# Investment Optimization

SpineOpt offers numerous ways to optimise investment decisions energy system models and in particular, offers a number of methologogies for capturing increased detail in investment models while containing the impact on run time. The basic principles of investments will be discussed first and this will be followed by more advanced approaches.

## Key concepts for investments

Investment Decisions These are the investment decisions that SpineOpt currently supports. At a high level, this means that the activity of the entities in question is controlled by an investment decision variable. The current implementation supports investments in :

• unit:
• connection
• Storage - Note: while the above investment decisions correspond to an object class (i.e.) an investment in a unit or a connection, Storages are not an object class in themselves and are rather a property of a node. As such, a storage investment controls whether a particular node has a state variable or not.

Investment Variable Types In all cases the capacity of the unit or connection or the maximum node state of a node is multuplied by the investment variable which may either be continuous, binary or integer. This is determined, for units, by setting the unit_investment_variable_type parameter accordingly. Similary, for connections and node storages where the connection_investment_variable_type and storage_investment_variable_type are specified.

Identiying Investment Candidate Units, Connections and Storages The parameter candidate_units represents the number of units of this type that may be invested-in. candidate_units determines the upper bound of the investment variable and setting this to a value greater than 0 identifies the unit as an investment candidate unit in the optimisation. If the unit_investment_variable_type is set to :variable_type_integer, the investment variable can be interpreted as the number of discrete units that may be invested in. However, if unit_investment_variable_type is :variable_type_continuous and the unit_capacity is set to unity, the investment decision variable can then be intpreted as the capacity of the unit rather than the number of units with candidate_units being the maximum capacity that can be invested in. Finally, we can invest in discrete blocks of capacity by setting unit_capacity to the size of the investment capacity blocks and have unit_investment_variable_type set to :variable_type_integer with candidate_units representing the maximum number of capacity blocks that may be invested in. The key points here are:

Investment Costs Investment costs are specified by setting the appropriate *_investment\_cost parameter. The investment cost for units are specified by setting the unit unit_investment_cost parameter. This is currently interpreted as the full cost over the investment period for the unit. See the section below on investment temporal structure for setting the investment period. If the investment period is 1 year, then the corresponding unit_investment_cost is the annualised investment cost. For connections and storages, the investment cost parameters are connection_investment_cost and storage_investment_cost, respectively.

Temporal and Stochastic Structure of Investment Decisions SpineOpt's flexible stochastic and temporal structure extend to investments where individual investment decisions can have their own temporal and stochastic structure indepedent of other investment decisions and other model variables. A global temporal resolution for all investment decisions can be defined by specifying the relationship model__default_investment_temporal_block. If a specific temporal resolution is required for specific investment decisions, then one can specify the following relationships: - unit__investment_temporal_block for unit - connection__investment_temporal_block for connection - node__investment_temporal_block for storages. Specifying any of the above relationships will override the corresponding model__default_investment_temporal_block.

Similarly, a global stochastic structure can be defined for all investment decisions by specifying the relationship model__default_investment_stochastic_structure. If a specific stochastic structure is required for specific investment decisions, then one can specifying the following relationships: - unit__investment_stochastic_structure for unit - connection__investment_stochastic_structure for connection - node__investment_stochastic_structure for storages Specifying any of the above relationships will override the corresponding model__default_investment_stochastic_structure.

## Creating an Investment Candidate Unit Example

If we have model that is not currently set up for investments and we wish to create an investment candidate unit, we can take the following steps.

• Create the unit object with all the relationships and parameters necessary to describe its function.
• Ensure that the number_of_units parameter is set to zero so that the unit is unavailable unless invested-in
• Set the candidate_units parameter for the unit to 1 to specify that a maximum of 1 new unit of this type may be invested-in by the model.
• Set the unit_investment_variable_type to unit_investment_variable_type_integer to specify that this is a discrete unit investment decision.
• Specify the unit_investment_lifetime of the unit to, say, 1 year to specify that this is the minimum amount of time this new unit must be in existence after being invested-in.
• Specify the investment period for this unit's investment decision in one of two ways
• Similarly to the above, define the stochastic structure for the unit's investment decision by specifying either model__default_investment_stochastic_structure or unit__investment_stochastic_structure
• Specifying your unit's investment cost by setting the unit_investment_cost parameter. Since we have defined the investment period above as 1 year, this is therefore the unit's annualised investment cost.

## Model Reference

### Variables for investments

Variable NameIndicesDescription
units_invested_availableunit, s, tThe number of invested in units that are available at a given (s, t)
units_investedunit, s, tThe point-in-time investment decision corresponding to the number of units invested in at (s,t)
units_mothballedunit, s, t"Instantaneous" decision variable to mothball a unit
connections_invested_availableconnection, s, tThe number of invested-in connectionss that are available at a given (s, t)
connections_investedconnection, s, tThe point-in-time investment decision corresponding to the number of connectionss invested in at (s,t)
connections_decommissionedconnection, s, t"Instantaneous" decision variable to decommission a connection
storages_invested_availablenode, s, tThe number of invested-in storages that are available at a given (s, t)
storages_investednode, s, tThe point-in-time investment decision corresponding to the number of storages invested in at (s,t)
storages_decommissionednode, s, t"instantaneous" decision variable to decommission a storage

### Relationships for investments

Relationship NameRelated Object Class ListDescription
model__default_investment_temporal_blockmodel, temporal_blockDefault temporal resolution for investment decisions effective if unit__investmenttemporalblock is not specified
model__default_investment_stochastic_structuremodel, stochastic_structureDefault stochastic structure for investment decisions effective if unit__investmentstochasticstructure is not specified
unit__investment_temporal_blockunit, temporal_blockSet temporal resolution of investment decisions - overrides model__defaultinvestmenttemporal_block
unit__investment_stochastic_structureunit, stochastic_structureSet stochastic structure for investment decisions - overrides model__defaultinvestmentstochastic_structure

### Parameters for investments

Parameter NameObject Class ListDescription
candidate_unitsunitThe number of additional units of this type that can be invested in
unit_investment_costunitThe total overnight investment cost per candidate unit over the model horizon
unit_investment_lifetimeunitThe investment lifetime of the unit - once invested-in, a unit must exist for at least this amount of time
unit_investment_variable_typeunitWhether the units_invested_available variable is continuous, integer or binary
fix_units_investedunitFix the value of units_invested
fix_units_invested_availableunitFix the value of connections_invested_available
candidate_connectionsconnectionThe number of additional connections of this type that can be invested in
connection_investment_costconnectionThe total overnight investment cost per candidate connection over the model horizon
connection_investment_lifetimeconnectionThe investment lifetime of the connection - once invested-in, a connection must exist for at least this amount of time
connection_investment_variable_typeconnectionWhether the connections_invested_available variable is continuous, integer or binary
fix_connections_investedconnectionFix the value of connections_invested
fix_connections_invested_availableconnectionFix the value of connection_invested_available
candidate_storagesnodeThe number of additional storages of this type that can be invested in at node
storage_investment_costnodeThe total overnight investment cost per candidate storage over the model horizon
storage_investment_lifetimenodeThe investment lifetime of the storage - once invested-in, a storage must exist for at least this amount of time
storage_investment_variable_typenodeWhether the storages_invested_available variable is continuous, integer or binary
fix_storages_investednodeFix the value of storages_invested
fix_storages_invested_availablenodeFix the value of storages_invested_available
FilenameRelative PathDescription
constraintunitsinvested_available.jl\constraintsconstrains units_invested_available to be less than candidate_units
constraintunitsinvested_transition.jl\constraintsdefines the relationship between units_invested_available, units_invested and units_mothballed. Analagous to units_on, units_started and units_shutdown
constraintunitlifetime.jl\constraintsonce a unit is invested-in, it must remain in existence for at least unit_investment_lifetime - analagous to min_up_time.
constraintunitsavailable.jl\constraintsEnforces units_available is the sum of number_of_units and units_invested_available
constraintconnectionsinvested_available.jl\constraintsconstrains connections_invested_available to be less than candidate_connections
constraintconnectionsinvested_transition.jl\constraintsdefines the relationship between connections_invested_available, connections_invested and connections_decommissioned. Analagous to units_on, units_started and units_shutdown
constraintconnectionlifetime.jl\constraintsonce a connection is invested-in, it must remain in existence for at least connection_investment_lifetime - analagous to min_up_time.
constraintstoragesinvested_available.jl\constraintsconstrains storages_invested_available to be less than candidate_storages
constraintstoragesinvested_transition.jl\constraintsdefines the relationship between storages_invested_available, storages_invested and storages_decommissioned. Analagous to units_on, units_started and units_shutdown
constraintstoragelifetime.jl\constraintsonce a storage is invested-in, it must remain in existence for at least storage_investment_lifetime - analagous to min_up_time.