Analysis of pumped heat electricity storage process using exponential matrix solutions

• Matrix exponential solutions are obtained for cyclic steady state operations.
• Dimensionless analysis is performed for process design and development.
• Effects of heat transfer resistance and turbomachine efficiency are compared.
• Symmetric operation for PHES processes is favored over asymmetric operation.

Pumped heat electricity storage (PHES) is a recently proposed competitive energy storage solution for large scale electrical energy storage (EES). It is especially valuable for regions where specific geological structures are not available. The performance of PHES depends on two factors: the operations of turbomachines and the thermal storage system. The former is characterized by pressure ratio, polytropic efficiency and gas heat capacity ratio. The latter contains the parameters of heat regenerators that can be summarized into two dimensionless numbers: length Λ and step time π. The overall process operation can be described by temperature difference representing the energy stored per unit heat capacity, the storage bed utilization ratio and the turn-around efficiency. Exponential matrix solutions are obtained for a discretized heat transfer model of a typical pumped heat electricity storage process. Using the cyclic steady state and transient state solutions, we are able to analyze how dimensionless length and step time affect the storage bed utilization ratio as well as the turn-around efficiency. This model provides basic guidance for further development of such processes.