OCR Text |
Show where dls , d2s are ( 0,1) variables that identify whether or not the M& I and irrigation releases ( respectively) can be passed through the hydropower plant for reservoir s. The possible power production in each month is expressed as: PB - f3 ( HTB. STB) - cp HT„ ( c5, ST*') ( 5.10) where Cp is a factor for conversion to power ( MW) and c5s, c6s are the coefficient and exponent for a relation between available head and storage for reservoir s. The set of possible power production values Pst is then converted into an ordered set Psj, such that Psi ^ Ps2 ^ ^ PsT- The actual power production P s o for each month o ( from the ordered set) is then the minimum of Ps o and Gs. The algorithm for the determination of the optimal hydropower plant size Gs then considers each value of the ordered set Ps o as a candidate value for Gs. Then, for o equal to some value o', and Gs equal to Pso% the annual cost ACHS and annual revenue ARHS from hydropower are given as: c4 ACH = c3 P f ( 5.11) s s so Re °' ARHs= - ^ r * ( T-°') P » ' + S p M > ( 512) 0= 1 where c3s and c4s are the coefficient and exponent for a relation between annual generator cost and generator size, R3S is a unit revenue ($/ MWH) from hydro- energy, ce is a coefficient to convert to MWH, NY is the number of years and T is the number of months. The net annual revenue NARS from hydropower at site s is then obtained as the difference between ARHS and ACHS ( equations 5.12 and 5.11), given that Gs is equal to Pso'. It can be demonstrated that both ACHS and ARHS are monotonically increasing functions of Pso'. Then with o' increasing from 1 to T, a unique optimum ( maximum net revenue NARS ), must result at some value o* of o' between 1 and T. Further, this optimum is marked by a decrease in the value of NARS at any o* greater than o*. The procedure is then to proceed with calculations of NARS at each o' incremented from 1 to T, and to terminate the procedure as soon as the computed value of NARS at o' is less than the value of NARS at ( o'- l). Then o* is defined as ( o'- l) and the optimum hydropower plant size Gs as PSo*- The corresponding values of NARS is then used in the optimization model's objective function. Finally, if the optimal value of net annual revenue NARS, is negative, the optimal hydropower plant capacity, and cost and revenue are defined to be zero. Note that the true optimum for Gs lies between PS0* and PS0, and can be solved for using a numerical algorithm. However, when the total number of months T is large ( typically greater than 100) and/ or a firm release for hydropower is provided, the difference between PS0* and PS0 was consistently less than the tolerance specified. Since the number of months where PS0 exceeds Gs decreases as Gs increases the annual revenue is 109 |