Storage characterization

Introduction

KAIROS supports accurate modeling of electricity storage systems, incorporating key operational constraints and temporal dynamics. These constraints are essential for representing short- and long-duration storage assets in unit commitment, dispatch optimization, and energy planning models. The formulation includes energy balance equations, operational limits, and power flow restrictions.


1. Energy Balance Equation

The energy level of a storage unit evolves based on charging and discharging activity:

$$ SL_{s,t} - SL_{s,t-1} = ( s_{cha,s,t} · S_{CEf,s,t} - s_{dis,s,t} / S_{DEf,s,t} ) · Dur_{t} $$

Where:

  • \(SL_{s,t}\): energy stored at time (in MWh),

  • \(s_{cha,s,t}\): charging power (MW),

  • \(s_{dis,s,t}\): discharging power (MW),

  • \(S_{CEf,s,t}\): charging efficiency (unitless),

  • \(S_{DEf,s,t}\): discharging efficiency (unitless),

  • \(Dur_{t}\): duration of each time step (in hours).


2. Maximum Storage Level

The energy stored in the system must remain within physical bounds:

$$ SL_{s,t} \le S_{lmax,s,t} $$

Where:

  • \(S_{lmax,s,t}\): is the maximum storage capacity (in MWh),


3. Maximum Charging Rate

Charging is limited by converter and infrastructure capacity:

\(s_{cha,s,t} \le S_{cmax,s,t} \)

Where:

  • \(S_{cmax,s,t}\): is the maximum allowable charging power (in MW).


4. Maximum Discharging Rate

Similarly, the discharging power is constrained by technical ratings:

\(s_{dis,s,t} \le S_{dmax,s,t} \)

Where:

  • \(S_{dmax,s,t}\)`: is the maximum discharging power (in MW),


Conclusion

These constraints provide a comprehensive and flexible representation of electricity storage within KAIROS. They enable detailed analysis of energy shifting, arbitrage, grid support, and the role of storage in high-renewable energy systems.