Market for multi-dimensional flexibility with parametric demand response bidding

Demand side management (DSM) exploits flexibility of the end-user side to help improve the performance of the power grid. However, how to model and evaluate the multi-dimensional flexibility (MDF) of the energy consumers (such as the flexibilities in terms of energy, power, time period and locations, etc.) is an important and challenging issue. To handle this, we propose a day-ahead market design for the MDF services. In this market, the MDF aggregators need to submit the characteristics of their virtual battery models and parametric reward functions, which represent the aggregate load flexibilities and the required remunerations, respectively. One key feature of this new market is that the system operator is allowed to accept only a portion of every bid instead of the whole of them. This can bring more flexibilities for the operator to minimize the total system cost. With various case studies on a 6-bus transmission network, we show that this market can help flatten the locational marginal prices (LMPs) across the peak load period. Moreover, we show that even if the MDF bids at different buses are the same, the clearing results can be quite different, which reflect the practical values of different load flexibilities from the perspective of the system operator.