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...ow whigh − wlow )γ) (α̂k,p dk,m + β̂k,p), (10) or the CPAR sector demand prediction model in Eq. (7) can be rewritten as d̂k+p,m = ( 1− ( wk+p − wlow whigh − wlow )γ) (α̂k,p k∑ i=k−q+1 di,m + β̂k,p). =-=(11)-=- 5 of 10 American Institute of Aeronautics and Astronautics Using the echo tops information provides a more representative weather index, especially for the high sectors. If there are storms with low ...

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... the kth column of D, the cumulative p-step-ahead sector demand model at time step k can be described in terms of the cumulative sum of q past sector demands as dk+p = αk,p k∑ i=k−q+1 di + βk,p + ek, =-=(6)-=- where αk,p and βk,p are the coefficients that map the cumulative sector demand at the kth time step to the sector demand at the (k + p)th time step. Once the least-square solution of coefficients α̂k...

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...inute intervals. Given the observed 15-minute peak sector demands for n days, the sector demand data matrix is defined as D = d1,1 d2,1 . . . d96,1 ... ... . . . ... d1,n d2,n . . . d96,n , =-=(1)-=- where di,j represents the 15-minute peak sector demand at the ith time step on day j. For September 2007, D has a dimension of 30 by 96, and Fig. 2 shows the image of the matrix D. Assuming dk as the...

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... power of the distribution. To reflect the thresholds, the sector weather index in Eq. (8) is redefined as wk = wlow if Awk /A ≤ wlow Awk /A if wlow < A w k /A < whigh whigh if whigh ≤ Awk /A . =-=(9)-=- In order to adjust the weather impact on the sector demand prediction model, the weather forecast is used to compute the predicted sector weather index. Assume at time k, the predicted sector weather...

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... severe weather day (VIL) level three and above. Only storms with the echo tops above the lower boundary of the sector are considered. The sector weather index at time k is formulated as wk = Awk A , =-=(8)-=- where A is the area of the sector and Awk is the area of the sector covered by storms with the echo tops at or above the lower bound of the sector at time k. Note that if time k is a future time, the...

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... ek is the error of the model. The least-square solution of αk,p and βk,p that minimizes eTk ek in Eq. (2) can be written explicitly as α̂k,p = ∑n i=1(dk,i − d̄k)(dk+p,i − d̄k+p)∑n i=1(dk,i − d̄k)2 , =-=(3)-=- β̂k,p = d̄k+p − αk,pd̄k, (4) 2 of 10 American Institute of Aeronautics and Astronautics 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 0 1 2 3 0 2 4 6 8 10 12 14 16 18 20 Hour (EDT) Se ct orsD...

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.... The least-square solution of αk,p and βk,p that minimizes eTk ek in Eq. (2) can be written explicitly as α̂k,p = ∑n i=1(dk,i − d̄k)(dk+p,i − d̄k+p)∑n i=1(dk,i − d̄k)2 , (3) β̂k,p = d̄k+p − αk,pd̄k, =-=(4)-=- 2 of 10 American Institute of Aeronautics and Astronautics 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 0 1 2 3 0 2 4 6 8 10 12 14 16 18 20 Hour (EDT) Se ct orsD em an ds(ai rc ra ft) Sector...

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...the n days in the data set, the p-step prediction of the sector demand at the kth time step, d̂k+p,m, based on the observed sector demand, dk,m, can then be expressed as d̂k+p,m = α̂k,p dk,m + β̂k,p. =-=(5)-=- In the model, α̂k,p and β̂k,p, identified from the historical data, capture the periodic features during a day, and the observed sector demand dk,m provides the transient information. The model in Eq...

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...rediction of the sector demand at the kth time step for a day m, d̂k+p,m, based on the observed cumulative sector demand, ∑k i=k−q+1 di,m, can be expressed as d̂k+p,m = α̂k,p k∑ i=k−q+1 di,m + β̂k,p. =-=(7)-=- The model in Eq. (6) and Eq. (7) is referred to as the cumulative periodic auto-regressive (CPAR) sector demand prediction model. During the analysis, it is noticed that the CPAR model using the sum ...