Due to the effects of windless and sunless weather, new power systems dominated by renewable energy sources experience power supply shortages, which lead to severe electricity shortages. Because of the insufficient proportion of controllable thermal power in these systems, this problem must be addressed from the load side. This study proposes an orderly power utilization (OPU) method with load as the primary dispatching object to address the problem of severe electricity shortages. The principles and architecture of the new urban power grid (NUPG) OPU are proposed to complete the load curtailment task and minimize the effects on social production and daily life. A flexible load baseline division method is proposed that considers the effects of factors such as gross domestic product, pollutant emission, and carbon emission to increase the flexibility and applicability of the proposed method. In addition, an NUPG OPU model based on the load baseline is proposed, in which the electric quantity balance aggregator (EQBA) serves as a regular participant in the OPU and eliminates the need for other user involvement within its capacity range. The electric quantity reserve aggregator (EQRA) functions as a supplementary participant in the OPU and primarily performs the remaining tasks of the EQBA. The electric power balance aggregator primarily offsets the power fluctuations of the OPU. Case studies demonstrate the effectiveness and superiority of the proposed model in ensuring the completion of the load curtailment task, enhancing the flexibility and fairness of OPUs, and improving the applicability of the proposed method.