Concept#
A battery or a reservoir is only useful because of what happened before: what it can give tonight depends on how much it stored this afternoon. Energy planning models save time by simulating a few typical days instead of the whole year, and in doing so they can lose that link between hours and days. This section explains the problem in plain terms and introduces the four ways of modelling storage that the study compares.
How the study is put together#
The study runs one small test system through OSeMOSYS with each of the four storage methods and compares the results with a full-year hourly benchmark. Each block below opens with the details and the limitations stated in the paper; Storage method opens the four formulations side by side.
Test Reference System
- One VRE generator and one storage unit on a single electricity node that serves demand, over one year.
- The three scenarios share the same structure, costs, demand and storage parameters. Only the generator's hourly capacity-factor profile changes.
- Profiles are stylized archetypes built from British Columbia hourly data, not a specific year or plant portfolio.
- One generator at a time. Each run has a single generator with one profile. Wind, solar and hydro are tested separately, never together in one system, so mixed portfolios are untested.
- No network constraints, congestion or spatial diversity, as in real multi-node systems.
- Storage is one generic technology. Technologies with different duration, cycling or degradation may respond differently to aggregation.
- Charge and discharge rates are unconstrained, so capacity errors are upper bounds relative to a duration-limited technology.
- Where storage competes with transmission, demand response or dispatchable generation, state-of-charge errors also shift the choice between these options.
Representative days
- k-means groups the 365 days by their scaled daily capacity-factor and demand profiles.
- The day closest to each cluster centre becomes the representative day, and every day of the year is mapped to one.
- Clustering uses a fixed random state, so for a given k and h all four methods get identical days and mapping.
- k-means can smooth rare extremes and does not preserve multi-day scarcity sequences, both of which can matter for storage sizing.
- k is treated as an exogenous choice. The study does not determine an optimal number of days.
- Other day–hour pairings could add nuance to the accuracy–efficiency picture.
- Optimisation-based selection, which may better preserve extremes, was not tested.
OSeMOSYS
Long-term planning model
- A capacity-expansion model that chooses what to build and how to run it at the lowest total system cost.
- Only the storage component is swapped between runs. Everything else stays the same.
- The starting storage level is optimised, and storage must return to it by the end of the year.
- A separate stress test caps storage energy capacity so the limit binds.
- Single-year horizon. Long-term evolution of storage portfolios is not assessed.
- The binding-cap stress test covers the wind and solar scenarios only.
Solve
Time and memory change with the number of representative days, the block length and the storage method, even when everything else stays the same.
- Each case is a linear program, solved with GLPK 5.0 on an Intel Core i7 machine with 16 GB of memory.
- Reference case: the full year at hourly resolution.
- Runtime and memory figures hold for that environment.
- GLPK is comparatively slow, so runtime ratios between methods may not transfer to commercial solvers. Memory ratios reflect problem size and are expected to be more robust.
Results & recommendations
- Seasonal storage
- Niet · moderate k
- Short-duration storage
- Kotzur · Novo if intraday feasibility matters
- Welsch
- Use with caution
Each run is compared with the full-year hourly benchmark on total cost, storage capacity, state-of-charge trajectory and solve effort. Cost can look acceptable while storage capacity is far off, so check more than cost.
- Seasonal storage, little intraday variation: Niet with a moderate number of representative days.
- Short-duration storage, strong intraday variation: Kotzur for routine studies. Novo when intraday feasibility matters and resources allow.
- Welsch: use with caution under high intraday variation or tight capacity limits.
- Guidance is derived in a stylized class: one node, one storage technology, one year. It is not claimed to hold for multi-node, multi-technology or network-constrained systems.
- Read it as guidance for matching a formulation to the dominant temporal dynamics, not as universal rules.
- Formulation choice matters most when storage-energy limits bind.
The four storage methods
Niet
Mapping: none. Representative timeslices are linked in sequence and scaled by their weights.
- Fewest equations and variables, so more timeslices fit for the same effort.
- With few timeslices it misses variation within and between periods and tends to overestimate storage capacity.
Welsch
Mapping: user-defined seasons and day types. A typical day repeats within a season.
- Built into OSeMOSYS and well documented.
- Can oversize storage with few timeslices. Its equations are complex, which can hinder interpretability.
Kotzur
Mapping: each real day points to its cluster's representative day, in calendar order.
- Captures storage across days and seasons, with fast solves and modest memory.
- Hours within a day are not checked. In the wind and solar stress tests the hourly state of charge left its limits, even at full-year resolution.
Novo
Mapping: same as Kotzur.
- Highest fidelity of the four.
- Substantially higher memory use and solve time, especially in matrix generation.
Kotzur and Novo share the same mapping and differ only in where limits are checked, so comparing them isolates the effect of verification.
Based on Borba, Islam and Niet, Storage in Long-Term Energy Planning Models with Temporal Aggregation: Best Practices and Algorithms, Environmental Research Communications.