Glossary

Terminology used in the methodology chapters of this book, with Portuguese equivalents where they appear in Brazilian regulatory or operational documentation. Citations to source papers for the more technical entries live in Bibliography.

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Power System

English	Portuguese	Definition
Block	Patamar	An intra-stage time period (e.g., peak, shoulder, off-peak) representing load-level variation within a stage. Cobre supports two block topologies: parallel (independent dispatches) and chronological (sequential, with carry-over storage).
Bus	Barramento	A node in the electrical network where generation, demand, and transmission lines connect.
Line	Linha / Circuito	A transmission line or transformer connecting two buses, modelled with a directional capacity and an exchange cost.
Subsystem	Subsistema	A region of the interconnected grid (in Brazil: SE/CO, S, NE, N).
Exchange	Intercâmbio	Power transfer between buses across a transmission line.
Load	Carga / Demanda	Electrical power consumption at a bus, possibly varying per block via a load-factor table.
Deficit	Déficit	Unmet demand — load that cannot be served by available generation. Modelled as a slack variable with a high penalty cost.

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Hydro Generation

English	Portuguese	Definition
Hydro plant	Usina hidrelétrica (UHE)	A hydroelectric generating station.
Reservoir	Reservatório	Water storage volume behind a dam.
Storage	Armazenamento	Current water volume in a reservoir, in hm³. The primary state variable in SDDP.
Inflow	Afluência / Vazão natural	Natural water flow arriving at a reservoir, modelled stochastically by a PAR(p) model (or 0-order seasonal sampling for the $p = 0$ degenerate case).
Turbined outflow	Vazão turbinada	Water passing through turbines to generate electricity.
Spillage	Vertimento	Water released from a reservoir without generating electricity.
Cascade	Cascata	Sequence of hydro plants along the same river, where downstream reservoirs receive turbined plus spilled water from upstream plants.
Downstream	Jusante	Direction of water flow; the plant that receives outflow from upstream.
Upstream	Montante	Direction against water flow; the plant whose outflow feeds a downstream plant.
Productivity	Produtibilidade	Conversion factor from water flow (m³/s) to power (MW).
Run-of-river	Fio d’água	Hydro plant with no significant storage capacity; storage variable bounds collapse to a single point.
Diversion	Desvio	Water bypassed to a separate channel, not passing through turbines.
Evaporation	Evaporação	Water loss from the reservoir surface; can be negative under monthly-net conventions, requiring a bidirectional slack.
Forebay level	Nível de montante	Water level at the upstream face of the dam, a function of reservoir storage.
Tailrace level	Nível de jusante	Water level at the downstream channel below the dam, a function of total outflow.
Head	Queda	Height difference between forebay and tailrace levels, determining generation efficiency.
FPHA	Função de Produção Hidrelétrica Aproximada	Approximate Hydroelectric Production Function — piecewise-linear model of hydro generation as a function of storage, turbined flow, and spillage. See Hydro Production Models.
Dead volume	Volume morto	The portion of the reservoir below the minimum operating storage; reservoirs in commissioning are filled to dead volume before entering normal operation.

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Thermal Generation

English	Portuguese	Definition
Thermal unit	Usina termelétrica (UTE)	A fossil-fuel or nuclear generating station.
Minimum generation	Geração mínima / Inflexibilidade	Minimum output when the unit is committed; modelled as a soft constraint with a penalty slack in Cobre.
Operating cost	Custo variável unitário (CVU)	Variable cost per MWh of generation.
Marginal cost (CMO)	Custo Marginal de Operação	Shadow price of the bus load-balance constraint — the cost of one additional MWh of demand at that bus.
Anticipated dispatch	Antecipação de despacho	A per-plant flag that splits the thermal decision into a commitment placed at stage $t$ and a delivered generation forced to match the commitment at stage $t + K$, where $K =$ lead_stages $\geq 1$. Originally motivated by LNG (GNL) fuel-ordering lead times. See System Elements §4.
Lead stages ($K$)	Antecedência (estágios)	Number of stages between commitment and delivery for an anticipated thermal. The commitment column at stage $t$ delivers physical generation at stage $t + K$.
Past anticipated commitments	Compromissos anticipados pré-horizonte	The $K_i$ pre-horizon commitments seeded into the ring buffer for plant $i$. Stored on initial_conditions.past_anticipated_commitments[].values_mw, with values_mw[k] delivering at study stage $k$.

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Stochastic Modelling

English	Portuguese	Definition
Scenario	Cenário	One realisation of uncertain quantities (inflows, load, non-controllable sources) along the planning horizon.
Stage	Estágio	A time period in the planning horizon — typically a month, week, or hour.
State variable	Variável de estado	Variables that link one stage to the next: storage volumes (always) and AR-lag state (only for PAR(p) with $p \geq 1$).
PAR(p)	PAR(p)	Periodic Autoregressive model of order $p$ for inflow generation. The order $p_m$ can vary by season $m$; $p_m = 0$ corresponds to white-noise (0-order) seasonal sampling.
0-order inflow	-	The degenerate $p = 0$ case of the PAR(p) model: $a_t = \mu_t + \sigma_t \varepsilon_t$ with $\varepsilon_t \sim \mathcal{N}(0,1)$ iid. No AR-lag state, no AR coefficients in the data file.
Innovation	Inovação	The independent standardised noise term $\varepsilon_t \sim \mathcal{N}(0,1)$ in the PAR(p) model, representing the unpredictable component after removing autoregressive structure.
AR lag	Defasagem	Past inflow values $a_{h, t-\ell}$ that enter the PAR(p) recursion for $p \geq 1$. Stored as state variables in the LP and pinned to the previous stage’s realised inflow via column bounds.
Yule-Walker equations	Equações de Yule-Walker	System of linear equations relating autoregressive coefficients to sample autocorrelations. Cobre uses the periodic Yule-Walker variant where the reference season shifts per row to handle multi-season covariance structure.
Spatial correlation	Correlação espacial	Cross-hydro covariance structure between innovations $\varepsilon_h$. Applied via spectral factorisation $\varepsilon = L\, z$ with $L L^{\top} = \Sigma$, where $z \sim \mathcal{N}(0, I)$.
Seasonal mean / std	Média / desvio sazonal	Per-season parameters $\mu_m, \sigma_m$ stored in inflow_seasonal_stats.parquet and used both for sampling 0-order inflows and for converting standardised PAR coefficients to original units.
Opening	Abertura	A pre-generated noise vector $\varepsilon$ used to evaluate the backward pass at one branch of the scenario tree.
Opening tree	Árvore de aberturas	The fixed set of pre-generated noise vectors used in the backward pass; generated once before training begins and reused across all iterations. Each stage carries num_scenarios openings. See Scenario Generation.
In-sample sampling	Amostragem in-sample	Forward-pass scheme that draws trajectories from the same opening tree the backward pass uses. Default in Cobre.
Out-of-sample sampling	Amostragem out-of-sample	Forward-pass scheme that draws trajectories from a separate, independent set of openings. Used for unbiased upper-bound estimation.

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SDDP Algorithm

English	Portuguese	Definition
Stage subproblem (stage LP)	Subproblema de estágio	The linear programme solved at one stage given an incoming state and a scenario realisation. Carries the cuts accumulated for that stage as constraints on the future-cost variable $\theta$.
Bellman recursion	Recursão de Bellman	Recursive equation $V_t(x_{t-1}) = \min_{x_t}\, c_t(x_t) + d \cdot \mathbb{E}[V_{t+1}(x_t)]$ that defines the cost-to-go functions and underlies the SDDP backward pass.
Cost-to-go function	Função de custo futuro (FCF)	Expected cost from the current stage to the end of the horizon, as a function of the incoming state. Convex and piecewise-linear under LP subproblems.
Cut (Benders cut)	Corte (de Benders)	A linear inequality $\theta \geq \alpha + \pi^{\top} x$ providing a lower bound on the future-cost function. Generated in the backward pass from the LP reduced costs of the pinned incoming-state columns at trial states.
Cut intercept	Intercepto	The scalar $\alpha$ in a cut, anchoring the hyperplane vertically.
Cut slope (cut coefficient)	Coeficiente do corte	The vector $\pi$ in a cut, giving the partial derivative of the future-cost function with respect to each state variable. Negative for storage (more storage means lower cost) under the methodology’s sign convention.
State pinning (column bounds)	Fixação de estado	Binding an incoming-state coordinate to the trial value $\hat{x}_{t-1}$ by setting equal lower/upper bounds on its dedicated LP column. The column’s reduced cost is the cut coefficient for that state directly, with no preprocessing. Replaces the earlier equality fixing-row mechanism (KKT-equivalent, fewer rows).
Trial point	Ponto amostral	The state visited during a forward pass, used as the anchor where the backward pass evaluates per-opening LPs and aggregates a cut.
Forward pass	Passagem direta	Phase that simulates the policy by solving stage LPs sequentially under sampled scenarios, producing trial points and a statistical upper-bound estimate.
Backward pass	Passagem reversa	Phase that walks stages in reverse, evaluates all openings at each trial point, extracts duals, and aggregates one cut per stage.
Single-cut formulation	Formulação de corte único	Aggregation scheme that produces one cut per (stage, trial point) by averaging per-opening cuts with probability weights. Cobre’s default. Contrasted with the multi-cut formulation (one cut per opening), which Cobre does not currently use.
Outer approximation	Aproximação exterior	The piecewise-linear lower bound on the future-cost function constructed from accumulated Benders cuts. The primary output of SDDP training.
Cut pool	Conjunto de cortes	Collection of all cuts at a given stage. Append-only across iterations within one training run; cuts occupy stable, deterministic slot indices and are never deleted — only deactivated and later reactivated, which keeps the cut order reproducible.
Level-1 cut selection	-	Cut-selection strategy that, at every visited trial point, keeps each cut within tie_tolerance of the per-state maximum cut value (evaluated over all populated cuts, active and inactive) and deactivates cuts that fall short at every visited state. Least aggressive of a value-based family that also includes LML1 (keeps only the oldest near-maximum cut per state) and Dominated (uses a domination_tolerance band); all three share one kernel and reactivate cuts symmetrically. See Cut Management §7.
Dynamic cut selection (DCS)	Seleção dinâmica de cortes	Cut-management mode (selection.method = "dynamic") that retains the full cut pool but loads only a small resident subset into each stage LP, growing it lazily until no omitted cut is violated — so the per-solve LP stays bounded as the pool grows while the solution remains exact (the resident-subset optimum equals the full-pool optimum). Mutually exclusive with the value-based pruning family (Level-1 / LML1 / Dominated). See Cut Management.
Lower bound	Limite inferior	Estimate from solving the stage-1 LP with all cuts active; non-decreasing as cuts accumulate.
Upper bound	Limite superior	Statistical estimate of policy cost from forward-pass simulations (in-sample or out-of-sample), or a deterministic estimate from an inner approximation.
Optimality gap	Gap de otimalidade	Relative difference between upper and lower bounds, the primary convergence diagnostic.
Bound stalling	-	Stopping criterion that fires when the lower bound stops increasing across a configurable window of iterations.
Dual variable	Variável dual / Multiplicador	Shadow price from an LP solution; indicates the marginal value of a constraint right-hand side. The companion sensitivity for a variable is its reduced cost — for a column pinned at equal bounds, the reduced cost is the marginal value of that bound, which is how Cobre extracts state cut coefficients.
Epigraph variable	-	The auxiliary LP variable $\theta$ that lower-bounds the true cost-to-go function $V_{t+1}(x_t)$; named after the epigraph of a convex function.
Relatively complete recourse	Recurso relativamente completo	Property that every stage LP is feasible for any incoming state and scenario realisation. Cobre ensures this via penalty slack variables on every constraint that could otherwise be violated.
Trajectory record	Trajetória	Data structure capturing one stage’s forward-pass result: primal solution, dual solution, stage cost, and end-of-stage state. Used for cut-coefficient extraction in the backward pass and for simulation output.

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Boundary Conditions and Horizon Modes

English	Portuguese	Definition
Policy graph	Grafo de política	Directed graph defining the stage structure and transitions of an SDDP problem. Cobre supports finite (acyclic chain) and cyclic policy graphs.
Finite horizon (acyclic mode)	Horizonte finito	Policy graph with a single terminal stage and zero terminal cost-to-go. Susceptible to the end-of-world effect: reservoirs are systematically emptied near the terminal stage.
Cyclic mode	Modo cíclico	Policy graph with a back-edge that returns from the last stage of a cycle to the first stage of the next repetition. Used for long-term studies where a finite terminal condition would distort the policy. Replaces what older Brazilian literature calls “infinite horizon”.
Season function $\tau(t)$	Função de estação	The position of stage $t$ within one cycle of length $P$: $\tau(t) = (t-1) \bmod P + 1$. In cyclic mode, cuts are pooled by season, not by absolute stage.
Cycle convergence inequality	-	The requirement $d_{\text{cycle}} = \prod_{t \in \text{cycle}} d_{t \to t+1} < 1$ for the cumulative discount around one cycle, ensuring the value function remains finite across infinite repetitions.
Discount factor	Fator de desconto	Multiplicative factor $d \in (0, 1]$ applied to the future-cost variable $\theta$ in the stage objective, reflecting the time value of future costs. Required (strictly less than 1) for cyclic-mode convergence.
Terminal boundary cut	-	A Benders cut on the terminal future-cost function imported from an upstream Cobre run, used to chain studies (e.g., a weekly run inheriting the monthly run’s terminal cuts).

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Risk Measures

English	Portuguese	Definition
Coherent risk measure	Medida de risco coerente	A risk measure satisfying monotonicity, translation equivariance, positive homogeneity, and subadditivity. CVaR is the canonical example used in SDDP.
CVaR	CVaR	Conditional Value at Risk at level $\alpha$ — the expected cost in the worst $\alpha\%$ of scenarios. The basis for risk-averse aggregation weights in SDDP.
EAVaR	-	Expectation plus Average Value-at-Risk: the convex combination $(1-\lambda)\,\mathbb{E}[Z] + \lambda \cdot \text{CVaR}_\alpha[Z]$ used as Cobre’s parameterised risk measure. $\lambda = 0$ recovers risk-neutral; $\lambda = 1$ gives pure CVaR.
Risk-neutral	Neutro ao risco	Optimisation that minimises expected cost only. Probability weights at cut aggregation are uniform $p_\omega = 1/N$.
Risk-averse	Averso ao risco	Optimisation that penalises high-cost tail scenarios. Cut aggregation reweights toward worse outcomes via the EAVaR formula.

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Solver and LP

English	Portuguese	Definition
LP	Programa Linear	Linear Program — an optimisation problem with a linear objective and linear constraints.
Simplex method	Método Simplex	Algorithm for solving linear programs by traversing vertices of the feasible polytope. Cobre’s default warm-start strategy targets simplex bases.
Basis	Base	The set of basic variables defining a vertex of the LP feasible region; reused across iterations for warm-starting.
Warm-start	Partida a quente	Reusing a previous solution basis to accelerate the simplex method on a modified LP, including reconstructing a stored basis onto a churned cut pool by slot identity. See LP Warm-Start.
HiGHS	-	Open-source LP / MIP solver used as Cobre’s default backend.
CLP	-	Open-source LP solver from COIN-OR, available as an alternative compile-time backend.

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Brazilian Power-System Ecosystem

Term	Definition
ONS	Operador Nacional do Sistema Elétrico — the Brazilian grid operator.
CEPEL	Centro de Pesquisas de Energia Elétrica — R&D centre that develops the official NEWAVE / DECOMP / DESSEM dispatch programs.
SIN	Sistema Interligado Nacional — the Brazilian interconnected power system.
NEWAVE	CEPEL’s long-term hydrothermal-dispatch model (monthly stages, multi-year horizon).
DECOMP	CEPEL’s medium-term dispatch model (weekly resolution). The “DECOMP-style” scenario tree (deterministic trunk with branching at the last stage) takes its name from this model.
DESSEM	CEPEL’s short-term dispatch model (hourly / half-hourly, day-ahead).
GEVAZP	CEPEL’s synthetic scenario-generation tool for hydro inflows.
CCEE	Câmara de Comercialização de Energia Elétrica — Brazilian electricity-trading chamber.