Pursuing the objective of improving the photovoltaic penetration rate in an electric mix dominated by thermal energy, the integration of the demand response is solicited to absorb the fluctuations and intermittencies induced by the energy from PV. In the work presented in this article hybrid loads (LPG and electrical) participate in the demand response, offering the advantage of targeting a household activity not yet taken into account in the load profile, but also avoiding the report and rebound effects often seen in Demand Side Management. It will be a question here of evaluating the capacity for these loads to absorb the energy surplus of origin PV whose quantity exceeds at certain time the demand coming from the conventional loads.

Factorial is extremely important in a combinatorial calculation. E.g., there are n! ways to arrange n numbers in different orders. One of the uses of factorial is to find the binomial coefficient, i.e., the number of ways of picking k unordered outcomes from n possibilities. Aside from combinatorial calculation, factorial also has a role in calculus (Taylor’s theorem), probability theory, and network security that use the prime field domain. But, another problem arose, i.e., how to efficiently compute the factorial. This paper will describe a new approach for efficiently calculating factorials in the prime field. Two testing models are involved in this paper: the correctness test by source-code submission to Sphere Online Judge, and the performance test by generating their chart of runtimes. Based on the testing result from the given case studies, it turns out that our approach has a better performance compared to the Multipoint Evaluation algorithm adaptation approach.