PaperlayerView exact revision on arXiv

Source-linked AI summary

Co-Optimized Generation, Transmission, and Storage Expansion: System Value and Optimal Duration of Pumped-Storage Hydropower

Rafael Benchimol Klausner, Rafael Kelman

arXiv:2608.27222v1math.OCeess.SY

TL;DR

Expansion models often fix storage duration before optimization, despite balancing needs occurring across multiple timescales. This paper co-optimizes duration-differentiated storage with generation and transmission in a stochastic hourly framework, finding that PSH changes Brazil’s storage portfolio and reduces system costs and thermal reliance.

  • Problem

    Storage planning commonly fixes duration before optimization, although solar, wind, and seasonal balancing services require different energy-to-power ratios.

  • Method

    The paper uses a rolling-horizon, two-stage stochastic generation–transmission–storage program in which 4–144-h PSH candidates compete with 4-h BESS under coherent hourly scenarios.

  • Results

    With PSH available, the model builds 31.2 GW / 755 GWh of PSH and no BESS, while the BESS-only case builds 38.0 GW / 152 GWh of batteries and 7.8 GW more gas-fired capacity.

  • Takeaways & Limitations

    Limiting storage candidates to a single duration understates optimal energy-storage requirements and overstates residual thermal-capacity needs.

  • Takeaways & Limitations

    The rolling horizon is myopic, capacity materializes without construction lead times, and perfect within-scenario foresight may overstate storage value.

Abstract

from arXiv · show

Expansion planning models usually fix storage duration before optimization, setting how much storage power to build but not for how long it can discharge. We present a generation-transmission-storage expansion framework in which candidates of many durations compete on annualized cost, making the duration mix an optimization outcome. It is a rolling-horizon, two-stage stochastic linear program, each five-year stage is a full year at hourly resolution under ten coherent inflow, wind, and solar scenarios. We apply it to the Brazilian Interconnected System over 2030-2050, where demand roughly doubles to 1,716 TWh/year and variable renewable energy (VRE) supplies most new capacity. Two cases are compared: 36 pumped-storage hydropower (PSH) candidates over four subsystems and nine durations (4-144 h) alongside 4-h battery energy storage systems (BESS), and BESS alone. With PSH available, the model builds 31.2 GW / 755 GWh of PSH and no BESS, dominated by 12-h capacity with 4.9 GW of 72-h units. Without PSH it builds 38 GW / 152 GWh of BESS and 7.8 GW more gas-fired capacity, mostly open-cycle peakers. PSH lowers 2050 annualized system cost by US$ 5.0 billion/year (6.8%), operating cost by 23.5%, thermal generation by 34 TWh/year, and long-run marginal cost by 20%; 2035 VRE curtailment falls from 8.4% to 3.2%. The magnitudes are specific to Brazil, but the underlying mechanism is general: limiting storage candidates to a single duration understates the system's optimal energy-storage requirement and overstates its residual need for thermal capacity.

Sets and indices

The model indexes time, scenarios, subsystems, plants, reservoirs, storage units, interconnections, and candidate projects, while defining costs, operating parameters, resource limits, and network data.

  • 8760 hourly periods and operating scenarios with probabilities index chronological operation under uncertainty.
  • Subsystems, renewable plants, thermal plants, hydro reservoirs, storage units, and interconnections define the modeled system components.
  • Annualized fixed cost, capital recovery factors, thermal operating cost, storage throughput cost, curtailment penalty, and unserved-energy cost parameterize planning and operation.
  • Demand, renewable capacity factors, thermal availability, must-run shares, reservoir inflows, storage bounds, and environmental outflows describe hourly system conditions.
  • Storage duration is the energy-to-power ratio, alongside charging and discharging efficiencies, depth-of-discharge reserve, and interconnection losses.
  • Existing transfer limits and project resource potentials constrain transmission and expansion choices.

Decision variables

The decision variables represent first-stage expansion choices and scenario-dependent operation for hydro, storage, transmission, and load shedding.

  • First-stage variables specify capacity built for projects and aggregate invested capacity at storage units and transmission corridors.
  • Hydro operating variables record generation, spillage, and reservoir storage by hour and scenario.
  • Storage and network operation are represented by charging, discharging, state of charge, interconnection flow, and load shedding.

1. Introduction

The paper addresses how storage duration should be selected in co-optimized expansion planning rather than fixed beforehand. It develops and tests a stochastic hourly framework that compares duration-differentiated PSH with 4-h BESS in Brazil.

  • 1. Introduction: High VRE shares create balancing needs spanning solar ramps, multi-day wind droughts, and seasonal hydro, wind, or demand imbalances.These services require different energy-to-power ratios.
  • 1. Introduction: Planning models commonly admit storage as a single class with duration fixed before optimization, leaving the duration mix assumed rather than selected.
  • 1. Introduction: The framework co-optimizes generation, transmission, and storage while duration classes compete on common hourly state-of-charge dynamics and duration-specific attributes.The optimizer jointly selects storage power, energy, location, and dispatch.
  • 1. Introduction: The Brazilian Interconnected System is evaluated over 2030–2050, with VRE supplying most growth to 1,716 TWh/year by 2050 under constrained firm hydropower additions.
  • 1. Introduction: The comparison uses identical non-storage assumptions: 36 PSH candidates with nine durations from 4–144 h compete with 4-h BESS, versus BESS alone.
  • 1. Introduction: The study asks how duration competition changes storage, generation, transmission, cost, curtailment, thermal generation, adequacy, and marginal cost.

2. Related work

Related work motivates joint chronological expansion modeling, duration-sensitive storage valuation, and explicit representation of PSH resources and configurations. Brazilian planning and procurement have begun incorporating storage, but PSH selection and duration remain unsettled.

  • 2. Related work: Capacity expansion studies jointly minimize investment and expected operating cost, requiring chronological operation and explicit state-of-charge dynamics.
  • 2. Related work: Long-duration storage value depends strongly on energy-to-power ratio, with duration classes serving functions from intra-day shifting to seasonal smoothing.
  • 2. Related work: Two-stage and multi-stage stochastic programming capture operational uncertainty in expansion decisions.
  • 2. Related work: PSH research covers mature technology configurations, broad closed-loop resource potential, and economy-of-duration cost effects.Reservoir costs scale with storage volume while powerhouse costs are largely fixed.
  • 2. Related work: PSH value estimates depend on candidate representation, with reservoir-level formulations differing from aggregated representations and arbitrage-only valuations.
  • 2. Related work: Brazil’s PDE 2034 includes storage, but its optimized results select no PSH and the first storage capacity-reserve auction was designed for batteries only.
  • 2. Related work: International practice includes co-optimizing storage and transmission in Australia and using capacity-and-energy remuneration for PSH in China.

3. Methodology

The framework co-optimizes storage, generation, and transmission investments with hourly stochastic operation, allowing duration, location, and dispatch to emerge from competing storage candidates.

  • Model formulation: The model jointly selects storage power, energy, location, and dispatch while PSH and BESS compete with generation and transmission investments.Storage classes share hourly state-of-charge equations but differ in duration, efficiency, usable depth of discharge, annualized cost, and deployment limits.
  • Model formulation: The expansion problem is a two-stage stochastic linear program with capacity investments in the first stage and scenario-specific hourly operation in the second.It represents electrical zones, hydro, thermal and renewable plants, storage units, and interconnections.
  • Objective: The objective minimizes annualized investment cost plus expected operating cost, including thermal, storage-throughput, curtailment, and energy-not-served costs.Energy not served is priced at 1,666 US$/MWh in this study.
  • Storage: Storage dynamics impose energy balance, power limits, depth-of-discharge reserves, and cyclic closure; PSH duration classes differ through the energy-to-power ratio τb.No operating service is assigned to a duration class in advance, so daily and multi-day roles emerge from optimized hourly dispatch.
  • Solution approach: The rolling horizon solves complete five-year planning steps from 2030 through 2050, carrying prior investments forward as lower bounds without endogenous retirements.Each step re-optimizes incremental capacity and full-year hourly operation.
  • Uncertainty representation: Operational uncertainty uses ten representative joint hydro–wind–solar scenarios derived from naturalized inflows and reanalysis-based hourly renewable profiles.Approximately 90 years of inflow records are processed into 200 synthetic monthly scenarios and reduced by variance-preserving clustering.

4. Case study: the Brazilian Interconnected System, 2030–2050

The Brazilian case study represents four interconnected subsystems through 2050, with rising demand, concentrated wind and load, thermal inflexibility, and competing PSH and BESS candidates.

  • System representation: The system comprises four subsystems, an Imperatriz hub, aggregated reservoirs, a large thermal fleet, and existing and contracted renewable generation.Hydropower is represented by four equivalent reservoirs totaling 112.2 GW and 563 TWh of useful storage.
  • Demand and geography: 2050 demand reaches 1,716 TWh/year, while the Southeast contains roughly 55% of demand and the Northeast concentrates the best wind resources.These spatial patterns make storage siting and the SE–NE transmission corridor strongly interdependent.
  • Thermal resources: The thermal fleet includes open-cycle peakers and combined-cycle units with opposite seasonal must-run windows, leaving inflexible thermal generation present year-round.Pre-salt gas contracts must run from December–May, while LNG contracts must run from June–November.
  • Storage candidates: Storage alternatives include one 4-h BESS candidate per subsystem and, in the PSH case, 36 closed-loop PSH candidates spanning nine durations from 4 to 144 h.PSH candidates use 80% round-trip efficiency and full depth of discharge; BESS uses 83% round-trip efficiency and a 20% depth-of-discharge reserve.
  • Experimental comparison: The cases hold demand, scenarios, renewable and thermal candidates, and transmission options constant, differing only in whether PSH candidates are available alongside 4-h BESS.All storage costs enter the model as annualized fixed values.

5. Results

Allowing PSH durations to compete reshapes the optimal storage and generation portfolio, with 12-hour units dominating and longer-duration units serving multi-day and seasonal balancing. PSH reduces system cost and operating stress while substituting mainly for thermal capacity and batteries rather than transmission.

  • PSH displaces BESS: 31.2 GW of PSH and zero stationary batteries are selected when duration-differentiated PSH competes with BESS.The PSH fleet provides approximately 755 GWh of usable storage, versus 91 GWh usable for the 38-GW BESS fleet without PSH.
  • Selected PSH durations: 22.6 GW of 12-h PSH dominates the 2050 portfolio, alongside 1.9 GW of 24-h, 1.8 GW of 48-h, and 4.9 GW of 72-h units.The 4–8-h and 100–144-h classes receive no investment; longer durations bridge multi-day wind lulls and seasonal must-run windows.
  • Changes in thermal and solar capacity: 7.8 GW of new gas-fired capacity and 2.7 GW of thermal re-contracting are avoided, while solar PV build-out increases by 15.6 GW.Onshore wind and interconnection reinforcements are nearly identical across cases, indicating substitution mainly for thermal capacity and batteries.
  • System costs: US$ 5.0 billion/year of 2050 annualized system cost is avoided, despite annualized CAPEX being 0.7% higher.Operating cost falls by US$ 5.4 billion/year, with operating savings exceeding additional investment over the horizon.
  • Operational value: 2035 VRE curtailment falls from 8.4% to 3.2%, while 2050 thermal generation falls by 34.1 TWh and demand-weighted LRMC falls by 20%.Expected energy not served also falls by 71%, although the no-PSH value is only 0.03% of demand.
  • Operating patterns: 12-h PSH cycles daily, whereas the 72-h fleet charges before low-wind periods and discharges across several consecutive days.The PSH fleet absorbs up to 27 GW of midday surplus and injects up to 18 GW during evening peaks; BESS cannot provide the same multi-day service.

6. Discussion

The discussion shows that allowing storage durations to compete changes both the storage portfolio and the surrounding generation investments. Under the modeled assumptions, PSH provides system value through daily and multi-day operation, but the results remain bounded by technology, network, foresight, and market assumptions.

  • Limitations: The comparison does not establish that PSH displaces BESS under all cost and deployment assumptions.Only a 4-h battery class is represented, and the BESS-only fleet reaches 95% of its national deployment limit.
  • Portfolio substitution: 7.8 GW less gas-fired capacity, including 5.4 GW of open-cycle peaking capacity, is built when PSH is admitted, while 15.6 GW more solar PV is installed.The unchanged 10 GW pre-salt combined-cycle block indicates that substitution acts on peaking and mid-merit capacity rather than must-run generation.
  • System value: 23.5% lower operating cost accompanies 0.7% higher annualized CAPEX with PSH, with most savings attributed to avoided thermal variable cost.Additional contributions come from lower curtailment and unserved energy, while benefits accrue across the system rather than necessarily through energy arbitrage alone.
  • Operational value: 12-h PSH narrows daily residual net load, whereas 72-h PSH completes a weekly energy excursion during a multi-day wind event.The reported value combines capacity substitution with operation across several timescales and persists under wet- and dry-season conditions.
  • Planning and procurement implications: Expansion studies should model storage power, energy, and multiple relevant durations, while procurement should specify deliverable energy or duration alongside MW capability.The model does not determine a preferred remuneration mechanism; technology-neutral qualification and site-specific assessments would still be required for Brazilian applications.

7. Conclusion

The co-optimized framework selects storage duration jointly with power, location, and dispatch, producing a multi-duration PSH portfolio that outperforms 4-h BESS economically and operationally. Results support resolving storage duration within expansion planning, while remaining conditional on modeled costs, foresight, and network representation.

  • The framework lets storage candidates of many durations compete, selecting storage power, energy, duration, location, and dispatch rather than assigning PSH a fixed operating role.
  • 31.2 GW / 755 GWh of PSH and no BESS are built by 2050 when PSH is available, with a dominant 12-h block and 8.6 GW of 24–72-h capacity.The BESS-only case builds 38.0 GW / 152 GWh of batteries and 7.8 GW more gas-fired capacity, including 5.4 GW of open-cycle peaking capacity.
  • US$ 5.0 billion/year is saved in 2050 with PSH, as operating cost falls 23.5% while annualized CAPEX differs by less than 1%.Most savings come from avoided thermal fuel; the PSH plan generates 34 TWh less thermal electricity and has a demand-weighted LRMC 20% lower.
  • Curtailment is 60–62% lower in 2035–2040 with PSH, while transmission expansion is nearly unchanged.
  • The conclusion is conditional on assumed storage costs, perfect foresight within each scenario, and the zonal network representation.Reported quantities depend on Brazilian costs, resources, and contract structures, although the duration-selection mechanism is presented as broader than Brazil.

CRediT authorship contribution statement

The authors divide contributions across conceptualization, methodology, software, analysis, investigation, visualization, supervision, funding acquisition, and writing.

  • Rafael Benchimol Klausner contributed to conceptualization, methodology, software, formal analysis, investigation, visualization, and the original draft.
  • Rafael Kelman contributed to conceptualization, methodology, supervision, funding acquisition, and review and editing.

Funding

The study was funded through an ANEEL research and development programme project sponsored by CTG Brasil, without funder involvement in the research or publication decision.

  • The Research and Development (PD&I) Programme of Brazil’s Electricity Regulatory Agency funded the work under project PD-00387-0125, sponsored by CTG Brasil.
  • The funding source had no role in study design, analysis, interpretation, or the decision to submit the article.
Loading 2608.27222v1…