The precise electrical load model under various operating conditions plays a critical role for power system analysis. A suitable load model can reflect the real condition of power system operation. This paper investigates the measurement-based static load modelling for power system analysis. For this purpose, practical measurement data, including voltage active and reactive power consumption, are used to obtain an accurate static model that represents the behaviour of electrical loads. In this paper, a method based on curve fitting and practical measurement data is proposed to select the appropriate time interval for accurate determination of load model coefficients. The study shows that a medium voltage distribution feeder can be modelled as a static load by a ZIP model whose coefficients are determined during the transformer tap changing operation. The obtained results show that the proposed method can accurately model the feeder load with the normalized root mean square error (NRMSE) during tap changes of about 0.22%, and 0.34% for active and reactive power, respectively.

Elliptic curve cryptosystems (ECC) are new generations of public key cryptosystems that have a smaller key size for the same level of security. The exponentiation on elliptic curve is the most important operation in ECC, so when the ECC is put into practice, the major problem is how to enhance the speed of the exponentiation. It is thus of great interest to develop algorithms for exponentiation, which allow e cient implementations of ECC. In this paper, we improve e cient algorithm for exponentiation on elliptic curves de ned over Fp in terms of a ne coordinates. The algorithm computes 2n2(2n1P +Q) directly from random points P and Q on an elliptic curve, without computing the intermediate points. Moreover, we apply the algorithm to exponentiation on elliptic curves with width{w Mutual Opposite Form (wMOF) and analyze their computational complexity. This algorithm can speed up the wMOF exponentiation of elliptic curves of size 160{bit about (21. 7%) as a result of its implementation with respect to a ne coordinates.