Abstract
Smart grids treat energy in a much more efficient manner than it is done currently by conventional power systems. One important aspect in the design and analysis of smart grids is to take into account some real characteristics of the power system and its loads. In this context, we propose a dynamic load model for residential applications based on a non-homogeneous Poisson process, whose parameters depend on the electrical characteristics of the loads and their time-varying power profiles. Some of the advantages of this model are its flexibility to represent any specific energetic scenario found in different regions of the globe and the possibility to independently control individual low-voltage loads of the evaluated system by modifying the activation function of the corresponding load model. This last characteristic is fundamental to represent adequately and analyze the behavior of smart grids. To demonstrate the accuracy and effectiveness of the proposed strategy, several load curves were generated with the aid of the proposed model and compared against real measurements.
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Appendix
Appendix
The use of the thinning algorithm to represent the load activation time instants based on a NHPP is justified by the following theorems (Lewis and Shedler 1979):
Theorem 1
Let \(\lambda (t)\) be a positive right-continuous function of \(t \ge 0\). Then \(T_1, T_2, \dots \) are the time to events from a NHPP with \(E[N(t)] = \lambda (t)\), if and only if \( T^*_1 = \varLambda (T_1), T^*_2 = \varLambda (T_2), \dots \) are the time to events in a HPP with rate 1.
Theorem 2
Consider the random variables \(T_1, T_2, \dots , T_n\) representing event times from a NHPP with intensity function \(\lambda (t)\) within the fixed interval \((0, t_0]\). Let \(\lambda (t)\) be an intensity function such that \(0 \le \lambda (t) \le \lambda _u\) for all \(t \in [0, t_0]\). If the ith event time \(T_i\) is independently discarded with probability \(1 - \lambda (t) / \lambda _u\) for \(i = 1, 2, \dots , n\), then the remaining event times form a NHPP with intensity function \(\lambda (t)\) in the interval \((0, t_0]\).
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Casella, I.R.S., Sanches, B.C.S., Filho, A.J.S. et al. A Dynamic Residential Load Model Based on a Non-homogeneous Poisson Process. J Control Autom Electr Syst 27, 670–679 (2016). https://doi.org/10.1007/s40313-016-0269-8
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DOI: https://doi.org/10.1007/s40313-016-0269-8