Archives: Paper

Reduction of the Optimal Power Flow Problem through Meta-Optimization

We introduce a method for solving Optimal Power Flow (OPF) using meta-optimization, which can substantially reduce solution times. A pre-trained classifier that predicts the binding constraints of the system is used to generate an initial reduced OPF problem, defined by removing the predicted non-binding constraints. Through an iterative pro- cedure, this initial set of constraints is then ex- tended by those constraints that are violated but not represented in the reduced OPF, guaranteeing an optimal solution of the original OPF problem with the full set of constraints. The classifier is trained using a meta-loss objective, defined by the computational cost of the series of reduced OPF problems.

GP-ALPS: Automatic Latent Process Selection for Multi-Output Gaussian Process Models

A simple and widely adopted approach to extend Gaussian processes (GPs) to multiple outputs is to model each output as a linear combination of a collection of shared, unobserved latent GPs. An issue with this approach is choosing the number of latent processes and their kernels. These choices are typically done manually, which can be […]

Learning an Optimally Reduced Formulation of OPF through Meta-optimization

We introduce a method for solving Optimal Power Flow (OPF) problems, which can substantially reduce solve times. A neural network that predicts the binding status of constraints of the system is used to generate an initial reduced OPF problem, defined by removing the predicted non-binding constraints. This reduced model is then extended in an iterative manner until guaranteeing an optimal solution to the full OPF problem. The classifier is trained using a meta-loss objective, defined by the total computational cost of solving the reduced OPF problems constructed during the iterative procedure. Using a wide range of DC- and AC-OPF problems we demonstrate that optimizing this meta-loss objective results in a classifier that significantly outperforms conventional loss functions used to train neural network classifiers. We also provide an extensive analysis of the investigated grids as well as an empirical limit of performance of machine learning techniques providing optimal OPF solutions.

Meta-Optimization of Optimal Power Flow

The planning and operation of electricity grids is carried out by solving various forms of con- strained optimization problems. With the increas- ing variability of system conditions due to the integration of renewable and other distributed en- ergy resources, such optimization problems are growing in complexity and need to be repeated daily, often limited to a 5 minute solve-time. To address this, we propose a meta-optimizer that is used to initialize interior-point solvers. This can significantly reduce the number of iterations to converge to optimality.

Memristive networks: From graph theory to statistical physics

This paper is an introduction to a very specific toy model of memristive networks, for which an exact differential equation for the internal memory which contains the Kirchhoff laws is known. In particular, we highlight how the circuit topology enters the dynamics via an analysis of directed graph. We try to highlight in particular the […]

Business models design space for electricity storage systems: Case study of the Netherlands

Chris Davis paper avatar

Because of weather uncertainty and dynamics, power generation from some renewable energy technologies is variable. Electricity storage is recognized as a solution to better integrate variable renewable generation into the electricity system. Despite considerable growth in the research on the electricity storage, implementation of electricity storage systems (ESS) is globally negligible because of technical, institutional, and business model challenges. We use literature review and data analysis to provide a conceptual framework and a design space for ESS business models in the case of Dutch electricity sector by taking technological, institutional, and business model considerations into account. We provide a map of single-application business models for ESS in the Netherlands which can be used as a basis for making ESS application portfolios and evaluating ESS business models in other parts of the world as well. Furthermore, this research can be used to inform models that explore the evolution of ESS.

The Gaussian Process Autoregressive Regression Model (GPAR)

Multi-output regression models must exploit dependencies between outputs to maximise predictive performance. The application of Gaussian processes (GPs) to this setting typically yields models that are computationally demanding and have limited representational power. We present the Gaussian Process Autoregressive Regression (GPAR) model, a scalable multi-output GP model that is able to capture nonlinear, possibly inputvarying, dependencies between outputs in a simple and tractable way: the product rule is used to decompose the joint distribution over the outputs into a set of conditionals, each of which is modelled by a standard GP. GPAR’s efficacy is demonstrated on a variety of synthetic and real-world problems, outperforming existing GP models and achieving state-of-the-art performance on the tasks with existing benchmarks.

Learning Causally-Generated Stationary Time Series

We present the Causal Gaussian Process Convolution Model (CGPCM), a doubly nonparametric model for causal, spectrally complex dynamical phenomena. The CGPCM is a generative model in which white noise is passed through a causal, nonparametric-window moving-average filter, a construction that we show to be equivalent to a Gaussian process with a nonparametric kernel that is biased towards causally-generated signals. We develop enhanced variational inference and learning schemes for the CGPCM and its previous acausal variant, the GPCM (Tobar et al., 2015b), that significantly improve statistical accuracy. These modelling and inferential contributions are demonstrated on a range of synthetic and real-world signals.

Correlations and Clustering in Wholesale Electricity Markets

We study the structure of locational marginal prices in day-ahead and real-time wholesale electricity markets. In particular, we consider the case of two North American markets and show that the price correlations contain information on the locational structure of the grid. We study various clustering methods and introduce a type of correlation function based on […]

The mise en scène of memristive networks: effective memory, dynamics and learning

We discuss the properties of the dynamics of purely memristive circuits. In particular, we show that the amount of memory in a memristive circuit is constrained by the conservation laws of the circuit, and that the dynamics preserves the symmetry by means of a projection on this subspace. We obtain these results both for current […]