Quantifying Operational Symmetry Breaking in Battery Energy Storage Scheduling under Synthetic Renewable Profiles

Introduction:

Battery energy storage system scheduling is commonly assessed through cost, emissions, feasibility, and grid exchange. However, the temporal structure of battery operation remains poorly quantified. In particular, the symmetry between charging and discharging actions across a daily horizon is rarely used to interpret storage behavior. This study addresses this gap by proposing symmetry indices for battery power and state-of-charge trajectories. The novelty of the study is the formulation of battery scheduling as a symmetry-breaking problem, where external signals and technical limits reshape charge–discharge balance.

Methods:

A 24 h single-node renewable energy system was simulated using synthetic demand, photovoltaic generation, electricity price, and carbon emission profiles. The battery model included state-of-charge limits, charging and discharging power limits, charge and discharge efficiencies, and end-of-day state-of-charge restoration. Five scenarios were optimized using PSO: energy balance operation, cost minimization, emission minimization, asymmetric efficiency, and restricted power exchange. The schedules were evaluated using total cost, emissions, grid imports and exports, battery throughput, grid exchange RMS, and two symmetry indices.

Results:

Cost minimization achieved the lowest operating cost, USD 109.57, representing an 8.02% reduction compared with energy balance operation, although emissions increased to 336.87 kgCO2. Emission minimization obtained the lowest emissions, 327.84 kgCO2, with a cost of USD 114.20. Restricted power exchange produced the highest power symmetry index, 0.324, and emissions of 331.49 kgCO2, with a cost only 1.21% above the cost minimum. Asymmetric efficiency yielded the highest state-of-charge symmetry index, 0.316. Energy balance operation showed the lowest battery throughput (219.45 kWh) and grid exchange RMS (34.15 kW), as well as the lowest symmetry indices.

Conclusions:

These results show that battery operational symmetry depends on objective functions, efficiency assumptions, and power limits. The proposed indices offer a simple metric to interpret how economic, environmental, and technical constraints reshape daily storage behavior.