This paper proposes a Lyapunov optimization-based online distributed (LOOD) algorithmic framework for active distribution networks (ADNs) with numerous photovoltaic inverters and inverter air conditionings (IACs). In the proposed scheme, ADNs can track an active power setpoint reference at the substation in response to transmission-level requests while concurrently minimizing the social utility loss and ensuring the security of voltages. Conventional distributed optimization methods are rarely feasible to track the optimal solutions in fast variable environments using a fine-grained sampling interval where the underlying optimization problem evolves with the iterations of the algorithms. In contrast, based on the framework of online convex optimization (OCO), the developed approach uses a distributed algebraic update to compute the next round decisions relying on the current feedback of measurements. Notably, the time-coupling constraints of IACs are decoupled for online implementation with Lyapunov optimization technique. An incentive scheme is tailored to coordinate the customer-owned assets in lieu of the direct control from network operators. Optimality and convergency are characterized analytically. Finally, we corroborate the proposed method on a modified version of 33-node test feeder. Benchmark tests show that the proposed method is computationally and economically efficient, and outperforming existing algorithms.

With the development of techniques, such as the Internet of Things (IoT) and edge computing, home energy management systems (HEMS) have been widely implemented to improve the electric energy efficiency of customers. In order to automatically optimize electric appliances’ operation schedules, this paper considers how to quantitatively evaluate a customer’s comfort satisfaction in energy-saving programs, and how to formulate the optimal energy-saving model based on this satisfaction evaluation. First, the paper categorizes the utility functions of current electric appliances into two types; time-sensitive utilities and temperature-sensitive utilities, which cover nearly all kinds of electric appliances in HEMS. Furthermore, considering the bounded rationality of customers, a novel concept called the energy-saving cost is defined by incorporating prospect theory in behavioral economics into general utility functions. The proposed energy-saving cost depicts the comfort loss risk for customers when their HEMS schedules the operation status of appliances, which is able to be set by residents as a coefficient in the automatic energy-saving program. An optimization model is formulated based on minimizing energy consumption. Because the energy-saving cost has already been evaluated in the context of the satisfaction of customers, the formulation of the optimization program is very simple and has high computational efficiency. The case study included in this paper is first performed on a general simulation system. Then, a case study is set up based on real field tests from a pilot project in Guangdong province, China, in which air-conditioners, lighting, and some other popular electric appliances were included. The total energy-saving rate reached 65.5% after the proposed energy-saving program was deployed in our project. The benchmark test shows our optimal strategy is able to considerably save electrical energy for residents while ensuring customers’ comfort satisfaction is maintained.