Smart Grids (SGs) represent electrical power systems that incorporate increased information processing and efficient technological solutions. The integration of local prosumers, demand response systems and storage allows novel possibilities with regard to energy balancing and optimization of grid operations. Unfortunately, the dependence on IT leaves the SG exposed to security violations. In this paper, we contribute to this challenge and provide a methodology for systematic risk assessment of cyber attacks in SG systems. We propose a threat model and identify possible vulnerabilities in low-voltage distribution grids. Then, we calculate exploitation probabilities from realistic attack scenarios. Lastly, we apply formal verification to check the stochastic model against attack properties. The obtained results provide insight into potential threats and the likeliness of successful attacks. We elaborate on the effects of a security violation with regard to security and privacy of energy clients. In the aftermath, we discuss future considerations for improving security in the critical energy sector.