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Renewable energy integration has progressively challenged the operating assumptions of electricity markets, questioning at first the deterministic nature of day-ahead and other forward electricity markets. As the integration of renewable resources became deeper, transmission grids began to experience congestion in unforeseen, dynamic and uncertain patterns, questioning now the management of transmission constraints in electricity markets. This dissertation proposes detailed models and algorithms for analyzing the impacts of uncertain renewable supply on different transmission-constrained electricity market designs, using parallel computing extensively in order to solve large-scale mathematical programs and to carry out simulations under different operating conditions for realistic systems. The contributions of the dissertation are organized in three chapters. Chapter 2 presents an asynchronous distributed algorithm for solving the stochastic unit commitment problem. The algorithm, deployed in parallel, is able to solve realistic instances of stochastic unit commitment within operationally acceptable tolerances and solution times. Chapter 3 proposes a consistent framework for modelling different zonal electricity markets. We develop cutting-plane algorithms to incorporate the N-1 criterion into this framework and we conduct simulations using single-period models for the Central Western European system under 768 000 different operating conditions. In chapter 4, we propose a hierarchy of mathematical programs that model the European zonal electricity market organization in detail in a multi-period setting. We compare the performance of this organization to the performances of a nodal market and the stochastic unit commitment model on the Central Western European system. Numerical results in chapters 3 and 4 indicate that failing to account for the limitations of the transmission grid, in a regime of large-scale renewable energy integration, can undermine system perform, (FSA - Sciences de l'ingénieur) -- UCL, 2018

We present a distributed computing architecture for smart grid management, composed of two applications at two different levels of the grid. At the high voltage level, we optimize operations using a stochastic unit commitment (SUC) model with hybrid time resolution. The SUC problem is solved with an asynchronous distributed subgradient method, for which we propose stepsize scaling and fast initialization techniques. The asynchronous algorithm is implemented in a high-performance computing cluster and benchmarked against a deterministic unit commitment model with exogenous reserve targets in an industrial scale test case of the Central Western European system (679 buses, 1037 lines, and 656 generators). At the distribution network level, we manage demand response from small clients through distributed stochastic control, which enables harnessing residential demand response while respecting the desire of consumers for control, privacy, and simplicity. The distributed stochastic control scheme is successfully tested on a test case with 10,000 controllable devices. Both applications demonstrate the potential for efficiently managing flexible resources in smart grids and for systematically coping with the uncertainty and variability introduced by renewable energy.

We present a distributed asynchronous algorithm for solving the two-stage stochastic unit commitment problem. The algorithm uses Lagrangian relaxation to decompose the problem by scenarios and applies an incremental method to solve the dual problem. At each incremental dual iteration, the algorithm evaluates the dual function, providing a lower bound, and recovers a feasible commitment for first stage units, which (through a feasibility recovery process) results in an upper bound. Both the incremental dual iterations as well as the feasibility recovery are executed asynchronously, resulting in more efficient utilization of parallel processors. The method is tested on a model of the Central Western European system, for which it achieved convergence three times faster than an equivalent distributed synchronous algorithm.

We provide a learning algorithm combining distributed Extreme Learning Machine and an information fusion rule based on the aggregation of experts advice, to build day ahead probabilistic solar PV power production forecasts. These forecasts use, apart from the current day solar PV power production, local meteorological inputs, the most valuable of which is shown to be precipitation. Experiments are then run in one French region, Provence-Alpes-Côte d’Azur, to evaluate the algorithm performance.

In this paper we present a stochastic model for multi-area wind production that is used for planning reserves in transmission-constrained systems with large amounts of integrated renewable power supply. The stochastic model accounts for the inter-temporal and spatial dependencies of multi-area wind power production. Results are presented for two case studies of the California and the German power system.

Generation Capacity Expansion Planning (GCEP) is the process of deciding on a set of optimal new investments in generation capacity to adequately supply future loads, while satisfying technical and reliability constraints. This paper shows the application of Stochastic Mixed-Integer Programming (SMIP) to account for hydrological uncertainty in GCEP for the Chilean Central Interconnected System, using a two-stage SMIP multiperiod model with investments and optimal power flow (OPF). The substantial computational challenges posed by GCEP imply compromising between the detail of the stochastic hydrological variables and the detail of the OPF. We selected a subset of hydrological scenarios to represent the historical hydro variability using moment-based scenario reduction techniques. The tradeoff between modeling accuracy and computational complexity was explored both regarding the simplification of the MIP problem and the differences in the variables of interest. Using a simplified OPF model we found the difference of using a subset of hydro scenarios to be small when compared with using a full representation of the stochastic variable. Overall, SMIP with scenario reduction provided optimal capacity expansion plans whose investment plus expected operational costs were between 1.3% and 1.9% cheaper than using a deterministic approach and proved to be more robust to hydro variability.