Our objective is to discover how the photovoltaic (PV) production profile and home energy management (HEM) strategy affect the economic profitability of an added battery in a residential PV system in a Nordic context. We have included battery usage costs due to degradation – an aspect often overlooked in techno-economic assessments. In the literature, various HEM strategies for PV-battery have been explored, but studies have been limited to conventional south-facing monofacial PV (MPV). This work uses real PV data, including a south-facing MPV and a vertical east-west oriented bifacial (VBPV) system from Finland, combined with a typical residential consumption profile. A rule-based (SCM) and a reinforcement-learning-based (RL) HEM strategy are investigated. These results show that adding a battery (13.5 kWh/5 kW) to a PV system (2.5 kWp) is economically unfeasible with the battery capital expenditures of €9000, increasing annual costs by 137% on average. The break-even capital expenditures ranged between €490–1050, suggesting that batteries must become significantly cheaper to be profitable under the historical electricity prices of Finland. RL outperformed SCM only in 2022 under high electricity prices. The average battery lifetimes for VBPV and MPV were 12.5 and 11.9 years, indicating that PV production profile impacts battery longevity.