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.

After each commodity market is settled, a 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 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 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 (\( \text{FOM} \)): \[ \text{AFC}_\text{existing} = \text{FOM} \]

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

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

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

Asset Capacity

A process is either divisible or non-divisible:

• A divisible process has a fixed unit_size (defined in processes.csv). Assets of this type consist of one or more discrete units, each of size unit_size. When commissioned, a divisible asset is split into individual units, each of which is appraised and retained or mothballed independently.
• A non-divisible process has no unit_size. Assets of this type are treated as a single entity: capacities may take any value within their allowable range, but cannot be split into independently appraised or mothballed units.

Existing assets

• Non-divisible: the asset is appraised as a whole at its full installed capacity.
• Divisible: each individual unit is appraised separately, one at a time. This allows partial retention — for example, some units of a multi-unit plant may be retained while others are mothballed.

Candidate assets

Before a candidate asset can be appraised, it is assigned a trial capacity which defines how much capacity can be installed in a single investment round (subject to further demand-limiting capacity and investment constraints, described below)

• Divisible: the trial capacity is set to one unit (one unit_size), representing a single unit being considered for investment.

• Non-divisible: the trial capacity is based on the capacity that would satisfy the total remaining demand if the asset operated at its maximum annual rate:

  \[ \text{TrialCapacity} = \frac{\sum_t \text{Demand}_t}{\text{MaxAnnualSupplyPerCapacity}} \times \text{CapacityLimitFactor} \]

  capacity_limit_factor (set in model.toml, must be > 0 and <= 1) controls the size of investment increments relative to total demand. Lower values produce smaller investment increments (requiring more investment rounds), while higher values produce larger increments.

Demand-limiting capacity (DLC)

In each investment round, a candidate’s trial capacity is further capped by the demand-limiting capacity, which is the minimum capacity required to satisfy the remaining demand across all time-slice selections:

\[ \text{DLC} = \max_{\text{selection}} \frac{\sum_{t \in \text{selection}} \text{Demand}_t} {\text{MaxSupplyPerCapacity}_\text{selection}} \]

Selections where the asset has zero maximum supply are excluded. The cap prevents over-investment (i.e. building more capacity than needed to meet remaining demand).

Investment constraints

Processes may have an addition_limit (see process_investment_constraints.csv) specifying the maximum new capacity that can be built per year. The installable capacity limit for a given MSY is:

\[ \text{MaxInstallableCapacity} = \text{AdditionLimit} \times \Delta_\text{MSY} \times \text{AgentPortion} \]

where \( \Delta_\text{MSY} \) is the number of years since the previous MSY and \( \text{AgentPortion} \) is the fraction of the commodity market for which this agent is responsible.

If the remaining installable capacity is exhausted, the candidate is excluded from further consideration.

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 \( f_{c,\text{primary}} \) 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:

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

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

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

where \( \text{RevenueFromFlows} \) is the sum of all commodity flow revenues and costs (positive for outputs, negative for inputs) valued at shadow prices, \( \text{OperatingCost} \) is the variable operating cost plus levies and flow costs, \( f_{c,\text{primary}} \) 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:

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

\( \phi_{c,r,t} \) 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:

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

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: \[ \mu_t^\text{LCOX} = \text{OperatingCost}(t) - \text{RevenueFromNonPrimaryFlows}(\pi, t) \]

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

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:

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

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:

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

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 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 (\( cost_\text{input} \), \( cost_\text{output} \)) 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 \( 10 \cdot act_{t_0} + (-10) \cdot act_{t_1} \), so it prefers to dispatch during \( t_0 \) and minimise activity during \( t_1 \), subject to demand and availability constraints.

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

LCOX Metric

Market costs (excluding primary output):

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

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

NPV Metric

Market costs (including primary output):

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

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

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.