Passive charging of an underground heat storage

Intro

Question:

How can I represent passive charging in a borehole heat storage within my energy system optimization model?

Answer:

It’s complicated … But the only generally applicable answer is: A custom addon. The underlying idea is to separate the passive charging from the storage, into a separate “artificial” Profile, that can then accurately depict the passive behavior.

The problem

When modeling a borehole heat storage - a deep underground heat storage surrounded by warm soil - it’s important to account for passive charging from the surrounding soil. This guide explains how to represent this passive energy input in your model.

Common misconception

You might consider using the state_percentage_loss parameter with a negative value to simulate passive charging:

state_percentage_loss: -0.01  # Attempting to charge 1% per timestep

However, state_percentage_loss is designed for losses based on the current storage level. Using a negative value would incorrectly charge the storage by a percentage of its existing energy content, not the energy it lacks.

Therefore, while -0.01 might be an allowed or in other cases even reasonable choice, it’s not made for what is needed here.

Recommended solution

Instead, model passive charging as an additional input that depends on how much energy the storage lacks. Here’s how:

Naive static charging

Create a new component using a ranged Profile:

passive_charging:
  type: Profile
  mode: ranged
  lb: 0
  ub: MAX_PASSIVE_POWER  # Use any estimation of maximum passive charging power

The mode setting ranged transforms a basic Profile (with default mode: fixed), that cannot change it’s value, to a more advanced one that can freely pick it’s value from the interval [0, MAX_PASSIVE_POWER] - independently for each snapshot. This means, charging 0 is a feasible choice, resulting in no charge happening when the storage is already full. If the storage is not full, it will charge how much is economically optimal: Most of the time it will fully use it’s passive charging power, but if - for any reason - getting rid of excess heat might not be possible, or very costly, it can choose to not use the passive charging (which in reality would not be possible).

Custom constraint

Use an addon to add a constraint limiting the passive charging based on the storage’s unfilled capacity. Assuming that heat_storage is the name of the stateful Node that represents the underground storage, then:

# ... other stuff in your addon ...

function add_passive_charging(model::JuMP.Model)
    c_passive_charging = IESopt.get_component(model, "passive_charging")
    c_storage = IESopt.get_component(model, "heat_storage")

    IESopt.@constraint(model, [t in T], c_passive_charging.exp.value[t] <= 0.01 * (c_storage.state_ub - c_storage.var.state[t]))
end

# ... other stuff in your addon ...

This ensures the passive charging at time t doesn’t exceed 1% of the storage’s remaining capacity.

Earlier we discussed the possibility of the model foregoing available passive charging, if economically beneficial. If that is something that you explicitly want to prevent, you can also use = in the above constraint, which will force the Profile to the exact value, without the possibility to charge less!

Summary

Steps to implement

1. Create the storage component: Define your underground storage Node without using state_percentage_loss for passive charging.

2. Add the Passive Charging Input: Introduce a Profile to represent the passive energy inflow.

3. Set Profile Bounds: Use the mode ranged for the Profile with appropriate lower (lb) and upper (ub) bounds.

4. Add the Constraint: Implement the constraint to tie the passive charging rate to the storage’s unfilled capacity.

5. Refine as Needed: Adjust the constraint for more complex behaviors if necessary. There might be a lot (!) that you might want to specialize.

Conclusion

By modeling passive charging as a constrained input energy flow based on the storage’s remaining capacity, you accurately represent the thermal interactions of an underground heat storage with its environment.