(667i) Data-Driven Modelling and Optimization for Managing the Load Distribution of Electric Motor-Operated Compressors

Electric motor-operated compressors are widely used in chemical process industries for pressurising gaseous fluids. A significant portion of the operating costs of electric motor-operated compressors is directed to energy consumption. A conventional approach for the operation of compressors includes the equal distribution of demanded load across parallel compressors. That is, compressors are loaded equally. In practice, this potentially leads to sub-optimal operation since compressors have non-uniform efficiencies even if they have identical designs. This presents a motivation for examining approaches for optimal distribution of loads among parallel compressors.

This paper demonstrates the application of a framework for data-driven modelling and optimization of mass load distribution for a system of parallel air compressors. Data are collected from a petrochemical facility located in Germany. The objective is to minimize overall electric energy consumption through varying the load distribution across parallel compressors.

Data-driven models are used for the prediction of electric power consumption of individual compressors based on process measurements of inlet and outlet streams. Process measurements include temperature, pressure, air flow rate, air humidity, electrical power consumption, and the position of inlet guide vanes. Process measurements are pre-processed for removal of stationary points and outliers, identification of steady states, and scaling of variables. Data-driven models are developed through regression of polynomials. The dependent variable is the electric power consumption of each individual compressor. A forward step-wise approach is employed for the selection of independent variables from the set of process measurements.

The Data-driven models are developed through a continuous moving-data window. That is, models are frequently updated where each modelling instance is based on process measurements for a pre-scribed duration (in days). This is in order to capture changing process dynamics and to minimize plant-model mismatch. The length of the moving data window is treated as a tuning parameter. It has been varied from relatively short periods (less than 10 days) to longer periods (10-14 days).

The objective of the optimization is to minimize the total electric power consumption of parallel compressor. The objective function is the sum of electric power consumption that is estimated through data-driven models corresponding to each individual compressor. The decision variable of the optimization problem is the mass load for each individual compressor. The constraints of optimization include meeting total demand of air for downstream processes. An additional constraint is imposed to ensure that the optimum solution does not violate the validity domain of the data-driven models. This is represented by maximum and minimum values of pre-processed measurements of air flow rates.

The optimization problem is formulated as a Quadratic Program with Quadratic polynomial function and a set of linear constraints. MATLAB ‘quadprog’ function is used to solve for optimum solutions. The optimization problem is solved through a series of simulation scenarios corresponding to collected process data. Results are compared with actual process measurements of total electric consumption to quantify benefits.

The research demonstrated that data-driven models in the form of second-order polynomials in terms of air flow rate provide adequate representation of the compressors. The resulted R-squared based on validation datasets exceed 98%. It was demonstrated that the inclusion of the other process measurements does not result in significant improvement in the predictive power of the data-driven models. This approach for simplification of development of data-driven models has resulted in reduced computational cost. In particular, this has led to faster conversion of the optimization solver. Furthermore, this research has demonstrated that data-driven models can lead to more efficient operation of systems of electric motor-operated compressors. The examined scenarios has shown improvements of up to 3% in overall energy consumption in comparison to the equal-load scenarios. In addition, this research has examined the influence of the varying the length of the moving data window as a tuning parameter for the development of data-driven models. It has been demonstrated that there is a trade-off between the quality of fit of the data-driven models and the robustness of the optimization solutions. Longer periods (10-14 days) have led to slightly better model fits, with higher R-squared values by approximately 1-3%, in comparison with shorter periods (<10 days). However, longer periods have resulted in relatively higher proportion of optimal solutions that are outside the validity domain of the data-driven models.

The presented approach for data-driven modelling and optimization of electric motor-operated compressors can be further integrated with online load-distribution control systems. This presents opportunities for future applied industrial research to examine real-time applications.