NASSAR AND SALAMA: ADAPTIVE SELF-ADEQUATE MICROGRIDS USING DYNAMIC BOUNDARIES 3 Fig. 1. Steps to divide bulky grids into adaptive self-adequate microgrids. e.g., customer loads, generation ratings, available generation, types of generation, and location of generation. When the agent is deactivated, it gives control to the active agent, which now knows only the aggregated generation and loads associ- ated with the components that have been newly added under its umbrella. The following sections discuss the application of steps 2–7 of the proposed methodology using the PG&E 69-bus system [ 4 ], [ 12 ] for demonstration purposes. Fig. 2. Functions of a microgrid agent. Fig. 3. Dynamic microgrid borders produced for two operating scenarios. (a) Scenario 1. (b) Scenario 2. III. M ODELING OF W IND , S OLAR , AND B IOMASS G ENERATION AND L OADS This section discusses step 2 of the methodology: the devel- opment of stochastic models of the output power of a variety of DGs and the loads, based on historical data. These models are then employed in further design steps. A. Wind To model the output power from wind-based DG, three successive years’ worth of historical wind speed data for a spe- cific site are used for the calculation of output power, as expressed [ 13 ]. The per unit output power on a rated power basis is then determined P ( v ) = ⎧ ⎪ ⎪ ⎪ ⎨ ⎪ ⎪ ⎪ ⎩ 0 0 ≤ v ≤ v ci P rated × v − v ci v r − v ci v ci ≤ v ≤ v r P rated v r ≤ v ≤ v co 0 v co ≤ v (1) where v is the wind speed; v ci , v co , and v r are the cut-in speed, cut-out speed, and rated speed of the wind turbine, respec- tively; P is turbine output power; and P rated is the turbine rated output power. These historical per unit wind output power data are next analyzed in order to generate an appropriate probability den- sity function (PDF) that represents wind per unit output power. In this wind model, the year is divided into four seasons, with
This article has been accepted for inclusion in a future issue of this journal. Content is final as presented, with the exception of pagination. 4 IEEE TRANSACTIONS ON SMART GRID TABLE I G OODNESS OF F IT T EST R ESULTS FOR E ACH S EASON the best PDF for each season selected to represent the wind per unit output power. Goodness of fit tests is used for the determination of the best PDF; the results obtained are presented in Table I . Because the number of samples exceeds 2000, the tests used are the Kolmogorov–Smirnov test (K-S), as expressed by ( 2 ), and the Anderson–Darling test (A-D), as expressed D = max 1 ≤ i ≤ n F ( X i ) − i − 1 n , i n − F ( X i ) (2) A 2 = − n − 1 n n i = 1 ( 2i − 1 ) ln F ( X i ) + ln ( 1 − F ( X n − i + 1 )) (3) where F is an empirical cumulative distribution func- tion (CDF), i is the sample, D is K-S statistic, A 2 is the A-D statistic, and n is the total number of samples.
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