Quantum Learning and Estimation for Coordinated Operation between Distribution Networks and Energy Communities

Price signals from distribution networks (DNs) guide energy communities (ECs) in adjusting their energy usage, enabling effective coordination for reliable power system operation. However, this coordinated operation faces significant challenges due to the limited availability of ECs' internal information (i.e., only the aggregated energy usage of ECs is available to DNs), and the high computational burden of accounting for uncertainties and the associated risks through numerous scenarios. To address these challenges, we propose a quantum learning and estimation approach to enhance coordinated operation between DNs and ECs. Specifically, by leveraging advanced quantum properties such as quantum superposition and entanglement, we develop a hybrid quantum temporal convolutional network-long short-term memory (Q-TCN-LSTM) model to establish an end-to-end mapping between ECs' responses and the price incentives from DNs. Moreover, we develop a quantum estimation method based on quantum amplitude estimation (QAE) and two phase-rotation circuits to significantly accelerate the optimization process under numerous uncertainty scenarios. Numerical experiments demonstrate that, compared to classical neural networks, the proposed Q-TCN-LSTM model improves the mapping accuracy by 69.2\% while reducing the model size by 99.75\%. Compared to classical Monte Carlo simulation, QAE achieves comparable accuracy with a substantial reduction in computational resources. In addition, the estimated computation time for quantum learning and estimation on ideal quantum devices is over 90\% shorter than that of traditional methods.