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:

• Easily define arbitrary numbers of input and output flows
• Easily create piecewise affine linear relationships between any two flows
• Anything more complicated can be done via user_constraints

unit__node__node relationship

The unit__node__node relationship allows you to constrain two nodes to each other via a number of different parameters.:

• fix_ratio_in_out_unit_flow: equivalent to an (incremental) heat rate. Input_flow = fix_ratio_in_out_unit_flow * output_flow + fix_units_on_coefficient_in_out * units_on. It can be piecewise linear, used in conjunction with operating_points with monotonically increasing coefficients (not enforced). Used in conjunction with fix_units_on_coefficient_in_out triggers a fixed flow when the unit is online and unit_start_flow triggers a flow on a unit start (start fuel consumption).
• fix_ratio_out_in_unit_flow: equivalent to an efficiency. Output_flow = fix_ratio_out_in_unit_flow x input_flow + fix_units_on_coefficient_out_in * units_on. Ordering of the nodes in the unit__node__node relationship matters. The first node will be the output flow and the second node will be treated as the input flow (consistently with the out_in in the parameter name. A units_on coefficient is added with fix_units_on_coefficient_out_in.
• In addition to fix_ratio_in_out_unit_flow and fix_ratio_out_in_unit_flow you have [constraint]_ratio_[direction1]_[direction2]_unit_flow where constraint can be min, max or fix and determines the sense of the constraint (max: <, min: >, fix: =) while direction1 and direction2 are used to interpret the direction of the flows involved. In signifies an input flow to the unit while out signifies an output flow from the unit. For each of these parameters, there is a corresponding [constraint]_[direction1]_[direction2]_units_on_coefficient. For example: max_ratio_in_out_unit_flow creates the following constraint:

input_flow < max_ratio_in_out_unit_flow * output_flow + max_units_on_coefficient_in_out * units_on

real world example: Compressed Air Energy Storage

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

known issues

That does not mean that this implementation is perfect; there are some known issues:

• Multiple ways to do the same thing (kind of)
• The ordering of nodes in unit__node__node relationship matters and this can be confusing
• When specifying a unit__node__node relationship, currently toolbox doesn’t constrain a user to choosing nodes that are connected to the unit. It’s possible to create a unit__node__node relationship between a unit and nodes where there are no flows. We actually need to define a relationship between two flows, which is really a relationship between a unit__[to/from]_node relationship and a unit__[to/from]_node relationship.
• There is a long list of parameters (24 in total) [fix/max/min]_ratio_[in/out]_[in/out]_[unit_flow/units_on_coefficient]