Ramping-Aware Flexibility Aggregation Scheme

• The paper introduces a novel framework that aggregates DER flexibility by integrating pre-ramping strategies to respect device ramp-rate limits.
• It employs a multi-period linear programming model that jointly optimizes envelope boundaries and pre-ramp moves, ensuring compliance with network and device constraints.
• Quantitative case studies on the IEEE-33 bus system demonstrate envelope improvements up to 19%, enhancing ancillary service revenues and operational feasibility.

A ramping-aware flexibility aggregation scheme constitutes a mathematical and operational framework for combining the flexibility of distributed energy resources (DERs), especially distributed generation and energy storage, such that ramping constraints—finite rates of change in resource outputs—are explicitly accounted for in network- and market-level flexibility offerings. By incorporating pre-ramping strategies, this class of approaches ensures both feasibility and optimality of aggregated flexibility envelopes at the transmission-distribution boundary. The paradigm guarantees that any scheduled flexibility service can be decomposed (disaggregated) into device-level schedules that strictly respect hardware ramp-rate limits and network constraints, overcoming conservatism and infeasibility that arise in naive aggregation methods lacking ramp awareness (Park et al., 21 Jan 2026).

1. Mathematical Modeling Framework

The core of a ramping-aware scheme is a large-scale, multi-period linear optimization problem, wherein decision variables represent setpoints and pre-ramp moves for each controllable DER (dispatchable generators, ESSs) across a finite horizon $\mathcal T$ (discretized in intervals $\Delta t$). For each generator $g$ and ESS $e$, the model introduces:

• Primary envelope variables $$p^{s}_{g,t},\,q^{s}_{g,t},\,p^{s}_{e,t},\,e^{s}_{e,t}$$ for upper ($\wedge$) and lower ($\vee$) flexibility boundaries.
• Pre-ramp variables $$p_{g,t}^{\mathrm{pre},s},\,p_{e,t}^{\mathrm{pre},s}$$ repositioning resources at $t-1$ to unlock extra ramp headroom at $t$, maintaining net grid injection invariance.

Objective: Maximize the aggregate envelope area,

$$\max \sum_{t=1}^{T} \left(p^{\mathrm{GCP},\wedge}_{t} - p^{\mathrm{GCP},\vee}_t\right)\,\Delta t,$$

subject to:

• Power and energy box constraints for all resources.
• Eight linear ramp-rate constraints per device per time step, combining corners of the envelope and pre-ramped setpoints.
• Linearized DistFlow or LinDistFlow network constraints on nodal voltage and line flows, applied to both envelope and pre-ramped device profiles.
• Storage SoC-evolution and pre-ramp energy-reserve constraints.
• GCP invariance: the sum of pre-ramp moves at each $t$ must be zero, so the upstream grid is unaffected statistically.

This single LP formulation enables simultaneous optimization of flexibility boundaries and the pre-moves needed to realize them (Park et al., 21 Jan 2026).

2. Ramping Constraint Formulation and Pre-ramping Mechanism

Ramping is handled through two complementary strategies in the aggregation context:

• Envelope Ramp Constraints: For each time interval, all feasible device trajectories between upper/lower bounds are enforced to satisfy device-specific ramp-up/down limits $R_g^{\uparrow},\,R_g^{\downarrow}$ at each corner, i.e.,

$$|p_{g,t}^{s_2} - p_{g,t-1}^{s_1\bullet}| \leq R_g^{\uparrow/\downarrow}, \quad s_1,s_2\in\{\wedge,\vee\}.$$

This convexification ensures strict device-level feasibility for all paths within the envelope.

• Pre-ramping Variables: $p_{g,t}^{\mathrm{pre},s}$, defining anticipatory moves at step $t-1$, create extra available margin for upward or downward ramping, essentially increasing the attainable width of flexibility envelopes without violating the instantaneous ramp-rate constraints. Pre-ramp moves are compensated to preserve total grid injection, so network power balance and measurements remain unchanged from the grid’s perspective.

These constructs together eradicate previously unavoidable conservatism inherent to baseline corner-to-corner ramping restrictions (Park et al., 21 Jan 2026).

3. Feasibility and Disaggregation Guarantees

A formal proof (see Appendices A–B of (Park et al., 21 Jan 2026)) shows that the feasible region defined by the ramping-aware pre-ramping envelope is convex and that any aggregate trajectory admissible within the envelope

$$p^{\mathrm{GCP},\vee}_t \leq p^{\mathrm{GCP},o}_t \leq p^{\mathrm{GCP},\wedge}_t \;\forall t,$$

can be exactly disaggregated into device-level schedules $\left\{p^{o}_{g,t},p^{o}_{e,t}\right\}$ by linear interpolation between the envelope corners: $$p^{o}_{g,t} = \lambda_t p_{g,t}^{\vee} + (1-\lambda_t) p_{g,t}^{\wedge}, \text{ for some } \lambda_t \in [0,1].$$ All device box limits, ramp constraints, SoC bounds, and voltage/flow restrictions remain satisfied for any convex combination, guaranteeing implementability of every aggregate flexibility signal in real-world operation.

4. Implementation Algorithm and Computational Aspects

A single LP suffices to co-optimize baseline and pre-ramping envelope variables. The implementation procedure involves:

• Parameter initialization (device limits, network matrices, forecasts).
• Baseline envelope optimization.
• Inclusion of pre-ramp terms for all eligible resources and enforcement of GCP invariance.
• LP solve via CPLEX, Gurobi, or open-source solvers.
• Extraction of envelope trajectories, per-period setpoints, and active pre-ramp schedules.

The method exhibits polynomial scaling: hundreds of resources/periods can be solved in seconds to minutes, facilitating integration in real-time market clearing and rolling-horizon operational schemes (Park et al., 21 Jan 2026).

5. Quantitative Case Studies and Envelope Improvements

Validation on the IEEE-33 bus distribution system demonstrates the efficacy of the scheme:

ESS Size (kW/kWh)	Baseline Envelope Area (kWh)	Pre-ramped Envelope Area (kWh)	Improvement (%)
12.5/50	2490.96	2619.90	5.2
62.5/250	8462.84	10100.60	19.2

Enlarged envelopes translate directly into increased standby ramping product revenues and enhanced ability to follow transmission system requests for ancillary services. Finer dispatch intervals (e.g., 5 min vs. 60 min) further magnify pre-ramping gains due to tighter ramp constraints (Park et al., 21 Jan 2026).

6. Design Guidelines and Network/Device Considerations

• Device ramp-rate bounds and energy ratings must be based on physical data sheets and mission requirements.
• Dispatch interval selection impacts flexibility magnitude; shorter intervals lead to tighter ramping and greater pre-ramp benefits.
• Storage sizing must account for cumulative pre-ramp energy in addition to linkages from energy-arbitrage requirements.
• Robust optimization with tightened voltage constraints mitigates the effect of forecast uncertainty.
• The linearized DistFlow model is adequate for radial networks; meshed or heavily reactive distribution systems may necessitate AC or SOCP relaxations.

Overly aggressive pre-ramping may deplete ESS SoC and reduce arbitrage profitability, necessitating careful tuning of pre-ramp magnitudes in coordination with energy market participation.

7. Broader Applicability and Generalization

The ramping-aware flexibility aggregation paradigm is extensible to any under-determined resource-network system facing endpoint or trajectory ramping infeasibilities, including but not limited to:

• Distribution-level resource aggregators (DMOs, VPPs).
• Transmission-distribution boundary FRP providers.
• Industrial load-shaping and critical infrastructure ramp-management.
• Ancillary service markets requiring deliverable ramping reserve products.

By co-designing envelopes and anticipatory pre-moves, the scheme systematically enlarges the true flexibility region that can be offered to upstream grids without sacrificing network security or physical realizability (Park et al., 21 Jan 2026).