Proliferation of photovoltaic (PV) panels may cause voltage increases in low voltage (LV) distribution feeders. This issue confines PV hosting capacity of the feeders. To overcome this issue and enable higher PV hosting capacity, a model to manage the operation cycles of the domestic electric water heater and heating, ventilation, and air conditioning loads in order to avoid the voltage rise, thereby increasing PV hosting capacity in LV feeders is presented in this study. The model respects users' thermal comfort by setting the associated temperatures within allowed ranges. To preserve customers' privacy, the presented model is then decomposed into a master problem and several sub-problems using the Dantzig-Wolfe decomposition algorithm. Thereafter, an effective scheme is designed to solve the decomposed problem in a distributed fashion. In the scheme, the master problem is solved by the system-wide module and the sub-problems are solved by house-wide modules. The problems are all in linear format which can be easily solved with affordable computation. Importantly, the proposed model can reach the optimal solution while minimal data is shared between houses and control centre.

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The advent of quantum computing can potentially revolutionize how complex problems are solved. This paper proposes a two-loop quantum-classical solution algorithm for generation scheduling by infusing quantum computing, machine learning, and distributed optimization. The aim is to facilitate employing noisy near-term quantum machines with a limited number of qubits to solve practical power system optimization problems such as generation scheduling. The outer loop is a 3-block quantum alternative direction method of multipliers (QADMM) algorithm that decomposes the generation scheduling problem into three subproblems, including one quadratically unconstrained binary optimization (QUBO) and two non-QUBOs. The inner loop is a trainable quantum approximate optimization algorithm (T-QAOA) for solving QUBO on a quantum computer. The proposed T-QAOA translates interactions of quantum-classical machines as sequential information and uses a recurrent neural network to estimate variational parameters of the quantum circuit with a proper sampling technique. T-QAOA determines the QUBO solution in a few quantum-learner iterations instead of hundreds of iterations needed for a quantumclassical solver. The outer 3-block ADMM coordinates QUBO and non-QUBO solutions to obtain the solution to the original problem. The conditions under which the proposed QADMM is guaranteed to converge are discussed. Two mathematical and three generation scheduling cases are studied. Analyses performed on quantum simulators and classical computers show the effectiveness of the proposed algorithm. The advantages of T-QAOA are discussed and numerically compared with QAOA which uses a stochastic gradient descent-based optimizer.

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