Glossary

Activity: The quantity representing how much an Asset operates during a given period. Its flow coefficients determine the resulting input and output flows of each Commodity.

Agent: A decision-making entity in the system. An Agent is responsible for serving a user-specified portion of a Commodity demand or Service Demand. Agents invest in and operate Assets to serve demands and produce Commodities.

Agent Objective: One or more objectives that an Agent considers when deciding which Process to invest in. Objectives can be economic, environmental, or others. An Agent can use multiple objectives when applying a Decision Rule.

Agent Share: The portion of a Commodity demand for which an Agent is responsible. Agent shares determine how total demand is divided between agents and can also scale investment limits. For example, if total electricity demand is 100 PJ and an Agent has a 25% Agent Share, that Agent is responsible for 25 PJ of demand.

Annualised Capital Cost: The annual cost equivalent of an upfront Capital Cost, calculated using the Capital Recovery Factor for the relevant Asset Lifetime and Discount Rate. For example, an Asset with a £1 million Capital Cost, a 10-year Lifetime, and a 5% Discount Rate has an annualised Capital Cost of approximately £129,500 per year.

Asset: A specific instance of a Process, representing installed or candidate capacity. It carries the Process’s technical and economic properties, and adds instance-specific information such as Capacity, ownership, location, commissioning Year, and operating state.

Asset Commissioning: The point at which an Asset becomes active and available for Dispatch. An Asset is commissioned according to its commission Year, either from user input or following an investment decision.

Asset Decommissioning: The permanent removal of an Asset from the active model. An Asset can be decommissioned when it reaches the end of its allowed Lifetime or after remaining mothballed for the configured period.

Asset Mothballing: The temporary withdrawal of an Asset or some of its tranches from the active pool when it is not selected for retention. A mothballed Asset is not dispatched, but may be reactivated in a later investment period; it is permanently decommissioned if it remains mothballed for longer than a configured number of years.

Asset Tranche: A discrete portion of an Asset’s Capacity. An Asset can consist of multiple Asset Tranches of equal size, which can be retained, mothballed, or decommissioned independently.

Availability: A Process property specifying the maximum, minimum, or fixed percentage of maximum Activity that its Assets can deliver over a period. It can be specified for a single Time Slice, a Season, or a Year. For example, an Asset with 100 MW of Capacity and 50% annual Availability can provide at most 50 MW over the year. This is a limit, not a measure of how much the Asset is actually used; that is its Utilisation.

Base Year: The starting Year of a model run. The Base Year is typically calibrated to known data, including Asset stock and Commodity consumption/production.

Calibration: The act of ensuring that the model represents the system being modelled in a historical base year. A set of Assets must exist in the Base Year sufficient to serve Base Year demands.

Candidate Asset: A hypothetical Asset representing a Process that is available for an Agent to invest in, but has not yet been selected or commissioned. Its Capacity is assigned for investment appraisal and can be adjusted during the investment process.

Capacity: The installed size of an Asset. Together with its Capacity-to-activity factor, it determines the maximum Activity the Asset can perform.

Capacity-to-activity factor: The factor that converts an Asset’s Capacity into its maximum annual Activity.

Capital Cost: The upfront cost per unit of Capacity established in an Asset. It does not vary directly with short-term Activity.

Capital Recovery Factor: The factor used to convert an upfront Capital Cost into an annualised cost over an Asset’s Lifetime at a given Discount Rate. It represents the proportion of the upfront capital cost that is paid each year to spread that cost over the asset’s lifetime. The factor increases with the discount rate and decreases as the lifetime increases. When the discount rate is zero, it is the reciprocal of the lifetime.

Circular Commodity Dependency: A dependency cycle in which the production or consumption of one Commodity depends, directly or indirectly, on another Commodity that eventually depends on the first. For example, electricity can be used to produce hydrogen, which is then used to produce electricity.

Commodity: A substance (e.g. CO₂) or form of energy (e.g. electricity) that can be produced and/or consumed by Processes in the model. A Service Demand is a type of Commodity that is defined at the end point of the system.

Commodity Graph: A directed graph built by MUSE2 for each Milestone Year, in which nodes are Commodity Markets and edges are Processes. It is used to validate the model, determine the Investment Order and identify Circular Commodity Dependencies.

Commodity Levy: Represents a tax, levy or other external cost on a Commodity. Levies can be applied to all Commodity production (sum of output of all Assets for that Commodity), net production (sum of output and input for all Assets), or all consumption (sum of input for all Assets). It can also be negative, indicating an incentive on Commodity production/consumption/net.

Commodity Market: The market for a particular Commodity in a Region. MUSE2 evaluates each market during investment and calculates prices for the Commodity based on the operation of relevant Assets and the applicable Pricing Strategy.

Decision Rule: The rule via which an Agent uses the Agent Objective(s) to decide between Process options to invest in.

Demand Distribution: The allocation of annual Service Demand across Time Slices within a Year. It specifies how much of the annual demand occurs in each Time Slice, while the total across the year remains equal to the annual demand.

Discount Rate: The proportion used to convert a Process’s future costs and benefits into present-value terms. For example, a discount rate of 0.05 means that £100 received in one year’s time is valued at approximately £95.24 today (100 / (1 + 0.05)).

Dispatch: The way in which Assets are operated to serve demand. Within the limits imposed by Availability, Commodity balances, and other user-defined constraints, MUSE2 effectively dispatches Assets in Merit Order: cheaper Assets are used first, up to their available capacity or until demand is met. The resulting operation is calculated by a least-cost linear programme.

End Year: The final year in the model Time Horizon.

Equivalent Annual Cost (EAC): The constant annual cost equivalent of an Asset’s upfront capital cost and operating costs over its Lifetime, accounting for the Discount Rate.

Fixed Operating Cost: The annual operating cost charged per unit of an Asset’s Capacity. Unlike Variable Operating Cost, it does not vary directly with Activity.

Flow Coefficient: The factor that converts one unit of Activity into the corresponding input or output flow of a Commodity. Positive coefficients represent production and negative coefficients represent consumption. For example, a flow coefficient of 2 means that one unit of Activity produces two units of that Commodity.

Full Cost: The cost of producing a unit of output including Marginal Cost, annualised Capital Cost, and Fixed Operating Cost. For example, a Process with low fuel costs but high Capital Cost may have a low Marginal Cost but a higher Full Cost.

Input Commodity: A Commodity that flows into a Process. A Process may have multiple input commodities.

Investment Appraisal: The process of evaluating existing and Candidate Assets to determine which investments an Agent should make in a particular Commodity Market and Milestone Year. Appraisal considers the Agent Objective, expected costs, commodity prices, and the asset’s expected operation.

Investment Order: The sequence in which Commodity markets are considered for investment. MUSE2 generally processes downstream markets before upstream markets, so that demand for input Commodities created by committed Assets is known when the upstream markets are evaluated. For example, investment in electricity generation is considered before investment in gas production when gas is used to generate electricity.

Ironing-out Loop: The repeated sequence of Agent investment and Dispatch used to resolve price instability introduced by new capacity commitments. The loop stops when time-slice-weighted market prices converge within the configured tolerance or the maximum number of iterations is reached.

Levelised Cost of X (LCOX): The cost per unit of output Commodity X from an Asset, calculated by dividing its discounted lifetime costs by its discounted lifetime output under a specified Discount Rate.

Lifetime: The expected operational duration of a Process, measured in years.

Marginal Cost: The cost of producing one additional unit of an output Commodity from an Asset. It combines the Process’s Variable Operating Cost with activity-dependent costs associated with the Asset’s commodity flows, such as input prices and levies. It excludes Capital Cost and Fixed Operating Cost.

Merit Order: A method of operating Assets where the cheapest is dispatched first, followed by the next most expensive, etc, until demand is served.

Milestone Year: A Year in the Time Horizon where model results are recorded. A model can have multiple Milestone Years. For example, with a 2025 Base Year and End Year 2100, a user might choose to record outputs in 5-year steps.

Net Present Value (NPV): The value of future costs and benefits expressed in the present, calculated by discounting them using a specified Discount Rate.

OTH (other)-type commodity: A Commodity that is not supply-demand balanced in the model. Includes side products and emissions such as CO₂, or any raw materials that are not output by modelled Processes.

Output Commodity: A Commodity that flows out of a Process. A Process may have multiple output commodities.

Partial Equilibrium: An equilibrium in which only the user-defined Commodities and markets are balanced. MUSE2 does not attempt to equilibrate the whole economy.

Pricing Strategy: The method used to calculate a Commodity’s price. This includes Marginal Cost pricing, Full Cost pricing, and Shadow Price pricing.

Process: A blueprint of an available Process that converts Input Commodities to Output Commodities. Processes have economic attributes of Capital Cost, Fixed Operating Cost per unit Capacity, Variable Operating Cost per unit Activity, and risk Discount Rate. They have physical attributes of quantity and type of Input Commodities and Output Commodities (which implicitly specify efficiency), Availability limits (by Time Slice, Season, and/or Year), and Lifetime (years). When a Process is selected by an Agent for investment an instance of it called an Asset is created.

Region: A geographical area represented in the model. Regions contain the Assets, Processes, Agents, demands, and Commodity markets that apply in that area, and define the boundaries within which trade and other regional interactions are modelled.

Search Space: The set of Processes an Agent is allowed to consider for investment, defined for a particular Commodity, Region, and Year. It determines which Candidate Assets are available during investment appraisal.

Season: A subdivision of a Year that groups related Time Slices. For example, summer, winter, or other.

Sector: Models are often broken down into sectors, each of which is associated with specific Service Demands or specific Commodity production. For example, the residential sector, the power sector, etc.

Service Demand (SVD): A Commodity consumed at the boundary of the modelled system to represent demand for a service. For example, tonne-kilometres of road freight or PJ of useful heat demand.

Shadow Price: The value of relaxing a Commodity balance constraint by one unit, as calculated by the Dispatch optimisation. For example, a high Shadow Price indicates that one additional unit of a Commodity would substantially improve the optimisation objective because supply is scarce.

Supply Equals Demand (SED): An SED Commodity is a type of Commodity that is both consumed and produced by Assets in the system. In fully resolved systems, supply of these Commodities is constrained to be equal to or greater than demand.

Time Horizon: The overall period modelled. For example, 2025–2100.

Time Slice: A discrete operational sub-period within a Year, identified by a Season and a time-of-day category. For example, a Time Slice might represent winter-day or summer-night. Time Slices are the within-year periods over which Activity, demand, and flows are modelled. A Time Slice can be grouped with other Time Slices in a Time-slice Selection to represent a Season, an entire Year, or another temporal grouping.

Time-slice Level: The temporal resolution at which a Commodity’s balance constraints are applied. MUSE2 supports annual, seasonal, and day-night levels, from a whole year to a particular time of day. For example, an annual level balances total supply and demand across the year, whereas a day-night level requires the balance to be met separately in each time-of-day group.

Time-slice Selection: A group of model Time Slices treated as one period when applying an Asset’s Activity or Availability constraints, or balancing a Commodity at its Time-slice Level. For example, a selection can group all winter Time Slices so that a seasonal Availability limit applies to their combined Activity.

Tranche Size: The capacity of one tranche of an Asset. Every Asset has a Tranche Size, either defined when the Asset is created or inferred when an investment is made. Tranche Size defines the granularity at which retention, mothballing, and decommissioning decisions are made. For example, a 100 MW Asset with a 25 MW Tranche Size has four tranches, which can be retained or mothballed independently.

Utilisation: The proportion of an Asset’s Capacity that is actually used to produce its Commodities, ranging from 0 to 1 inclusive. Can be measured at Time Slice, Season, or Year level. For example, an Asset operating at 25 MW from 100 MW of available Capacity has 0.25 Utilisation. Availability describes what the Asset could provide; Utilisation describes what it actually provides.

Variable Operating Cost: A Process parameter specifying the generic operating cost per unit of Activity. It excludes costs associated with commodity flows, such as input prices and levies.

Year: A calendar year used to identify a Base Year, Milestone Year, or End Year and to specify when an Asset is commissioned or decommissioned.