Investment Appraisal

This section describes the investment and asset retention process applied at each milestone year (MSY). For each commodity market (a commodity–region pair), processed in investment order (see below), agents evaluate every available supply option — existing commissioned assets and new candidate assets from their search space — and select the best option to commit. The committed asset’s production is subtracted from the remaining demand for that market, and the process repeats until demand is met or no feasible options remain. Demands for ServiceDemand (SVD) commodities are fixed from the input data, while demands for SupplyEqualsDemand (SED) commodities accumulate as assets are committed earlier in the investment order.

Investment Order

Investment decisions are made sequentially, starting from the most downstream commodity markets and moving upstream. For example, in a model where gas may be used to generate electricity, investment in electricity generation would happen before investment in gas production.

This ordering ensures that when an upstream market is being invested in, the demand created by already-committed downstream assets is already known.

Markets are processed in layers: a layer is a set of commodity markets that are independent of one another (i.e. at the same depth in the commodity graph and with no dependencies between them). All markets within a layer are settled before moving to the next layer. After each layer is settled, a single partial system dispatch is run over all assets selected so far. This quantifies the input commodity flows consumed by newly committed assets — for example, a gas generator committed during electricity market investment will consume gas, creating demand that the gas market investment must subsequently meet.

Only commodities of type ServiceDemand and SupplyEqualsDemand are subject to investment decisions. Other commodity types (e.g. OTH) are excluded.

Note: the investment order is the reverse of the price calculation order, where prices are computed upstream first.

Circularities

When commodity markets form a cycle (e.g. electricity → hydrogen → electricity), the markets in the cycle are resolved in sequence within one pass. After each market in the cycle is visited, a partial system dispatch is run to rebalance demand. Newly committed assets within the cycle are given limited capacity flexibility, controlled by the capacity_margin parameter (defined in model.toml), to absorb small demand shifts caused by later markets in the cycle. If these shifts exceed capacity_margin, the simulation terminates with an error, and the user should increase this parameter.

Commodity Prices Used in Appraisal

Investment appraisal uses two distinct price sets, both sourced from the previous MSY’s dispatch (or from the previous ironing-out loop iteration if enabled):

• Shadow prices \( \lambda_{c,r,t} \): used for activity coefficients in the mini dispatch optimisation step of each appraisal (see Mini Dispatch Optimisation).
• Market prices \( \pi_{c,r,t} \): used to calculate the investment metric (Cost Index or SNAS) after dispatch.
• Fallback prices \( \phi_{c,r,t} \): used to incentivise dispatch in the mini dispatch optimisation when shadow prices alone are insufficient (see Mini Dispatch Optimisation). Calculated using the strategy defined by fallback_pricing_strategy in model.toml.

See Commodity Prices for how these price sets are calculated.

Agent Shares

Each commodity market may be served by multiple agents, each responsible for a defined share (or portion) of the total demand. An agent’s portion determines:

• The fraction of the total demand that the agent is responsible for meeting.
• The scaling applied to any addition_limit and total_capacity_limit investment constraints (see Investment Constraints).

Agent portions for each commodity and milestone year are defined in the agent input files.

Investment Options

For each commodity market, agents consider two categories of supply option:

• Existing assets: already-commissioned assets owned by the agent that produce the commodity of interest as their primary output.
• Candidate assets: processes in the agent’s search space with the commodity of interest as their primary output, available to be newly built.

Annualised Fixed Cost

The annualised fixed cost (AFC) per unit of capacity differs between the two categories:

• Existing assets: AFC comprises only the fixed operations and maintenance (O&M) cost (\( \mathrm{FOM} \)): \[ \mathrm{AFC}_{\mathrm{existing}} = \mathrm{FOM} \]

• Candidate assets: AFC includes annualised capital expenditure plus fixed O&M: \[ \mathrm{AFC}_{\mathrm{candidate}} = \mathrm{CAPEX} \times \mathrm{CRF} + \mathrm{FOM} \]

  where the Capital Recovery Factor (CRF) annualises the upfront capital cost over the asset’s lifetime \( L \) at discount rate \( d \): \[ \mathrm{CRF} = \frac{d \cdot (1 + d)^L}{(1 + d)^L - 1} \]

  If \( d = 0 \), then \( \mathrm{CRF} = 1/L \).

Asset Capacities

Every asset consists of one or more equal-capacity tranches. A single-tranche asset is retained or mothballed as a whole, while the tranches of a multi-tranche asset can be retained or mothballed independently (see Mothballing and Decommissioning).

• For assets defined in assets.csv, an explicitly supplied num_tranches determines the tranche size. Otherwise, a process tranche_size determines the tranche size. If neither is supplied, the asset consists of one tranche with its full capacity.
• Assets invested in by MUSE are commissioned one tranche at a time, using the process tranche_size if defined, or a tranche size inferred from demand at the time of investment (see “trial capacity” below).

Existing assets

Existing assets (i.e assets that have already been commissioned, whether via assets.csv or by MUSE) are appraised one tranche at a time to decide how many tranches to retain. This allows partial retention — for example, some tranches of a multi-tranche plant may be retained while others are mothballed.

Candidate assets

Before a candidate asset for new investment can be appraised, it is assigned a trial capacity. This is the capacity of one tranche, or the amount of capacity that can be installed in a single investment round.

If a process has a defined tranche_size, the trial capacity is set to that tranche size. Otherwise, the tranche size is inferred from the capacity that would satisfy the total annual demand if the asset operated at its maximum annual rate:

\[ \mathrm{TrialCapacity} = \frac{\sum_t \mathrm{Demand}_t}{\mathrm{MaxAnnualSupplyPerCapacity}} \times \mathrm{CapacityTrancheFraction} \]

capacity_tranche_fraction (set in model.toml, must be > 0 and <= 1) controls the size of inferred investment tranches relative to this demand-based capacity. Lower values produce smaller tranches and therefore require more investment rounds, while higher values produce larger tranches.

Investment constraints

Processes may be subject to investment constraints defined in process_investment_constraints.csv: an addition_limit constraining new-build capacity, and a total_capacity_limit constraining total installed capacity.

In multi-agent simulations, both limits are scaled by \( \mathrm{AgentPortion} \), the fraction of the commodity market for which an agent is responsible, to give a limit for each agent. One agent falling short of its own limits does not allow others to exceed theirs. Therefore, the overall limits can only ever be reached if all agents max out their own individual limits.

Addition limits

The addition_limit specifies the maximum new capacity that can be built per year, and applies only to candidate (new-build) assets. The installable capacity limit for a given process (\( p \)), agent (\( g \)), region (\( r \)), commodity (\( c \)) and milestone year (\( y \)) is:

\[ \mathrm{MaxInstallableCapacity}_{p,r,y,g} = \mathrm{AdditionLimit}_{p,r,y} \cdot \Delta_{\mathrm{MSY}} \cdot \mathrm{AgentPortion}_{c,r,y,g} \]

where \( \Delta_{\mathrm{MSY}} \) is the number of years since the previous milestone year.

Each selection of a candidate asset tranche counts towards the \(\mathrm{MaxInstallableCapacity} \) of that process. A candidate asset tranche is excluded from consideration if its capacity would exceed the remaining limit.

Total capacity limits

The total_capacity_limit specifies a hard upper limit on the total capacity of a process that may exist at any given time. This includes both existing assets which are considered for retention, and candidate assets which are considered for commissioning. The total capacity limit for a given process, agent, region, commodity and milestone year is:

\[ \mathrm{MaxTotalCapacity}_{p,r,y,g} = \mathrm{TotalCapacityLimit}_{p,r,y} \cdot \mathrm{AgentPortion}_{c,r,y,g} \]

Each selection of a candidate asset tranche, or retention of an existing asset tranche, counts towards the \(\mathrm{MaxTotalCapacity} \) of their respective process. Any tranche (whether for a candidate asset or an existing asset) is excluded from consideration if it would exceed the remaining limit.

Mini Dispatch Optimisation

For each supply option being appraised, a small linear programme (LP) is solved to determine the optimal activity profile given the current remaining demand.

Activity coefficients

The mini dispatch optimisation implicitly frames each time slice as a choice: the asset can either produce the commodity of interest, or it can be treated as procured from an alternative source at the fallback price \( \phi_{c,r,t} \). Each unit of activity produces \( f_{c,\mathrm{primary}} \) units of output, displacing that quantity from the fallback source. The optimiser therefore dispatches the asset whenever doing so is cheaper than procuring from elsewhere.

This is captured by the activity coefficient \( \alpha_t \), which combines two components:

\[ \mathrm{NetOperatingCost}_t = \mathrm{OperatingCost}(t) - \mathrm{RevenueFromFlows}(\lambda, t) \]

\[ \mathrm{FallbackCost} = \phi_{c,r,t} \cdot f_{c,\mathrm{primary}} \]

\[ \alpha_t = \mathrm{FallbackCost} - \mathrm{NetOperatingCost}_t + \varepsilon \]

where \( \mathrm{RevenueFromFlows} \) is the sum of all commodity flow revenues and costs (positive for outputs, negative for inputs) valued at shadow prices, \( \mathrm{OperatingCost} \) is the variable operating cost plus levies and flow costs, \( f_{c,\mathrm{primary}} \) is the primary output flow coefficient, and \( \varepsilon \) is a small positive constant added to ensure that break-even assets are still dispatched.

NetOperatingCost is the net cost of running the asset for one unit of activity at shadow prices — negative when the asset is profitable (revenues exceed costs).

FallbackCost is the cost of procuring one unit of activity’s worth of primary output from an alternative source at the fallback price.

The asset dispatches when \( \alpha_t > 0 \), i.e. when:

\[ \mathrm{NetOperatingCost}_t < \mathrm{FallbackCost} \]

\( \phi_{c,r,t} \) is calculated according to the strategy defined by fallback_pricing_strategy in model.toml.

Constraints

• Activity bounds: the sum of activity within each time-slice selection is bounded by the asset’s availability limits multiplied by its capacity.
• Demand constraints: demand for a commodity is balanced at the commodity’s defined time-slice level (e.g. annual, seasonal, or time-slice). The total supply (activity × flow coefficient) within each balance bucket must not exceed the remaining demand for that bucket.

Objective

The optimisation maximises the total net revenue across all time slices, subject to the above constraints:

\[ \max \sum_t \alpha_t \cdot \mathrm{Activity}_t \]

Metric Calculation

After the dispatch LP is solved, an investment metric is calculated from the resulting activity profile using market prices.

Market costs per time slice

The market cost \( \mu_t \) is calculated differently depending on the objective type:

• LCOX: the net cost of operating, excluding revenues from the primary output commodity: \[ \mu_t^{\mathrm{LCOX}} = \mathrm{OperatingCost}(t) - \mathrm{RevenueFromNonPrimaryFlows}(\pi, t) \]

• NPV: the net cost of operating, including all commodity flows (so negative values represent profit): \[ \mu_t^{\mathrm{NPV}} = \mathrm{OperatingCost}(t) - \mathrm{RevenueFromFlows}(\pi, t) \]

LCOX metric (objective_type = "lcox")

The LCOX metric is calculated as the total annualised cost divided by total annual output, using the above defined market costs which exclude the primary output commodity:

\[ \mathrm{LCOXMetric} = \frac{\mathrm{AFC} \times \mathrm{Capacity} + \sum_t \mathrm{Activity}_t \times \mu_t^{\mathrm{LCOX}}} {\sum_t \mathrm{Activity}_t} \]

Lower values indicate lower-cost investments.

NPV metric (objective_type = "npv")

The NPV metric is based on the Specific Net Annualised Surplus (SNAS). This the net surplus per unit of activity, using market costs that include the primary output commodity:

\[ \mathrm{SNAS} = \frac{-\left(\mathrm{AFC} \times \mathrm{Capacity} + \sum_t \mathrm{Activity}_t \times \mu_t^{\mathrm{NPV}}\right)}{\sum_t \mathrm{Activity}_t} \]

Higher values indicate more profitable investments.

For both metrics, any option with zero total activity after the mini dispatch LP is excluded from consideration, as it cannot contribute to meeting demand. This will generally happen if all time slices have negative activity coefficients, unless the process has lower-bound activity constraints that force activity.

Asset Selection

Sorting and tie-breaking

All feasible options are appraised and ranked by their metric. When two options have approximately equal metrics, the following tie-breaking rules are applied in order:

1. Existing commissioned assets are preferred over new candidates.
2. Among existing assets, newer assets (commissioned more recently) are preferred.
3. If the tie is still unresolved, the first option in the ordering is selected arbitrarily, and a debug-level log message is emitted.

Selection loop

The best-ranked asset is committed. Its production profile from the mini dispatch optimisation is subtracted from the remaining demand, and the loop repeats with the updated demand profile. This continues until:

• The remaining demand falls below remaining_demand_absolute_tolerance (in model.toml), or
• No feasible options remain. In this case, a warning is logged and the loop ends early. The unmet demand may still be satisfied during the full system dispatch, but is not guaranteed.

If demand cannot be met at all due to overly restrictive investment constraints, the simulation terminates with an error.

Note: only production of the primary output commodity is counted against the remaining demand. If a committed asset also produces other commodities as secondary outputs, that side-production does not reduce the demand targets of those other commodity markets. This behaviour may be revised in a future release.

Mothballing and Decommissioning

After investment is complete for a given MSY, any previously commissioned assets (or individual tranches making up the asset) that were not selected for retention are mothballed: their mothball year is recorded and they are removed from the active asset pool. They remain available for potential re-selection in future MSYs.

A mothballed asset that remains unused for mothball_years consecutive years (as defined in model.toml) is decommissioned — permanently removed from the asset pool and excluded from all future investment and dispatch.

Example: Gas Power Plant

The following illustrates how LCOX and NPV metrics are calculated for a gas combined-cycle power plant, evaluated across two time slices: \( t_0 \) (peak) and \( t_1 \) (off-peak).

Parameters

Asset flows and operating costs

All per-flow costs (\( \mathrm{cost}_{\mathrm{input}} \), \( \mathrm{cost}_{\mathrm{output}} \)) are zero.

Fixed costs and capacity

Prices (both shadow and market prices are equal in this example)

Mini Dispatch Optimisation (identical for LCOX and NPV)

Activity coefficients use shadow prices:

\( t_0 \): \[ \alpha_{t_0} = (1.0 \times 90) + (0.5 \times 25) + (-2.5 \times 35) - 5 = \text{£10/MWh} \]

\( t_1 \): \[ \alpha_{t_1} = (1.0 \times 50) + (0.5 \times 15) + (-2.5 \times 25) - 5 = \text{£}{-10}\text{/MWh} \]

The optimiser maximises \( 10 \cdot \mathrm{Activity}{t_0} + (-10) \cdot \mathrm{Activity}{t_1} \), so it prefers to dispatch during \( t_0 \) and minimise activity during \( t_1 \), subject to demand and availability constraints.

Suppose the optimiser determines \( \mathrm{Activity}{t_0} = 80 \) MWh and \( \mathrm{Activity}{t_1} = 20 \) MWh.

LCOX Metric

Market costs (excluding primary output):

\[ \begin{aligned} \mu_{t_0}^{\mathrm{LCOX}} &= 5 + (2.5 \times 35) - (0.5 \times 25) = \text{£80/MWh} \\ \mu_{t_1}^{\mathrm{LCOX}} &= 5 + (2.5 \times 25) - (0.5 \times 15) = \text{£60/MWh} \end{aligned} \]

Cost Index: \[ \begin{aligned} \mathrm{CostIndex} &= \frac{(1{,}000 \times 100) + (80 \times 80) + (20 \times 60)}{80 + 20} \\ &= \text{£1,076/MWh} \end{aligned} \]

NPV Metric

Market costs (including primary output):

\[ \begin{aligned} \mu_{t_0}^{\mathrm{NPV}} &= 5 - (1.0 \times 90) - (0.5 \times 25) + (2.5 \times 35) = \text{£}{-10}\text{/MWh} \\ \mu_{t_1}^{\mathrm{NPV}} &= 5 - (1.0 \times 50) - (0.5 \times 15) + (2.5 \times 25) = \text{£10/MWh} \end{aligned} \]

SNAS: \[ \begin{aligned} \mathrm{SNAS} &= \frac{-\left[(1{,}000 \times 100) + (80 \times (-10)) + (20 \times 10)\right]} {80 + 20} \\ &= \text{£}{-994}\text{/MWh} \end{aligned} \]

The negative SNAS indicates that at current market prices, this asset does not generate a surplus over its annualised costs. It would still be selected if it has the highest SNAS among all available options.

Partial System Dispatch

After each layer of commodity markets is settled during the investment loop, a partial system dispatch is run over all assets selected so far. This is a standard dispatch optimisation solve, with three key modifications described below.

Market subset

Only the commodity markets visited so far — i.e. the current market and all those settled in earlier investment rounds — are subject to commodity balance constraints. Markets that are upstream of the current investment frontier are not yet constrained, because no assets have been committed to serve them yet.

Input prices for upstream commodities

Because upstream markets are unconstrained, their commodities have no balance constraints and therefore no shadow prices in this dispatch. Without any signal on the cost of upstream inputs, those inputs would appear free to the solver.

To avoid this, the shadow prices \( \lambda_{c,r,t} \) from the previous MSY (see Commodity Prices Used in Appraisal) are passed as explicit cost penalties on any input flows corresponding to upstream, unconstrained commodities. This ensures the dispatch correctly accounts for the cost of consuming upstream resources, even before those markets have been invested in.

Capacity flexibility in circularities

When markets form a cycle, the partial dispatch after each market in the cycle uses flexible capacity variables for all newly committed assets in the cycle. Rather than fixing the capacity of these assets at their committed value, the solver may adjust the number of selected tranches within the bounds:

\[ \bigl[(1 - \mathrm{capacity_margin}) \cdot \mathrm{NumTranches}_a, \space (1 + \mathrm{capacity_margin}) \cdot \mathrm{NumTranches}_a\bigr] \]

where \( \mathrm{NumTranches}_a \) is the initially committed number of tranches of asset \( a \). The upper bound is additionally capped by the process’s MaxInstallableCapacity.

Note: Total capacity limits are not yet accounted for - this is a known bug which will be addressed in future versions.

Each flexible capacity variable enters the dispatch as an integer variable, with a cost coefficient equal to the asset’s AFC (annualised capital cost plus fixed O&M) multiplied by the tranche size. This flexibility allows the dispatch to absorb small demand shifts caused by subsequent markets in the cycle.

If the demand shift for a previously settled market in the cycle exceeds what the flexible capacity can accommodate, the simulation terminates with an error. The user should increase the capacity_margin parameter (defined in model.toml) in this case.

Using the partial dispatch result

The flow map from the partial dispatch is used to update the net demand seen by each upstream market. For each newly committed asset, its input commodity flows are added to the demand for the corresponding upstream markets, and its primary output flows reduce the remaining demand for the current market. Only primary output flows are counted against demand; secondary outputs do not affect the demand targets of other commodity markets. These updated demands then drive the next investment decisions as the process moves along the investment order, with each market’s committed assets shaping the demand seen by those upstream.