Optimal management of bio-based energy supply chains under parametric uncertainty through a data-driven decision-support framework

This paper addresses the optimal management of a multi-objective bio-based energy supply chain network subjected to multiple sources of uncertainty. The complexity to obtain an optimal solution using traditional uncertainty management methods dramatically increases with the number of uncertain factors considered. Such a complexity produces that, if tractable, the problem is solved after a large computational effort. Therefore, in this work a data-driven decision-making framework is proposed to address this issue. Such a framework exploits machine learning techniques to efficiently approximate the optimal management decisions considering a set of uncertain parameters that continuously influence the process behavior as an input. A design of computer experiments technique is used in order to combine these parameters and produce a matrix of representative information. These data are used to optimize the deterministic multi-objective bio-based energy network problem through conventional optimization methods, leading to a detailed (but elementary) map of the optimal management decisions based on the uncertain parameters. Afterwards, the detailed data-driven relations are described/identified using an Ordinary Kriging meta-model. The result exhibits a very high accuracy of the parametric meta-models for predicting the optimal decision variables in comparison with the traditional stochastic approach. Besides, and more importantly, a dramatic reduction of the computational effort required to obtain these optimal values in response to the change of the uncertain parameters is achieved. Thus the use of the proposed data-driven decision tool promotes a time-effective optimal decision making, which represents a step forward to use data-driven strategy in large-scale/complex industrial problems.Peer ReviewedPostprint (published version

Stability Verification of Neural Network Controllers using Mixed-Integer Programming

We propose a framework for the stability verification of Mixed-Integer Linear Programming (MILP) representable control policies. This framework compares a fixed candidate policy, which admits an efficient parameterization and can be evaluated at a low computational cost, against a fixed baseline policy, which is known to be stable but expensive to evaluate. We provide sufficient conditions for the closed-loop stability of the candidate policy in terms of the worst-case approximation error with respect to the baseline policy, and we show that these conditions can be checked by solving a Mixed-Integer Quadratic Program (MIQP). Additionally, we demonstrate that an outer and inner approximation of the stability region of the candidate policy can be computed by solving an MILP. The proposed framework is sufficiently general to accommodate a broad range of candidate policies including ReLU Neural Networks (NNs), optimal solution maps of parametric quadratic programs, and Model Predictive Control (MPC) policies. We also present an open-source toolbox in Python based on the proposed framework, which allows for the easy verification of custom NN architectures and MPC formulations. We showcase the flexibility and reliability of our framework in the context of a DC-DC power converter case study and investigate its computational complexity

Multi-parametric Analysis for Mixed Integer Linear Programming: An Application to Transmission Planning and Congestion Control

Enhancing existing transmission lines is a useful tool to combat transmission congestion and guarantee transmission security with increasing demand and boosting the renewable energy source. This study concerns the selection of lines whose capacity should be expanded and by how much from the perspective of independent system operator (ISO) to minimize the system cost with the consideration of transmission line constraints and electricity generation and demand balance conditions, and incorporating ramp-up and startup ramp rates, shutdown ramp rates, ramp-down rate limits and minimum up and minimum down times. For that purpose, we develop the ISO unit commitment and economic dispatch model and show it as a right-hand side uncertainty multiple parametric analysis for the mixed integer linear programming (MILP) problem. We first relax the binary variable to continuous variables and employ the Lagrange method and Karush-Kuhn-Tucker conditions to obtain optimal solutions (optimal decision variables and objective function) and critical regions associated with active and inactive constraints. Further, we extend the traditional branch and bound method for the large-scale MILP problem by determining the upper bound of the problem at each node, then comparing the difference between the upper and lower bounds and reaching the approximate optimal solution within the decision makers' tolerated error range. In additional, the objective function's first derivative on the parameters of each line is used to inform the selection of lines to ease congestion and maximize social welfare. Finally, the amount of capacity upgrade will be chosen by balancing the cost-reduction rate of the objective function on parameters and the cost of the line upgrade. Our findings are supported by numerical simulation and provide transmission line planners with decision-making guidance

Model predictive control techniques for hybrid systems

This paper describes the main issues encountered when applying model predictive control to hybrid processes. Hybrid model predictive control (HMPC) is a research field non-fully developed with many open challenges. The paper describes some of the techniques proposed by the research community to overcome the main problems encountered. Issues related to the stability and the solution of the optimization problem are also discussed. The paper ends by describing the results of a benchmark exercise in which several HMPC schemes were applied to a solar air conditioning plant.Ministerio de Eduación y Ciencia DPI2007-66718-C04-01Ministerio de Eduación y Ciencia DPI2008-0581

A receding horizon event-driven control strategy for intelligent traffic management

AbstractIn this paper, the intelligent traffic management within a smart city environment is addressed by developing an ad-hoc model predictive control strategy based on an event-driven formulation. To this end, a constrained hybrid system description is considered for safety verification purposes and a low-demanding receding horizon controller is then derived by exploiting set-theoretic arguments. Simulations are performed on the train-gate benchmark system to show the effectiveness and benefits of the proposed methodology

Chance-Constrained Outage Scheduling using a Machine Learning Proxy

Outage scheduling aims at defining, over a horizon of several months to years, when different components needing maintenance should be taken out of operation. Its objective is to minimize operation-cost expectation while satisfying reliability-related constraints. We propose a distributed scenario-based chance-constrained optimization formulation for this problem. To tackle tractability issues arising in large networks, we use machine learning to build a proxy for predicting outcomes of power system operation processes in this context. On the IEEE-RTS79 and IEEE-RTS96 networks, our solution obtains cheaper and more reliable plans than other candidates

WIND POWER PROBABILISTIC PREDICTION AND UNCERTAINTY MODELING FOR OPERATION OF LARGE-SCALE POWER SYSTEMS

Over the last decade, large scale renewable energy generation has been integrated into power systems. Wind power generation is known as a widely-used and interesting kind of renewable energy generation around the world. However, the high uncertainty of wind power generation leads to some unavoidable error in wind power prediction process; consequently, it makes the optimal operation and control of power systems very challenging. Since wind power prediction error cannot be entirely removed, providing accurate models for wind power uncertainty can assist power system operators in mitigating its negative effects on decision making conditions. There are efficient ways to show the wind power uncertainty, (i) accurate wind power prediction error probability distribution modeling in the form of probability density functions and (ii) construction of reliable and sharp prediction intervals. Construction of accurate probability density functions and high-quality prediction intervals are difficult because wind power time series is non-stationary. In addition, incorporation of probability density functions and prediction intervals in power systems’ decision-making problems are challenging. In this thesis, the goal is to propose comprehensive frameworks for wind power uncertainty modeling in the form of both probability density functions and prediction intervals and incorporation of each model in power systems’ decision-making problems such as look-ahead economic dispatch. To accurately quantify the uncertainty of wind power generation, different approaches are studied, and a comprehensive framework is then proposed to construct the probability density functions using a mixture of beta kernels. The framework outperforms benchmarks because it can validly capture the actual features of wind power probability density function such as main mass, boundaries, high skewness, and fat tails from the wind power sample moments. Also, using the proposed framework, a generic convex model is proposed for chance-constrained look-ahead economic dispatch problems. It allows power system operators to use piecewise linearization techniques to convert the problem to a mixed-integer linear programming problem. Numerical simulations using IEEE 118-bus test system show that compared with widely used sequential linear programming approaches, the proposed mixed-integer linear programming model leads to less system’s total cost. A framework based on the concept of bandwidth selection for a new and flexible kernel density estimator is proposed for construction of prediction intervals. Unlike previous related works, the proposed framework uses neither a cost function-based optimization problem nor point prediction results; rather, a diffusion-based kernel density estimator is utilized to achieve high-quality prediction intervals for non-stationary wind power time series. The proposed prediction interval construction framework is also founded based on a parallel computing procedure to promote the computational efficiency for practical applications in power systems. Simulation results demonstrate the high performance of the proposed framework compared to well-known conventional benchmarks such as bootstrap extreme learning machine, lower upper bound estimation, quantile regression, auto-regressive integrated moving average, and linear programming-based quantile regression. Finally, a new adjustable robust optimization approach is used to incorporate the constructed prediction intervals with the proposed fuzzy and adaptive diffusion estimator-based prediction interval construction framework. However, to accurately model the correlation and dependence structure of wind farms, especially in high dimensional cases, C-Vine copula models are used for prediction interval construction. The simulation results show that uncertainty modeling using C-Vine copula can lead the system operators to get more realistic sense about the level of overall uncertainty in the system, and consequently more conservative results for energy and reserve scheduling are obtained