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Smart energy networks provide an effective means to accommodate high penetrations of variable renewable energy sources like solar and wind, which are key for the deep decarbonisation of energy production. However, given the variability of the renewables as well as the energy demand, it is imperative to develop effective control and energy storage schemes to manage the variable energy generation and achieve desired system economics and environmental goals. In this paper, we introduce a hybrid energy storage system composed of battery and hydrogen energy storage to handle the uncertainties related to electricity prices, renewable energy production, and consumption. We aim to improve renewable energy utilisation and minimise energy costs and carbon emissions while ensuring energy reliability and stability within the network. To achieve this, we propose a multi-agent deep deterministic policy gradient approach, which is a deep reinforcement learning-based control strategy to optimise the scheduling of the hybrid energy storage system and energy demand in real time. The proposed approach is model-free and does not require explicit knowledge and rigorous mathematical models of the smart energy network environment. Simulation results based on real-world data show that (i) integration and optimised operation of the hybrid energy storage system and energy demand reduce carbon emissions by 78.69%, improve cost savings by 23.5%, and improve renewable energy utilisation by over 13.2% compared to other baseline models; and (ii) the proposed algorithm outperforms the state-of-the-art self-learning algorithms like the deep-Q network. [ABSTRACT FROM AUTHOR]