Time Weights Output

Overview

File: time_weights.csv

time_weights.csv maps every optimization time step to the number of full-year hours it represents. This file is essential for converting representative-period results (flows, storage levels, curtailment, non-served demand) into annual totals.

When time-domain reduction (TDR) is used, the full year (typically 8,760 hours) is compressed into a smaller set of representative periods. Each representative period stands in for multiple full-year periods. The weight of a time step encodes how many full-year hours that time step represents — allowing weighted sums over the representative period to recover annual totals accurately.

Without TDR (i.e., when all time steps are modeled directly), every time step receives a weight of 1.0, and the weighted sum equals a simple unweighted sum.

Columns

Column	Type	Description
`time`	Int	Time step index (1-based integer, matches the `time` column in `flows.csv`, `storage_level.csv`, `curtailment.csv`, and `non_served_demand.csv`)
`subperiod_index`	Int	Index of the representative sub-period this time step belongs to (1-based). All time steps within the same representative sub-period share the same `subperiod_index` and `weight`.
`weight`	Float64	Number of full-year sub-periods represented by this representative sub-period. All time steps in the same representative sub-period share this weight.

How Weights Are Calculated

Weights are normalized so that the weighted sum of hours equals TotalHoursModeled (typically 8,760):

\[\sum_{k} \text{weight}(k) \times \text{hours\_per\_subperiod}(k) = \text{TotalHoursModeled}\]

where the sum is over all representative sub-periods $k$, and hours_per_subperiod is the number of time steps in each sub-period.

Example: If the full year has 52 weekly sub-periods (each 168 hours) and TDR selects 3 representative weeks:

Representative week A is chosen to represent 21 actual weeks → weight = 21.05775
Representative week B represents 18 weeks → weight = 18.0495
Representative week C represents 13 weeks → weight = 13.03575
Check: $21.05775 \times 168 + 18.0495 \times 168 + 13.03575 \times 168 = 52.143 \times 168 = 8760$ ✓

All 168 time steps within representative week A share weight = 21.05775; all steps within week B share weight = 18.0495, etc.

For a detailed explanation of representative periods and TDR, see Time Data.

Using Weights

The most common use of time_weights.csv is to convert time-step-level values from representative periods into annual totals:

Annual energy (MWh)

For any flow or curtailment variable, the annual energy equivalent is:

\[\text{Annual energy} = \sum_{t} \text{value}(t) \times \text{weight}(t) \times \text{hours\_per\_timestep}\]

where hours_per_timestep is typically 1 (for hourly resolution models).

Annual revenue

\[\text{Revenue} = \sum_{t} \text{flow}(t) \times \text{price}(t) \times \text{weight}(t)\]

where price(t) is the locational marginal price from balance_duals.csv.

Weights are sub-period weights, not timestep weights

All time steps within the same representative sub-period share the same weight. The weight is a property of the sub-period, not the individual time step. This is why subperiod_index is included in the output — it tells you which representative sub-period each time step belongs to.

Examples

Example Output (3 representative weeks of 168 hours each)

time	subperiod_index	weight
1	7	21.05775
2	7	21.05775
…	…	…
168	7	21.05775
169	15	18.0495
170	15	18.0495
…	…	…
336	15	18.0495
337	42	13.03575
…	…	…
504	42	13.03575

Here, time steps 1–168 belong to representative sub-period 7 (which stands for 21 actual weeks), time steps 169–336 belong to sub-period 15 (18 weeks), and time steps 337–504 belong to sub-period 42 (13 weeks).

Computing Annual Electricity Generation

using CSV, DataFrames

flows = CSV.read("results/flows.csv", DataFrame)
weights = CSV.read("results/time_weights.csv", DataFrame)

# Join weights to flows
df = leftjoin(flows, weights, on=:time)

# Annual MWh per component (assuming hourly timesteps, hours_per_timestep = 1)
df.annual_MWh = df.value .* df.weight
annual = combine(groupby(df, [:resource_id, :component_id]), :annual_MWh => sum)

Checking Weight Consistency

using CSV, DataFrames

weights = CSV.read("results/time_weights.csv", DataFrame)
hours_per_subperiod = 168  # for weekly sub-periods

# Should equal TotalHoursModeled (e.g., 8760 for 52 weeks × 168 hours)
total_hours = sum(combine(groupby(weights, :subperiod_index), :weight => first => :w).w .* hours_per_subperiod)