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# Non-intrusive load modeling using Newton-phaselet frames

## Abstract

Power system companies, including Canadian ones, have been making remarkable efforts towards implementing smart grid functions within their service domains. These efforts are spearheaded by establishing demand response programs for residential and small commercial loads (RSCLs). Demand response programs face a major challenge in their capacities to offer effective and economic options for customers in RSCLs, and thus fail to attract wide customer participation. The major challenge facing demand response programs is the lack of accurate models for energy demands and patterns of consumption in RSCLs. Available models of RSCLs are based on statistical methods, which require collecting significant amounts of data for energy demands of RSCLs over different hours each season. Statistical methods generally produce approximate models that may not accurately represent energy demands and patterns of consumption in RSCLs over different seasons. Furthermore, data collection from RSCLs can raise the costs of implementing smart grid functions, as extra instrumentation is required to monitor and record energy consumption of RSCLs. The main objective of this research is to develop new models for RSCLs using numerical methods and orthogonal multi-frames. The proposed modeling method uses one value of the active power P to calculate one value of the apparent power | ¯ S|, while it employs six phaselet frames to calculate a value of the angle θ (the phase of ¯ S). Calculated | ¯ S| and θ are used to calculate a value of the active power Pc, which is compared to P in order to adjust | ¯ S| for the next Newton iteration. Calculated values of Pc, | ¯ S|, and θ at each iteration are employed to determine a value of the reactive power Q at the same iteration. Determined values for Pc, | ¯ S|, θ, and Q, for each value of P, are employed to complete the constant impedance (Z), constant current (I) and constant power (P) modeling, commonly called the ZIP model, for RSCLs. In these loads, changes in the voltage, due to ON-OFF switching, are assumed negligible, where constant power and constant current loads become of a similar class in the ZIP model. The complete ZIP model has standardized parameters for the power consumption in each appliance, and thus the ON-OFF status of each appliance can be determined using its standardized parameter. This approach is implemented as an algorithm, and realized for performance evaluation using different sets of collected power measurements. Performance results show simple implementation, accurate determination of ON-OFF status, and a low memory requirement.