Dynamic Demand Profile Alignment: Time-Shifted Load Matching with Rolling Horizon Optimization
Matching when energy is stored and when it’s needed—shifting heat supply to match changing industrial demand, using smart short-term planning that updates every few hours.
⚠️ Why It Matters
📘 Definition
Dynamic Demand Profile Alignment (DDPA) is a model-predictive control strategy for thermal energy storage (TES) systems that aligns time-shifted load profiles with real-time process heat requirements via rolling horizon optimization (RHO). It integrates forecasted demand, TES state-of-charge dynamics, thermodynamic constraints, and exergy-aware dispatch rules to minimize curtailment, avoid thermal degradation, and maximize system-level exergetic efficiency over a receding time window (typically 4–24 h). The approach explicitly accounts for non-linear charge/discharge kinetics, temperature-dependent material properties, and grid-coupled energy pricing signals where applicable.
🎨 Concept Diagram
AI-generated illustration for visual understanding
💡 Engineering Insight
Never optimize TES dispatch on energy alone—always anchor the objective function to exergy flow. A molten salt tank charged to 565°C but discharged at 320°C to meet low-grade drying demand wastes >40% of its available work potential. Rolling horizon optimization only delivers value when exergy sinks (process streams) are modeled with their true temperature-level constraints—not just kW targets.
📖 Detailed Explanation
Modern DDPA embeds first-principles TES models—such as discretized enthalpy-based finite volume equations for molten salt tanks or effective conductivity models for PCM capsules—within the RHO framework. These models capture temperature stratification, phase front propagation, and HTF-side pressure drop penalties, enabling physically consistent constraints. The optimizer then balances competing objectives: minimizing exergy loss across the heat exchanger network, avoiding thermal cycling fatigue in containment materials, and respecting real-world actuator slew rates.
Advanced implementations integrate digital twin feedback: real-time temperature sensor arrays (e.g., fiber-optic DTS along tank height) feed correction terms into the RHO’s state estimator. Furthermore, multi-timescale coordination is emerging—where DDPA (minutes-hours) interfaces with plant-wide Model Predictive Control (MPC) (hours-days) and long-term economic dispatch (weeks-months)—forming a hierarchical control architecture aligned with ISO/IEC 62933-5-1 interoperability standards. This prevents local optima from violating enterprise-level carbon or cost KPIs.
🔄 Engineering Workflow
📋 Decision Guide
| Rock/Field Condition | Recommended Design Action |
|---|---|
| High-variability batch process (e.g., steel annealing furnace, chemical reactor cycles) | Use 15-min timesteps, 8-h horizon, include stochastic scenario tree for demand uncertainty, enforce ≥10% thermal reserve buffer |
| Steady-state continuous process (e.g., pulp drying, food pasteurization) with <5% load variation | Adopt 30-min timesteps, 4-h horizon, deterministic RHO, prioritize exergy recovery over reserve margin |
| Hybrid grid-connected plant with time-of-use electricity pricing and steam export constraints | Embed dual-objective RHO (minimize LCOH + maximize grid revenue), add price-sensitive charge scheduling, constrain discharge rate to steam header pressure stability limits |
📊 Key Properties & Parameters
Time Horizon Resolution
15–60 minDuration of each discrete optimization timestep in the RHO framework
Finer resolution captures rapid demand transients but increases computational load; coarser resolution risks missing critical ramp events
Rolling Horizon Length
4–24 hTotal duration of the forward-looking optimization window updated at each decision step
Short horizons improve responsiveness but increase risk of myopic decisions; long horizons improve global optimality but reduce adaptability to forecast errors
TES Exergy Efficiency Factor (η_ex)
0.55–0.82 (dimensionless)Ratio of usable exergy delivered during discharge to exergy stored during charge, accounting for temperature glide and irreversibilities
Directly determines minimum required storage mass and influences optimal charge temperature setpoints
Charge/Discharge Rate Mismatch Tolerance
±8–12% of rated TES thermal powerMaximum allowable deviation between scheduled and actual thermal power flow during transient operation
Tighter tolerances require faster-responding heat exchangers and tighter control valve actuation bandwidth
Demand Forecast Uncertainty Band
±7–15% (1σ, 1-h ahead)Standard deviation envelope around predicted process heat load profile, typically expressed as % of peak load
Drives robustness requirements in RHO formulation—larger bands necessitate conservative scheduling and reserve buffer allocation
📐 Key Formulas
Exergy Efficiency Factor (η_ex)
η_ex = (ṁ·[h_out − h_amb − T_amb·(s_out − s_amb)]) / (ṁ·[h_in − h_amb − T_amb·(s_in − s_amb)])Exergetic efficiency of TES discharge relative to charge, based on specific flow exergy at inlet/outlet states
| Symbol | Name | Unit | Description |
|---|---|---|---|
| η_ex | Exergy Efficiency Factor | dimensionless | Exergetic efficiency of TES discharge relative to charge, based on specific flow exergy at inlet/outlet states |
| ṁ | Mass flow rate | kg/s | Mass flow rate of the working fluid |
| h_out | Specific enthalpy at outlet | kJ/kg | Specific enthalpy of the fluid at the outlet state |
| h_amb | Specific enthalpy at ambient | kJ/kg | Specific enthalpy of the fluid at ambient conditions |
| T_amb | Ambient temperature | K | Thermodynamic temperature of the ambient environment |
| s_out | Specific entropy at outlet | kJ/(kg·K) | Specific entropy of the fluid at the outlet state |
| s_amb | Specific entropy at ambient | kJ/(kg·K) | Specific entropy of the fluid at ambient conditions |
| h_in | Specific enthalpy at inlet | kJ/kg | Specific enthalpy of the fluid at the inlet state |
| s_in | Specific entropy at inlet | kJ/(kg·K) | Specific entropy of the fluid at the inlet state |
Rolling Horizon Objective Weighting
J = α·Σ(ε_ex,i) + β·Σ(P_curtailed,i) + γ·Σ(C_grid,i)Weighted multi-objective cost function minimized over horizon N
| Symbol | Name | Unit | Description |
|---|---|---|---|
| J | Total Cost | currency | Weighted multi-objective cost function to be minimized |
| α | Demand Violation Weight | currency/unit | Weight coefficient for sum of demand violations |
| ε_ex,i | Excess Demand Violation | kW or MW | Excess energy not supplied at time step i |
| β | Curtailment Weight | currency/unit | Weight coefficient for sum of curtailments |
| P_curtailed,i | Curtailment Power | kW or MW | Power curtailed from renewable generation at time step i |
| γ | Grid Cost Weight | currency/unit | Weight coefficient for sum of grid energy costs |
| C_grid,i | Grid Energy Cost | currency | Cost of energy purchased from the grid at time step i |
🏭 Engineering Example
ArcelorMittal Ghent Steelworks (Belgium)
N/A — industrial process heat system🏗️ Applications
- Steel reheat furnace load leveling
- Chemical reactor batch scheduling support
- Concentrated solar power (CSP) hybridization with industrial heat
- District heating network thermal buffering
📋 Real Project Case
Concentrated Solar Power (CSP) Integration with Cement Kiln Preheater
Heidelberg Materials plant, Morocco