Truction and commissioning times, therefore the delay amongst the selection to invest and the asset becoming FAUC 365 custom synthesis operational is diverse for line reinforcements and power storage. This needs the inclusion of non-sequential state equations that link choice variables and constraints across all stages inside the multistage formulation, which prevents the straightforward Leupeptin hemisulfate Biological Activity application of a temporal decomposition scheme. In an effort to apply the advanced temporal decomposition system, auxiliary state variables are introduced that carry details on investments and their operational status across distinctive states. The definition of those variables plus the corresponding reformulation of non-sequential state equations for the application inside the decomposed arranging problem are presented in [31]. 3.two. Mathematical Formulation As described in Section two, the planning framework aims to propose the optimal long-term network expansion method below multi-dimensional uncertainty from an incredibly large quantity of investment possibilities taking into consideration the type, size, location, and timing of investments. As such, the stochastic problem requires an extremely massive quantity of continuous and binary choice variables and is, as a result, formulated as a mixed-integer linear programming dilemma. Below the applied temporal decomposition process, a separate optimization difficulty is formulated for every situation tree node m, described by Equations (1)40). The present temporal decomposition hyperlinks choice variables at a offered stage to variables inside the earlier stage only, and it extends the formulation in [31] to include lifespan of candidate storage technologies. To characterize when investment and commissioning of the candidate technologies are readily available, details on their building-delays and L lifespan requires to become utilised. For this goal, let max max max 1, l, , W , Smax (h) max1, h , and Smax (h) max1, h + h , h T . Note that, as H M explained within the prior subsection, the formulation in the master complications Pm follows S all binary variables are relaxed. the presented formulation, while within the subproblems Pmxm ,m jRlmin Vm ( xm ) + jN + (m) m j(1)whereI O Vm = m Vm + rO m) Vm ((2)Energies 2021, 14,six ofI Vm =L,v I S I lL W r L(m) (l, Fm,l, + l, m,l, ) + h T rh, H L, f O Vm =S,v (m) m,hI Sm,h(3) (four)b B Wbtb Tg G cg Pm,t,g + n N cVoLL dm,t,nsubject toI m,l, 0, 1, l L , W(five) (six) (7) (eight) (9) (ten) (11) (12) (13) (14) (15)xm,l, = y p(m),l, : m,l, , l L , Wc xm,l, = yc (m),l, : c m,l, , l L , W p F L xm,l, = y F(m),l,i, : c m,l,i, , l L , i = 1, . . . , max ( ), W , p S S T xm,h,i = yS(m),h,i : S m,h,i , i = 1, . . . , max ( h ), h H p T S S xm,h,i = yS(m),h,i : S m,h,i , i = 1, . . . , max ( h ), h H pR R R RWI xm,l, + m,l, 1, l LI ym,l, = xm,l, + m,l, , l L , W c max I I xm,l, + Fl, m,l, – Fm,l, 0, l L , W c max I I yc m,l, = xm,l, + Fl, m,l, – Fm,l, , l L , W I Fm,l = F ym,l,i, = LWL,0 I F xm,l,1, + Bl, Fm,l, , l LL F L I max j=1 Al,i,j, xm,l,j, + Bl,i, Fm,l, ,L l L , W , i = 1, . . . , max (16)I ^ Sm,h Sh , h T H S,0 I I S S Sm,h = xm,h,1 – xm,h,1 + Bh Sm,h , h T HR(17) (18) (19)yS m,h,iR yS m,h,iS max=j =S maxS S I AS xm,h,j + Bh,i Sm,h , i = 1, . . . , Smax (h), h T H h,i,j=j =S S I S AS xm,h,j + Bh,i Sm,h , i = 1, . . . , max (h), h T H h,i,jRRRR(20)0 Pm,t,g Pm,t,g , g g \ Pm,t-1,g – RDg Pm,t,g Pm,t-1,g + RUg , g G \H H Hdrr,resG d , t b , b B TH(21) (22) (23) (24) (25) (26) (27).