Units and Dimensions

MUSE2 does not impose one universal system of physical units. Instead, the input files define the unit conventions used by each model. Commodity units are provided in the units field of commodities.csv, while the optional currency field in model.toml documents the currency and, if needed, its reference year. Process flow coefficients and capacity_to_activity then define the relationships between activity, commodity flows, and capacity.

MUSE2 requires commodity unit labels to be present and uses them to check consistency, but it does not interpret their contents, convert between units, or perform general dimensional analysis. For example, PJ, tonnes, and ktCO2 are simply labels to MUSE2; their physical meanings come from the conventions chosen by the modeller. Similarly, the currency value is just a label: MUSE2 does not perform currency conversions or adjust monetary values for inflation.

The main relationships are:

• Activity describes how much a Process operates.
• Commodity units label the quantities produced and consumed by a Process.
• Flow coefficients convert activity into input and output flows of each Commodity.
• Capacity-to-activity relates installed capacity to maximum annual activity.
• Capacity limits the activity an Asset can perform.
• Monetary units describe how costs and prices are expressed.

For the example models, energy commodities are measured in PJ, generation capacity is expressed in GW, emissions are measured in ktCO2, and monetary values are expressed in millions of US dollars.

Commodity flows and flow coefficients

Every commodity must provide a unit label in the units field of commodities.csv. The label is useful for documentation purposes, and is only used by MUSE2 for consistency checks; MUSE2 does not parse it or convert between labels. The “simple” example uses:

If any process has multiple SED or SVD output commodities, these commodities must all use exactly the same unit label - this is checked and enforced during input file loading. Inputs and OTH outputs are not subject to this check.

A process flow coefficient converts one activity unit into the corresponding commodity flow. Positive coefficients represent production and negative coefficients represent consumption. A flow coefficient therefore maps a dimensionless activity quantity to the corresponding commodity-flow quantity. The coefficient must be interpreted together with the commodity’s unit label.

For example, the “simple” example defines the gas combined-cycle turbine with these flows:

Activity

Activity is a dimensionless, process-specific quantity used by MUSE2 to describe how much an asset operates in a time slice. It has no intrinsic physical unit. Its physical interpretation is supplied by the process’s flow coefficients and commodity-unit labels, while its maximum annual amount is constrained by the asset’s capacity and capacity_to_activity.

Capacity and capacity-to-activity

Capacity is the installed size of an Asset. Its unit depends on the technology and the model. For example, a power station might have capacity in MW or GW, while a material-processing process might use tonnes per year.

The capacity_to_activity factor gives the maximum annual activity per unit of capacity. The factor, flow coefficients, and commodity-unit labels work together to define what the capacity unit represents physically.

In the “simple” example, the wind-farm and gas-turbine processes use capacity_to_activity = 31.54. Since electricity output is labelled PJ and has a coefficient of 1.0, this value was chosen so that one capacity unit corresponds to 1 GW of electricity-generating capacity, able to produce up to 31.54 PJ of electricity per year. This follows from:

1 GW x 31,536,000 seconds per year = 31,536,000,000,000,000 J per year = 31.536 PJ per year

The model’s value of 31.54 is rounded from 31.536. At full activity, the gas-turbine coefficients (above) then imply 47.31 PJ of natural-gas consumption per year, and approximately 2,419 ktCO2 of emissions. In practice, availability limits may reduce actual activity below this maximum.

Conversely, a coal-producing process where coal is measured in tonnes, with an output coefficient of 1.0, might use capacity_to_activity = 1, so that one capacity unit represents an amount of capacity able to produce up to one tonne of coal per year.

Monetary units

MUSE2 does not convert currencies or adjust monetary values for inflation. Therefore, all monetary inputs and outputs must be expressed using a consistent currency and reference year. For documentation purposes, the currency and reference year can be included in the currency label in model.toml, such as:

currency = "MUSD2020"

This is a free-text label for documenting the monetary convention used by a model. It has no prescribed format, so modellers can use it to record a currency, reference year, or any other relevant information.

Here, MUSD2020 means million US dollars expressed in 2020 terms. The label is descriptive metadata only; it does not determine the units of monetary data or affect model calculations.

For example, with currency = "MUSD2020" and capacity measured in GW, the monetary quantities would be expressed as follows:

For example, a variable_operating_cost of 0.55 in a model defined with currency = "MUSD2020" means that one activity unit incurs a variable operating cost of 0.55 MUSD2020 (i.e. $550,000 in 2020 terms).

Choosing consistent units

When building a model:

1. Choose units for each commodity, such as PJ for energy and ktCO2 for emissions.
2. Choose a capacity unit for each process, such as GW for a power plant.
3. Set capacity_to_activity so that capacity converts to the appropriate annual activity scale.
4. Define flow coefficients so that activity produces and consumes the intended commodity quantities.
5. Express all costs and prices using the same currency convention and the relevant capacity, activity, or commodity-flow denominator.

MUSE2 validates some unit relationships, but it does not perform general unit conversion. A model can use different physical units for different commodities, provided that each process’s capacity, activity, flow, and cost data are dimensionally consistent.