Hydrogen technologies have gained momentum in recent years in the context of achieving fully renewable energy systems. Apart from the ability of electrolyzers and fuel cells to consume and generate green energy, the latest research on their technical characteristics also promotes them as providers of balancing services in both power and gas (either hydrogen or natural gas) systems. The balancing services provision is a highly uncertain process and is not scheduled in advance, however, due to signed contracts and rules, the provision of these services to the TSO is not considered as a deviation from the agreed schedule. Contrary to battery storage, whose operation only affects the power system power flows, the operation of power-to-hydrogen and hydrogen-to-power units in one system (e.g. power system) has an impact on the other system (e.g. gas) as well. Because of that, the unscheduled balancing services provision to one TSO will cause an imbalance towards the TSO in the other system. This impact remains unexplored in the available literature. In this paper, we propose a model of a PV-battery-hydrogen power plant participating in both the power and gas (hydrogen) system markets while acting as a provider of balancing services and the responsible party of its own balancing group in both systems as well. We analyze how considering the influence that energy-conversion units simultaneously have on both observed systems affects the realized profit of the power plant and we show that neglecting this impact increases the total imbalance costs of the power plant, and consequently reduces its overall profit.