How to define an efficiency

relationships between the inputs and outputs of a unit

The image below shows an overview of the possible relationships between the inputs and outputs of a unit.

The key capability requirements are:

(NOTE! The figure uses the old input data structure)

The flow_ratio_equality_coefficient parameter of the unit_flow__unit_flow relationship class allows you to constrain two unit_flow relationships to each other. Ordering of the unit_flow entities in the unit_flow__unit_flow relationship matters:

node__to_unit ǀ unit__to_node: equivalent to an (incremental) heat rate when the unit is the same in both.Input_flow = flow_ratio_equality_coefficient * output_flow + flow_ratio_equality_online_coefficient * units_on. It can be piecewise linear, used in conjunction with operating_points with monotonically increasing coefficients (not enforced). Used in conjunction with flow_ratio_equality_online_coefficient triggers a fixed flow when the unit is online and flow_ratio_start_flow triggers a flow on a unit start (start fuel consumption).
unit__to_node ǀ node__to_unit: equivalent to an efficiency when the unit is the same in both. output_flow = flow_ratio_equality_coefficient * input_flow + flow_ratio_equality_online_coefficient * units_on. The units online variable coefficient is added with flow_ratio_equality_online_coefficient.
In addition to node__to_unit ǀ unit__to_node and unit__to_node ǀ node__to_unit relationships, you can also define the flow_ratio_equality_coefficient parameter for node__to_unit ǀ node__to_unit and unit__to_node ǀ unit__to_node relationships.
Furthermore, you can have flow_ratio_less_than_coefficient and flow_ratio_greater_than_coefficient for any two unit_flow entities. For example: flow_ratio_less_than_coefficient for node__to_unit ǀ unit__to_node creates the following constraint:

To give a feeling for why these functionalities are useful, consider the following real world example for Compressed Air Energy Storage: