Real-time optimization of an experimental solid-oxide fuel-cell system

There still exists a large gap between simulation work and industrial applications in the context of control and optimization of solid-oxide fuel-cell (SOFC) systems. In an effort to bridge this gap, this study describes the experimental implementation of steady-state real-time optimization (RTO) to an SOFC system that consists of both hardware and software components. The proposed adaptive optimization scheme uses an approximate steady-state model of the fuel-cell system and corrects it "appropriately" so that it becomes "excellent" for optimization. This way, the plant can be steered efficiently toward optimality, while meeting the varying electric power demand. In these experiments, the plant efficiency was increased from 55% to 62% through application of RTO. Furthermore, although the SOFC system is characterized by slow thermal dynamics that may take a few hours to settle to steady state, it has been possible to reduce the time necessary to reach the power setpoint from 1 h to about 5 min thanks to the use of transient measurements and a dynamic model. This experimental work has shown that it is possible, not only to control the SOFC system at a desired operating point, but also to operate it near optimality despite changes in power demand.

Real-Time Optimization of Solid Oxide Fuel Cell Systems

Tafarel de Avila Ferreira

Optimization of industrial processes aims at minimizing operating cost or maximizing economic profit while respecting plant constraints. In process industry, real-time optimization (RTO) is often considered to ensure optimal plant operation and constraint satisfaction. Solid-oxide fuel-cell (SOFC) devices oxidize fuels such as hydrogen and methane to produce electric energy through electrochemical reactions at very high efficiency. To reduce the emission of carbon dioxide and the high cost of non-renewable energies, fuel cells have become popular as an alternative energy source with a wide range of applications. The optimal operation of SOFC systems, while being subjected to changing operating conditions such as variations in the electrical power demand, remains a challenging problem in the field of control and optimization. In addition, these types of devices are characterized by slow dynamics and drifts such as degradation. This motivates the use of real-time optimization for optimizing and controlling the operation of SOFC systems. The most popular RTO technique in industry is the so-called two-step approach. This approach consists in estimating the model parameters based on measurements by solving a parameter estimation problem, and computing the next operating point by solving an optimization problem using the updated model. However, this technique is highly dependent on model accuracy and tends to fail in the presence of structural plant-model mismatch. As an alternative, modifier adaptation has been developed to enforce convergence to the plant optimum even in presence of structural plant-model mismatch. Since plant optimality is often characterized by active constraints, it is possible to use a simpler version of modifier adaptation, called constraint adaptation (CA). This approach corrects the constraints in the model-based optimization problem by means of bias terms computed from the differences between the measured and predicted values of the constraints. The active plant constraintsâi.e. the intersection of the constraints where the plant opti- mum liesâfor each mode of operation is typically known from experience. Therefore, as the optimum of SOFC systems typically lies on active plant constraints, we can apply constraint adaptation. One of the drawbacks of static RTO is the fact that it is necessary to wait until the plant reaches its steady state. Since this may be inappropriate for slow processes, we propose an RTO approach that can speed up the procedure by using transient measurements combined with a dynamic tendency model. In this work, we apply constraint adaptation combined with transient measurements and a dynamic model to experimental SOFC systems. The proposed approach is applied to two SOFC systems: (i) an SOFC system with 6 cells that consists of both hardware and software components; (ii) a commercial SOFC system named BlueGEN. The results obtained are very promising. For both systems, the proposed approach can reach the power demand much faster than the time it takes for the process to settle to steady state. The optimizer is quick at finding and tracking the correct set of active constraints, thus avoiding large constraint violations. In addition, we study the effect of the RTO period on the convergence rate. Finally, we show that CA acts simultaneously as a controller and an optimizer that is able to efficiently detect and track the correct set of active constraints.

EPFL2019

Robust Real-Time Optimization of a Solid Oxide Fuel Cell Stack

Dominique Bonvin, Benoît Chachuat, Alejandro Gabriel Marchetti, Arata Nakajo, Leonidas Tsikonis, Jan Van Herle, Zacharie Wuillemin

On-line control and optimization can improve the eﬃciency of fuel cell systems whilst simultaneously ensuring that the operation remains within a safe region. Also, fuel cells are subject to frequent variations in their power demand. This paper investigates the real-time optimization (RTO) of a solid oxide fuel cell (SOFC) stack. An optimization problem maximizing the efficiency subject to operating constraints is deﬁned. Due to inevitable model inaccuracies, the open-loop implementation of optimal inputs evaluated oﬀ-line may be suboptimal, or worse, infeasible. Infeasibility can be avoided by controlling the constrained quantities. However, the constraints that determine optimal operation might switch with varying power demand, thus requiring a change in the regulator structure.

2011

Use of Transient Measurements for the Optimization of Steady-State Performance via Modifier Adaptation

Dominique Bonvin, Grégory François

Real-time optimization (RTO) methods use measurements to offset the effect of uncertainty and drive the plant to optimality. RTO schemes differ in the way measurements are incorporated in the optimization framework. Explicit RTO schemes solve a static optimization problem repeatedly, with each iteration requiring transient operation of the plant to steady state. In contrast, implicit RTO methods use transient measurements to bring the plant to steady-state optimality in a single iteration, provided the set of active constraints is known. This paper considers the explicit RTO scheme "modifier adaptation" (MA) and proposes a framework that allows using transient measurements for the purpose of steady-state optimization. It is shown that convergence to the plant optimum can be achieved in a single transient operation provided the plant gradients can be estimated accurately. The approach is illustrated through the simulated example of a continuous stirred-tank reactor. The time needed for convergence is of the order of the plant settling time, while more than five iterations to steady state are required with conventional static MA. In other words, MA using transient information is able to compete in performance with RTO schemes based on gradient control, with the additional ability to handle plant constraints.

American Chemical Society2014

Real-Time Optimization of Solid Oxide Fuel Cell Systems

Tafarel de Avila Ferreira

EPFL2019