An overview of the proposed smart distribution system operational framework with uncontrolled price-responsive loads is presented in Fig. 1. It is assumed that customers would be equipped with home energy management systems (HEMS) [23], based on which they respond to price ρk by adjusting their consumption PDk(ρk). Two different pricedemand relationships, namely, linear and exponential, are considered for the studies.
The reason for choosing the linear model is its simplicity in representing the price-demand relationship, while the exponential model is chosen since it represents a typical nonlinear price-demand relationship [7]–[9]. The price-responsiveness of customers can effectively be determined
in real-life through historical data of price and load demand, or using a thorough customer survey; hence the parameters of the proposed models can be estimated using historical data sets. In Fig. 1, it is also assumed that the LDC would be equipped with a smart load estimator (SLE), which receives real-time load consumption data from customers’ smart meters to develop price-responsive models for the loads. These priceresponsive load models, estimated by the SLE, would be used as an input by the LDC for real-time smart distribution system operation through the proposed DOPF to optimally control the distribution feeder using a model predictive control (MPC) approach [28]. Thus, the proposed model would be executed based on the frequency of the incoming real-time data, which could be every 5, 10, or 15 min to take care of the changes in the system parameters, particularly load demand, which can change dynamically. Furthermore, it is assumed that some fraction of the loads would respond to electricity prices by increasing or decreasing their consumption as per their convenience, or behaving as deferrable loads, while the rest is considered to be fixed or critical loads