Molten Salt Thermal Storage Discharge Calculator

Overview: What This Calculator Estimates

This calculator estimates how long a molten salt thermal energy storage tank can discharge at a specified plant power draw. Using tank volume, hot and cold operating temperatures, specific heat, density, and an overall system efficiency, it computes the approximate number of hours your plant can run at full power before the hot tank cools down to its lower operating limit. An optional target duration lets you compare the calculated discharge time against a desired contract or operational requirement.

Core Formula for Stored Thermal Energy

The model treats the molten salt tank as a well-mixed sensible heat storage system. The usable thermal energy is calculated from the temperature difference between the hot and cold states:

Step 1: Mass of molten salt

The mass of salt in the tank is

where:

• m = mass of molten salt (kg)
• V = storage volume (m³)
• ρ = density of molten salt (kg/m³)

Step 2: Sensible heat stored

The stored sensible heat between the hot and cold temperatures is

with:

• E = thermal energy (kJ, using the default units here)
• cp = specific heat capacity of molten salt (kJ/kg·K)
• ΔT = temperature difference between hot and cold tanks (K or °C)

The calculator uses:

• ΔT = T_hot − T_cold
• T_hot and T_cold in °C (a difference in °C is numerically equal to K)

Step 3: Convert energy to kWh

One kilowatt-hour equals 3600 kilojoules. To convert from kJ to kWh:

Step 4: Apply system efficiency

Not all stored heat becomes electrical output. The overall efficiency accounts for thermal losses and conversion inefficiencies:

where:

• Euse = usable electrical energy (kWh)
• η = overall efficiency as a fraction (e.g., 0.9 for 90 %)

Step 5: Discharge duration

Plant power is entered in megawatts and converted to kilowatts for consistency:

• P_kW = P_MW × 1000

The full-power discharge duration is then

where t is in hours.

Inputs Explained

• Storage Volume (m³) – Total molten salt volume in the hot tank. Larger volumes increase stored energy linearly.
• Hot Temperature (°C) – Upper operating temperature of the hot tank. Typical nitrate salts in CSP plants operate around 560–600 °C.
• Cold Temperature (°C) – Return temperature to the cold tank, often around 280–300 °C for nitrate salts.
• Specific Heat (kJ/kg·K) – Heat capacity of the salt mixture. A common value for solar salt is about 1.5 kJ/kg·K, but it varies with composition and temperature.
• Density (kg/m³) – Density of molten salt at typical operating temperature. Around 1800–1900 kg/m³ is common for nitrate mixtures.
• Plant Power Draw (MW) – Net electrical output the plant is expected to deliver during discharge. A higher power draw shortens discharge time for a fixed storage system.
• System Efficiency (%) – Overall fraction of stored thermal energy that is converted into net electrical energy. It bundles together thermal losses (piping, tanks, heat exchangers) and power-block efficiency.
• Desired Discharge Duration (h) – A target number of hours you would like the system to sustain the specified power output. The calculator can compare the computed duration against this target using an illustrative risk metric.

Interpreting the Discharge Duration

The primary output is the estimated discharge duration in hours. Interpreting it in context:

• If the computed duration is greater than your desired discharge duration, the storage system is likely oversized for that target under the model assumptions.
• If the computed duration is less than the desired discharge duration, the modeled system appears undersized for that requirement. You can increase volume, widen the temperature window (within material limits), or reduce the plant power draw to close the gap.
• A result close to your target (for example, 6.1 hours for a 6-hour target) should be treated cautiously, because real-world losses and operating constraints may reduce usable duration.

Typical molten salt CSP systems deliver several hours of storage (for example, 3–12 hours at full power). If your calculated duration is far outside that range, it may indicate unrealistic input values or a mismatch between tank size and turbine rating.

Worked Example

Consider a plant with these characteristics:

• Storage Volume: 1000 m³
• Hot Temperature: 565 °C
• Cold Temperature: 290 °C
• Specific Heat: 1.5 kJ/kg·K
• Density: 1800 kg/m³
• Plant Power Draw: 100 MW
• System Efficiency: 90 %

Step 1: Mass

m = 1000 m³ × 1800 kg/m³ = 1 800 000 kg

Step 2: Temperature difference

ΔT = 565 °C − 290 °C = 275 K

Step 3: Stored thermal energy

E = 1 800 000 kg × 1.5 kJ/kg·K × 275 K

E = 1 800 000 × 1.5 × 275 kJ

E = 742 500 000 kJ

Step 4: Convert to kWh

E_kWh = 742 500 000 kJ / 3600 ≈ 206 250 kWh

Step 5: Apply efficiency

E_use = 206 250 kWh × 0.90 ≈ 185 625 kWh

Step 6: Compute duration

P_kW = 100 MW × 1000 = 100 000 kW

t = 185 625 kWh / 100 000 kW ≈ 1.86 h

In this simplified example, the system delivers just under 2 hours at 100 MW under the stated assumptions. If your target is 6 hours, you could:

• Increase storage volume (for example, to roughly 3000 m³, holding other parameters constant), or
• Reduce plant power draw, for instance operating at 50 MW instead of 100 MW, or
• Optimize both storage and power rating to reach a feasible compromise.

Risk or Shortfall Probability Metric

The calculator may present a risk of shortfall value when you enter a desired discharge duration. Internally, this is based on a smooth logistic curve centered on your target duration. Conceptually:

• If the computed discharge duration is much greater than the desired duration, the risk value will be close to 0 % (low risk of failing to meet the target under the simplified model).
• If the computed duration is much less than the desired duration, the risk will move toward 100 % (high likelihood that the modeled system cannot sustain the requested hours).
• When the modeled duration is near the desired duration, the risk will fall in an intermediate range (for example, 40–60 %), reflecting uncertainty in all the real-world factors not explicitly modeled.

This risk metric is heuristic only. It does not represent a detailed reliability analysis or a probability of failure for a specific plant. Instead, it is meant to give a qualitative sense of how comfortably the storage design meets a target duration within the simplified assumptions of this calculator.

Comparison of Key Design Levers

The table below summarizes how different design choices influence calculated discharge duration while other parameters are held constant.

How to Use the Results in Practice

• Check feasibility: Compare the calculated discharge duration to your target (for example, a 4-hour or 8-hour PPA requirement). If there is a large gap, your current concept may not be feasible without major changes.
• Iterate design options: Adjust individual inputs to see which design lever (volume, temperature window, efficiency, power rating) most efficiently closes the shortfall. This supports early-stage sizing exercises and scenario comparisons.
• Assess comfort margin: Aim for a calculated duration comfortably above your target to allow for unmodeled losses, part-load efficiency effects, and operational constraints.
• Communicate assumptions: When sharing results, include a note that the values come from a simple sensible heat model and should be refined with detailed engineering tools before financial or safety-critical decisions.

Assumptions and Limitations

This calculator is intentionally simplified to provide quick, order-of-magnitude estimates. Key assumptions and limitations include:

• Well-mixed tanks: The hot tank is treated as perfectly mixed, with uniform temperature. Thermal stratification, hot spots, and layering are not modeled.
• Constant properties: Specific heat and density are assumed constant over the entire temperature range. In reality, both vary with temperature and composition.
• No ambient heat loss over time: Heat losses through insulation, foundations, and piping during charging, storage, and discharge are not explicitly modeled. Using a lower overall efficiency can partially account for these losses in an average sense.
• Steady power draw: Plant power is assumed constant during discharge. Ramping, part-load operation, start-up and shut-down transients, and auxiliary power consumption are not resolved in detail.
• Single storage loop: The model treats storage as a single hot tank volume tied directly to one power block. Complex layouts with multiple tanks, cascaded systems, or hybrid storage are outside its scope.
• No degradation or fouling over life: Effects such as salt decomposition, corrosion products, and heat exchanger fouling are not dynamically modeled. These phenomena can reduce effective capacity and efficiency over time.
• Heuristic risk metric: Any “risk of shortfall” or probability output is based on an illustrative logistic curve using the difference between modeled and desired duration. It is not a formal reliability analysis and should not be used for safety or investment-grade decisions.
• No financial or regulatory modeling: The calculator does not consider capital costs, operating expenses, emissions regulations, or grid codes. It is purely a technical sizing aid.

Because of these limitations, the results should be viewed as screening-level estimates. For detailed design, performance guarantees, grid interconnection studies, or financing, more sophisticated simulations and project-specific engineering data are required.

When to Use a More Detailed Model

The calculator is best suited to early concept development, education, and simple sensitivity studies. Consider a higher-fidelity model or professional engineering analysis when you need to:

• Optimize dispatch strategies across many days with changing solar input and market prices.
• Account for dynamic thermal behavior, including transient start-up and shut-down cycles.
• Evaluate detailed piping layouts, pressure drops, pump sizing, and freeze protection requirements.
• Quantify long-term degradation of salt quality, insulation performance, and power-block efficiency.
• Support bankability studies, safety assessments, or contractual performance guarantees.

Within its scope, this molten salt thermal storage discharge calculator provides a transparent, physics-based way to connect tank volume, operating temperatures, and plant power draw to an estimated discharge duration, while highlighting how design choices influence overall storage performance.