Existing studies propose different demand response models and often test them on islands that represent test-beds for new technologies. However, proposed models are often simplified and integrated into energy system models that do not consider the existing limitations of the power grid. This study proposes a novel demand response model based on price differentials on the day-ahead electricity market. The model is implemented in the distribution system that considers all relevant grid constraints. The case study is conducted in an archipelago characterised by a medium-voltage distribution system connected to the mainland grid. The obtained results showed that the implementation of the proposed demand response model caused a 0.13 kV voltage deviation which did not cause voltage issues for the observed distribution system. The breakpoint incentive was achieved for an incentive value of 23% of the day-ahead market, and the demand response was not activated for higher values than the breakpoint incentive. The highest savings amounted to 258.7 € for the scenario with the highest flexibility allowed. The results implicate that implementing the demand response model in the grid would benefit all observed stakeholders in the system.