Real-time optimization of load sharing for gas compressors in the presence of uncertainty

This paper investigates the problem of load-sharing optimization of gas compressors in the presence of uncertainty. The objective is to operate a set of compressor units in an energy-efficient way, while at the same time meeting a varying load demand. The main challenge is the fact that the available models, and in particular the compressor efficiency maps, carry a significant amount of uncertainty. For this task, real-time optimization (RTO) techniques that rely on plant measurements and correct the model are available in the literature. This paper is tailored to the application of RTO to the compressor load-sharing optimization problem. An adaptive optimization approach that guarantees optimal plant operation upon convergence is used. To this end, we use appropriate measurements to estimate plant gradients and correct the model in such a way that it exhibits the same optimality conditions as the plant. This way, the challenge is shifted from having an accurate model to being able to estimate experimental gradients accurately. We show how the specific problem structure can be exploited for the purpose of efficient estimation of plant gradients. We consider both parallel and serial compressor configurations as well as operation close to surge constraints. The simulation of an industrial case study demonstrates the efficiency of the proposed approach.

Real-Time Optimization of Interconnected Systems via Modifier Adaptation, with Application to Gas-Compressor Stations

Predrag Milosavljevic

The process industries are characterized by a large number of continuously operating plants, for which optimal operation is of economic and ecological importance. Many industrial systems can be regarded as an arrangement of several subsystems, where outputs of certain subsystems are inputs to others. This gives rise to the notion of interconnected systems. Plant optimality is difficult to achieve when the model used in optimization is inaccurate or in the presence of process disturbances. However, in the presence of plant-model mismatch, optimal operation can be enforced via specific real-time optimization methods. Specifically, this thesis considers so-called Modifier-Adaptation schemes which achieve plant optimality by direct incorporation of process measurements in the form of first-order corrections. As a first contribution, this thesis proposes a novel problem formulation for modifier adaptation. Specifically, it is focused on plants consisting of multiple interconnected subsystems that allows problem decomposition and application of distributed optimization strategies. The underlying key idea is the use of measurements and global plant gradients in place of an interconnection model. As a second contribution, this thesis investigates modifier adaptation for interconnected systems relying on local gradients by using an interconnection model. We show that the use of local information in terms of model, gradients and measurements is sufficient to optimize the steady-state performance of the plant. Finally, we propose a distributed modifier-adaptation algorithm that, besides the interconnection model and local gradients, employs a coordinator. For this scheme, we prove feasible-side convergence to the plant optimum, where a coordinator ensures that the local optimal inputs computed for each subsystem are consistent with the interconnection model. The experimental effort necessary to estimate the plant gradients increases with the number of plant inputs and may become intractable and sometimes not feasible or reliable for large-scale interconnected systems. The proposed approaches that use the interconnection model and local gradients overcome this problem. As an application case study of industrial relevance, this thesis investigates the problem of optimal load-sharing for serial and parallel gas compressors. The aim of load-sharing optimization is operating compressor units in an energy-efficient way, while at the same time satisfying varying load demands. We show how the structure of both the parallel and serial compressor configurations can be exploited in the design of tailored modifier adaptation algorithms based on efficient estimation of local gradients. Our findings show that the complexity of this estimation is independent of the number of compressors. In addition, we discuss gradient estimation for the case where the compressors are operating close to the surge conditions, which induces discontinuities in the problem.

EPFL2018

Real-Time Optimization of Interconnected Systems via Modifier Adaptation, with Application to Gas-Compressor Stations

Predrag Milosavljevic

EPFL2018