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Energy Operations

Decision horizons · system layers · eleven models

Energy operations research asks how a grid operator, utility, market participant, or energy planner can keep the lights on — reliably, affordably, and increasingly, without carbon — across horizons that stretch from a multi-decade capacity-investment plan to a sub-second frequency-regulation response. This section presents eleven canonical OR problems, each as a live interactive solver grounded in a real power-systems or electricity-market decision, organized along the decision-horizon × energy-system-layer taxonomy of Wood, Wollenberg & Sheblé (2013) with modern extensions for renewables, storage, and sector coupling.

Why energy OR matters

Scale of the problem · three anchor statistics

~73%
of global greenhouse-gas emissions come from the energy system (electricity, heat, transport, industry) — decarbonizing it is the single largest climate lever.
IEA, CO2 Emissions in 2023 · iea.org
~30%
of global electricity generation now comes from renewable sources (2023) — variable supply that requires fundamentally new unit commitment, dispatch, and market-clearing optimization.
IEA, Renewables 2023 Analysis · iea.org/renewables-2023
~$1.7T
invested globally in clean energy in 2023 — capacity-expansion, transmission, and storage decisions worth trillions hinge on mixed-integer optimization models.
IEA, World Energy Investment 2023 · iea.org/wei-2023

Decision framework

Four lenses on the same eleven applications

The canonical taxonomy of Wood, Wollenberg & Sheblé (2013) organizes power-systems decisions along two axes: the decision horizon (long-term planning, medium-term, short-term operations, real-time) and the energy-system layer (supply, transmission, distribution, demand, storage, markets). Every application in this section occupies one cell. Dashed cells are honest gaps — decisions that exist in practice but are not yet modelled here.

Horizon ↓  ·  Layer →
Supplygeneration
TransmissionHV network
DistributionMV & LV
Demandload & flex
Storagebattery, hydro
Marketswholesale & AS
Long-termyears – decades
Gap · distribution network expansion (DNEP)
Gap · long-term demand elasticity
Gap · storage investment
Gap · capacity-market clearing
Medium-termweeks – year
Gap · transmission outage planning
Gap · feeder reconfiguration
Gap · seasonal DR planning
Gap · seasonal storage strategy
Short-termday-ahead – hours
Gap · Volt/VAR optimization
Real-timeminutes – seconds
Gap · congestion management
Gap · real-time re-dispatch
Gap · real-time DR activation
Gap · frequency-regulation storage
Gap · real-time market

The OR-research grouping reorganizes the same eleven applications by the mathematical problem family they belong to. Grid operators see this as the table of contents of Wood & Wollenberg or Conejo et al. (2016): unit commitment, economic dispatch, and optimal power flow form the operations triad; expansion planning and storage cover long-horizon investment; markets and demand-side close the loop.

Unit Commitment
Binary on/off decisions over a day-ahead horizon with start-up costs, ramp limits, min up/down times. Stochastic and robust variants handle renewable forecast uncertainty.
Economic Dispatch
Continuous allocation of load among committed units every 5–15 minutes. Quadratic cost, equal-incremental-cost principle. Security-constrained ED (SCED) adds network limits.
Optimal Power Flow
Minimize generation cost subject to network power-flow equations and line limits. DC-OPF linearizes; AC-OPF keeps the full nonconvex equations; SOCP/SDP relaxations lie in between.
Expansion Planning
Multi-year capital investment: which generators, lines, and storage assets to build where, when, and at what capacity. Couples investment binaries with operational subproblems across representative periods.
Storage & Hydro
Intertemporal coupling through state-of-charge constraints, efficiencies, and reservoir inflows. Short-term arbitrage meets long-term reservoir-valuation via stochastic dual DP.
Electricity Markets
Auction design, bidding strategies, and contract portfolios. Day-ahead uniform-price clearing plus real-time adjustment and ancillary-services markets set locational marginal prices.
Demand-Side & Flexibility
Aggregated load as a controllable resource: time-shifting, curtailment, direct load control, aggregator bidding. Bi-level formulations couple aggregator and system-operator objectives.

Modern energy OR is defined by how it handles uncertainty: wind and solar forecast errors, demand variability, equipment failures, fuel-price swings. This lens cross-tabulates the same applications by decision horizon and uncertainty-treatment method, following Morales, Conejo, Madsen, Pinson & Zugno (2014) and the stochastic-UC review of Zheng, Wang & Liu (2015). Most cells are sparse today — the field is actively moving from deterministic toward stochastic, robust, and data-driven formulations.

Horizon ↓  ·  Method →
Deterministicfixed forecast
Stochasticscenario tree
Robustbudgeted uncertainty
Chance-constrainedprob. guarantee
DROambiguity sets
Data-drivenML / RL
Long-term
Section · stochastic GEP / TEP with representative periods
Section · robust GEP / TEP (adjustable)
Gap
Gap · DRO for long-horizon planning
Gap
Medium-term
Gap
Gap
Gap
Gap
Short-term
Gap · DRO UC / OPF
Gap · RL for dispatch
Real-time
Gap
Gap
Gap
Gap
Gap · online RL / MPC

The energy transition — decarbonizing electricity, integrating variable renewables, coupling sectors (electricity + heat + gas + hydrogen), and evolving market design — is the defining story of twenty-first-century energy OR. This lens groups the same eleven applications by which transition pillar they advance, following the framings of Pfenninger, Hawkes & Keirstead (2014) and Mancarella (2014) on multi-energy systems.

Decarbonization
Expanding low-carbon generation, retiring fossil assets, pricing emissions, and re-designing markets for a net-zero grid.
Renewable Integration
Managing wind and solar variability through stochastic commitment, reserve adequacy, storage, and flexible demand.
Sector Coupling
Linking electricity to heat, gas, hydrogen, and mobility to unlock flexibility and deep decarbonization. Multi-energy modelling is a rapidly opening research frontier.
Hydrothermal Coordination SDDP Hydrogen Supply Chain (planned) MILP EV Charging & V2G (planned) MILP
Market Evolution
Redesigning wholesale clearing, ancillary services, and capacity mechanisms for a grid with near-zero marginal-cost generation and strategic storage.

Application catalog

All seventeen pages · click a card to open the interactive solver

MILP Short-term
Unit Commitment (UC)
Decide which thermal generators to start, stop, and run over a 24-hour horizon to meet load at minimum total cost, subject to start-up costs, minimum up/down times, ramp limits, and spinning reserves. Stochastic and security-constrained variants treat renewable forecast and contingency uncertainty.
QP Real-time
Economic Dispatch (ED)
Allocate load among already-committed generators every 5–15 minutes by equalizing incremental cost across units, subject to capacity limits and the power-balance constraint. Security-constrained ED (SCED) extends the formulation with network limits.
LP / NLP / SOCP Short-term
Optimal Power Flow (OPF)
Minimize generation cost subject to Kirchhoff's laws, line thermal limits, voltage bounds, and generator limits. DC-OPF linearizes (LP), AC-OPF keeps the full nonconvex power-flow equations (NLP), and SOCP/SDP relaxations give provably-optimal lower bounds.
MIP Long-term
Generation Expansion Planning (GEP)
Decide which new generators to build, where, and when, over a multi-decade horizon to meet growing demand at minimum net-present-value cost. Couples binary investment decisions with operational subproblems across representative hours, demand scenarios, and fuel-price trajectories.
MIP Long-term
Transmission Expansion Planning (TEP)
Select which new transmission lines to build over a multi-year horizon to integrate new generation, eliminate congestion, and meet reliability (N−1) criteria. Investment binaries sit above a DC-OPF routing subproblem, with scenarios for demand growth and generation siting.
Linear Programming Short-term
Battery Storage Optimization
Schedule hourly charging and discharging of a grid-scale battery to maximize arbitrage profit under a 24-hour electricity-price forecast, subject to state-of-charge bounds, power ratings, and round-trip efficiency. Peak-shaving and ancillary-services variants extend the base LP.
Multi-stage SP (SDDP) Medium-term
Hydrothermal Scheduling
Plan reservoir releases and thermal dispatch over weeks to months under stochastic inflows, balancing immediate generation against future water value. Stochastic dual dynamic programming (SDDP) computes Bender cuts over a scenario tree to approximate the future cost function.
MILP / bi-level Short-term
Demand Response Optimization
Curtail, shift, or incentivize load to flatten peaks, absorb renewable surpluses, or provide ancillary services. Bi-level models capture the aggregator-operator interaction; direct-load-control and price-based variants yield tractable MILP formulations.
LP / MILP Short-term
Electricity Market Clearing
Clear a day-ahead uniform-price auction by solving an LP (or MILP with non-convex bids) that minimizes total declared bid cost subject to load balance and network flows. The locational marginal price (LMP) emerges as the dual of the nodal balance constraint.
Stochastic UC Short-term
Renewable Integration
Jointly commit and dispatch thermal units, storage, and flexible demand to accommodate wind and solar forecast uncertainty. Scenario-based two-stage stochastic programs, adjustable-robust formulations, and chance-constrained variants each trade cost for reliability differently.
Stochastic / Robust Medium-term
Energy Portfolio (Robust)
Build a contract-and-asset portfolio (bilateral contracts, market exposure, storage, RE PPAs) that hedges against price volatility and volume risk over a medium-term horizon. Two-stage stochastic and budget-robust formulations yield policies that trade expected cost for worst-case protection.
MILP Short-term
Microgrid Operation
Co-optimize distributed generation, storage, flexible demand, and grid exchange under islanded or grid-connected mode. MILP with per-period on/off binaries and islanding constraints.
MIP · Multi-echelon Long-term
Hydrogen Supply Chain
Design the electrolyzer-to-consumer H2 network: producer siting, pipeline vs truck transport, storage sizing, and demand satisfaction. MIP following Almansoori & Shah (2006).
LP · V2G Short-term
EV Charging Scheduling
Coordinate a fleet of EVs across a day to minimize cost, respect transformer limits, and satisfy each vehicle's departure SOC. Optional V2G discharge adds an arbitrage revenue stream.
Bi-level MPEC Short-term
Strategic Bidding
Compute the profit-maximizing bid curve for a producer that can move the clearing price. Bi-level MPEC with KKT reformulation; supply-function equilibrium for Nash games.
Large LP/MIP Multi-decade
Energy Systems Planning
Whole-system multi-sector decarbonization pathways via TIMES, MESSAGE, OSeMOSYS. Reference Energy System, technology choice, resource extraction, emissions constraints.
Multi-commodity LP Short-term
Multi-Energy Systems
Joint optimization of electricity, heat, gas, H2 networks with power-to-X sector coupling. Energy-hub formulation (Geidl-Andersson 2007); 10-25% cost savings via sector coupling.

Decision timescales

The multi-scale view · complementary to the matrix above

The same eleven applications, arrayed on a logarithmic time axis from multi-decade capacity planning on the left to sub-second frequency response on the right. Power-systems operations span nine orders of magnitude in time; the same concept (commit-and-dispatch) appears in different forms at different scales. Color by energy-system layer.

Supply Transmission Storage Demand Markets

Current research frontiers

Where energy OR is actively evolving

Uncertainty at scale for renewable-heavy grids

Stochastic, robust, and distributionally-robust formulations for UC and OPF that scale to real system sizes, paired with scenario-reduction and decomposition methods. Still an open problem for continental interconnections at minute resolution under high wind and solar penetration.

Convex relaxations and tight formulations for AC-OPF

Second-order-cone and semidefinite relaxations (Low 2014, Molzahn & Hiskens 2019) can give provably optimal solutions on a growing class of networks; tighter MILP formulations for UC (Morales-España et al. 2013) have collapsed branch-and-bound times by orders of magnitude.

Sector coupling and multi-energy optimization

Joint optimization of electricity, heat, gas, hydrogen, and transport networks (Mancarella 2014, Lund et al. smart-energy-systems programme). Hydrogen supply-chain design is opening as a full sub-field, with 2020+ reviews building on Almansoori & Shah (2006).

Machine learning and RL for grid operations

Data-driven surrogates for AC-OPF and UC, safe reinforcement learning for real-time dispatch, and physics-informed neural networks for contingency screening. An active but still operationally immature frontier — safety guarantees and interpretability remain core open questions.

Key references

Cited above · DOIs & permanent URLs

Wood, A. J., Wollenberg, B. F., & Sheblé, G. B. (2013).
Power Generation, Operation, and Control (3rd ed.).
Wiley. wiley.com
Kirschen, D. S., & Strbac, G. (2018).
Fundamentals of Power System Economics (2nd ed.).
Conejo, A. J., Baringo, L., Kazempour, S. J., & Siddiqui, A. S. (2016).
Investment in Electricity Generation and Transmission: Decision Making under Uncertainty.
Morales, J. M., Conejo, A. J., Madsen, H., Pinson, P., & Zugno, M. (2014).
Integrating Renewables in Electricity Markets: Operational Problems.
Springer, International Series in Operations Research & Management Science, 205. doi:10.1007/978-1-4614-9411-9
Padhy, N. P. (2004).
“Unit commitment — a bibliographical survey.”
IEEE Transactions on Power Systems, 19(2), 1196–1205. doi:10.1109/TPWRS.2003.821611
Zheng, Q. P., Wang, J., & Liu, A. L. (2015).
“Stochastic optimization for unit commitment — a review.”
IEEE Transactions on Power Systems, 30(4), 1913–1924. doi:10.1109/TPWRS.2014.2355204
Cain, M. B., O'Neill, R. P., & Castillo, A. (2012).
“History of optimal power flow and formulations.”
Federal Energy Regulatory Commission staff technical paper. ferc.gov/acopf-1
Low, S. H. (2014).
“Convex relaxation of optimal power flow — Part I: Formulations and equivalence; Part II: Exactness.”
IEEE Transactions on Control of Network Systems, 1(1–2). doi:10.1109/TCNS.2014.2309732
Molzahn, D. K., & Hiskens, I. A. (2019).
A Survey of Relaxations and Approximations of the Power Flow Equations.
Foundations and Trends in Electric Energy Systems, 4(1–2). doi:10.1561/3100000012
Hemmati, R., Hooshmand, R.-A., & Khodabakhshian, A. (2013).
“State-of-the-art of transmission expansion planning: Comprehensive review.”
Renewable and Sustainable Energy Reviews, 23, 312–319. doi:10.1016/j.rser.2013.03.015
Koltsaklis, N. E., & Dagoumas, A. S. (2018).
“State-of-the-art generation expansion planning: A review.”
Applied Energy, 230, 563–589. doi:10.1016/j.apenergy.2018.08.087
Pfenninger, S., Hawkes, A., & Keirstead, J. (2014).
“Energy systems modeling for twenty-first century energy challenges.”
Renewable and Sustainable Energy Reviews, 33, 74–86. doi:10.1016/j.rser.2014.02.003
Pereira, M. V. F., & Pinto, L. M. V. G. (1991).
“Multi-stage stochastic optimization applied to energy planning.”
Mathematical Programming, 52(1–3), 359–375. doi:10.1007/BF01582895
Sioshansi, R., Denholm, P., Jenkin, T., & Weiss, J. (2009).
“Estimating the value of electricity storage in PJM: Arbitrage and some welfare effects.”
Energy Economics, 31(2), 269–277. doi:10.1016/j.eneco.2008.10.005
Mancarella, P. (2014).
“MES (multi-energy systems): An overview of concepts and evaluation models.”
Albadi, M. H., & El-Saadany, E. F. (2008).
“A summary of demand response in electricity markets.”
Electric Power Systems Research, 78(11), 1989–1996. doi:10.1016/j.epsr.2008.04.002
IEA. (2023).
World Energy Outlook 2023, Renewables 2023, and World Energy Investment 2023.
International Energy Agency. iea.org/reports

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