VII. C ONCLUSION This paper has presented a novel design approach for divid- ing bulky grids into adaptive self-adequate microgrids. The proposed dynamic microgrid paradigm ensures self-adequacy at all times, taking into consideration the stochastic nature of loads and renewable-based DGs. An appropriate num- ber of isolation switches are allocated in order to allow the constructed microgrids to island during contingencies while supplying their loads; this feature improves reliability and prevents the spread of disturbances. The use of the pro- posed paradigm results in constructed microgrids that have clearly defined electrical borders, islanding capability (isola- tion switches and self-adequacy at all times), and single-entity controllability. None of these properties can be achieved based on the previously proposed static boundary paradigm. An addi- tional benefit is that adaptive self-adequate microgrids also provide a more suitable environment for the application of smart grid features such as self-healing. The results of this paper clearly demonstrate the superiority of the proposed dynamic boundary technique compared to the static boundary paradigm described in the literature. A PPENDIX A. Johnson SB PDF A Johnson distribution is a four-parameter distribution that is related to a normal distribution through a transformation
This article has been accepted for inclusion in a future issue of this journal. Content is final as presented, with the exception of pagination. NASSAR AND SALAMA: ADAPTIVE SELF-ADEQUATE MICROGRIDS USING DYNAMIC BOUNDARIES 9 Fig. 13. Johnson SB PDFs for a variety of parameters. (bounded transformation for Johnson SB) [ 18 ]. Because it has four parameters ( δ , λ , γ , ζ ), this distribution is very flexible for fitting empirical data. A Johnson SB PDF is expressed as follows: ⎧ ⎪ ⎪ ⎨ ⎪ ⎪ ⎩ f ( x ) = δ λ √ 2 π z ( 1 − z ) e − 1 2 γ + δ ln z 1 − z 2 ζ ≤ x ≤ ζ + λ z = x − ζ λ (7) where δ , γ are shape parameters; ζ is a location parameter; and λ is a scale parameter. Fig. 13 shows Johnson SB PDFs for differently shaped parameters. As can be seen from the figure, a Johnson SB has a high degree of flexibility for fitting a variety of empirical data shapes. B. Computational Time The algorithms were simulated using CPU with the follow- ing specifications: Intel core i7 860 @ 2.8 GHz, 64 bit, and 8 GB RAM. The total run time was found to be 54381.822 s (15.106 h). R EFERENCES  Q. Fu, “Modeling, analyses and assessment of microgrids consider- ing high renewable energy penetration,” Ph.D. dissertation, Dept. Elect. Eng., Wisconsin-Milwaukee Univ., Milwaukee, WI, USA, 2013.  M. Smith and D. Ton, “Key connections: The U.S. Department of Energy’s microgrid initiative,” IEEE Power Energy Mag. , vol. 11, no. 4, pp. 22–27, Aug. 2013.
- Fall '10