Risk-averse stochastic multi-objective optimization for time-of-use demand response pricing in smart microgrids

This paper presents a multi-objective optimization approach for the pricing of a time-of-use (TOU) demand response program in a smart microgrid (MG), addressing the perspectives of the MG operator, aggregators, and clients. The MG operator's objective is to maximize profit by balancing production costs and revenue, which varies with the implementation of TOU, while minimizing bonuses paid to aggregators. The aggregators aim to maximize the bonus received from the MG operator while minimizing both the compensation paid to clients for aligning their consumption with renewable generation and the discomfort experienced by clients. Clients seek to maximize their compensation while minimizing discomfort caused by adjusting their consumption patterns. The model includes uncertain parameters like solar radiation, wind speed, and load demand, characterized by probability density functions (PDFs) to generate scenarios, with backward scenario reduction technique used to manage computational complexity. The multi-objective optimization problem is modeled stochastically and solved using the Normal Boundary Intersection (NBI) method, with the Conditional Value at Risk (CVaR) index integrated to account for a risk-averse perspective. The proposed framework is validated on the IEEE 33-node test network from different perspectives. In all studied cases, TOU pricing incorporates higher tariffs during peak and mid-peak hours and lower tariffs during off-peak hours, resulting in load reduction during peak and mid-peak hours and load shifting to off-peak hours. When the microgrid operator's objective is prioritized, its average value is $945, with a CVaR of $903.5. The aggregator's average objective value is $150.1, while the clients' average objective value is $-44. This scenario achieves the highest operator profit and the lowest operating costs. When the aggregator's objective is prioritized, its average value increases to $158, with a CVaR of $141.8. The microgrid operator's average objective value decreases to $923, while the clients' average objective value becomes $127.4, remaining positive across all scenarios. When the clients' objective is prioritized, their average objective value significantly increases to $227, with a CVaR of $206.1. The microgrid operator's and aggregator's average objective values decrease to $898.5 and $66.56, respectively. This scenario yields the highest compensation costs and the lowest discomfort costs.