(661a) Generalized Disjunctive Programming (GDP) Model for the Optimal Capacity Planning of Reliable Power Generation Systems

As evidenced by the Texas power crisis in 2021, power generation systems should be designed to have high reliability to supply uninterrupted electric power to industries. Reliability measures the probability that a system will perform its required function accounting for the possible failures of equipment. One method to improve the reliability of the systems is to add redundant units (i.e., backup units) to prevent the system from completely failing. This approach is known as ‘reliability-based design optimization,’ and various studies on this topic have been conducted [1-3]. The authors of previous works mainly focus on optimizing the number of redundant units. However, since power systems operate in unsteady state due to time-varying power demand, the reliability is also influenced by the operational strategies that the systems use to satisfy the load demand. Specifically, the redundant units have a dual role: they can either remain as backups or else participate in power production depending on the power demand.

One of the conventional methods used to evaluate the reliability of power systems is “N-1 reliability”. The N-1 reliability assumes that a power system can withstand an unexpected failure of a single component [4]. This implies that power systems may not function properly if multiple units fail simultaneously. The failures of multiple generators may reduce the power output but not necessarily fail the entire system. Hence, a rigorous method anticipating every possible failure state, and selecting the proper number and size of the backup generators should be developed to design and plan reliable power generation systems.

This paper aims to develop a new Generalized Disjunctive Programming (GDP) model for the rigorous optimal capacity planning of reliable power generation systems. The model optimizes the number and size of redundant units to maximize the reliability, and to minimize the cost by considering operation strategies that can affect the system reliability. We develop a GDP model, which involves Boolean and continuous variables, algebraic equations, and logic propositions, to represent the reliability and expected power production rigorously. It also includes in the objective function penalties for the loss of expected power. The resulting GDP model, which involves embedded disjunctions, can be reformulated as a mixed-integer linear programming (MILP) using either Big-M and hull-relaxation methods [5]. The proposed GDP model is tested with an expansion planning problem of a power generation system, and compared with a simple sequential design approach. The results show that the proposed model can effectively design reliable power generation systems, and yield significant economic savings compared to simplified design approaches.

References

[1] Chen, Y., Ye, Y., Grossmann, I.E., Chen, B., “Integrating Reliability and Uncertainty in Process Synthesis”, Computer Aided Chemical Engineering, 50, 107-114 (2021).

[2] Ortiz-Espinoza, A.P., Ye, Y., Grossmann, I.E., Jiménez-Gutiérrez, A., “Multi-Objective Optimization for the Incorporation of Safety and Reliability Considerations in Process Design”, Computer Aided Chemical Engineering, 50, 101-106 (2021).

[3] Ye, Y., Grossmann, I.E., Pinto, J.M., “Mixed-Integer Nonlinear Programming Models for Optimal Design of Reliable Chemical Plants”, Computers and Chemical Engineering, 116, 3-16 (2018).

[4] Ballireddy, T. R. R., & Modi, P. K. Power System Expansion Planning Incorporating Renewable Energy Technologies with Reliability Consideration: A State of Art Literature. International Journal of Recent Technology and Engineering, 8, 12403-12414 (2019).

[5] Grossmann, I.E., and Trespalacios, F., “Systematic Modeling of Discrete-Continuous Optimization Models through Generalized Disjunctive Programming,” AIChE Journal, 59, 3276-3295 (2013).