustrating numerical examples that show both PCE and PolyChaos in action.

eess.SY↗

arXiv2019

Time Delay in the Swing Equation: A Variety of Bifurcations

The present paper addresses the swing equation with additional delayed damping as an example for pendulum-like systems. In this context, it is proved that recurring sub- and supercritical Hopf bifurcations occur if time delay is increased. To this end, a general formula for the first Lyapunov coefficient in second order systems with additional delayed damping and delay-free nonlinearity is given. In so far the paper extends results about stability switching of equilibria in linear time delay systems from Cooke and Grossman. In addition to the analytical results, periodic solutions are numerically dealt with. The numerical results demonstrate how a variety of qualitative behaviors is generated in the simple swing equation by only introducing time delay in a damping term.

math.DS↗

arXiv2019

A Comparison of Partitioning Strategies in AC Optimal Power Flow

The highly non-convex AC optimal power flow problem is known to scale very poorly with respect to the number of lines and buses. To achieve improved computational speed and scalability, we apply a distributed optimization algorithm, the so-called Augmented Lagrangian based Alternating Direction Inexact Newton (ALADIN) method. However, the question of how to optimally partition a power grid for use in distributed optimization remains open in the literature. In the present paper, we compare four partitioning strategies using the standard IEEE 9, 14, 30, 39, 57, 118, 300 bus models as the performance benchmark. To this end, we apply the graph partitioners KaFFPa and METIS as well as two spectral clustering methods to the aforementioned bus models. For larger grids, KaFFPa yields the best results on average.

cs.DC↗

arXiv2019

Partially Distributed Outer Approximation

This paper presents a novel partially distributed outer approximation algorithm, named PaDOA, for solving a class of structured mixed integer convex programming (MICP) problems to global optimality. The proposed scheme uses an iterative outer approximation method for coupled mixed integer optimization problems with separable convex objective functions, affine coupling constraints, and compact domain. PaDOA proceeds by alternating between solving large-scale structured mixed-integer linear programming problems and partially decoupled mixed-integer nonlinear programming subproblems that comprise much fewer integer variables. We establish conditions under which PaDOA converges to global minimizers after a finite number of iterations and verify these properties with an application to thermostatically controlled loads.

math.OC↗

arXiv2019

Data-driven charging strategies for grid-beneficial, customer-oriented and battery-preserving electric mobility

Electric Vehicle (EV) penetration and renewable energies enables synergies between energy supply, vehicle users, and the mobility sector. However, also new issues arise for car manufacturers: During charging and discharging of EV batteries a degradation (battery aging) occurs that correlates with a value depreciation of the entire EV. As EV users' satisfaction depends on reliable and value-stable products, car manufacturers offer charging assistants for simplified and sustainable EV usage by considering individual customer needs and battery aging. Hitherto models to quantify battery aging have limited practicability due to a complex execution. Data-driven methods hold feasible alternatives for SOH estimation. However, the existing approaches barely use user-related data. By means of a linear and a neural network regression model, we first estimate the energy consumption for driving considering individual driving styles and environmental conditions. In following work, the consumption model trained on data from batteries without degradation can be used to estimate the energy consumption for EVs with aged batteries. A discrepancy between the estimation and the real consumption indicates a battery aging caused by increased internal losses. We then target to evaluate the influence of charging strategies on battery degradation.

cs.OH↗

arXiv2019

Towards Optimality Preserving Aggregation for Scheduling Distributed Energy Resources

Scheduling the power exchange between a population of heterogeneous distributed energy resources and the corresponding upper-level system is an important control problem in power systems. A key challenge is the large number of (partially uncertain) parameters and decision variables that increase the computational burden and that complicate the structured consideration of uncertainties. Reducing the number of decision variables by means of aggregation can alleviate these issues. However, despite the frequent use of aggregation for storage, few works in the literature provide formal justification. In the present paper, we investigate aggregation of heterogeneous (storage) devices with time-varying power and energy constraints. In particular, we propose mild conditions on the constraints of each device guaranteeing the applicability of an aggregated model in scheduling without any loss of optimality in comparison to the complete problem. We conclude with a discussion of limitations and possible extensions of our findings.

eess.SY↗

arXiv2019

Flat Hybrid Automata as a Class of Reachable Systems: Introductory Theory and Examples

Controlling hybrid systems is mostly very challenging due to the variety of dynamics these systems can exhibit. Inspired by the concept of differential flatness of nonlinear continuous systems and their inherent invertibility property, the present contribution is focused on explicit input trajectory calculation. To this end, a new class of hybrid systems called Flat Hybrid Automata is introduced as a realisation of deterministic, reachable and explicitly invertible hybrid automata. Relevant system properties are derived, an approach for construction and for trajectory calculation is proposed and two demonstrative examples are presented. The results constitute a generalisation of control of invertible hybrid systems which is very useful if, e.g., fast reaction for stabilisation or transitions is relevant.

eess.SY↗

arXiv2019

Probabilistic Energy Forecasting using Quantile Regressions based on a new Nearest Neighbors Quantile Filter

Parametric quantile regressions are a useful tool for creating probabilistic energy forecasts. Nonetheless, since classical quantile regressions are trained using a non-differentiable cost function, their creation using complex data mining techniques (e.g., artificial neural networks) may be complicated. This article presents a method that uses a new nearest neighbors quantile filter to obtain quantile regressions independently of the utilized data mining technique and without the non-differentiable cost function. Thereafter, a validation of the presented method using the dataset of the Global Energy Forecasting Competition of 2014 is undertaken. The results show that the presented method is able to solve the competition's task with a similar accuracy and in a similar time as the competition's winner, but requiring a much less powerful computer. This property may be relevant in an online forecasting service for which the fast computation of probabilistic forecasts using not so powerful machines is required.

cs.LG↗

arXiv2018

Optimal Power Flow: An Introduction to Predictive, Distributed and Stochastic Control Challenges

The Energiewende is a paradigm change that can be witnessed at latest since the political decision to step out of nuclear energy. Moreover, despite common roots in Electrical Engineering, the control community and the power systems community face a lack of common vocabulary. In this context, this paper aims at providing a systems-and-control specific introduction to optimal power flow problems which are pivotal in the operation of energy systems. Based on a concise problem statement, we introduce a common description of optimal power flow variants including multi-stage-problems and predictive control, stochastic uncertainties, and issues of distributed optimization. Moreover, we sketch open questions that might be of interest for the systems and control community.

eess.SY↗

arXiv2018

A Generalized Framework for Chance-constrained Optimal Power Flow

Deregulated energy markets, demand forecasting, and the continuously increasing share of renewable energy sources call---among others---for a structured consideration of uncertainties in optimal power flow problems. The main challenge is to guarantee power balance while maintaining economic and secure operation. In the presence of Gaussian uncertainties affine feedback policies are known to be viable options for this task. The present paper advocates a general framework for chance-constrained OPF problems in terms of continuous random variables. It is shown that, irrespective of the type of distribution, the random-variable minimizers lead to affine feedback policies. Introducing a three-step methodology that exploits polynomial chaos expansion, the present paper provides a constructive approach to chance-constrained optimal power flow problems that does not assume a specific distribution, e.g. Gaussian, for the uncertainties. We illustrate our findings by means of a tutorial example and a 300-bus test case.

math.OC↗

arXiv2018

The Price of Uncertainty: Chance-constrained OPF vs. In-hindsight OPF

The operation of power systems has become more challenging due to feed-in of volatile renewable energy sources. Chance-constrained optimal power flow (ccOPF) is one possibility to explicitly consider volatility via probabilistic uncertainties resulting in mean-optimal feedback policies. These policies are computed before knowledge of the realization of the uncertainty is available. On the other hand, the hypothetical case of computing the power injections knowing every realization beforehand---called in-hindsight OPF(hOPF)---cannot be outperformed w.r.t. costs and constraint satisfaction. In this paper, we investigate how ccOPF feedback relates to the full-information hOPF. To this end, we introduce different dimensions of the price of uncertainty. Using mild assumptions on the uncertainty we present sufficient conditions when ccOPF is identical to hOPF. We suggest using the total variational distance of probability densities to quantify the performance gap of hOPF and ccOPF. Finally, we draw upon a tutorial example to illustrate our results.

math.OC↗

arXiv2017

Comments on Truncation Errors for Polynomial Chaos Expansions

Methods based on polynomial chaos expansion allow to approximate the behavior of systems with uncertain parameters by deterministic dynamics. These methods are used in a wide range of applications, spanning from simulation of uncertain systems to estimation and control. For practical purposes the exploited spectral series expansion is typically truncated to allow for efficient computation, which leads to approximation errors. Despite the Hilbert space nature of polynomial chaos, there are only a few results in the literature that explicitly discuss and quantify these approximation errors. This work derives error bounds for polynomial chaos approximations of polynomial and non-polynomial mappings. Sufficient conditions are established, which allow investigating the question whether zero truncation errors can be achieved and which series order is required to achieve this. Furthermore, convex quadratic programs, whose argmin operator is a special case of a piecewise polynomial mapping, are studied due to their relevance in predictive control. Several simulation examples illustrate our findings.

eess.SY↗

arXiv2017

Nearest-Neighbor Based Non-Parametric Probabilistic Forecasting with Applications in Photovoltaic Systems

The present contribution offers a simple methodology for the obtainment of data-driven interval forecasting models by combining pairs of quantile regressions. Those regressions are created without the usage of the non-differentiable pinball-loss function, but through a k-nearest-neighbors based training set transformation and traditional regression approaches. By leaving the underlying training algorithms of the data mining techniques unchanged, the presented approach simplifies the creation of quantile regressions with more complex techniques (e.g. artificial neural networks). The quality of the presented methodology is tested on the usecase of photovoltaic power forecasting, for which quantile regressions using polynomial models as well as artificial neural networks and support vector regressions are created. From the resulting evaluation values it can be concluded that acceptable interval forecasting models are created.

eess.SY↗