Pbcap ⎧ ⎨ ⎩ ∑ m Pb = ∑ n= 1 ( i k, m) Nc( i, k − n + 1, m) , (24) Pb Plan sub-period for cost recovery of plant costs, years 4.2.2 Load Flow Equations In this planning model the DC load flow equations are used for the purpose of keeping the model as a mixed-integer linear programming model. Detailed load flow equations including the reactive power and voltage variables are not considered critical here because of the study time-frame of 15 years, and this helps avoid the introduction of non-linear constraints in the model. ⎫ Pg ⎬ ∑ , ⎭ j ( i, b, k, m) + EP( i, b, k) − BD( i, b, k) = − b( i, j) ∗{ δ ( i, b, k) − δ ( j, b k) } BD(i,b,k) Active power demand at bus i during demand block e in year k, MW b(i,j) YBus Suseptance between transmission line i-j, Ω -1 δ(i,b,k) Voltage angle at bus i during demand block e in year k, Radians 4.2.3 Line Flow Equations As discussed in the previous section, in the present model the DC load flow equations are used. Accordingly, the active power line flows in the network are determined by the DC line flow equations, as given below: { ( i, b, k) ( j, b k) } Pflow ( i, j, b, k) = b( i, j) ∗ δ − δ , (26) Pflow(i,j,b,k) Active power flow from bus i to bus j during demand block b in year k, MW It is to be noted here that the present model includes the line flow equations only for the purpose of computing the line flows and overloads resulting from new generating units. Line flow limits are not considered in this work and therefore, they do not impact the investment decisions of the investor. 48 (25)

The issue of imposing line flow limits is essentially the responsibility of the central planning authority which has to take into account all investment proposals and incorporate them into its operations studies with security constraints, and hence examine whether such proposals are acceptable or not. Such studies are beyond the scope of this thesis, and need to be taken up in the future. 4.2.4 New Capacity Installation variable In this modeling approach the new capacity Nc(i,k,m), based on m technology plant that is commissioning at bus i in year k, is a discrete size as considered in Chapter-3, the selection of these units to be installed based on a binary variable that decides whether the unit should ininstalled in particular year or not to maximize the objective function. The modeling equation for this variable is given below: ( i, k, m) = ID( i, k, m) ∗ ADCS( m) ALO( i, k, m) bin( k) Nc ∗ ∗ ID(i,k,m) Binary decision variable to decide whether m technology unit should be ⎧1 bin( k) = ⎨ ⎩0 ⎨ ⎩ ⎧1 ID( i, k, m) = 0 if P − k + 1 ≥ pb if P − k + 1 < pb Binary Variable denoting selection of Otherwise installed at bus i in year k or not ADCS(m) Available discrete capacity size of m technology plant that can be commissioned in a year, MW ALO(i,k,m) Available Location options to install m technology plant at bus i in year k, 0 or 1 bin(k) Binary decision parameter for the capacity installation in year k 49 capacity (27) (28) (29)