Public API Reference

HybridDispatchWithReserves

Device formulation for a hybrid system (single point of common coupling (PCC) with renewable, thermal, and storage) that participates in both energy and ancillary services markets. Implements the centralized production cost modeling (PCM) model where the hybrid plant's net power at the PCC is constrained by $P_{\max,\text{pcc}}$ and ancillary service allocations ($sb^{\text{out}}_{p,t}$, $sb^{\text{in}}_{p,t}$) are assigned to internal assets (thermal, renewable, charge, discharge) per the four-quadrant ancillary service model.

Use with a hybrid system in a PowerSimulations.DeviceModel for unit commitment or economic dispatch.

Variables:

• PowerSimulations.ActivePowerOutVariable:

  • Bounds: [0.0, $P_{\max,\text{pcc}}$]
  • Symbol: $p^{\text{out}}_t$

• PowerSimulations.ActivePowerInVariable:

  • Bounds: [0.0, $P_{\max,\text{pcc}}$]
  • Symbol: $p^{\text{in}}_t$

• PowerSimulations.ReservationVariable:

  • Bounds: {0, 1}
  • Symbol: $u^{\text{st}}_t$

• ThermalPower:

  • Bounds: [0.0, $P_{\max,\text{th}}$] when on
  • Symbol: $p^{\text{th}}_t$

• PowerSimulations.OnVariable:

  • Bounds: {0, 1}
  • Symbol: $u^{\text{th}}_t$

• RenewablePower:

  • Bounds: [0.0, $P^{*,\text{re}}_t$]
  • Symbol: $p^{\text{re}}_t$

• BatteryCharge:

  • Bounds: [0.0, $P_{\max,\text{ch}}$] when charging
  • Symbol: $p^{\text{ch}}_t$

• BatteryDischarge:

  • Bounds: [0.0, $P_{\max,\text{ds}}$] when discharging
  • Symbol: $p^{\text{ds}}_t$

• PowerSimulations.EnergyVariable:

  • Bounds: [0.0, $E_{\max,\text{st}}$]
  • Symbol: $e^{\text{st}}_t$

• BatteryStatus:

  • Bounds: {0, 1}
  • Symbol: $ss^{\text{st}}_t$ (0 = charge, 1 = discharge)

• ReserveVariableOut:

  • Bounds: [0.0, ]
  • Symbol: $sb^{\text{out}}_t$

• ReserveVariableIn:

  • Bounds: [0.0, ]
  • Symbol: $sb^{\text{in}}_t$

Time Series Parameters:

Data requirements:

• Device: A PowerSystems.HybridSystem with at least one of: thermal unit (PowerSystems.get_thermal_unit), renewable unit (PowerSystems.get_renewable_unit), storage (PowerSystems.get_storage), and optionally electric load (PowerSystems.get_electric_load).
• Time series: Each hybrid must have forecast time series attached with the default names above (or custom names passed when adding parameters).

Static Parameters:

• $P_{\max,\text{pcc}}$ = PowerSystems.get_output_active_power_limits(device).max
• $P_{\max,\text{th}}$ = PowerSystems.get_active_power_limits(thermal_unit).max
• $P_{\min,\text{th}}$ = PowerSystems.get_active_power_limits(thermal_unit).min
• $P_{\max,\text{ch}}$ = PowerSystems.get_input_active_power_limits(storage).max
• $P_{\max,\text{ds}}$ = PowerSystems.get_output_active_power_limits(storage).max
• $\eta_{\text{ch}}$ = PowerSystems.get_efficiency(storage).in
• $\eta_{\text{ds}}$ = PowerSystems.get_efficiency(storage).out
• $E_{\max,\text{st}}$ = PowerSystems.get_storage_level_limits(storage).max × capacity
• $E^{\text{st}}_0$ = initial storage energy
• $R^{*}_{p,t}$ = ancillary service deployment forecast for service $p$ at time $t$
• $F_p$ = fraction of $P_{\max,\text{pcc}}$ allowed for service $p$
• $N_p$ = number of periods of compliance for service $p$

Expressions:

Adds $p^{\text{out}}_t$ and $p^{\text{in}}_t$ to PowerSimulations' ActivePowerBalance expression for use in network balance constraints. When services are present, adds reserve expressions (TotalReserveOutUpExpression, TotalReserveOutDownExpression, TotalReserveInUpExpression, TotalReserveInDownExpression) and served reserve expressions for tracking deployed reserves.

Constraints:

Let $\mathcal{T} = \{1, \dots, T\}$ denote the set of time steps.

PCC and status (PowerSimulations.InputActivePowerVariableLimitsConstraint, PowerSimulations.OutputActivePowerVariableLimitsConstraint, StatusOutOn, StatusInOn):

\[\begin{align*} & 0 \leq p^{\text{in}}_t \leq P_{\max,\text{pcc}}, \quad 0 \leq p^{\text{out}}_t \leq P_{\max,\text{pcc}}, \quad \forall t \in \mathcal{T} \\ & u^{\text{st}}_t \in \{0,1\} \quad \text{(output/input status at PCC)} \end{align*}\]

Energy asset balance (EnergyAssetBalance):

\[p^{\text{th}}_t + p^{\text{re}}_t + p^{\text{ds}}_t - p^{\text{ch}}_t - P^{\text{ld}}_t = p^{\text{out}}_t - p^{\text{in}}_t, \quad \forall t \in \mathcal{T}\]

Thermal limits (ThermalOnVariableUb, ThermalOnVariableLb):

\[u^{\text{th}}_t P_{\min,\text{th}} \leq p^{\text{th}}_t \leq u^{\text{th}}_t P_{\max,\text{th}}, \quad u^{\text{th}}_t \in \{0,1\}, \quad \forall t \in \mathcal{T}\]

Renewable limit (RenewableActivePowerLimitConstraint):

\[0 \leq p^{\text{re}}_t \leq P^{*,\text{re}}_t, \quad \forall t \in \mathcal{T}\]

Storage charge/discharge status (BatteryStatusChargeOn, BatteryStatusDischargeOn):

\[\begin{align*} & p^{\text{ch}}_t \leq (1 - ss^{\text{st}}_t) P_{\max,\text{ch}}, \quad p^{\text{ds}}_t \leq ss^{\text{st}}_t P_{\max,\text{ds}}, \quad \forall t \in \mathcal{T} \\ & ss^{\text{st}}_t \in \{0,1\} \quad \text{(0 = charge, 1 = discharge)} \end{align*}\]

Storage energy balance (BatteryBalance):

\[e^{\text{st}}_t = e^{\text{st}}_{t-1} + \Delta t \left( \eta_{\text{ch}} p^{\text{ch}}_t - \frac{p^{\text{ds}}_t}{\eta_{\text{ds}}} \right), \quad \forall t \in \mathcal{T}, \quad e^{\text{st}}_0 = E^{\text{st}}_0\]

When ancillary services are present: ThermalReserveLimit, RenewableReserveLimit, ChargingReservePowerLimit, DischargingReservePowerLimit, ReserveCoverageConstraint, ReserveCoverageConstraintEndOfPeriod, HybridReserveAssignmentConstraint, ReserveBalance.

Cycling limits (if "cycling" => true), (CyclingCharge, CyclingDischarge):

\[\begin{align*} & \eta_{\text{ch}} \Delta t \sum_{t \in \mathcal{T}} p^{\text{ch}}_t \leq C_{\text{st}} E_{\max,\text{st}} \\ & \frac{\Delta t}{\eta_{\text{ds}}} \sum_{t \in \mathcal{T}} p^{\text{ds}}_t \leq C_{\text{st}} E_{\max,\text{st}} \end{align*}\]

End-of-horizon energy target (if "energy_target" => true), (StateofChargeTargetConstraint):

\[e^{\text{st}}_T = E^{\text{st}}_T\]

Regularization (if "regularization" => true): ChargeRegularizationConstraint, DischargeRegularizationConstraint.

Objective:

Adds cost terms for thermal generation (variable and fixed costs), storage variable O&M, renewable variable cost, and penalties for energy target deviations (if enabled).

HybridEnergyOnlyDispatch

Device formulation for a hybrid system that participates in energy only (no ancillary services). Net power at the point of common coupling (PCC) is $p^{\text{out}}_t - p^{\text{in}}_t$ from thermal, renewable, discharge, minus charge and load; subject to $P_{\max,\text{pcc}}$ and asset limits.

Variables:

• PowerSimulations.ActivePowerOutVariable:

  • Bounds: [0.0, $P_{\max,\text{pcc}}$]
  • Symbol: $p^{\text{out}}_t$

• PowerSimulations.ActivePowerInVariable:

  • Bounds: [0.0, $P_{\max,\text{pcc}}$]
  • Symbol: $p^{\text{in}}_t$

• PowerSimulations.ReservationVariable:

  • Bounds: {0, 1}
  • Symbol: $u^{\text{st}}_t$

• ThermalPower:

  • Bounds: [0.0, $P_{\max,\text{th}}$] when on
  • Symbol: $p^{\text{th}}_t$

• PowerSimulations.OnVariable:

  • Bounds: {0, 1}
  • Symbol: $u^{\text{th}}_t$

• RenewablePower:

  • Bounds: [0.0, $P^{*,\text{re}}_t$]
  • Symbol: $p^{\text{re}}_t$

• BatteryCharge:

  • Bounds: [0.0, $P_{\max,\text{ch}}$] when charging
  • Symbol: $p^{\text{ch}}_t$

• BatteryDischarge:

  • Bounds: [0.0, $P_{\max,\text{ds}}$] when discharging
  • Symbol: $p^{\text{ds}}_t$

• PowerSimulations.EnergyVariable:

  • Bounds: [0.0, $E_{\max,\text{st}}$]
  • Symbol: $e^{\text{st}}_t$

• BatteryStatus:

  • Bounds: {0, 1}
  • Symbol: $ss^{\text{st}}_t$ (0 = charge, 1 = discharge)

Time Series Parameters:

Data requirements:

• Device: A PowerSystems.HybridSystem with at least one of: thermal unit (PowerSystems.get_thermal_unit), renewable unit (PowerSystems.get_renewable_unit), storage (PowerSystems.get_storage), and optionally electric load (PowerSystems.get_electric_load).
• Time series: Each hybrid must have forecast time series attached with the default names above (or custom names passed when adding parameters).

Static Parameters:

• $P_{\max,\text{pcc}}$ = PowerSystems.get_output_active_power_limits(device).max
• $P_{\max,\text{th}}$ = PowerSystems.get_active_power_limits(thermal_unit).max
• $P_{\min,\text{th}}$ = PowerSystems.get_active_power_limits(thermal_unit).min
• $P_{\max,\text{ch}}$ = PowerSystems.get_input_active_power_limits(storage).max
• $P_{\max,\text{ds}}$ = PowerSystems.get_output_active_power_limits(storage).max
• $\eta_{\text{ch}}$ = PowerSystems.get_efficiency(storage).in
• $\eta_{\text{ds}}$ = PowerSystems.get_efficiency(storage).out
• $E_{\max,\text{st}}$ = PowerSystems.get_storage_level_limits(storage).max × capacity
• $E^{\text{st}}_0$ = initial storage energy

Expressions:

Adds $p^{\text{out}}_t$ and $p^{\text{in}}_t$ to PowerSimulations' ActivePowerBalance expression for use in network balance constraints.

Constraints:

Let $\mathcal{T} = \{1, \dots, T\}$ denote the set of time steps.

PCC and status (PowerSimulations.InputActivePowerVariableLimitsConstraint, PowerSimulations.OutputActivePowerVariableLimitsConstraint, StatusOutOn, StatusInOn):

\[\begin{align*} & 0 \leq p^{\text{in}}_t \leq P_{\max,\text{pcc}}, \quad 0 \leq p^{\text{out}}_t \leq P_{\max,\text{pcc}}, \quad \forall t \in \mathcal{T} \\ & u^{\text{st}}_t \in \{0,1\} \quad \text{(output/input status at PCC)} \end{align*}\]

Energy asset balance (EnergyAssetBalance):

\[p^{\text{th}}_t + p^{\text{re}}_t + p^{\text{ds}}_t - p^{\text{ch}}_t - P^{\text{ld}}_t = p^{\text{out}}_t - p^{\text{in}}_t, \quad \forall t \in \mathcal{T}\]

Thermal limits (ThermalOnVariableUb, ThermalOnVariableLb):

\[u^{\text{th}}_t P_{\min,\text{th}} \leq p^{\text{th}}_t \leq u^{\text{th}}_t P_{\max,\text{th}}, \quad u^{\text{th}}_t \in \{0,1\}, \quad \forall t \in \mathcal{T}\]

Renewable limit (RenewableActivePowerLimitConstraint):

\[0 \leq p^{\text{re}}_t \leq P^{*,\text{re}}_t, \quad \forall t \in \mathcal{T}\]

Storage charge/discharge status (BatteryStatusChargeOn, BatteryStatusDischargeOn):

\[\begin{align*} & p^{\text{ch}}_t \leq (1 - ss^{\text{st}}_t) P_{\max,\text{ch}}, \quad p^{\text{ds}}_t \leq ss^{\text{st}}_t P_{\max,\text{ds}}, \quad \forall t \in \mathcal{T} \\ & ss^{\text{st}}_t \in \{0,1\} \quad \text{(0 = charge, 1 = discharge)} \end{align*}\]

Storage energy balance (BatteryBalance):

\[e^{\text{st}}_t = e^{\text{st}}_{t-1} + \Delta t \left( \eta_{\text{ch}} p^{\text{ch}}_t - \frac{p^{\text{ds}}_t}{\eta_{\text{ds}}} \right), \quad \forall t \in \mathcal{T}, \quad e^{\text{st}}_0 = E^{\text{st}}_0\]

Cycling limits (if "cycling" => true), (CyclingCharge, CyclingDischarge):

\[\begin{align*} & \eta_{\text{ch}} \Delta t \sum_{t \in \mathcal{T}} p^{\text{ch}}_t \leq C_{\text{st}} E_{\max,\text{st}} \\ & \frac{\Delta t}{\eta_{\text{ds}}} \sum_{t \in \mathcal{T}} p^{\text{ds}}_t \leq C_{\text{st}} E_{\max,\text{st}} \end{align*}\]

End-of-horizon energy target (if "energy_target" => true), (StateofChargeTargetConstraint):

\[e^{\text{st}}_T = E^{\text{st}}_T\]

Regularization (if "regularization" => true): ChargeRegularizationConstraint, DischargeRegularizationConstraint.

Objective:

Adds cost terms for thermal generation (variable and fixed costs), storage variable O&M, renewable variable cost, and penalties for energy target deviations (if enabled).

HybridFixedDA

Device formulation for a hybrid system with day-ahead (DA) energy bids/offers fixed; used in multi-step simulations when the real-time (RT) subproblem is solved with locked DA positions (e.g. merchant co-optimization with "then vs. now" RT adjustment).

Variables:

• PowerSimulations.ActivePowerOutVariable:

  • Bounds: [0.0, $P_{\max,\text{pcc}}$]
  • Symbol: $p^{\text{out}}_t$

• PowerSimulations.ActivePowerInVariable:

  • Bounds: [0.0, $P_{\max,\text{pcc}}$]
  • Symbol: $p^{\text{in}}_t$

• TotalReserve (if services present):

  • Bounds: [0.0, ]
  • Symbol: total reserve at PCC

Data requirements:

• Device: A PowerSystems.HybridSystem with PCC limits. Internal asset composition is not modeled in this formulation; only net power at the PCC and optional total reserve are used.
• Price and horizon data: Horizon and price data are provided through the merchant decision models (e.g. MerchantHybridEnergyCase, MerchantHybridCooptimizerCase) using the ext supplemental data dictionary on the system and hybrids as described in their docstrings.

Expressions:

Adds $p^{\text{out}}_t$ and $p^{\text{in}}_t$ to PowerSimulations' ActivePowerBalance expression for use in network balance constraints.

Constraints:

PCC power limits (PowerSimulations.InputActivePowerVariableLimitsConstraint, PowerSimulations.OutputActivePowerVariableLimitsConstraint):

\[0 \leq p^{\text{in}}_t \leq P_{\max,\text{pcc}}, \quad 0 \leq p^{\text{out}}_t \leq P_{\max,\text{pcc}}, \quad \forall t \in \mathcal{T}\]

When ancillary services are present: HybridReserveAssignmentConstraint links component reserves to total reserve at the PCC.

MerchantHybridEnergyCase

Decision problem for a merchant hybrid resource that co-optimizes energy bids/offers in day-ahead and real-time markets only (no ancillary services). The hybrid optimizer maximizes profit from energy (e.g. DA/RT spread) subject to internal asset limits.

Data requirements:

• System: A PowerSystems.System containing at least one PowerSystems.HybridSystem with the subcomponents required by the chosen device formulation (e.g. HybridEnergyOnlyDispatch).

• Attached scalar time series (each hybrid): Market prices are bus-selected InfrastructureSystems.SingleTimeSeries objects with distinct names for each logical key (defaults "DA" / "RT"): see hybrid_energy_price_time_series_name. Profiles use the standard renewable/load names below. Override keys via model.ext["day_ahead_time_series_key"] / "real_time_time_series_key" on the PowerSimulations.DecisionModel.

  Role	Time series name
  Day-ahead energy price	hybrid_energy_price_time_series_name(day_ahead_time_series_key)
  Real-time energy price	hybrid_energy_price_time_series_name(real_time_time_series_key)
  Renewable availability	"RenewableDispatch__max_active_power"
  Electric load	"PowerLoad__max_active_power"

Horizons, resolutions, and DA↔RT step alignment come from model settings plus series metadata (not from System/Hybrid ext DataFrames or "λ_*" keys).

MerchantHybridEnergyFixedDA

Decision problem for a merchant hybrid with fixed day-ahead energy positions; used when solving the real-time subproblem with locked DA bids/offers.

Data requirements:

• Same PowerSystems.System, PowerSystems.HybridSystem, and hybrid-attached time-series contract as MerchantHybridEnergyCase (keyed scalar DA/RT prices and profiles on each hybrid).

MerchantHybridCooptimizerCase

Decision problem for a merchant hybrid that co-optimizes energy and ancillary services in day-ahead and real-time markets. Maximizes $d'y - c_h' x$ (revenue from bids/offers minus operating cost) subject to market and asset constraints; ancillary services are committed in DA and fulfilled by internal asset allocation in RT.

Data requirements:

• System: As for MerchantHybridEnergyCase. The problem template must include a PowerSimulations.DeviceModel constructed as DeviceModel(PSY.HybridSystem, HybridDispatchWithReserves) (or another appropriate hybrid formulation with reserves).
• Hybrid-attached time series: Same DA/RT keyed energy prices and renewable/load series as MerchantHybridEnergyCase. Additionally, for each ancillary product attached to the hybrid, attach a scalar SingleTimeSeries named hybrid_ancillary_service_price_time_series_name(<service_name>, <day_ahead_key>).

MerchantHybridBilevelCase

Decision problem implementing a bilevel formulation for the merchant hybrid (e.g. upper level: bids/offers, lower level: internal dispatch); used for equilibrium or regulatory analysis.

Data requirements:

• System: Same as MerchantHybridEnergyCase (at least one PowerSystems.HybridSystem with required forecasts).
• Hybrid-attached time series: Same keyed scalar DA/RT market and profile series as MerchantHybridEnergyCase.

EnergyDABidOut

Variable type for day-ahead energy offer (generating power) at the point of common coupling (PCC).

Docs abbreviation: $e^{\text{out}}_{\text{DA},t} \in [0, P_{\max,\text{pcc}}]$ [MW].

EnergyDABidIn

Variable type for day-ahead energy bid (consuming power) at the point of common coupling (PCC).

Docs abbreviation: $e^{\text{in}}_{\text{DA},t} \in [0, P_{\max,\text{pcc}}]$ [MW].

EnergyRTBidOut

Variable type for real-time energy offer at the point of common coupling (PCC).

Docs abbreviation: $e^{\text{out}}_{\text{RT},t}$. Net RT position with DA locked is used in the merchant profit expression (e.g. DART spread).

EnergyRTBidIn

Variable type for real-time energy bid at the point of common coupling (PCC).

Docs abbreviation: $e^{\text{in}}_{\text{RT},t}$.

BidReserveVariableOut

Variable type for day-ahead ancillary service offer (generation direction) for the hybrid at the point of common coupling (PCC).

Docs abbreviation: $sb^{\text{out}}_{p,t} \in [0, F_p P_{\max,\text{pcc}}]$ for product $p$.

BidReserveVariableIn

Variable type for day-ahead ancillary service bid (consumption direction) for the hybrid at the point of common coupling (PCC).

Docs abbreviation: $sb^{\text{in}}_{p,t} \in [0, F_p P_{\max,\text{pcc}}]$ for product $p$.

ReserveVariableOut

Variable type for ancillary service reserve quantity in the "out" (generation) direction allocated to the hybrid's internal assets ($sb^{\text{th}}$, $sb^{\text{re}}$, $sb^{\text{ds}}$, $sb^{\text{ch}}$).

ReserveVariableIn

Variable type for ancillary service reserve quantity in the "in" (consumption) direction allocated to the hybrid's internal assets.

TotalReserve

Auxiliary variable type for the total reserve quantity (sum of component reserves) at the point of common coupling (PCC). Used in reserve balance constraints; not written to results by default.

CyclingChargeLimitFeedforward

Feedforward that enforces a cumulative charging cycle limit on the hybrid's storage over the simulation. The constraint is $\eta_{\text{ch}} \Delta t \sum_t (p_{\text{ch},t} + s^{\text{down}}_{\text{reg},t} - s^{\text{up}}_{\text{reg},t}) \leq \text{limit}$, where $s^{\text{up}}_{\text{reg},t}$ and $s^{\text{down}}_{\text{reg},t}$ denote served reserve (up/down). The limit is from CyclingChargeLimitParameter in recurrent solves or $C_{\text{horizon}} \times E_{\max,\text{st}}$ otherwise. Use with PowerSimulations' add_feedforward! in a PowerSimulations.DeviceModel for HybridDispatchWithReserves or HybridEnergyOnlyDispatch.

Input data:

• Storage limits: Limit supplied by CyclingChargeLimitParameter, which is derived from the hybrid's storage using PowerSystems.get_cycle_limits and PowerSystems.get_storage_level_limits.
• Not compatible with the device attribute "cycling" => true (cycling limits are then enforced in the formulation).

CyclingDischargeLimitFeedforward

Feedforward that enforces a cumulative discharging cycle limit on the hybrid's storage: $(1/\eta_{\text{ds}}) \Delta t \sum_t (p_{\text{ds},t} + s^{\text{up}}_{\text{reg},t} - s^{\text{down}}_{\text{reg},t}) \leq \text{limit}$, where $s^{\text{up}}_{\text{reg},t}$ and $s^{\text{down}}_{\text{reg},t}$ denote served reserve (up/down). The limit comes from CyclingDischargeLimitParameter in recurrent runs. See CyclingChargeLimitFeedforward for usage pattern.

Input data:

• Same as CyclingChargeLimitFeedforward: limit from CyclingDischargeLimitParameter, derived from the hybrid's storage using PowerSystems.get_cycle_limits and PowerSystems.get_storage_level_limits.
• Not compatible with device attribute "cycling" => true.

OptConditionThermalPower

Constraint enforcing Karush-Kuhn-Tucker (KKT) stationarity for thermal power in the merchant (lower-level) model: links dual of thermal limits ($\mu^{\text{ThUb}}$, $\mu^{\text{ThLb}}$) to the thermal power variable. Used in bilevel/mathematical program with equilibrium constraints (MPEC) formulations.

OptConditionRenewablePower

Constraint enforcing Karush-Kuhn-Tucker (KKT) stationarity for renewable power ($p_{\text{re},t}$) in the merchant model; ties duals of renewable limit ($\mu^{\text{ReUb}}$, $\mu^{\text{ReLb}}$) to the renewable power variable.

OptConditionBatteryCharge

Constraint enforcing Karush-Kuhn-Tucker (KKT) stationarity for storage charging ($p_{\text{ch},t}$) in the merchant model; involves duals $\mu^{\text{ChUb}}$, $\mu^{\text{ChLb}}$ and charge limits.

OptConditionBatteryDischarge

Constraint enforcing Karush-Kuhn-Tucker (KKT) stationarity for storage discharging ($p_{\text{ds},t}$) in the merchant model; involves duals $\mu^{\text{DsUb}}$, $\mu^{\text{DsLb}}$.

OptConditionEnergyVariable

Constraint enforcing Karush-Kuhn-Tucker (KKT) stationarity for the energy variable at the point of common coupling (PCC) in the merchant model.

ComplementarySlacknessEnergyAssetBalanceUb

Complementary slackness constraint (upper bound) for the energy asset balance equation in the merchant model; used in mathematical program with equilibrium constraints (MPEC)/bilevel reformulation.

ComplementarySlacknessEnergyAssetBalanceLb

Complementary slackness constraint (lower bound) for the energy asset balance.

ComplementarySlacknessRenewableActivePowerLimitConstraintUb

Complementary slackness (upper bound) for renewable active power limit ($p_{\text{re},t} \leq P^*_{\text{re},t}$).

ComplementarySlacknessRenewableActivePowerLimitConstraintLb

Complementary slackness (lower bound) for renewable active power limit.

ComplementarySlacknessBatteryStatusDischargeOnUb

Complementary slackness (upper bound) for battery status discharge-on constraint ($ss_{\text{st},t}$).

ComplementarySlacknessBatteryStatusDischargeOnLb

Complementary slackness (lower bound) for battery status discharge-on constraint.

ComplementarySlacknessBatteryStatusChargeOnUb

Complementary slackness (upper bound) for battery status charge-on constraint.

ComplementarySlacknessBatteryStatusChargeOnLb

Complementary slackness (lower bound) for battery status charge-on constraint.

ComplementarySlacknessBatteryBalanceUb

Complementary slackness (upper bound) for storage energy balance ($e_{\text{st},t}$).

ComplementarySlacknessBatteryBalanceLb

Complementary slackness (lower bound) for storage energy balance.

ComplementarySlacknessCyclingCharge

Complementary slackness for the charging cycle limit ($c_{\text{ch}}^-$).

ComplementarySlacknessCyclingDischarge

Complementary slackness for the discharging cycle limit ($c_{\text{ds}}^-$).

ComplementarySlacknessEnergyLimitUb

Complementary slackness (upper bound) for storage energy capacity ($e_{\text{st},t} \leq E_{\max,\text{st}}$).

ComplementarySlacknessEnergyLimitLb

Complementary slackness (lower bound) for storage energy capacity.

StrongDualityCut

Constraint that enforces strong duality for the merchant (lower-level) problem in a bilevel formulation: objective value equals dual objective (or equivalent cut), so that the lower level is replaced by its Karush-Kuhn-Tucker (KKT) conditions.

DayAheadEnergyPrice

Objective function parameter for day-ahead energy price.

Docs abbreviation: $\Pi^*_{\text{DA},t}$ (USD/MWh). Used in the merchant objective (e.g. $f_{\text{DA},t}$ term) when building the decision model.

Input data:

• Hybrid-attached time series: Each PowerSystems.HybridSystem must have a bus-selected scalar day-ahead energy price series whose name is given by hybrid_energy_price_time_series_name(<day_ahead_key>) (default key "DA"), stored as InfrastructureSystems.SingleTimeSeries / deterministic forecast. Values are taken over the model horizon from forecast timestamps starting at the problem initial time.

RealTimeEnergyPrice

Objective function parameter for real-time energy price.

Docs abbreviation: $\Pi^*_{\text{RT},t}$ (USD/MWh). Used in the merchant profit expression for RT energy and DART spread.

Input data:

• Hybrid-attached time series: Real-time energy price uses hybrid_energy_price_time_series_name(<real_time_key>) (default key "RT"). Day-ahead ↔ real-time alignment for spread terms uses variable axis sizes and an internal index map derived from model horizons, not hybrid ext.

AncillaryServicePrice

Objective function parameter for ancillary service price.

Docs abbreviation: $\Pi^*_{p,t}$ (USD/MWh) for service $p \in P$. Used in the DA profit term for ancillary services ($sb^{\text{out}}$ + $sb^{\text{in}}$).

Input data:

• Hybrid-attached time series: For each attached ancillary product, a scalar series named per hybrid_ancillary_service_price_time_series_name(<service_name>, <day_ahead_key>). Used by MerchantHybridCooptimizerCase when services are attached to the hybrid.

CyclingChargeLimitParameter

Variable-value parameter that provides the right-hand side for the storage charging cycle limit: $\eta_{\text{ch}} \Delta t \sum_t p_{\text{ch},t} - c_{\text{ch}}^- \leq C_{\text{st}} E_{\max,\text{st}}$. Used with CyclingChargeLimitFeedforward in recurrent simulations to pass cumulative cycling from previous horizons.

Input data:

• Storage limits: Initial values (when not updated from state) are computed from the hybrid's storage using PowerSystems.get_cycle_limits and PowerSystems.get_storage_level_limits.
• State updates: In recurrent runs, values are updated from the simulation state (cumulative charge usage).

CyclingDischargeLimitParameter

Variable-value parameter for the storage discharging cycle limit: $(\Delta t/\eta_{\text{ds}}) \sum_t p_{\text{ds},t} - c_{\text{ds}}^- \leq C_{\text{st}} E_{\max,\text{st}}$. Used with CyclingDischargeLimitFeedforward.

Input data:

• Same as CyclingChargeLimitParameter: initial values based on PowerSystems.get_cycle_limits and PowerSystems.get_storage_level_limits for the hybrid's storage; in recurrent runs, updated from state (cumulative discharge usage).