21 families · 122 variants
Multi-axis taxonomy (v2): horizon × decision_type × uncertainty × math_class. Families span real-time (state estimation · frequency / voltage control) · short-term (ED · OPF · market clearing · storage · DR · network-security ops) · medium-term (UC · reserves · hydrothermal · maintenance) · long-term (capacity / transmission / integrated-system / distribution planning) · cross-horizon (security & reliability · resilience · adversarial · benchmarks).
Frequency control
Real-time frequency stability — AGC setpoint allocation, droop tuning, inertia procurement, fast-frequency-response optimisation. Seconds-to-minutes timescale.
| AGC setpoint allocation | LP | production | |
| Primary-frequency droop tuning | QP | production | |
| Inertia procurement | MILP | partial | |
| Fast-frequency response (FFR) optimisation | LP / MILP | production | |
| RoCoF-limit constrained UC | MILP | partial |
State estimation
Real-time estimation of bus voltages / angles / flows from redundant measurements. SCADA-paced, QP at core; robustness / dynamics / distribution decompositions are the main variants.
| Weighted Least Squares (WLS) | QP | production | |
| Least Absolute Value (LAV) | LP | production | |
| Robust SE (Huber loss) | QP | production | |
| Dynamic SE (Kalman filter) | Kalman | stochastic | production |
| Distributed SE (area decomposition) | QP (decomposed) | partial |
Voltage / reactive control
Real-time voltage regulation — volt-VAR optimisation, tap/capacitor coordination, reactive-power dispatch, grid-forming inverter setpoint control. Distribution-network-flavoured.
| Volt-VAR optimisation (VVO) | MILP | production | |
| Distributed VVO (area decomposition) | MILP (decomposed) | partial | |
| Tap / capacitor coordination | MILP | production | |
| Reactive-power dispatch | NLP | production | |
| Grid-forming inverter setpoint control | NLP | research |
Storage dispatch / arbitrage
Storage scheduling — battery, pumped hydro, H₂, thermal. Merged merchant (arbitrage) and system-cost views; `objective` flag disambiguates. Benchmark oracles live here because storage-against-prices is the canonical closed-form case.
| Price-taker arbitrage, linear efficiency | LP | trivial | |
| Price-taker with degradation cost | QP | production | |
| Multi-service stacking (energy + FCR + FFR) | MILP | production | |
| Rolling-horizon under price / forecast uncertainty (MPC) | Stochastic LP / MPC | stochastic | production |
| Robust dispatch against bounded forecast error | Robust LP | robust | partial |
| Embedded inside ED / UC (system-cost objective) | LP / MILP | production | |
| Battery sizing + dispatch joint | MILP | partial | |
| Perfect-foresight greedy closed-form (benchmark upper bound) | Analytical | trivial |
Optimal power flow (OPF)
Steady-state network analysis, from pure feasibility (power flow: 'given a dispatch, what's the grid state?') up to full cost-minimising OPF ('which dispatch minimises cost subject to Kirchhoff + line/voltage limits?'). AC-OPF is the 'holy grail' — proven NP-hard (Bienstock & Verma, 2015). Most market clearing uses DC-OPF; convex relaxations (SOCP / SDP) are exact for radial networks under known conditions and approximate otherwise. Feasibility-only power flow is included as the zero-objective special case.
| DC power flow (linear approximation, feasibility-only) | Linear system | trivial | |
| AC power flow (Newton-Raphson, feasibility-only) | Nonlinear root-find | production | |
| AC power flow with continuation (P-V / Q-V curves) | Parametric NLP | production | |
| Probabilistic / Monte-Carlo power flow | Sampled NLP | stochastic | partial |
| DC-OPF — linearised (angle or PTDF) | LP | production | |
| DC-OPF with losses (piecewise-linear) | LP | production | |
| AC-OPF — full Kirchhoff laws (non-convex) | NLP (non-convex, NP-hard) | partial | |
| SOCP relaxation of AC-OPF (Jabr) | SOCP (convex) | production | |
| SDP relaxation of AC-OPF (Low / Lavaei) | SDP (convex) | partial | |
| Chordal SDP relaxation (scalable SDP) | SDP (decomposed) | partial | |
| Multi-objective OPF (cost / losses / emissions) | NLP / LP (weighted sum or ε-constraint) | production | |
| Stochastic OPF under renewable uncertainty | Stochastic LP / NLP | stochastic | partial |
| Robust OPF (bounded load + RES deviation) | Robust LP / NLP | robust | partial |
Demand-side optimisation
Scheduling flexible demand — shiftable / interruptible loads, aggregator bidding, EV fleet charging, building / microgrid EMS. Combinatorial activation logic makes these MILP even for single aggregators.
| Price-responsive shiftable loads | MILP | production | |
| Capacity / interruptible programs with call windows | MILP | production | |
| Aggregator bidding with recovery constraints | MILP | production | |
| Stochastic DR under activation-price uncertainty | Stochastic MILP | stochastic | partial |
| EV fleet charging optimisation | MILP | production | |
| Building / microgrid EMS | MILP / NLP | production |
Economic dispatch
Merit-order dispatch with fixed commitment. The LP baseline — copper-plate (no network) or lightly-constrained; network-aware variants live in `optimal_power_flow`. ISO markets use ED in real-time / balancing after UC has decided commitment.
| Merit-order / copper-plate ED | LP | trivial | |
| ED with quadratic losses | QP | production | |
| Co-optimised energy + reserves | LP | production | |
| Multi-area ED with tie lines | LP | production | |
| Stochastic ED under RES uncertainty | Stochastic LP | stochastic | partial |
| Robust ED | Robust LP | robust | partial |
Market clearing
Wholesale electricity market clearing — the auction that sets price and dispatch. Day-ahead is typically MILP (EPEX / Nord Pool EUPHEMIA is one of the world's largest MILPs, ~10⁸ variables); intraday auctions LP/MILP; intraday-continuous is order-matching rather than optimisation; balancing / real-time is LP.
| Day-ahead auction — simple hourly orders (LP) | LP | production | |
| Day-ahead auction — block + complex orders (EUPHEMIA-style) | MILP | partial | |
| Intraday auction clearing | LP / MILP | production | |
| Intraday continuous order-book matching | Matching heuristic (not optimisation) | production | |
| Balancing / real-time clearing | LP | production | |
| Stochastic market clearing under RES uncertainty | Stochastic LP / MILP | stochastic | partial |
Network security operations
Topology-control and curtailment decisions that maintain grid security in operations — transmission switching, network reconfiguration (distribution), corrective redispatch, curtailment allocation, remedial action schemes.
| Optimal transmission switching (OTS) | MILP / MINLP | research | |
| Network reconfiguration (distribution) | MILP | production | |
| Corrective redispatch | LP | production | |
| Curtailment allocation (fair / minimum-cost) | LP | production | |
| Remedial action scheme (RAS) optimisation | MILP | partial |
Unit commitment
Which generators to commit each hour — integer on/off decisions with min-up / min-down constraints.
| Economic dispatch only (fixed commitment) | LP or QP | trivial | |
| UC with linear costs, DC power flow | MILP | production | |
| Security-constrained UC (N-1 contingencies) | MILP | production | |
| UC with quadratic costs | MIQP (usually linearised → MILP) | production | |
| UC with AC power flow | MINLP | research | |
| Stochastic UC (scenario-tree recourse) | Multi-stage MILP | stochastic | partial |
| Robust UC (adjustable robust, budget of uncertainty) | Robust MILP | robust | partial |
Hydrothermal coordination
Multi-reservoir water value / thermal generation coordination over weeks to years. SDDP is the canonical solver for large stochastic instances (Brazil's NEWAVE, Norway's EMPS, NZ's vSPD). The 'expected-value of a stored unit of water' drives real-time dispatch downstream.
| Deterministic multi-reservoir coordination | LP / MILP | production | |
| Stochastic Dual Dynamic Programming (SDDP) | Multi-stage SDDP | stochastic | production |
| Scenario-tree hydrothermal | Multi-stage stochastic MILP | stochastic | partial |
| Joint hydro-thermal UC | MILP | production | |
| Lagrangian-decomposed coordination | LP / Lagrangian | partial |
Maintenance scheduling
Generator and transmission outage scheduling over weeks-to-years. Usually MILP with couplings to UC and adequacy constraints. Risk-adjusted variants use CVaR or LOLE targets.
| Generator maintenance windows | MILP | production | |
| Transmission outage coordination | MILP | production | |
| Joint UC + maintenance | MILP | partial | |
| Risk-adjusted maintenance (CVaR) | MILP (CVaR) | stochastic | partial |
Reserve / ancillary-services procurement
Joint procurement of energy + spinning / non-spinning / regulation reserves. In ISO markets this is almost always folded into SCUC as a single co-optimised MILP, so the cleared energy price and the reserve clearing prices are internally consistent.
| Energy + spinning reserve co-optimisation | MILP | production | |
| Energy + regulation + spinning + non-spinning | MILP | production | |
| Within SCUC (joint MILP — ISO market default) | MILP (SCUC) | production | |
| Stochastic reserve co-optimisation | Multi-stage stochastic MILP | stochastic | partial |
| Robust reserve procurement (budget of uncertainty) | Robust MILP | robust | partial |
Capacity expansion (GEP + all-assets)
Least-cost investment in generation (and optionally storage / demand-side) over a planning horizon. `scope` flag distinguishes generation-only (GEP), generation + transmission (TEP+GEP), and all-assets (IRP-flavour) investment problems.
| Screening curves / LDC (generation-only) | LP | trivial | |
| Greenfield GEP with representative days | LP | production | |
| Integer build decisions (discrete plants) | MILP | production | |
| Benders-decomposed GEP (invest master + dispatch sub) | MILP (decomposed) | production | |
| Co-optimised transmission + generation (TEP+GEP) | MILP | partial | |
| All-assets expansion (gen + storage + demand-side) | MILP | production | |
| Multi-stage stochastic with scenario trees | Multi-stage stochastic LP/MILP | stochastic | partial |
| Robust capacity expansion | Robust MILP | robust | partial |
| Endogenous learning / retirements | MINLP | research |
Distribution planning
Medium- and low-voltage network design — radial topology, DER hosting-capacity, VVO-aware planning, storage siting. Typically MILP with AC-feasibility side-constraints.
| Radial network design | MILP | production | |
| DER hosting-capacity planning | NLP / MILP | production | |
| VVO-aware distribution planning | MILP | partial | |
| Storage siting in distribution | MILP | partial |
Integrated system planning (IRP / multi-sector)
Joint optimisation of generation, transmission, storage, demand-side and sector-coupled resources (power + gas + H₂ + heat). Solved by full-system tools like PLEXOS, PyPSA, GenX, Switch, OSeMOSYS, Calliope, TIMES / MARKAL and Temoa.
| Deterministic IRP (generation + storage + demand-side) | MILP | production | |
| Full IRP with transmission co-optimisation | MILP | partial | |
| Sector-coupled (power + gas + H₂ + heat) | MILP / MINLP | partial | |
| Stochastic IRP (scenario tree over demand, prices, policy) | Multi-stage stochastic MILP | stochastic | partial |
| Robust IRP against worst-case scenarios | Robust MILP | robust | partial |
Transmission expansion planning (TEP)
Which lines and substations to build. MILP with network-design structure — closely related to the fixed-charge network-flow problem. Typically co-optimised with generation (TEP + GEP) in modern planning studies.
| Static TEP (single target year) | MILP (fixed-charge network flow) | production | |
| Multi-stage TEP (time-phased investments) | MILP | partial | |
| Co-optimised TEP + GEP | MILP | partial | |
| Stochastic TEP (scenarios over demand + RES growth) | Multi-stage stochastic MILP | stochastic | partial |
| Robust TEP (N-1 + contingency sets) | Robust MILP | robust | partial |
Adversarial and bilevel
Defender-attacker and strategic-bidding problems — network interdiction, Stackelberg games, market-power analysis, cyber-physical attack modelling. Bilevel structure is the defining feature; MIBLP / MINLP in general.
| Interdiction (defender-attacker) | Bilevel MILP | partial | |
| Strategic bidding (Stackelberg) | Bilevel MILP / MINLP | partial | |
| Market-power / Cournot analysis | Bilevel LP / equilibrium | production | |
| Cyber-physical attack model | Bilevel MILP | research |
Benchmarks and oracles
Reference policies used to score other methodologies — perfect-foresight oracle LP, rolling-horizon MPC, greedy closed-form, myopic, ex-post counterfactual. Applied across every tier; not deployable schedulers but the yardstick for regret / cost-of-uncertainty analysis.
| Perfect-foresight oracle LP (full-horizon) | LP | trivial | |
| Rolling-horizon MPC baseline | Stochastic LP / MPC | stochastic | production |
| Greedy closed-form storage benchmark | Analytical | trivial | |
| Myopic policy (single-step) | LP | trivial | |
| Ex-post counterfactual replay | LP | production |
Resilience and restoration
Post-disturbance recovery — black-start sequencing, restoration schedule, microgrid islanding, disaster-aware pre-positioning. Combinatorial by nature; typically MILP. Spans real-time ops to long-term hardening investments.
| Black-start sequencing | MILP | production | |
| Restoration scheduling | MILP | production | |
| Microgrid islanding | MILP | partial | |
| Disaster-aware pre-positioning / hardening | MILP (two-stage) | stochastic | partial |
Security and reliability
Security-constrained optimisation and adequacy assessment — N-1 / N-k contingency, cascading failure, reliability-constrained OPF, LOLE / EUE adequacy. Spans short-term operations (SCOPF) to long-term planning (adequacy targets).
| N-1 contingency screening | LP (enumerated) | production | |
| SCOPF — DC-OPF + N-1 contingencies | LP (large) | production | |
| SCOPF — AC-OPF + N-1 contingencies | NLP (very large) | research | |
| N-k cascading failure analysis | MILP | partial | |
| Adequacy assessment (LOLE / EUE) | Monte-Carlo simulation | stochastic | production |
| Probabilistic reliability-constrained OPF (PLOC) | Chance-constrained LP / NLP | chance_constrained | partial |